Finite Group Databasebeta

← #35570224

Subgroups — #35570224

Order 21248.

2576 conjugacy classes of subgroups.

The subgroup lattice has 1666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128443C211yesmaximal, characteristic
2#24910603C211yesmaximal, characteristic, complemented
3#24910603C211yesmaximal, characteristic, complemented
4#24910601C211yesmaximal, characteristic, complemented
5#24910574C211yesmaximal, characteristic, complemented
6#24910571C211yesmaximal, characteristic, complemented
7#24910570C211yesmaximal, characteristic, complemented
8#24910539C211yesmaximal, characteristic, complemented
9#24910538C211yesmaximal, characteristic, complemented
10#24910537C211yesmaximal, characteristic, complemented
11#24910534C211yesmaximal, characteristic, complemented
12#24910532C211yesmaximal, characteristic, complemented
13#24910529C211yesmaximal, characteristic, complemented
14#24910445C211yesmaximal, characteristic, complemented
15#24910443C211yesmaximal, characteristic, complemented
16#24910441C211yesmaximal, characteristic, complemented
17#24910277C211yesmaximal, characteristic, complemented
18#24910275C211yesmaximal, characteristic, complemented
19#24910273C211yesmaximal, characteristic, complemented
20#24910273C211yesmaximal, characteristic, complemented
21#24910271C211yesmaximal, characteristic, complemented
22#24910177C211yesmaximal, characteristic, complemented
23#24910172C211yesmaximal, characteristic, complemented
24#24910169C211yesmaximal, characteristic, complemented
25#24910120C211yesmaximal, characteristic, complemented
26#24910119C211yesmaximal, characteristic, complemented
27#24910116C211yesmaximal, characteristic, complemented
28#24909968C211yesmaximal, characteristic, complemented
29C4×#14581762C211yesmaximal, characteristic, complemented
30#24909964C211yesmaximal, characteristic, complemented
31C83×#2337C211yesmaximal, characteristic, complemented
32C23×C4×D83C2211yescharacteristic, complemented
33#19128443C4116yescomplemented
34C2×#14581781C2211yescharacteristic
35C2×#14581781C2211yescharacteristic
36C2×#14581780C2211yescharacteristic
37C2×#14581780C2211yescharacteristic
38C2×#14581778C2211yescharacteristic
39C2×#14581778C2211yescharacteristic
40C2×#14581778C2211yescharacteristic
41C2×#14581778C2211yescharacteristic
42C2×#14581762C2211yescharacteristic
43C2×#14581762C2211yescharacteristic
44C2×#14581762C2211yescharacteristic
45C2×#14581762C2211yescharacteristic
46C2×#14581760C2211yescharacteristic
47C2×#14581760C2211yescharacteristic
48C2×Q8×Dic83C2211yescharacteristic, complemented
49C2×C4×Dic166C2211yescharacteristic, complemented
50C2×#14581757C2211yescharacteristic, complemented
51C2×C4×D332C2211yescharacteristic
52C2×C4×D332C2211yescharacteristic
53C2×D4×Dic83C2211yescharacteristic
54C2×#14581754C2211yescharacteristic
55C2×#14581754C2211yescharacteristic
56C2×C4×C22⋊D83C2211yescharacteristic
57C2×(C22⋊D83)⋊C4C2211yescharacteristic
58C2×(C22⋊D83)⋊C4C2211yescharacteristic
59C2×(C22⋊D83)⋊C4C2211yescharacteristic
60C22×(C2×D83)⋊C4C2211yescharacteristic, complemented
61C2×C22⋊C4×D83C2211yescharacteristic, complemented
62C2×C22⋊C4×D83C2211yescharacteristic, complemented
63#19127608C2211yescharacteristic, complemented
64#19127607C2211yescharacteristic, complemented
65#19127606C2211yescharacteristic, complemented
66#19127605C2211yescharacteristic, complemented
67#19127605C2211yescharacteristic, complemented
68#19127605C2211yescharacteristic, complemented
69#19127605C2211yescharacteristic, complemented
70#19127604C2211yescharacteristic
71#19127603C2211yescharacteristic
72#19127603C2211yescharacteristic
73#19127602C2211yescharacteristic
74#19127602C2211yescharacteristic
75#19127601C2211yescharacteristic
76#19127601C2211yescharacteristic
77#19127601C2211yescharacteristic
78#19127601C2211yescharacteristic
79#19127595C2211yescharacteristic, complemented
80#19127595C2211yescharacteristic, complemented
81#19127594C2211yescharacteristic, complemented
82#19127594C2211yescharacteristic, complemented
83#19127594C2211yescharacteristic, complemented
84#19127594C2211yescharacteristic, complemented
85#19127593C2211yescharacteristic, complemented
86#19127593C2211yescharacteristic, complemented
87#19127593C2211yescharacteristic, complemented
88#19127593C2211yescharacteristic, complemented
89#19127593C2211yescharacteristic, complemented
90#19127593C2211yescharacteristic, complemented
91#19127593C2211yescharacteristic, complemented
92#19127592C2211yescharacteristic, complemented
93#19127592C2211yescharacteristic, complemented
94#19127592C2211yescharacteristic, complemented
95#19127591C2211yescharacteristic, complemented
96#19127591C2211yescharacteristic, complemented
97#19127591C2211yescharacteristic, complemented
98#19127591C2211yescharacteristic, complemented
99#19127591C2211yescharacteristic, complemented
100#19127590C2211yescharacteristic, complemented
101#19127590C2211yescharacteristic, complemented
102#19127590C2211yescharacteristic, complemented
103#19127590C2211yescharacteristic, complemented
104#19127590C2211yescharacteristic, complemented
105#19127590C2211yescharacteristic, complemented
106#19127590C2211yescharacteristic, complemented
107#19127590C2211yescharacteristic, complemented
108#19127590C2211yescharacteristic, complemented
109#19127589C2211yescharacteristic, complemented
110#19127589C2211yescharacteristic, complemented
111#19127580C2211yescharacteristic
112#19127580C2211yescharacteristic
113#19127580C2211yescharacteristic
114#19127579C2211yescharacteristic
115#19127579C2211yescharacteristic
116#19127579C2211yescharacteristic
117#19127579C2211yescharacteristic
118#19127579C2211yescharacteristic
119#19127579C2211yescharacteristic
120#19127579C2211yescharacteristic
121#19127579C2211yescharacteristic
122#19127578C2211yescharacteristic
123#19127577C2211yescharacteristic
124#19127577C2211yescharacteristic
125#19127577C2211yescharacteristic
126#19127577C2211yescharacteristic
127#19127576C2211yescharacteristic, complemented
128#19127576C2211yescharacteristic, complemented
129#19127575C2211yescharacteristic, complemented
130#19127575C2211yescharacteristic, complemented
131#19127575C2211yescharacteristic, complemented
132#19127575C2211yescharacteristic, complemented
133#19127575C2211yescharacteristic, complemented
134#19127575C2211yescharacteristic, complemented
135#19127575C2211yescharacteristic, complemented
136#19127575C2211yescharacteristic, complemented
137#19127575C2211yescharacteristic, complemented
138#19127574C2211yescharacteristic, complemented
139#19127573C2211yescharacteristic, complemented
140#19127572C2211yescharacteristic, complemented
141#19127572C2211yescharacteristic, complemented
142#19127572C2211yescharacteristic, complemented
143#19127570C2211yescharacteristic, complemented
144#19127568C2211yescharacteristic, complemented
145#19127556C2211yescharacteristic, complemented
146#19127556C2211yescharacteristic, complemented
147#19127556C2211yescharacteristic, complemented
148#19127556C2211yescharacteristic, complemented
149C4⋊C4×Dic83C2211yescharacteristic, complemented
150C4×Dic83⋊C4C2211yescharacteristic, complemented
151C4×C4⋊Dic83C2211yescharacteristic, complemented
152C4×C4⋊Dic83C2211yescharacteristic, complemented
153#19127552C2211yescharacteristic, complemented
154C22⋊C4×Dic83C2211yescharacteristic, complemented
155C22⋊C4×Dic83C2211yescharacteristic, complemented
156C22⋊C4×Dic83C2211yescharacteristic, complemented
157C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
158C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
159C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
160C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
161C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
162C4×C22⋊Dic83C2211yescharacteristic, complemented
163#19127548C2211yescharacteristic, complemented
164#19127548C2211yescharacteristic, complemented
165#19127548C2211yescharacteristic, complemented
166#19127548C2211yescharacteristic, complemented
167#19127548C2211yescharacteristic, complemented
168#19127548C2211yescharacteristic, complemented
169#19127548C2211yescharacteristic, complemented
170#19127547C2211yescharacteristic, complemented
171#19127546C2211yescharacteristic, complemented
172#19127546C2211yescharacteristic, complemented
173C2×#124×C83C2211yescharacteristic
174#391×C83C2211yescharacteristic, complemented
175#391×C83C2211yescharacteristic, complemented
176#388×C83C2211yescharacteristic, complemented
177#388×C83C2211yescharacteristic, complemented
178#388×C83C2211yescharacteristic, complemented
179#388×C83C2211yescharacteristic, complemented
180#386×C83C2211yescharacteristic
181#386×C83C2211yescharacteristic
182#385×C83C2211yescharacteristic, complemented
183#385×C83C2211yescharacteristic, complemented
184#383×C83C2211yescharacteristic, complemented
185C4×C4⋊C4×C83C2211yescharacteristic, complemented
186C4×C22⋊C4×C83C2211yescharacteristic, complemented
187C4×C22⋊C4×C83C2211yescharacteristic, complemented
188C24×D83C2311yescharacteristic
189C24×D83C2311yescharacteristic
190C22×Dic166C2311yescharacteristic
191C22×Dic166C2311yescharacteristic
192C22×D332C2311yescharacteristic
193C22×D332C2311yescharacteristic
194C22×D332C2311yescharacteristic
195C22×D332C2311yescharacteristic
196C22×C22⋊D83C2311yescharacteristic
197C22×C22⋊D83C2311yescharacteristic
198C22×C22⋊D83C2311yescharacteristic
199C22×C22⋊D83C2311yescharacteristic
200C23×Dic83C2311yescharacteristic
201C23×Dic83C2311yescharacteristic
202C22×C4×D83—42no—
203C22×C4×D83—42no—
204C22×C4×D83—42no—
205C22×C4×D83C2311yescharacteristic
206C22×C4×D83C2311yescharacteristic
207C22×C4×D83C2311yescharacteristic
208C22×C4×D83C2311yescharacteristic
209C22×C4×D83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
211C22×C4×D83C2311yescharacteristic
212C22×C4×D83C2311yescharacteristic
213#14581781C2×C418yescomplemented
214#14581781C2×C418yescomplemented
215#14581780C2×C418yescomplemented
216#14581780C2×C418yescomplemented
217#14581778C2×C418yescomplemented
218#14581778C2×C418yescomplemented
219#14581778C2×C418yescomplemented
220#14581778C2×C418yescomplemented
221#14581762C2×C418yescomplemented
222#14581762C2×C418yescomplemented
223#14581762C2×C418yescomplemented
224#14581762C2×C418yescomplemented
225#14581760C2×C418yescomplemented
226#14581760C2×C418yescomplemented
227Q8×Dic83—42no—
228C4×Dic166—42no—
229#14581757—42no—
230C4×D332—42no—
231C4×D332—42no—
232D4×Dic83—42no—
233#14581754—42no—
234#14581754—42no—
235C4×C22⋊D83—42no—
236(C22⋊D83)⋊C4—42no—
237(C22⋊D83)⋊C4—42no—
238(C22⋊D83)⋊C4—42no—
239C2×C4⋊Dic83C2311yescharacteristic
240C2×C4⋊Dic83C2311yescharacteristic
241C2×C4⋊Dic83C2311yescharacteristic
242C2×C4⋊Dic83C2311yescharacteristic
243C2×C4⋊Dic83C2311yescharacteristic
244C2×C4⋊Dic83C2311yescharacteristic
245C2×Dic83⋊C4C2311yescharacteristic
246C2×Dic83⋊C4C2311yescharacteristic
247C2×Dic83⋊C4C2311yescharacteristic
248C2×Dic83⋊C4C2311yescharacteristic
249C2×Dic83⋊C4C2311yescharacteristic
250C2×Dic83⋊C4C2311yescharacteristic
251C2×Dic83⋊C4C2311yescharacteristic
252C2×Dic83⋊C4C2311yescharacteristic
253C2×C22⋊Dic83C2311yescharacteristic
254C2×C22⋊Dic83C2311yescharacteristic
255C2×C22⋊Dic83C2311yescharacteristic
256C2×C22⋊Dic83C2311yescharacteristic
257C2×C22⋊Dic83C2311yescharacteristic
258C2×C22⋊Dic83C2311yescharacteristic
259C2×C22⋊Dic83C2311yescharacteristic
260C2×C22⋊Dic83C2311yescharacteristic
261C2×(C2×D83)⋊C4—42no—
262C2×(C2×D83)⋊C4C2311yescharacteristic
263C2×(C2×D83)⋊C4C2311yescharacteristic
264C2×(C2×D83)⋊C4C2311yescharacteristic
265C2×(C2×D83)⋊C4C2311yescharacteristic
266C2×(C2×D83)⋊C4C2311yescharacteristic
267C2×(C2×D83)⋊C4C2311yescharacteristic
268C2×(C2×D83)⋊C4C2311yescharacteristic
269C2×(C2×D83)⋊C4C2311yescharacteristic
270C2×(C2×D83)⋊C4C2311yescharacteristic
271C2×(C2×D83)⋊C4C2311yescharacteristic
272C2×(C2×D83)⋊C4C2311yescharacteristic
273C2×(C2×D83)⋊C4C2311yescharacteristic
274C2×(C2×D83)⋊C4C2311yescharacteristic
275C2×(C2×D83)⋊C4C2311yescharacteristic
276C2×(C2×D83)⋊C4C2311yescharacteristic
277C2×(C2×D83)⋊C4C2311yescharacteristic
278C2×(C2×D83)⋊C4C2311yescharacteristic
279C2×(C2×D83)⋊C4C2311yescharacteristic
280C2×(C2×D83)⋊C4C2311yescharacteristic
281C2×(C2×D83)⋊C4C2311yescharacteristic
282C2×(C2×D83)⋊C4C2311yescharacteristic
283C2×(C2×D83)⋊C4C2311yescharacteristic
284C2×(C2×D83)⋊C4C2311yescharacteristic
285C2×(C2×D83)⋊C4C2311yescharacteristic
286C2×(C2×D83)⋊C4C2311yescharacteristic
287C2×(C2×D83)⋊C4C2311yescharacteristic
288C2×(C2×D83)⋊C4C2311yescharacteristic
289C2×(C2×D83)⋊C4C2311yescharacteristic
290C2×(C2×D83)⋊C4C2311yescharacteristic
291C2×(C2×D83)⋊C4C2311yescharacteristic
292C2×(C2×D83)⋊C4C2311yescharacteristic
293C2×(C2×D83)⋊C4C2311yescharacteristic
294C2×(C2×D83)⋊C4C2311yescharacteristic
295C2×(C2×D83)⋊C4C2311yescharacteristic
296C2×(C2×D83)⋊C4C2311yescharacteristic
297C2×(C2×D83)⋊C4C2311yescharacteristic
298C22⋊C4×D83—42no—
299C22⋊C4×D83—42no—
300C2×C4×Dic83C2311yescharacteristic
301C2×C4×Dic83C2311yescharacteristic
302C2×C4×Dic83C2311yescharacteristic
303C2×C4×Dic83C2311yescharacteristic
304C2×C4×Dic83C2311yescharacteristic
305C2×C4×Dic83C2311yescharacteristic
306C2×C4×Dic83C2311yescharacteristic
307C2×C4×Dic83C2311yescharacteristic
308C2×C4×Dic83C2311yescharacteristic
309C2×C4×Dic83C2311yescharacteristic
310C2×C4×Dic83C2311yescharacteristic
311C2×C4×Dic83C2311yescharacteristic
312C2×C4×Dic83C2311yescharacteristic
313C2×C4×Dic83C2311yescharacteristic
314C2×C4×Dic83C2311yescharacteristic
315C2×C4×Dic83C2311yescharacteristic
316C83⋊#95C2311yescharacteristic
317C83⋊#95C2311yescharacteristic
318C83⋊#95C2311yescharacteristic
319C83⋊#95C2311yescharacteristic
320C83⋊#95C2311yescharacteristic
321C83⋊#95C2311yescharacteristic
322C83⋊#95C2311yescharacteristic
323C83⋊#95C2311yescharacteristic
324C83⋊#95C2311yescharacteristic
325C83⋊#95C2311yescharacteristic
326C83⋊#95C2311yescharacteristic
327C83⋊#95C2311yescharacteristic
328C83⋊#95C2311yescharacteristic
329C83⋊#95C2311yescharacteristic
330C83⋊#95C2311yescharacteristic
331C83⋊#95C2311yescharacteristic
332C83⋊#95C2311yescharacteristic
333C83⋊#95C2311yescharacteristic
334C83⋊#95C2311yescharacteristic
335C83⋊#95C2311yescharacteristic
336C83⋊#95C2311yescharacteristic
337C83⋊#95C2311yescharacteristic
338C83⋊#95C2311yescharacteristic
339C83⋊#95C2311yescharacteristic
340C22×Q8×C83C2311yescharacteristic
341C22×D4×C83C2311yescharacteristic
342C23×C4×C83C2311yescharacteristic
343C23×C4×C83C2311yescharacteristic
344#124×C83C2×C418yescomplemented
345C2×C4⋊C4×C83C2311yescharacteristic
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C4⋊C4×C83C2311yescharacteristic
348C2×C4⋊C4×C83C2311yescharacteristic
349C2×C22⋊C4×C83C2311yescharacteristic
350C2×C22⋊C4×C83C2311yescharacteristic
351C2×C22⋊C4×C83C2311yescharacteristic
352C2×C22⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C22⋊C4×C83C2311yescharacteristic
355C2×C22⋊C4×C83C2311yescharacteristic
356C2×C22⋊C4×C83C2311yescharacteristic
357C2×C22⋊C4×C83C2311yescharacteristic
358C2×C22⋊C4×C83C2311yescharacteristic
359C2×C42×C83C2311yescharacteristic
360C2×C42×C83C2311yescharacteristic
361C2×C42×C83C2311yescharacteristic
362C2×C42×C83C2311yescharacteristic
363C2×C42×C83C2311yescharacteristic
364#95×C83C2311yescharacteristic
365#95×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369#95×C83C2311yescharacteristic
370#95×C83C2311yescharacteristic
371#95×C83C2311yescharacteristic
372#95×C83C2311yescharacteristic
373#95×C83C2311yescharacteristic
374#95×C83C2311yescharacteristic
375#95×C83C2311yescharacteristic
376C23×D83—41no—
377C23×D83—41no—
378C23×D83—41no—
379C23×D83—41no—
380C23×D83—41no—
381C23×D83—41no—
382C23×D83—41no—
383C23×D83—41no—
384C23×D83—41no—
385C23×D83—41no—
386C23×D83—41no—
387C23×D83—41no—
388C23×D83C22×C414yes—
389C23×D83C22×C414yescomplemented
390C23×D83C2411yescharacteristic
391C23×D83C2411yescharacteristic
392C23×D83C2411yescharacteristic
393C23×D83C2411yescharacteristic
394C2×Dic166—41no—
395C2×Dic166—41no—
396C2×Dic166—41no—
397C2×Dic166—41no—
398C2×Dic166C22×C414yescomplemented
399C2×Dic166C22×C414yescomplemented
400C2×D332—41no—
401C2×D332—41no—
402C2×D332—41no—
403C2×D332—41no—
404C2×D332—41no—
405C2×D332—41no—
406C2×D332—41no—
407C2×D332—41no—
408C2×D332C22×C414yes—
409C2×D332C22×C414yes—
410C2×D332C22×C414yes—
411C2×D332C22×C414yes—
412C2×C22⋊D83—41no—
413C2×C22⋊D83—41no—
414C2×C22⋊D83—41no—
415C2×C22⋊D83—41no—
416C2×C22⋊D83—41no—
417C2×C22⋊D83—41no—
418C2×C22⋊D83—41no—
419C2×C22⋊D83—41no—
420C2×C22⋊D83C22×C414yes—
421C2×C22⋊D83C22×C414yes—
422C2×C22⋊D83C22×C414yes—
423C2×C22⋊D83C22×C414yes—
424C22×Dic83—22no—
425C22×Dic83—22no—
426C22×Dic83—22no—
427C22×Dic83—41no—
428C22×Dic83—41no—
429C22×Dic83—41no—
430C22×Dic83C2411yescharacteristic
431C22×Dic83C2411yescharacteristic
432C22×Dic83C2411yescharacteristic
433C22×Dic83C2411yescharacteristic
434C22×Dic83C2411yescharacteristic
435C22×Dic83C2411yescharacteristic
436C22×Dic83C2411yescharacteristic
437C22×Dic83C2411yescharacteristic
438C22×Dic83C2411yescharacteristic
439C22×Dic83C2411yescharacteristic
440C22×Dic83C2411yescharacteristic
441C22×Dic83C2411yescharacteristic
442C2×C4×D83—22no—
443C2×C4×D83—22no—
444C2×C4×D83—22no—
445C2×C4×D83—22no—
446C2×C4×D83—22no—
447C2×C4×D83—22no—
448C2×C4×D83—22no—
449C2×C4×D83—22no—
450C2×C4×D83—41no—
451C2×C4×D83—41no—
452C2×C4×D83—41no—
453C2×C4×D83—41no—
454C2×C4×D83—41no—
455C2×C4×D83—41no—
456C2×C4×D83—416no—
457C2×C4×D83—41no—
458C2×C4×D83—41no—
459C2×C4×D83—41no—
460C2×C4×D83—41no—
461C2×C4×D83—41no—
462C2×C4×D83—41no—
463C2×C4×D83—41no—
464C2×C4×D83—41no—
465C2×C4×D83—41no—
466C2×C4×D83—41no—
467C4⋊Dic83—22no—
468C4⋊Dic83—22no—
469C4⋊Dic83—22no—
470C4⋊Dic83—41no—
471C4⋊Dic83—41no—
472C4⋊Dic83—41no—
473Dic83⋊C4—22no—
474Dic83⋊C4—22no—
475Dic83⋊C4—41no—
476Dic83⋊C4—41no—
477Dic83⋊C4—41no—
478Dic83⋊C4—41no—
479Dic83⋊C4—41no—
480Dic83⋊C4—41no—
481C22⋊Dic83—22no—
482C22⋊Dic83—41no—
483C22⋊Dic83—41no—
484C22⋊Dic83—41no—
485C22⋊Dic83—41no—
486C22⋊Dic83—41no—
487C22⋊Dic83C22×C414yes—
488C22⋊Dic83C22×C414yescomplemented
489(C2×D83)⋊C4—22no—
490(C2×D83)⋊C4—22no—
491(C2×D83)⋊C4—22no—
492(C2×D83)⋊C4—22no—
493(C2×D83)⋊C4—41no—
494(C2×D83)⋊C4—41no—
495(C2×D83)⋊C4—41no—
496(C2×D83)⋊C4—41no—
497(C2×D83)⋊C4—41no—
498(C2×D83)⋊C4—41no—
499(C2×D83)⋊C4—41no—
500(C2×D83)⋊C4—41no—
501(C2×D83)⋊C4—41no—
502(C2×D83)⋊C4—41no—
503(C2×D83)⋊C4—41no—
504(C2×D83)⋊C4—41no—
505(C2×D83)⋊C4—41no—
506(C2×D83)⋊C4—41no—
507(C2×D83)⋊C4—41no—
508(C2×D83)⋊C4—41no—
509(C2×D83)⋊C4—41no—
510(C2×D83)⋊C4—41no—
511(C2×D83)⋊C4—41no—
512(C2×D83)⋊C4—41no—
513(C2×D83)⋊C4C22×C414yes—
514(C2×D83)⋊C4C22×C414yes—
515(C2×D83)⋊C4C22×C414yes—
516(C2×D83)⋊C4C22×C414yes—
517(C2×D83)⋊C4C22×C414yes—
518(C2×D83)⋊C4C22×C414yes—
519(C2×D83)⋊C4C22×C414yescomplemented
520(C2×D83)⋊C4C22×C414yescomplemented
521(C2×D83)⋊C4C22×C414yescomplemented
522(C2×D83)⋊C4C22×C414yescomplemented
523(C2×D83)⋊C4C22×C414yescomplemented
524(C2×D83)⋊C4C22×C414yescomplemented
525C4×Dic83—22no—
526C4×Dic83—22no—
527C4×Dic83—22no—
528C4×Dic83—41no—
529C4×Dic83—41no—
530C4×Dic83—41no—
531C4×Dic83—41no—
532C4×Dic83—41no—
533C4×Dic83—41no—
534C4×Dic83—41no—
535C4×Dic83—41no—
536C4×Dic83—41no—
537C4×Dic83—41no—
538C4×Dic83—41no—
539C4×Dic83C22×C414yescomplemented
540C4×Dic83C22×C414yescomplemented
541C24×C83C2411yescharacteristic
542C24×C83C2411yescharacteristic
543C2×Q8×C83—41no—
544C2×Q8×C83—41no—
545C2×Q8×C83C22×C414yescomplemented
546C2×D4×C83—41no—
547C2×D4×C83—41no—
548C2×D4×C83C22×C414yes—
549C22×C4×C83—22no—
550C22×C4×C83—41no—
551C22×C4×C83—41no—
552C22×C4×C83—41no—
553C22×C4×C83—41no—
554C22×C4×C83—41no—
555C22×C4×C83C2411yescharacteristic
556C22×C4×C83C2411yescharacteristic
557C22×C4×C83C2411yescharacteristic
558C22×C4×C83C2411yescharacteristic
559C22×C4×C83C2411yescharacteristic
560C22×C4×C83C2411yescharacteristic
561C22×C4×C83C2411yescharacteristic
562C22×C4×C83C2411yescharacteristic
563C22×C4×C83C2411yescharacteristic
564C22×C4×C83C2411yescharacteristic
565C22×C4×C83C2411yescharacteristic
566C22×C4×C83C2411yescharacteristic
567C22×C4×C83C2411yescharacteristic
568C4⋊C4×C83—22no—
569C4⋊C4×C83—41no—
570C4⋊C4×C83—41no—
571C4⋊C4×C83—41no—
572C22⋊C4×C83—22no—
573C22⋊C4×C83—41no—
574C22⋊C4×C83—41no—
575C22⋊C4×C83—41no—
576C22⋊C4×C83—41no—
577C22⋊C4×C83—41no—
578C22⋊C4×C83C22×C414yes—
579C22⋊C4×C83C22×C414yes—
580C22⋊C4×C83C22×C414yescomplemented
581C22⋊C4×C83C22×C414yescomplemented
582C42×C83—41no—
583C42×C83—41no—
584C42×C83—41no—
585C42×C83—41no—
586C42×C83C22×C414yescomplemented
587C23×C83—21no—
588C23×C83—21no—
589C23×C83—21no—
590C23×C83—21no—
591C23×C83—21no—
592C23×C83—21no—
593C23×C83—21no—
594C23×C83—21no—
595C23×C83—21no—
596C23×C83—21no—
597C23×C83—21no—
598C23×C83—21no—
599C23×C83C23×C412yes—
600C23×C83C23×C412yes—
601C23×C83C2511yescharacteristic
602C22×D83—21no—
603C22×D83—21no—
604C22×D83—21no—
605C22×D83—21no—
606C22×D83—21no—
607C22×D83—21no—
608C22×D83—21no—
609C22×D83—21no—
610C22×D83—21no—
611C22×D83—21no—
612C22×D83—21no—
613C22×D83—21no—
614C22×D83—21no—
615C22×D83—21no—
616C22×D83—21no—
617C22×D83—21no—
618C22×D83—21no—
619C22×D83—21no—
620C22×D83—21no—
621C22×D83—21no—
622C22×D83—21no—
623C22×D83—21no—
624C22×D83—21no—
625C22×D83—21no—
626C22×D83—44no—
627C22×D83—44no—
628C22×D83—44no—
629C22×D83—44no—
630C22×D83—44no—
631C22×D83—44no—
632C22×D83—44no—
633C22×D83—44no—
634C22×D83—44no—
635C22×D83—44no—
636C22×D83—82no—
637C22×D83—82no—
638C22×D83—82no—
639C22×D83—82no—
640C22×D83C23×C412yes—
641C22×D83C23×C412yes—
642C22×D83C23×C412yes—
643C22×D83C23×C412yes—
644Q8×C83—44no—
645D4×C83—44no—
646C2×C4×C83—21no—
647C2×C4×C83—21no—
648C2×C4×C83—21no—
649C2×C4×C83—21no—
650C2×C4×C83—21no—
651C2×C4×C83—21no—
652C2×C4×C83—21no—
653C2×C4×C83—21no—
654C2×C4×C83—21no—
655C2×C4×C83—21no—
656C2×C4×C83—21no—
657C2×C4×C83—21no—
658C2×C4×C83—21no—
659C2×C4×C83—21no—
660C2×C4×C83—21no—
661C2×C4×C83—21no—
662C2×C4×C83—21no—
663C2×C4×C83—21no—
664C2×C4×C83—21no—
665C2×C4×C83—21no—
666C2×C4×C83—21no—
667C2×C4×C83—21no—
668C2×C4×C83—21no—
669C2×C4×C83—21no—
670C2×C4×C83—21no—
671C2×C4×C83—21no—
672C2×C4×C83—21no—
673C2×C4×C83—21no—
674C2×C4×C83—21no—
675C2×C4×C83—21no—
676C2×C4×C83—21no—
677C2×C4×C83—21no—
678C2×C4×C83—21no—
679C2×C4×C83—44no—
680C2×C4×C83—82no—
681C2×C4×C83C23×C412yes—
682C2×C4×C83C23×C412yes—
683C2×C4×C83C23×C412yes—
684C2×C4×C83C23×C412yes—
685C2×C4×C83C23×C412yes—
686C2×C4×C83H(5,𝔽2)12yes—
687C22⋊D83—44no—
688C22⋊D83—44no—
689C22⋊D83—44no—
690C22⋊D83—44no—
691C2×Dic83—21no—
692C2×Dic83—21no—
693C2×Dic83—21no—
694C2×Dic83—21no—
695C2×Dic83—21no—
696C2×Dic83—21no—
697C2×Dic83—21no—
698C2×Dic83—21no—
699C2×Dic83—21no—
700C2×Dic83—21no—
701C2×Dic83—21no—
702C2×Dic83—21no—
703C2×Dic83—21no—
704C2×Dic83—21no—
705C2×Dic83—21no—
706C2×Dic83—21no—
707C2×Dic83—21no—
708C2×Dic83—21no—
709C2×Dic83—21no—
710C2×Dic83—21no—
711C2×Dic83—21no—
712C2×Dic83—21no—
713C2×Dic83—21no—
714C2×Dic83—21no—
715C2×Dic83—21no—
716C2×Dic83—21no—
717C2×Dic83—21no—
718C2×Dic83—21no—
719C2×Dic83—21no—
720C2×Dic83—21no—
721C2×Dic83—44no—
722C2×Dic83—82no—
723C2×Dic83C23×C412yes—
724C2×Dic83C23×C412yes—
725C2×Dic83C23×C412yes—
726C2×Dic83C23×C412yes—
727C2×Dic83H(5,𝔽2)12yes—
728C2×Dic83H(5,𝔽2)12yes—
729D332—44no—
730D332—44no—
731D332—44no—
732D332—44no—
733C4×D83—44no—
734C4×D83—44no—
735C4×D83—44no—
736C4×D83—44no—
737C4×D83—82no—
738C4×D83—82no—
739C4×D83—82no—
740C4×D83—82no—
741Dic166—44no—
742Dic166—44no—
743C22×C83—22no—
744C22×C83—22no—
745C22×C83—22no—
746C22×C83—22no—
747C22×C83—22no—
748C22×C83—22no—
749C22×C83—41no—
750C22×C83—41no—
751C22×C83—41no—
752C22×C83—41no—
753C22×C83—41no—
754C22×C83—41no—
755C22×C83—41no—
756C22×C83—41no—
757C22×C83C24×C411yescharacteristic
758C22×C83C2×H(5,𝔽2)11yescharacteristic
759C22×C83C2×H(5,𝔽2)11yescharacteristic
760C22×C83C2×H(5,𝔽2)11yescharacteristic
761C22×C83#58511yescharacteristic
762C22×C83#58511yescharacteristic
763C22×C83#58511yescharacteristic
764C2×D83—22no—
765C2×D83—22no—
766C2×D83—22no—
767C2×D83—22no—
768C2×D83—22no—
769C2×D83—22no—
770C2×D83—22no—
771C2×D83—22no—
772C2×D83—22no—
773C2×D83—22no—
774C2×D83—22no—
775C2×D83—22no—
776C2×D83—416no—
777C2×D83—41no—
778C2×D83—41no—
779C2×D83—41no—
780C2×D83—41no—
781C2×D83—41no—
782C2×D83—41no—
783C2×D83—41no—
784C2×D83—41no—
785C2×D83—41no—
786C2×D83—41no—
787C2×D83—41no—
788C2×D83—41no—
789C2×D83—41no—
790C2×D83—41no—
791C2×D83—41no—
792C2×D83—41no—
793C2×D83—88no—
794C4×C83—22no—
795C4×C83—22no—
796C4×C83—22no—
797C4×C83—22no—
798C4×C83—22no—
799C4×C83—22no—
800C4×C83—41no—
801C4×C83—41no—
802C4×C83—41no—
803C4×C83—41no—
804C4×C83—41no—
805C4×C83—41no—
806C4×C83—41no—
807Dic83—22no—
808Dic83—22no—
809Dic83—22no—
810Dic83—22no—
811Dic83—22no—
812Dic83—22no—
813Dic83—41no—
814Dic83—41no—
815Dic83—41no—
816Dic83—41no—
817Dic83—41no—
818Dic83—41no—
819#34512—831nomaximal, Sylow
820C2×C83—42no—
821C2×C83—42no—
822C2×C83C4×H(5,𝔽2)11yescharacteristic
823C2×C83C4×H(5,𝔽2)11yescharacteristic
824C2×C83C4×H(5,𝔽2)11yescharacteristic
825C2×C83#353211yescharacteristic
826C2×C83#354011yescharacteristic
827C2×C83#354011yescharacteristic
828C2×C83#354011yescharacteristic
829D83—42no—
830D83—42no—
831D83—42no—
832D83—42no—
833C2×H(3,𝔽4)—831no—
834#2375—831no—
835#2375—831no—
836#2375—831no—
837#2372—831no—
838#2372—831no—
839#2372—831no—
840#2367—831no—
841#2367—831no—
842#2367—831no—
843#2367—831no—
844#2367—831no—
845#2367—831no—
846#2358—831no—
847#2358—831no—
848#2358—831no—
849#2337—831no—
850#2337—831no—
851#2337—831no—
852#2337—831no—
853#2337—831no—
854#2337D8311yescharacteristic, complemented
855#2326—831no—
856#2326—831no—
857#2326—831no—
858#2321—831no—
859#2321—831no—
860#2321—831no—
861C4×#120—831no—
862C4×#120—831no—
863C4×#120—831no—
864C83#3451211yescharacteristic, complemented, Sylow
865C24×C4—831no—
866H(3,𝔽4)—8316no—
867C2×#124—831no—
868C2×#124—831no—
869C2×#124—831no—
870C2×#124—831no—
871C2×#124—831no—
872C2×#124—831no—
873C2×#124—831no—
874C2×#124—831no—
875C2×#124C2×D8311yescharacteristic
876C2×#120—831no—
877C2×#120—831no—
878C2×#120—831no—
879C2×#120—831no—
880C2×#120—831no—
881C2×#120—831no—
882C2×C4×Q8—831no—
883C2×C4×Q8—831no—
884C2×C4×Q8—831no—
885C2×C4×D4—831no—
886C2×C4×D4—831no—
887C2×C4×D4—831no—
888C2×C4×D4—831no—
889C2×C4×D4—831no—
890C2×C4×D4—831no—
891C2×C4×D4—831no—
892C2×C4×D4—831no—
893C2×C4×D4—831no—
894C22×C22⋊C4—831no—
895C22×C22⋊C4—831no—
896C22×C22⋊C4—831no—
897#391—831no—
898#391—831no—
899#391—831no—
900#391—831no—
901#391—831no—
902#391—831no—
903#391—831no—
904#391C2×D8311yescharacteristic, complemented
905#391C2×D8311yescharacteristic, complemented
906#390—831no—
907#390—831no—
908#390—831no—
909#390—831no—
910#390—831no—
911#390—831no—
912#390—831no—
913#390—831no—
914#390—831no—
915#388—831no—
916#388—831no—
917#388—831no—
918#388—831no—
919#388—831no—
920#388—831no—
921#388—831no—
922#388—831no—
923#388—831no—
924#388—831no—
925#388—831no—
926#388—831no—
927#388—831no—
928#388—831no—
929#388—831no—
930#388—831no—
931#388—831no—
932#388—831no—
933#388—831no—
934#388—831no—
935#388—831no—
936#388—831no—
937#388—831no—
938#388—831no—
939#388—831no—
940#388—831no—
941#388—831no—
942#388—831no—
943#388—831no—
944#388—831no—
945#388—831no—
946#388—831no—
947#388C2×D8311yescharacteristic, complemented
948#388C2×D8311yescharacteristic, complemented
949#388C2×D8311yescharacteristic, complemented
950#388C2×D8311yescharacteristic, complemented
951#386—831no—
952#386—831no—
953#386—831no—
954#386—831no—
955#386—831no—
956#386—831no—
957#386—831no—
958#386—831no—
959#386—831no—
960#386—831no—
961#386—831no—
962#386—831no—
963#386—831no—
964#386—831no—
965#386—831no—
966#386—831no—
967#386C2×D8311yescharacteristic
968#386C2×D8311yescharacteristic
969#385—831no—
970#385—831no—
971#385—831no—
972#385—831no—
973#385—831no—
974#385—831no—
975#385—831no—
976#385—831no—
977#385—831no—
978#385—831no—
979#385—831no—
980#385—831no—
981#385—831no—
982#385—831no—
983#385—831no—
984#385—831no—
985#385C2×D8311yescharacteristic, complemented
986#385C2×D8311yescharacteristic, complemented
987#384—831no—
988#383—831no—
989#383C2×D8311yescharacteristic, complemented
990#379—831no—
991#379—831no—
992#379—831no—
993#379—831no—
994C4×C4⋊C4—831no—
995C4×C4⋊C4—831no—
996C4×C4⋊C4—831no—
997C4×C4⋊C4—831no—
998C4×C4⋊C4—831no—
999C4×C4⋊C4C2×D8311yescharacteristic, complemented
1000C4×C22⋊C4—831no—
1001C4×C22⋊C4—831no—
1002C4×C22⋊C4—831no—
1003C4×C22⋊C4—831no—
1004C4×C22⋊C4—831no—
1005C4×C22⋊C4—831no—
1006C4×C22⋊C4—831no—
1007C4×C22⋊C4—831no—
1008C4×C22⋊C4—831no—
1009C4×C22⋊C4—831no—
1010C4×C22⋊C4—831no—
1011C4×C22⋊C4—831no—
1012C4×C22⋊C4—831no—
1013C4×C22⋊C4—831no—
1014C4×C22⋊C4—831no—
1015C4×C22⋊C4—831no—
1016C4×C22⋊C4C2×D8311yescharacteristic, complemented
1017C4×C22⋊C4C2×D8311yescharacteristic, complemented
1018#376—831no—
1019#376—831no—
1020#376—831no—
1021C25—831no—
1022C25—831no—
1023C22×Q8—831no—
1024C22×Q8—831no—
1025C22×Q8C22×D8311yescharacteristic
1026C22×D4—831no—
1027C22×D4—831no—
1028C22×D4—831no—
1029C22×D4—831no—
1030C22×D4—831no—
1031C22×D4—831no—
1032C22×D4—831no—
1033C22×D4—831no—
1034C22×D4C22×D8311yescharacteristic
1035C23×C4—3322no—
1036C23×C4—3322no—
1037C23×C4—3322no—
1038C23×C4—831no—
1039C23×C4—831no—
1040C23×C4—831no—
1041C23×C4—831no—
1042C23×C4—831no—
1043C23×C4—831no—
1044C23×C4—831no—
1045C23×C4—831no—
1046C23×C4—831no—
1047C23×C4—831no—
1048C23×C4C22×D8311yescharacteristic
1049C23×C4C22×D8311yescharacteristic
1050#124—838no—
1051#124—838no—
1052#124—838no—
1053#124—838no—
1054#124—838no—
1055#124—838no—
1056#124—838no—
1057#124—838no—
1058#124C4×D8318yescomplemented
1059#120—838no—
1060#120—838no—
1061#120—838no—
1062#120—838no—
1063#120—838no—
1064#120—838no—
1065C4×Q8—3322no—
1066C4×Q8—3322no—
1067C4×Q8—3322no—
1068C4×D4—3322no—
1069C4×D4—3322no—
1070C4×D4—3322no—
1071C4×D4—3322no—
1072C4×D4—3322no—
1073C4×D4—3322no—
1074C4×D4—3322no—
1075C4×D4—3322no—
1076C4×D4—3322no—
1077C2×C4⋊C4—831no—
1078C2×C4⋊C4—831no—
1079C2×C4⋊C4—831no—
1080C2×C4⋊C4—831no—
1081C2×C4⋊C4—831no—
1082C2×C4⋊C4—831no—
1083C2×C4⋊C4—831no—
1084C2×C4⋊C4—831no—
1085C2×C4⋊C4—831no—
1086C2×C4⋊C4—831no—
1087C2×C4⋊C4—831no—
1088C2×C4⋊C4—831no—
1089C2×C4⋊C4—831no—
1090C2×C4⋊C4—831no—
1091C2×C4⋊C4C22×D8311yescharacteristic
1092C2×C4⋊C4C22×D8311yescharacteristic
1093C2×C4⋊C4C22×D8311yescharacteristic
1094C2×C4⋊C4C22×D8311yescharacteristic
1095C2×C22⋊C4—3322no—
1096C2×C22⋊C4—3322no—
1097C2×C22⋊C4—3322no—
1098C2×C22⋊C4—831no—
1099C2×C22⋊C4—831no—
1100C2×C22⋊C4—831no—
1101C2×C22⋊C4—831no—
1102C2×C22⋊C4—831no—
1103C2×C22⋊C4—831no—
1104C2×C22⋊C4—831no—
1105C2×C22⋊C4—831no—
1106C2×C22⋊C4—831no—
1107C2×C22⋊C4—831no—
1108C2×C22⋊C4—831no—
1109C2×C22⋊C4—831no—
1110C2×C22⋊C4—831no—
1111C2×C22⋊C4—831no—
1112C2×C22⋊C4—831no—
1113C2×C22⋊C4—831no—
1114C2×C22⋊C4—831no—
1115C2×C22⋊C4—831no—
1116C2×C22⋊C4—831no—
1117C2×C22⋊C4—831no—
1118C2×C22⋊C4—831no—
1119C2×C22⋊C4—831no—
1120C2×C22⋊C4—831no—
1121C2×C22⋊C4—831no—
1122C2×C22⋊C4—831no—
1123C2×C22⋊C4—831no—
1124C2×C22⋊C4—831no—
1125C2×C22⋊C4—831no—
1126C2×C22⋊C4—831no—
1127C2×C22⋊C4—831no—
1128C2×C22⋊C4—831no—
1129C2×C22⋊C4—831no—
1130C2×C22⋊C4—831no—
1131C2×C22⋊C4—831no—
1132C2×C22⋊C4—831no—
1133C2×C22⋊C4—831no—
1134C2×C22⋊C4—831no—
1135C2×C22⋊C4—831no—
1136C2×C22⋊C4—831no—
1137C2×C22⋊C4—831no—
1138C2×C22⋊C4—831no—
1139C2×C22⋊C4—831no—
1140C2×C22⋊C4—831no—
1141C2×C22⋊C4—831no—
1142C2×C22⋊C4C22×D8311yescharacteristic
1143C2×C22⋊C4C22×D8311yescharacteristic
1144C2×C22⋊C4C22×D8311yescharacteristic
1145C2×C22⋊C4C22×D8311yescharacteristic
1146C2×C22⋊C4C22×D8311yescharacteristic
1147C2×C22⋊C4C22×D8311yescharacteristic
1148C2×C22⋊C4C22×D8311yescharacteristic
1149C2×C22⋊C4C22×D8311yescharacteristic
1150C2×C22⋊C4C22×D8311yescharacteristic
1151C2×C22⋊C4C22×D8311yescharacteristic
1152C2×C42—831no—
1153C2×C42—831no—
1154C2×C42—831no—
1155C2×C42—831no—
1156C2×C42—831no—
1157C2×C42—831no—
1158C2×C42—831no—
1159C2×C42—831no—
1160C2×C42—831no—
1161C2×C42—831no—
1162C2×C42—831no—
1163C2×C42—831no—
1164C2×C42—831no—
1165C2×C42—831no—
1166C2×C42—831no—
1167C2×C42—831no—
1168C2×C42C22×D8311yescharacteristic
1169C2×C42C22×D8311yescharacteristic
1170C2×C42C22×D8311yescharacteristic
1171C2×C42C22×D8311yescharacteristic
1172C2×C42C22×D8311yescharacteristic
1173#95—831no—
1174#95—831no—
1175#95—831no—
1176#95—831no—
1177#95—831no—
1178#95—831no—
1179#95—831no—
1180#95—831no—
1181#95—831no—
1182#95—831no—
1183#95—831no—
1184#95—831no—
1185#95—831no—
1186#95—831no—
1187#95—831no—
1188#95—831no—
1189#95—831no—
1190#95—831no—
1191#95—831no—
1192#95—831no—
1193#95—831no—
1194#95—831no—
1195#95—831no—
1196#95—831no—
1197#95C22×D8311yescharacteristic
1198#95C22×D8311yescharacteristic
1199#95C22×D8311yescharacteristic
1200#95C22×D8311yescharacteristic
1201#95C22×D8311yescharacteristic
1202#95C22×D8311yescharacteristic
1203#95C22×D8311yescharacteristic
1204#95C22×D8311yescharacteristic
1205#95C22×D8311yescharacteristic
1206#95C22×D8311yescharacteristic
1207#95C22×D8311yescharacteristic
1208#95C22×D8311yescharacteristic
1209C24—3321no—
1210C24—3321no—
1211C24—3321no—
1212C24—3321no—
1213C24—3321no—
1214C24—3321no—
1215C24—3321no—
1216C24—3321no—
1217C24—3321no—
1218C24—3321no—
1219C24—3321no—
1220C24—3321no—
1221C24—834no—
1222C24—834no—
1223C24—831no—
1224C24—831no—
1225C24—831no—
1226C24—831no—
1227C24C23×D8311yescharacteristic
1228C24C23×D8311yescharacteristic
1229C2×Q8—41no—
1230C2×Q8—41no—
1231C2×Q8—3321no—
1232C2×Q8—3321no—
1233C2×Q8—3321no—
1234C2×Q8—3321no—
1235C2×Q8—834no—
1236C2×Q8—834no—
1237C2×Q8C2×C4×D8314yescomplemented
1238C2×D4—41no—
1239C2×D4—41no—
1240C2×D4—3321no—
1241C2×D4—3321no—
1242C2×D4—3321no—
1243C2×D4—3321no—
1244C2×D4—3321no—
1245C2×D4—3321no—
1246C2×D4—3321no—
1247C2×D4—3321no—
1248C2×D4—3321no—
1249C2×D4—3321no—
1250C2×D4—3321no—
1251C2×D4—3321no—
1252C2×D4—3321no—
1253C2×D4—3321no—
1254C2×D4—3321no—
1255C2×D4—3321no—
1256C2×D4—834no—
1257C2×D4—834no—
1258C2×D4—834no—
1259C2×D4—834no—
1260C2×D4—834no—
1261C2×D4—834no—
1262C2×D4—834no—
1263C2×D4—834no—
1264C2×D4C2×C4×D8314yes—
1265C22×C4—22no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—41no—
1269C22×C4—41no—
1270C22×C4—41no—
1271C22×C4—3321no—
1272C22×C4—3321no—
1273C22×C4—3321no—
1274C22×C4—3321no—
1275C22×C4—3321no—
1276C22×C4—3321no—
1277C22×C4—3321no—
1278C22×C4—3321no—
1279C22×C4—3321no—
1280C22×C4—3321no—
1281C22×C4—3321no—
1282C22×C4—3321no—
1283C22×C4—3321no—
1284C22×C4—3321no—
1285C22×C4—3321no—
1286C22×C4—3321no—
1287C22×C4—33216no—
1288C22×C4—3321no—
1289C22×C4—3321no—
1290C22×C4—3321no—
1291C22×C4—831no—
1292C22×C4—831no—
1293C22×C4—831no—
1294C22×C4—831no—
1295C22×C4—831no—
1296C22×C4—831no—
1297C22×C4—831no—
1298C22×C4—831no—
1299C22×C4—831no—
1300C22×C4—831no—
1301C22×C4—831no—
1302C22×C4—831no—
1303C22×C4—1662no—
1304C22×C4—1662no—
1305C22×C4—1662no—
1306C22×C4—1662no—
1307C22×C4—1662no—
1308C22×C4—1662no—
1309C22×C4—1662no—
1310C22×C4—1662no—
1311C22×C4—1662no—
1312C22×C4—1662no—
1313C22×C4—1662no—
1314C22×C4C23×D8311yescharacteristic
1315C22×C4C23×D8311yescharacteristic
1316C22×C4C23×D8311yescharacteristic
1317C22×C4C23×D8311yescharacteristic
1318C22×C4C23×D8311yescharacteristic
1319C22×C4C23×D8311yescharacteristic
1320C22×C4C23×D8311yescharacteristic
1321C22×C4C23×D8311yescharacteristic
1322C22×C4C23×D8311yescharacteristic
1323C22×C4C23×D8311yescharacteristic
1324C22×C4C23×D8311yescharacteristic
1325C22×C4C23×D8311yescharacteristic
1326C22×C4C23×D8311yescharacteristic
1327C4⋊C4—22no—
1328C4⋊C4—41no—
1329C4⋊C4—41no—
1330C4⋊C4—41no—
1331C4⋊C4—3321no—
1332C4⋊C4—3321no—
1333C4⋊C4—3321no—
1334C4⋊C4—3321no—
1335C4⋊C4—3321no—
1336C4⋊C4—3321no—
1337C4⋊C4—3321no—
1338C4⋊C4—3321no—
1339C4⋊C4—3321no—
1340C4⋊C4—1662no—
1341C4⋊C4—1662no—
1342C4⋊C4—1662no—
1343C4⋊C4—1662no—
1344C4⋊C4—1662no—
1345C22⋊C4—22no—
1346C22⋊C4—41no—
1347C22⋊C4—41no—
1348C22⋊C4—41no—
1349C22⋊C4—41no—
1350C22⋊C4—41no—
1351C22⋊C4—3321no—
1352C22⋊C4—3321no—
1353C22⋊C4—3321no—
1354C22⋊C4—3321no—
1355C22⋊C4—3321no—
1356C22⋊C4—3321no—
1357C22⋊C4—3321no—
1358C22⋊C4—3321no—
1359C22⋊C4—3321no—
1360C22⋊C4—3321no—
1361C22⋊C4—3321no—
1362C22⋊C4—3321no—
1363C22⋊C4—3321no—
1364C22⋊C4—3321no—
1365C22⋊C4—3321no—
1366C22⋊C4—3321no—
1367C22⋊C4—3321no—
1368C22⋊C4—3321no—
1369C22⋊C4—3321no—
1370C22⋊C4—3321no—
1371C22⋊C4—3321no—
1372C22⋊C4—3321no—
1373C22⋊C4—3321no—
1374C22⋊C4—3321no—
1375C22⋊C4—3321no—
1376C22⋊C4—834no—
1377C22⋊C4—834no—
1378C22⋊C4—834no—
1379C22⋊C4—834no—
1380C22⋊C4—834no—
1381C22⋊C4—834no—
1382C22⋊C4—834no—
1383C22⋊C4—834no—
1384C22⋊C4—834no—
1385C22⋊C4—834no—
1386C22⋊C4—834no—
1387C22⋊C4—834no—
1388C22⋊C4—834no—
1389C22⋊C4—834no—
1390C22⋊C4—1662no—
1391C22⋊C4—1662no—
1392C22⋊C4—1662no—
1393C22⋊C4—1662no—
1394C22⋊C4—1662no—
1395C22⋊C4C2×C4×D8314yes—
1396C22⋊C4C2×C4×D8314yes—
1397C22⋊C4C2×C4×D8314yescomplemented
1398C22⋊C4C2×C4×D8314yescomplemented
1399C42—41no—
1400C42—41no—
1401C42—41no—
1402C42—41no—
1403C42—3321no—
1404C42—3321no—
1405C42—3321no—
1406C42—3321no—
1407C42—3321no—
1408C42—3321no—
1409C42—3321no—
1410C42—3321no—
1411C42—3321no—
1412C42—3321no—
1413C42—3321no—
1414C42—834no—
1415C42—834no—
1416C42—1662no—
1417C42—1662no—
1418C42—1662no—
1419C42C2×C4×D8314yescomplemented
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—3324no—
1433C23—3324no—
1434C23—3324no—
1435C23—3324no—
1436C23—3324no—
1437C23—3324no—
1438C23—3324no—
1439C23—3324no—
1440C23—3324no—
1441C23—3324no—
1442C23—832no—
1443C23—832no—
1444C23—832no—
1445C23—832no—
1446C23—6642no—
1447C23—6642no—
1448C23—6642no—
1449C23—6642no—
1450C23—1661no—
1451C23—1661no—
1452C23—1661no—
1453C23—1661no—
1454C23—1661no—
1455C23—1661no—
1456C23—1661no—
1457C23—1661no—
1458C23—1661no—
1459C23—1661no—
1460C23—1661no—
1461C23—1661no—
1462C23—1661no—
1463C23—1661no—
1464C23—1661no—
1465C23—1661no—
1466C23—1661no—
1467C23—1661no—
1468C23—1661no—
1469C23—1661no—
1470C23—1661no—
1471C23—1661no—
1472C23—1661no—
1473C23—1661no—
1474C23C22×C4×D8312yes—
1475C23C22×C4×D8312yes—
1476C23C24×D8311yescharacteristic
1477Q8—44no—
1478Q8—3324no—
1479Q8—3324no—
1480D4—44no—
1481D4—3324no—
1482D4—3324no—
1483D4—3324no—
1484D4—3324no—
1485D4—3324no—
1486D4—3324no—
1487D4—3324no—
1488D4—3324no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—44no—
1523C2×C4—82no—
1524C2×C4—3324no—
1525C2×C4—3324no—
1526C2×C4—3324no—
1527C2×C4—3324no—
1528C2×C4—3324no—
1529C2×C4—832no—
1530C2×C4—832no—
1531C2×C4—832no—
1532C2×C4—832no—
1533C2×C4—832no—
1534C2×C4—832no—
1535C2×C4—6642no—
1536C2×C4—6642no—
1537C2×C4—6642no—
1538C2×C4—6642no—
1539C2×C4—6642no—
1540C2×C4—1661no—
1541C2×C4—1661no—
1542C2×C4—1661no—
1543C2×C4—1661no—
1544C2×C4—1661no—
1545C2×C4—1661no—
1546C2×C4—1661no—
1547C2×C4—1661no—
1548C2×C4—1661no—
1549C2×C4—1661no—
1550C2×C4—1661no—
1551C2×C4—1661no—
1552C2×C4—1661no—
1553C2×C4—1661no—
1554C2×C4—1661no—
1555C2×C4—1661no—
1556C2×C4—1661no—
1557C2×C4—1661no—
1558C2×C4—1661no—
1559C2×C4—1661no—
1560C2×C4—1661no—
1561C2×C4—1661no—
1562C2×C4—1661no—
1563C2×C4—1661no—
1564C2×C4—1661no—
1565C2×C4—1661no—
1566C2×C4—1661no—
1567C2×C4—1661no—
1568C2×C4—1661no—
1569C2×C4—1661no—
1570C2×C4C22×C4×D8312yes—
1571C2×C4C22×C4×D8312yes—
1572C2×C4C22×C4×D8312yes—
1573C2×C4C22×C4×D8312yes—
1574C2×C4C22×C4×D8312yes—
1575C2×C4#1458183812yes—
1576C22—22no—
1577C22—22no—
1578C22—22no—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—41no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—33216no—
1591C22—3321no—
1592C22—3321no—
1593C22—3321no—
1594C22—3321no—
1595C22—3321no—
1596C22—3321no—
1597C22—3321no—
1598C22—3321no—
1599C22—3321no—
1600C22—3321no—
1601C22—3321no—
1602C22—3321no—
1603C22—3321no—
1604C22—3321no—
1605C22—3321no—
1606C22—3321no—
1607C22—6648no—
1608C22—1662no—
1609C22—1662no—
1610C22—1662no—
1611C22—1662no—
1612C22—1662no—
1613C22—1662no—
1614C22—1662no—
1615C22—1662no—
1616C22—1662no—
1617C22—1662no—
1618C22—1662no—
1619C22—1662no—
1620C22C23×C4×D8311yescharacteristic
1621C22H(5,𝔽2)×D8311yescharacteristic
1622C22H(5,𝔽2)×D8311yescharacteristic
1623C22C2×#1458183811yescharacteristic
1624C22#1912853611yescharacteristic
1625C22#1912853711yescharacteristic
1626C22#1912853811yescharacteristic
1627C4—22no—
1628C4—22no—
1629C4—22no—
1630C4—22no—
1631C4—22no—
1632C4—22no—
1633C4—41no—
1634C4—41no—
1635C4—41no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—3321no—
1641C4—3321no—
1642C4—3321no—
1643C4—3321no—
1644C4—3321no—
1645C4—3321no—
1646C4—1662no—
1647C4—1662no—
1648C4—1662no—
1649C4—1662no—
1650C4—1662no—
1651C4—1662no—
1652C2—42no—
1653C2—42no—
1654C2—3322no—
1655C2—3322no—
1656C2—3322no—
1657C2—3322no—
1658C2#2492066711yescharacteristic
1659C2#2492066911yescharacteristic
1660C2C4×#1458183811yescharacteristic
1661C2#2492161411yescharacteristic
1662C2#2492172811yescharacteristic
1663C2#2492173411yescharacteristic
1664C2#2492173511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2337C2
socle, cosocleC23×C83C25
prime radicalC2×#19128443C2
hypercenter#2337D83
hypocenterC83#34512
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2337

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #24910603C2semidirect
3. #24910603C2semidirect
4. #24910601C2semidirect
5. #24910574C2semidirect
6. #24910571C2semidirect
7. #24910570C2semidirect
8. #24910539C2semidirect
9. #24910538C2semidirect
10. #24910537C2semidirect
11. #24910534C2semidirect
12. #24910532C2semidirect
13. #24910529C2semidirect
14. #24910445C2semidirect
15. #24910443C2semidirect
16. #24910441C2semidirect
17. #24910277C2semidirect
18. #24910275C2semidirect
19. #24910273C2semidirect
20. #24910273C2semidirect
21. #24910271C2semidirect
22. #24910177C2semidirect
23. #24910172C2semidirect
24. #24910169C2semidirect
25. #24910120C2semidirect
26. #24910119C2semidirect
27. #24910116C2semidirect
28. #24909968C2semidirect
29. C4×#14581762C2semidirect
30. #24909964C2semidirect
31. C83×#2337C2semidirect
32. C23×C4×D83C22semidirect
33. #19128443C4semidirect
48. C2×Q8×Dic83C22semidirect
49. C2×C4×Dic166C22semidirect
50. C2×#14581757C22semidirect
60. C22×(C2×D83)⋊C4C22semidirect
61. C2×C22⋊C4×D83C22semidirect
62. C2×C22⋊C4×D83C22semidirect
63. #19127608C22semidirect
64. #19127607C22semidirect
65. #19127606C22semidirect
66. #19127605C22semidirect
67. #19127605C22semidirect
68. #19127605C22semidirect
69. #19127605C22semidirect
79. #19127595C22semidirect
80. #19127595C22semidirect
81. #19127594C22semidirect
82. #19127594C22semidirect
83. #19127594C22semidirect
84. #19127594C22semidirect
85. #19127593C22semidirect
86. #19127593C22semidirect
87. #19127593C22semidirect
88. #19127593C22semidirect
89. #19127593C22semidirect
90. #19127593C22semidirect
91. #19127593C22semidirect
92. #19127592C22semidirect
93. #19127592C22semidirect
94. #19127592C22semidirect
95. #19127591C22semidirect
96. #19127591C22semidirect
97. #19127591C22semidirect
98. #19127591C22semidirect
99. #19127591C22semidirect
100. #19127590C22semidirect
101. #19127590C22semidirect
102. #19127590C22semidirect
103. #19127590C22semidirect
104. #19127590C22semidirect
105. #19127590C22semidirect
106. #19127590C22semidirect
107. #19127590C22semidirect
108. #19127590C22semidirect
109. #19127589C22semidirect
110. #19127589C22semidirect
127. #19127576C22semidirect
128. #19127576C22semidirect
129. #19127575C22semidirect
130. #19127575C22semidirect
131. #19127575C22semidirect
132. #19127575C22semidirect
133. #19127575C22semidirect
134. #19127575C22semidirect
135. #19127575C22semidirect
136. #19127575C22semidirect
137. #19127575C22semidirect
138. #19127574C22semidirect
139. #19127573C22semidirect
140. #19127572C22semidirect
141. #19127572C22semidirect
142. #19127572C22semidirect
143. #19127570C22semidirect
144. #19127568C22semidirect
145. #19127556C22semidirect
146. #19127556C22semidirect
147. #19127556C22semidirect
148. #19127556C22semidirect
149. C4⋊C4×Dic83C22semidirect
150. C4×Dic83⋊C4C22semidirect
151. C4×C4⋊Dic83C22semidirect
152. C4×C4⋊Dic83C22semidirect
153. #19127552C22semidirect
154. C22⋊C4×Dic83C22semidirect
155. C22⋊C4×Dic83C22semidirect
156. C22⋊C4×Dic83C22semidirect
157. C4×(C2×D83)⋊C4C22semidirect
158. C4×(C2×D83)⋊C4C22semidirect
159. C4×(C2×D83)⋊C4C22semidirect
160. C4×(C2×D83)⋊C4C22semidirect
161. C4×(C2×D83)⋊C4C22semidirect
162. C4×C22⋊Dic83C22semidirect
163. #19127548C22semidirect
164. #19127548C22semidirect
165. #19127548C22semidirect
166. #19127548C22semidirect
167. #19127548C22semidirect
168. #19127548C22semidirect
169. #19127548C22semidirect
170. #19127547C22semidirect
171. #19127546C22semidirect
172. #19127546C22semidirect
174. #391×C83C22semidirect
175. #391×C83C22semidirect
176. #388×C83C22semidirect
177. #388×C83C22semidirect
178. #388×C83C22semidirect
179. #388×C83C22semidirect
182. #385×C83C22semidirect
183. #385×C83C22semidirect
184. #383×C83C22semidirect
185. C4×C4⋊C4×C83C22semidirect
186. C4×C22⋊C4×C83C22semidirect
187. C4×C22⋊C4×C83C22semidirect
213. #14581781C2×C4semidirect
214. #14581781C2×C4semidirect
215. #14581780C2×C4semidirect
216. #14581780C2×C4semidirect
217. #14581778C2×C4semidirect
218. #14581778C2×C4semidirect
219. #14581778C2×C4semidirect
220. #14581778C2×C4semidirect
221. #14581762C2×C4semidirect
222. #14581762C2×C4semidirect
223. #14581762C2×C4semidirect
224. #14581762C2×C4semidirect
225. #14581760C2×C4semidirect
226. #14581760C2×C4semidirect
344. #124×C83C2×C4semidirect
389. C23×D83C22×C4semidirect
398. C2×Dic166C22×C4semidirect
399. C2×Dic166C22×C4semidirect
488. C22⋊Dic83C22×C4semidirect
519. (C2×D83)⋊C4C22×C4semidirect
520. (C2×D83)⋊C4C22×C4semidirect
521. (C2×D83)⋊C4C22×C4semidirect
522. (C2×D83)⋊C4C22×C4semidirect
523. (C2×D83)⋊C4C22×C4semidirect
524. (C2×D83)⋊C4C22×C4semidirect
539. C4×Dic83C22×C4semidirect
540. C4×Dic83C22×C4semidirect
545. C2×Q8×C83C22×C4semidirect
580. C22⋊C4×C83C22×C4semidirect
581. C22⋊C4×C83C22×C4semidirect
586. C42×C83C22×C4semidirect
854. #2337D83semidirect
864. C83#34512semidirect
904. #391C2×D83semidirect
905. #391C2×D83semidirect
947. #388C2×D83semidirect
948. #388C2×D83semidirect
949. #388C2×D83semidirect
950. #388C2×D83semidirect
985. #385C2×D83semidirect
986. #385C2×D83semidirect
989. #383C2×D83semidirect
999. C4×C4⋊C4C2×D83semidirect
1016. C4×C22⋊C4C2×D83semidirect
1017. C4×C22⋊C4C2×D83semidirect
1058. #124C4×D83semidirect
1237. C2×Q8C2×C4×D83semidirect
1397. C22⋊C4C2×C4×D83semidirect
1398. C22⋊C4C2×C4×D83semidirect
1419. C42C2×C4×D83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191284432
#249106032
#249106012
#249105742
#249105712
#249105702
#249105392
#249105382
#249105372
#249105342
#249105322
#249105292
#249104452
#249104432
#249104412
#249102772
#249102752
#249102732
#249102712
#249101772
#249101722
#249101692
#249101202
#249101192
#249101162
#249099682
C4×#145817622
#249099642
C83×#23372
#3451283