Finite Group Databasebeta

← #35569814

Subgroups — #35569814

Order 21248.

2600 conjugacy classes of subgroups.

The subgroup lattice has 1664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128340C211yesmaximal, characteristic
2#24910610C211yesmaximal, characteristic, complemented
3#24910606C211yesmaximal, characteristic, complemented
4#24910601C211yesmaximal, characteristic, complemented
5#24910600C211yesmaximal, characteristic, complemented
6#24910535C211yesmaximal, characteristic, complemented
7#24910505C211yesmaximal, characteristic, complemented
8#24910502C211yesmaximal, characteristic, complemented
9#24910485C211yesmaximal, characteristic, complemented
10#24910474C211yesmaximal, characteristic, complemented
11#24910431C211yesmaximal, characteristic, complemented
12#24910386C211yesmaximal, characteristic, complemented
13#24910306C211yesmaximal, characteristic, complemented
14#24910305C211yesmaximal, characteristic, complemented
15#24910302C211yesmaximal, characteristic, complemented
16#24910281C211yesmaximal, characteristic, complemented
17#24910259C211yesmaximal, characteristic, complemented
18#24910250C211yesmaximal, characteristic, complemented
19#24910226C211yesmaximal, characteristic, complemented
20#24910153C211yesmaximal, characteristic, complemented
21#24910144C211yesmaximal, characteristic, complemented
22#24910126C211yesmaximal, characteristic, complemented
23#24910119C211yesmaximal, characteristic, complemented
24#24910058C211yesmaximal, characteristic, complemented
25#24910057C211yesmaximal, characteristic, complemented
26#24910050C211yesmaximal, characteristic, complemented
27#24910042C211yesmaximal, characteristic, complemented
28#24910004C211yesmaximal, characteristic, complemented
29#24909926C211yesmaximal, characteristic, complemented
30#24909923C211yesmaximal, characteristic, complemented
31C83×#2333C211yesmaximal, characteristic, complemented
32C22×#13050589C2211yescharacteristic
33C22×D4×D83C2211yescharacteristic
34#19128340C4116yescomplemented
35C2×#14581778C2211yescharacteristic
36C2×#14581777C2211yescharacteristic
37C2×#14581773C2211yescharacteristic
38C2×#14581770C2211yescharacteristic
39C2×#14581765C2211yescharacteristic
40C2×#14581764C2211yescharacteristic
41C2×#14581760C2211yescharacteristic
42C2×#14581760C2211yescharacteristic
43C2×C4×Dic166C2211yescharacteristic, complemented
44C2×#14581757C2211yescharacteristic, complemented
45C2×D4×Dic83C2211yescharacteristic, complemented
46C2×C4×C22⋊D83C2211yescharacteristic
47C2×C4×C22⋊D83C2211yescharacteristic
48C2×C4×C22⋊D83C2211yescharacteristic, complemented
49C2×(C22⋊D83)⋊C4C2211yescharacteristic
50C2×(C22⋊D83)⋊C4C2211yescharacteristic
51C2×#14581751C2211yescharacteristic, complemented
52C2×#14581750C2211yescharacteristic
53C2×#14581749C2211yescharacteristic
54C2×#14581749C2211yescharacteristic, complemented
55C2×#14581748C2211yescharacteristic, complemented
56C22×Dic83⋊C4C2211yescharacteristic, complemented
57C22×(C2×D83)⋊C4C2211yescharacteristic
58C22×(C2×D83)⋊C4C2211yescharacteristic
59C2×C22⋊C4×D83C2211yescharacteristic
60C2×C22⋊C4×D83C2211yescharacteristic
61#19127605C2211yescharacteristic, complemented
62#19127605C2211yescharacteristic, complemented
63#19127604C2211yescharacteristic
64#19127604C2211yescharacteristic, complemented
65#19127604C2211yescharacteristic, complemented
66#19127603C2211yescharacteristic
67#19127602C2211yescharacteristic
68#19127601C2211yescharacteristic
69#19127601C2211yescharacteristic
70#19127601C2211yescharacteristic
71#19127601C2211yescharacteristic
72#19127601C2211yescharacteristic
73#19127601C2211yescharacteristic
74#19127601C2211yescharacteristic
75#19127601C2211yescharacteristic
76#19127601C2211yescharacteristic, complemented
77#19127601C2211yescharacteristic, complemented
78#19127601C2211yescharacteristic, complemented
79#19127600C2211yescharacteristic, complemented
80#19127598C2211yescharacteristic, complemented
81#19127598C2211yescharacteristic, complemented
82#19127598C2211yescharacteristic, complemented
83#19127598C2211yescharacteristic, complemented
84#19127596C2211yescharacteristic, complemented
85#19127595C2211yescharacteristic, complemented
86#19127595C2211yescharacteristic, complemented
87#19127595C2211yescharacteristic, complemented
88#19127594C2211yescharacteristic, complemented
89#19127594C2211yescharacteristic, complemented
90#19127593C2211yescharacteristic
91#19127593C2211yescharacteristic
92#19127593C2211yescharacteristic
93#19127593C2211yescharacteristic, complemented
94#19127593C2211yescharacteristic, complemented
95#19127592C2211yescharacteristic
96#19127592C2211yescharacteristic
97#19127592C2211yescharacteristic
98#19127592C2211yescharacteristic, complemented
99#19127592C2211yescharacteristic, complemented
100#19127592C2211yescharacteristic, complemented
101#19127591C2211yescharacteristic
102#19127591C2211yescharacteristic, complemented
103#19127590C2211yescharacteristic
104#19127590C2211yescharacteristic
105#19127590C2211yescharacteristic
106#19127590C2211yescharacteristic
107#19127590C2211yescharacteristic
108#19127590C2211yescharacteristic, complemented
109#19127590C2211yescharacteristic, complemented
110#19127590C2211yescharacteristic, complemented
111#19127590C2211yescharacteristic, complemented
112#19127589C2211yescharacteristic, complemented
113#19127589C2211yescharacteristic, complemented
114#19127589C2211yescharacteristic, complemented
115#19127589C2211yescharacteristic, complemented
116#19127589C2211yescharacteristic, complemented
117#19127585C2211yescharacteristic, complemented
118#19127583C2211yescharacteristic, complemented
119#19127583C2211yescharacteristic, complemented
120#19127582C2211yescharacteristic, complemented
121#19127581C2211yescharacteristic
122#19127581C2211yescharacteristic, complemented
123#19127580C2211yescharacteristic
124#19127580C2211yescharacteristic, complemented
125#19127579C2211yescharacteristic
126#19127579C2211yescharacteristic
127#19127578C2211yescharacteristic
128#19127578C2211yescharacteristic, complemented
129#19127578C2211yescharacteristic, complemented
130#19127577C2211yescharacteristic, complemented
131#19127575C2211yescharacteristic, complemented
132#19127575C2211yescharacteristic, complemented
133#19127575C2211yescharacteristic, complemented
134#19127574C2211yescharacteristic, complemented
135#19127574C2211yescharacteristic, complemented
136#19127573C2211yescharacteristic, complemented
137#19127565C2211yescharacteristic, complemented
138#19127563C2211yescharacteristic, complemented
139#19127560C2211yescharacteristic
140#19127560C2211yescharacteristic, complemented
141#19127560C2211yescharacteristic, complemented
142#19127559C2211yescharacteristic, complemented
143#19127559C2211yescharacteristic, complemented
144#19127559C2211yescharacteristic, complemented
145#19127559C2211yescharacteristic, complemented
146#19127558C2211yescharacteristic, complemented
147#19127556C2211yescharacteristic
148#19127556C2211yescharacteristic
149#19127556C2211yescharacteristic
150#19127556C2211yescharacteristic
151#19127556C2211yescharacteristic
152#19127556C2211yescharacteristic
153C4⋊C4×Dic83C2211yescharacteristic, complemented
154C4×Dic83⋊C4C2211yescharacteristic, complemented
155C4×Dic83⋊C4C2211yescharacteristic, complemented
156#19127552C2211yescharacteristic, complemented
157#19127552C2211yescharacteristic, complemented
158#19127552C2211yescharacteristic, complemented
159C22⋊C4×Dic83C2211yescharacteristic, complemented
160C22⋊C4×Dic83C2211yescharacteristic, complemented
161C22⋊C4×Dic83C2211yescharacteristic, complemented
162C22⋊C4×Dic83C2211yescharacteristic, complemented
163C22⋊C4×Dic83C2211yescharacteristic, complemented
164C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
165C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
166C4×C22⋊Dic83C2211yescharacteristic, complemented
167#19127548C2211yescharacteristic
168#19127548C2211yescharacteristic, complemented
169#19127548C2211yescharacteristic, complemented
170#19127548C2211yescharacteristic, complemented
171#19127548C2211yescharacteristic, complemented
172C42×Dic83C2211yescharacteristic, complemented
173C2×#121×C83C2211yescharacteristic
174#390×C83C2211yescharacteristic
175#390×C83C2211yescharacteristic, complemented
176#388×C83C2211yescharacteristic, complemented
177#388×C83C2211yescharacteristic, complemented
178#387×C83C2211yescharacteristic, complemented
179#387×C83C2211yescharacteristic, complemented
180#386×C83C2211yescharacteristic
181#386×C83C2211yescharacteristic, complemented
182#386×C83C2211yescharacteristic, complemented
183#386×C83C2211yescharacteristic, complemented
184#381×C83C2211yescharacteristic, complemented
185C4×C22⋊C4×C83C2211yescharacteristic, complemented
186C4×C22⋊C4×C83C2211yescharacteristic, complemented
187C4×C22⋊C4×C83C2211yescharacteristic, complemented
188C24×D83C2311yescharacteristic
189C24×D83C2311yescharacteristic
190C2×#13050589—42no—
191C2×#13050589—42no—
192C2×#13050589C2×C418yescomplemented
193C22×Dic166C2311yescharacteristic
194C22×D332C2311yescharacteristic
195C22×C22⋊D83C2311yescharacteristic
196C22×C22⋊D83C2311yescharacteristic
197C22×C22⋊D83C2311yescharacteristic
198C22×C22⋊D83C2311yescharacteristic
199C22×C22⋊D83C2311yescharacteristic
200C2×D4×D83—42no—
201C2×D4×D83—42no—
202C2×D4×D83C2×C418yescomplemented
203C23×Dic83C2311yescharacteristic
204C23×Dic83C2311yescharacteristic
205C23×Dic83C2311yescharacteristic
206C23×Dic83C2311yescharacteristic
207C22×C4×D83C2311yescharacteristic
208C22×C4×D83C2311yescharacteristic
209C22×C4×D83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
211C22×C4×D83C2311yescharacteristic
212#14581778C2×C418yescomplemented
213#14581777C2×C418yescomplemented
214#14581773C2×C418yescomplemented
215#14581770C2×C418yescomplemented
216#14581765C2×C418yescomplemented
217#14581764C2×C418yes—
218#14581760C2×C418yescomplemented
219#14581760C2×C418yescomplemented
220C4×Dic166—42no—
221#14581757—42no—
222D4×Dic83—42no—
223C4×C22⋊D83—42no—
224C4×C22⋊D83—42no—
225C4×C22⋊D83C2×C418yescomplemented
226(C22⋊D83)⋊C4—42no—
227(C22⋊D83)⋊C4C2×C418yescomplemented
228#14581751—42no—
229#14581750—42no—
230#14581749—42no—
231#14581749—42no—
232#14581748—42no—
233C2×C4⋊Dic83C2311yescharacteristic
234C2×C4⋊Dic83C2311yescharacteristic
235C2×C4⋊Dic83C2311yescharacteristic
236C2×C4⋊Dic83C2311yescharacteristic
237C2×Dic83⋊C4—42no—
238C2×Dic83⋊C4C2311yescharacteristic
239C2×Dic83⋊C4C2311yescharacteristic
240C2×Dic83⋊C4C2311yescharacteristic
241C2×Dic83⋊C4C2311yescharacteristic
242C2×Dic83⋊C4C2311yescharacteristic
243C2×Dic83⋊C4C2311yescharacteristic
244C2×Dic83⋊C4C2311yescharacteristic
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×Dic83⋊C4C2311yescharacteristic
254C2×Dic83⋊C4C2311yescharacteristic
255C2×C22⋊Dic83C2311yescharacteristic
256C2×C22⋊Dic83C2311yescharacteristic
257C2×C22⋊Dic83C2311yescharacteristic
258C2×C22⋊Dic83C2311yescharacteristic
259C2×C22⋊Dic83C2311yescharacteristic
260C2×C22⋊Dic83C2311yescharacteristic
261C2×C22⋊Dic83C2311yescharacteristic
262C2×C22⋊Dic83C2311yescharacteristic
263C2×C22⋊Dic83C2311yescharacteristic
264C2×C22⋊Dic83C2311yescharacteristic
265C2×C22⋊Dic83C2311yescharacteristic
266C2×C22⋊Dic83C2311yescharacteristic
267C2×C22⋊Dic83C2311yescharacteristic
268C2×(C2×D83)⋊C4—42no—
269C2×(C2×D83)⋊C4C2×C418yescomplemented
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
298C2×(C2×D83)⋊C4C2311yescharacteristic
299C22⋊C4×D83—42no—
300C22⋊C4×D83C2×C418yescomplemented
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
316C2×C4×Dic83C2311yescharacteristic
317C2×C4×Dic83C2311yescharacteristic
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×D4×C83C2311yescharacteristic
341C22×D4×C83C2311yescharacteristic
342C22×D4×C83C2311yescharacteristic
343C23×C4×C83C2311yescharacteristic
344C23×C4×C83C2311yescharacteristic
345C23×C4×C83C2311yescharacteristic
346#121×C83C2×C418yescomplemented
347C2×C4⋊C4×C83C2311yescharacteristic
348C2×C4⋊C4×C83C2311yescharacteristic
349C2×C4⋊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×C22⋊C4×C83C2311yescharacteristic
360C2×C22⋊C4×C83C2311yescharacteristic
361C2×C22⋊C4×C83C2311yescharacteristic
362C2×C42×C83C2311yescharacteristic
363C2×C42×C83C2311yescharacteristic
364C2×C42×C83C2311yescharacteristic
365C2×C42×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×C414yes—
390C23×D83C2411yescharacteristic
391C23×D83C2411yescharacteristic
392C23×D83C2411yescharacteristic
393#13050589—416no—
394C2×Dic166—22no—
395C2×Dic166—22no—
396C2×Dic166C22×C414yes—
397C2×D332—41no—
398C2×D332—41no—
399C2×D332C22×C414yes—
400C2×C22⋊D83—22no—
401C2×C22⋊D83—22no—
402C2×C22⋊D83—22no—
403C2×C22⋊D83—22no—
404C2×C22⋊D83—41no—
405C2×C22⋊D83—41no—
406C2×C22⋊D83—41no—
407C2×C22⋊D83—41no—
408C2×C22⋊D83—41no—
409C2×C22⋊D83—41no—
410C2×C22⋊D83C22×C414yes—
411C2×C22⋊D83C22×C414yes—
412C2×C22⋊D83C22×C414yes—
413C2×C22⋊D83C22×C414yes—
414C2×C22⋊D83C22×C414yes—
415D4×D83—416no—
416C22×Dic83—22no—
417C22×Dic83—22no—
418C22×Dic83—22no—
419C22×Dic83—41no—
420C22×Dic83—41no—
421C22×Dic83—41no—
422C22×Dic83—41no—
423C22×Dic83—41no—
424C22×Dic83—41no—
425C22×Dic83—41no—
426C22×Dic83C22×C414yes—
427C22×Dic83C22×C414yes—
428C22×Dic83C2411yescharacteristic
429C22×Dic83C2411yescharacteristic
430C22×Dic83C2411yescharacteristic
431C22×Dic83C2411yescharacteristic
432C22×Dic83C2411yescharacteristic
433C22×Dic83C2411yescharacteristic
434C22×Dic83C2411yescharacteristic
435C22×Dic83C2411yescharacteristic
436C22×Dic83C2411yescharacteristic
437C22×Dic83C2411yescharacteristic
438C22×Dic83C2411yescharacteristic
439C22×Dic83C2411yescharacteristic
440C22×Dic83C2411yescharacteristic
441C2×C4×D83—22no—
442C2×C4×D83—22no—
443C2×C4×D83—22no—
444C2×C4×D83—41no—
445C2×C4×D83—41no—
446C2×C4×D83—41no—
447C2×C4×D83—41no—
448C2×C4×D83—41no—
449C2×C4×D83—41no—
450C2×C4×D83—41no—
451C2×C4×D83—41no—
452C2×C4×D83—41no—
453C2×C4×D83C22×C414yes—
454C2×C4×D83C22×C414yes—
455C2×C4×D83C22×C414yes—
456C4⋊Dic83—22no—
457C4⋊Dic83—41no—
458C4⋊Dic83—41no—
459C4⋊Dic83—41no—
460Dic83⋊C4—22no—
461Dic83⋊C4—22no—
462Dic83⋊C4—22no—
463Dic83⋊C4—22no—
464Dic83⋊C4—22no—
465Dic83⋊C4—41no—
466Dic83⋊C4—41no—
467Dic83⋊C4—41no—
468Dic83⋊C4—41no—
469Dic83⋊C4—41no—
470Dic83⋊C4—41no—
471Dic83⋊C4—41no—
472Dic83⋊C4—41no—
473Dic83⋊C4—41no—
474Dic83⋊C4C22×C414yes—
475Dic83⋊C4C22×C414yes—
476Dic83⋊C4C22×C414yes—
477C22⋊Dic83—22no—
478C22⋊Dic83—22no—
479C22⋊Dic83—41no—
480C22⋊Dic83—41no—
481C22⋊Dic83—41no—
482C22⋊Dic83—41no—
483C22⋊Dic83—41no—
484C22⋊Dic83—41no—
485C22⋊Dic83—41no—
486C22⋊Dic83—41no—
487C22⋊Dic83C22×C414yes—
488C22⋊Dic83C22×C414yes—
489C22⋊Dic83C22×C414yes—
490(C2×D83)⋊C4—22no—
491(C2×D83)⋊C4—22no—
492(C2×D83)⋊C4—41no—
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)⋊C4C22×C414yes—
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—
519C4×Dic83—22no—
520C4×Dic83—22no—
521C4×Dic83—22no—
522C4×Dic83—22no—
523C4×Dic83—22no—
524C4×Dic83—41no—
525C4×Dic83—41no—
526C4×Dic83—41no—
527C4×Dic83—41no—
528C4×Dic83—41no—
529C4×Dic83—41no—
530C4×Dic83—41no—
531C4×Dic83—41no—
532C4×Dic83—41no—
533C4×Dic83—41no—
534C4×Dic83—41no—
535C4×Dic83C22×C414yes—
536C24×C83C2411yescharacteristic
537C24×C83C2411yescharacteristic
538C24×C83C2411yescharacteristic
539C2×D4×C83—41no—
540C2×D4×C83—41no—
541C2×D4×C83—41no—
542C2×D4×C83—41no—
543C2×D4×C83—41no—
544C2×D4×C83—41no—
545C2×D4×C83C22×C414yes—
546C2×D4×C83C22×C414yes—
547C2×D4×C83C22×C414yes—
548C22×C4×C83—41no—
549C22×C4×C83—41no—
550C22×C4×C83—41no—
551C22×C4×C83—41no—
552C22×C4×C83—41no—
553C22×C4×C83—41no—
554C22×C4×C83—41no—
555C22×C4×C83—41no—
556C22×C4×C83C22×C414yes—
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
568C22×C4×C83C2411yescharacteristic
569C4⋊C4×C83—41no—
570C4⋊C4×C83—41no—
571C4⋊C4×C83C22×C414yes—
572C22⋊C4×C83—41no—
573C22⋊C4×C83—41no—
574C22⋊C4×C83—41no—
575C22⋊C4×C83—41no—
576C22⋊C4×C83—41no—
577C22⋊C4×C83—41no—
578C22⋊C4×C83—41no—
579C22⋊C4×C83—41no—
580C22⋊C4×C83—41no—
581C22⋊C4×C83—41no—
582C22⋊C4×C83C22×C414yes—
583C22⋊C4×C83C22×C414yes—
584C42×C83—41no—
585C42×C83—41no—
586C42×C83—41no—
587C42×C83—41no—
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×C83—21no—
600C23×C83—21no—
601C23×C83—21no—
602C23×C83—21no—
603C23×C83—21no—
604C23×C83—21no—
605C23×C83—21no—
606C23×C83C23×C412yes—
607C23×C83C23×C412yes—
608C23×C83C23×C412yes—
609C23×C83C2511yescharacteristic
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—21no—
627C22×D83—21no—
628C22×D83—44no—
629C22×D83—44no—
630C22×D83—44no—
631C22×D83—44no—
632C22×D83—44no—
633C22×D83—44no—
634C22×D83—82no—
635C22×D83—82no—
636C22×D83—82no—
637C22×D83—82no—
638C22×D83—82no—
639C22×D83—82no—
640C22×D83—82no—
641C22×D83—82no—
642C22×D83C23×C412yes—
643C22×D83C23×C412yes—
644C22×D83C23×C412yes—
645D4×C83—44no—
646D4×C83—44no—
647D4×C83—44no—
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—21no—
680C2×C4×C83—44no—
681C2×C4×C83—82no—
682C2×C4×C83—82no—
683C2×C4×C83C23×C412yes—
684C2×C4×C83C23×C412yes—
685C2×C4×C83C23×C412yes—
686C2×C4×C83C23×C412yes—
687C22⋊D83—28no—
688C22⋊D83—28no—
689C22⋊D83—44no—
690C22⋊D83—44no—
691C22⋊D83—44no—
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—28no—
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—21no—
722C2×Dic83—21no—
723C2×Dic83—21no—
724C2×Dic83—44no—
725C2×Dic83—82no—
726C2×Dic83—82no—
727C2×Dic83C23×C412yes—
728C2×Dic83C23×C412yes—
729C2×Dic83C23×C412yes—
730C2×Dic83C23×C412yes—
731C2×Dic83C23×C412yes—
732C2×Dic83H(5,𝔽2)12yes—
733C2×Dic83H(5,𝔽2)12yes—
734C2×Dic83H(5,𝔽2)12yes—
735D332—44no—
736C4×D83—28no—
737C4×D83—44no—
738C4×D83—44no—
739C4×D83—82no—
740C4×D83—82no—
741Dic166—28no—
742C22×C83—22no—
743C22×C83—22no—
744C22×C83—22no—
745C22×C83—22no—
746C22×C83—22no—
747C22×C83—22no—
748C22×C83—22no—
749C22×C83—22no—
750C22×C83—22no—
751C22×C83—41no—
752C22×C83—41no—
753C22×C83—41no—
754C22×C83—41no—
755C22×C83—41no—
756C22×C83—41no—
757C22×C83—41no—
758C22×C83—41no—
759C22×C83—41no—
760C22×C83—41no—
761C22×C83—41no—
762C22×C83—41no—
763C22×C83C24×C411yescharacteristic
764C22×C83C2×H(5,𝔽2)11yescharacteristic
765C22×C83C2×H(5,𝔽2)11yescharacteristic
766C22×C83C2×H(5,𝔽2)11yescharacteristic
767C22×C83#58511yescharacteristic
768C22×C83#58511yescharacteristic
769C22×C83#58511yescharacteristic
770C2×D83—22no—
771C2×D83—22no—
772C2×D83—22no—
773C2×D83—22no—
774C2×D83—22no—
775C2×D83—22no—
776C2×D83—22no—
777C2×D83—22no—
778C2×D83—22no—
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—88no—
792C2×D83—88no—
793C4×C83—22no—
794C4×C83—22no—
795C4×C83—22no—
796C4×C83—22no—
797C4×C83—41no—
798C4×C83—41no—
799C4×C83—41no—
800C4×C83—41no—
801C4×C83—41no—
802C4×C83—41no—
803C4×C83—41no—
804C4×C83—41no—
805Dic83—22no—
806Dic83—22no—
807Dic83—22no—
808Dic83—22no—
809Dic83—22no—
810Dic83—41no—
811Dic83—41no—
812Dic83—41no—
813Dic83—41no—
814Dic83—41no—
815Dic83—41no—
816Dic83—41no—
817Dic83#51814yes—
818#34495—831nomaximal, Sylow
819C2×C83—42no—
820C2×C83—42no—
821C2×C83—42no—
822C2×C83C2×#51811yescharacteristic
823C2×C83#342811yescharacteristic
824C2×C83C4×H(5,𝔽2)11yescharacteristic
825C2×C83#354611yescharacteristic
826C2×C83#355111yescharacteristic
827C2×C83#355811yescharacteristic
828C2×C83#356211yescharacteristic
829D83—42no—
830D83—42no—
831D83—42no—
832C2×#546—831no—
833#2376—831no—
834#2376—831no—
835#2375—831no—
836#2375—831no—
837#2367—831no—
838#2363—831no—
839#2363—831no—
840#2362—831no—
841#2361—831no—
842#2357—831no—
843#2352—831no—
844#2342—831no—
845#2342—831no—
846#2341—831no—
847D4×C22⋊C4—831no—
848#2335—831no—
849#2335—831no—
850#2333—831no—
851#2333D8311yescharacteristic, complemented
852#2324—831no—
853#2323—831no—
854#2321—831no—
855#2321—831no—
856#2312—831no—
857#2312—831no—
858#2311—831no—
859#2309—831no—
860C4×#124—831no—
861#2293—831no—
862#2293—831no—
863C83#3449511yescharacteristic, complemented, Sylow
864C22×#41—831no—
865C23×D4—831no—
866#546—8316no—
867C2×#124—831no—
868C2×#123—831no—
869C2×#123—831no—
870C2×C22⋊Q8—831no—
871C2×#121—831no—
872C2×#121—831no—
873C2×#121C2×D8311yescharacteristic
874C2×#120—831no—
875C2×#120—831no—
876C2×C4×Q8—831no—
877C2×C4×Q8—831no—
878C2×C4×D4—831no—
879C2×C4×D4—831no—
880C2×C4×D4—831no—
881C2×C4×D4—831no—
882C2×C4×D4—831no—
883C2×C4×D4—831no—
884C2×#117—831no—
885C2×#117—831no—
886C2×#117—831no—
887C2×#117—831no—
888C2×#117—831no—
889C22×C4⋊C4—831no—
890C22×C22⋊C4—831no—
891C22×C22⋊C4—831no—
892C22×C22⋊C4—831no—
893C22×C22⋊C4—831no—
894#391—831no—
895#391—831no—
896#390—831no—
897#390—831no—
898#390—831no—
899#390—831no—
900#390—831no—
901#390—831no—
902#390—831no—
903#390—831no—
904#390—831no—
905#390—831no—
906#390—831no—
907#390—831no—
908#390—831no—
909#390—831no—
910#390—831no—
911#390—831no—
912#390C2×D8311yescharacteristic
913#390C2×D8311yescharacteristic, complemented
914#389—831no—
915#389—831no—
916#389—831no—
917#389—831no—
918#389—831no—
919#389—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#388—831no—
948#388—831no—
949#388—831no—
950#388—831no—
951#388—831no—
952#388C2×D8311yescharacteristic, complemented
953#388C2×D8311yescharacteristic, complemented
954#387—831no—
955#387—831no—
956#387—831no—
957#387—831no—
958#387C2×D8311yescharacteristic, complemented
959#387C2×D8311yescharacteristic, complemented
960#386—831no—
961#386—831no—
962#386—831no—
963#386—831no—
964#386—831no—
965#386—831no—
966#386—831no—
967#386—831no—
968#386—831no—
969#386—831no—
970#386C2×D8311yescharacteristic
971#386C2×D8311yescharacteristic, complemented
972#386C2×D8311yescharacteristic, complemented
973#386C2×D8311yescharacteristic, complemented
974#385—831no—
975#385—831no—
976#385—831no—
977#385—831no—
978#385—831no—
979#385—831no—
980#382—831no—
981#381—831no—
982#381C2×D8311yescharacteristic, complemented
983#380—831no—
984#380—831no—
985#380—831no—
986#380—831no—
987#380—831no—
988#380—831no—
989#380—831no—
990#380—831no—
991#379—831no—
992#379—831no—
993#379—831no—
994#379—831no—
995#379—831no—
996#379—831no—
997C4×C4⋊C4—831no—
998C4×C4⋊C4—831no—
999C4×C4⋊C4—831no—
1000C4×C4⋊C4—831no—
1001C4×C4⋊C4—831no—
1002C4×C4⋊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
1018C4×C22⋊C4C2×D8311yescharacteristic, complemented
1019C43—831no—
1020C25—831no—
1021C25—831no—
1022C2×#41—3322no—
1023C2×#41—3322no—
1024C2×#41—838no—
1025C22×Q8—831no—
1026C22×D4—3322no—
1027C22×D4—3322no—
1028C22×D4—831no—
1029C22×D4—831no—
1030C22×D4—831no—
1031C22×D4—838no—
1032C22×D4—831no—
1033C22×D4—831no—
1034C22×D4—831no—
1035C22×D4C22×D8311yescharacteristic
1036C22×D4C22×D8311yescharacteristic
1037C22×D4C22×D8311yescharacteristic
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×C4C22×D8311yescharacteristic
1048C23×C4C22×D8311yescharacteristic
1049C23×C4C22×D8311yescharacteristic
1050#124—838no—
1051#123—838no—
1052#123—838no—
1053C22⋊Q8—838no—
1054#121—838no—
1055#121—838no—
1056#121C4×D8318yescomplemented
1057#120—838no—
1058#120—838no—
1059C4×Q8—3322no—
1060C4×Q8—3322no—
1061C4×D4—3322no—
1062C4×D4—3322no—
1063C4×D4—3322no—
1064C4×D4—3322no—
1065C4×D4—838no—
1066C4×D4—838no—
1067#117—3322no—
1068#117—3322no—
1069#117—3322no—
1070#117—3322no—
1071#117—3322no—
1072C2×C4⋊C4—3322no—
1073C2×C4⋊C4—831no—
1074C2×C4⋊C4—831no—
1075C2×C4⋊C4—831no—
1076C2×C4⋊C4—831no—
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⋊C4—831no—
1092C2×C4⋊C4—831no—
1093C2×C4⋊C4—831no—
1094C2×C4⋊C4C22×D8311yescharacteristic
1095C2×C4⋊C4C22×D8311yescharacteristic
1096C2×C4⋊C4C22×D8311yescharacteristic
1097C2×C22⋊C4—3322no—
1098C2×C22⋊C4—3322no—
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—838no—
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—838no—
1139C2×C22⋊C4—831no—
1140C2×C22⋊C4—831no—
1141C2×C22⋊C4—831no—
1142C2×C22⋊C4—831no—
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×C22⋊C4C22×D8311yescharacteristic
1153C2×C22⋊C4C22×D8311yescharacteristic
1154C2×C22⋊C4C22×D8311yescharacteristic
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×C42—831no—
1169C2×C42—831no—
1170C2×C42—831no—
1171C2×C42—831no—
1172C2×C42C22×D8311yescharacteristic
1173C2×C42C22×D8311yescharacteristic
1174C2×C42C22×D8311yescharacteristic
1175C2×C42C22×D8311yescharacteristic
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#95—831no—
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
1208C24—3321no—
1209C24—3321no—
1210C24—3321no—
1211C24—3321no—
1212C24—3321no—
1213C24—3321no—
1214C24—3321no—
1215C24—3321no—
1216C24—3321no—
1217C24—3321no—
1218C24—3321no—
1219C24—3321no—
1220C24—834no—
1221C24—834no—
1222C24—831no—
1223C24—831no—
1224C24—831no—
1225C24C23×D8311yescharacteristic
1226C24C23×D8311yescharacteristic
1227C24C23×D8311yescharacteristic
1228#41—33216no—
1229C2×Q8—834no—
1230C2×Q8—1662no—
1231C2×Q8—1662no—
1232C2×D4—41no—
1233C2×D4—41no—
1234C2×D4—41no—
1235C2×D4—41no—
1236C2×D4—41no—
1237C2×D4—41no—
1238C2×D4—3321no—
1239C2×D4—3321no—
1240C2×D4—33216no—
1241C2×D4—3321no—
1242C2×D4—3321no—
1243C2×D4—3321no—
1244C2×D4—3321no—
1245C2×D4—3321no—
1246C2×D4—3321no—
1247C2×D4—834no—
1248C2×D4—834no—
1249C2×D4—834no—
1250C2×D4—834no—
1251C2×D4—834no—
1252C2×D4—834no—
1253C2×D4—1662no—
1254C2×D4—1662no—
1255C2×D4—1662no—
1256C2×D4—1662no—
1257C2×D4C2×C4×D8314yes—
1258C2×D4C2×C4×D8314yes—
1259C2×D4C2×C4×D8314yes—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—41no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—3321no—
1269C22×C4—3321no—
1270C22×C4—3321no—
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—834no—
1285C22×C4—834no—
1286C22×C4—834no—
1287C22×C4—831no—
1288C22×C4—834no—
1289C22×C4—831no—
1290C22×C4—831no—
1291C22×C4—831no—
1292C22×C4—831no—
1293C22×C4—831no—
1294C22×C4—834no—
1295C22×C4—831no—
1296C22×C4—831no—
1297C22×C4—831no—
1298C22×C4—831no—
1299C22×C4—831no—
1300C22×C4—831no—
1301C22×C4—831no—
1302C22×C4—1662no—
1303C22×C4—1662no—
1304C22×C4—1662no—
1305C22×C4—1662no—
1306C22×C4—1662no—
1307C22×C4—1662no—
1308C22×C4C2×C4×D8314yes—
1309C22×C4C23×D8311yescharacteristic
1310C22×C4C23×D8311yescharacteristic
1311C22×C4C23×D8311yescharacteristic
1312C22×C4C23×D8311yescharacteristic
1313C22×C4C23×D8311yescharacteristic
1314C22×C4C23×D8311yescharacteristic
1315C22×C4C23×D8311yescharacteristic
1316C22×C4C23×D8311yescharacteristic
1317C22×C4C23×D8311yescharacteristic
1318C22×C4C23×D8311yescharacteristic
1319C22×C4C23×D8311yescharacteristic
1320C22×C4C23×D8311yescharacteristic
1321C4⋊C4—41no—
1322C4⋊C4—41no—
1323C4⋊C4—3321no—
1324C4⋊C4—3321no—
1325C4⋊C4—3321no—
1326C4⋊C4—3321no—
1327C4⋊C4—3321no—
1328C4⋊C4—3321no—
1329C4⋊C4—3321no—
1330C4⋊C4—3321no—
1331C4⋊C4—3321no—
1332C4⋊C4—3321no—
1333C4⋊C4—3321no—
1334C4⋊C4—3321no—
1335C4⋊C4—834no—
1336C4⋊C4—834no—
1337C4⋊C4—834no—
1338C4⋊C4—1662no—
1339C4⋊C4—1662no—
1340C4⋊C4—1662no—
1341C4⋊C4—1662no—
1342C4⋊C4—1662no—
1343C4⋊C4—1662no—
1344C4⋊C4C2×C4×D8314yes—
1345C22⋊C4—41no—
1346C22⋊C4—41no—
1347C22⋊C4—41no—
1348C22⋊C4—41no—
1349C22⋊C4—41no—
1350C22⋊C4—41no—
1351C22⋊C4—41no—
1352C22⋊C4—41no—
1353C22⋊C4—41no—
1354C22⋊C4—41no—
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—3321no—
1377C22⋊C4—3321no—
1378C22⋊C4—3321no—
1379C22⋊C4—3321no—
1380C22⋊C4—3321no—
1381C22⋊C4—3321no—
1382C22⋊C4—3321no—
1383C22⋊C4—834no—
1384C22⋊C4—834no—
1385C22⋊C4—834no—
1386C22⋊C4—834no—
1387C22⋊C4—834no—
1388C22⋊C4—834no—
1389C22⋊C4—834no—
1390C22⋊C4—834no—
1391C22⋊C4—834no—
1392C22⋊C4—834no—
1393C22⋊C4—1662no—
1394C22⋊C4—1662no—
1395C22⋊C4—1662no—
1396C22⋊C4—1662no—
1397C22⋊C4C2×C4×D8314yes—
1398C22⋊C4C2×C4×D8314yes—
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—1662no—
1416C42—1662no—
1417C42—1662no—
1418C42—1662no—
1419C42—1662no—
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—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—3324no—
1439C23—3324no—
1440C23—3324no—
1441C23—3324no—
1442C23—3324no—
1443C23—3324no—
1444C23—832no—
1445C23—832no—
1446C23—832no—
1447C23—6642no—
1448C23—6642no—
1449C23—6642no—
1450C23—6642no—
1451C23—6642no—
1452C23—6642no—
1453C23—6642no—
1454C23—6642no—
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—
1473C23C22×C4×D8312yes—
1474C23C22×C4×D8312yes—
1475C23C22×C4×D8312yes—
1476C23C24×D8311yescharacteristic
1477Q8—1668no—
1478D4—44no—
1479D4—44no—
1480D4—44no—
1481D4—3324no—
1482D4—3324no—
1483D4—3324no—
1484D4—3324no—
1485D4—1668no—
1486D4—1668no—
1487C2×C4—21no—
1488C2×C4—21no—
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—44no—
1520C2×C4—82no—
1521C2×C4—82no—
1522C2×C4—3324no—
1523C2×C4—3324no—
1524C2×C4—3324no—
1525C2×C4—832no—
1526C2×C4—832no—
1527C2×C4—832no—
1528C2×C4—832no—
1529C2×C4—832no—
1530C2×C4—832no—
1531C2×C4—832no—
1532C2×C4—832no—
1533C2×C4—6642no—
1534C2×C4—6642no—
1535C2×C4—6642no—
1536C2×C4—6642no—
1537C2×C4—1668no—
1538C2×C4—1661no—
1539C2×C4—1661no—
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—1668no—
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—
1574C22—22no—
1575C22—22no—
1576C22—22no—
1577C22—22no—
1578C22—22no—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—22no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
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—6648no—
1609C22—1662no—
1610C22—1662no—
1611C22—1662no—
1612C22—1662no—
1613C22—1662no—
1614C22—1662no—
1615C22—1662no—
1616C22—1662no—
1617C22—1662no—
1618C22C23×C4×D8311yescharacteristic
1619C22H(5,𝔽2)×D8311yescharacteristic
1620C22H(5,𝔽2)×D8311yescharacteristic
1621C22H(5,𝔽2)×D8311yescharacteristic
1622C22#1912853611yescharacteristic
1623C22#1912853711yescharacteristic
1624C22#1912853711yescharacteristic
1625C4—22no—
1626C4—22no—
1627C4—22no—
1628C4—22no—
1629C4—41no—
1630C4—41no—
1631C4—41no—
1632C4—41no—
1633C4—41no—
1634C4—41no—
1635C4—41no—
1636C4—41no—
1637C4—3321no—
1638C4—3321no—
1639C4—3321no—
1640C4—3321no—
1641C4—3321no—
1642C4—3321no—
1643C4—3321no—
1644C4—834no—
1645C4—1662no—
1646C4—1662no—
1647C4—1662no—
1648C4—1662no—
1649C4—1662no—
1650C2—42no—
1651C2—42no—
1652C2—42no—
1653C2—3322no—
1654C2—3322no—
1655C2—3322no—
1656C2#518×D8311yescharacteristic
1657C2#2492066211yescharacteristic
1658C2#2492066711yescharacteristic
1659C2#2492182811yescharacteristic
1660C2#2492188411yescharacteristic
1661C2#2492197411yescharacteristic
1662C2#2492204211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2333C2
socle, cosocleC23×C83C25
prime radicalC2×#19128340C2
hypercenter#2333D83
hypocenterC83#34495
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2333

Complements

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

NH ≅ G/Ntype
2. #24910610C2semidirect
3. #24910606C2semidirect
4. #24910601C2semidirect
5. #24910600C2semidirect
6. #24910535C2semidirect
7. #24910505C2semidirect
8. #24910502C2semidirect
9. #24910485C2semidirect
10. #24910474C2semidirect
11. #24910431C2semidirect
12. #24910386C2semidirect
13. #24910306C2semidirect
14. #24910305C2semidirect
15. #24910302C2semidirect
16. #24910281C2semidirect
17. #24910259C2semidirect
18. #24910250C2semidirect
19. #24910226C2semidirect
20. #24910153C2semidirect
21. #24910144C2semidirect
22. #24910126C2semidirect
23. #24910119C2semidirect
24. #24910058C2semidirect
25. #24910057C2semidirect
26. #24910050C2semidirect
27. #24910042C2semidirect
28. #24910004C2semidirect
29. #24909926C2semidirect
30. #24909923C2semidirect
31. C83×#2333C2semidirect
34. #19128340C4semidirect
43. C2×C4×Dic166C22semidirect
44. C2×#14581757C22semidirect
45. C2×D4×Dic83C22semidirect
48. C2×C4×C22⋊D83C22semidirect
51. C2×#14581751C22semidirect
54. C2×#14581749C22semidirect
55. C2×#14581748C22semidirect
56. C22×Dic83⋊C4C22semidirect
61. #19127605C22semidirect
62. #19127605C22semidirect
64. #19127604C22semidirect
65. #19127604C22semidirect
76. #19127601C22semidirect
77. #19127601C22semidirect
78. #19127601C22semidirect
79. #19127600C22semidirect
80. #19127598C22semidirect
81. #19127598C22semidirect
82. #19127598C22semidirect
83. #19127598C22semidirect
84. #19127596C22semidirect
85. #19127595C22semidirect
86. #19127595C22semidirect
87. #19127595C22semidirect
88. #19127594C22semidirect
89. #19127594C22semidirect
93. #19127593C22semidirect
94. #19127593C22semidirect
98. #19127592C22semidirect
99. #19127592C22semidirect
100. #19127592C22semidirect
102. #19127591C22semidirect
108. #19127590C22semidirect
109. #19127590C22semidirect
110. #19127590C22semidirect
111. #19127590C22semidirect
112. #19127589C22semidirect
113. #19127589C22semidirect
114. #19127589C22semidirect
115. #19127589C22semidirect
116. #19127589C22semidirect
117. #19127585C22semidirect
118. #19127583C22semidirect
119. #19127583C22semidirect
120. #19127582C22semidirect
122. #19127581C22semidirect
124. #19127580C22semidirect
128. #19127578C22semidirect
129. #19127578C22semidirect
130. #19127577C22semidirect
131. #19127575C22semidirect
132. #19127575C22semidirect
133. #19127575C22semidirect
134. #19127574C22semidirect
135. #19127574C22semidirect
136. #19127573C22semidirect
137. #19127565C22semidirect
138. #19127563C22semidirect
140. #19127560C22semidirect
141. #19127560C22semidirect
142. #19127559C22semidirect
143. #19127559C22semidirect
144. #19127559C22semidirect
145. #19127559C22semidirect
146. #19127558C22semidirect
153. C4⋊C4×Dic83C22semidirect
154. C4×Dic83⋊C4C22semidirect
155. C4×Dic83⋊C4C22semidirect
156. #19127552C22semidirect
157. #19127552C22semidirect
158. #19127552C22semidirect
159. C22⋊C4×Dic83C22semidirect
160. C22⋊C4×Dic83C22semidirect
161. C22⋊C4×Dic83C22semidirect
162. C22⋊C4×Dic83C22semidirect
163. C22⋊C4×Dic83C22semidirect
164. C4×(C2×D83)⋊C4C22semidirect
165. C4×(C2×D83)⋊C4C22semidirect
166. C4×C22⋊Dic83C22semidirect
168. #19127548C22semidirect
169. #19127548C22semidirect
170. #19127548C22semidirect
171. #19127548C22semidirect
172. C42×Dic83C22semidirect
175. #390×C83C22semidirect
176. #388×C83C22semidirect
177. #388×C83C22semidirect
178. #387×C83C22semidirect
179. #387×C83C22semidirect
181. #386×C83C22semidirect
182. #386×C83C22semidirect
183. #386×C83C22semidirect
184. #381×C83C22semidirect
185. C4×C22⋊C4×C83C22semidirect
186. C4×C22⋊C4×C83C22semidirect
187. C4×C22⋊C4×C83C22semidirect
192. C2×#13050589C2×C4semidirect
202. C2×D4×D83C2×C4semidirect
212. #14581778C2×C4semidirect
213. #14581777C2×C4semidirect
214. #14581773C2×C4semidirect
215. #14581770C2×C4semidirect
216. #14581765C2×C4semidirect
218. #14581760C2×C4semidirect
219. #14581760C2×C4semidirect
225. C4×C22⋊D83C2×C4semidirect
227. (C22⋊D83)⋊C4C2×C4semidirect
269. C2×(C2×D83)⋊C4C2×C4semidirect
300. C22⋊C4×D83C2×C4semidirect
346. #121×C83C2×C4semidirect
851. #2333D83semidirect
863. C83#34495semidirect
913. #390C2×D83semidirect
952. #388C2×D83semidirect
953. #388C2×D83semidirect
958. #387C2×D83semidirect
959. #387C2×D83semidirect
971. #386C2×D83semidirect
972. #386C2×D83semidirect
973. #386C2×D83semidirect
982. #381C2×D83semidirect
1016. C4×C22⋊C4C2×D83semidirect
1017. C4×C22⋊C4C2×D83semidirect
1018. C4×C22⋊C4C2×D83semidirect
1056. #121C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283402
#249106102
#249106062
#249106012
#249106002
#249105352
#249105052
#249105022
#249104852
#249104742
#249104312
#249103862
#249103062
#249103052
#249103022
#249102812
#249102592
#249102502
#249102262
#249101532
#249101442
#249101262
#249101192
#249100582
#249100572
#249100502
#249100422
#249100042
#249099262
#249099232
C83×#23332
#3449583