Finite Group Databasebeta

← #35569746

Subgroups — #35569746

Order 21248.

2636 conjugacy classes of subgroups.

The subgroup lattice has 1672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128341C211yesmaximal, characteristic
2#24910630C211yesmaximal, characteristic, complemented
3#24910619C211yesmaximal, characteristic, complemented
4#24910612C211yesmaximal, characteristic, complemented
5#24910603C211yesmaximal, characteristic, complemented
6#24910571C211yesmaximal, characteristic, complemented
7#24910513C211yesmaximal, characteristic, complemented
8#24910502C211yesmaximal, characteristic, complemented
9#24910455C211yesmaximal, characteristic, complemented
10#24910442C211yesmaximal, characteristic, complemented
11#24910405C211yesmaximal, characteristic, complemented
12#24910398C211yesmaximal, characteristic, complemented
13#24910307C211yesmaximal, characteristic, complemented
14#24910287C211yesmaximal, characteristic, complemented
15#24910279C211yesmaximal, characteristic, complemented
16#24910271C211yesmaximal, characteristic, complemented
17#24910248C211yesmaximal, characteristic, complemented
18#24910223C211yesmaximal, characteristic, complemented
19#24910213C211yesmaximal, characteristic, complemented
20#24910160C211yesmaximal, characteristic, complemented
21#24910129C211yesmaximal, characteristic, complemented
22#24910118C211yesmaximal, characteristic, complemented
23#24910116C211yesmaximal, characteristic, complemented
24#24910104C211yesmaximal, characteristic, complemented
25#24910057C211yesmaximal, characteristic, complemented
26#24910051C211yesmaximal, characteristic, complemented
27#24910038C211yesmaximal, characteristic, complemented
28#24909969C211yesmaximal, characteristic, complemented
29#24909902C211yesmaximal, characteristic, complemented
30C2×#19127594C211yesmaximal, characteristic, complemented
31C83×#2342C211yesmaximal, characteristic, complemented
32C22×#13050590C2211yescharacteristic
33C23×C22⋊D83C2211yescharacteristic
34#19128341C4116yescomplemented
35C2×#14581778C2211yescharacteristic
36C2×#14581775C2211yescharacteristic
37C2×#14581774C2211yescharacteristic
38C2×#14581769C2211yescharacteristic
39C2×#14581766C2211yescharacteristic
40C2×#14581765C2211yescharacteristic
41C2×#14581765C2211yescharacteristic
42C2×#14581762C2211yescharacteristic
43C2×#14581761C2211yescharacteristic
44C2×#14581754C2211yescharacteristic, complemented
45C2×C4×C22⋊D83C2211yescharacteristic
46C2×C4×C22⋊D83C2211yescharacteristic, complemented
47C2×(C22⋊D83)⋊C4C2211yescharacteristic
48C2×(C22⋊D83)⋊C4C2211yescharacteristic
49C2×(C22⋊D83)⋊C4C2211yescharacteristic
50C2×(C22⋊D83)⋊C4C2211yescharacteristic, complemented
51C2×(C22⋊D83)⋊C4C2211yescharacteristic, complemented
52C2×#14581749C2211yescharacteristic, complemented
53C22×C4⋊Dic83C2211yescharacteristic, complemented
54C22×C22⋊Dic83C2211yescharacteristic
55C22×C22⋊Dic83C2211yescharacteristic
56C2×C22⋊C4×D83C2211yescharacteristic
57C2×C22⋊C4×D83C2211yescharacteristic
58C22×C4×Dic83C2211yescharacteristic, complemented
59#19127607C2211yescharacteristic, complemented
60#19127607C2211yescharacteristic, complemented
61#19127605C2211yescharacteristic, complemented
62#19127605C2211yescharacteristic, complemented
63#19127603C2211yescharacteristic, complemented
64#19127603C2211yescharacteristic, complemented
65#19127602C2211yescharacteristic, complemented
66#19127601C2211yescharacteristic
67#19127601C2211yescharacteristic
68#19127601C2211yescharacteristic
69#19127601C2211yescharacteristic
70#19127601C2211yescharacteristic, complemented
71#19127598C2211yescharacteristic, complemented
72#19127598C2211yescharacteristic, complemented
73#19127597C2211yescharacteristic, complemented
74#19127596C2211yescharacteristic, complemented
75#19127595C2211yescharacteristic
76#19127595C2211yescharacteristic
77#19127595C2211yescharacteristic, complemented
78#19127594C2211yescharacteristic
79#19127594C2211yescharacteristic
80#19127594C2211yescharacteristic
81#19127594C2211yescharacteristic
82#19127594C2211yescharacteristic, complemented
83#19127594C2211yescharacteristic, complemented
84#19127594C2211yescharacteristic, complemented
85#19127594C2211yescharacteristic, complemented
86#19127593C2211yescharacteristic, complemented
87#19127593C2211yescharacteristic, complemented
88#19127592C2211yescharacteristic, complemented
89#19127592C2211yescharacteristic, complemented
90#19127592C2211yescharacteristic, complemented
91#19127591C2211yescharacteristic, complemented
92#19127591C2211yescharacteristic, complemented
93#19127591C2211yescharacteristic, complemented
94#19127590C2211yescharacteristic, complemented
95#19127590C2211yescharacteristic, complemented
96#19127590C2211yescharacteristic, complemented
97#19127590C2211yescharacteristic, complemented
98#19127589C2211yescharacteristic
99#19127589C2211yescharacteristic
100#19127589C2211yescharacteristic, complemented
101#19127588C2211yescharacteristic, complemented
102#19127588C2211yescharacteristic, complemented
103#19127586C2211yescharacteristic, complemented
104#19127586C2211yescharacteristic, complemented
105#19127585C2211yescharacteristic, complemented
106#19127583C2211yescharacteristic, complemented
107#19127583C2211yescharacteristic, complemented
108#19127582C2211yescharacteristic, complemented
109#19127582C2211yescharacteristic, complemented
110#19127582C2211yescharacteristic, complemented
111#19127580C2211yescharacteristic
112#19127580C2211yescharacteristic
113#19127580C2211yescharacteristic
114#19127580C2211yescharacteristic
115#19127580C2211yescharacteristic, complemented
116#19127579C2211yescharacteristic, complemented
117#19127579C2211yescharacteristic, complemented
118#19127579C2211yescharacteristic, complemented
119#19127579C2211yescharacteristic, complemented
120#19127578C2211yescharacteristic
121#19127578C2211yescharacteristic
122#19127578C2211yescharacteristic
123#19127578C2211yescharacteristic
124#19127578C2211yescharacteristic
125#19127578C2211yescharacteristic
126#19127578C2211yescharacteristic, complemented
127#19127578C2211yescharacteristic, complemented
128#19127577C2211yescharacteristic
129#19127577C2211yescharacteristic
130#19127577C2211yescharacteristic
131#19127577C2211yescharacteristic
132#19127577C2211yescharacteristic, complemented
133#19127575C2211yescharacteristic, complemented
134#19127575C2211yescharacteristic, complemented
135#19127574C2211yescharacteristic, complemented
136#19127573C2211yescharacteristic, complemented
137#19127573C2211yescharacteristic, complemented
138#19127572C2211yescharacteristic, complemented
139#19127568C2211yescharacteristic, complemented
140#19127563C2211yescharacteristic, complemented
141#19127563C2211yescharacteristic, complemented
142#19127562C2211yescharacteristic
143#19127562C2211yescharacteristic
144#19127560C2211yescharacteristic, complemented
145#19127559C2211yescharacteristic
146#19127558C2211yescharacteristic, complemented
147#19127558C2211yescharacteristic, complemented
148#19127558C2211yescharacteristic, complemented
149#19127558C2211yescharacteristic, complemented
150#19127556C2211yescharacteristic
151#19127556C2211yescharacteristic
152#19127556C2211yescharacteristic
153C4⋊C4×Dic83C2211yescharacteristic, complemented
154C4×Dic83⋊C4C2211yescharacteristic, complemented
155C4×Dic83⋊C4C2211yescharacteristic, complemented
156C22⋊C4×Dic83C2211yescharacteristic
157C22⋊C4×Dic83C2211yescharacteristic, complemented
158C22⋊C4×Dic83C2211yescharacteristic, complemented
159C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
160C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
161C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
162C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
163C4×C22⋊Dic83C2211yescharacteristic, complemented
164#19127548C2211yescharacteristic, complemented
165#19127548C2211yescharacteristic, complemented
166#19127548C2211yescharacteristic, complemented
167#19127548C2211yescharacteristic, complemented
168#19127547C2211yescharacteristic, complemented
169#19127546C2211yescharacteristic, complemented
170C2×C83⋊#95C2211yescharacteristic, complemented
171C2×C83⋊#95C2211yescharacteristic, complemented
172#95×D83C2211yescharacteristic, complemented
173C2×#117×C83C2211yescharacteristic, complemented
174C22×C22⋊C4×C83C2211yescharacteristic
175C22×C22⋊C4×C83C2211yescharacteristic
176#388×C83C2211yescharacteristic
177#388×C83C2211yescharacteristic
178#388×C83C2211yescharacteristic
179#388×C83C2211yescharacteristic
180#385×C83C2211yescharacteristic, complemented
181#385×C83C2211yescharacteristic, complemented
182#381×C83C2211yescharacteristic, complemented
183#380×C83C2211yescharacteristic, complemented
184#379×C83C2211yescharacteristic
185C4×C22⋊C4×C83C2211yescharacteristic, complemented
186C4×C22⋊C4×C83C2211yescharacteristic, complemented
187C4×C22⋊C4×C83C2211yescharacteristic, complemented
188C24×D83C2311yescharacteristic
189C2×#13050590—42no—
190C2×#13050590—42no—
191C2×#13050590C2×C418yescomplemented
192C22×Dic166C2311yescharacteristic
193C22×D332C2311yescharacteristic
194C22×D332C2311yescharacteristic
195C22×C22⋊D83—42no—
196C22×C22⋊D83—42no—
197C22×C22⋊D83C2×C418yescomplemented
198C22×C22⋊D83C2311yescharacteristic
199C22×C22⋊D83C2311yescharacteristic
200C22×C22⋊D83C2311yescharacteristic
201C22×C22⋊D83C2311yescharacteristic
202C22×C22⋊D83C2311yescharacteristic
203C22×C22⋊D83C2311yescharacteristic
204C22×C22⋊D83C2311yescharacteristic
205C23×Dic83C2311yescharacteristic
206C23×Dic83C2311yescharacteristic
207C23×Dic83C2311yescharacteristic
208C23×Dic83C2311yescharacteristic
209C23×Dic83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
211C22×C4×D83C2311yescharacteristic
212C22×C4×D83C2311yescharacteristic
213C22×C4×D83C2311yescharacteristic
214C22×C4×D83C2311yescharacteristic
215C22×C4×D83C2311yescharacteristic
216C22×C4×D83C2311yescharacteristic
217#14581778C2×C418yescomplemented
218#14581775C2×C418yescomplemented
219#14581774C2×C418yescomplemented
220#14581769C2×C418yescomplemented
221#14581766C2×C418yescomplemented
222#14581765C2×C418yescomplemented
223#14581765C2×C418yescomplemented
224#14581762C2×C418yescomplemented
225#14581761C2×C418yescomplemented
226#14581754—42no—
227C4×C22⋊D83—42no—
228C4×C22⋊D83C2×C418yescomplemented
229(C22⋊D83)⋊C4—42no—
230(C22⋊D83)⋊C4—42no—
231(C22⋊D83)⋊C4—42no—
232(C22⋊D83)⋊C4—42no—
233(C22⋊D83)⋊C4C2×C418yescomplemented
234#14581749—42no—
235C2×C4⋊Dic83—42no—
236C2×C4⋊Dic83C2311yescharacteristic
237C2×C4⋊Dic83C2311yescharacteristic
238C2×C4⋊Dic83C2311yescharacteristic
239C2×C4⋊Dic83C2311yescharacteristic
240C2×C4⋊Dic83C2311yescharacteristic
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×C22⋊Dic83—42no—
253C2×C22⋊Dic83—42no—
254C2×C22⋊Dic83C2311yescharacteristic
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×(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
290C22⋊C4×D83—42no—
291C22⋊C4×D83C2×C418yescomplemented
292C2×C4×Dic83—42no—
293C2×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C2×C4×Dic83C2311yescharacteristic
296C2×C4×Dic83C2311yescharacteristic
297C2×C4×Dic83C2311yescharacteristic
298C2×C4×Dic83C2311yescharacteristic
299C2×C4×Dic83C2311yescharacteristic
300C2×C4×Dic83C2311yescharacteristic
301C2×C4×Dic83C2311yescharacteristic
302C2×C4×Dic83C2311yescharacteristic
303C2×C4×Dic83C2311yescharacteristic
304C2×C4×Dic83C2311yescharacteristic
305C2×C4×Dic83C2311yescharacteristic
306C83⋊#95C2311yescharacteristic
307C83⋊#95C2311yescharacteristic
308C83⋊#95C2311yescharacteristic
309C83⋊#95C2311yescharacteristic
310C83⋊#95C2311yescharacteristic
311C83⋊#95C2311yescharacteristic
312C83⋊#95C2311yescharacteristic
313C83⋊#95C2311yescharacteristic
314C83⋊#95C2311yescharacteristic
315C83⋊#95C2311yescharacteristic
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
338C25×C83C2311yescharacteristic
339C23×C4×C83C2311yescharacteristic
340C23×C4×C83C2311yescharacteristic
341C23×C4×C83C2311yescharacteristic
342C23×C4×C83C2311yescharacteristic
343#117×C83—42no—
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C4⋊C4×C83C2311yescharacteristic
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C4⋊C4×C83C2311yescharacteristic
348C2×C22⋊C4×C83—42no—
349C2×C22⋊C4×C83C2×C418yescomplemented
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×C22⋊C4×C83C2311yescharacteristic
363C2×C22⋊C4×C83C2311yescharacteristic
364C2×C42×C83C2311yescharacteristic
365C2×C42×C83C2311yescharacteristic
366C2×C42×C83C2311yescharacteristic
367C2×C42×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×D83C22×C414yes—
383C23×D83C2411yescharacteristic
384C23×D83C2411yescharacteristic
385C23×D83C2411yescharacteristic
386#13050590—416no—
387C2×Dic166—41no—
388C2×Dic166—41no—
389C2×Dic166C22×C414yes—
390C2×D332—41no—
391C2×D332—41no—
392C2×D332—41no—
393C2×D332—41no—
394C2×D332C22×C414yes—
395C2×D332C22×C414yes—
396C2×C22⋊D83—22no—
397C2×C22⋊D83—22no—
398C2×C22⋊D83—22no—
399C2×C22⋊D83—22no—
400C2×C22⋊D83—22no—
401C2×C22⋊D83—22no—
402C2×C22⋊D83—41no—
403C2×C22⋊D83—41no—
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⋊D83—416no—
411C2×C22⋊D83C22×C414yes—
412C2×C22⋊D83C22×C414yes—
413C2×C22⋊D83C22×C414yes—
414C2×C22⋊D83C22×C414yes—
415C2×C22⋊D83C22×C414yes—
416C2×C22⋊D83C22×C414yes—
417C2×C22⋊D83C22×C414yes—
418C22×Dic83—22no—
419C22×Dic83—22no—
420C22×Dic83—22no—
421C22×Dic83—22no—
422C22×Dic83—22no—
423C22×Dic83—41no—
424C22×Dic83—41no—
425C22×Dic83—41no—
426C22×Dic83—41no—
427C22×Dic83—41no—
428C22×Dic83—41no—
429C22×Dic83—41no—
430C22×Dic83—41no—
431C22×Dic83—41no—
432C22×Dic83C22×C414yes—
433C22×Dic83C2411yescharacteristic
434C22×Dic83C2411yescharacteristic
435C22×Dic83C2411yescharacteristic
436C22×Dic83C2411yescharacteristic
437C22×Dic83C2411yescharacteristic
438C22×Dic83C2411yescharacteristic
439C22×Dic83C2411yescharacteristic
440C22×Dic83C2411yescharacteristic
441C22×Dic83C2411yescharacteristic
442C22×Dic83C2411yescharacteristic
443C22×Dic83C2411yescharacteristic
444C22×Dic83C2411yescharacteristic
445C22×Dic83C2411yescharacteristic
446C2×C4×D83—22no—
447C2×C4×D83—22no—
448C2×C4×D83—41no—
449C2×C4×D83—41no—
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—41no—
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×D83C22×C414yes—
465C2×C4×D83C22×C414yes—
466C2×C4×D83C22×C414yes—
467C4⋊Dic83—41no—
468C4⋊Dic83—41no—
469C4⋊Dic83—41no—
470C4⋊Dic83—41no—
471C4⋊Dic83C22×C414yes—
472Dic83⋊C4—22no—
473Dic83⋊C4—41no—
474Dic83⋊C4—41no—
475Dic83⋊C4—41no—
476Dic83⋊C4—41no—
477Dic83⋊C4—41no—
478Dic83⋊C4—41no—
479Dic83⋊C4—41no—
480Dic83⋊C4C22×C414yes—
481Dic83⋊C4C22×C414yes—
482Dic83⋊C4C22×C414yes—
483C22⋊Dic83—22no—
484C22⋊Dic83—22no—
485C22⋊Dic83—41no—
486C22⋊Dic83—41no—
487C22⋊Dic83—41no—
488C22⋊Dic83—41no—
489C22⋊Dic83—41no—
490C22⋊Dic83—41no—
491C22⋊Dic83C22×C414yes—
492C22⋊Dic83C22×C414yes—
493C22⋊Dic83C22×C414yes—
494(C2×D83)⋊C4—22no—
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)⋊C4—41no—
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—41no—
522C4×Dic83—41no—
523C4×Dic83—41no—
524C4×Dic83—41no—
525C4×Dic83—41no—
526C4×Dic83—41no—
527C4×Dic83—41no—
528C4×Dic83—41no—
529C4×Dic83—41no—
530C4×Dic83—41no—
531C4×Dic83C22×C414yes—
532C24×C83—22no—
533C24×C83—22no—
534C24×C83—41no—
535C24×C83—41no—
536C24×C83—41no—
537C24×C83—41no—
538C24×C83C22×C414yes—
539C24×C83C2411yescharacteristic
540C24×C83C2411yescharacteristic
541C24×C83C2411yescharacteristic
542C22×C4×C83—22no—
543C22×C4×C83—22no—
544C22×C4×C83—41no—
545C22×C4×C83—41no—
546C22×C4×C83—41no—
547C22×C4×C83—41no—
548C22×C4×C83—41no—
549C22×C4×C83—41no—
550C22×C4×C83—41no—
551C22×C4×C83—41no—
552C22×C4×C83C22×C414yes—
553C22×C4×C83C22×C414yes—
554C22×C4×C83C2411yescharacteristic
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
566C4⋊C4×C83—41no—
567C4⋊C4×C83—41no—
568C4⋊C4×C83—41no—
569C4⋊C4×C83—41no—
570C22⋊C4×C83—22no—
571C22⋊C4×C83—22no—
572C22⋊C4×C83—22no—
573C22⋊C4×C83—22no—
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×C83C22×C414yes—
581C22⋊C4×C83C22×C414yes—
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—28no—
605C23×C83—44no—
606C23×C83—44no—
607C23×C83—82no—
608C23×C83—82no—
609C23×C83—82no—
610C23×C83—82no—
611C23×C83C23×C412yes—
612C23×C83C23×C412yes—
613C23×C83C23×C412yes—
614C23×C83H(5,𝔽2)12yes—
615C23×C83H(5,𝔽2)12yes—
616C23×C83C2511yescharacteristic
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—21no—
629C22×D83—21no—
630C22×D83—21no—
631C22×D83—21no—
632C22×D83—21no—
633C22×D83—21no—
634C22×D83—21no—
635C22×D83—44no—
636C22×D83—44no—
637C22×D83—44no—
638C22×D83—82no—
639C22×D83—82no—
640C22×D83—82no—
641C22×D83—82no—
642C22×D83C23×C412yes—
643C22×D83C23×C412yes—
644C22×D83C23×C412yes—
645C2×C4×C83—28no—
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—44no—
679C2×C4×C83—82no—
680C2×C4×C83—82no—
681C2×C4×C83C23×C412yes—
682C2×C4×C83C23×C412yes—
683C2×C4×C83C23×C412yes—
684C2×C4×C83C23×C412yes—
685C22⋊D83—28no—
686C22⋊D83—28no—
687C22⋊D83—28no—
688C22⋊D83—44no—
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—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—21no—
722C2×Dic83—21no—
723C2×Dic83—21no—
724C2×Dic83—21no—
725C2×Dic83—44no—
726C2×Dic83—44no—
727C2×Dic83—44no—
728C2×Dic83—82no—
729C2×Dic83—82no—
730C2×Dic83C23×C412yes—
731C2×Dic83C23×C412yes—
732C2×Dic83C23×C412yes—
733C2×Dic83C23×C412yes—
734C2×Dic83C23×C412yes—
735C2×Dic83H(5,𝔽2)12yes—
736D332—44no—
737D332—44no—
738C4×D83—44no—
739C4×D83—44no—
740C4×D83—44no—
741C4×D83—82no—
742C4×D83—82no—
743C4×D83—82no—
744C4×D83—82no—
745Dic166—44no—
746C22×C83—22no—
747C22×C83—22no—
748C22×C83—22no—
749C22×C83—22no—
750C22×C83—22no—
751C22×C83—22no—
752C22×C83—22no—
753C22×C83—22no—
754C22×C83—22no—
755C22×C83—22no—
756C22×C83—22no—
757C22×C83—22no—
758C22×C83—41no—
759C22×C83—41no—
760C22×C83—41no—
761C22×C83—41no—
762C22×C83—41no—
763C22×C83—41no—
764C22×C83—41no—
765C22×C83—41no—
766C22×C83—88no—
767C22×C83#51814yes—
768C22×C83C24×C411yescharacteristic
769C22×C83C2×H(5,𝔽2)11yescharacteristic
770C22×C83C2×H(5,𝔽2)11yescharacteristic
771C22×C83C2×H(5,𝔽2)11yescharacteristic
772C22×C83#58511yescharacteristic
773C22×C83#58511yescharacteristic
774C22×C83#58511yescharacteristic
775C2×D83—22no—
776C2×D83—22no—
777C2×D83—22no—
778C2×D83—22no—
779C2×D83—22no—
780C2×D83—22no—
781C2×D83—22no—
782C2×D83—22no—
783C2×D83—22no—
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—41no—
794C2×D83—41no—
795C2×D83—41no—
796C2×D83—88no—
797C4×C83—22no—
798C4×C83—22no—
799C4×C83—22no—
800C4×C83—22no—
801C4×C83—41no—
802C4×C83—41no—
803C4×C83—41no—
804C4×C83—41no—
805C4×C83—41no—
806C4×C83—41no—
807C4×C83—41no—
808C4×C83—41no—
809Dic83—22no—
810Dic83—22no—
811Dic83—22no—
812Dic83—22no—
813Dic83—22no—
814Dic83—22no—
815Dic83—41no—
816Dic83—41no—
817Dic83—41no—
818Dic83—41no—
819Dic83—41no—
820Dic83—41no—
821Dic83—41no—
822#34492—831nomaximal, Sylow
823C2×C83—24no—
824C2×C83—42no—
825C2×C83—42no—
826C2×C83C2×#51811yescharacteristic
827C2×C83#342811yescharacteristic
828C2×C83C4×H(5,𝔽2)11yescharacteristic
829C2×C83#353411yescharacteristic
830C2×C83#354211yescharacteristic
831C2×C83#354511yescharacteristic
832C2×C83#356011yescharacteristic
833D83—42no—
834D83—42no—
835D83—42no—
836C2×#546—831no—
837#2378—831no—
838#2377—831no—
839#2376—831no—
840#2375—831no—
841#2372—831no—
842#2364—831no—
843#2363—831no—
844#2359—831no—
845#2358—831no—
846#2353—831no—
847#2353—831no—
848#2342—831no—
849#2342D8311yescharacteristic, complemented
850#2339—831no—
851D4×C22⋊C4—831no—
852#2337—831no—
853#2335—831no—
854#2333—831no—
855#2332—831no—
856#2325—831no—
857#2322—831no—
858#2321—831no—
859#2321—831no—
860#2319—831no—
861#2312—831no—
862#2311—831no—
863#2308—831no—
864C4×#121—831no—
865#2290—831no—
866C2×#388—831no—
867C83#3449211yescharacteristic, complemented, Sylow
868C22×#41—831no—
869C23×D4—831no—
870#546—8316no—
871C2×#124—831no—
872C2×#123—831no—
873C2×#123—831no—
874C2×C22⋊Q8—831no—
875C2×#121—831no—
876C2×#121—831no—
877C2×#121—831no—
878C2×#120—831no—
879C2×#120—831no—
880C2×C4×D4—831no—
881C2×C4×D4—831no—
882C2×C4×D4—831no—
883C2×C4×D4—831no—
884C2×C4×D4—831no—
885C2×C4×D4—831no—
886C2×C4×D4—831no—
887C2×C4×D4—831no—
888C2×#117—831no—
889C2×#117C2×D8311yescharacteristic, complemented
890C22×C4⋊C4—831no—
891C22×C22⋊C4—831no—
892C22×C22⋊C4—831no—
893C22×C22⋊C4—831no—
894C22×C22⋊C4—831no—
895C22×C22⋊C4C2×D8311yescharacteristic
896C22×C22⋊C4C2×D8311yescharacteristic
897C22×C42—831no—
898#391—831no—
899#391—831no—
900#391—831no—
901#391—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#389—831no—
911#389—831no—
912#389—831no—
913#389—831no—
914#388—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#388C2×D8311yescharacteristic
941#388C2×D8311yescharacteristic
942#388C2×D8311yescharacteristic
943#388C2×D8311yescharacteristic
944#387—831no—
945#387—831no—
946#387—831no—
947#387—831no—
948#387—831no—
949#387—831no—
950#387—831no—
951#387—831no—
952#387—831no—
953#387—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#386—831no—
968#386—831no—
969#386—831no—
970#386—831no—
971#386—831no—
972#386—831no—
973#386—831no—
974#386—831no—
975#386—831no—
976#385—831no—
977#385—831no—
978#385—831no—
979#385—831no—
980#385—831no—
981#385—831no—
982#385C2×D8311yescharacteristic, complemented
983#385C2×D8311yescharacteristic, complemented
984#383—831no—
985#381—831no—
986#381—831no—
987#381—831no—
988#381—831no—
989#381C2×D8311yescharacteristic, complemented
990#380—831no—
991#380—831no—
992#380—831no—
993#380—831no—
994#380—831no—
995#380—831no—
996#380C2×D8311yescharacteristic, complemented
997#379—831no—
998#379—831no—
999#379—831no—
1000#379C2×D8311yescharacteristic
1001C4×C4⋊C4—831no—
1002C4×C4⋊C4—831no—
1003C4×C4⋊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
1019#376—831no—
1020#376—831no—
1021C2×#95—831no—
1022C2×#95—831no—
1023C2×#95—831no—
1024C25—831no—
1025C25C22×D8311yescharacteristic
1026C2×#41—3322no—
1027C2×#41—3322no—
1028C2×#41—838no—
1029C22×Q8—831no—
1030C22×D4—3322no—
1031C22×D4—3322no—
1032C22×D4—838no—
1033C22×D4—831no—
1034C22×D4—831no—
1035C22×D4—831no—
1036C22×D4—831no—
1037C22×D4—831no—
1038C22×D4—831no—
1039C22×D4—831no—
1040C22×D4—831no—
1041C22×D4—831no—
1042C23×C4—831no—
1043C23×C4—831no—
1044C23×C4—831no—
1045C23×C4—831no—
1046C23×C4—831no—
1047C23×C4—831no—
1048C23×C4—831no—
1049C23×C4—831no—
1050C23×C4—831no—
1051C23×C4—831no—
1052C23×C4—831no—
1053C23×C4—831no—
1054C23×C4C22×D8311yescharacteristic
1055C23×C4C22×D8311yescharacteristic
1056C23×C4C22×D8311yescharacteristic
1057C23×C4C22×D8311yescharacteristic
1058#124—838no—
1059#123—838no—
1060#123—838no—
1061C22⋊Q8—838no—
1062#121—838no—
1063#121—838no—
1064#121—838no—
1065#120—838no—
1066#120—838no—
1067C4×D4—3322no—
1068C4×D4—3322no—
1069C4×D4—3322no—
1070C4×D4—3322no—
1071C4×D4—3322no—
1072C4×D4—3322no—
1073C4×D4—838no—
1074C4×D4—838no—
1075#117—42no—
1076#117—3322no—
1077C2×C4⋊C4—3322no—
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×C4⋊C4C22×D8311yescharacteristic
1098C2×C22⋊C4—42no—
1099C2×C22⋊C4—3322no—
1100C2×C22⋊C4—3322no—
1101C2×C22⋊C4—3322no—
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—838no—
1136C2×C22⋊C4—831no—
1137C2×C22⋊C4—831no—
1138C2×C22⋊C4—831no—
1139C2×C22⋊C4C4×D8318yescomplemented
1140C2×C22⋊C4C22×D8311yescharacteristic
1141C2×C22⋊C4C22×D8311yescharacteristic
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×C22⋊C4C22×D8311yescharacteristic
1153C2×C22⋊C4C22×D8311yescharacteristic
1154C2×C42—3322no—
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
1172#95—831no—
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#95—831no—
1198#95—831no—
1199#95—831no—
1200#95—831no—
1201#95—831no—
1202#95—831no—
1203#95—831no—
1204#95C22×D8311yescharacteristic
1205#95C22×D8311yescharacteristic
1206#95C22×D8311yescharacteristic
1207#95C22×D8311yescharacteristic
1208#95C22×D8311yescharacteristic
1209#95C22×D8311yescharacteristic
1210#95C22×D8311yescharacteristic
1211#95C22×D8311yescharacteristic
1212C24—22no—
1213C24—22no—
1214C24—41no—
1215C24—41no—
1216C24—41no—
1217C24—41no—
1218C24—3321no—
1219C24—3321no—
1220C24—3321no—
1221C24—3321no—
1222C24—3321no—
1223C24—3321no—
1224C24—834no—
1225C24—831no—
1226C24—831no—
1227C24—831no—
1228C24C2×C4×D8314yes—
1229C24C23×D8311yescharacteristic
1230C24C23×D8311yescharacteristic
1231C24C23×D8311yescharacteristic
1232#41—33216no—
1233C2×Q8—3321no—
1234C2×Q8—3321no—
1235C2×Q8—834no—
1236C2×D4—3321no—
1237C2×D4—3321no—
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—3321no—
1248C2×D4—3321no—
1249C2×D4—834no—
1250C2×D4—834no—
1251C2×D4—834no—
1252C2×D4—834no—
1253C2×D4—834no—
1254C2×D4—834no—
1255C2×D4—834no—
1256C2×D4—834no—
1257C2×D4—834no—
1258C2×D4—1662no—
1259C2×D4—1662no—
1260C2×D4—1662no—
1261C2×D4—1662no—
1262C2×D4—1662no—
1263C2×D4—1662no—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—41no—
1269C22×C4—41no—
1270C22×C4—41no—
1271C22×C4—41no—
1272C22×C4—41no—
1273C22×C4—41no—
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—3321no—
1288C22×C4—3321no—
1289C22×C4—3321no—
1290C22×C4—3321no—
1291C22×C4—3321no—
1292C22×C4—3321no—
1293C22×C4—3321no—
1294C22×C4—3321no—
1295C22×C4—3321no—
1296C22×C4—3321no—
1297C22×C4—3321no—
1298C22×C4—3321no—
1299C22×C4—834no—
1300C22×C4—834no—
1301C22×C4—834no—
1302C22×C4—834no—
1303C22×C4—831no—
1304C22×C4—831no—
1305C22×C4—831no—
1306C22×C4—831no—
1307C22×C4—831no—
1308C22×C4—831no—
1309C22×C4—831no—
1310C22×C4—831no—
1311C22×C4—831no—
1312C22×C4—831no—
1313C22×C4—831no—
1314C22×C4—831no—
1315C22×C4—831no—
1316C22×C4—1662no—
1317C22×C4—1662no—
1318C22×C4—1662no—
1319C22×C4—1662no—
1320C22×C4—1662no—
1321C22×C4—1662no—
1322C22×C4—1662no—
1323C22×C4C2×C4×D8314yes—
1324C22×C4C2×C4×D8314yes—
1325C22×C4C23×D8311yescharacteristic
1326C22×C4C23×D8311yescharacteristic
1327C22×C4C23×D8311yescharacteristic
1328C22×C4C23×D8311yescharacteristic
1329C22×C4C23×D8311yescharacteristic
1330C22×C4C23×D8311yescharacteristic
1331C22×C4C23×D8311yescharacteristic
1332C22×C4C23×D8311yescharacteristic
1333C22×C4C23×D8311yescharacteristic
1334C22×C4C23×D8311yescharacteristic
1335C22×C4C23×D8311yescharacteristic
1336C22×C4C23×D8311yescharacteristic
1337C4⋊C4—41no—
1338C4⋊C4—41no—
1339C4⋊C4—41no—
1340C4⋊C4—41no—
1341C4⋊C4—3321no—
1342C4⋊C4—3321no—
1343C4⋊C4—3321no—
1344C4⋊C4—3321no—
1345C4⋊C4—3321no—
1346C4⋊C4—3321no—
1347C4⋊C4—3321no—
1348C4⋊C4—3321no—
1349C4⋊C4—3321no—
1350C4⋊C4—3321no—
1351C4⋊C4—3321no—
1352C4⋊C4—834no—
1353C4⋊C4—834no—
1354C4⋊C4—834no—
1355C4⋊C4—834no—
1356C4⋊C4—1662no—
1357C22⋊C4—22no—
1358C22⋊C4—22no—
1359C22⋊C4—22no—
1360C22⋊C4—22no—
1361C22⋊C4—41no—
1362C22⋊C4—41no—
1363C22⋊C4—41no—
1364C22⋊C4—41no—
1365C22⋊C4—41no—
1366C22⋊C4—41no—
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—3321no—
1384C22⋊C4—3321no—
1385C22⋊C4—3321no—
1386C22⋊C4—3321no—
1387C22⋊C4—3321no—
1388C22⋊C4—3321no—
1389C22⋊C4—3321no—
1390C22⋊C4—3321no—
1391C22⋊C4—3321no—
1392C22⋊C4—834no—
1393C22⋊C4—834no—
1394C22⋊C4—834no—
1395C22⋊C4—834no—
1396C22⋊C4—834no—
1397C22⋊C4—834no—
1398C22⋊C4—834no—
1399C22⋊C4—834no—
1400C22⋊C4—1662no—
1401C22⋊C4—1662no—
1402C22⋊C4—1662no—
1403C22⋊C4C2×C4×D8314yes—
1404C22⋊C4C2×C4×D8314yes—
1405C22⋊C4C2×C4×D8314yes—
1406C22⋊C4C2×C4×D8314yes—
1407C42—41no—
1408C42—41no—
1409C42—41no—
1410C42—41no—
1411C42—3321no—
1412C42—3321no—
1413C42—3321no—
1414C42—3321no—
1415C42—3321no—
1416C42—3321no—
1417C42—3321no—
1418C42—3321no—
1419C42—3321no—
1420C42—3321no—
1421C42—834no—
1422C42—1662no—
1423C42—1662no—
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—21no—
1439C23—21no—
1440C23—28no—
1441C23—44no—
1442C23—44no—
1443C23—82no—
1444C23—82no—
1445C23—82no—
1446C23—82no—
1447C23—3324no—
1448C23—3324no—
1449C23—3324no—
1450C23—832no—
1451C23—832no—
1452C23—832no—
1453C23—6642no—
1454C23—6642no—
1455C23—6642no—
1456C23—6642no—
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—
1474C23—1661no—
1475C23C22×C4×D8312yes—
1476C23C22×C4×D8312yes—
1477C23C22×C4×D8312yes—
1478C23#1458183712yes—
1479C23#1458183812yes—
1480C23C24×D8311yescharacteristic
1481Q8—3324no—
1482D4—3324no—
1483D4—3324no—
1484D4—3324no—
1485D4—3324no—
1486D4—3324no—
1487D4—3324no—
1488D4—1668no—
1489D4—1668no—
1490D4—1668no—
1491C2×C4—28no—
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—21no—
1523C2×C4—21no—
1524C2×C4—44no—
1525C2×C4—82no—
1526C2×C4—82no—
1527C2×C4—3324no—
1528C2×C4—3324no—
1529C2×C4—3324no—
1530C2×C4—3324no—
1531C2×C4—3324no—
1532C2×C4—3324no—
1533C2×C4—832no—
1534C2×C4—832no—
1535C2×C4—832no—
1536C2×C4—832no—
1537C2×C4—832no—
1538C2×C4—832no—
1539C2×C4—6642no—
1540C2×C4—6642no—
1541C2×C4—6642no—
1542C2×C4—6642no—
1543C2×C4—6642no—
1544C2×C4—6642no—
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×C4—1661no—
1571C2×C4—1661no—
1572C2×C4—1661no—
1573C2×C4—1661no—
1574C2×C4—1661no—
1575C2×C4—1661no—
1576C2×C4—1661no—
1577C2×C4—1661no—
1578C2×C4C22×C4×D8312yes—
1579C2×C4C22×C4×D8312yes—
1580C2×C4C22×C4×D8312yes—
1581C2×C4C22×C4×D8312yes—
1582C22—22no—
1583C22—22no—
1584C22—22no—
1585C22—22no—
1586C22—22no—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—22no—
1591C22—22no—
1592C22—22no—
1593C22—22no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—88no—
1603C22—3321no—
1604C22—3321no—
1605C22—3321no—
1606C22—3321no—
1607C22—3321no—
1608C22—3321no—
1609C22—3321no—
1610C22—3321no—
1611C22—3321no—
1612C22—3321no—
1613C22—3321no—
1614C22—3321no—
1615C22—6648no—
1616C22—1662no—
1617C22—1662no—
1618C22—1662no—
1619C22—1662no—
1620C22—1662no—
1621C22—1662no—
1622C22—1662no—
1623C22—1662no—
1624C22—1662no—
1625C22#1912817314yes—
1626C22C23×C4×D8311yescharacteristic
1627C22H(5,𝔽2)×D8311yescharacteristic
1628C22C2×#1458183711yescharacteristic
1629C22C2×#1458183811yescharacteristic
1630C22#1912853611yescharacteristic
1631C22#1912853711yescharacteristic
1632C22#1912853711yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—22no—
1636C4—22no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—3321no—
1646C4—3321no—
1647C4—3321no—
1648C4—3321no—
1649C4—3321no—
1650C4—3321no—
1651C4—3321no—
1652C4—1662no—
1653C4—1662no—
1654C4—1662no—
1655C4—1662no—
1656C4—1662no—
1657C4—1662no—
1658C2—24no—
1659C2—42no—
1660C2—42no—
1661C2—3322no—
1662C2—3322no—
1663C2—3322no—
1664C2C2×#1912817311yescharacteristic
1665C2#2492066411yescharacteristic
1666C2#2492066711yescharacteristic
1667C2#2492164811yescharacteristic
1668C2#2492177211yescharacteristic
1669C2#2492181911yescharacteristic
1670C2#2492200711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2342C2
socle, cosocleC23×C83C25
prime radicalC2×#19128341C2
hypercenter#2342D83
hypocenterC83#34492
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #24910630C2semidirect
3. #24910619C2semidirect
4. #24910612C2semidirect
5. #24910603C2semidirect
6. #24910571C2semidirect
7. #24910513C2semidirect
8. #24910502C2semidirect
9. #24910455C2semidirect
10. #24910442C2semidirect
11. #24910405C2semidirect
12. #24910398C2semidirect
13. #24910307C2semidirect
14. #24910287C2semidirect
15. #24910279C2semidirect
16. #24910271C2semidirect
17. #24910248C2semidirect
18. #24910223C2semidirect
19. #24910213C2semidirect
20. #24910160C2semidirect
21. #24910129C2semidirect
22. #24910118C2semidirect
23. #24910116C2semidirect
24. #24910104C2semidirect
25. #24910057C2semidirect
26. #24910051C2semidirect
27. #24910038C2semidirect
28. #24909969C2semidirect
29. #24909902C2semidirect
30. C2×#19127594C2semidirect
31. C83×#2342C2semidirect
34. #19128341C4semidirect
44. C2×#14581754C22semidirect
46. C2×C4×C22⋊D83C22semidirect
50. C2×(C22⋊D83)⋊C4C22semidirect
51. C2×(C22⋊D83)⋊C4C22semidirect
52. C2×#14581749C22semidirect
53. C22×C4⋊Dic83C22semidirect
58. C22×C4×Dic83C22semidirect
59. #19127607C22semidirect
60. #19127607C22semidirect
61. #19127605C22semidirect
62. #19127605C22semidirect
63. #19127603C22semidirect
64. #19127603C22semidirect
65. #19127602C22semidirect
70. #19127601C22semidirect
71. #19127598C22semidirect
72. #19127598C22semidirect
73. #19127597C22semidirect
74. #19127596C22semidirect
77. #19127595C22semidirect
82. #19127594C22semidirect
83. #19127594C22semidirect
84. #19127594C22semidirect
85. #19127594C22semidirect
86. #19127593C22semidirect
87. #19127593C22semidirect
88. #19127592C22semidirect
89. #19127592C22semidirect
90. #19127592C22semidirect
91. #19127591C22semidirect
92. #19127591C22semidirect
93. #19127591C22semidirect
94. #19127590C22semidirect
95. #19127590C22semidirect
96. #19127590C22semidirect
97. #19127590C22semidirect
100. #19127589C22semidirect
101. #19127588C22semidirect
102. #19127588C22semidirect
103. #19127586C22semidirect
104. #19127586C22semidirect
105. #19127585C22semidirect
106. #19127583C22semidirect
107. #19127583C22semidirect
108. #19127582C22semidirect
109. #19127582C22semidirect
110. #19127582C22semidirect
115. #19127580C22semidirect
116. #19127579C22semidirect
117. #19127579C22semidirect
118. #19127579C22semidirect
119. #19127579C22semidirect
126. #19127578C22semidirect
127. #19127578C22semidirect
132. #19127577C22semidirect
133. #19127575C22semidirect
134. #19127575C22semidirect
135. #19127574C22semidirect
136. #19127573C22semidirect
137. #19127573C22semidirect
138. #19127572C22semidirect
139. #19127568C22semidirect
140. #19127563C22semidirect
141. #19127563C22semidirect
144. #19127560C22semidirect
146. #19127558C22semidirect
147. #19127558C22semidirect
148. #19127558C22semidirect
149. #19127558C22semidirect
153. C4⋊C4×Dic83C22semidirect
154. C4×Dic83⋊C4C22semidirect
155. C4×Dic83⋊C4C22semidirect
157. C22⋊C4×Dic83C22semidirect
158. C22⋊C4×Dic83C22semidirect
159. C4×(C2×D83)⋊C4C22semidirect
160. C4×(C2×D83)⋊C4C22semidirect
161. C4×(C2×D83)⋊C4C22semidirect
162. C4×(C2×D83)⋊C4C22semidirect
163. C4×C22⋊Dic83C22semidirect
164. #19127548C22semidirect
165. #19127548C22semidirect
166. #19127548C22semidirect
167. #19127548C22semidirect
168. #19127547C22semidirect
169. #19127546C22semidirect
170. C2×C83⋊#95C22semidirect
171. C2×C83⋊#95C22semidirect
172. #95×D83C22semidirect
173. C2×#117×C83C22semidirect
180. #385×C83C22semidirect
181. #385×C83C22semidirect
182. #381×C83C22semidirect
183. #380×C83C22semidirect
185. C4×C22⋊C4×C83C22semidirect
186. C4×C22⋊C4×C83C22semidirect
187. C4×C22⋊C4×C83C22semidirect
191. C2×#13050590C2×C4semidirect
197. C22×C22⋊D83C2×C4semidirect
217. #14581778C2×C4semidirect
218. #14581775C2×C4semidirect
219. #14581774C2×C4semidirect
220. #14581769C2×C4semidirect
221. #14581766C2×C4semidirect
222. #14581765C2×C4semidirect
223. #14581765C2×C4semidirect
224. #14581762C2×C4semidirect
225. #14581761C2×C4semidirect
228. C4×C22⋊D83C2×C4semidirect
233. (C22⋊D83)⋊C4C2×C4semidirect
291. C22⋊C4×D83C2×C4semidirect
349. C2×C22⋊C4×C83C2×C4semidirect
849. #2342D83semidirect
867. C83#34492semidirect
889. C2×#117C2×D83semidirect
982. #385C2×D83semidirect
983. #385C2×D83semidirect
989. #381C2×D83semidirect
996. #380C2×D83semidirect
1016. C4×C22⋊C4C2×D83semidirect
1017. C4×C22⋊C4C2×D83semidirect
1018. C4×C22⋊C4C2×D83semidirect
1139. C2×C22⋊C4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283412
#249106302
#249106192
#249106122
#249106032
#249105712
#249105132
#249105022
#249104552
#249104422
#249104052
#249103982
#249103072
#249102872
#249102792
#249102712
#249102482
#249102232
#249102132
#249101602
#249101292
#249101182
#249101162
#249101042
#249100572
#249100512
#249100382
#249099692
#249099022
C2×#191275942
C83×#23422
#3449283