Finite Group Databasebeta

← #35612010

Subgroups — #35612010

Order 21248.

2146 conjugacy classes of subgroups.

The subgroup lattice has 1602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915751C211yesmaximal, characteristic, complemented
2#24915749C211yesmaximal, characteristic, complemented
3#24915407C211yesmaximal, characteristic, complemented
4#24915166C211yesmaximal, characteristic, complemented
5#24915163C211yesmaximal, characteristic, complemented
6#24915117C211yesmaximal, characteristic, complemented
7#24915114C211yesmaximal, characteristic, complemented
8#24915110C211yesmaximal, characteristic, complemented
9#24915105C211yesmaximal, characteristic, complemented
10#24914671C211yesmaximal, characteristic, complemented
11#24914671C211yesmaximal, characteristic, complemented
12#24914484C211yesmaximal, characteristic, complemented
13#24914484C211yesmaximal, characteristic, complemented
14#24913966C211yesmaximal, characteristic, complemented
15#24913961C211yesmaximal, characteristic, complemented
16#24913957C211yesmaximal, characteristic, complemented
17#24913954C211yesmaximal, characteristic, complemented
18#24913834C211yesmaximal, characteristic, complemented
19#24913274C211yesmaximal, characteristic, complemented
20#24913270C211yesmaximal, characteristic, complemented
21#24911141C211yesmaximal, characteristic, complemented
22#24911139C211yesmaximal, characteristic, complemented
23#24911133C211yesmaximal, characteristic, complemented
24#24911131C211yesmaximal, characteristic, complemented
25#24911128C211yesmaximal, characteristic, complemented
26#24911127C211yesmaximal, characteristic, complemented
27#24911126C211yesmaximal, characteristic, complemented
28#24910043C211yesmaximal, characteristic
29#24910040C211yesmaximal, characteristic
30C2×#19127579C211yesmaximal, characteristic
31C83×#2438C211yesmaximal, characteristic, complemented
32C23×D332C2211yescharacteristic
33C23×C4×D83C2211yescharacteristic
34C2×#14581772C2211yescharacteristic, complemented
35C2×#14581772C2211yescharacteristic, complemented
36C2×#14581772C2211yescharacteristic, complemented
37C2×#14581771C2211yescharacteristic
38C2×#14581770C2211yescharacteristic, complemented
39C2×#14581770C2211yescharacteristic, complemented
40C2×#14581770C2211yescharacteristic, complemented
41C2×#14581770C2211yescharacteristic, complemented
42C2×#14581769C2211yescharacteristic
43C2×#14581769C2211yescharacteristic
44C2×#14581768C2211yescharacteristic, complemented
45C2×#14581751C2211yescharacteristic
46C22×(C2×D83)⋊C4C2211yescharacteristic
47C22×(C2×D83)⋊C4C2211yescharacteristic
48C22×(C2×D83)⋊C4C2211yescharacteristic
49C2×C22⋊C4×D83C2211yescharacteristic
50C2×C22⋊C4×D83C2211yescharacteristic
51#19127643C2211yescharacteristic, complemented
52#19127643C2211yescharacteristic, complemented
53#19127640C2211yescharacteristic, complemented
54#19127638C2211yescharacteristic, complemented
55#19127636C2211yescharacteristic, complemented
56#19127636C2211yescharacteristic, complemented
57#19127636C2211yescharacteristic, complemented
58#19127636C2211yescharacteristic, complemented
59#19127636C2211yescharacteristic, complemented
60#19127636C2211yescharacteristic, complemented
61#19127636C2211yescharacteristic, complemented
62#19127635C2211yescharacteristic, complemented
63#19127635C2211yescharacteristic, complemented
64#19127634C2211yescharacteristic, complemented
65#19127634C2211yescharacteristic, complemented
66#19127633C2211yescharacteristic, complemented
67#19127633C2211yescharacteristic, complemented
68#19127625C2211yescharacteristic, complemented
69#19127625C2211yescharacteristic, complemented
70#19127625C2211yescharacteristic, complemented
71#19127625C2211yescharacteristic, complemented
72#19127623C2211yescharacteristic, complemented
73#19127623C2211yescharacteristic, complemented
74#19127623C2211yescharacteristic, complemented
75#19127623C2211yescharacteristic, complemented
76#19127623C2211yescharacteristic, complemented
77#19127623C2211yescharacteristic, complemented
78#19127623C2211yescharacteristic, complemented
79#19127623C2211yescharacteristic, complemented
80#19127623C2211yescharacteristic, complemented
81#19127623C2211yescharacteristic, complemented
82#19127623C2211yescharacteristic, complemented
83#19127623C2211yescharacteristic, complemented
84#19127622C2211yescharacteristic, complemented
85#19127622C2211yescharacteristic, complemented
86#19127621C2211yescharacteristic, complemented
87#19127614C2211yescharacteristic, complemented
88#19127614C2211yescharacteristic, complemented
89#19127614C2211yescharacteristic, complemented
90#19127614C2211yescharacteristic, complemented
91#19127614C2211yescharacteristic, complemented
92#19127612C2211yescharacteristic, complemented
93#19127612C2211yescharacteristic, complemented
94#19127612C2211yescharacteristic, complemented
95#19127607C2211yescharacteristic, complemented
96#19127605C2211yescharacteristic, complemented
97#19127605C2211yescharacteristic, complemented
98#19127603C2211yescharacteristic
99#19127603C2211yescharacteristic
100#19127603C2211yescharacteristic
101#19127603C2211yescharacteristic
102#19127602C2211yescharacteristic
103#19127602C2211yescharacteristic
104#19127602C2211yescharacteristic
105#19127602C2211yescharacteristic
106#19127599C2211yescharacteristic, complemented
107#19127598C2211yescharacteristic, complemented
108#19127598C2211yescharacteristic, complemented
109#19127588C2211yescharacteristic, complemented
110#19127588C2211yescharacteristic, complemented
111#19127585C2211yescharacteristic, complemented
112#19127585C2211yescharacteristic, complemented
113#19127584C2211yescharacteristic, complemented
114#19127584C2211yescharacteristic, complemented
115#19127579C2211yescharacteristic
116#19127579C2211yescharacteristic
117#19127579C2211yescharacteristic
118#19127579C2211yescharacteristic
119#19127579C2211yescharacteristic
120#19127579C2211yescharacteristic
121#19127579C2211yescharacteristic
122#19127579C2211yescharacteristic
123#19127579C2211yescharacteristic
124#19127579C2211yescharacteristic
125#19127579C2211yescharacteristic
126#19127579C2211yescharacteristic
127#19127579C2211yescharacteristic
128#19127579C2211yescharacteristic
129#19127579C2211yescharacteristic
130#19127579C2211yescharacteristic
131#19127576C2211yescharacteristic
132#19127576C2211yescharacteristic
133#19127575C2211yescharacteristic, complemented
134#19127575C2211yescharacteristic, complemented
135#19127575C2211yescharacteristic, complemented
136#19127575C2211yescharacteristic, complemented
137#19127575C2211yescharacteristic, complemented
138#19127575C2211yescharacteristic, complemented
139#19127575C2211yescharacteristic, complemented
140#19127575C2211yescharacteristic, complemented
141#19127575C2211yescharacteristic, complemented
142#19127575C2211yescharacteristic, complemented
143#19127574C2211yescharacteristic
144#19127574C2211yescharacteristic
145#19127573C2211yescharacteristic
146#19127573C2211yescharacteristic
147#19127572C2211yescharacteristic, complemented
148#19127572C2211yescharacteristic, complemented
149#19127572C2211yescharacteristic, complemented
150#19127572C2211yescharacteristic, complemented
151#19127572C2211yescharacteristic, complemented
152#19127572C2211yescharacteristic, complemented
153#19127564C2211yescharacteristic
154#19127561C2211yescharacteristic
155#19127560C2211yescharacteristic, complemented
156#19127560C2211yescharacteristic, complemented
157#19127560C2211yescharacteristic, complemented
158#19127560C2211yescharacteristic, complemented
159#19127559C2211yescharacteristic
160#19127559C2211yescharacteristic
161#19127558C2211yescharacteristic, complemented
162#19127558C2211yescharacteristic, complemented
163#19127558C2211yescharacteristic, complemented
164#19127558C2211yescharacteristic, complemented
165#19127556C2211yescharacteristic
166#19127556C2211yescharacteristic
167#19127556C2211yescharacteristic
168#19127556C2211yescharacteristic
169#19127556C2211yescharacteristic
170#19127556C2211yescharacteristic
171C2×C83⋊#95C2211yescharacteristic
172C2×C22⋊Q8×C83C2211yescharacteristic
173C2×#117×C83C2211yescharacteristic
174#400×C83C2211yescharacteristic, complemented
175#398×C83C2211yescharacteristic, complemented
176#398×C83C2211yescharacteristic, complemented
177#395×C83C2211yescharacteristic, complemented
178#391×C83C2211yescharacteristic, complemented
179#389×C83C2211yescharacteristic, complemented
180#387×C83C2211yescharacteristic, complemented
181#387×C83C2211yescharacteristic, complemented
182#385×C83C2211yescharacteristic
183#385×C83C2211yescharacteristic
184#381×C83C2211yescharacteristic
185#380×C83C2211yescharacteristic
186C2×#95×C83C2211yescharacteristic
187C24×D83C2311yescharacteristic
188C24×D83C2311yescharacteristic
189C22×Dic166C2311yescharacteristic
190C22×Dic166C2311yescharacteristic
191C22×Dic166C2311yescharacteristic
192C22×D332—42no—
193C22×D332—42no—
194C22×D332Q818yescomplemented
195C22×D332C2311yescharacteristic
196C22×D332C2311yescharacteristic
197C22×D332C2311yescharacteristic
198C22×D332C2311yescharacteristic
199C23×Dic83C2311yescharacteristic
200C23×Dic83C2311yescharacteristic
201C22×C4×D83—42no—
202C22×C4×D83—42no—
203C22×C4×D83—42no—
204C22×C4×D83C2311yescharacteristic
205C22×C4×D83C2311yescharacteristic
206C22×C4×D83C2311yescharacteristic
207C22×C4×D83C2311yescharacteristic
208C22×C4×D83C2311yescharacteristic
209C22×C4×D83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
211C22×C4×D83C2311yescharacteristic
212#14581772—42no—
213#14581772—42no—
214#14581772—42no—
215#14581771—42no—
216#14581770—42no—
217#14581770—42no—
218#14581770—42no—
219#14581770—42no—
220#14581769—42no—
221#14581769—42no—
222#14581768—42no—
223#14581751—42no—
224C2×C4⋊Dic83C2311yescharacteristic
225C2×C4⋊Dic83C2311yescharacteristic
226C2×C4⋊Dic83C2311yescharacteristic
227C2×C4⋊Dic83C2311yescharacteristic
228C2×C4⋊Dic83C2311yescharacteristic
229C2×C4⋊Dic83C2311yescharacteristic
230C2×C4⋊Dic83C2311yescharacteristic
231C2×C4⋊Dic83C2311yescharacteristic
232C2×C4⋊Dic83C2311yescharacteristic
233C2×C4⋊Dic83C2311yescharacteristic
234C2×C4⋊Dic83C2311yescharacteristic
235C2×Dic83⋊C4C2311yescharacteristic
236C2×Dic83⋊C4C2311yescharacteristic
237C2×Dic83⋊C4C2311yescharacteristic
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×C22⋊Dic83C2311yescharacteristic
254C2×C22⋊Dic83C2311yescharacteristic
255C2×C22⋊Dic83C2311yescharacteristic
256C2×C22⋊Dic83C2311yescharacteristic
257C2×(C2×D83)⋊C4—42no—
258C2×(C2×D83)⋊C4—42no—
259C2×(C2×D83)⋊C4—42no—
260C2×(C2×D83)⋊C4C2311yescharacteristic
261C2×(C2×D83)⋊C4C2311yescharacteristic
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
298C2×(C2×D83)⋊C4C2311yescharacteristic
299C2×(C2×D83)⋊C4C2311yescharacteristic
300C22⋊C4×D83—42no—
301C22⋊C4×D83—42no—
302C2×C4×Dic83C2311yescharacteristic
303C2×C4×Dic83C2311yescharacteristic
304C83⋊#95C2311yescharacteristic
305C83⋊#95C2311yescharacteristic
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
330C22×Q8×C83C2311yescharacteristic
331C23×C4×C83C2311yescharacteristic
332C23×C4×C83C2311yescharacteristic
333C23×C4×C83C2311yescharacteristic
334C22⋊Q8×C83—42no—
335#117×C83—42no—
336C2×C4⋊C4×C83C2311yescharacteristic
337C2×C4⋊C4×C83C2311yescharacteristic
338C2×C4⋊C4×C83C2311yescharacteristic
339C2×C4⋊C4×C83C2311yescharacteristic
340C2×C4⋊C4×C83C2311yescharacteristic
341C2×C4⋊C4×C83C2311yescharacteristic
342C2×C4⋊C4×C83C2311yescharacteristic
343C2×C4⋊C4×C83C2311yescharacteristic
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C4⋊C4×C83C2311yescharacteristic
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C22⋊C4×C83C2311yescharacteristic
348C2×C22⋊C4×C83C2311yescharacteristic
349C2×C22⋊C4×C83C2311yescharacteristic
350C2×C22⋊C4×C83C2311yescharacteristic
351C2×C42×C83C2311yescharacteristic
352C2×C42×C83C2311yescharacteristic
353#95×C83C2311yescharacteristic
354#95×C83C2311yescharacteristic
355#95×C83C2311yescharacteristic
356#95×C83C2311yescharacteristic
357#95×C83C2311yescharacteristic
358#95×C83C2311yescharacteristic
359#95×C83C2311yescharacteristic
360#95×C83C2311yescharacteristic
361#95×C83C2311yescharacteristic
362#95×C83C2311yescharacteristic
363#95×C83C2311yescharacteristic
364#95×C83C2311yescharacteristic
365#95×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367C23×D83—22no—
368C23×D83—22no—
369C23×D83—22no—
370C23×D83—22no—
371C23×D83—41no—
372C23×D83—41no—
373C23×D83—41no—
374C23×D83—41no—
375C23×D83—41no—
376C23×D83—41no—
377C23×D83—41no—
378C23×D83—41no—
379C23×D83C2×Q814yes—
380C23×D83C2×Q814yes—
381C23×D83C2411yescharacteristic
382C23×D83C2411yescharacteristic
383C23×D83C2411yescharacteristic
384C23×D83C2411yescharacteristic
385C2×Dic166—22no—
386C2×Dic166—22no—
387C2×Dic166—41no—
388C2×Dic166—41no—
389C2×Dic166—41no—
390C2×Dic166—41no—
391C2×Dic166—41no—
392C2×Dic166—41no—
393C2×Dic166—41no—
394C2×D332—416no—
395C2×D332—41no—
396C2×D332—41no—
397C2×D332—41no—
398C2×D332—41no—
399C2×D332—41no—
400C2×D332—41no—
401C2×D332—41no—
402C2×D332—41no—
403C2×D332C2×Q814yes—
404C2×D332C2×Q814yes—
405C2×D332C2×Q814yes—
406C2×D332C2×Q814yes—
407C22×Dic83—22no—
408C22×Dic83—22no—
409C22×Dic83—22no—
410C22×Dic83—41no—
411C22×Dic83—41no—
412C22×Dic83—41no—
413C22×Dic83C2411yescharacteristic
414C22×Dic83C2411yescharacteristic
415C22×Dic83C2411yescharacteristic
416C22×Dic83C2411yescharacteristic
417C22×Dic83C2411yescharacteristic
418C22×Dic83C2411yescharacteristic
419C22×Dic83C2411yescharacteristic
420C22×Dic83C2411yescharacteristic
421C22×Dic83C2411yescharacteristic
422C22×Dic83C2411yescharacteristic
423C22×Dic83C2411yescharacteristic
424C22×Dic83C2411yescharacteristic
425C2×C4×D83—22no—
426C2×C4×D83—22no—
427C2×C4×D83—22no—
428C2×C4×D83—22no—
429C2×C4×D83—41no—
430C2×C4×D83—41no—
431C2×C4×D83—41no—
432C2×C4×D83—41no—
433C2×C4×D83—41no—
434C2×C4×D83—41no—
435C2×C4×D83—41no—
436C2×C4×D83—41no—
437C2×C4×D83—416no—
438C2×C4×D83—41no—
439C2×C4×D83—41no—
440C2×C4×D83—41no—
441C2×C4×D83—41no—
442C2×C4×D83—41no—
443C2×C4×D83—41no—
444C2×C4×D83—41no—
445C2×C4×D83—41no—
446C2×C4×D83—41no—
447C2×C4×D83—41no—
448C2×C4×D83—41no—
449C2×C4×D83—41no—
450C4⋊Dic83—22no—
451C4⋊Dic83—22no—
452C4⋊Dic83—41no—
453C4⋊Dic83—41no—
454C4⋊Dic83—41no—
455C4⋊Dic83—41no—
456C4⋊Dic83—41no—
457C4⋊Dic83—41no—
458C4⋊Dic83—41no—
459C4⋊Dic83—41no—
460C4⋊Dic83—41no—
461Dic83⋊C4—22no—
462Dic83⋊C4—22no—
463Dic83⋊C4—41no—
464Dic83⋊C4—41no—
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⋊C4—41no—
475Dic83⋊C4—41no—
476Dic83⋊C4—41no—
477Dic83⋊C4—41no—
478Dic83⋊C4—41no—
479C22⋊Dic83—22no—
480C22⋊Dic83—22no—
481C22⋊Dic83—22no—
482C22⋊Dic83—22no—
483(C2×D83)⋊C4—22no—
484(C2×D83)⋊C4—22no—
485(C2×D83)⋊C4—22no—
486(C2×D83)⋊C4—22no—
487(C2×D83)⋊C4—41no—
488(C2×D83)⋊C4—41no—
489(C2×D83)⋊C4—41no—
490(C2×D83)⋊C4—41no—
491(C2×D83)⋊C4—41no—
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)⋊C4—41no—
513(C2×D83)⋊C4—41no—
514(C2×D83)⋊C4—41no—
515(C2×D83)⋊C4—41no—
516(C2×D83)⋊C4—41no—
517(C2×D83)⋊C4—41no—
518(C2×D83)⋊C4—41no—
519(C2×D83)⋊C4—41no—
520(C2×D83)⋊C4—41no—
521(C2×D83)⋊C4—41no—
522(C2×D83)⋊C4—41no—
523C4×Dic83—41no—
524C4×Dic83—41no—
525C24×C83C2411yescharacteristic
526C2×Q8×C83—41no—
527C2×Q8×C83—41no—
528C2×Q8×C83—41no—
529C22×C4×C83—22no—
530C22×C4×C83—22no—
531C22×C4×C83—22no—
532C22×C4×C83—22no—
533C22×C4×C83—22no—
534C22×C4×C83—41no—
535C22×C4×C83—41no—
536C22×C4×C83—41no—
537C22×C4×C83C2×Q814yes—
538C22×C4×C83C2411yescharacteristic
539C22×C4×C83C2411yescharacteristic
540C22×C4×C83C2411yescharacteristic
541C22×C4×C83C2411yescharacteristic
542C22×C4×C83C2411yescharacteristic
543C22×C4×C83C2411yescharacteristic
544C22×C4×C83C2411yescharacteristic
545C22×C4×C83C2411yescharacteristic
546C22×C4×C83C2411yescharacteristic
547C22×C4×C83C2411yescharacteristic
548C22×C4×C83C2411yescharacteristic
549C22×C4×C83C2411yescharacteristic
550C22×C4×C83C2411yescharacteristic
551C22×C4×C83C2411yescharacteristic
552C4⋊C4×C83—22no—
553C4⋊C4×C83—22no—
554C4⋊C4×C83—41no—
555C4⋊C4×C83—41no—
556C4⋊C4×C83—41no—
557C4⋊C4×C83—41no—
558C4⋊C4×C83—41no—
559C4⋊C4×C83—41no—
560C4⋊C4×C83—41no—
561C4⋊C4×C83—41no—
562C4⋊C4×C83—41no—
563C22⋊C4×C83—22no—
564C22⋊C4×C83—22no—
565C22⋊C4×C83—22no—
566C22⋊C4×C83—22no—
567C42×C83—41no—
568C42×C83—41no—
569C23×C83—21no—
570C23×C83—21no—
571C23×C83—21no—
572C23×C83—21no—
573C23×C83C22×Q812yes—
574C23×C83H(5,𝔽2)12yes—
575C23×C83H(5,𝔽2)12yes—
576C23×C83C2511yescharacteristic
577C22×D83—28no—
578C22×D83—21no—
579C22×D83—21no—
580C22×D83—21no—
581C22×D83—21no—
582C22×D83—21no—
583C22×D83—21no—
584C22×D83—21no—
585C22×D83—21no—
586C22×D83—21no—
587C22×D83—21no—
588C22×D83—21no—
589C22×D83—21no—
590C22×D83—21no—
591C22×D83—21no—
592C22×D83—21no—
593C22×D83—21no—
594C22×D83—21no—
595C22×D83—21no—
596C22×D83—21no—
597C22×D83—21no—
598C22×D83—21no—
599C22×D83—21no—
600C22×D83—21no—
601C22×D83—21no—
602C22×D83—28no—
603C22×D83—44no—
604C22×D83—44no—
605C22×D83—44no—
606C22×D83—44no—
607C22×D83—44no—
608C22×D83—44no—
609C22×D83—44no—
610C22×D83—44no—
611C22×D83—82no—
612C22×D83—82no—
613C22×D83—82no—
614C22×D83—82no—
615C22×D83C22×Q812yes—
616C22×D83C22×Q812yes—
617C22×D83C22×Q812yes—
618C22×D83C22×Q812yes—
619Q8×C83—82no—
620C2×C4×C83—28no—
621C2×C4×C83—21no—
622C2×C4×C83—21no—
623C2×C4×C83—21no—
624C2×C4×C83—21no—
625C2×C4×C83—21no—
626C2×C4×C83—21no—
627C2×C4×C83—21no—
628C2×C4×C83—21no—
629C2×C4×C83—21no—
630C2×C4×C83—21no—
631C2×C4×C83—21no—
632C2×C4×C83—21no—
633C2×C4×C83—21no—
634C2×C4×C83—21no—
635C2×C4×C83—21no—
636C2×C4×C83—21no—
637C2×C4×C83—21no—
638C2×C4×C83—21no—
639C2×C4×C83—21no—
640C2×C4×C83—21no—
641C2×C4×C83—21no—
642C2×C4×C83—21no—
643C2×C4×C83—21no—
644C2×C4×C83—21no—
645C2×C4×C83—21no—
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—44no—
661C2×C4×C83—82no—
662C2×C4×C83C22×Q812yes—
663C2×C4×C83C22×Q812yes—
664C2×C4×C83H(5,𝔽2)12yes—
665C2×Dic83—21no—
666C2×Dic83—21no—
667C2×Dic83—21no—
668C2×Dic83—21no—
669C2×Dic83—21no—
670C2×Dic83—21no—
671C2×Dic83—21no—
672C2×Dic83—21no—
673C2×Dic83—21no—
674C2×Dic83—21no—
675C2×Dic83—21no—
676C2×Dic83—21no—
677C2×Dic83—21no—
678C2×Dic83—21no—
679C2×Dic83—21no—
680C2×Dic83—21no—
681C2×Dic83—21no—
682C2×Dic83—21no—
683C2×Dic83—21no—
684C2×Dic83—21no—
685C2×Dic83—21no—
686C2×Dic83—21no—
687C2×Dic83—21no—
688C2×Dic83—21no—
689C2×Dic83—21no—
690C2×Dic83—21no—
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—44no—
701C2×Dic83—82no—
702C2×Dic83H(5,𝔽2)12yes—
703D332—44no—
704D332—44no—
705D332—44no—
706D332—44no—
707C4×D83—44no—
708C4×D83—44no—
709C4×D83—44no—
710C4×D83—44no—
711C4×D83—82no—
712C4×D83—82no—
713C4×D83—82no—
714C4×D83—82no—
715Dic166—82no—
716Dic166—82no—
717Dic166—82no—
718C22×C83—22no—
719C22×C83—22no—
720C22×C83—22no—
721C22×C83—22no—
722C22×C83—22no—
723C22×C83—22no—
724C22×C83#54314yes—
725C22×C83C23×Q811yescharacteristic
726C22×C83C2×H(5,𝔽2)11yescharacteristic
727C22×C83C2×H(5,𝔽2)11yescharacteristic
728C22×C83C2×H(5,𝔽2)11yescharacteristic
729C22×C83C2×H(5,𝔽2)11yescharacteristic
730C22×C83#58511yescharacteristic
731C22×C83#58511yescharacteristic
732C2×D83—22no—
733C2×D83—22no—
734C2×D83—22no—
735C2×D83—22no—
736C2×D83—22no—
737C2×D83—22no—
738C2×D83—22no—
739C2×D83—22no—
740C2×D83—22no—
741C2×D83—22no—
742C2×D83—22no—
743C2×D83—22no—
744C2×D83—416no—
745C2×D83—41no—
746C2×D83—41no—
747C2×D83—41no—
748C2×D83—41no—
749C2×D83—41no—
750C2×D83—41no—
751C2×D83—41no—
752C2×D83—41no—
753C2×D83—41no—
754C2×D83—41no—
755C2×D83—41no—
756C2×D83—41no—
757C2×D83—41no—
758C2×D83—41no—
759C2×D83—41no—
760C2×D83—41no—
761C2×D83—88no—
762C4×C83—22no—
763C4×C83—22no—
764C4×C83—22no—
765C4×C83—41no—
766C4×C83—41no—
767C4×C83—41no—
768C4×C83—41no—
769C4×C83—41no—
770C4×C83—41no—
771C4×C83—41no—
772C4×C83—41no—
773C4×C83—41no—
774C4×C83—41no—
775C4×C83—41no—
776Dic83—22no—
777Dic83—41no—
778Dic83—41no—
779Dic83—41no—
780Dic83—41no—
781Dic83—41no—
782Dic83—41no—
783Dic83—41no—
784Dic83—41no—
785Dic83—41no—
786Dic83—41no—
787Dic83—41no—
788#36747—831nomaximal, Sylow
789C2×C83—24no—
790C2×C83C2×#54311yescharacteristic
791C2×C83#350111yescharacteristic
792C2×C83#350111yescharacteristic
793C2×C83#353211yescharacteristic
794C2×C83#353311yescharacteristic
795C2×C83#354211yescharacteristic
796C2×C83#354211yescharacteristic
797D83—42no—
798D83—42no—
799D83—42no—
800D83—42no—
801#2848—831no—
802#2848—831no—
803#2804—831no—
804#2784—831no—
805#2784—831no—
806#2780—831no—
807#2780—831no—
808#2780—831no—
809#2780—831no—
810#2748—831no—
811#2748—831no—
812#2732—831no—
813#2732—831no—
814#2692—831no—
815#2692—831no—
816#2692—831no—
817#2692—831no—
818#2683—831no—
819#2626—831no—
820#2626—831no—
821#2438—831no—
822#2438—831no—
823#2438—831no—
824#2438D8311yescharacteristic, complemented
825#2437—831no—
826#2437—831no—
827#2437—831no—
828#2437—831no—
829#2309—831no—
830#2308—831no—
831C2×#386—831no—
832C83#3674711yescharacteristic, complemented, Sylow
833C23×D4—831no—
834C24×C4—831no—
835C2×C22⋊Q8—831no—
836C2×C22⋊Q8—831no—
837C2×C22⋊Q8—831no—
838C2×C22⋊Q8—831no—
839C2×C22⋊Q8—831no—
840C2×C22⋊Q8—831no—
841C2×C22⋊Q8—831no—
842C2×C22⋊Q8—831no—
843C2×C22⋊Q8—831no—
844C2×C22⋊Q8—831no—
845C2×C22⋊Q8—831no—
846C2×C22⋊Q8C2×D8311yescharacteristic
847C2×#117—831no—
848C2×#117C2×D8311yescharacteristic
849C22×C22⋊C4—831no—
850C22×C22⋊C4—831no—
851C22×C22⋊C4—831no—
852C22×C22⋊C4—831no—
853C22×C22⋊C4—831no—
854#400—831no—
855#400—831no—
856#400—831no—
857#400C2×D8311yescharacteristic, complemented
858#399—831no—
859#399—831no—
860#399—831no—
861#399—831no—
862#399—831no—
863#399—831no—
864#399—831no—
865#399—831no—
866#398—831no—
867#398—831no—
868#398—831no—
869#398—831no—
870#398—831no—
871#398—831no—
872#398C2×D8311yescharacteristic, complemented
873#398C2×D8311yescharacteristic, complemented
874#396—831no—
875#396—831no—
876#396—831no—
877#396—831no—
878#396—831no—
879#396—831no—
880#396—831no—
881#396—831no—
882#396—831no—
883#396—831no—
884#396—831no—
885#396—831no—
886#396—831no—
887#396—831no—
888#396—831no—
889#396—831no—
890#395—831no—
891#395—831no—
892#395—831no—
893#395C2×D8311yescharacteristic, complemented
894#393—831no—
895#393—831no—
896#393—831no—
897#393—831no—
898#393—831no—
899#393—831no—
900#393—831no—
901#393—831no—
902#391—831no—
903#391—831no—
904#391—831no—
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#389—831no—
915#389—831no—
916#389—831no—
917#389C2×D8311yescharacteristic, complemented
918#387—831no—
919#387—831no—
920#387—831no—
921#387—831no—
922#387—831no—
923#387—831no—
924#387C2×D8311yescharacteristic, complemented
925#387C2×D8311yescharacteristic, complemented
926#386—831no—
927#386—831no—
928#386—831no—
929#386—831no—
930#386—831no—
931#386—831no—
932#386—831no—
933#386—831no—
934#386—831no—
935#386—831no—
936#386—831no—
937#386—831no—
938#386—831no—
939#386—831no—
940#386—831no—
941#386—831no—
942#385—831no—
943#385—831no—
944#385—831no—
945#385—831no—
946#385—831no—
947#385—831no—
948#385—831no—
949#385—831no—
950#385—831no—
951#385—831no—
952#385—831no—
953#385—831no—
954#385—831no—
955#385—831no—
956#385—831no—
957#385—831no—
958#385—831no—
959#385—831no—
960#385—831no—
961#385—831no—
962#385—831no—
963#385—831no—
964#385C2×D8311yescharacteristic
965#385C2×D8311yescharacteristic
966#381—831no—
967#381C2×D8311yescharacteristic
968#380—831no—
969#380—831no—
970#380—831no—
971#380—831no—
972#380—831no—
973#380—831no—
974#380—831no—
975#380—831no—
976#380—831no—
977#380—831no—
978#380—831no—
979#380C2×D8311yescharacteristic
980#379—831no—
981#379—831no—
982#379—831no—
983#379—831no—
984#379—831no—
985#379—831no—
986C2×#95—831no—
987C2×#95C2×D8311yescharacteristic
988C25—831no—
989C25—831no—
990C22×Q8—831no—
991C22×Q8—831no—
992C22×Q8—831no—
993C22×Q8C22×D8311yescharacteristic
994C22×D4—3322no—
995C22×D4—3322no—
996C22×D4—838no—
997C22×D4—831no—
998C22×D4—831no—
999C22×D4—831no—
1000C22×D4—831no—
1001C23×C4—3322no—
1002C23×C4—3322no—
1003C23×C4—3322no—
1004C23×C4—831no—
1005C23×C4—831no—
1006C23×C4—831no—
1007C23×C4—831no—
1008C23×C4—831no—
1009C23×C4—831no—
1010C23×C4—831no—
1011C23×C4—831no—
1012C23×C4—831no—
1013C23×C4—831no—
1014C23×C4C22×D8311yescharacteristic
1015C23×C4C22×D8311yescharacteristic
1016C23×C4C22×D8311yescharacteristic
1017C22⋊Q8—42no—
1018C22⋊Q8—3322no—
1019C22⋊Q8—3322no—
1020C22⋊Q8—3322no—
1021C22⋊Q8—3322no—
1022C22⋊Q8—3322no—
1023C22⋊Q8—3322no—
1024C22⋊Q8—3322no—
1025C22⋊Q8—3322no—
1026C22⋊Q8—3322no—
1027C22⋊Q8—3322no—
1028C22⋊Q8—3322no—
1029#117—42no—
1030#117—3322no—
1031C2×C4⋊C4—831no—
1032C2×C4⋊C4—831no—
1033C2×C4⋊C4—831no—
1034C2×C4⋊C4—831no—
1035C2×C4⋊C4—831no—
1036C2×C4⋊C4—831no—
1037C2×C4⋊C4—831no—
1038C2×C4⋊C4—831no—
1039C2×C4⋊C4—831no—
1040C2×C4⋊C4—831no—
1041C2×C4⋊C4—831no—
1042C2×C4⋊C4—831no—
1043C2×C4⋊C4—831no—
1044C2×C4⋊C4—831no—
1045C2×C4⋊C4—831no—
1046C2×C4⋊C4—831no—
1047C2×C4⋊C4—831no—
1048C2×C4⋊C4—831no—
1049C2×C4⋊C4—831no—
1050C2×C4⋊C4—831no—
1051C2×C4⋊C4—831no—
1052C2×C4⋊C4—831no—
1053C2×C4⋊C4—831no—
1054C2×C4⋊C4—831no—
1055C2×C4⋊C4—831no—
1056C2×C4⋊C4—831no—
1057C2×C4⋊C4—831no—
1058C2×C4⋊C4—831no—
1059C2×C4⋊C4—831no—
1060C2×C4⋊C4C22×D8311yescharacteristic
1061C2×C4⋊C4C22×D8311yescharacteristic
1062C2×C4⋊C4C22×D8311yescharacteristic
1063C2×C4⋊C4C22×D8311yescharacteristic
1064C2×C4⋊C4C22×D8311yescharacteristic
1065C2×C4⋊C4C22×D8311yescharacteristic
1066C2×C4⋊C4C22×D8311yescharacteristic
1067C2×C4⋊C4C22×D8311yescharacteristic
1068C2×C4⋊C4C22×D8311yescharacteristic
1069C2×C4⋊C4C22×D8311yescharacteristic
1070C2×C4⋊C4C22×D8311yescharacteristic
1071C2×C22⋊C4—3322no—
1072C2×C22⋊C4—3322no—
1073C2×C22⋊C4—3322no—
1074C2×C22⋊C4—3322no—
1075C2×C22⋊C4—3322no—
1076C2×C22⋊C4—831no—
1077C2×C22⋊C4—831no—
1078C2×C22⋊C4—831no—
1079C2×C22⋊C4—831no—
1080C2×C22⋊C4—831no—
1081C2×C22⋊C4—831no—
1082C2×C22⋊C4—831no—
1083C2×C22⋊C4—831no—
1084C2×C22⋊C4—831no—
1085C2×C22⋊C4—831no—
1086C2×C22⋊C4—831no—
1087C2×C22⋊C4—831no—
1088C2×C22⋊C4—831no—
1089C2×C22⋊C4—831no—
1090C2×C22⋊C4—831no—
1091C2×C22⋊C4—831no—
1092C2×C22⋊C4—831no—
1093C2×C22⋊C4—831no—
1094C2×C22⋊C4—831no—
1095C2×C22⋊C4—831no—
1096C2×C22⋊C4—831no—
1097C2×C22⋊C4—831no—
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⋊C4C22×D8311yescharacteristic
1121C2×C22⋊C4C22×D8311yescharacteristic
1122C2×C22⋊C4C22×D8311yescharacteristic
1123C2×C22⋊C4C22×D8311yescharacteristic
1124C2×C42—831no—
1125C2×C42—831no—
1126C2×C42C22×D8311yescharacteristic
1127C2×C42C22×D8311yescharacteristic
1128#95—831no—
1129#95—831no—
1130#95—831no—
1131#95—831no—
1132#95—831no—
1133#95—831no—
1134#95—831no—
1135#95—831no—
1136#95—831no—
1137#95—831no—
1138#95—831no—
1139#95—831no—
1140#95—831no—
1141#95—831no—
1142#95—831no—
1143#95—831no—
1144#95—831no—
1145#95—831no—
1146#95—831no—
1147#95—831no—
1148#95—831no—
1149#95—831no—
1150#95—831no—
1151#95—831no—
1152#95—831no—
1153#95—831no—
1154#95C22×D8311yescharacteristic
1155#95C22×D8311yescharacteristic
1156#95C22×D8311yescharacteristic
1157#95C22×D8311yescharacteristic
1158#95C22×D8311yescharacteristic
1159#95C22×D8311yescharacteristic
1160#95C22×D8311yescharacteristic
1161#95C22×D8311yescharacteristic
1162#95C22×D8311yescharacteristic
1163#95C22×D8311yescharacteristic
1164#95C22×D8311yescharacteristic
1165#95C22×D8311yescharacteristic
1166#95C22×D8311yescharacteristic
1167#95C22×D8311yescharacteristic
1168C24—3321no—
1169C24—3321no—
1170C24—3321no—
1171C24—3321no—
1172C24—3321no—
1173C24—3321no—
1174C24—3321no—
1175C24—3321no—
1176C24—834no—
1177C24—834no—
1178C24—831no—
1179C24—831no—
1180C24—831no—
1181C24—831no—
1182C24—1662no—
1183C24—1662no—
1184C24—1662no—
1185C24—1662no—
1186C24C23×D8311yescharacteristic
1187C2×Q8—41no—
1188C2×Q8—41no—
1189C2×Q8—41no—
1190C2×Q8—3321no—
1191C2×Q8—3321no—
1192C2×Q8—3321no—
1193C2×Q8—3321no—
1194C2×Q8—3321no—
1195C2×Q8—3321no—
1196C2×Q8—3321no—
1197C2×Q8—1662no—
1198C2×Q8—1662no—
1199C2×D4—33216no—
1200C2×D4—3321no—
1201C2×D4—3321no—
1202C2×D4—3321no—
1203C2×D4—3321no—
1204C2×D4—3321no—
1205C2×D4—3321no—
1206C2×D4—3321no—
1207C2×D4—3321no—
1208C2×D4—834no—
1209C2×D4—834no—
1210C2×D4—834no—
1211C2×D4—834no—
1212C22×C4—22no—
1213C22×C4—22no—
1214C22×C4—22no—
1215C22×C4—22no—
1216C22×C4—22no—
1217C22×C4—41no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—3321no—
1221C22×C4—3321no—
1222C22×C4—3321no—
1223C22×C4—3321no—
1224C22×C4—3321no—
1225C22×C4—3321no—
1226C22×C4—3321no—
1227C22×C4—3321no—
1228C22×C4—3321no—
1229C22×C4—3321no—
1230C22×C4—3321no—
1231C22×C4—3321no—
1232C22×C4—3321no—
1233C22×C4—3321no—
1234C22×C4—3321no—
1235C22×C4—3321no—
1236C22×C4—3321no—
1237C22×C4—3321no—
1238C22×C4—3321no—
1239C22×C4—3321no—
1240C22×C4—33216no—
1241C22×C4—3321no—
1242C22×C4—3321no—
1243C22×C4—3321no—
1244C22×C4—831no—
1245C22×C4—831no—
1246C22×C4—831no—
1247C22×C4—831no—
1248C22×C4—831no—
1249C22×C4—831no—
1250C22×C4—831no—
1251C22×C4—831no—
1252C22×C4—831no—
1253C22×C4—831no—
1254C22×C4—831no—
1255C22×C4—831no—
1256C22×C4—1662no—
1257C22×C4—1662no—
1258C22×C4—1662no—
1259C22×C4—1662no—
1260C22×C4—1662no—
1261C22×C4—1662no—
1262C22×C4—1662no—
1263C22×C4Q8×D8314yes—
1264C22×C4C23×D8311yescharacteristic
1265C22×C4C23×D8311yescharacteristic
1266C22×C4C23×D8311yescharacteristic
1267C22×C4C23×D8311yescharacteristic
1268C22×C4C23×D8311yescharacteristic
1269C22×C4C23×D8311yescharacteristic
1270C22×C4C23×D8311yescharacteristic
1271C22×C4C23×D8311yescharacteristic
1272C22×C4C23×D8311yescharacteristic
1273C22×C4C23×D8311yescharacteristic
1274C22×C4C23×D8311yescharacteristic
1275C22×C4C23×D8311yescharacteristic
1276C22×C4C23×D8311yescharacteristic
1277C22×C4C23×D8311yescharacteristic
1278C4⋊C4—22no—
1279C4⋊C4—22no—
1280C4⋊C4—41no—
1281C4⋊C4—41no—
1282C4⋊C4—41no—
1283C4⋊C4—41no—
1284C4⋊C4—41no—
1285C4⋊C4—41no—
1286C4⋊C4—41no—
1287C4⋊C4—41no—
1288C4⋊C4—41no—
1289C4⋊C4—3321no—
1290C4⋊C4—3321no—
1291C4⋊C4—3321no—
1292C4⋊C4—3321no—
1293C4⋊C4—3321no—
1294C4⋊C4—3321no—
1295C4⋊C4—3321no—
1296C4⋊C4—3321no—
1297C4⋊C4—3321no—
1298C4⋊C4—3321no—
1299C4⋊C4—3321no—
1300C4⋊C4—3321no—
1301C4⋊C4—3321no—
1302C4⋊C4—3321no—
1303C4⋊C4—3321no—
1304C4⋊C4—3321no—
1305C4⋊C4—3321no—
1306C4⋊C4—3321no—
1307C4⋊C4—3321no—
1308C4⋊C4—3321no—
1309C4⋊C4—3321no—
1310C4⋊C4—3321no—
1311C4⋊C4—3321no—
1312C4⋊C4—3321no—
1313C4⋊C4—3321no—
1314C4⋊C4—1662no—
1315C4⋊C4—1662no—
1316C4⋊C4—1662no—
1317C4⋊C4—1662no—
1318C22⋊C4—22no—
1319C22⋊C4—22no—
1320C22⋊C4—22no—
1321C22⋊C4—22no—
1322C22⋊C4—3321no—
1323C22⋊C4—3321no—
1324C22⋊C4—3321no—
1325C22⋊C4—3321no—
1326C22⋊C4—3321no—
1327C22⋊C4—3321no—
1328C22⋊C4—3321no—
1329C22⋊C4—3321no—
1330C22⋊C4—3321no—
1331C22⋊C4—3321no—
1332C22⋊C4—3321no—
1333C22⋊C4—3321no—
1334C22⋊C4—3321no—
1335C22⋊C4—3321no—
1336C22⋊C4—3321no—
1337C22⋊C4—3321no—
1338C22⋊C4—3321no—
1339C22⋊C4—3321no—
1340C22⋊C4—3321no—
1341C22⋊C4—3321no—
1342C22⋊C4—3321no—
1343C22⋊C4—3321no—
1344C22⋊C4—3321no—
1345C22⋊C4—3321no—
1346C22⋊C4—3321no—
1347C22⋊C4—3321no—
1348C22⋊C4—3321no—
1349C22⋊C4—3321no—
1350C22⋊C4—3321no—
1351C22⋊C4—3321no—
1352C22⋊C4—3321no—
1353C22⋊C4—3321no—
1354C22⋊C4—3321no—
1355C22⋊C4—3321no—
1356C22⋊C4—3321no—
1357C22⋊C4—3321no—
1358C22⋊C4—1662no—
1359C22⋊C4—1662no—
1360C22⋊C4—1662no—
1361C22⋊C4—1662no—
1362C22⋊C4—1662no—
1363C22⋊C4—1662no—
1364C22⋊C4—1662no—
1365C22⋊C4—1662no—
1366C42—41no—
1367C42—41no—
1368C42—3321no—
1369C42—3321no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—3324no—
1375C23—3324no—
1376C23—3324no—
1377C23—3324no—
1378C23—3324no—
1379C23—3324no—
1380C23—3324no—
1381C23—3324no—
1382C23—832no—
1383C23—832no—
1384C23—832no—
1385C23—832no—
1386C23—6642no—
1387C23—6642no—
1388C23—6642no—
1389C23—6642no—
1390C23—1668no—
1391C23—1661no—
1392C23—1661no—
1393C23—1661no—
1394C23—1661no—
1395C23—1661no—
1396C23—1661no—
1397C23—1661no—
1398C23—1661no—
1399C23—1661no—
1400C23—1661no—
1401C23—1661no—
1402C23—1661no—
1403C23—1661no—
1404C23—1661no—
1405C23—1661no—
1406C23—1661no—
1407C23—1661no—
1408C23—1661no—
1409C23—1661no—
1410C23—1661no—
1411C23—1661no—
1412C23—1661no—
1413C23—1661no—
1414C23—1661no—
1415C23—1668no—
1416C23C2×Q8×D8312yes—
1417C23#1458183712yes—
1418C23#1458183812yes—
1419C23C24×D8311yescharacteristic
1420Q8—82no—
1421Q8—6642no—
1422Q8—6642no—
1423Q8—6642no—
1424D4—3324no—
1425D4—3324no—
1426D4—3324no—
1427D4—3324no—
1428C2×C4—28no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—44no—
1469C2×C4—82no—
1470C2×C4—3324no—
1471C2×C4—3324no—
1472C2×C4—3324no—
1473C2×C4—3324no—
1474C2×C4—3324no—
1475C2×C4—832no—
1476C2×C4—6642no—
1477C2×C4—6642no—
1478C2×C4—6642no—
1479C2×C4—6642no—
1480C2×C4—6642no—
1481C2×C4—1661no—
1482C2×C4—1661no—
1483C2×C4—1661no—
1484C2×C4—1661no—
1485C2×C4—1661no—
1486C2×C4—1661no—
1487C2×C4—1661no—
1488C2×C4—1661no—
1489C2×C4—1661no—
1490C2×C4—1661no—
1491C2×C4—1661no—
1492C2×C4—1661no—
1493C2×C4—1661no—
1494C2×C4—1661no—
1495C2×C4—1661no—
1496C2×C4—1661no—
1497C2×C4—1661no—
1498C2×C4—1661no—
1499C2×C4—1661no—
1500C2×C4—1661no—
1501C2×C4—1661no—
1502C2×C4—1661no—
1503C2×C4—1661no—
1504C2×C4—1661no—
1505C2×C4—1661no—
1506C2×C4—1661no—
1507C2×C4—1661no—
1508C2×C4—1661no—
1509C2×C4—1661no—
1510C2×C4—1661no—
1511C2×C4—1661no—
1512C2×C4—1661no—
1513C2×C4—1661no—
1514C2×C4—1661no—
1515C2×C4—1661no—
1516C2×C4C2×Q8×D8312yes—
1517C2×C4C2×Q8×D8312yes—
1518C2×C4#1458183812yes—
1519C22—22no—
1520C22—22no—
1521C22—22no—
1522C22—22no—
1523C22—22no—
1524C22—22no—
1525C22—33216no—
1526C22—3321no—
1527C22—3321no—
1528C22—3321no—
1529C22—3321no—
1530C22—3321no—
1531C22—3321no—
1532C22—3321no—
1533C22—3321no—
1534C22—3321no—
1535C22—3321no—
1536C22—3321no—
1537C22—3321no—
1538C22—3321no—
1539C22—3321no—
1540C22—3321no—
1541C22—3321no—
1542C22—6648no—
1543C22—1662no—
1544C22—1662no—
1545C22—1662no—
1546C22—1662no—
1547C22—1662no—
1548C22—1662no—
1549C22—1662no—
1550C22—1662no—
1551C22—1662no—
1552C22—1662no—
1553C22—1662no—
1554C22—1662no—
1555C22#1912832614yes—
1556C22C22×Q8×D8311yescharacteristic
1557C22H(5,𝔽2)×D8311yescharacteristic
1558C22C2×#1458183711yescharacteristic
1559C22C2×#1458183811yescharacteristic
1560C22C2×#1458183811yescharacteristic
1561C22#1912853711yescharacteristic
1562C22#1912853811yescharacteristic
1563C4—22no—
1564C4—22no—
1565C4—22no—
1566C4—41no—
1567C4—41no—
1568C4—41no—
1569C4—41no—
1570C4—41no—
1571C4—41no—
1572C4—41no—
1573C4—41no—
1574C4—41no—
1575C4—41no—
1576C4—41no—
1577C4—3321no—
1578C4—3321no—
1579C4—3321no—
1580C4—3321no—
1581C4—3321no—
1582C4—3321no—
1583C4—3321no—
1584C4—3321no—
1585C4—3321no—
1586C4—3321no—
1587C4—3321no—
1588C4—1662no—
1589C2—24no—
1590C2—3322no—
1591C2—3322no—
1592C2—3322no—
1593C2—3322no—
1594C2C2×#1912832611yescharacteristic
1595C2#2492126411yescharacteristic
1596C2#2492126511yescharacteristic
1597C2#2492161911yescharacteristic
1598C2#2492162911yescharacteristic
1599C2#2492176411yescharacteristic
1600C2#2492178011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2438C2
prime radicalC23×D332C22
hypercenter#2438D83
hypocenterC83#36747
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2438

Complements

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

NH ≅ G/Ntype
1. #24915751C2semidirect
2. #24915749C2semidirect
3. #24915407C2semidirect
4. #24915166C2semidirect
5. #24915163C2semidirect
6. #24915117C2semidirect
7. #24915114C2semidirect
8. #24915110C2semidirect
9. #24915105C2semidirect
10. #24914671C2semidirect
11. #24914671C2semidirect
12. #24914484C2semidirect
13. #24914484C2semidirect
14. #24913966C2semidirect
15. #24913961C2semidirect
16. #24913957C2semidirect
17. #24913954C2semidirect
18. #24913834C2semidirect
19. #24913274C2semidirect
20. #24913270C2semidirect
21. #24911141C2semidirect
22. #24911139C2semidirect
23. #24911133C2semidirect
24. #24911131C2semidirect
25. #24911128C2semidirect
26. #24911127C2semidirect
27. #24911126C2semidirect
31. C83×#2438C2semidirect
34. C2×#14581772C22semidirect
35. C2×#14581772C22semidirect
36. C2×#14581772C22semidirect
38. C2×#14581770C22semidirect
39. C2×#14581770C22semidirect
40. C2×#14581770C22semidirect
41. C2×#14581770C22semidirect
44. C2×#14581768C22semidirect
51. #19127643C22semidirect
52. #19127643C22semidirect
53. #19127640C22semidirect
54. #19127638C22semidirect
55. #19127636C22semidirect
56. #19127636C22semidirect
57. #19127636C22semidirect
58. #19127636C22semidirect
59. #19127636C22semidirect
60. #19127636C22semidirect
61. #19127636C22semidirect
62. #19127635C22semidirect
63. #19127635C22semidirect
64. #19127634C22semidirect
65. #19127634C22semidirect
66. #19127633C22semidirect
67. #19127633C22semidirect
68. #19127625C22semidirect
69. #19127625C22semidirect
70. #19127625C22semidirect
71. #19127625C22semidirect
72. #19127623C22semidirect
73. #19127623C22semidirect
74. #19127623C22semidirect
75. #19127623C22semidirect
76. #19127623C22semidirect
77. #19127623C22semidirect
78. #19127623C22semidirect
79. #19127623C22semidirect
80. #19127623C22semidirect
81. #19127623C22semidirect
82. #19127623C22semidirect
83. #19127623C22semidirect
84. #19127622C22semidirect
85. #19127622C22semidirect
86. #19127621C22semidirect
87. #19127614C22semidirect
88. #19127614C22semidirect
89. #19127614C22semidirect
90. #19127614C22semidirect
91. #19127614C22semidirect
92. #19127612C22semidirect
93. #19127612C22semidirect
94. #19127612C22semidirect
95. #19127607C22semidirect
96. #19127605C22semidirect
97. #19127605C22semidirect
106. #19127599C22semidirect
107. #19127598C22semidirect
108. #19127598C22semidirect
109. #19127588C22semidirect
110. #19127588C22semidirect
111. #19127585C22semidirect
112. #19127585C22semidirect
113. #19127584C22semidirect
114. #19127584C22semidirect
133. #19127575C22semidirect
134. #19127575C22semidirect
135. #19127575C22semidirect
136. #19127575C22semidirect
137. #19127575C22semidirect
138. #19127575C22semidirect
139. #19127575C22semidirect
140. #19127575C22semidirect
141. #19127575C22semidirect
142. #19127575C22semidirect
147. #19127572C22semidirect
148. #19127572C22semidirect
149. #19127572C22semidirect
150. #19127572C22semidirect
151. #19127572C22semidirect
152. #19127572C22semidirect
155. #19127560C22semidirect
156. #19127560C22semidirect
157. #19127560C22semidirect
158. #19127560C22semidirect
161. #19127558C22semidirect
162. #19127558C22semidirect
163. #19127558C22semidirect
164. #19127558C22semidirect
174. #400×C83C22semidirect
175. #398×C83C22semidirect
176. #398×C83C22semidirect
177. #395×C83C22semidirect
178. #391×C83C22semidirect
179. #389×C83C22semidirect
180. #387×C83C22semidirect
181. #387×C83C22semidirect
194. C22×D332Q8semidirect
824. #2438D83semidirect
832. C83#36747semidirect
857. #400C2×D83semidirect
872. #398C2×D83semidirect
873. #398C2×D83semidirect
893. #395C2×D83semidirect
905. #391C2×D83semidirect
917. #389C2×D83semidirect
924. #387C2×D83semidirect
925. #387C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249157512
#249157492
#249154072
#249151662
#249151632
#249151172
#249151142
#249151102
#249151052
#249146712
#249144842
#249139662
#249139612
#249139572
#249139542
#249138342
#249132742
#249132702
#249111412
#249111392
#249111332
#249111312
#249111282
#249111272
#249111262
#249100432
#249100402
C2×#191275792
C83×#24382
#3674783