Finite Group Databasebeta

← #14961563

Subgroups — #14961563

Order 2816.

1512 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076951C211yesmaximal, characteristic, complemented
2#13076923C211yesmaximal, characteristic, complemented
3#13076568C211yesmaximal, characteristic, complemented
4#13076561C211yesmaximal, characteristic
5#13076382C211yesmaximal, characteristic, complemented
6#13076365C211yesmaximal, characteristic, complemented
7#13076360C211yesmaximal, characteristic, complemented
8#13076316C211yesmaximal, characteristic
9#13076270C211yesmaximal, characteristic
10#13076173C211yesmaximal, characteristic, complemented
11#13076029C211yesmaximal, characteristic, complemented
12#13076029C211yesmaximal, characteristic, complemented
13#13075929C211yesmaximal, characteristic, complemented
14#13075743C211yesmaximal, characteristic, complemented
15#13075593C211yesmaximal, characteristic, complemented
16#13075491C211yesmaximal, characteristic, complemented
17#13075404C211yesmaximal, characteristic, complemented
18#13075114C211yesmaximal, characteristic
19#13074792C211yesmaximal, characteristic, complemented
20#13074792C211yesmaximal, characteristic, complemented
21#13074324C211yesmaximal, characteristic, complemented
22#13074280C211yesmaximal, characteristic, complemented
23#13074259C211yesmaximal, characteristic, complemented
24#13074259C211yesmaximal, characteristic, complemented
25#13073839C211yesmaximal, characteristic, complemented
26#13072306C211yesmaximal, characteristic, complemented
27#13072291C211yesmaximal, characteristic, complemented
28#13071254C211yesmaximal, characteristic
29#13071252C211yesmaximal, characteristic
30#13071057C211yesmaximal, characteristic
31C11×#2570C211yesmaximal, characteristic, complemented
32C2×#66949C2211yescharacteristic
33C2×#66949C2211yescharacteristic
34C2×#66942C2211yescharacteristic
35C2×#66941C2211yescharacteristic
36C2×C4×D44C2211yescharacteristic
37C2×#66925C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C11×#400C2211yescharacteristic
40C11×#400C2211yescharacteristic
41C11×#398C2211yescharacteristic
42C11×#398C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#387C2211yescharacteristic
46C11×#387C2211yescharacteristic
47C11×#387C2211yescharacteristic
48C11×#387C2211yescharacteristic
49C11×#384C2211yescharacteristic
50C11×#382C2211yescharacteristic
51C11×#382C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54#10622607C2211yescharacteristic
55#10622607C2211yescharacteristic
56#10622607C2211yescharacteristic
57#10622607C2211yescharacteristic
58#10622607C2211yescharacteristic
59#10622607C2211yescharacteristic
60#10622605C2211yescharacteristic
61#10622605C2211yescharacteristic
62#10622603C2211yescharacteristic
63#10622603C2211yescharacteristic
64#10622603C2211yescharacteristic
65#10622603C2211yescharacteristic
66#10622602C2211yescharacteristic
67#10622602C2211yescharacteristic
68#10622602C2211yescharacteristic
69#10622602C2211yescharacteristic
70#10622602C2211yescharacteristic
71#10622602C2211yescharacteristic
72#10622602C2211yescharacteristic
73#10622602C2211yescharacteristic
74#10622601C2211yescharacteristic
75#10622601C2211yescharacteristic
76#10622600C2211yescharacteristic
77#10622600C2211yescharacteristic
78#10622599C2211yescharacteristic
79#10622599C2211yescharacteristic
80#10622599C2211yescharacteristic
81#10622599C2211yescharacteristic
82#10622599C2211yescharacteristic
83#10622597C2211yescharacteristic
84#10622597C2211yescharacteristic
85#10622597C2211yescharacteristic
86#10622597C2211yescharacteristic
87#10622596C2211yescharacteristic
88#10622595C2211yescharacteristic
89#10622595C2211yescharacteristic
90#10622593C2211yescharacteristic
91#10622592C2211yescharacteristic
92#10622592C2211yescharacteristic
93#10622592C2211yescharacteristic
94#10622592C2211yescharacteristic
95#10622592C2211yescharacteristic
96#10622592C2211yescharacteristic
97#10622592C2211yescharacteristic
98#10622591C2211yescharacteristic
99#10622591C2211yescharacteristic
100#10622587C2211yescharacteristic
101#10622586C2211yescharacteristic
102#10622586C2211yescharacteristic
103#10622585C2211yescharacteristic
104#10622585C2211yescharacteristic
105#10622585C2211yescharacteristic
106#10622553C2211yescharacteristic
107#10622553C2211yescharacteristic
108#10622553C2211yescharacteristic
109#10622553C2211yescharacteristic
110C4×(C2×D11)⋊C4C2211yescharacteristic
111C4×(C2×D11)⋊C4C2211yescharacteristic
112#10622550C2211yescharacteristic
113#10622546C2211yescharacteristic
114#10622546C2211yescharacteristic
115#10622546C2211yescharacteristic
116#10622546C2211yescharacteristic
117#10622545C2211yescharacteristic
118#10622545C2211yescharacteristic
119#10622542C2211yescharacteristic
120#10622542C2211yescharacteristic
121#10622542C2211yescharacteristic
122#10622542C2211yescharacteristic
123#10622286C2211yescharacteristic
124#10622286C2211yescharacteristic
125#10622286C2211yescharacteristic
126#10622286C2211yescharacteristic
127#10622286C2211yescharacteristic
128#10622286C2211yescharacteristic
129#10622286C2211yescharacteristic
130#10622286C2211yescharacteristic
131#10622281C2211yescharacteristic
132#10622281C2211yescharacteristic
133#10622281C2211yescharacteristic
134#10622281C2211yescharacteristic
135#10622281C2211yescharacteristic
136#10622281C2211yescharacteristic
137#10622280C2211yescharacteristic
138#10622280C2211yescharacteristic
139#10622280C2211yescharacteristic
140#10622280C2211yescharacteristic
141#10622280C2211yescharacteristic
142#10622279C2211yescharacteristic
143#10622278C2211yescharacteristic
144#10622278C2211yescharacteristic
145#10622278C2211yescharacteristic
146#10622278C2211yescharacteristic
147#10622277C2211yescharacteristic
148#10622277C2211yescharacteristic
149#10622277C2211yescharacteristic
150D11×#95C2211yescharacteristic
151#10622271C2211yescharacteristic
152#10622271C2211yescharacteristic
153#10622271C2211yescharacteristic
154#10622271C2211yescharacteristic
155#10622271C2211yescharacteristic
156#10622269C2211yescharacteristic
157#10622269C2211yescharacteristic
158#10622269C2211yescharacteristic
159#10622268C2211yescharacteristic
160#10622268C2211yescharacteristic
161#10622267C2211yescharacteristic
162#10622267C2211yescharacteristic
163#10622267C2211yescharacteristic
164#10622267C2211yescharacteristic
165#10622267C2211yescharacteristic
166#10622267C2211yescharacteristic
167#10622267C2211yescharacteristic
168#10622267C2211yescharacteristic
169#10622266C2211yescharacteristic
170#10622266C2211yescharacteristic
171#10622266C2211yescharacteristic
172#10622265C2211yescharacteristic
173#10622263C2211yescharacteristic
174#10622263C2211yescharacteristic
175#10622260C2211yescharacteristic
176#10622260C2211yescharacteristic
177#10622260C2211yescharacteristic
178#10622260C2211yescharacteristic
179#10622259C2211yescharacteristic
180#10622259C2211yescharacteristic
181#10622259C2211yescharacteristic
182#10622259C2211yescharacteristic
183#10622259C2211yescharacteristic
184#10622259C2211yescharacteristic
185#10622259C2211yescharacteristic
186#10622259C2211yescharacteristic
187C22×D44C2311yescharacteristic
188C22×C4×D11C2311yescharacteristic
189C22×C4×D11C2311yescharacteristic
190C22×C4×D11C2311yescharacteristic
191C22×C4×D11C2311yescharacteristic
192C22×C4×D11C2311yescharacteristic
193C22×C4×D11C2311yescharacteristic
194C22×Dic22C2311yescharacteristic
195C22×Dic22C2311yescharacteristic
196C22×Dic22C2311yescharacteristic
197C22×Dic22C2311yescharacteristic
198C22×Dic22C2311yescharacteristic
199C2×C11×C4⋊C4C2311yescharacteristic
200C2×C11×C4⋊C4C2311yescharacteristic
201C2×C11×C4⋊C4C2311yescharacteristic
202C2×C11×C4⋊C4C2311yescharacteristic
203C2×C11×C4⋊C4C2311yescharacteristic
204C2×C11×C4⋊C4C2311yescharacteristic
205C2×C11×C4⋊C4C2311yescharacteristic
206C2×C11×C4⋊C4C2311yescharacteristic
207C2×C11×C4⋊C4C2311yescharacteristic
208C2×C11×C4⋊C4C2311yescharacteristic
209C2×C11×C4⋊C4C2311yescharacteristic
210C2×C11×C4⋊C4C2311yescharacteristic
211C2×C11×C4⋊C4C2311yescharacteristic
212C2×C11×C4⋊C4C2311yescharacteristic
213C2×C42×C11C2311yescharacteristic
214C2×C42×C11C2311yescharacteristic
215C2×C42×C11C2311yescharacteristic
216C2×C42×C11C2311yescharacteristic
217C2×C42×C11C2311yescharacteristic
218C2×(C2×D11)⋊C4C2311yescharacteristic
219C2×(C2×D11)⋊C4C2311yescharacteristic
220C2×(C2×D11)⋊C4C2311yescharacteristic
221C2×(C2×D11)⋊C4C2311yescharacteristic
222C2×(C2×D11)⋊C4C2311yescharacteristic
223C2×(C2×D11)⋊C4C2311yescharacteristic
224C2×(C2×D11)⋊C4C2311yescharacteristic
225C2×(C2×D11)⋊C4C2311yescharacteristic
226C2×(C2×D11)⋊C4C2311yescharacteristic
227C2×(C2×D11)⋊C4C2311yescharacteristic
228C2×(C2×D11)⋊C4C2311yescharacteristic
229C2×(C2×D11)⋊C4C2311yescharacteristic
230C2×(C2×D11)⋊C4C2311yescharacteristic
231C2×(C2×D11)⋊C4C2311yescharacteristic
232C2×(C2×D11)⋊C4C2311yescharacteristic
233C2×(C2×D11)⋊C4C2311yescharacteristic
234C2×(C2×D11)⋊C4C2311yescharacteristic
235C2×(C2×D11)⋊C4C2311yescharacteristic
236C2×(C2×D11)⋊C4C2311yescharacteristic
237C2×(C2×D11)⋊C4C2311yescharacteristic
238C2×(C2×D11)⋊C4C2311yescharacteristic
239C2×(C2×D11)⋊C4C2311yescharacteristic
240C2×C4⋊Dic11C2311yescharacteristic
241C2×C4⋊Dic11C2311yescharacteristic
242C2×C4⋊Dic11C2311yescharacteristic
243C2×C4⋊Dic11C2311yescharacteristic
244C2×C4⋊Dic11C2311yescharacteristic
245C2×C4⋊Dic11C2311yescharacteristic
246C2×C4⋊Dic11C2311yescharacteristic
247C2×C4⋊Dic11C2311yescharacteristic
248C2×Dic11⋊C4C2311yescharacteristic
249C2×Dic11⋊C4C2311yescharacteristic
250C2×Dic11⋊C4C2311yescharacteristic
251C2×Dic11⋊C4C2311yescharacteristic
252C2×Dic11⋊C4C2311yescharacteristic
253C2×Dic11⋊C4C2311yescharacteristic
254C2×Dic11⋊C4C2311yescharacteristic
255C2×Dic11⋊C4C2311yescharacteristic
256C2×Dic11⋊C4C2311yescharacteristic
257C2×Dic11⋊C4C2311yescharacteristic
258C2×Dic11⋊C4C2311yescharacteristic
259C2×Dic11⋊C4C2311yescharacteristic
260C2×Dic11⋊C4C2311yescharacteristic
261C2×Dic11⋊C4C2311yescharacteristic
262C2×Dic11⋊C4C2311yescharacteristic
263C2×Dic11⋊C4C2311yescharacteristic
264C2×Dic11⋊C4C2311yescharacteristic
265C2×Dic11⋊C4C2311yescharacteristic
266C2×Dic11⋊C4C2311yescharacteristic
267C2×Dic11⋊C4C2311yescharacteristic
268C2×Dic11⋊C4C2311yescharacteristic
269C2×Dic11⋊C4C2311yescharacteristic
270C2×C4×Dic11C2311yescharacteristic
271C2×C4×Dic11C2311yescharacteristic
272C2×C4×Dic11C2311yescharacteristic
273C2×C4×Dic11C2311yescharacteristic
274C2×C4×Dic11C2311yescharacteristic
275C2×C4×Dic11C2311yescharacteristic
276C2×C4×Dic11C2311yescharacteristic
277C2×C4×Dic11C2311yescharacteristic
278#66949—42no—
279#66949—42no—
280#66942—42no—
281#66941—42no—
282C4×D44Q818yescomplemented
283#66925—42no—
284C42×D11—42no—
285C11×#95C2311yescharacteristic
286C11×#95C2311yescharacteristic
287C11×#95C2311yescharacteristic
288C11×#95C2311yescharacteristic
289C11×#95C2311yescharacteristic
290C11×#95C2311yescharacteristic
291C11×#95C2311yescharacteristic
292C11×#95C2311yescharacteristic
293C11×#95C2311yescharacteristic
294C11×#95C2311yescharacteristic
295C11×#95C2311yescharacteristic
296C11×#95C2311yescharacteristic
297C11×#95C2311yescharacteristic
298C11×#95C2311yescharacteristic
299C11×#95C2311yescharacteristic
300C11×#95C2311yescharacteristic
301C11⋊#95C2311yescharacteristic
302C11⋊#95C2311yescharacteristic
303C11⋊#95C2311yescharacteristic
304C11⋊#95C2311yescharacteristic
305C11⋊#95C2311yescharacteristic
306C11⋊#95C2311yescharacteristic
307C11⋊#95C2311yescharacteristic
308C11⋊#95C2311yescharacteristic
309C11⋊#95C2311yescharacteristic
310C11⋊#95C2311yescharacteristic
311C11⋊#95C2311yescharacteristic
312C11⋊#95C2311yescharacteristic
313C11⋊#95C2311yescharacteristic
314C11⋊#95C2311yescharacteristic
315C11⋊#95C2311yescharacteristic
316C11⋊#95C2311yescharacteristic
317C11⋊#95C2311yescharacteristic
318C11⋊#95C2311yescharacteristic
319C11⋊#95C2311yescharacteristic
320C11⋊#95C2311yescharacteristic
321C11⋊#95C2311yescharacteristic
322C11⋊#95C2311yescharacteristic
323C11⋊#95C2311yescharacteristic
324C11⋊#95C2311yescharacteristic
325C11⋊#95C2311yescharacteristic
326C11⋊#95C2311yescharacteristic
327C11⋊#95C2311yescharacteristic
328C11⋊#95C2311yescharacteristic
329C11⋊#95C2311yescharacteristic
330C11⋊#95C2311yescharacteristic
331C11⋊#95C2311yescharacteristic
332C11⋊#95C2311yescharacteristic
333C11⋊#95C2311yescharacteristic
334C11⋊#95C2311yescharacteristic
335C11⋊#95C2311yescharacteristic
336C11⋊#95C2311yescharacteristic
337C11⋊#95C2311yescharacteristic
338C11⋊#95C2311yescharacteristic
339C11⋊#95C2311yescharacteristic
340C11⋊#95C2311yescharacteristic
341C11⋊#95C2311yescharacteristic
342C11⋊#95C2311yescharacteristic
343C11⋊#95C2311yescharacteristic
344C11⋊#95C2311yescharacteristic
345C11⋊#95C2311yescharacteristic
346C11⋊#95C2311yescharacteristic
347C11⋊#95C2311yescharacteristic
348C11⋊#95C2311yescharacteristic
349#36755—111nomaximal, Sylow
350C23×D11C2411yescharacteristic
351C23×D11C2411yescharacteristic
352C22×C4×C11C2411yescharacteristic
353C22×C4×C11C2411yescharacteristic
354C22×C4×C11C2411yescharacteristic
355C22×C4×C11C2411yescharacteristic
356C22×C4×C11C2411yescharacteristic
357C22×C4×C11C2411yescharacteristic
358C22×C4×C11C2411yescharacteristic
359C22×C4×C11C2411yescharacteristic
360C22×C4×C11C2411yescharacteristic
361C22×C4×C11C2411yescharacteristic
362C22×C4×C11C2411yescharacteristic
363C22×C4×C11C2411yescharacteristic
364C22×C4×C11C2411yescharacteristic
365C22×C4×C11C2411yescharacteristic
366C22×C4×C11C2411yescharacteristic
367C22×Dic11C2411yescharacteristic
368C22×Dic11C2411yescharacteristic
369C22×Dic11C2411yescharacteristic
370C22×Dic11C2411yescharacteristic
371C22×Dic11C2411yescharacteristic
372C22×Dic11C2411yescharacteristic
373C22×Dic11C2411yescharacteristic
374C22×Dic11C2411yescharacteristic
375C22×Dic11C2411yescharacteristic
376C22×Dic11C2411yescharacteristic
377C22×Dic11C2411yescharacteristic
378C22×Dic11C2411yescharacteristic
379C22×Dic11C2411yescharacteristic
380C22×Dic11C2411yescharacteristic
381C2×D44—41no—
382C2×D44—41no—
383C2×D44C2×Q814yes—
384C2×C4×D11—22no—
385C2×C4×D11—41no—
386C2×C4×D11—41no—
387C2×C4×D11—41no—
388C2×C4×D11—41no—
389C2×C4×D11—41no—
390C2×C4×D11—41no—
391C2×C4×D11—41no—
392C2×C4×D11—41no—
393C2×C4×D11—41no—
394C2×C4×D11—41no—
395C2×C4×D11—41no—
396C2×C4×D11—41no—
397C2×C4×D11—41no—
398C2×C4×D11—41no—
399C2×C4×D11—41no—
400C2×C4×D11C2×Q814yes—
401C2×C4×D11C2×Q814yes—
402C2×Dic22—22no—
403C2×Dic22—41no—
404C2×Dic22—41no—
405C2×Dic22—41no—
406C2×Dic22—41no—
407C2×Dic22—41no—
408C2×Dic22—41no—
409C2×Dic22—41no—
410C2×Dic22—41no—
411C2×Dic22—41no—
412C2×Dic22—41no—
413C2×Dic22—41no—
414C2×Dic22—41no—
415C2×Dic22—41no—
416C2×Dic22—41no—
417C11×C4⋊C4—41no—
418C11×C4⋊C4—41no—
419C11×C4⋊C4—41no—
420C11×C4⋊C4—41no—
421C11×C4⋊C4—41no—
422C11×C4⋊C4—41no—
423C11×C4⋊C4—41no—
424C11×C4⋊C4—41no—
425C11×C4⋊C4—41no—
426C11×C4⋊C4—41no—
427C11×C4⋊C4—41no—
428C11×C4⋊C4—41no—
429C11×C4⋊C4—41no—
430C11×C4⋊C4—41no—
431C42×C11—41no—
432C42×C11—41no—
433C42×C11—41no—
434C42×C11—41no—
435C42×C11C2×Q814yes—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—41no—
438(C2×D11)⋊C4—41no—
439(C2×D11)⋊C4—41no—
440(C2×D11)⋊C4—41no—
441(C2×D11)⋊C4—41no—
442(C2×D11)⋊C4—41no—
443(C2×D11)⋊C4—41no—
444(C2×D11)⋊C4—41no—
445(C2×D11)⋊C4—41no—
446(C2×D11)⋊C4—41no—
447(C2×D11)⋊C4—41no—
448(C2×D11)⋊C4—41no—
449(C2×D11)⋊C4—41no—
450(C2×D11)⋊C4—41no—
451(C2×D11)⋊C4—41no—
452(C2×D11)⋊C4—41no—
453(C2×D11)⋊C4—41no—
454(C2×D11)⋊C4—41no—
455(C2×D11)⋊C4—41no—
456(C2×D11)⋊C4C2×Q814yes—
457(C2×D11)⋊C4C2×Q814yes—
458C4⋊Dic11—22no—
459C4⋊Dic11—41no—
460C4⋊Dic11—41no—
461C4⋊Dic11—41no—
462C4⋊Dic11—41no—
463C4⋊Dic11—41no—
464C4⋊Dic11—41no—
465C4⋊Dic11C2×Q814yes—
466Dic11⋊C4—22no—
467Dic11⋊C4—22no—
468Dic11⋊C4—22no—
469Dic11⋊C4—41no—
470Dic11⋊C4—41no—
471Dic11⋊C4—41no—
472Dic11⋊C4—41no—
473Dic11⋊C4—41no—
474Dic11⋊C4—41no—
475Dic11⋊C4—41no—
476Dic11⋊C4—41no—
477Dic11⋊C4—41no—
478Dic11⋊C4—41no—
479Dic11⋊C4—41no—
480Dic11⋊C4—41no—
481Dic11⋊C4—41no—
482Dic11⋊C4—41no—
483Dic11⋊C4—41no—
484Dic11⋊C4—41no—
485Dic11⋊C4—41no—
486Dic11⋊C4—41no—
487Dic11⋊C4—41no—
488C4×Dic11—22no—
489C4×Dic11—22no—
490C4×Dic11—41no—
491C4×Dic11—41no—
492C4×Dic11—41no—
493C4×Dic11—41no—
494C4×Dic11—41no—
495C4×Dic11—41no—
496#2855—111no—
497#2851—111no—
498#2805—111no—
499#2804—111no—
500#2790—111no—
501#2788—111no—
502#2788—111no—
503#2784—111no—
504#2780—111no—
505#2774—111no—
506#2763—111no—
507#2763—111no—
508#2755—111no—
509#2742—111no—
510#2729—111no—
511#2720—111no—
512#2713—111no—
513#2692—111no—
514#2665—111no—
515#2665—111no—
516#2612—111no—
517#2607—111no—
518#2605—111no—
519#2605—111no—
520#2570D1111yescharacteristic, complemented
521#2569—111no—
522#2439—111no—
523#2438—111no—
524#2319—111no—
525#2318—111no—
526#2290—111no—
527C23×C11C2511yescharacteristic
528C22×D11—21no—
529C22×D11—21no—
530C22×D11—21no—
531C22×D11—21no—
532C22×D11—21no—
533C22×D11—21no—
534C22×D11—21no—
535C22×D11—21no—
536C22×D11—21no—
537C22×D11—21no—
538C22×D11—21no—
539C22×D11—21no—
540C22×D11C22×Q812yes—
541C22×D11C22×Q812yes—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—21no—
548C2×C4×C11—21no—
549C2×C4×C11—21no—
550C2×C4×C11—21no—
551C2×C4×C11—21no—
552C2×C4×C11—21no—
553C2×C4×C11—21no—
554C2×C4×C11—21no—
555C2×C4×C11—21no—
556C2×C4×C11—21no—
557C2×C4×C11—21no—
558C2×C4×C11—21no—
559C2×C4×C11—21no—
560C2×C4×C11—21no—
561C2×C4×C11—21no—
562C2×C4×C11—21no—
563C2×C4×C11—21no—
564C2×C4×C11—21no—
565C2×C4×C11—21no—
566C2×C4×C11—21no—
567C2×C4×C11—21no—
568C2×C4×C11—21no—
569C2×C4×C11—21no—
570C2×C4×C11—21no—
571C2×C4×C11—21no—
572C2×C4×C11—21no—
573C2×C4×C11—21no—
574C2×C4×C11—21no—
575C2×C4×C11—21no—
576C2×C4×C11—21no—
577C2×C4×C11—21no—
578C2×C4×C11—21no—
579C2×C4×C11—21no—
580C2×C4×C11—21no—
581C2×C4×C11—21no—
582C2×C4×C11—21no—
583C2×C4×C11—21no—
584C2×C4×C11C22×Q812yes—
585C2×C4×C11C22×Q812yes—
586C2×C4×C11C22×Q812yes—
587C2×Dic11—21no—
588C2×Dic11—21no—
589C2×Dic11—21no—
590C2×Dic11—21no—
591C2×Dic11—21no—
592C2×Dic11—21no—
593C2×Dic11—21no—
594C2×Dic11—21no—
595C2×Dic11—21no—
596C2×Dic11—21no—
597C2×Dic11—21no—
598C2×Dic11—21no—
599C2×Dic11—21no—
600C2×Dic11—21no—
601C2×Dic11—21no—
602C2×Dic11—21no—
603C2×Dic11—21no—
604C2×Dic11—21no—
605C2×Dic11—21no—
606C2×Dic11—21no—
607C2×Dic11—21no—
608C2×Dic11—21no—
609C2×Dic11—21no—
610C2×Dic11—21no—
611C2×Dic11—21no—
612C2×Dic11—21no—
613C2×Dic11—21no—
614C2×Dic11—21no—
615C2×Dic11—21no—
616C2×Dic11—21no—
617C2×Dic11—21no—
618C2×Dic11—21no—
619C2×Dic11—21no—
620C2×Dic11—21no—
621C2×Dic11—21no—
622C2×Dic11—21no—
623C2×Dic11—21no—
624C2×Dic11—21no—
625C2×Dic11—21no—
626C2×Dic11C22×Q812yes—
627C2×Dic11C22×Q812yes—
628C2×Dic11H(5,𝔽2)12yes—
629D44—44no—
630C4×D11—44no—
631C4×D11—44no—
632C4×D11—44no—
633C4×D11—44no—
634C4×D11—82no—
635C4×D11—82no—
636Dic22—82no—
637Dic22—82no—
638Dic22—82no—
639Dic22—82no—
640Dic22—82no—
641C2×C4⋊Q8—111no—
642C2×#125—111no—
643C2×C22⋊Q8—111no—
644C2×C22⋊Q8—111no—
645C2×C4×D4—111no—
646C2×#117—111no—
647C22×C42—111no—
648#400—111no—
649#400—111no—
650#400—111no—
651#400—111no—
652#400—111no—
653#400—111no—
654#400—111no—
655#400—111no—
656#400—111no—
657#400—111no—
658#400—111no—
659#400—111no—
660#400C2×D1111yescharacteristic
661#400C2×D1111yescharacteristic
662#399—111no—
663#399—111no—
664#398—111no—
665#398—111no—
666#398—111no—
667#398—111no—
668#398—111no—
669#398—111no—
670#398C2×D1111yescharacteristic
671#398C2×D1111yescharacteristic
672#396—111no—
673#396—111no—
674#396—111no—
675#396—111no—
676#396—111no—
677#396—111no—
678#395—111no—
679#395—111no—
680#395—111no—
681#395—111no—
682#395—111no—
683#395—111no—
684#395—111no—
685#395—111no—
686#395—111no—
687#395—111no—
688#393—111no—
689#393—111no—
690#393—111no—
691#393—111no—
692#393—111no—
693#393—111no—
694#393—111no—
695#393—111no—
696#391—111no—
697#391—111no—
698#391—111no—
699#391—111no—
700#391—111no—
701#391—111no—
702#391—111no—
703#391—111no—
704#391—111no—
705#391—111no—
706#391—111no—
707#391—111no—
708#391—111no—
709#390—111no—
710#390—111no—
711#389—111no—
712#389—111no—
713#389—111no—
714#389—111no—
715#389—111no—
716#389—111no—
717#389—111no—
718#389—111no—
719#389—111no—
720#389C2×D1111yescharacteristic
721#389C2×D1111yescharacteristic
722#388—111no—
723#388—111no—
724#388—111no—
725#388—111no—
726#388—111no—
727#388—111no—
728#388—111no—
729#388—111no—
730#387—111no—
731#387—111no—
732#387—111no—
733#387—111no—
734#387—111no—
735#387—111no—
736#387—111no—
737#387—111no—
738#387—111no—
739#387—111no—
740#387—111no—
741#387—111no—
742#387—111no—
743#387—111no—
744#387—111no—
745#387—111no—
746#387—111no—
747#387—111no—
748#387—111no—
749#387—111no—
750#387C2×D1111yescharacteristic
751#387C2×D1111yescharacteristic
752#387C2×D1111yescharacteristic
753#387C2×D1111yescharacteristic
754#386—111no—
755#386—111no—
756#386—111no—
757#386—111no—
758#385—111no—
759#385—111no—
760#385—111no—
761#385—111no—
762#385—111no—
763#385—111no—
764#385—111no—
765#385—111no—
766#385—111no—
767#385—111no—
768#385—111no—
769#385—111no—
770#385—111no—
771#385—111no—
772#384C2×D1111yescharacteristic
773#383—111no—
774#382—111no—
775#382—111no—
776#382C2×D1111yescharacteristic
777#382C2×D1111yescharacteristic
778#381—111no—
779#381—111no—
780#381—111no—
781#380—111no—
782#380—111no—
783#380—111no—
784#380—111no—
785#380—111no—
786#380—111no—
787#380—111no—
788C4×C4⋊C4C2×D1111yescharacteristic
789C4×C4⋊C4C2×D1111yescharacteristic
790C4×C22⋊C4—111no—
791C4×C22⋊C4—111no—
792C4×C22⋊C4—111no—
793#376—111no—
794#376—111no—
795C2×#95—111no—
796C22×C11C23×Q811yescharacteristic
797C22×C11C2×H(5,𝔽2)11yescharacteristic
798C22×C11#58511yescharacteristic
799C22×C11#58511yescharacteristic
800C22×C11#58511yescharacteristic
801C22×C11#58511yescharacteristic
802C22×C11#58511yescharacteristic
803C2×D11—22no—
804C2×D11—22no—
805C2×D11—22no—
806C2×D11—22no—
807C2×D11—22no—
808C2×D11—22no—
809C2×D11—41no—
810C2×D11—41no—
811C2×D11—41no—
812C2×D11—41no—
813C2×D11—41no—
814C2×D11—41no—
815C2×D11—41no—
816C2×D11—41no—
817C4×C11—22no—
818C4×C11—22no—
819C4×C11—22no—
820C4×C11—41no—
821C4×C11—41no—
822C4×C11—41no—
823C4×C11—41no—
824C4×C11—41no—
825C4×C11—41no—
826C4×C11—41no—
827C4×C11—41no—
828C4×C11—41no—
829C4×C11—41no—
830C4×C11—41no—
831C4×C11—41no—
832Dic11—22no—
833Dic11—22no—
834Dic11—22no—
835Dic11—41no—
836Dic11—41no—
837Dic11—41no—
838Dic11—41no—
839Dic11—41no—
840Dic11—41no—
841Dic11—41no—
842Dic11—41no—
843Dic11—41no—
844Dic11—41no—
845Dic11—41no—
846C22×Q8—111no—
847C22×Q8—111no—
848C22×Q8—111no—
849C22×Q8—111no—
850C22×Q8—111no—
851C22×D4—111no—
852C23×C4—111no—
853C23×C4—111no—
854C23×C4—111no—
855C23×C4—111no—
856C23×C4—111no—
857C23×C4—111no—
858C4⋊Q8—442no—
859#125—442no—
860C22⋊Q8—442no—
861C22⋊Q8—442no—
862C4×D4—118no—
863#117—442no—
864C2×C4⋊C4—111no—
865C2×C4⋊C4—111no—
866C2×C4⋊C4—111no—
867C2×C4⋊C4—111no—
868C2×C4⋊C4—111no—
869C2×C4⋊C4—111no—
870C2×C4⋊C4—111no—
871C2×C4⋊C4—111no—
872C2×C4⋊C4—111no—
873C2×C4⋊C4—111no—
874C2×C4⋊C4—111no—
875C2×C4⋊C4—111no—
876C2×C4⋊C4—111no—
877C2×C4⋊C4—111no—
878C2×C4⋊C4—111no—
879C2×C4⋊C4—111no—
880C2×C4⋊C4—111no—
881C2×C4⋊C4—111no—
882C2×C4⋊C4—111no—
883C2×C4⋊C4—111no—
884C2×C4⋊C4—111no—
885C2×C4⋊C4—111no—
886C2×C4⋊C4—111no—
887C2×C4⋊C4—111no—
888C2×C4⋊C4—111no—
889C2×C4⋊C4—111no—
890C2×C4⋊C4—111no—
891C2×C4⋊C4—111no—
892C2×C4⋊C4—111no—
893C2×C4⋊C4—111no—
894C2×C4⋊C4C22×D1111yescharacteristic
895C2×C4⋊C4C22×D1111yescharacteristic
896C2×C4⋊C4C22×D1111yescharacteristic
897C2×C4⋊C4C22×D1111yescharacteristic
898C2×C4⋊C4C22×D1111yescharacteristic
899C2×C4⋊C4C22×D1111yescharacteristic
900C2×C4⋊C4C22×D1111yescharacteristic
901C2×C4⋊C4C22×D1111yescharacteristic
902C2×C4⋊C4C22×D1111yescharacteristic
903C2×C4⋊C4C22×D1111yescharacteristic
904C2×C4⋊C4C22×D1111yescharacteristic
905C2×C4⋊C4C22×D1111yescharacteristic
906C2×C4⋊C4C22×D1111yescharacteristic
907C2×C4⋊C4C22×D1111yescharacteristic
908C2×C22⋊C4—111no—
909C2×C22⋊C4—111no—
910C2×C22⋊C4—111no—
911C2×C22⋊C4—111no—
912C2×C22⋊C4—111no—
913C2×C22⋊C4—111no—
914C2×C22⋊C4—111no—
915C2×C22⋊C4—111no—
916C2×C22⋊C4—111no—
917C2×C22⋊C4—111no—
918C2×C22⋊C4—111no—
919C2×C22⋊C4—111no—
920C2×C22⋊C4—111no—
921C2×C22⋊C4—111no—
922C2×C22⋊C4—111no—
923C2×C22⋊C4—111no—
924C2×C22⋊C4—111no—
925C2×C22⋊C4—111no—
926C2×C22⋊C4—111no—
927C2×C22⋊C4—111no—
928C2×C22⋊C4—111no—
929C2×C22⋊C4—111no—
930C2×C42—111no—
931C2×C42—111no—
932C2×C42—111no—
933C2×C42—111no—
934C2×C42—111no—
935C2×C42—111no—
936C2×C42—111no—
937C2×C42—111no—
938C2×C42—442no—
939C2×C42C22×D1111yescharacteristic
940C2×C42C22×D1111yescharacteristic
941C2×C42C22×D1111yescharacteristic
942C2×C42C22×D1111yescharacteristic
943C2×C42C22×D1111yescharacteristic
944#95—111no—
945#95—111no—
946#95—111no—
947#95—111no—
948#95—111no—
949#95—111no—
950#95—111no—
951#95—111no—
952#95—111no—
953#95—111no—
954#95—111no—
955#95—111no—
956#95—111no—
957#95—111no—
958#95—111no—
959#95—111no—
960#95—111no—
961#95—111no—
962#95—111no—
963#95—111no—
964#95—111no—
965#95—111no—
966#95—111no—
967#95—111no—
968#95—111no—
969#95—111no—
970#95—111no—
971#95—111no—
972#95—111no—
973#95—111no—
974#95—111no—
975#95—111no—
976#95—111no—
977#95—111no—
978#95—111no—
979#95—111no—
980#95—111no—
981#95—111no—
982#95—111no—
983#95—111no—
984#95—111no—
985#95—111no—
986#95—111no—
987#95—111no—
988#95—111no—
989#95—111no—
990#95—111no—
991#95—111no—
992#95C22×D1111yescharacteristic
993#95C22×D1111yescharacteristic
994#95C22×D1111yescharacteristic
995#95C22×D1111yescharacteristic
996#95C22×D1111yescharacteristic
997#95C22×D1111yescharacteristic
998#95C22×D1111yescharacteristic
999#95C22×D1111yescharacteristic
1000#95C22×D1111yescharacteristic
1001#95C22×D1111yescharacteristic
1002#95C22×D1111yescharacteristic
1003#95C22×D1111yescharacteristic
1004#95C22×D1111yescharacteristic
1005#95C22×D1111yescharacteristic
1006#95C22×D1111yescharacteristic
1007#95C22×D1111yescharacteristic
1008C2×C11#345811yescharacteristic
1009C2×C11#350111yescharacteristic
1010C2×C11#350411yescharacteristic
1011C2×C11#353311yescharacteristic
1012C2×C11#354011yescharacteristic
1013C2×C11#356611yescharacteristic
1014C2×C11#356811yescharacteristic
1015D11—42no—
1016D11—42no—
1017C24—111no—
1018C24—111no—
1019C2×Q8—222no—
1020C2×Q8—441no—
1021C2×Q8—441no—
1022C2×Q8—441no—
1023C2×Q8—441no—
1024C2×Q8—441no—
1025C2×Q8—441no—
1026C2×Q8—441no—
1027C2×Q8—441no—
1028C2×Q8—441no—
1029C2×Q8—441no—
1030C2×Q8—441no—
1031C2×Q8—441no—
1032C2×Q8—441no—
1033C2×Q8—441no—
1034C2×D4—114no—
1035C2×D4—441no—
1036C2×D4—441no—
1037C22×C4—111no—
1038C22×C4—111no—
1039C22×C4—111no—
1040C22×C4—114no—
1041C22×C4—114no—
1042C22×C4—111no—
1043C22×C4—111no—
1044C22×C4—111no—
1045C22×C4—111no—
1046C22×C4—111no—
1047C22×C4—111no—
1048C22×C4—111no—
1049C22×C4—111no—
1050C22×C4—111no—
1051C22×C4—111no—
1052C22×C4—111no—
1053C22×C4—222no—
1054C22×C4—441no—
1055C22×C4—441no—
1056C22×C4—441no—
1057C22×C4—441no—
1058C22×C4—441no—
1059C22×C4—441no—
1060C22×C4—441no—
1061C22×C4—441no—
1062C22×C4—441no—
1063C22×C4—441no—
1064C22×C4—441no—
1065C22×C4—441no—
1066C22×C4—441no—
1067C22×C4—441no—
1068C22×C4—441no—
1069C22×C4C23×D1111yescharacteristic
1070C22×C4C23×D1111yescharacteristic
1071C22×C4C23×D1111yescharacteristic
1072C22×C4C23×D1111yescharacteristic
1073C22×C4C23×D1111yescharacteristic
1074C22×C4C23×D1111yescharacteristic
1075C22×C4C23×D1111yescharacteristic
1076C22×C4C23×D1111yescharacteristic
1077C22×C4C23×D1111yescharacteristic
1078C22×C4C23×D1111yescharacteristic
1079C22×C4C23×D1111yescharacteristic
1080C22×C4C23×D1111yescharacteristic
1081C22×C4C23×D1111yescharacteristic
1082C22×C4C23×D1111yescharacteristic
1083C22×C4C23×D1111yescharacteristic
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—41no—
1092C4⋊C4—41no—
1093C4⋊C4—41no—
1094C4⋊C4—41no—
1095C4⋊C4—41no—
1096C4⋊C4—41no—
1097C4⋊C4—41no—
1098C4⋊C4—114no—
1099C4⋊C4—222no—
1100C4⋊C4—222no—
1101C4⋊C4—222no—
1102C4⋊C4—222no—
1103C4⋊C4—441no—
1104C4⋊C4—441no—
1105C4⋊C4—441no—
1106C4⋊C4—441no—
1107C4⋊C4—441no—
1108C4⋊C4—441no—
1109C4⋊C4—441no—
1110C4⋊C4—441no—
1111C4⋊C4—441no—
1112C4⋊C4—441no—
1113C4⋊C4—441no—
1114C4⋊C4—441no—
1115C4⋊C4—441no—
1116C4⋊C4—441no—
1117C4⋊C4—441no—
1118C4⋊C4—441no—
1119C4⋊C4—441no—
1120C4⋊C4—441no—
1121C4⋊C4—441no—
1122C4⋊C4—441no—
1123C4⋊C4—441no—
1124C4⋊C4—441no—
1125C4⋊C4—441no—
1126C4⋊C4—441no—
1127C4⋊C4—441no—
1128C22⋊C4—114no—
1129C22⋊C4—114no—
1130C22⋊C4—222no—
1131C22⋊C4—441no—
1132C22⋊C4—441no—
1133C22⋊C4—441no—
1134C22⋊C4—441no—
1135C22⋊C4—441no—
1136C22⋊C4—441no—
1137C22⋊C4—441no—
1138C22⋊C4—441no—
1139C22⋊C4—441no—
1140C22⋊C4—441no—
1141C22⋊C4—441no—
1142C22⋊C4—441no—
1143C22⋊C4—441no—
1144C22⋊C4—441no—
1145C22⋊C4—441no—
1146C22⋊C4—441no—
1147C22⋊C4—441no—
1148C22⋊C4—441no—
1149C22⋊C4—441no—
1150C42—41no—
1151C42—41no—
1152C42—41no—
1153C42—41no—
1154C42—222no—
1155C42—222no—
1156C42—441no—
1157C42—441no—
1158C42—441no—
1159C42—441no—
1160C42—441no—
1161C42—441no—
1162C42Q8×D1114yes—
1163C11#3675511yescharacteristic, complemented, Sylow
1164C23—112no—
1165C23—112no—
1166C23—221no—
1167C23—221no—
1168C23—221no—
1169C23—221no—
1170C23—221no—
1171C23—221no—
1172C23—221no—
1173C23—221no—
1174C23—221no—
1175C23—221no—
1176C23—221no—
1177C23—221no—
1178C23C24×D1111yescharacteristic
1179Q8—882no—
1180Q8—882no—
1181Q8—882no—
1182Q8—882no—
1183Q8—882no—
1184D4—444no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—112no—
1228C2×C4—112no—
1229C2×C4—112no—
1230C2×C4—221no—
1231C2×C4—221no—
1232C2×C4—221no—
1233C2×C4—221no—
1234C2×C4—221no—
1235C2×C4—221no—
1236C2×C4—221no—
1237C2×C4—221no—
1238C2×C4—221no—
1239C2×C4—221no—
1240C2×C4—221no—
1241C2×C4—221no—
1242C2×C4—221no—
1243C2×C4—221no—
1244C2×C4—221no—
1245C2×C4—221no—
1246C2×C4—221no—
1247C2×C4—221no—
1248C2×C4—221no—
1249C2×C4—221no—
1250C2×C4—221no—
1251C2×C4—221no—
1252C2×C4—221no—
1253C2×C4—221no—
1254C2×C4—221no—
1255C2×C4—221no—
1256C2×C4—221no—
1257C2×C4—221no—
1258C2×C4—221no—
1259C2×C4—221no—
1260C2×C4—221no—
1261C2×C4—221no—
1262C2×C4—221no—
1263C2×C4—221no—
1264C2×C4—221no—
1265C2×C4—221no—
1266C2×C4—221no—
1267C2×C4—221no—
1268C2×C4—221no—
1269C2×C4—444no—
1270C2×C4—444no—
1271C2×C4—444no—
1272C2×C4—444no—
1273C2×C4—882no—
1274C2×C4—882no—
1275C2×C4C2×Q8×D1112yes—
1276C2×C4C2×Q8×D1112yes—
1277C2×C4C2×Q8×D1112yes—
1278C22—222no—
1279C22—222no—
1280C22—222no—
1281C22—222no—
1282C22—222no—
1283C22—222no—
1284C22—441no—
1285C22—441no—
1286C22—441no—
1287C22—441no—
1288C22—441no—
1289C22—441no—
1290C22—441no—
1291C22—441no—
1292C22C22×Q8×D1111yescharacteristic
1293C22#1062345311yescharacteristic
1294C22#1062345311yescharacteristic
1295C22#1062345311yescharacteristic
1296C22#1062345311yescharacteristic
1297C22D11×H(5,𝔽2)11yescharacteristic
1298C22#1062345711yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—222no—
1315C4—222no—
1316C4—222no—
1317C4—441no—
1318C4—441no—
1319C4—441no—
1320C4—441no—
1321C4—441no—
1322C4—441no—
1323C4—441no—
1324C4—441no—
1325C4—441no—
1326C4—441no—
1327C4—441no—
1328C2—442no—
1329C2—442no—
1330C2#1308201911yescharacteristic
1331C2#1308241811yescharacteristic
1332C2#1308244011yescharacteristic
1333C2#1308277411yescharacteristic
1334C2#1308287911yescharacteristic
1335C2#1308329811yescharacteristic
1336C2#1308331111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2570C2
prime radicalC22×D44C23
hypercenter#2570D11
hypocenterC11#36755
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2570

Complements

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

NH ≅ G/Ntype
1. #13076951C2semidirect
2. #13076923C2semidirect
3. #13076568C2semidirect
5. #13076382C2semidirect
6. #13076365C2semidirect
7. #13076360C2semidirect
10. #13076173C2semidirect
11. #13076029C2semidirect
12. #13076029C2semidirect
13. #13075929C2semidirect
14. #13075743C2semidirect
15. #13075593C2semidirect
16. #13075491C2semidirect
17. #13075404C2semidirect
19. #13074792C2semidirect
20. #13074792C2semidirect
21. #13074324C2semidirect
22. #13074280C2semidirect
23. #13074259C2semidirect
24. #13074259C2semidirect
25. #13073839C2semidirect
26. #13072306C2semidirect
27. #13072291C2semidirect
31. C11×#2570C2semidirect
282. C4×D44Q8semidirect
520. #2570D11semidirect
1163. C11#36755semidirect

Maximal subgroups

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

subgroupindex
#130769512
#130769232
#130765682
#130765612
#130763822
#130763652
#130763602
#130763162
#130762702
#130761732
#130760292
#130759292
#130757432
#130755932
#130754912
#130754042
#130751142
#130747922
#130743242
#130742802
#130742592
#130738392
#130723062
#130722912
#130712542
#130712522
#130710572
C11×#25702
#3675511