Finite Group Databasebeta

← #14917197

Subgroups — #14917197

Order 2816.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic
2#13071768C212yesmaximal, complemented
3#13071767C212yesmaximal, complemented
4#13071665C212yesmaximal, complemented
5#13071654C211yesmaximal, characteristic, complemented
6#13071651C212yesmaximal, complemented
7#13071643C211yesmaximal, characteristic, complemented
8#13071632C211yesmaximal, characteristic, complemented
9#13071621C211yesmaximal, characteristic, complemented
10#13071495C211yesmaximal, characteristic, complemented
11#13071487C211yesmaximal, characteristic, complemented
12#13071453C211yesmaximal, characteristic, complemented
13#13071444C211yesmaximal, characteristic, complemented
14#13071382C212yesmaximal, complemented
15#13071371C212yesmaximal, complemented
16#13071348C212yesmaximal, complemented
17#13071306C212yesmaximal, complemented
18#13071305C211yesmaximal, characteristic, complemented
19#13071294C211yesmaximal, characteristic, complemented
20#13071144C211yesmaximal, characteristic, complemented
21#13071122C211yesmaximal, characteristic, complemented
22#13071107C211yesmaximal, characteristic, complemented
23C11×#2311C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28#10623364C4116yescomplemented
29C2×#66999C2212yes—
30C2×#66992C2212yes—
31C2×#66992C2212yes—
32C2×#66991C2212yes—
33C2×#66983C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×C4×C22⋊D11C2212yes—
36C2×#66979C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C2×#66977C2211yescharacteristic
39C2×#66977C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C2×#66946C2211yescharacteristic
42C2×#66946C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×#66940C2211yescharacteristic
45C2×(C22⋊D11)⋊C4C2212yes—
46C2×#66930C2212yes—
47C11×#391C2212yes—
48C11×#390C2212yes—
49C11×#386C2212yes—
50C11×#386C2212yes—
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic
53C11×#380C2211yescharacteristic
54C11×#380C2211yescharacteristic
55#10622843C2211yescharacteristic
56#10622843C2211yescharacteristic
57#10622834C2211yescharacteristic
58#10622834C2211yescharacteristic
59#10622833C2211yescharacteristic
60#10622833C2211yescharacteristic
61#10622833C2211yescharacteristic
62#10622833C2211yescharacteristic
63#10622826C2212yes—
64#10622823C2212yes—
65C4×C22⋊Dic11C2211yescharacteristic
66C4×C22⋊Dic11C2211yescharacteristic
67C4×C22⋊Dic11C2211yescharacteristic
68C4×C22⋊Dic11C2211yescharacteristic
69C4×C22⋊Dic11C2212yes—
70#10622603C2212yes—
71#10622602C2212yes—
72#10622601C2211yescharacteristic
73#10622601C2211yescharacteristic
74#10622591C2212yes—
75C4⋊C4×Dic11C2211yescharacteristic
76C4⋊C4×Dic11C2211yescharacteristic
77C4⋊C4×Dic11C2211yescharacteristic
78C4⋊C4×Dic11C2211yescharacteristic
79#10622587C2211yescharacteristic
80#10622587C2211yescharacteristic
81#10622586C2211yescharacteristic
82#10622586C2211yescharacteristic
83#10622586C2211yescharacteristic
84#10622586C2211yescharacteristic
85#10622585C2212yes—
86#10622571C2212yes—
87#10622570C2212yes—
88#10622570C2212yes—
89#10622570C2212yes—
90#10622570C2212yes—
91#10622569C2212yes—
92#10622569C2212yes—
93#10622569C2212yes—
94#10622569C2212yes—
95#10622559C2212yes—
96#10622558C2212yes—
97#10622558C2212yes—
98#10622557C2212yes—
99#10622557C2212yes—
100#10622556C2212yes—
101#10622555C2212yes—
102C22⋊C4×Dic11C2212yes—
103C22⋊C4×Dic11C2212yes—
104#10622553C2212yes—
105C4×(C2×D11)⋊C4C2212yes—
106#10622546C2212yes—
107C4×Dic11⋊C4C2212yes—
108#10622283C2212yes—
109#10622282C2212yes—
110#10622281C2212yes—
111#10622280C2212yes—
112#10622279C2212yes—
113#10622279C2212yes—
114#10622277C2212yes—
115D11×#95C2212yes—
116#10622268C2212yes—
117#10622267C2212yes—
118#10622267C2212yes—
119#10622266C2212yes—
120#10622266C2212yes—
121#10622265C2212yes—
122#10622262C2212yes—
123#10622260C2212yes—
124C2×C11×#41—42no—
125C2×C11×#41—42no—
126C2×C11×#41C2×C418yescomplemented
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C23×Dic11C2311yescharacteristic
139C23×Dic11C2311yescharacteristic
140C23×Dic11C2312yes—
141C2×#4339—42no—
142C2×#4339—42no—
143C2×#4339C2×C418yescomplemented
144C22×D44C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×Dic22C2311yescharacteristic
149C11×#117—42no—
150C2×C11×C4⋊C4—42no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C42×C11C2312yes—
162C2×C22⋊Dic11C2311yescharacteristic
163C2×C22⋊Dic11C2311yescharacteristic
164C2×C22⋊Dic11C2311yescharacteristic
165C2×C22⋊Dic11C2311yescharacteristic
166C2×C22⋊Dic11C2311yescharacteristic
167C2×C22⋊Dic11C2311yescharacteristic
168C2×C22⋊Dic11C2311yescharacteristic
169C2×C22⋊Dic11C2311yescharacteristic
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174#66999C2×C4116yescomplemented
175#66992C2×C4116yescomplemented
176#66992C2×C4116yescomplemented
177#66991C2×C4116yescomplemented
178#66983C2×C418yescomplemented
179#66983C2×C418yescomplemented
180C4×C22⋊D11—44no—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189#66979—42no—
190C2×C4⋊Dic11C2×C418yescomplemented
191C2×C4⋊Dic11C2311yescharacteristic
192C2×C4⋊Dic11C2311yescharacteristic
193C2×C4⋊Dic11C2312yes—
194C2×C4⋊Dic11C2311yescharacteristic
195C2×C4⋊Dic11C2311yescharacteristic
196#66977C2×C418yescomplemented
197#66977C2×C418yescomplemented
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×C4×Dic11—42no—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2312yes—
219#66946—42no—
220#66946—42no—
221#66940—42no—
222#66940—42no—
223(C22⋊D11)⋊C4—44no—
224#66930—44no—
225C11×#95C2312yes—
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249#34410—111nomaximal, Sylow
250C24×C11C2411yescharacteristic
251C24×C11C2411yescharacteristic
252C24×C11C2411yescharacteristic
253C23×D11C2412yes—
254C11×#41—416no—
255C2×Q8×C11—41no—
256C2×Q8×C11—41no—
257C2×Q8×C11C22×C414yes—
258C2×D4×C11—41no—
259C2×D4×C11—41no—
260C2×D4×C11—41no—
261C2×D4×C11—41no—
262C2×D4×C11—41no—
263C2×D4×C11—41no—
264C2×D4×C11C22×C414yes—
265C2×D4×C11C22×C414yes—
266C2×D4×C11C22×C414yes—
267C22×C4×C11—22no—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11C22×C414yes—
277C22×C4×C11C22×C414yes—
278C22×C4×C11C22×C414yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2412yes—
282C22×C4×C11C2412yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C2×C22⋊D11—42no—
288C2×C22⋊D11—42no—
289C2×C22⋊D11—42no—
290C2×C22⋊D11—42no—
291C2×C22⋊D11—42no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11C22×C418yes—
294C2×C22⋊D11C22×C418yes—
295C2×C22⋊D11C22×C418yes—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—42no—
299C22×Dic11—41no—
300C22×Dic11—41no—
301C22×Dic11—42no—
302C22×Dic11—41no—
303C22×Dic11—41no—
304C22×Dic11C22×C418yes—
305C22×Dic11C2411yescharacteristic
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2412yes—
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316#4339—416no—
317C2×D44—22no—
318C2×D44—22no—
319C2×D44C22×C414yes—
320C2×C4×D11—24no—
321C2×C4×D11—42no—
322C2×C4×D11—42no—
323C2×C4×D11—42no—
324C2×C4×D11—42no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11C22×C418yes—
329C2×Dic22—22no—
330C2×Dic22—22no—
331C2×Dic22C22×C414yes—
332C11×C4⋊C4—22no—
333C11×C4⋊C4—22no—
334C11×C4⋊C4—22no—
335C11×C4⋊C4—22no—
336C11×C4⋊C4—42no—
337C11×C22⋊C4—42no—
338C11×C22⋊C4—42no—
339C11×C22⋊C4—42no—
340C11×C22⋊C4—42no—
341C11×C22⋊C4—42no—
342C42×C11—42no—
343C22⋊Dic11—22no—
344C22⋊Dic11—22no—
345C22⋊Dic11—22no—
346C22⋊Dic11—22no—
347C22⋊Dic11—41no—
348C22⋊Dic11—41no—
349C22⋊Dic11—41no—
350C22⋊Dic11—41no—
351C22⋊Dic11—41no—
352C22⋊Dic11—41no—
353C22⋊Dic11C22×C418yes—
354C22⋊Dic11C22×C418yes—
355(C2×D11)⋊C4—24no—
356(C2×D11)⋊C4—42no—
357(C2×D11)⋊C4—42no—
358(C2×D11)⋊C4—42no—
359(C2×D11)⋊C4—42no—
360(C2×D11)⋊C4—42no—
361(C2×D11)⋊C4C22×C418yes—
362(C2×D11)⋊C4C22×C418yes—
363C4⋊Dic11—41no—
364C4⋊Dic11—41no—
365C4⋊Dic11C22×C414yes—
366C4⋊Dic11C22×C414yes—
367C4⋊Dic11C22×C418yes—
368Dic11⋊C4—24no—
369Dic11⋊C4—42no—
370Dic11⋊C4—42no—
371Dic11⋊C4—42no—
372Dic11⋊C4—42no—
373Dic11⋊C4—42no—
374Dic11⋊C4C22×C418yes—
375Dic11⋊C4C22×C418yes—
376C4×Dic11—24no—
377C4×Dic11—22no—
378C4×Dic11—22no—
379C4×Dic11—22no—
380C4×Dic11—22no—
381C4×Dic11—42no—
382C4×Dic11—42no—
383C4×Dic11—42no—
384C4×Dic11—42no—
385C4×Dic11—41no—
386C4×Dic11—41no—
387C4×Dic11—42no—
388C2×#537—111no—
389#2377—112no—
390#2377—112no—
391#2364—112no—
392#2363—112no—
393#2363—111no—
394#2362—111no—
395#2361—111no—
396#2360—111no—
397#2345—111no—
398#2344—111no—
399#2341—111no—
400#2339—111no—
401#2333—112no—
402#2332—112no—
403#2329—112no—
404#2324—112no—
405#2324—111no—
406#2323—111no—
407#2311D1111yescharacteristic, complemented
408C4×C22⋊Q8—111no—
409C4×#121—111no—
410#2297—111no—
411C23×C11—21no—
412C23×C11—21no—
413C23×C11—21no—
414C23×C11—21no—
415C23×C11—21no—
416C23×C11—21no—
417C23×C11—21no—
418C23×C11—21no—
419C23×C11—21no—
420C23×C11—21no—
421C23×C11—21no—
422C23×C11—21no—
423C23×C11—21no—
424C23×C11—21no—
425C23×C11—21no—
426C23×C11—21no—
427C23×C11—21no—
428C23×C11—21no—
429C23×C11C23×C412yes—
430C23×C11C23×C412yes—
431C23×C11C23×C412yes—
432C23×C11C2511yescharacteristic
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11C23×C414yes—
440Q8×C11—44no—
441D4×C11—44no—
442D4×C11—44no—
443D4×C11—44no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—21no—
450C2×C4×C11—28no—
451C2×C4×C11—28no—
452C2×C4×C11—28no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—84no—
466C2×C4×C11C23×C412yes—
467C2×C4×C11C23×C412yes—
468C2×C4×C11C23×C412yes—
469C2×C4×C11C23×C412yes—
470C2×C4×C11H(5,𝔽2)12yes—
471C2×C4×C11H(5,𝔽2)12yes—
472C22⋊D11—48no—
473C22⋊D11—48no—
474C22⋊D11—48no—
475C2×Dic11—21no—
476C2×Dic11—22no—
477C2×Dic11—21no—
478C2×Dic11—21no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—21no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—21no—
486C2×Dic11—21no—
487C2×Dic11—21no—
488C2×Dic11—21no—
489C2×Dic11—21no—
490C2×Dic11—21no—
491C2×Dic11—21no—
492C2×Dic11—21no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—48no—
504C2×Dic11—44no—
505C2×Dic11—44no—
506C2×Dic11C23×C414yes—
507C2×Dic11C23×C414yes—
508C2×Dic11C23×C414yes—
509C2×Dic11H(5,𝔽2)12yes—
510C2×Dic112−1+412yes—
511D44—28no—
512C4×D11—48no—
513C4×D11—84no—
514C4×D11—84no—
515Dic22—28no—
516C22×#41—111no—
517C22×#41C2×D1111yescharacteristic
518#537—1116no—
519C2×C22⋊Q8—112no—
520C2×C22⋊Q8—111no—
521C2×C22⋊Q8—111no—
522C2×#121—112no—
523C2×#121—112no—
524C2×#121—112no—
525C2×#121—111no—
526C2×#121—111no—
527C2×C4×Q8—111no—
528C2×C4×Q8—111no—
529C2×C4×D4—112no—
530C2×C4×D4—111no—
531C2×C4×D4—111no—
532C2×C4×D4—112no—
533C2×#117—111no—
534C2×#117—112no—
535C2×#117C2×D1111yescharacteristic
536C22×C4⋊C4—111no—
537C22×C4⋊C4C2×D1111yescharacteristic
538C22×C42—111no—
539#391—111no—
540#391—111no—
541#391—111no—
542#391—111no—
543#391C2×D1112yes—
544#390—111no—
545#390—111no—
546#390—111no—
547#390—111no—
548#390—112no—
549#390—112no—
550#390—112no—
551#390—112no—
552#390C2×D1112yes—
553#389—111no—
554#389—111no—
555#389—112no—
556#389—111no—
557#389—111no—
558#389—112no—
559#388—112no—
560#388—112no—
561#388—112no—
562#388—112no—
563#388—112no—
564#388—112no—
565#388—112no—
566#388—112no—
567#387—112no—
568#387—112no—
569#387—112no—
570#387—112no—
571#387—112no—
572#387—112no—
573#387—112no—
574#387—112no—
575#386—111no—
576#386—111no—
577#386—111no—
578#386—111no—
579#386—112no—
580#386—112no—
581#386—112no—
582#386—112no—
583#386—112no—
584#386—112no—
585#386C2×D1112yes—
586#386C2×D1112yes—
587#385—112no—
588#385—112no—
589#385—112no—
590#385—112no—
591#381—112no—
592#381—112no—
593#380—112no—
594#380—112no—
595#380C2×D1111yescharacteristic
596#380C2×D1111yescharacteristic
597#380C2×D1111yescharacteristic
598#380C2×D1111yescharacteristic
599C4×C4⋊C4—111no—
600C4×C4⋊C4—111no—
601C4×C4⋊C4—111no—
602C4×C4⋊C4—111no—
603C4×C4⋊C4—112no—
604C4×C4⋊C4—112no—
605C4×C22⋊C4—112no—
606C4×C22⋊C4—111no—
607C4×C22⋊C4—111no—
608C4×C22⋊C4—111no—
609C4×C22⋊C4—111no—
610C4×C22⋊C4—112no—
611C4×C22⋊C4—112no—
612C4×C22⋊C4—112no—
613C4×C22⋊C4—112no—
614C4×C22⋊C4—112no—
615C2×#95—112no—
616C22×C11—22no—
617C22×C11—22no—
618C22×C11—22no—
619C22×C11—22no—
620C22×C11—22no—
621C22×C11—22no—
622C22×C11—22no—
623C22×C11—22no—
624C22×C11—22no—
625C22×C11—41no—
626C22×C11—41no—
627C22×C11—41no—
628C22×C11—41no—
629C22×C11—41no—
630C22×C11—41no—
631C22×C11—41no—
632C22×C11—41no—
633C22×C11—41no—
634C22×C11—41no—
635C22×C11—41no—
636C22×C11—41no—
637C22×C11C24×C411yescharacteristic
638C22×C11C2×H(5,𝔽2)11yescharacteristic
639C22×C11C2×H(5,𝔽2)11yescharacteristic
640C22×C11C2×H(5,𝔽2)11yescharacteristic
641C22×C11C2×2−1+411yescharacteristic
642C22×C11#58511yescharacteristic
643C22×C11#58511yescharacteristic
644C2×D11—24no—
645C2×D11—24no—
646C2×D11—24no—
647C2×D11—42no—
648C2×D11—42no—
649C2×D11—42no—
650C2×D11—42no—
651C4×C11—22no—
652C4×C11—22no—
653C4×C11—22no—
654C4×C11—42no—
655C4×C11—42no—
656C4×C11—42no—
657C4×C11—42no—
658C4×C11#51814yes—
659Dic11—24no—
660Dic11—24no—
661Dic11—24no—
662Dic11—22no—
663Dic11—22no—
664Dic11—41no—
665Dic11—41no—
666Dic11—41no—
667Dic11—41no—
668Dic11—41no—
669Dic11—41no—
670C2×#41—42no—
671C2×#41—42no—
672C2×#41—118no—
673C2×#41—442no—
674C2×#41—442no—
675C2×#41C4×D1118yescomplemented
676C22×Q8—111no—
677C22×Q8C22×D1111yescharacteristic
678C22×D4—112no—
679C22×D4—112no—
680C22×D4—112no—
681C22×D4—111no—
682C22×D4C22×D1111yescharacteristic
683C22×D4C22×D1111yescharacteristic
684C22×D4C22×D1111yescharacteristic
685C23×C4—112no—
686C23×C4—112no—
687C23×C4—111no—
688C23×C4—111no—
689C23×C4—112no—
690C23×C4—112no—
691C23×C4C22×D1111yescharacteristic
692C23×C4C22×D1111yescharacteristic
693C23×C4C22×D1111yescharacteristic
694C23×C4C22×D1112yes—
695C22⋊Q8—1116no—
696C22⋊Q8—118no—
697C22⋊Q8—118no—
698#121—1116no—
699#121—1116no—
700#121—1116no—
701#121—118no—
702#121—118no—
703C4×Q8—442no—
704C4×Q8—442no—
705C4×D4—444no—
706C4×D4—442no—
707C4×D4—442no—
708C4×D4—444no—
709#117—42no—
710#117—442no—
711#117—444no—
712C2×C4⋊C4—42no—
713C2×C4⋊C4—118no—
714C2×C4⋊C4—111no—
715C2×C4⋊C4—111no—
716C2×C4⋊C4—112no—
717C2×C4⋊C4—112no—
718C2×C4⋊C4—112no—
719C2×C4⋊C4—112no—
720C2×C4⋊C4—112no—
721C2×C4⋊C4—111no—
722C2×C4⋊C4—111no—
723C2×C4⋊C4—112no—
724C2×C4⋊C4—112no—
725C2×C4⋊C4—112no—
726C2×C4⋊C4—112no—
727C2×C4⋊C4C22×D1111yescharacteristic
728C2×C4⋊C4C22×D1111yescharacteristic
729C2×C4⋊C4C22×D1111yescharacteristic
730C2×C4⋊C4C22×D1111yescharacteristic
731C2×C4⋊C4C22×D1112yes—
732C2×C22⋊C4—112no—
733C2×C22⋊C4—112no—
734C2×C22⋊C4—112no—
735C2×C22⋊C4—112no—
736C2×C22⋊C4—111no—
737C2×C22⋊C4—111no—
738C2×C22⋊C4—111no—
739C2×C22⋊C4—111no—
740C2×C22⋊C4—112no—
741C2×C22⋊C4—111no—
742C2×C22⋊C4—111no—
743C2×C22⋊C4—111no—
744C2×C22⋊C4—111no—
745C2×C22⋊C4—111no—
746C2×C22⋊C4—111no—
747C2×C22⋊C4—112no—
748C2×C22⋊C4—112no—
749C2×C22⋊C4—112no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4C22×D1112yes—
753C2×C22⋊C4C22×D1112yes—
754C2×C22⋊C4C22×D1112yes—
755C2×C22⋊C4C22×D1112yes—
756C2×C22⋊C4C22×D1112yes—
757C2×C42—111no—
758C2×C42—112no—
759C2×C42—111no—
760C2×C42—111no—
761C2×C42—111no—
762C2×C42—112no—
763C2×C42—112no—
764C2×C42—112no—
765C2×C42—112no—
766C2×C42—111no—
767C2×C42—112no—
768C2×C42—111no—
769C2×C42—442no—
770C2×C42C22×D1112yes—
771#95—111no—
772#95—112no—
773#95—112no—
774#95—112no—
775#95—111no—
776#95—111no—
777#95—111no—
778#95—111no—
779#95—111no—
780#95—112no—
781#95—112no—
782#95—111no—
783#95—112no—
784#95—111no—
785#95—112no—
786#95—112no—
787#95—112no—
788#95—112no—
789#95—112no—
790#95—112no—
791#95C22×D1112yes—
792#95C22×D1112yes—
793#95C22×D1112yes—
794#95C22×D1112yes—
795C2×C11—42no—
796C2×C11—42no—
797C2×C11—42no—
798C2×C11C2×#51811yescharacteristic
799C2×C11C4×H(5,𝔽2)11yescharacteristic
800C2×C11C4×2−1+411yescharacteristic
801C2×C11#353611yescharacteristic
802C2×C11#353911yescharacteristic
803C2×C11#354611yescharacteristic
804C2×C11#354711yescharacteristic
805D11—44no—
806C24—112no—
807C24C23×D1111yescharacteristic
808C24C23×D1111yescharacteristic
809C24C23×D1111yescharacteristic
810#41—416no—
811#41—4416no—
812C2×Q8—41no—
813C2×Q8—41no—
814C2×Q8—114no—
815C2×Q8—222no—
816C2×Q8—222no—
817C2×Q8C2×C4×D1114yes—
818C2×D4—41no—
819C2×D4—41no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—118no—
825C2×D4—118no—
826C2×D4—118no—
827C2×D4—114no—
828C2×D4—222no—
829C2×D4—222no—
830C2×D4—442no—
831C2×D4—442no—
832C2×D4—442no—
833C2×D4—442no—
834C2×D4—442no—
835C2×D4—442no—
836C2×D4C2×C4×D1114yes—
837C2×D4C2×C4×D1114yes—
838C2×D4C2×C4×D1114yes—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—111no—
849C22×C4—112no—
850C22×C4—112no—
851C22×C4—112no—
852C22×C4—111no—
853C22×C4—118no—
854C22×C4—118no—
855C22×C4—111no—
856C22×C4—111no—
857C22×C4—111no—
858C22×C4—111no—
859C22×C4—111no—
860C22×C4—111no—
861C22×C4—224no—
862C22×C4—222no—
863C22×C4—222no—
864C22×C4—442no—
865C22×C4—442no—
866C22×C4—442no—
867C22×C4—442no—
868C22×C4—442no—
869C22×C4—442no—
870C22×C4—442no—
871C22×C4—441no—
872C22×C4—441no—
873C22×C4—442no—
874C22×C4—442no—
875C22×C4—441no—
876C22×C4—441no—
877C22×C4C2×C4×D1114yes—
878C22×C4C2×C4×D1114yes—
879C22×C4C2×C4×D1114yes—
880C22×C4C23×D1112yes—
881C22×C4C23×D1112yes—
882C22×C4C23×D1112yes—
883C22×C4C23×D1112yes—
884C22×C4C23×D1111yescharacteristic
885C22×C4C23×D1111yescharacteristic
886C22×C4C23×D1111yescharacteristic
887C22×C4C23×D1111yescharacteristic
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—42no—
893C4⋊C4—118no—
894C4⋊C4—114no—
895C4⋊C4—114no—
896C4⋊C4—118no—
897C4⋊C4—118no—
898C4⋊C4—224no—
899C4⋊C4—442no—
900C4⋊C4—441no—
901C4⋊C4—441no—
902C4⋊C4—442no—
903C4⋊C4—442no—
904C4⋊C4—442no—
905C4⋊C4—442no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—42no—
910C22⋊C4—42no—
911C22⋊C4—118no—
912C22⋊C4—118no—
913C22⋊C4—118no—
914C22⋊C4—118no—
915C22⋊C4—224no—
916C22⋊C4—222no—
917C22⋊C4—222no—
918C22⋊C4—222no—
919C22⋊C4—222no—
920C22⋊C4—442no—
921C22⋊C4—442no—
922C22⋊C4—442no—
923C22⋊C4—442no—
924C22⋊C4—442no—
925C22⋊C4—441no—
926C22⋊C4—441no—
927C22⋊C4—441no—
928C22⋊C4—441no—
929C22⋊C4—441no—
930C22⋊C4—441no—
931C42—42no—
932C42—224no—
933C42—222no—
934C42—222no—
935C42—222no—
936C42—222no—
937C42—441no—
938C42—441no—
939C42—442no—
940C42—442no—
941C42—442no—
942C42—442no—
943C42—442no—
944C11#3441011yescharacteristic, complemented, Sylow
945C23—21no—
946C23—21no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—21no—
953C23—21no—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23—114no—
964C23—222no—
965C23—222no—
966C23—222no—
967C23—222no—
968C23—222no—
969C23—222no—
970C23C22×C4×D1112yes—
971C23C22×C4×D1112yes—
972C23C22×C4×D1112yes—
973C23C24×D1111yescharacteristic
974Q8—44no—
975Q8—228no—
976D4—44no—
977D4—44no—
978D4—44no—
979D4—228no—
980D4—448no—
981D4—448no—
982D4—448no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—28no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—84no—
1005C2×C4—114no—
1006C2×C4—114no—
1007C2×C4—114no—
1008C2×C4—112no—
1009C2×C4—112no—
1010C2×C4—221no—
1011C2×C4—221no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—221no—
1016C2×C4—222no—
1017C2×C4—221no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—221no—
1021C2×C4—221no—
1022C2×C4—221no—
1023C2×C4—221no—
1024C2×C4—221no—
1025C2×C4—221no—
1026C2×C4—221no—
1027C2×C4—221no—
1028C2×C4—221no—
1029C2×C4—221no—
1030C2×C4—221no—
1031C2×C4—221no—
1032C2×C4—221no—
1033C2×C4—221no—
1034C2×C4—221no—
1035C2×C4—221no—
1036C2×C4—221no—
1037C2×C4—221no—
1038C2×C4—448no—
1039C2×C4—448no—
1040C2×C4—444no—
1041C2×C4—444no—
1042C2×C4—884no—
1043C2×C4—884no—
1044C2×C4C22×C4×D1112yes—
1045C2×C4C22×C4×D1112yes—
1046C2×C4C22×C4×D1112yes—
1047C2×C4C22×C4×D1112yes—
1048C2×C4#6703712yes—
1049C2×C4#6703712yes—
1050C22—22no—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—22no—
1055C22—22no—
1056C22—22no—
1057C22—22no—
1058C22—22no—
1059C22—41no—
1060C22—41no—
1061C22—41no—
1062C22—41no—
1063C22—41no—
1064C22—41no—
1065C22—41no—
1066C22—41no—
1067C22—41no—
1068C22—41no—
1069C22—41no—
1070C22—41no—
1071C22—224no—
1072C22—224no—
1073C22—224no—
1074C22—442no—
1075C22—442no—
1076C22—442no—
1077C22—442no—
1078C22C23×C4×D1111yescharacteristic
1079C22C2×#6703711yescharacteristic
1080C22C2×#6703711yescharacteristic
1081C22D11×H(5,𝔽2)11yescharacteristic
1082C22#1062345511yescharacteristic
1083C22D11×2−1+411yescharacteristic
1084C22#1062345711yescharacteristic
1085C4—22no—
1086C4—22no—
1087C4—22no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—224no—
1093C4—222no—
1094C4—222no—
1095C4—224no—
1096C4—224no—
1097C4—441no—
1098C4—441no—
1099C4—441no—
1100C4—441no—
1101C4—441no—
1102C4—441no—
1103C4#1062301714yes—
1104C2—42no—
1105C2—42no—
1106C2—42no—
1107C2—444no—
1108C2C2×#1062301711yescharacteristic
1109C2#1308182211yescharacteristic
1110C2#1308182711yescharacteristic
1111C2#1308283411yescharacteristic
1112C2#1308286911yescharacteristic
1113C2#1308298611yescharacteristic
1114C2#1308300311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2311C2
socle, cosocleC23×C11C25
prime radicalC2×#10623364C2
hypercenter#2311D11
hypocenterC11#34410
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #13071768C2semidirect
3. #13071767C2semidirect
4. #13071665C2semidirect
5. #13071654C2semidirect
6. #13071651C2semidirect
7. #13071643C2semidirect
8. #13071632C2semidirect
9. #13071621C2semidirect
10. #13071495C2semidirect
11. #13071487C2semidirect
12. #13071453C2semidirect
13. #13071444C2semidirect
14. #13071382C2semidirect
15. #13071371C2semidirect
16. #13071348C2semidirect
17. #13071306C2semidirect
18. #13071305C2semidirect
19. #13071294C2semidirect
20. #13071144C2semidirect
21. #13071122C2semidirect
22. #13071107C2semidirect
23. C11×#2311C2semidirect
28. #10623364C4semidirect
126. C2×C11×#41C2×C4semidirect
143. C2×#4339C2×C4semidirect
174. #66999C2×C4semidirect
175. #66992C2×C4semidirect
176. #66992C2×C4semidirect
177. #66991C2×C4semidirect
178. #66983C2×C4semidirect
179. #66983C2×C4semidirect
190. C2×C4⋊Dic11C2×C4semidirect
196. #66977C2×C4semidirect
197. #66977C2×C4semidirect
407. #2311D11semidirect
675. C2×#41C4×D11semidirect
944. C11#34410semidirect

Maximal subgroups

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

subgroupindex
C2×#106233642
#130717682
#130717672
#130716652
#130716542
#130716512
#130716432
#130716322
#130716212
#130714952
#130714872
#130714532
#130714442
#130713822
#130713712
#130713482
#130713062
#130713052
#130712942
#130711442
#130711222
#130711072
C11×#23112
#3441011