Finite Group Databasebeta

← #14916561

Subgroups — #14916561

Order 2816.

2586 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2#13071777C212yesmaximal, complemented
3#13071768C212yesmaximal, complemented
4#13071695C212yesmaximal, complemented
5#13071665C212yesmaximal, complemented
6#13071566C211yesmaximal, characteristic, complemented
7#13071560C211yesmaximal, characteristic, complemented
8#13071547C211yesmaximal, characteristic, complemented
9#13071546C211yesmaximal, characteristic, complemented
10#13071541C211yesmaximal, characteristic, complemented
11#13071538C211yesmaximal, characteristic, complemented
12C4⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
13#13071512C211yesmaximal, characteristic, complemented
14#13071407C212yesmaximal, complemented
15#13071403C212yesmaximal, complemented
16#13071275C212yesmaximal, complemented
17#13071272C212yesmaximal, complemented
18#13071223C211yesmaximal, characteristic, complemented
19#13071223C211yesmaximal, characteristic, complemented
20#13071208C211yesmaximal, characteristic, complemented
21#13070998C211yesmaximal, characteristic, complemented
22D11×#380C211yesmaximal, characteristic, complemented
23C11×#2311C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic, complemented
27C22×C11×C4⋊C4C2211yescharacteristic, complemented
28#10623359C4116yescomplemented
29C2×#66999C2211yescharacteristic
30C2×#66999C2211yescharacteristic
31C2×#66991C2211yescharacteristic
32C2×#66991C2211yescharacteristic
33C2×#66990C2211yescharacteristic
34C2×#66990C2211yescharacteristic
35C2×#66988C2211yescharacteristic
36C2×#66988C2211yescharacteristic
37C2×C4×C22⋊D11C2212yes—
38C2×C4×C22⋊D11C2211yescharacteristic
39C2×C4×C22⋊D11C2211yescharacteristic
40C2×C4×C22⋊D11C2211yescharacteristic
41C2×C4×C22⋊D11C2211yescharacteristic
42C2×#66979C2211yescharacteristic
43C2×#66979C2211yescharacteristic, complemented
44C22×C4⋊Dic11C2211yescharacteristic, complemented
45C2×#66945C2211yescharacteristic
46C2×#66945C2211yescharacteristic
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×C4⋊C4×D11C2211yescharacteristic
49C2×(C22⋊D11)⋊C4C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C11×#391C2212yescomplemented
52C11×#390C2212yes—
53C11×#386C2212yes—
54C11×#386C2212yescomplemented
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C11×#380C2211yescharacteristic, complemented
58C11×#380C2211yescharacteristic, complemented
59#10622843C2212yescomplemented
60#10622834C2212yes—
61#10622833C2212yes—
62#10622833C2212yescomplemented
63#10622826C2212yes—
64#10622825C2211yescharacteristic
65#10622825C2211yescharacteristic
66#10622825C2211yescharacteristic, complemented
67#10622825C2211yescharacteristic, complemented
68#10622823C2212yescomplemented
69C4×C22⋊Dic11C2212yescomplemented
70#10622603C2212yes—
71#10622602C2212yes—
72#10622600C2211yescharacteristic
73#10622600C2211yescharacteristic
74#10622600C2211yescharacteristic
75#10622600C2211yescharacteristic
76#10622591C2212yescomplemented
77#10622590C2211yescharacteristic, complemented
78#10622590C2211yescharacteristic, complemented
79#10622589C2211yescharacteristic, complemented
80#10622589C2211yescharacteristic, complemented
81C4⋊C4×Dic11C2211yescharacteristic, complemented
82C4⋊C4×Dic11C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84C4⋊C4×Dic11C2211yescharacteristic, complemented
85#10622585C2212yescomplemented
86#10622571C2212yes—
87#10622570C2212yes—
88#10622570C2212yes—
89#10622569C2212yes—
90#10622569C2212yes—
91#10622568C2212yes—
92#10622559C2212yescomplemented
93#10622558C2212yes—
94#10622558C2212yes—
95#10622558C2212yescomplemented
96#10622558C2212yescomplemented
97#10622557C2212yes—
98#10622557C2212yes—
99#10622557C2212yescomplemented
100#10622557C2212yescomplemented
101#10622555C2212yes—
102C22⋊C4×Dic11C2212yes—
103C22⋊C4×Dic11C2212yescomplemented
104#10622553C2212yes—
105C4×(C2×D11)⋊C4C2212yes—
106#10622546C2212yescomplemented
107C4×Dic11⋊C4C2212yescomplemented
108#10622283C2212yes—
109#10622282C2212yes—
110#10622281C2212yes—
111#10622280C2212yes—
112#10622279C2212yes—
113#10622279C2212yes—
114#10622277C2212yes—
115D11×#95C2212yes—
116#10622268C2212yescomplemented
117#10622267C2212yescomplemented
118#10622267C2212yescomplemented
119#10622266C2212yescomplemented
120#10622266C2212yescomplemented
121#10622265C2212yescomplemented
122#10622262C2212yescomplemented
123#10622260C2212yescomplemented
124C24×D11C2311yescharacteristic
125C2×C11×#41—42no—
126C2×C11×#41—42no—
127C2×C11×#41C2×C418yescomplemented
128C22×Q8×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2311yescharacteristic
131C22×D4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2311yescharacteristic
135C23×C4×C11C2312yes—
136C22×C22⋊D11C2311yescharacteristic
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2311yescharacteristic
140C23×Dic11C2312yes—
141C23×Dic11C2311yescharacteristic
142C22×C4×D11—42no—
143C22×C4×D11—42no—
144C22×C4×D11C2×C418yescomplemented
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C11×#117—42no—
152C2×C11×C4⋊C4—42no—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11C2312yes—
164C2×C22⋊Dic11C2312yes—
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2311yescharacteristic
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175#66999C2×C418yescomplemented
176#66999C2×C418yescomplemented
177#66991C2×C418yes—
178#66991C2×C418yescomplemented
179#66990C2×C418yescomplemented
180#66990C2×C418yescomplemented
181#66988C2×C418yescomplemented
182#66988C2×C418yescomplemented
183C4×C22⋊D11—44no—
184C4×C22⋊D11C2×C418yescomplemented
185C4×C22⋊D11C2×C418yescomplemented
186C4×C22⋊D11C2×C418yescomplemented
187C4×C22⋊D11C2×C418yescomplemented
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198#66979—42no—
199#66979C2×C418yescomplemented
200C2×C4⋊Dic11—42no—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2312yes—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227#66945—42no—
228#66945—42no—
229C4⋊C4×D11—42no—
230C4⋊C4×D11—42no—
231(C22⋊D11)⋊C4—44no—
232C22⋊C4×D11—44no—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253#34362—111nomaximal, Sylow
254C24×C11C2411yescharacteristic
255C24×C11C2411yescharacteristic
256C24×C11C2411yescharacteristic
257C23×D11—22no—
258C23×D11—22no—
259C23×D11—41no—
260C23×D11—41no—
261C23×D11—41no—
262C23×D11—41no—
263C23×D11C22×C414yes—
264C23×D11C2411yescharacteristic
265C23×D11C2411yescharacteristic
266C11×#41—416no—
267C2×Q8×C11—41no—
268C2×Q8×C11—41no—
269C2×Q8×C11C22×C414yes—
270C2×D4×C11—41no—
271C2×D4×C11—41no—
272C2×D4×C11—41no—
273C2×D4×C11—41no—
274C2×D4×C11—41no—
275C2×D4×C11—41no—
276C2×D4×C11C22×C414yes—
277C2×D4×C11C22×C414yes—
278C2×D4×C11C22×C414yes—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11C22×C414yes—
289C22×C4×C11C22×C414yes—
290C22×C4×C11C22×C414yes—
291C22×C4×C11C2412yes—
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—41no—
304C2×C22⋊D11—41no—
305C2×C22⋊D11—41no—
306C2×C22⋊D11—41no—
307C2×C22⋊D11C22×C414yes—
308C2×C22⋊D11C22×C414yes—
309C2×C22⋊D11C22×C414yes—
310C2×C22⋊D11C22×C414yes—
311C22×Dic11—41no—
312C22×Dic11—41no—
313C22×Dic11—42no—
314C22×Dic11—42no—
315C22×Dic11—42no—
316C22×Dic11C22×C414yes—
317C22×Dic11C2412yes—
318C22×Dic11C2412yes—
319C22×Dic11C2412yes—
320C22×Dic11C2412yes—
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327C2×C4×D11—24no—
328C2×C4×D11—24no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—41no—
334C2×C4×D11—41no—
335C2×C4×D11—41no—
336C2×C4×D11—41no—
337C2×C4×D11—42no—
338C2×C4×D11—42no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—416no—
342C2×C4×D11C22×C414yes—
343C2×C4×D11C22×C414yes—
344C2×C4×D11C22×C414yes—
345C2×C4×D11C22×C414yes—
346C11×C4⋊C4—22no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—42no—
351C11×C22⋊C4—42no—
352C11×C22⋊C4—42no—
353C11×C22⋊C4—42no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C42×C11—42no—
357C22⋊Dic11—42no—
358C22⋊Dic11—42no—
359C22⋊Dic11—42no—
360C22⋊Dic11—42no—
361C22⋊Dic11—42no—
362C22⋊Dic11C22×C414yes—
363C22⋊Dic11C22×C414yes—
364C22⋊Dic11C22×C414yes—
365C22⋊Dic11C22×C414yes—
366C22⋊Dic11C22×C414yes—
367C22⋊Dic11C22×C414yes—
368(C2×D11)⋊C4—24no—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4C22×C414yes—
375(C2×D11)⋊C4C22×C414yes—
376(C2×D11)⋊C4C22×C414yes—
377(C2×D11)⋊C4C22×C414yes—
378C4⋊Dic11—22no—
379C4⋊Dic11—22no—
380C4⋊Dic11—22no—
381C4⋊Dic11—22no—
382C4⋊Dic11—42no—
383C4⋊Dic11C22×C414yes—
384C4⋊Dic11C22×C414yes—
385Dic11⋊C4—42no—
386Dic11⋊C4—42no—
387Dic11⋊C4—42no—
388Dic11⋊C4—42no—
389Dic11⋊C4—42no—
390Dic11⋊C4—42no—
391Dic11⋊C4C22×C414yes—
392Dic11⋊C4C22×C414yes—
393Dic11⋊C4C22×C414yes—
394Dic11⋊C4C22×C414yes—
395C4×Dic11—42no—
396C4×Dic11—42no—
397C4×Dic11—42no—
398C4×Dic11—42no—
399C4×Dic11—42no—
400C4×Dic11—42no—
401C4×Dic11—42no—
402C4×Dic11C22×C414yes—
403C4×Dic11C22×C414yes—
404C2×#525—111no—
405#2378—112no—
406#2377—112no—
407#2368—112no—
408#2364—112no—
409#2354—111no—
410#2354—111no—
411#2352—111no—
412#2352—111no—
413#2352—111no—
414#2352—111no—
415D4×C4⋊C4—111no—
416D4×C4⋊C4—111no—
417#2335—112no—
418#2335—112no—
419#2321—112no—
420#2321—112no—
421#2314—111no—
422#2314—111no—
423#2311—111no—
424#2311D1111yescharacteristic, complemented
425#2280—111no—
426C2×#380—111no—
427C23×C11—21no—
428C23×C11—21no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—21no—
433C23×C11—21no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—21no—
441C23×C11—21no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11C23×C412yes—
446C23×C11C23×C412yes—
447C23×C11C23×C412yes—
448C23×C11C2511yescharacteristic
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—28no—
460C22×D11—44no—
461C22×D11—44no—
462C22×D11—44no—
463C22×D11—44no—
464C22×D11—44no—
465C22×D11—44no—
466C22×D11C23×C412yes—
467C22×D11C23×C412yes—
468C22×D11H(5,𝔽2)12yes—
469C22×D112−1+412yes—
470Q8×C11—44no—
471D4×C11—44no—
472D4×C11—44no—
473D4×C11—44no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—28no—
481C2×C4×C11—28no—
482C2×C4×C11—28no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—84no—
496C2×C4×C11C23×C412yes—
497C2×C4×C11C23×C412yes—
498C2×C4×C11C23×C412yes—
499C2×C4×C11C23×C412yes—
500C2×C4×C11H(5,𝔽2)12yes—
501C2×C4×C11H(5,𝔽2)12yes—
502C22⋊D11—28no—
503C22⋊D11—28no—
504C22⋊D11—44no—
505C22⋊D11—44no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—44no—
531C2×Dic11—84no—
532C2×Dic11C23×C412yes—
533C2×Dic11C23×C412yes—
534C2×Dic11C23×C412yes—
535C2×Dic11C23×C412yes—
536C2×Dic11C23×C412yes—
537C2×Dic11C23×C412yes—
538C4×D11—28no—
539C4×D11—28no—
540C4×D11—44no—
541C4×D11—44no—
542C4×D11—84no—
543C4×D11—84no—
544C22×#41C2×D1111yescharacteristic
545C24×C4—111no—
546#525—1116no—
547C2×#123—111no—
548C2×#123—111no—
549C2×C22⋊Q8—111no—
550C2×C22⋊Q8—111no—
551C2×#121—111no—
552C2×#121—111no—
553C2×#120—111no—
554C2×#120—111no—
555C2×C4×D4—111no—
556C2×C4×D4—111no—
557C2×C4×D4—111no—
558C2×C4×D4—111no—
559C2×C4×D4—112no—
560C2×C4×D4—112no—
561C2×#117—111no—
562C2×#117—111no—
563C2×#117—111no—
564C2×#117—111no—
565C2×#117C2×D1111yescharacteristic, complemented
566C22×C4⋊C4—111no—
567C22×C4⋊C4—111no—
568C22×C4⋊C4—111no—
569C22×C4⋊C4C2×D1111yescharacteristic, complemented
570C22×C22⋊C4—112no—
571#391—112no—
572#391C2×D1112yescomplemented
573#390—112no—
574#390—112no—
575#390—112no—
576#390C2×D1112yes—
577#389—112no—
578#389—112no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388—112no—
583#388—112no—
584#388—112no—
585#388—112no—
586#388—112no—
587#388—112no—
588#388—112no—
589#388—112no—
590#388—112no—
591#387—112no—
592#387—112no—
593#387—112no—
594#387—112no—
595#387—112no—
596#387—112no—
597#387—112no—
598#387—112no—
599#386—112no—
600#386—112no—
601#386—112no—
602#386—112no—
603#386—112no—
604#386—112no—
605#386C2×D1112yes—
606#386C2×D1112yescomplemented
607#385—112no—
608#385—112no—
609#385—112no—
610#385—112no—
611#384—111no—
612#384—111no—
613#382—111no—
614#382—111no—
615#381—112no—
616#380—111no—
617#380—111no—
618#380—111no—
619#380—111no—
620#380—111no—
621#380—111no—
622#380—111no—
623#380—111no—
624#380—112no—
625#380—112no—
626#380C2×D1111yescharacteristic
627#380C2×D1111yescharacteristic
628#380C2×D1111yescharacteristic, complemented
629#380C2×D1111yescharacteristic, complemented
630#379—112no—
631C4×C4⋊C4—111no—
632C4×C4⋊C4—111no—
633C4×C4⋊C4—111no—
634C4×C4⋊C4—111no—
635C4×C4⋊C4—112no—
636C4×C4⋊C4—112no—
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C2×#95—112no—
644C22×C11—22no—
645C22×C11—22no—
646C22×C11—22no—
647C22×C11—22no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—22no—
652C22×C11—22no—
653C22×C11—41no—
654C22×C11—41no—
655C22×C11—41no—
656C22×C11—41no—
657C22×C11—41no—
658C22×C11—41no—
659C22×C11—41no—
660C22×C11—41no—
661C22×C11—41no—
662C22×C11—41no—
663C22×C11—41no—
664C22×C11—41no—
665C22×C11C24×C411yescharacteristic
666C22×C11C2×H(5,𝔽2)11yescharacteristic
667C22×C11C2×H(5,𝔽2)11yescharacteristic
668C22×C11C2×H(5,𝔽2)11yescharacteristic
669C22×C11C2×2−1+411yescharacteristic
670C22×C11#58511yescharacteristic
671C22×C11#58511yescharacteristic
672C2×D11—22no—
673C2×D11—22no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—416no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11#52014yes—
687C4×C11—22no—
688C4×C11—22no—
689C4×C11—22no—
690C4×C11—42no—
691C4×C11—42no—
692C4×C11—42no—
693C4×C11—42no—
694C4×C11#51814yes—
695Dic11—22no—
696Dic11—22no—
697Dic11—22no—
698Dic11—22no—
699Dic11—22no—
700Dic11—22no—
701Dic11—42no—
702Dic11—42no—
703Dic11—42no—
704Dic11—42no—
705C25—111no—
706C2×#41—42no—
707C2×#41—42no—
708C2×#41C4×D1118yescomplemented
709C22×Q8C22×D1111yescharacteristic
710C22×D4—111no—
711C22×D4—111no—
712C22×D4—111no—
713C22×D4—111no—
714C22×D4C22×D1111yescharacteristic
715C22×D4C22×D1111yescharacteristic
716C22×D4C22×D1111yescharacteristic
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—111no—
720C23×C4—118no—
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—112no—
724C23×C4—112no—
725C23×C4—112no—
726C23×C4—442no—
727C23×C4—442no—
728C23×C4C22×D1111yescharacteristic
729C23×C4C22×D1111yescharacteristic
730C23×C4C22×D1111yescharacteristic
731C23×C4C22×D1112yes—
732#123—118no—
733#123—118no—
734C22⋊Q8—118no—
735C22⋊Q8—118no—
736#121—118no—
737#121—118no—
738#120—118no—
739#120—118no—
740C4×D4—118no—
741C4×D4—118no—
742C4×D4—118no—
743C4×D4—118no—
744C4×D4—444no—
745C4×D4—444no—
746#117—42no—
747#117—118no—
748#117—442no—
749#117—442no—
750#117—442no—
751C2×C4⋊C4—42no—
752C2×C4⋊C4—111no—
753C2×C4⋊C4—111no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—111no—
758C2×C4⋊C4—111no—
759C2×C4⋊C4—111no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—442no—
770C2×C4⋊C4—442no—
771C2×C4⋊C4—442no—
772C2×C4⋊C4C22×D1111yescharacteristic
773C2×C4⋊C4C22×D1111yescharacteristic
774C2×C4⋊C4C22×D1111yescharacteristic
775C2×C4⋊C4C22×D1111yescharacteristic
776C2×C4⋊C4C22×D1112yes—
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—444no—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1112yes—
802C2×C22⋊C4C22×D1112yes—
803C2×C22⋊C4C22×D1112yes—
804C2×C42—111no—
805C2×C42—111no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—112no—
810C2×C42—112no—
811C2×C42—112no—
812C2×C42—112no—
813C2×C42C22×D1112yes—
814#95—112no—
815#95—112no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—112no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95C22×D1112yes—
831#95C22×D1112yes—
832#95C22×D1112yes—
833#95C22×D1112yes—
834C2×C11—42no—
835C2×C11—42no—
836C2×C11—42no—
837C2×C11C2×#51811yescharacteristic
838C2×C11C2×#52011yescharacteristic
839C2×C11#342811yescharacteristic
840C2×C11#354111yescharacteristic
841C2×C11#354111yescharacteristic
842C2×C11#354211yescharacteristic
843C2×C11#354211yescharacteristic
844D11—24no—
845D11—42no—
846C24—111no—
847C24—111no—
848C24—114no—
849C24—222no—
850C24—222no—
851C24—441no—
852C24—441no—
853C24—441no—
854C24—441no—
855C24C23×D1111yescharacteristic
856C24C23×D1111yescharacteristic
857C24C23×D1111yescharacteristic
858#41—416no—
859C2×Q8—41no—
860C2×Q8—41no—
861C2×Q8C2×C4×D1114yes—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—114no—
869C2×D4—114no—
870C2×D4—114no—
871C2×D4—114no—
872C2×D4—222no—
873C2×D4—222no—
874C2×D4—222no—
875C2×D4—222no—
876C2×D4—441no—
877C2×D4—441no—
878C2×D4—441no—
879C2×D4—441no—
880C2×D4C2×C4×D1114yes—
881C2×D4C2×C4×D1114yes—
882C2×D4C2×C4×D1114yes—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—111no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—111no—
896C22×C4—111no—
897C22×C4—111no—
898C22×C4—114no—
899C22×C4—114no—
900C22×C4—114no—
901C22×C4—114no—
902C22×C4—114no—
903C22×C4—112no—
904C22×C4—112no—
905C22×C4—112no—
906C22×C4—112no—
907C22×C4—224no—
908C22×C4—224no—
909C22×C4—222no—
910C22×C4—222no—
911C22×C4—222no—
912C22×C4—222no—
913C22×C4—4416no—
914C22×C4—441no—
915C22×C4—441no—
916C22×C4—441no—
917C22×C4—441no—
918C22×C4—442no—
919C22×C4—442no—
920C22×C4—442no—
921C22×C4—442no—
922C22×C4—441no—
923C22×C4—441no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4—442no—
927C22×C4C2×C4×D1114yes—
928C22×C4C2×C4×D1114yes—
929C22×C4C2×C4×D1114yes—
930C22×C4C23×D1112yes—
931C22×C4C23×D1112yes—
932C22×C4C23×D1112yes—
933C22×C4C23×D1112yes—
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1111yescharacteristic
936C22×C4C23×D1111yescharacteristic
937C22×C4C23×D1111yescharacteristic
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—42no—
943C4⋊C4—114no—
944C4⋊C4—114no—
945C4⋊C4—114no—
946C4⋊C4—114no—
947C4⋊C4—114no—
948C4⋊C4—114no—
949C4⋊C4—222no—
950C4⋊C4—222no—
951C4⋊C4—222no—
952C4⋊C4—222no—
953C4⋊C4—442no—
954C4⋊C4—442no—
955C4⋊C4—442no—
956C4⋊C4—442no—
957C4⋊C4—442no—
958C4⋊C4—442no—
959C4⋊C4—442no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—114no—
966C22⋊C4—114no—
967C22⋊C4—114no—
968C22⋊C4—114no—
969C22⋊C4—114no—
970C22⋊C4—114no—
971C22⋊C4—114no—
972C22⋊C4—114no—
973C22⋊C4—114no—
974C22⋊C4—114no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—442no—
978C22⋊C4—442no—
979C22⋊C4—442no—
980C22⋊C4—442no—
981C22⋊C4—442no—
982C22⋊C4—442no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C42—42no—
987C42—114no—
988C42—114no—
989C42—442no—
990C42—442no—
991C42—442no—
992C42—442no—
993C42—442no—
994C42—442no—
995C42—442no—
996C11#3436211yescharacteristic, complemented, Sylow
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—112no—
1016C23—112no—
1017C23—112no—
1018C23—112no—
1019C23—228no—
1020C23—221no—
1021C23—221no—
1022C23—221no—
1023C23—221no—
1024C23—221no—
1025C23—221no—
1026C23—221no—
1027C23—221no—
1028C23—221no—
1029C23—221no—
1030C23—444no—
1031C23—444no—
1032C23—444no—
1033C23—444no—
1034C23—444no—
1035C23—444no—
1036C23C22×C4×D1112yes—
1037C23C22×C4×D1112yes—
1038C23C22×C4×D1112yes—
1039C23C24×D1111yescharacteristic
1040Q8—44no—
1041D4—44no—
1042D4—44no—
1043D4—44no—
1044D4—228no—
1045D4—228no—
1046D4—444no—
1047D4—444no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—28no—
1055C2×C4—28no—
1056C2×C4—28no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—84no—
1070C2×C4—112no—
1071C2×C4—112no—
1072C2×C4—112no—
1073C2×C4—112no—
1074C2×C4—112no—
1075C2×C4—112no—
1076C2×C4—221no—
1077C2×C4—221no—
1078C2×C4—221no—
1079C2×C4—221no—
1080C2×C4—221no—
1081C2×C4—221no—
1082C2×C4—221no—
1083C2×C4—221no—
1084C2×C4—221no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—221no—
1088C2×C4—228no—
1089C2×C4—228no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—444no—
1103C2×C4—444no—
1104C2×C4—444no—
1105C2×C4—884no—
1106C2×C4—884no—
1107C2×C4—884no—
1108C2×C4C22×C4×D1112yes—
1109C2×C4C22×C4×D1112yes—
1110C2×C4C22×C4×D1112yes—
1111C2×C4C22×C4×D1112yes—
1112C2×C4#6703712yes—
1113C2×C4#6703712yes—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—114no—
1136C22—222no—
1137C22—222no—
1138C22—222no—
1139C22—222no—
1140C22—222no—
1141C22—222no—
1142C22—222no—
1143C22—222no—
1144C22—222no—
1145C22—4416no—
1146C22—441no—
1147C22—441no—
1148C22—441no—
1149C22—441no—
1150C22C23×C4×D1111yescharacteristic
1151C22C2×#6703711yescharacteristic
1152C22C2×#6703711yescharacteristic
1153C22D11×H(5,𝔽2)11yescharacteristic
1154C22#1062345511yescharacteristic
1155C22D11×2−1+411yescharacteristic
1156C22#1062345711yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—222no—
1165C4—222no—
1166C4—222no—
1167C4—222no—
1168C4—222no—
1169C4—222no—
1170C4—442no—
1171C4—442no—
1172C4—442no—
1173C4—442no—
1174C4#1062301714yes—
1175C2—42no—
1176C2—42no—
1177C2—42no—
1178C2—224no—
1179C2—442no—
1180C2C2×#1062301711yescharacteristic
1181C2D11×#52011yescharacteristic
1182C2#1308181611yescharacteristic
1183C2#1308289711yescharacteristic
1184C2#1308291111yescharacteristic
1185C2#1308292011yescharacteristic
1186C2#1308293411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2311C2
socle, cosocleC23×C11C25
prime radicalC2×#10623359C2
hypercenter#2311D11
hypocenterC11#34362
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #13071777C2semidirect
3. #13071768C2semidirect
4. #13071695C2semidirect
5. #13071665C2semidirect
6. #13071566C2semidirect
7. #13071560C2semidirect
8. #13071547C2semidirect
9. #13071546C2semidirect
10. #13071541C2semidirect
11. #13071538C2semidirect
12. C4⋊C4×C22⋊D11C2semidirect
13. #13071512C2semidirect
14. #13071407C2semidirect
15. #13071403C2semidirect
16. #13071275C2semidirect
17. #13071272C2semidirect
18. #13071223C2semidirect
19. #13071223C2semidirect
20. #13071208C2semidirect
21. #13070998C2semidirect
22. D11×#380C2semidirect
23. C11×#2311C2semidirect
26. C2×C11×#117C22semidirect
27. C22×C11×C4⋊C4C22semidirect
28. #10623359C4semidirect
43. C2×#66979C22semidirect
44. C22×C4⋊Dic11C22semidirect
51. C11×#391C22semidirect
54. C11×#386C22semidirect
57. C11×#380C22semidirect
58. C11×#380C22semidirect
59. #10622843C22semidirect
62. #10622833C22semidirect
66. #10622825C22semidirect
67. #10622825C22semidirect
68. #10622823C22semidirect
69. C4×C22⋊Dic11C22semidirect
76. #10622591C22semidirect
77. #10622590C22semidirect
78. #10622590C22semidirect
79. #10622589C22semidirect
80. #10622589C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. #10622585C22semidirect
92. #10622559C22semidirect
95. #10622558C22semidirect
96. #10622558C22semidirect
99. #10622557C22semidirect
100. #10622557C22semidirect
103. C22⋊C4×Dic11C22semidirect
106. #10622546C22semidirect
107. C4×Dic11⋊C4C22semidirect
116. #10622268C22semidirect
117. #10622267C22semidirect
118. #10622267C22semidirect
119. #10622266C22semidirect
120. #10622266C22semidirect
121. #10622265C22semidirect
122. #10622262C22semidirect
123. #10622260C22semidirect
127. C2×C11×#41C2×C4semidirect
144. C22×C4×D11C2×C4semidirect
175. #66999C2×C4semidirect
176. #66999C2×C4semidirect
178. #66991C2×C4semidirect
179. #66990C2×C4semidirect
180. #66990C2×C4semidirect
181. #66988C2×C4semidirect
182. #66988C2×C4semidirect
184. C4×C22⋊D11C2×C4semidirect
185. C4×C22⋊D11C2×C4semidirect
186. C4×C22⋊D11C2×C4semidirect
187. C4×C22⋊D11C2×C4semidirect
199. #66979C2×C4semidirect
424. #2311D11semidirect
565. C2×#117C2×D11semidirect
569. C22×C4⋊C4C2×D11semidirect
572. #391C2×D11semidirect
606. #386C2×D11semidirect
628. #380C2×D11semidirect
629. #380C2×D11semidirect
708. C2×#41C4×D11semidirect
996. C11#34362semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
#130717772
#130717682
#130716952
#130716652
#130715662
#130715602
#130715472
#130715462
#130715412
#130715382
C4⋊C4×C22⋊D112
#130715122
#130714072
#130714032
#130712752
#130712722
#130712232
#130712082
#130709982
D11×#3802
C11×#23112
#3436211