Finite Group Databasebeta

← #14769341

Subgroups — #14769341

Order 2816.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623163C211yesmaximal, characteristic
2C2×#10622343C211yesmaximal, characteristic
3C2×#10622415C211yesmaximal, characteristic, complemented
4C22×#66874C211yesmaximal, characteristic, complemented
5#13071541C211yesmaximal, characteristic
6#13069537C211yesmaximal, characteristic, complemented
7#13069434C211yesmaximal, characteristic, complemented
8#13069048C211yesmaximal, characteristic, complemented
9#13069040C211yesmaximal, characteristic, complemented
10#13068927C211yesmaximal, characteristic, complemented
11#13068630C211yesmaximal, characteristic, complemented
12#13068552C211yesmaximal, characteristic, complemented
13#13068549C211yesmaximal, characteristic, complemented
14#13068445C211yesmaximal, characteristic, complemented
15C11×#1872C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66997C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24#10623163—24no—
25#10623163C418yescomplemented
26C2×#66950C2211yescharacteristic
27C2×#66949—21no—
28C2×#66945C2211yescharacteristic
29C2×#66941—21no—
30C2×#66940C2211yescharacteristic
31C2×(C22⋊D11)⋊C4—21no—
32C2×#66931—21no—
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622826—21no—
39#10622825C2211yescharacteristic
40C4×C22⋊Dic11—21no—
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44C2×#66880C2211yescharacteristic
45C2×#66880C2211yescharacteristic
46C2×#66879C2211yescharacteristic
47C2×Dic11⋊C8C2211yescharacteristic
48#10622603—21no—
49#10622600C2211yescharacteristic
50#10622591—21no—
51#10622590C2211yescharacteristic
52C4⋊C4×Dic11C2211yescharacteristic
53C2×#66874—24no—
54C2×#66874C2211yescharacteristic
55C2×#66874C2211yescharacteristic
56C2×#66874C2211yescharacteristic
57C2×#66874C2211yescharacteristic
58#10622415—24no—
59#10622343—24no—
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11D411yescharacteristic
68C23×Dic11—21no—
69C2×Q8×D11—22no—
70C2×Q8×D11—22no—
71C2×Q8×D11—22no—
72C2×Q8×D11—41no—
73C2×Q8×D11—41no—
74C2×Q8×D11C2×C414yescomplemented
75C22×C4×D11—21no—
76C22×C4×D11C2311yescharacteristic
77C22×Dic22—22no—
78C22×Dic22—22no—
79C22×Dic22—21no—
80C22×Dic22—22no—
81C22×Dic22—21no—
82C22×Dic22—41no—
83C22×Dic22—41no—
84C22×Dic22C2×C414yes—
85C22×Dic22C2311yescharacteristic
86C22×Dic22C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8C2×C414yes—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11D411yescharacteristic
101#66997—22no—
102#66997C2×C414yescomplemented
103C4×C22⋊D11C2×C414yes—
104C4×C22⋊D11D414yes—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4D411yescharacteristic
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4D411yescharacteristic
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118C2×C4×Dic11—21no—
119C2×C4×Dic11C2311yescharacteristic
120C22×C11⋊C8—22no—
121C22×C11⋊C8—22no—
122C22×C11⋊C8—41no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C2×#4313—22no—
126C2×#4313—22no—
127C2×#4313—41no—
128#66950—22no—
129#66950C2×C414yescomplemented
130#66949—28no—
131#66945—22no—
132#66945—41no—
133#66941—28no—
134#66940—22no—
135#66940C2×C414yescomplemented
136(C22⋊D11)⋊C4—28no—
137#66931—28no—
138C11×#103—22no—
139C11×#103—41no—
140C11×C22⋊C8—22no—
141#66899—22no—
142#66899—41no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148(C2×D11)⋊C8—22no—
149#66880—22no—
150#66880—22no—
151#66880—41no—
152#66880—41no—
153#66879—22no—
154Dic11⋊C8—22no—
155#66874—22no—
156#66874—22no—
157#66874—22no—
158#66874D414yescomplemented
159#22425—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C23×D11C2×D411yescharacteristic
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11C22×C412yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11—81no—
179C22×C4×C11C22×C412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2411yescharacteristic
183C2×C22⋊D11—22no—
184C2×C22⋊D11—22no—
185C2×C22⋊D11C22⋊C414yes—
186C22×Dic11—24no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—42no—
192C22×Dic11—42no—
193C22×Dic11C2×D411yescharacteristic
194C22×Dic11C2×D411yescharacteristic
195C22×Dic11C2×D411yescharacteristic
196Q8×D11—28no—
197Q8×D11—44no—
198Q8×D11—44no—
199Q8×D11—44no—
200C2×C4×D11—24no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—42no—
206C2×C4×D11—42no—
207C2×C4×D11C22×C412yes—
208C2×C4×D11C2×D412yes—
209C2×Dic22—28no—
210C2×Dic22—24no—
211C2×Dic22—24no—
212C2×Dic22—21no—
213C2×Dic22—21no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—21no—
220C2×Dic22—44no—
221C2×Dic22—44no—
222C2×Dic22—44no—
223C2×Dic22—42no—
224C2×Dic22—42no—
225C2×Dic22—42no—
226C2×Dic22—42no—
227C2×Dic22C22×C412yes—
228C2×Dic22C22×C412yes—
229C2×Dic22C2×D412yes—
230C2×Dic22#4112yes—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—42no—
243C11×C4⋊C4C22×C412yes—
244C11×C4⋊C4C2×D412yes—
245C11×C22⋊C4—24no—
246C22⋊Dic11—42no—
247C22⋊Dic11C22⋊C414yes—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—42no—
250(C2×D11)⋊C4—81no—
251(C2×D11)⋊C4C22⋊C414yes—
252C4⋊Dic11—24no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4C22⋊C414yes—
261C4×Dic11—24no—
262C4×Dic11—42no—
263C4×Dic11—81no—
264C4×Dic11C22×C412yes—
265C4×Dic11C2×D412yes—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—44no—
272C2×C11⋊C8C2×D412yes—
273#4313—44no—
274C2×D4×Q8—111no—
275C2×#435—111no—
276C2×#419—111no—
277C22×#103—111no—
278#2352—111no—
279#1981—111no—
280#1960—111no—
281#1894—111no—
282#1892—111no—
283#1873—111no—
284#1872D1111yescharacteristic, complemented
285#1805—111no—
286#1787—111no—
287#1787—111no—
288#1763—111no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11C2×C22⋊C412yes—
294C23×C11#13712yes—
295C23×C11#13712yes—
296C23×C11C22×D411yescharacteristic
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—21no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11C2×C22⋊C412yes—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—41no—
307Q8×C11—41no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—84no—
327C2×C4×C11C2×C22⋊C412yes—
328C2×C4×C11C23×C411yescharacteristic
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11H(5,𝔽2)11yescharacteristic
333C2×C4×C11H(5,𝔽2)11yescharacteristic
334C22⋊D11—28no—
335C2×Dic11—22no—
336C2×Dic11—21no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—22no—
345C2×Dic11—48no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11C2×C22⋊C412yes—
355C2×Dic11C2×C22⋊C412yes—
356C2×Dic11C2×C22⋊C412yes—
357C4×D11—22no—
358C4×D11—22no—
359C4×D11—22no—
360C4×D11—22no—
361C4×D11—48no—
362Dic22—22no—
363Dic22—22no—
364Dic22—22no—
365Dic22—22no—
366Dic22—22no—
367Dic22—48no—
368Dic22—48no—
369Dic22—41no—
370Dic22—41no—
371Dic22C4×D414yes—
372C8×C11—41no—
373C8×C11—41no—
374C11⋊C8—22no—
375C11⋊C8—41no—
376C23×Q8—111no—
377C23×Q8—111no—
378C22×M16—111no—
379C23×C8—111no—
380D4×Q8—118no—
381D4×Q8—224no—
382C2×C4⋊Q8—111no—
383C2×C4⋊Q8—221no—
384C2×C22⋊Q8—111no—
385C2×C22⋊Q8—221no—
386C2×C22⋊Q8—221no—
387C2×C22⋊Q8C2×D1111yescharacteristic
388C2×C4×Q8—111no—
389C2×C4×D4—111no—
390C2×C4×D4—221no—
391C2×#117—111no—
392C22×C4⋊C4C2×D1111yescharacteristic
393#435—224no—
394C2×C4⋊C8—111no—
395#419—224no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—224no—
407C2×#103C2×D1111yescharacteristic
408C2×#103C2×D1111yescharacteristic
409C2×C22⋊C8—111no—
410C2×C22⋊C8C2×D1111yescharacteristic
411C2×#97—111no—
412#388—221no—
413#387—221no—
414#386—221no—
415#382—111no—
416#380—111no—
417#380—111no—
418C4×C4⋊C4—111no—
419C4×C22⋊C4—221no—
420#340—111no—
421#340—111no—
422#340C2×D1111yescharacteristic
423#340C2×D1111yescharacteristic
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11#41914yescomplemented
431C22×C11C22×C22⋊C411yescharacteristic
432C22×C11D4211yescharacteristic
433C22×C11#54611yescharacteristic
434C22×C11C2×#13711yescharacteristic
435C22×C11C2×#13711yescharacteristic
436C22×C11#57711yescharacteristic
437C22×C11#57811yescharacteristic
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—22no—
441C2×D11—41no—
442C2×D11—41no—
443C2×D11—41no—
444C2×D11—41no—
445C4×C11—22no—
446C4×C11—42no—
447C4×C11—42no—
448C4×C11—42no—
449C4×C11—81no—
450C4×C11C2×C4×D411yescharacteristic
451C4×C11#51811yescharacteristic
452C4×C11D4211yescharacteristic
453C4×C11#54611yescharacteristic
454Dic11—24no—
455Dic11—22no—
456Dic11—22no—
457Dic11—22no—
458Dic11—42no—
459Dic11—81no—
460Dic11—81no—
461C22×Q8—114no—
462C22×Q8—114no—
463C22×Q8—111no—
464C22×Q8—111no—
465C22×Q8—221no—
466C22×Q8—222no—
467C22×Q8—222no—
468C22×Q8—222no—
469C22×Q8—221no—
470C22×Q8—222no—
471C22×Q8—222no—
472C22×Q8—222no—
473C22×Q8—441no—
474C22×Q8—441no—
475C22×Q8—441no—
476C22×Q8—441no—
477C22×Q8C22×D1111yescharacteristic
478C22×D4—111no—
479C23×C4—21no—
480C23×C4—111no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4C22×D1111yescharacteristic
484C2×M16—222no—
485C2×M16—222no—
486C2×M16—441no—
487C22×C8—111no—
488C22×C8—111no—
489C22×C8—222no—
490C22×C8—222no—
491C22×C8—441no—
492C22×C8C22×D1111yescharacteristic
493C22×C8C22×D1111yescharacteristic
494C4⋊Q8—114no—
495C4⋊Q8—222no—
496C4⋊Q8—228no—
497C22⋊Q8—22no—
498C22⋊Q8—114no—
499C22⋊Q8—228no—
500C22⋊Q8—228no—
501C22⋊Q8—222no—
502C22⋊Q8C4×D1114yes—
503C4×Q8—114no—
504C4×Q8—222no—
505C4×D4—114no—
506C4×D4—114no—
507C4×D4—228no—
508#117—222no—
509#117—441no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4C22×D1111yescharacteristic
522C2×C4⋊C4C22×D1111yescharacteristic
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—111no—
526C2×C22⋊C4—111no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C42—111no—
532C2×C42—221no—
533C2×C42—221no—
534C2×C42—221no—
535C4⋊C8—222no—
536#103—22no—
537#103—41no—
538#103—114no—
539#103—222no—
540#103—222no—
541#103—222no—
542#103—222no—
543#103—222no—
544#103—222no—
545#103—441no—
546#103—441no—
547#103—441no—
548C22⋊C8—22no—
549C22⋊C8—222no—
550#97—222no—
551#95—221no—
552#95—221no—
553#95—221no—
554#95—221no—
555#95—221no—
556C2×C11—24no—
557C2×C11D4×C22⋊C411yescharacteristic
558C2×C11C2×#41911yescharacteristic
559C2×C11#289811yescharacteristic
560C2×C11#326611yescharacteristic
561C2×C11#327011yescharacteristic
562C2×C11#331211yescharacteristic
563C2×C11#332011yescharacteristic
564D11—42no—
565C24—111no—
566C24D4×D1111yescharacteristic
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—112no—
573C2×Q8—112no—
574C2×Q8—112no—
575C2×Q8—112no—
576C2×Q8—224no—
577C2×Q8—228no—
578C2×Q8—224no—
579C2×Q8—221no—
580C2×Q8—221no—
581C2×Q8—221no—
582C2×Q8—221no—
583C2×Q8—228no—
584C2×Q8—221no—
585C2×Q8—221no—
586C2×Q8—221no—
587C2×Q8—221no—
588C2×Q8—442no—
589C2×Q8—442no—
590C2×Q8—444no—
591C2×Q8—444no—
592C2×Q8—444no—
593C2×Q8—442no—
594C2×Q8—442no—
595C2×Q8—444no—
596C2×Q8—444no—
597C2×Q8—444no—
598C2×Q8C2×C4×D1112yes—
599C2×D4—114no—
600C2×D4—222no—
601C2×D4—222no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—111no—
614C22×C4—111no—
615C22×C4—111no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—224no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—224no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—442no—
629C22×C4—442no—
630C22×C4—442no—
631C22×C4—442no—
632C22×C4C2×C4×D1112yes—
633C22×C4D4×D1111yescharacteristic
634C22×C4D4×D1112yes—
635C22×C4C23×D1111yescharacteristic
636M16—444no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—112no—
644C2×C8—221no—
645C2×C8—221no—
646C2×C8—221no—
647C2×C8—221no—
648C2×C8—221no—
649C2×C8—444no—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—114no—
657C4⋊C4—224no—
658C4⋊C4—224no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—221no—
662C4⋊C4—221no—
663C4⋊C4—221no—
664C4⋊C4—221no—
665C4⋊C4C2×C4×D1112yes—
666C4⋊C4D4×D1112yes—
667C22⋊C4—24no—
668C22⋊C4—114no—
669C22⋊C4—114no—
670C22⋊C4—224no—
671C22⋊C4—442no—
672C22⋊C4—442no—
673C22⋊C4—881no—
674C42—112no—
675C42—112no—
676C42—224no—
677C42—442no—
678C42—881no—
679C11#2242511yescharacteristic, complemented, Sylow
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—112no—
685C23—221no—
686C23—221no—
687C23—221no—
688C23—221no—
689C23—221no—
690C23—221no—
691C23C22⋊C4×D1112yes—
692C23#6696812yes—
693C23#6697112yes—
694C23C2×D4×D1111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—41no—
698Q8—41no—
699Q8—114no—
700Q8—222no—
701Q8—222no—
702Q8—222no—
703Q8—222no—
704Q8—222no—
705Q8—448no—
706Q8—448no—
707Q8—441no—
708Q8—441no—
709D4—228no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—84no—
729C2×C4—112no—
730C2×C4—112no—
731C2×C4—112no—
732C2×C4—222no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—221no—
736C2×C4—221no—
737C2×C4—221no—
738C2×C4—222no—
739C2×C4—221no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—448no—
747C2×C4—448no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4C22⋊C4×D1112yes—
757C2×C4C22×C4×D1111yescharacteristic
758C2×C4C2×D4×D1111yescharacteristic
759C2×C4C2×D4×D1111yescharacteristic
760C2×C4#6703711yescharacteristic
761C2×C4#41×D1111yescharacteristic
762C2×C4#6704211yescharacteristic
763C8—41no—
764C8—41no—
765C8—222no—
766C8—441no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—222no—
774C22—222no—
775C22—222no—
776C22—441no—
777C22—441no—
778C22—441no—
779C22—441no—
780C22#1062241514yescomplemented
781C22C2×C22⋊C4×D1111yescharacteristic
782C22#1062312111yescharacteristic
783C22#1062318511yescharacteristic
784C22C2×#6696811yescharacteristic
785C22C2×#6697111yescharacteristic
786C22#1062330611yescharacteristic
787C22#1062331011yescharacteristic
788C4—22no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—81no—
793C4—222no—
794C4—224no—
795C4—222no—
796C4—222no—
797C4—442no—
798C4—881no—
799C4—881no—
800C4C4×D4×D1111yescharacteristic
801C4#1062307611yescharacteristic
802C4#1062314011yescharacteristic
803C4#1062314111yescharacteristic
804C2—24no—
805C2—442no—
806C2#1307143411yescharacteristic
807C2C2×#1062241511yescharacteristic
808C2#1307714711yescharacteristic
809C2#1308013011yescharacteristic
810C2#1308019011yescharacteristic
811C2#1308066511yescharacteristic
812C2#1308078511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
cosocleC22×C4×C11C24
hypercenter#1872D11
hypocenterC11#22425
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C2×#10622415C2semidirect
4. C22×#66874C2semidirect
6. #13069537C2semidirect
7. #13069434C2semidirect
8. #13069048C2semidirect
9. #13069040C2semidirect
10. #13068927C2semidirect
11. #13068630C2semidirect
12. #13068552C2semidirect
13. #13068549C2semidirect
14. #13068445C2semidirect
15. C11×#1872C2semidirect
25. #10623163C4semidirect
74. C2×Q8×D11C2×C4semidirect
102. #66997C2×C4semidirect
129. #66950C2×C4semidirect
135. #66940C2×C4semidirect
158. #66874D4semidirect
284. #1872D11semidirect
430. C22×C11#419semidirect
679. C11#22425semidirect
780. C22#10622415semidirect

Maximal subgroups

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

subgroupindex
C2×#106231632
C2×#106223432
C2×#106224152
C22×#668742
#130715412
#130695372
#130694342
#130690482
#130690402
#130689272
#130686302
#130685522
#130685492
#130684452
C11×#18722
#2242511