Finite Group Databasebeta

← #14788917

Subgroups — #14788917

Order 2816.

1420 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622670C211yesmaximal, characteristic, complemented
2C2×#10622696C211yesmaximal, characteristic, complemented
3C2×#10622851C211yesmaximal, characteristic
4C2×#10622840C211yesmaximal, characteristic, complemented
5#13071309C211yesmaximal, characteristic, complemented
6#13069859C211yesmaximal, characteristic, complemented
7#13069852C211yesmaximal, characteristic, complemented
8#13069699C211yesmaximal, characteristic, complemented
9#13069693C211yesmaximal, characteristic, complemented
10#13069549C211yesmaximal, characteristic, complemented
11#13069540C211yesmaximal, characteristic, complemented
12#13068600C211yesmaximal, characteristic, complemented
13#13068556C211yesmaximal, characteristic, complemented
14#13068551C211yesmaximal, characteristic, complemented
15C2×C11×#536C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C11×#536—24no—
19C11×#536—24no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×#123—21no—
25C2×C11×#123—21no—
26C2×C11×C22⋊Q8—21no—
27C2×C11×C22⋊Q8—21no—
28C2×C11×#117C2211yescharacteristic
29C22×#4325C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C22×#4323C2211yescharacteristic
33C2×#66983C2211yescharacteristic
34C2×C4×D44C2211yescharacteristic
35#10622851—24no—
36#10622840—24no—
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66899C2211yescharacteristic
44C2×#66899C2211yescharacteristic
45C2×#66899C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49#10622825C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52#10622696—24no—
53#10622670—24no—
54#10622603—21no—
55#10622602—21no—
56#10622570—21no—
57#10622569—21no—
58#10622552C2211yescharacteristic
59C4×C4⋊Dic11C2211yescharacteristic
60#10622541C2211yescharacteristic
61C2×C4⋊(C11⋊C8)C2211yescharacteristic
62C2×C4⋊(C11⋊C8)C2211yescharacteristic
63#10622162C2211yescharacteristic
64#10622162C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C22×Q8×C11—22no—
72C22×Q8×C11—22no—
73C22×Q8×C11—21no—
74C22×Q8×C11—22no—
75C22×Q8×C11—22no—
76C22×Q8×C11—41no—
77C22×Q8×C11—41no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11—21no—
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—21no—
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C11×C4⋊Q8—22no—
90C11×C4⋊Q8—22no—
91C11×C4⋊Q8—22no—
92C11×C4⋊Q8D414yescomplemented
93C11×#124—22no—
94C11×#124—22no—
95C11×#124—22no—
96C11×#124D414yescomplemented
97C11×#123—28no—
98C11×#123—28no—
99C11×C22⋊Q8—28no—
100C11×C22⋊Q8—28no—
101C11×#117—22no—
102C11×#117—22no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C22⋊Dic11—21no—
118C2×#4325—22no—
119C2×#4325—22no—
120C2×#4325—22no—
121C2×#4325—22no—
122C2×#4325—22no—
123C2×#4325—22no—
124C2×#4325—41no—
125C2×#4325—41no—
126C2×#4325—41no—
127C2×#4323—22no—
128C2×#4323—22no—
129C2×#4323—41no—
130#66983—22no—
131#66983D414yes—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×Dic11⋊C4—21no—
140C2×C4×Dic11—21no—
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145C4×D44—22no—
146C4×D44—22no—
147#66899—22no—
148#66899—22no—
149#66899—22no—
150#66899—22no—
151#66899—22no—
152#66899—22no—
153#66899—41no—
154#66899—41no—
155#66899—41no—
156#66896—22no—
157#66896—22no—
158#66896—41no—
159C11⋊#95—21no—
160C11⋊#95—21no—
161C11⋊#95—21no—
162C22⋊(C11⋊C8)—22no—
163C22⋊(C11⋊C8)—22no—
164C4⋊(C11⋊C8)—22no—
165C4⋊(C11⋊C8)—22no—
166#24219—111nomaximal, Sylow
167C24×C11—21no—
168C24×C11C2×D411yescharacteristic
169C23×D11—21no—
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—44no—
174C2×Q8×C11—24no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—44no—
191C2×Q8×C11—44no—
192C2×Q8×C11—44no—
193C2×Q8×C11—44no—
194C2×Q8×C11—42no—
195C2×Q8×C11—42no—
196C2×Q8×C11C2×D412yes—
197C2×Q8×C11C2×D412yes—
198C2×Q8×C11C2×D412yes—
199C2×D4×C11—24no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11C2×D412yes—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—24no—
213C22×C4×C11—24no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—42no—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11—42no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D412yes—
227C22×C4×C11#4112yes—
228C22×C4×C11C2411yescharacteristic
229C2×C22⋊D11—24no—
230C2×C22⋊D11—81no—
231C2×C22⋊D11—81no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C2×D44—21no—
236C2×D44—21no—
237C2×D44—21no—
238C2×D44—21no—
239C2×D44—21no—
240C2×D44C2×D412yes—
241C2×C4×D11—42no—
242C2×C4×D11—81no—
243C2×C4×D11—81no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—22no—
249C11×C4⋊C4—22no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—22no—
255C11×C22⋊C4—22no—
256C42×C11—21no—
257C42×C11—21no—
258C42×C11C2×D412yes—
259C42×C11C2×D412yes—
260C22⋊Dic11—81no—
261#4325—44no—
262#4325—44no—
263#4325—44no—
264#4323—44no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—42no—
267(C2×D11)⋊C4—81no—
268(C2×D11)⋊C4—81no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11C2×D412yes—
275Dic11⋊C4—81no—
276C4×Dic11—81no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—21no—
286C2×C11⋊C8—21no—
287C2×C11⋊C8—21no—
288C2×C11⋊C8—21no—
289C2×#536D1111yescharacteristic, complemented
290C2×#463—111no—
291C2×#461—111no—
292C2×#449—111no—
293C2×#448—111no—
294#2324—111no—
295#2043—111no—
296#2042—111no—
297#2013—111no—
298#2012—111no—
299#1983—111no—
300#1981—111no—
301#1798—111no—
302#1788—111no—
303#1787—111no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—22no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11#12112yes—
318C23×C11C22×D411yescharacteristic
319C22×D11—22no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—48no—
333Q8×C11—41no—
334Q8×C11—41no—
335Q8×C11—41no—
336Q8×C11—41no—
337Q8×C11—41no—
338Q8×C11—41no—
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—48no—
342D4×C11—41no—
343D4×C11—41no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—48no—
364C2×C4×C11—48no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11#12012yes—
372C2×C4×C11#12012yes—
373C2×C4×C11#12112yes—
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C2×#4111yescharacteristic
378C2×C4×C11H(5,𝔽2)11yescharacteristic
379C2×C4×C11H(5,𝔽2)11yescharacteristic
380C22⋊D11—84no—
381C2×Dic11—22no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390D44—22no—
391D44—22no—
392D44—41no—
393D44—41no—
394C4×D11—84no—
395C11⋊C8—41no—
396C11⋊C8—41no—
397C11⋊C8—41no—
398C11⋊C8—41no—
399C22×#41C2×D1111yescharacteristic
400C23×Q8C2×D1111yescharacteristic
401C22×SD16—111no—
402C22×SD16—111no—
403C22×SD16—111no—
404C22×D8—111no—
405#536—24no—
406#536—24no—
407C2×C4⋊Q8C2×D1111yescharacteristic
408C2×C4⋊Q8C2×D1111yescharacteristic
409C2×#124C2×D1111yescharacteristic
410C2×#124C2×D1111yescharacteristic
411C2×#123—21no—
412C2×#123—21no—
413C2×C22⋊Q8—21no—
414C2×C22⋊Q8—21no—
415C2×#121—111no—
416C2×C4×D4—111no—
417C2×#117C2×D1111yescharacteristic
418#463—224no—
419#461—224no—
420#449—224no—
421#448—224no—
422C2×C4⋊C8—111no—
423C2×C4⋊C8—111no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×C22⋊C8—111no—
437C2×C22⋊C8—111no—
438#390—111no—
439#390—221no—
440#389—111no—
441#388—221no—
442#386—221no—
443#385—221no—
444#380—111no—
445C4×C4⋊C4—111no—
446#336—111no—
447#336—111no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—81no—
459C22×C11—81no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11C2×#12011yescharacteristic
463C22×C11C2×#12111yescharacteristic
464C22×C11#53511yescharacteristic
465C22×C11#57711yescharacteristic
466C22×C11#57711yescharacteristic
467C22×C11#57711yescharacteristic
468C22×C11#57811yescharacteristic
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—81no—
473C2×D11—81no—
474C2×D11—81no—
475C2×D11—81no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11—22no—
479C4×C11—42no—
480C4×C11—42no—
481C4×C11—42no—
482C4×C11—41no—
483C4×C11—41no—
484C4×C11D4211yescharacteristic
485C4×C11D4211yescharacteristic
486C4×C11#54611yescharacteristic
487C4×C11#54611yescharacteristic
488Dic11—42no—
489Dic11—81no—
490Dic11—81no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—22no—
498C22×Q8—22no—
499C22×Q8—21no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8C22×D1111yescharacteristic
505C22×Q8C22×D1111yescharacteristic
506C22×Q8C22×D1111yescharacteristic
507C22×D4—21no—
508C22×D4—111no—
509C22×D4—221no—
510C22×D4C22×D1111yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—221no—
514C23×C4C22×D1111yescharacteristic
515C2×SD16—222no—
516C2×SD16—222no—
517C2×SD16—222no—
518C2×SD16—222no—
519C2×SD16—222no—
520C2×SD16—222no—
521C2×SD16—441no—
522C2×SD16—441no—
523C2×SD16—441no—
524C2×D8—222no—
525C2×D8—222no—
526C2×D8—441no—
527C22×C8—111no—
528C22×C8—111no—
529C22×C8—111no—
530C22×C8—111no—
531C4⋊Q8—22no—
532C4⋊Q8—22no—
533C4⋊Q8—22no—
534C4⋊Q8C22⋊D1114yescomplemented
535#124—22no—
536#124—22no—
537#124—22no—
538#124C22⋊D1114yescomplemented
539#123—28no—
540#123—28no—
541C22⋊Q8—28no—
542C22⋊Q8—28no—
543#121—114no—
544#121—222no—
545C4×D4—222no—
546C4×D4—222no—
547#117—22no—
548#117—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—221no—
557C2×C4⋊C4C22⋊D1111yescharacteristic
558C2×C4⋊C4C22⋊D1111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4C22⋊D1111yescharacteristic
569C2×C22⋊C4C22⋊D1111yescharacteristic
570C2×C42—221no—
571C2×C42C22×D1111yescharacteristic
572C2×C42C22×D1111yescharacteristic
573C4⋊C8—222no—
574C4⋊C8—222no—
575#103—222no—
576#103—222no—
577#103—222no—
578#103—222no—
579#103—222no—
580#103—222no—
581#103—441no—
582#103—441no—
583#103—441no—
584#102—222no—
585#102—222no—
586#102—441no—
587C22⋊C8—222no—
588C22⋊C8—222no—
589#95—221no—
590#95—221no—
591#95—221no—
592C2×C11—42no—
593C2×C11—82no—
594C2×C11#240811yescharacteristic
595C2×C11#301011yescharacteristic
596C2×C11#301311yescharacteristic
597C2×C11#304211yescharacteristic
598C2×C11#304611yescharacteristic
599C2×C11#322111yescharacteristic
600C2×C11#322511yescharacteristic
601D11—82no—
602C24—21no—
603C24—221no—
604C24C2×C22⋊D1111yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—24no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—44no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—42no—
630C2×Q8—42no—
631C2×Q8C2×C22⋊D1112yes—
632C2×Q8C2×C22⋊D1112yes—
633C2×Q8C2×C22⋊D1112yes—
634C2×D4—24no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—112no—
643C2×D4—224no—
644C2×D4—221no—
645C2×D4—221no—
646C2×D4—221no—
647C2×D4—221no—
648C2×D4—221no—
649C2×D4—881no—
650C2×D4—881no—
651C2×D4C2×C22⋊D1112yes—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—442no—
669C22×C4—881no—
670C22×C4—881no—
671C22×C4D4×D1112yes—
672C22×C4#434112yes—
673C22×C4C2×C22⋊D1111yescharacteristic
674C22×C4C2×C22⋊D1111yescharacteristic
675C22×C4C2×C22⋊D1111yescharacteristic
676C22×C4C2×C22⋊D1111yescharacteristic
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C23×D1111yescharacteristic
679SD16—444no—
680SD16—444no—
681SD16—444no—
682D8—444no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—112no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—881no—
708C22⋊C4—24no—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—224no—
715C22⋊C4—442no—
716C22⋊C4—881no—
717C22⋊C4—881no—
718C22⋊C4—881no—
719C42—21no—
720C42—21no—
721C42—881no—
722C42C2×C22⋊D1112yes—
723C42C2×C22⋊D1112yes—
724C11#2421911yescharacteristic, complemented, Sylow
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—222no—
739C23—441no—
740C23—441no—
741C23—441no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23#6699112yes—
746C23C22×C22⋊D1111yescharacteristic
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—48no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757Q8—41no—
758Q8—41no—
759Q8—41no—
760D4—22no—
761D4—22no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—222no—
766D4—222no—
767D4—441no—
768D4—441no—
769D4—884no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—48no—
790C2×C4—48no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—222no—
798C2×C4—441no—
799C2×C4—441no—
800C2×C4—441no—
801C2×C4—441no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—884no—
807C2×C4#6699112yes—
808C2×C4#6700612yes—
809C2×C4#6700612yes—
810C2×C4C2×D4×D1111yescharacteristic
811C2×C4C2×#434111yescharacteristic
812C2×C4#6703711yescharacteristic
813C2×C4#6703711yescharacteristic
814C2×C4C22×C22⋊D1111yescharacteristic
815C2×C4C22×C22⋊D1111yescharacteristic
816C8—441no—
817C8—441no—
818C8—441no—
819C8—441no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—881no—
838C22—881no—
839C22—881no—
840C22—881no—
841C22C2×#6699111yescharacteristic
842C22#1062333611yescharacteristic
843C22#1062336811yescharacteristic
844C22#1062336811yescharacteristic
845C22#1062336811yescharacteristic
846C22#1062336911yescharacteristic
847C22C2×#6700611yescharacteristic
848C4—22no—
849C4—22no—
850C4—22no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—442no—
857C4—881no—
858C4—881no—
859C4D4×C22⋊D1111yescharacteristic
860C4D4×C22⋊D1111yescharacteristic
861C4#1062333711yescharacteristic
862C4#1062333711yescharacteristic
863C2—42no—
864C2—82no—
865C2—882no—
866C2#1307196611yescharacteristic
867C2#1307790211yescharacteristic
868C2#1307793111yescharacteristic
869C2#1307812411yescharacteristic
870C2#1307816211yescharacteristic
871C2#1307967711yescharacteristic
872C2#1307972511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC2×#10622851C2
hypercenterC2×#536D11
hypocenterC11#24219
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#10622670C2semidirect
2. C2×#10622696C2semidirect
4. C2×#10622840C2semidirect
5. #13071309C2semidirect
6. #13069859C2semidirect
7. #13069852C2semidirect
8. #13069699C2semidirect
9. #13069693C2semidirect
10. #13069549C2semidirect
11. #13069540C2semidirect
12. #13068600C2semidirect
13. #13068556C2semidirect
14. #13068551C2semidirect
15. C2×C11×#536C2semidirect
92. C11×C4⋊Q8D4semidirect
96. C11×#124D4semidirect
289. C2×#536D11semidirect
534. C4⋊Q8C22⋊D11semidirect
538. #124C22⋊D11semidirect
724. C11#24219semidirect

Maximal subgroups

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

subgroupindex
C2×#106226702
C2×#106226962
C2×#106228512
C2×#106228402
#130713092
#130698592
#130698522
#130696992
#130696932
#130695492
#130695402
#130686002
#130685562
#130685512
C2×C11×#5362
#2421911