Finite Group Databasebeta

← #14791424

Subgroups — #14791424

Order 2816.

1448 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622664C211yesmaximal, characteristic, complemented
2C2×#10622852C211yesmaximal, characteristic, complemented
3C2×#10622852C211yesmaximal, characteristic, complemented
4C2×#10622846C211yesmaximal, characteristic, complemented
5#13072045C211yesmaximal, characteristic, complemented
6#13069859C211yesmaximal, characteristic, complemented
7#13069816C211yesmaximal, characteristic, complemented
8#13069716C211yesmaximal, characteristic, complemented
9#13069624C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic, complemented
11#13068929C211yesmaximal, characteristic, complemented
12#13068909C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068556C211yesmaximal, characteristic, complemented
15C2×C11×#547C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C11×#547—24no—
19C11×#547—24no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C4⋊C4—21no—
29C22×#4326C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4324C2211yescharacteristic
32C2×#66979C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C23×C11⋊C8C2211yescharacteristic
36#10622852—24no—
37#10622852—24no—
38#10622846—24no—
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66899C2211yescharacteristic
44C2×#66899C2211yescharacteristic
45#10622835—21no—
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49#10622825C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53#10622664—24no—
54#10622585—21no—
55C2×#66874C2211yescharacteristic
56C2×#66871C2211yescharacteristic
57#10622565—21no—
58#10622558—21no—
59#10622542C2211yescharacteristic
60#10622541C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622162C2211yescharacteristic
64#10622162C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—22no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C2×C11×#41—41no—
76C2×C11×#41D414yes—
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11D411yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C11×C4⋊Q8—22no—
90C11×C4⋊Q8—22no—
91C11×#123—28no—
92C11×#123—28no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8D414yes—
97C11×#121—28no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C2×C11×C4⋊C4—28no—
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⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119C2×#4326—22no—
120C2×#4326—22no—
121C2×#4326—22no—
122C2×#4326—41no—
123C2×#4326—41no—
124C2×#4326—41no—
125C2×#4324—22no—
126C2×#4324—22no—
127C2×#4324—22no—
128#66979—22no—
129#66979—41no—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133#66977—22no—
134#66977—22no—
135#66977—22no—
136#66977—41no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×C4×Dic11—21no—
141C22×C11⋊C8—22no—
142C22×C11⋊C8—22no—
143C22×C11⋊C8—41no—
144C22×C11⋊C8C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148#66899—22no—
149#66899—22no—
150#66899—22no—
151#66899—22no—
152#66899—22no—
153#66899—41no—
154#66896—22no—
155#66896—22no—
156#66896D414yescomplemented
157C11⋊#95—21no—
158C11⋊#95—21no—
159C11⋊#95—21no—
160C11⋊#95—21no—
161C22⋊(C11⋊C8)—22no—
162C22⋊(C11⋊C8)—22no—
163C22⋊(C11⋊C8)—41no—
164#66874—22no—
165#66871—22no—
166#24430—111nomaximal, Sylow
167C24×C11—21no—
168C24×C11C2×D411yescharacteristic
169C24×C11C2×D411yescharacteristic
170C11×#41—28no—
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C11×#41—44no—
176C11×#41—44no—
177C11×#41—44no—
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×C11C2×D412yes—
189C2×Q8×C11C2×D412yes—
190C2×D4×C11—24no—
191C2×D4×C11—22no—
192C2×D4×C11—24no—
193C2×D4×C11—22no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—41no—
198C2×D4×C11—42no—
199C2×D4×C11—42no—
200C2×D4×C11—42no—
201C2×D4×C11—42no—
202C2×D4×C11C2×D412yes—
203C2×D4×C11C2×D412yes—
204C2×D4×C11#4112yes—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—24no—
210C22×C4×C11—24no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—24no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—42no—
222C22×C4×C11—42no—
223C22×C4×C11—42no—
224C22×C4×C11—42no—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2411yescharacteristic
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C2×Dic22—21no—
239C2×Dic22—21no—
240C2×Dic22—21no—
241C2×Dic22—21no—
242C2×Dic22—21no—
243C2×Dic22—21no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—22no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4C2×D412yes—
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—
258C22⋊Dic11—42no—
259C22⋊Dic11—42no—
260C22⋊Dic11—42no—
261C22⋊Dic11—42no—
262#4326—44no—
263#4326—44no—
264#4324—44no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11C2×D412yes—
271Dic11⋊C4—42no—
272Dic11⋊C4—42no—
273Dic11⋊C4—42no—
274C4×Dic11—42no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
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—44no—
287C2×C11⋊C8C2×D412yes—
288C2×#547D1111yescharacteristic
289C2×#467—111no—
290C2×#452—111no—
291C2×#452—111no—
292C2×#416—111no—
293#2415—111no—
294#2043—111no—
295#2036—111no—
296#2016—111no—
297#2001—111no—
298#1877—111no—
299#1873—111no—
300#1869—111no—
301#1862—111no—
302#1788—111no—
303C23×C11—22no—
304C23×C11—21no—
305C23×C11—22no—
306C23×C11—21no—
307C23×C11—22no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11#12012yes—
324C23×C11C22×D411yescharacteristic
325Q8×C11—22no—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—41no—
330Q8×C11—41no—
331Q8×C11—41no—
332Q8×C11—41no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—44no—
337D4×C11—48no—
338D4×C11—48no—
339D4×C11#12114yes—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—21no—
349C2×C4×C11—22no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—48no—
358C2×C4×C11—48no—
359C2×C4×C11—48no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11#12012yes—
371C2×C4×C11#13512yes—
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C2×#4111yescharacteristic
376C2×C4×C11H(5,𝔽2)11yescharacteristic
377C2×C4×C11H(5,𝔽2)11yescharacteristic
378C2×Dic11—22no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390Dic22—41no—
391Dic22—41no—
392Dic22—41no—
393Dic22—41no—
394C11⋊C8—22no—
395C11⋊C8—41no—
396C11⋊C8—41no—
397C11⋊C8—41no—
398C22×#41C2×D1111yescharacteristic
399C22×#41C2×D1111yescharacteristic
400C22×Q16—111no—
401C22×Q16—111no—
402C22×SD16—111no—
403C23×C8—111no—
404#547—24no—
405#547—24no—
406C2×C4⋊Q8C2×D1111yescharacteristic
407C2×#123—21no—
408C2×#123—21no—
409C2×C22⋊Q8—111no—
410C2×C22⋊Q8—111no—
411C2×C22⋊Q8C2×D1111yescharacteristic
412C2×C22⋊Q8C2×D1111yescharacteristic
413C2×#121—21no—
414C2×C4×D4C2×D1111yescharacteristic
415C2×C4×D4C2×D1111yescharacteristic
416C2×#117—111no—
417C22×C4⋊C4—21no—
418#467—224no—
419#452—224no—
420#452—224no—
421C2×#107—111no—
422#416—224no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×C22⋊C8—111no—
434C2×C22⋊C8—111no—
435C2×C22⋊C8—111no—
436#397—221no—
437#394—221no—
438#391—111no—
439#389—111no—
440#389—221no—
441#388—221no—
442#380—111no—
443#340—111no—
444#340—111no—
445#336—111no—
446#336—111no—
447C22×C11—22no—
448C22×C11—24no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—41no—
454C22×C11—42no—
455C22×C11—41no—
456C22×C11—42no—
457C22×C11—41no—
458C22×C11—42no—
459C22×C11—41no—
460C22×C11—42no—
461C22×C11—41no—
462C22×C11—41no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11C2×#12011yescharacteristic
469C22×C11D4211yescharacteristic
470C22×C11#54611yescharacteristic
471C22×C11C2×#13511yescharacteristic
472C22×C11#57511yescharacteristic
473C22×C11#57811yescharacteristic
474C22×C11#57811yescharacteristic
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—41no—
478C4×C11—42no—
479C4×C11—42no—
480C4×C11—42no—
481C4×C11—41no—
482C4×C11C2×#12111yescharacteristic
483C4×C11#53411yescharacteristic
484C4×C11D4211yescharacteristic
485C4×C11#54611yescharacteristic
486Dic11—42no—
487Dic11—81no—
488Dic11—81no—
489Dic11—81no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41C22⋊D1114yes—
502C22×Q8—111no—
503C22×Q8C22×D1111yescharacteristic
504C22×Q8C22×D1111yescharacteristic
505C22×D4—21no—
506C22×D4—21no—
507C22×D4C22⋊D1111yescharacteristic
508C22×D4C22×D1111yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C22×D1111yescharacteristic
513C23×C4C22×D1111yescharacteristic
514C2×Q16—222no—
515C2×Q16—222no—
516C2×Q16—222no—
517C2×Q16—441no—
518C2×Q16—441no—
519C2×Q16—441no—
520C2×SD16—222no—
521C2×SD16—222no—
522C2×SD16—222no—
523C22×C8—111no—
524C22×C8—111no—
525C22×C8—111no—
526C22×C8—111no—
527C22×C8—222no—
528C22×C8—222no—
529C22×C8—441no—
530C4⋊Q8—22no—
531C4⋊Q8—22no—
532#123—28no—
533#123—28no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—222no—
538C22⋊Q8—222no—
539C22⋊Q8—222no—
540C22⋊Q8—441no—
541C22⋊Q8C22⋊D1114yes—
542#121—28no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—22no—
547#117—222no—
548#117—441no—
549C2×C4⋊C4—28no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—221no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4C22⋊D1111yescharacteristic
561C2×C4⋊C4C22×D1111yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4C22⋊D1111yescharacteristic
570C2×C22⋊C4C22⋊D1111yescharacteristic
571C2×C42—221no—
572C2×C42C22×D1111yescharacteristic
573#107—222no—
574#103—222no—
575#103—222no—
576#103—222no—
577#103—222no—
578#103—222no—
579#103—222no—
580#103—441no—
581#102—114no—
582#102—222no—
583#102—222no—
584C22⋊C8—222no—
585C22⋊C8—222no—
586C22⋊C8—441no—
587#95—221no—
588#95—221no—
589#95—221no—
590#95—221no—
591C2×C11—42no—
592C2×C11—44no—
593C2×C11—81no—
594C2×C11#241011yescharacteristic
595C2×C11#300211yescharacteristic
596C2×C11#301111yescharacteristic
597C2×C11#326911yescharacteristic
598C2×C11#328311yescharacteristic
599C2×C11#330211yescharacteristic
600C2×C11#331511yescharacteristic
601C24—21no—
602C24C2×C22⋊D1111yescharacteristic
603C24C2×C22⋊D1111yescharacteristic
604#41—28no—
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
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—221no—
623C2×Q8—221no—
624C2×Q8—221no—
625C2×Q8—221no—
626C2×Q8—221no—
627C2×Q8—221no—
628C2×Q8C2×C22⋊D1112yes—
629C2×Q8C2×C22⋊D1112yes—
630C2×D4—24no—
631C2×D4—22no—
632C2×D4—24no—
633C2×D4—22no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—41no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4D4×D1112yes—
643C2×D4#434112yes—
644C2×D4C2×C22⋊D1112yes—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4C2×C22⋊D1111yescharacteristic
672C22×C4C2×C22⋊D1111yescharacteristic
673C22×C4C2×C22⋊D1111yescharacteristic
674C22×C4C2×C22⋊D1111yescharacteristic
675C22×C4C2×C22⋊D1112yes—
676C22×C4C2×C22⋊D1112yes—
677C22×C4C23×D1111yescharacteristic
678Q16—444no—
679Q16—444no—
680SD16—444no—
681C2×C8—112no—
682C2×C8—221no—
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—444no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—22no—
698C4⋊C4—24no—
699C4⋊C4—21no—
700C4⋊C4—112no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—442no—
707C4⋊C4—442no—
708C4⋊C4—442no—
709C4⋊C4C2×C22⋊D1112yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—442no—
716C22⋊C4—442no—
717C22⋊C4—442no—
718C22⋊C4—442no—
719C42—21no—
720C42—21no—
721C42—442no—
722C11#2443011yescharacteristic, complemented, Sylow
723C23—21no—
724C23—22no—
725C23—21no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23#6700612yes—
744C23C22×C22⋊D1111yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—41no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—441no—
754Q8—441no—
755Q8—441no—
756Q8—441no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—48no—
762D4—48no—
763D4#6699214yes—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—222no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
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#6700312yes—
807C2×C4#6700612yes—
808C2×C4C2×D4×D1111yescharacteristic
809C2×C4C2×#434111yescharacteristic
810C2×C4#6703711yescharacteristic
811C2×C4#6703711yescharacteristic
812C2×C4C22×C22⋊D1111yescharacteristic
813C2×C4C22×C22⋊D1111yescharacteristic
814C8—222no—
815C8—441no—
816C8—441no—
817C8—441no—
818C22—22no—
819C22—22no—
820C22—24no—
821C22—22no—
822C22—41no—
823C22—42no—
824C22—42no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22D4×C22⋊D1111yescharacteristic
840C22#1062333711yescharacteristic
841C22C2×#6700311yescharacteristic
842C22#1062335311yescharacteristic
843C22#1062336911yescharacteristic
844C22#1062336911yescharacteristic
845C22C2×#6700611yescharacteristic
846C4—22no—
847C4—22no—
848C4—42no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—41no—
853C4—442no—
854C4—881no—
855C4—881no—
856C4—881no—
857C4D4×C22⋊D1111yescharacteristic
858C4C2×#6699211yescharacteristic
859C4#1062333511yescharacteristic
860C4#1062333711yescharacteristic
861C2—42no—
862C2—44no—
863C2—81no—
864C2#1307199011yescharacteristic
865C2#1307783411yescharacteristic
866C2#1307791111yescharacteristic
867C2#1308016711yescharacteristic
868C2#1308033411yescharacteristic
869C2#1308053311yescharacteristic
870C2#1308071211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11#24430
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10622664C2semidirect
2. C2×#10622852C2semidirect
3. C2×#10622852C2semidirect
4. C2×#10622846C2semidirect
5. #13072045C2semidirect
6. #13069859C2semidirect
7. #13069816C2semidirect
8. #13069716C2semidirect
9. #13069624C2semidirect
10. #13068950C2semidirect
11. #13068929C2semidirect
12. #13068909C2semidirect
13. #13068863C2semidirect
14. #13068556C2semidirect
156. #66896D4semidirect
722. C11#24430semidirect

Maximal subgroups

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

subgroupindex
C2×#106226642
C2×#106228522
C2×#106228462
#130720452
#130698592
#130698162
#130697162
#130696242
#130689502
#130689292
#130689092
#130688632
#130685562
C2×C11×#5472
#2443011