Finite Group Databasebeta

← #14788947

Subgroups — #14788947

Order 2816.

1364 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622667C211yesmaximal, characteristic, complemented
2C2×#10622703C211yesmaximal, characteristic, complemented
3C2×#10622852C211yesmaximal, characteristic
4C2×#10622841C211yesmaximal, characteristic, complemented
5#13071298C211yesmaximal, characteristic, complemented
6#13069859C211yesmaximal, characteristic, complemented
7#13069852C211yesmaximal, characteristic, complemented
8#13069716C211yesmaximal, characteristic, complemented
9#13069710C211yesmaximal, characteristic, complemented
10#13069549C211yesmaximal, characteristic, complemented
11#13069540C211yesmaximal, characteristic, complemented
12#13068600C211yesmaximal, characteristic, complemented
13#13068556C211yesmaximal, characteristic
14#13068551C211yesmaximal, characteristic, complemented
15C2×C11×#536C211yesmaximal, characteristic
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×#4326C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C22×#4324C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35#10622852—24no—
36#10622841—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#10622703—24no—
53#10622667—24no—
54#10622591—21no—
55#10622585—21no—
56#10622558—21no—
57#10622557—21no—
58C4×C4⋊Dic11C2211yescharacteristic
59#10622542C2211yescharacteristic
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×Dic22C2311yescharacteristic
87C11×C4⋊Q8—22no—
88C11×C4⋊Q8—22no—
89C11×C4⋊Q8—22no—
90C11×C4⋊Q8D414yes—
91C11×#124—22no—
92C11×#124—22no—
93C11×#124—22no—
94C11×#124D414yes—
95C11×#123—28no—
96C11×#123—28no—
97C11×C22⋊Q8—28no—
98C11×C22⋊Q8—28no—
99C11×#117—22no—
100C11×#117—22no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4D411yescharacteristic
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×#4326—22no—
118C2×#4326—22no—
119C2×#4326—22no—
120C2×#4326—22no—
121C2×#4326—22no—
122C2×#4326—22no—
123C2×#4326—41no—
124C2×#4326—41no—
125C2×#4326—41no—
126C2×#4324—22no—
127C2×#4324—22no—
128C2×#4324—41no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132#66977—22no—
133#66977D414yes—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C4×Dic22—22no—
144C4×Dic22—22no—
145#66899—22no—
146#66899—22no—
147#66899—22no—
148#66899—22no—
149#66899—22no—
150#66899—22no—
151#66899—41no—
152#66899—41no—
153#66899—41no—
154#66896—22no—
155#66896—22no—
156#66896—41no—
157C11⋊#95—21no—
158C11⋊#95—21no—
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#24221—111nomaximal, Sylow
167C24×C11—21no—
168C24×C11C2×D411yescharacteristic
169C11×#41—44no—
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—44no—
173C2×Q8×C11—24no—
174C2×Q8×C11—21no—
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—44no—
190C2×Q8×C11—44no—
191C2×Q8×C11—44no—
192C2×Q8×C11—44no—
193C2×Q8×C11—42no—
194C2×Q8×C11—42no—
195C2×Q8×C11C2×D412yes—
196C2×Q8×C11C2×D412yes—
197C2×Q8×C11C2×D412yes—
198C2×D4×C11—24no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11C2×D412yes—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—24no—
212C22×C4×C11—24no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—42no—
217C22×C4×C11—42no—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D412yes—
226C22×C4×C11#4112yes—
227C22×C4×C11C2411yescharacteristic
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C2×Dic22—21no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22C2×D412yes—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—22no—
243C11×C4⋊C4—22no—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—22no—
249C11×C22⋊C4—22no—
250C42×C11—21no—
251C42×C11—21no—
252C42×C11C2×D412yes—
253C42×C11C2×D412yes—
254C22⋊Dic11—24no—
255C22⋊Dic11—81no—
256#4326—44no—
257#4326—44no—
258#4326—44no—
259#4324—44no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11C2×D412yes—
266Dic11⋊C4—24no—
267Dic11⋊C4—42no—
268Dic11⋊C4—81no—
269C4×Dic11—42no—
270C4×Dic11—81no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
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×#536D1111yescharacteristic
284C2×#464—111no—
285C2×#462—111no—
286C2×#452—111no—
287C2×#451—111no—
288#2323—111no—
289#2043—111no—
290#2042—111no—
291#2016—111no—
292#2015—111no—
293#1983—111no—
294#1981—111no—
295#1798—111no—
296#1788—111no—
297#1787—111no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—22no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11#12112yes—
312C23×C11C22×D411yescharacteristic
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—22no—
318Q8×C11—22no—
319Q8×C11—48no—
320Q8×C11—41no—
321Q8×C11—41no—
322Q8×C11—41no—
323Q8×C11—41no—
324Q8×C11—41no—
325Q8×C11—41no—
326D4×C11—22no—
327D4×C11—22no—
328D4×C11—48no—
329D4×C11—41no—
330D4×C11—41no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—48no—
351C2×C4×C11—48no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11#12012yes—
359C2×C4×C11#12012yes—
360C2×C4×C11#12112yes—
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11C2×#4111yescharacteristic
365C2×C4×C11H(5,𝔽2)11yescharacteristic
366C2×C4×C11H(5,𝔽2)11yescharacteristic
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379Dic22—22no—
380Dic22—22no—
381Dic22—41no—
382Dic22—41no—
383C11⋊C8—41no—
384C11⋊C8—41no—
385C11⋊C8—41no—
386C11⋊C8—41no—
387C22×#41C2×D1111yescharacteristic
388C23×Q8C2×D1111yescharacteristic
389C22×Q16—111no—
390C22×Q16—111no—
391C22×Q16—111no—
392C22×SD16—111no—
393#536—24no—
394#536—24no—
395C2×C4⋊Q8C2×D1111yescharacteristic
396C2×C4⋊Q8C2×D1111yescharacteristic
397C2×#124C2×D1111yescharacteristic
398C2×#124C2×D1111yescharacteristic
399C2×#123—21no—
400C2×#123—21no—
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8—21no—
403C2×C22⋊Q8—111no—
404C2×C4×Q8—111no—
405C2×#117C2×D1111yescharacteristic
406#464—224no—
407#462—224no—
408#452—224no—
409#451—224no—
410C2×C4⋊C8—111no—
411C2×C4⋊C8—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#103—111no—
420C2×#103—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×C22⋊C8—111no—
425C2×C22⋊C8—111no—
426#391—111no—
427#389—111no—
428#389—221no—
429#388—221no—
430#388—221no—
431#387—221no—
432#380—111no—
433C4×C4⋊C4—111no—
434#336—111no—
435#336—111no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—81no—
447C22×C11—81no—
448C22×C11—81no—
449C22×C11—81no—
450C22×C11C2×#12011yescharacteristic
451C22×C11C2×#12111yescharacteristic
452C22×C11#53511yescharacteristic
453C22×C11#57711yescharacteristic
454C22×C11#57811yescharacteristic
455C22×C11#57811yescharacteristic
456C22×C11#57811yescharacteristic
457C4×C11—22no—
458C4×C11—22no—
459C4×C11—22no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11—42no—
463C4×C11—41no—
464C4×C11—41no—
465C4×C11D4211yescharacteristic
466C4×C11D4211yescharacteristic
467C4×C11#54611yescharacteristic
468C4×C11#54611yescharacteristic
469Dic11—42no—
470Dic11—42no—
471Dic11—81no—
472Dic11—81no—
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—41no—
478C2×#41—41no—
479C22×Q8—22no—
480C22×Q8—22no—
481C22×Q8—21no—
482C22×Q8—22no—
483C22×Q8—22no—
484C22×Q8—41no—
485C22×Q8—41no—
486C22×Q8—111no—
487C22×Q8C22×D1111yescharacteristic
488C22×Q8C22×D1111yescharacteristic
489C22×Q8C22×D1111yescharacteristic
490C22×D4—21no—
491C22×D4C22×D1111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C22×D1111yescharacteristic
495C2×Q16—222no—
496C2×Q16—222no—
497C2×Q16—222no—
498C2×Q16—222no—
499C2×Q16—222no—
500C2×Q16—222no—
501C2×Q16—441no—
502C2×Q16—441no—
503C2×Q16—441no—
504C2×SD16—222no—
505C2×SD16—222no—
506C2×SD16—441no—
507C22×C8—111no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—111no—
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8C22⋊D1114yes—
515#124—22no—
516#124—22no—
517#124—22no—
518#124C22⋊D1114yes—
519#123—28no—
520#123—28no—
521C22⋊Q8—28no—
522C22⋊Q8—28no—
523C22⋊Q8—114no—
524C22⋊Q8—222no—
525C4×Q8—222no—
526C4×Q8—222no—
527#117—22no—
528#117—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—111no—
535C2×C4⋊C4—111no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4C22⋊D1111yescharacteristic
540C2×C4⋊C4C22⋊D1111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4C22⋊D1111yescharacteristic
548C2×C22⋊C4C22⋊D1111yescharacteristic
549C2×C42—221no—
550C2×C42—221no—
551C2×C42C22×D1111yescharacteristic
552C2×C42C22×D1111yescharacteristic
553C4⋊C8—222no—
554C4⋊C8—222no—
555#103—222no—
556#103—222no—
557#103—222no—
558#103—222no—
559#103—222no—
560#103—222no—
561#103—441no—
562#103—441no—
563#103—441no—
564#102—222no—
565#102—222no—
566#102—441no—
567C22⋊C8—222no—
568C22⋊C8—222no—
569#95—221no—
570#95—221no—
571#95—221no—
572#95—221no—
573#95—221no—
574C2×C11—42no—
575C2×C11—82no—
576C2×C11#240811yescharacteristic
577C2×C11#301111yescharacteristic
578C2×C11#301311yescharacteristic
579C2×C11#304411yescharacteristic
580C2×C11#304611yescharacteristic
581C2×C11#322311yescharacteristic
582C2×C11#322511yescharacteristic
583C24—21no—
584C24C2×C22⋊D1111yescharacteristic
585#41—44no—
586#41—44no—
587#41—44no—
588#41—44no—
589C2×Q8—24no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8—112no—
612C2×Q8—221no—
613C2×Q8—221no—
614C2×Q8—221no—
615C2×Q8—221no—
616C2×Q8—221no—
617C2×Q8C2×C22⋊D1112yes—
618C2×Q8C2×C22⋊D1112yes—
619C2×Q8C2×C22⋊D1112yes—
620C2×D4—24no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4C2×C22⋊D1112yes—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4D4×D1112yes—
647C22×C4#434112yes—
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C2×C22⋊D1111yescharacteristic
653C22×C4C23×D1111yescharacteristic
654Q16—444no—
655Q16—444no—
656Q16—444no—
657SD16—444no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—221no—
664C2×C8—221no—
665C2×C8—221no—
666C2×C8—221no—
667C2×C8—221no—
668C2×C8—221no—
669C2×C8—221no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—112no—
677C4⋊C4—224no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—221no—
681C4⋊C4—221no—
682C4⋊C4—221no—
683C4⋊C4—442no—
684C4⋊C4—881no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—224no—
692C22⋊C4—881no—
693C42—21no—
694C42—21no—
695C42—442no—
696C42—881no—
697C42C2×C22⋊D1112yes—
698C42C2×C22⋊D1112yes—
699C11#2422111yescharacteristic, complemented, Sylow
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23#6699112yes—
714C23C22×C22⋊D1111yescharacteristic
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—48no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727Q8—41no—
728Q8—222no—
729Q8—222no—
730Q8—441no—
731Q8—441no—
732D4—22no—
733D4—22no—
734D4—48no—
735D4—41no—
736D4—41no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—48no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4#6699112yes—
777C2×C4#6700612yes—
778C2×C4#6700612yes—
779C2×C4C2×D4×D1111yescharacteristic
780C2×C4C2×#434111yescharacteristic
781C2×C4#6703711yescharacteristic
782C2×C4#6703711yescharacteristic
783C2×C4C22×C22⋊D1111yescharacteristic
784C2×C4C22×C22⋊D1111yescharacteristic
785C8—441no—
786C8—441no—
787C8—441no—
788C8—441no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#6699111yescharacteristic
804C22#1062333611yescharacteristic
805C22#1062336811yescharacteristic
806C22#1062336911yescharacteristic
807C22#1062336911yescharacteristic
808C22#1062336911yescharacteristic
809C22C2×#6700611yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—41no—
817C4—41no—
818C4—442no—
819C4—442no—
820C4—881no—
821C4—881no—
822C4D4×C22⋊D1111yescharacteristic
823C4D4×C22⋊D1111yescharacteristic
824C4#1062333711yescharacteristic
825C4#1062333711yescharacteristic
826C2—42no—
827C2—82no—
828C2#1307196611yescharacteristic
829C2#1307791111yescharacteristic
830C2#1307793111yescharacteristic
831C2#1307814211yescharacteristic
832C2#1307816211yescharacteristic
833C2#1307969911yescharacteristic
834C2#1307972511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#536D11
hypocenterC11#24221
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×#10622667C2semidirect
2. C2×#10622703C2semidirect
4. C2×#10622841C2semidirect
5. #13071298C2semidirect
6. #13069859C2semidirect
7. #13069852C2semidirect
8. #13069716C2semidirect
9. #13069710C2semidirect
10. #13069549C2semidirect
11. #13069540C2semidirect
12. #13068600C2semidirect
14. #13068551C2semidirect
699. C11#24221semidirect

Maximal subgroups

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

subgroupindex
C2×#106226672
C2×#106227032
C2×#106228522
C2×#106228412
#130712982
#130698592
#130698522
#130697162
#130697102
#130695492
#130695402
#130686002
#130685562
#130685512
C2×C11×#5362
#2422111