Finite Group Databasebeta

← #14769268

Subgroups — #14769268

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4#13071545C211yesmaximal, characteristic, complemented
5#13069540C211yesmaximal, characteristic, complemented
6#13069437C211yesmaximal, characteristic, complemented
7#13069050C211yesmaximal, characteristic, complemented
8#13069040C211yesmaximal, characteristic, complemented
9#13068929C211yesmaximal, characteristic, complemented
10#13068924C211yesmaximal, characteristic, complemented
11#13068626C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068556C211yesmaximal, characteristic, complemented
14#13068441C211yesmaximal, characteristic, complemented
15C2×C11×#547C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C11×#547—24no—
19C11×#547C418yescomplemented
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—
29C2×#66979C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C23×C11⋊C8C2211yescharacteristic
33#10622846—24no—
34#10622845—24no—
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43#10622833—21no—
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48#10622825C2211yescharacteristic
49#10622825C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52#10622624—24no—
53#10622594—21no—
54#10622564—21no—
55C22⋊C4×Dic11—21no—
56#10622549C2211yescharacteristic
57C4×C4⋊Dic11C2211yescharacteristic
58C2×C4⋊(C11⋊C8)C2211yescharacteristic
59C2×#66867C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41C2×C414yes—
75C2×C11×#41C2×C414yescomplemented
76C22×Q8×C11C2311yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×Dic11—21no—
88C11×C4⋊Q8—22no—
89C11×C4⋊Q8C2×C414yescomplemented
90C11×#123—28no—
91C11×#123—28no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8C2×C414yes—
95C11×C22⋊Q8C2×C414yescomplemented
96C11×#121—28no—
97C4×D4×C11—22no—
98C4×D4×C11C2×C414yes—
99C4×D4×C11C2×C414yescomplemented
100C4×D4×C11D414yes—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—28no—
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
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×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#66979—22no—
118#66979—41no—
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—41no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4×Dic11—21no—
127C2×C4×Dic11—21no—
128C2×#4318—22no—
129C2×#4318—22no—
130C2×#4318—41no—
131C22×C11⋊C8—22no—
132C22×C11⋊C8—22no—
133C22×C11⋊C8—41no—
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138#66899—22no—
139#66899—22no—
140#66899—22no—
141#66899—22no—
142#66899—41no—
143#66899—41no—
144#66899—41no—
145#66899—41no—
146#66896—22no—
147#66896—22no—
148#66896—22no—
149#66896D414yescomplemented
150C11⋊#95—21no—
151C11⋊#95—21no—
152C11⋊#95—21no—
153C11⋊#95—21no—
154C11⋊#95—21no—
155C22⋊(C11⋊C8)—22no—
156C22⋊(C11⋊C8)—22no—
157C4⋊(C11⋊C8)—22no—
158#66867—22no—
159#22420—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11C2×D411yescharacteristic
162C24×C11C2×D411yescharacteristic
163C11×#41—28no—
164C11×#41—28no—
165C11×#41—44no—
166C11×#41—44no—
167C11×#41—44no—
168C11×#41—44no—
169C11×#41—44no—
170C11×#41—44no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
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×C11C22×C412yes—
182C2×Q8×C11C22×C412yes—
183C2×D4×C11—24no—
184C2×D4×C11—24no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—41no—
189C2×D4×C11—41no—
190C2×D4×C11—42no—
191C2×D4×C11—42no—
192C2×D4×C11—42no—
193C2×D4×C11—42no—
194C2×D4×C11C22⋊C414yes—
195C2×D4×C11C22×C412yes—
196C2×D4×C11C2×D412yes—
197C2×D4×C11#4112yes—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
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—24no—
212C22×C4×C11—42no—
213C22×C4×C11—42no—
214C22×C4×C11—42no—
215C22×C4×C11—42no—
216C22×C4×C11—42no—
217C22×C4×C11—42no—
218C22×C4×C11C22×C412yes—
219C22×C4×C11C22×C412yes—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D412yes—
225C22×C4×C11C2×D412yes—
226C22×C4×C11C2411yescharacteristic
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—42no—
232C22×Dic11—42no—
233C22×Dic11—81no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—24no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4C22⋊C414yes—
240C11×C4⋊C4C22×C412yes—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—24no—
244C11×C22⋊C4C22⋊C414yes—
245C11×C22⋊C4C22⋊C414yes—
246C42×C11C22×C412yes—
247C42×C11C2×D412yes—
248C22⋊Dic11—42no—
249C22⋊Dic11—42no—
250C22⋊Dic11—81no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11—42no—
259C4⋊Dic11C2×D412yes—
260C4×Dic11—42no—
261C4×Dic11—81no—
262#4318—44no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—44no—
275C2×C11⋊C8C2×D412yes—
276C2×#547D1111yescharacteristic
277C2×#435—111no—
278C2×#417—111no—
279C2×#416—111no—
280#2352—111no—
281#1981—111no—
282#1960—111no—
283#1894—111no—
284#1892—111no—
285#1873—111no—
286#1872—111no—
287#1804—111no—
288#1788—111no—
289#1788—111no—
290#1762—111no—
291C23×C11—22no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—22no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11C2×C22⋊C412yes—
311C23×C11C2×C22⋊C412yes—
312C23×C11C22×D411yescharacteristic
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—41no—
318Q8×C11—41no—
319Q8×C11—41no—
320Q8×C11—41no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—44no—
325D4×C11—48no—
326D4×C11—48no—
327D4×C11C4×D414yes—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—48no—
348C2×C4×C11—48no—
349C2×C4×C11—48no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11C2×C22⋊C412yes—
357C2×C4×C11C2×C22⋊C412yes—
358C2×C4×C11C2×C22⋊C412yes—
359C2×C4×C11C2×C22⋊C412yes—
360C2×C4×C11C23×C411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C2×#4111yescharacteristic
364C2×C4×C11H(5,𝔽2)11yescharacteristic
365C2×C4×C11H(5,𝔽2)11yescharacteristic
366C2×Dic11—22no—
367C2×Dic11—41no—
368C2×Dic11—41no—
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—84no—
379C11⋊C8—22no—
380C11⋊C8—41no—
381C11⋊C8—41no—
382C11⋊C8—41no—
383C22×#41C2×D1111yescharacteristic
384C22×#41C2×D1111yescharacteristic
385C22×M16—111no—
386C23×C8—111no—
387#547—24no—
388#547Dic1118yescomplemented
389C2×C4⋊Q8C2×D1111yescharacteristic
390C2×#123—21no—
391C2×#123—21no—
392C2×C22⋊Q8C2×D1111yescharacteristic
393C2×C22⋊Q8C2×D1111yescharacteristic
394C2×#121—21no—
395C2×C4×D4C2×D1111yescharacteristic
396C2×C4×D4C2×D1111yescharacteristic
397C2×#117—111no—
398C22×C4⋊C4—21no—
399C22×C4⋊C4—111no—
400#435—224no—
401C2×C4⋊C8—111no—
402#417—224no—
403#416—224no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×C22⋊C8—111no—
417C2×C22⋊C8—111no—
418C2×#97—111no—
419#388—221no—
420#387—221no—
421#386—221no—
422#382—111no—
423#380—111no—
424#380—111no—
425C4×C4⋊C4—111no—
426C4×C22⋊C4—221no—
427#340—111no—
428#340—111no—
429#340—111no—
430#340—111no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—24no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—42no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—42no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—42no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—42no—
452C22×C11C22×C22⋊C411yescharacteristic
453C22×C11D4211yescharacteristic
454C22×C11#54611yescharacteristic
455C22×C11#57511yescharacteristic
456C22×C11#57511yescharacteristic
457C22×C11#57711yescharacteristic
458C22×C11#57811yescharacteristic
459C4×C11—22no—
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11C2×C4×D411yescharacteristic
467C4×C11#51811yescharacteristic
468C4×C11D4211yescharacteristic
469C4×C11#54611yescharacteristic
470Dic11—42no—
471Dic11—81no—
472Dic11—81no—
473Dic11—81no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—41no—
481C2×#41—41no—
482C2×#41—41no—
483C2×#41—41no—
484C2×#41C2×Dic1114yes—
485C2×#41C2×Dic1114yescomplemented
486C22×Q8C22×D1111yescharacteristic
487C22×Q8C22×D1111yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C22⋊D1111yescharacteristic
491C22×D4C22×D1111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×M16—222no—
499C2×M16—222no—
500C2×M16—441no—
501C22×C8—111no—
502C22×C8—111no—
503C22×C8—111no—
504C22×C8—111no—
505C22×C8—222no—
506C22×C8—222no—
507C22×C8—441no—
508C4⋊Q8—22no—
509C4⋊Q8C2×Dic1114yescomplemented
510#123—28no—
511#123—28no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8C2×Dic1114yes—
515C22⋊Q8C2×Dic1114yescomplemented
516#121—28no—
517C4×D4—22no—
518C4×D4C2×Dic1114yes—
519C4×D4C2×Dic1114yescomplemented
520C4×D4C22⋊D1114yes—
521#117—222no—
522#117—441no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—28no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—222no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—441no—
535C2×C4⋊C4C22⋊D1111yescharacteristic
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4C22⋊D1111yescharacteristic
544C2×C22⋊C4C22⋊D1111yescharacteristic
545C2×C42—221no—
546C2×C42—221no—
547C2×C42C22×D1111yescharacteristic
548C4⋊C8—222no—
549#103—222no—
550#103—222no—
551#103—222no—
552#103—222no—
553#103—441no—
554#103—441no—
555#103—441no—
556#103—441no—
557#102—114no—
558#102—222no—
559#102—222no—
560#102—222no—
561C22⋊C8—222no—
562C22⋊C8—222no—
563#97—222no—
564#95—221no—
565#95—221no—
566#95—221no—
567#95—221no—
568#95—221no—
569C2×C11—42no—
570C2×C11—42no—
571C2×C11—44no—
572C2×C11D4×C22⋊C411yescharacteristic
573C2×C11#289611yescharacteristic
574C2×C11#289811yescharacteristic
575C2×C11#326711yescharacteristic
576C2×C11#326911yescharacteristic
577C2×C11#330711yescharacteristic
578C2×C11#331511yescharacteristic
579C24—21no—
580C24C2×C22⋊D1111yescharacteristic
581C24C2×C22⋊D1111yescharacteristic
582#41—28no—
583#41—28no—
584#41—44no—
585#41—44no—
586#41—44no—
587#41—44no—
588#41—44no—
589#41—44no—
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×Q8C22×Dic1112yes—
601C2×Q8C22×Dic1112yes—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4C22⋊Dic1114yes—
614C2×D4D4×D1112yes—
615C2×D4#434112yes—
616C2×D4C22×Dic1112yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—442no—
642C22×C4—442no—
643C22×C4—881no—
644C22×C4C22×Dic1112yes—
645C22×C4C22×Dic1112yes—
646C22×C4C2×C22⋊D1111yescharacteristic
647C22×C4C2×C22⋊D1111yescharacteristic
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1112yes—
651C22×C4C2×C22⋊D1112yes—
652C22×C4C23×D1111yescharacteristic
653M16—444no—
654C2×C8—112no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
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—444no—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—112no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4—221no—
676C4⋊C4—221no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—442no—
681C4⋊C4C22⋊Dic1114yes—
682C4⋊C4C22×Dic1112yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—442no—
687C22⋊C4—442no—
688C22⋊C4—881no—
689C22⋊C4C22⋊Dic1114yes—
690C22⋊C4C22⋊Dic1114yes—
691C42—442no—
692C42—881no—
693C42C22×Dic1112yes—
694C42C2×C22⋊D1112yes—
695C11#2242011yescharacteristic, complemented, Sylow
696C23—21no—
697C23—21no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—22no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C2×C22⋊Dic1112yes—
716C23C2×C22⋊Dic1112yes—
717C23C22×C22⋊D1111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—44no—
730D4—48no—
731D4—48no—
732D4D4×Dic1114yes—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—48no—
754C2×C4—48no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—222no—
762C2×C4—441no—
763C2×C4—441no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—884no—
774C2×C4C2×C22⋊Dic1112yes—
775C2×C4C2×C22⋊Dic1112yes—
776C2×C4C2×C22⋊Dic1112yes—
777C2×C4C2×C22⋊Dic1112yes—
778C2×C4C2×D4×D1111yescharacteristic
779C2×C4C2×#434111yescharacteristic
780C2×C4#6703711yescharacteristic
781C2×C4#6703711yescharacteristic
782C2×C4C23×Dic1111yescharacteristic
783C2×C4C22×C22⋊D1111yescharacteristic
784C8—222no—
785C8—441no—
786C8—441no—
787C8—441no—
788C22—22no—
789C22—22no—
790C22—24no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22D4×C22⋊D1111yescharacteristic
810C22#1062333711yescharacteristic
811C22#1062335311yescharacteristic
812C22#1062335311yescharacteristic
813C22#1062336811yescharacteristic
814C22#1062336911yescharacteristic
815C22C22×C22⋊Dic1111yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—442no—
824C4—881no—
825C4—881no—
826C4—881no—
827C4C2×D4×Dic1111yescharacteristic
828C4#1062332911yescharacteristic
829C4D4×C22⋊D1111yescharacteristic
830C4#1062333711yescharacteristic
831C2—42no—
832C2—42no—
833C2—44no—
834C2D4×C22⋊Dic1111yescharacteristic
835C2#1307713511yescharacteristic
836C2#1307714911yescharacteristic
837C2#1308014211yescharacteristic
838C2#1308016711yescharacteristic
839C2#1308059211yescharacteristic
840C2#1308071211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#547D11
hypocenterC11#22420
LCSG ▷ C2×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×#10622624C2semidirect
2. C2×#10622845C2semidirect
3. C2×#10622846C2semidirect
4. #13071545C2semidirect
5. #13069540C2semidirect
6. #13069437C2semidirect
7. #13069050C2semidirect
8. #13069040C2semidirect
9. #13068929C2semidirect
10. #13068924C2semidirect
11. #13068626C2semidirect
12. #13068556C2semidirect
13. #13068556C2semidirect
14. #13068441C2semidirect
19. C11×#547C4semidirect
75. C2×C11×#41C2×C4semidirect
89. C11×C4⋊Q8C2×C4semidirect
95. C11×C22⋊Q8C2×C4semidirect
99. C4×D4×C11C2×C4semidirect
149. #66896D4semidirect
388. #547Dic11semidirect
485. C2×#41C2×Dic11semidirect
509. C4⋊Q8C2×Dic11semidirect
515. C22⋊Q8C2×Dic11semidirect
519. C4×D4C2×Dic11semidirect
695. C11#22420semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C2×#106228452
C2×#106228462
#130715452
#130695402
#130694372
#130690502
#130690402
#130689292
#130689242
#130686262
#130685562
#130684412
C2×C11×#5472
#2242011