Finite Group Databasebeta

← #14764057

Subgroups — #14764057

Order 2816.

1090 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622339C211yesmaximal, characteristic
2#13070998C211yesmaximal, characteristic
3#13070995C211yesmaximal, characteristic
4#13068818C211yesmaximal, characteristic, complemented
5#13068817C211yesmaximal, characteristic, complemented
6#13068816C211yesmaximal, characteristic, complemented
7#13068815C211yesmaximal, characteristic, complemented
8#13068814C211yesmaximal, characteristic, complemented
9#13068813C211yesmaximal, characteristic, complemented
10#13068812C211yesmaximal, characteristic, complemented
11#13068650C211yesmaximal, characteristic, complemented
12#13068648C211yesmaximal, characteristic, complemented
13#13068648C211yesmaximal, characteristic, complemented
14#13068646C211yesmaximal, characteristic, complemented
15C11×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×#66945C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic, complemented
24C2×C11×#106C2211yescharacteristic, complemented
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66882C2211yescharacteristic, complemented
32C2×#66881C2211yescharacteristic, complemented
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39C2×#66872C2211yescharacteristic, complemented
40C2×#66872C2211yescharacteristic, complemented
41C2×#66871C2211yescharacteristic, complemented
42C2×#66871C2211yescharacteristic, complemented
43#10622568—21no—
44#10622568—21no—
45#10622556—21no—
46C22⋊C4×Dic11—21no—
47C4×(C2×D11)⋊C4—21no—
48C4×(C2×D11)⋊C4—21no—
49#10622339C418yescomplemented
50#10622279—21no—
51#10622277—21no—
52C11×#340C2211yescharacteristic, complemented
53C11×#340C2211yescharacteristic, complemented
54#10622189C2211yescharacteristic, complemented
55#10622189C2211yescharacteristic, complemented
56#10622167C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60C24×D11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11D411yescharacteristic
63C22×C4×D11—41no—
64C22×C4×D11—41no—
65C22×C4×D11—41no—
66C22×C4×D11—41no—
67C22×C4×D11C2×C414yes—
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D411yescharacteristic
70C22×C4×D11Q814yes—
71C22×C4×D11C2311yescharacteristic
72C22×C4×D11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×#117—41no—
76C11×#117—41no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94#66979—41no—
95#66979—41no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C2×#4313—41no—
106C2×#4313—41no—
107C2×#4313—41no—
108C2×#4313—41no—
109C2×#4313C2×C414yes—
110C2×#4313C2×C414yes—
111#66945—41no—
112#66945—41no—
113#66945—41no—
114#66945—41no—
115C11×#107—41no—
116C11×#106—41no—
117C11×C22⋊C8C2×C414yes—
118C11×#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C22⋊(C11⋊C8)C2×C414yes—
127(C2×D11)⋊C8C2×C414yes—
128(C2×D11)⋊C8C2×C414yes—
129#66882—41no—
130#66881—41no—
131#66872—41no—
132#66872—41no—
133#66871—41no—
134#66871—41no—
135#21943—111nomaximal, Sylow
136C24×C11C2×D411yescharacteristic
137C23×D11—41no—
138C23×D11—41no—
139C23×D11—41no—
140C23×D11—41no—
141C23×D11—41no—
142C23×D11—41no—
143C23×D11C4⋊C414yes—
144C23×D11C2×D411yescharacteristic
145C23×D11C2×D411yescharacteristic
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×Q812yes—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—41no—
163C22×Dic11—41no—
164C22×Dic11C4⋊C414yes—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—41no—
176C2×C4×D11—41no—
177C2×C4×D11—41no—
178C2×C4×D11—41no—
179C2×C4×D11—44no—
180C2×C4×D11—44no—
181C2×C4×D11—44no—
182C2×C4×D11—44no—
183C2×C4×D11C4⋊C414yes—
184C2×C4×D11C4⋊C414yes—
185C2×C4×D11C22×C412yes—
186C2×C4×D11C22×C412yes—
187C2×C4×D11C2×Q812yes—
188C2×C4×D11C2×Q812yes—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11C22×C412yes—
194C2×C8×C11C22×C412yes—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C42×C11—42no—
206C22⋊Dic11—42no—
207C22⋊Dic11—42no—
208(C2×D11)⋊C4—42no—
209(C2×D11)⋊C4—42no—
210(C2×D11)⋊C4—42no—
211(C2×D11)⋊C4—42no—
212(C2×D11)⋊C4—42no—
213(C2×D11)⋊C4—42no—
214(C2×D11)⋊C4—42no—
215(C2×D11)⋊C4—42no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4×Dic11—42no—
225C4×Dic11—42no—
226C4×Dic11—42no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8C22×C412yes—
232C2×C11⋊C8C22×C412yes—
233#4313—44no—
234#4313—44no—
235C2×#407—111no—
236#2280—111no—
237#2280—111no—
238#1854—111no—
239#1854—111no—
240#1854—111no—
241#1854—111no—
242#1854—111no—
243#1854—111no—
244#1854—111no—
245#1854D1111yescharacteristic, complemented
246#1809—111no—
247#1809—111no—
248#1809—111no—
249#1809—111no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11C2×C4⋊C412yes—
257C23×C11C22×D411yescharacteristic
258C22×D11—21no—
259C22×D11—21no—
260C22×D11—21no—
261C22×D11—21no—
262C22×D11—21no—
263C22×D11—21no—
264C22×D11—21no—
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—21no—
270C22×D11—44no—
271C22×D11—44no—
272C22×D11—44no—
273C22×D11—44no—
274C22×D11—44no—
275C22×D11—44no—
276C22×D11—44no—
277C22×D11C2×C4⋊C412yes—
278C22×D11C2×C4⋊C412yes—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11C2×C4⋊C412yes—
298C2×C4×C11C23×C411yescharacteristic
299C2×C4×C11C22×Q811yescharacteristic
300C2×C4×C11H(5,𝔽2)11yescharacteristic
301C2×C4×C11H(5,𝔽2)11yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—21no—
308C2×Dic11—44no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11C2×C4⋊C412yes—
322C2×Dic11C2×C4⋊C412yes—
323C4×D11—22no—
324C4×D11—22no—
325C4×D11—22no—
326C4×D11—22no—
327C4×D11—22no—
328C4×D11—22no—
329C4×D11—22no—
330C4×D11—22no—
331C4×D11—44no—
332C4×D11—44no—
333C8×C11—22no—
334C8×C11—22no—
335C11⋊C8—22no—
336C11⋊C8—22no—
337C24×C4—111no—
338C22×M16—111no—
339C22×M16—111no—
340C2×#117—111no—
341C2×#117—111no—
342C2×#117—111no—
343C2×#117C2×D1111yescharacteristic
344C2×#107—111no—
345C2×#107—111no—
346C2×#107—111no—
347C2×#107C2×D1111yescharacteristic, complemented
348C2×#106—111no—
349C2×#106—111no—
350C2×#106—111no—
351C2×#106C2×D1111yescharacteristic, complemented
352#407—118no—
353C2×C22⋊C8—111no—
354C2×C22⋊C8—111no—
355C2×C22⋊C8—111no—
356C2×C22⋊C8C2×D1111yescharacteristic
357#381—221no—
358#381—221no—
359#380—111no—
360#380—111no—
361#380—111no—
362#380—111no—
363#380—111no—
364#380—111no—
365#380—111no—
366#380C2×D1111yescharacteristic
367#379—221no—
368#379—221no—
369C4×C22⋊C4—221no—
370C4×C22⋊C4—221no—
371C4×C22⋊C4—221no—
372C4×C22⋊C4—221no—
373#340—111no—
374#340—111no—
375#340—111no—
376#340—111no—
377#340—111no—
378#340—111no—
379#340C2×D1111yescharacteristic, complemented
380#340C2×D1111yescharacteristic, complemented
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11C22×C4⋊C411yescharacteristic
389C22×C11#53411yescharacteristic
390C22×C11#53411yescharacteristic
391C22×C11#57511yescharacteristic
392C22×C11#57511yescharacteristic
393C22×C11#57511yescharacteristic
394C22×C11#57511yescharacteristic
395C2×D11—22no—
396C2×D11—22no—
397C2×D11—22no—
398C2×D11—22no—
399C2×D11—22no—
400C2×D11—22no—
401C2×D11—416no—
402C2×D11—41no—
403C2×D11—41no—
404C2×D11—41no—
405C2×D11—41no—
406C2×D11—41no—
407C2×D11—41no—
408C2×D11—41no—
409C2×D11—41no—
410C4×C11—22no—
411C4×C11—81no—
412C4×C11—81no—
413C4×C11—81no—
414C4×C11—81no—
415C4×C11#51811yescharacteristic
416C4×C11#51811yescharacteristic
417C4×C11#54311yescharacteristic
418C4×C11#54311yescharacteristic
419Dic11—22no—
420Dic11—22no—
421Dic11—81no—
422Dic11—81no—
423Dic11—81no—
424Dic11—81no—
425C25—111no—
426C23×C4—111no—
427C23×C4—111no—
428C23×C4—111no—
429C23×C4—114no—
430C23×C4—111no—
431C23×C4—111no—
432C23×C4—114no—
433C23×C4—441no—
434C23×C4—441no—
435C23×C4—441no—
436C23×C4—441no—
437C23×C4C22×D1111yescharacteristic
438C2×M16—114no—
439C2×M16—114no—
440C2×M16—441no—
441C2×M16—441no—
442C2×M16—441no—
443C2×M16—441no—
444C22×C8—111no—
445C22×C8—111no—
446C22×C8C22×D1111yescharacteristic
447C22×C8C22×D1111yescharacteristic
448#117—41no—
449#117—41no—
450#117—441no—
451#117—441no—
452#117—441no—
453#117—441no—
454#117—441no—
455#117—441no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4C22×D1111yescharacteristic
461C2×C4⋊C4C22×D1111yescharacteristic
462C2×C4⋊C4C22×D1111yescharacteristic
463C2×C4⋊C4C22×D1111yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—221no—
467C2×C22⋊C4—221no—
468C2×C22⋊C4—221no—
469C2×C22⋊C4—221no—
470C2×C22⋊C4—221no—
471C2×C22⋊C4—221no—
472C2×C22⋊C4—221no—
473C2×C22⋊C4—221no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C42—21no—
477C2×C42—221no—
478C2×C42—221no—
479C2×C42—221no—
480#107—41no—
481#107—441no—
482#107—441no—
483#107—441no—
484#106—41no—
485#106—441no—
486#106—441no—
487#106—441no—
488C22⋊C8—114no—
489C22⋊C8—114no—
490C22⋊C8—114no—
491C22⋊C8C4×D1114yes—
492#95—21no—
493#95—221no—
494#95—221no—
495#95—221no—
496#95—221no—
497#95—221no—
498#95—221no—
499#95—221no—
500C2×C11—42no—
501C2×C11#231511yescharacteristic
502C2×C11#291111yescharacteristic
503C2×C11#291111yescharacteristic
504C2×C11#319711yescharacteristic
505C2×C11#319711yescharacteristic
506C2×C11#319711yescharacteristic
507C2×C11#319711yescharacteristic
508D11—42no—
509D11—42no—
510C24—111no—
511C24—111no—
512C24—114no—
513C24—441no—
514C24—441no—
515C24—441no—
516C24—441no—
517C24—441no—
518C24—441no—
519C24D4×D1111yescharacteristic
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—111no—
529C22×C4—111no—
530C22×C4—114no—
531C22×C4—112no—
532C22×C4—112no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—114no—
536C22×C4—114no—
537C22×C4—221no—
538C22×C4—221no—
539C22×C4—221no—
540C22×C4—221no—
541C22×C4—221no—
542C22×C4—221no—
543C22×C4—221no—
544C22×C4—221no—
545C22×C4—221no—
546C22×C4—221no—
547C22×C4—221no—
548C22×C4—221no—
549C22×C4—444no—
550C22×C4—444no—
551C22×C4—444no—
552C22×C4—444no—
553C22×C4—441no—
554C22×C4—441no—
555C22×C4—441no—
556C22×C4—441no—
557C22×C4—441no—
558C22×C4—441no—
559C22×C4C2×C4×D1112yes—
560C22×C4D4×D1111yescharacteristic
561C22×C4Q8×D1112yes—
562C22×C4C23×D1111yescharacteristic
563M16—444no—
564M16—444no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—112no—
570C2×C8—112no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8C2×C4×D1112yes—
576C2×C8C2×C4×D1112yes—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—221no—
586C4⋊C4—221no—
587C4⋊C4—221no—
588C4⋊C4—221no—
589C4⋊C4—221no—
590C4⋊C4—221no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—442no—
596C22⋊C4—442no—
597C22⋊C4—442no—
598C22⋊C4—442no—
599C22⋊C4—442no—
600C22⋊C4—442no—
601C22⋊C4—442no—
602C22⋊C4—442no—
603C22⋊C4—442no—
604C22⋊C4—442no—
605C42—42no—
606C42—442no—
607C42—442no—
608C42—442no—
609C11#2194311yescharacteristic, complemented, Sylow
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—112no—
617C23—112no—
618C23—221no—
619C23—221no—
620C23—221no—
621C23—221no—
622C23—221no—
623C23—221no—
624C23—221no—
625C23—221no—
626C23—221no—
627C23—221no—
628C23—221no—
629C23—221no—
630C23—444no—
631C23—444no—
632C23—444no—
633C23—444no—
634C23—444no—
635C23—444no—
636C23—444no—
637C23C4⋊C4×D1112yes—
638C23C2×D4×D1111yescharacteristic
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—112no—
658C2×C4—112no—
659C2×C4—221no—
660C2×C4—221no—
661C2×C4—221no—
662C2×C4—221no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—444no—
672C2×C4—444no—
673C2×C4—444no—
674C2×C4—441no—
675C2×C4—441no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4C4⋊C4×D1112yes—
687C2×C4C22×C4×D1111yescharacteristic
688C2×C4#6703711yescharacteristic
689C2×C4#6703711yescharacteristic
690C2×C4C2×Q8×D1111yescharacteristic
691C2×C4#6704211yescharacteristic
692C2×C4#6704211yescharacteristic
693C8—22no—
694C8—22no—
695C8—222no—
696C8—222no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—222no—
705C22—222no—
706C22—222no—
707C22—222no—
708C22—222no—
709C22—222no—
710C22—4416no—
711C22—441no—
712C22—441no—
713C22—441no—
714C22—441no—
715C22—441no—
716C22—441no—
717C22—441no—
718C22—441no—
719C22C2×C4⋊C4×D1111yescharacteristic
720C22#1062312011yescharacteristic
721C22#1062318411yescharacteristic
722C22#1062329911yescharacteristic
723C22#1062329911yescharacteristic
724C22#1062330411yescharacteristic
725C22#1062330811yescharacteristic
726C4—22no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4—222no—
732C4—222no—
733C4—881no—
734C4—881no—
735C4—881no—
736C4—881no—
737C4#1062307611yescharacteristic
738C4#1062307611yescharacteristic
739C4#1062316511yescharacteristic
740C4#1062316511yescharacteristic
741C2—42no—
742C2—442no—
743C2—442no—
744C2#1307122711yescharacteristic
745C2#1307720311yescharacteristic
746C2#1307720411yescharacteristic
747C2#1307945511yescharacteristic
748C2#1307945611yescharacteristic
749C2#1307945711yescharacteristic
750C2#1307946011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1854D11
hypocenterC11#21943
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #13068818C2semidirect
5. #13068817C2semidirect
6. #13068816C2semidirect
7. #13068815C2semidirect
8. #13068814C2semidirect
9. #13068813C2semidirect
10. #13068812C2semidirect
11. #13068650C2semidirect
12. #13068648C2semidirect
13. #13068648C2semidirect
14. #13068646C2semidirect
15. C11×#1854C2semidirect
23. C2×C11×#107C22semidirect
24. C2×C11×#106C22semidirect
31. C2×#66882C22semidirect
32. C2×#66881C22semidirect
39. C2×#66872C22semidirect
40. C2×#66872C22semidirect
41. C2×#66871C22semidirect
42. C2×#66871C22semidirect
49. #10622339C4semidirect
52. C11×#340C22semidirect
53. C11×#340C22semidirect
54. #10622189C22semidirect
55. #10622189C22semidirect
56. #10622167C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
245. #1854D11semidirect
347. C2×#107C2×D11semidirect
351. C2×#106C2×D11semidirect
379. #340C2×D11semidirect
380. #340C2×D11semidirect
609. C11#21943semidirect

Maximal subgroups

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

subgroupindex
C2×#106223392
#130709982
#130709952
#130688182
#130688172
#130688162
#130688152
#130688142
#130688132
#130688122
#130686502
#130686482
#130686462
C11×#18542
#2194311