Finite Group Databasebeta

← #14764072

Subgroups — #14764072

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622340C211yesmaximal, characteristic
2#13071205C211yesmaximal, characteristic
3#13071204C211yesmaximal, characteristic
4#13068816C211yesmaximal, characteristic, complemented
5#13068816C211yesmaximal, characteristic, complemented
6#13068815C211yesmaximal, characteristic, complemented
7#13068811C211yesmaximal, characteristic, complemented
8#13068807C211yesmaximal, characteristic, complemented
9#13068803C211yesmaximal, characteristic, complemented
10#13068802C211yesmaximal, characteristic, complemented
11#13068650C211yesmaximal, characteristic, complemented
12#13068648C211yesmaximal, characteristic, complemented
13#13068644C211yesmaximal, characteristic, complemented
14#13068638C211yesmaximal, characteristic, complemented
15C11×#1854C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622571—21no—
44#10622571—21no—
45#10622570—21no—
46#10622569—21no—
47#10622552—21no—
48#10622542—21no—
49#10622340C418yescomplemented
50#10622278—21no—
51#10622259—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11D411yescharacteristic
62C22×C22⋊D11D411yescharacteristic
63C23×Dic11—21no—
64C2×#4339—41no—
65C2×#4339—41no—
66C2×#4339—41no—
67C2×#4339—41no—
68C2×#4339C2×C414yes—
69C2×#4339Q814yes—
70C22×D44D411yescharacteristic
71C22×C4×D11—21no—
72C22×C4×D11C2311yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×Dic22D411yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#117—41no—
78C11×#117—41no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11—21no—
86C2×C22⋊Dic11—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—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11—41no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C2×#4313—41no—
106C2×#4313—41no—
107C2×#4313C2×C414yescomplemented
108C2×C8×D11—41no—
109C2×C8×D11—41no—
110C2×C8×D11C2×C414yescomplemented
111#66945—41no—
112#66945—41no—
113C4⋊C4×D11—41no—
114C4⋊C4×D11—41no—
115C11×#107—41no—
116C11×#106—41no—
117C11×C22⋊C8C2×C414yescomplemented
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×C414yescomplemented
127(C2×D11)⋊C8C2×C414yescomplemented
128(C2×D11)⋊C8C2×C414yescomplemented
129#66881—41no—
130#66881—41no—
131#66872—41no—
132#66871—41no—
133#66871—41no—
134#66871—41no—
135#21945—111nomaximal, Sylow
136C24×C11C2×D411yescharacteristic
137C23×D11C2×D411yescharacteristic
138C23×D11C2×D411yescharacteristic
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×Q812yes—
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—41no—
152C2×C22⋊D11—41no—
153C2×C22⋊D11—41no—
154C2×C22⋊D11—41no—
155C2×C22⋊D11C4⋊C414yes—
156C2×C22⋊D11C4⋊C414yes—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—42no—
162C22×Dic11—81no—
163C22×Dic11—81no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166#4339—44no—
167#4339—44no—
168#4339—44no—
169#4339—44no—
170C2×D44—41no—
171C2×D44—41no—
172C2×D44C4⋊C414yes—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×C4×D11—42no—
182C2×C4×D11—81no—
183C2×C4×D11—81no—
184C2×C4×D11C22×C412yes—
185C2×C4×D11C22×C412yes—
186C2×C4×D11C2×Q812yes—
187C2×C4×D11C2×Q812yes—
188C2×Dic22—41no—
189C2×Dic22—41no—
190C2×Dic22C4⋊C414yes—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11C22×C412yes—
196C2×C8×C11C22×C412yes—
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×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—81no—
207C42×C11—42no—
208C22⋊Dic11—81no—
209(C2×D11)⋊C4—42no—
210(C2×D11)⋊C4—81no—
211(C2×D11)⋊C4—81no—
212(C2×D11)⋊C4—81no—
213(C2×D11)⋊C4—81no—
214(C2×D11)⋊C4—81no—
215(C2×D11)⋊C4—81no—
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—
225Dic11⋊C4—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—
234C8×D11—44no—
235C2×#408—111no—
236#2311—111no—
237#2311—111no—
238#1854—111no—
239#1854—111no—
240#1854—111no—
241#1854D1111yescharacteristic, complemented
242#1853—111no—
243#1853—111no—
244#1852—111no—
245#1852—111no—
246#1809—111no—
247#1809—111no—
248#1808—111no—
249#1807—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×D11C2×C4⋊C412yes—
271C22×D11C2×C4⋊C412yes—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11C2×C4⋊C412yes—
291C2×C4×C11C23×C411yescharacteristic
292C2×C4×C11C22×Q811yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C2×C4×C11H(5,𝔽2)11yescharacteristic
296C2×C4×C11H(5,𝔽2)11yescharacteristic
297C22⋊D11—44no—
298C22⋊D11—44no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—84no—
316C2×Dic11C2×C4⋊C412yes—
317C2×Dic11C2×C4⋊C412yes—
318D44—44no—
319C4×D11—22no—
320C4×D11—22no—
321C4×D11—22no—
322C4×D11—22no—
323C4×D11—22no—
324C4×D11—22no—
325C4×D11—22no—
326C4×D11—22no—
327C4×D11—84no—
328Dic22—44no—
329C8×C11—22no—
330C8×C11—22no—
331C11⋊C8—22no—
332C11⋊C8—22no—
333C22×#41—111no—
334C22×M16—111no—
335C23×C8—111no—
336C2×#117—111no—
337C2×#117C2×D1111yescharacteristic
338C22×C4⋊C4—111no—
339C22×C4⋊C4—111no—
340C2×#107—111no—
341C2×#107—111no—
342C2×#107—111no—
343C2×#107C2×D1111yescharacteristic
344C2×#106—111no—
345C2×#106—111no—
346C2×#106—111no—
347C2×#106C2×D1111yescharacteristic
348#408—118no—
349C2×C22⋊C8—111no—
350C2×C22⋊C8—111no—
351C2×C22⋊C8—111no—
352C2×C22⋊C8C2×D1111yescharacteristic
353#391—221no—
354#391—221no—
355#390—221no—
356#390—221no—
357#386—221no—
358#386—221no—
359#386—221no—
360#386—221no—
361#380—111no—
362#380—111no—
363#380—111no—
364#380—111no—
365#380—111no—
366#380—111no—
367#380—111no—
368#380C2×D1111yescharacteristic
369#340—111no—
370#340—111no—
371#340—111no—
372#340—111no—
373#340—111no—
374#340—111no—
375#340C2×D1111yescharacteristic
376#340C2×D1111yescharacteristic
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11C22×C4⋊C411yescharacteristic
385C22×C11#53411yescharacteristic
386C22×C11#53411yescharacteristic
387C22×C11#57611yescharacteristic
388C22×C11#57711yescharacteristic
389C22×C11#57711yescharacteristic
390C22×C11#57811yescharacteristic
391C2×D11—22no—
392C2×D11—22no—
393C2×D11—22no—
394C2×D11—22no—
395C2×D11—22no—
396C2×D11—22no—
397C2×D11—41no—
398C2×D11—41no—
399C2×D11—41no—
400C2×D11—41no—
401C2×D11—41no—
402C2×D11—41no—
403C2×D11—41no—
404C2×D11—41no—
405C4×C11—22no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11—81no—
409C4×C11—81no—
410C4×C11#51811yescharacteristic
411C4×C11#51811yescharacteristic
412C4×C11#54311yescharacteristic
413C4×C11#54311yescharacteristic
414Dic11—22no—
415Dic11—22no—
416Dic11—81no—
417Dic11—81no—
418Dic11—81no—
419Dic11—81no—
420C2×#41—114no—
421C2×#41—114no—
422C2×#41—441no—
423C2×#41—441no—
424C2×#41—441no—
425C2×#41—441no—
426C22×Q8—111no—
427C22×D4—111no—
428C22×D4—111no—
429C22×D4—111no—
430C23×C4—111no—
431C23×C4—111no—
432C23×C4—221no—
433C23×C4—221no—
434C23×C4C22×D1111yescharacteristic
435C2×M16—114no—
436C2×M16—441no—
437C2×M16—441no—
438C22×C8—111no—
439C22×C8—111no—
440C22×C8—114no—
441C22×C8—441no—
442C22×C8—441no—
443C22×C8C22×D1111yescharacteristic
444C22×C8C22×D1111yescharacteristic
445#117—41no—
446#117—41no—
447#117—441no—
448#117—441no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—111no—
451C2×C4⋊C4—111no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—221no—
454C2×C4⋊C4—221no—
455C2×C4⋊C4—441no—
456C2×C4⋊C4—441no—
457C2×C4⋊C4—441no—
458C2×C4⋊C4—441no—
459C2×C4⋊C4C22×D1111yescharacteristic
460C2×C4⋊C4C22×D1111yescharacteristic
461C2×C4⋊C4C22×D1111yescharacteristic
462C2×C4⋊C4C22×D1111yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—221no—
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×C42—21no—
474C2×C42—221no—
475#107—41no—
476#107—441no—
477#107—441no—
478#107—441no—
479#106—41no—
480#106—441no—
481#106—441no—
482#106—441no—
483C22⋊C8—114no—
484C22⋊C8—114no—
485C22⋊C8—114no—
486C22⋊C8C4×D1114yescomplemented
487#95—21no—
488#95—221no—
489#95—221no—
490#95—221no—
491#95—221no—
492#95—221no—
493#95—221no—
494#95—221no—
495C2×C11—42no—
496C2×C11#231511yescharacteristic
497C2×C11#291211yescharacteristic
498C2×C11#291311yescharacteristic
499C2×C11#319811yescharacteristic
500C2×C11#319811yescharacteristic
501C2×C11#320111yescharacteristic
502C2×C11#320111yescharacteristic
503D11—42no—
504D11—42no—
505C24—111no—
506C24—111no—
507C24D4×D1111yescharacteristic
508#41—444no—
509#41—444no—
510#41—444no—
511#41—444no—
512C2×Q8—114no—
513C2×Q8—441no—
514C2×Q8—441no—
515C2×D4—114no—
516C2×D4—114no—
517C2×D4—114no—
518C2×D4—441no—
519C2×D4—441no—
520C2×D4—441no—
521C2×D4—441no—
522C2×D4—441no—
523C2×D4—441no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—111no—
533C22×C4—111no—
534C22×C4—112no—
535C22×C4—112no—
536C22×C4—112no—
537C22×C4—112no—
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—221no—
550C22×C4—442no—
551C22×C4—442no—
552C22×C4—881no—
553C22×C4—881no—
554C22×C4—881no—
555C22×C4—881no—
556C22×C4C2×C4×D1112yes—
557C22×C4D4×D1111yescharacteristic
558C22×C4Q8×D1112yes—
559C22×C4C23×D1111yescharacteristic
560M16—444no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—112no—
566C2×C8—112no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—444no—
572C2×C8C2×C4×D1112yes—
573C2×C8C2×C4×D1112yes—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—221no—
583C4⋊C4—221no—
584C4⋊C4—221no—
585C4⋊C4—221no—
586C4⋊C4—221no—
587C4⋊C4—221no—
588C4⋊C4—221no—
589C4⋊C4—221no—
590C4⋊C4—442no—
591C4⋊C4—442no—
592C22⋊C4—42no—
593C22⋊C4—81no—
594C22⋊C4—442no—
595C22⋊C4—881no—
596C22⋊C4—881no—
597C22⋊C4—881no—
598C22⋊C4—881no—
599C22⋊C4—881no—
600C22⋊C4—881no—
601C22⋊C4—881no—
602C42—42no—
603C42—442no—
604C11#2194511yescharacteristic, complemented, Sylow
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—112no—
612C23—112no—
613C23—221no—
614C23—221no—
615C23—221no—
616C23—221no—
617C23—221no—
618C23—221no—
619C23—221no—
620C23—221no—
621C23—221no—
622C23—221no—
623C23—221no—
624C23—221no—
625C23C4⋊C4×D1112yes—
626C23C2×D4×D1111yescharacteristic
627Q8—444no—
628D4—444no—
629D4—444no—
630D4—444no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—112no—
650C2×C4—112no—
651C2×C4—221no—
652C2×C4—221no—
653C2×C4—221no—
654C2×C4—221no—
655C2×C4—222no—
656C2×C4—222no—
657C2×C4—222no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—441no—
664C2×C4—441no—
665C2×C4—441no—
666C2×C4—441no—
667C2×C4—441no—
668C2×C4—441no—
669C2×C4—441no—
670C2×C4—441no—
671C2×C4—441no—
672C2×C4—441no—
673C2×C4—441no—
674C2×C4—441no—
675C2×C4—884no—
676C2×C4—884no—
677C2×C4C4⋊C4×D1112yes—
678C2×C4C22×C4×D1111yescharacteristic
679C2×C4#6703711yescharacteristic
680C2×C4#6703711yescharacteristic
681C2×C4C2×Q8×D1111yescharacteristic
682C2×C4#6704211yescharacteristic
683C2×C4#6704211yescharacteristic
684C8—22no—
685C8—22no—
686C8—222no—
687C8—222no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—222no—
696C22—222no—
697C22—222no—
698C22—222no—
699C22—222no—
700C22—222no—
701C22—441no—
702C22—441no—
703C22—441no—
704C22—441no—
705C22—441no—
706C22—441no—
707C22—441no—
708C22—441no—
709C22C2×C4⋊C4×D1111yescharacteristic
710C22#1062312011yescharacteristic
711C22#1062318411yescharacteristic
712C22#1062330111yescharacteristic
713C22#1062330111yescharacteristic
714C22#1062330511yescharacteristic
715C22#1062331011yescharacteristic
716C4—22no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4—222no—
722C4—222no—
723C4—881no—
724C4—881no—
725C4—881no—
726C4—881no—
727C4#1062307611yescharacteristic
728C4#1062307611yescharacteristic
729C4#1062316511yescharacteristic
730C4#1062316511yescharacteristic
731C2—42no—
732C2—442no—
733C2—442no—
734C2#1307122711yescharacteristic
735C2#1307720811yescharacteristic
736C2#1307721511yescharacteristic
737C2#1307946611yescharacteristic
738C2#1307946711yescharacteristic
739C2#1307949511yescharacteristic
740C2#1307950411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1854D11
hypocenterC11#21945
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. #13068816C2semidirect
5. #13068816C2semidirect
6. #13068815C2semidirect
7. #13068811C2semidirect
8. #13068807C2semidirect
9. #13068803C2semidirect
10. #13068802C2semidirect
11. #13068650C2semidirect
12. #13068648C2semidirect
13. #13068644C2semidirect
14. #13068638C2semidirect
15. C11×#1854C2semidirect
49. #10622340C4semidirect
107. C2×#4313C2×C4semidirect
110. C2×C8×D11C2×C4semidirect
117. C11×C22⋊C8C2×C4semidirect
126. C22⋊(C11⋊C8)C2×C4semidirect
127. (C2×D11)⋊C8C2×C4semidirect
128. (C2×D11)⋊C8C2×C4semidirect
241. #1854D11semidirect
486. C22⋊C8C4×D11semidirect
604. C11#21945semidirect

Maximal subgroups

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

subgroupindex
C2×#106223402
#130712052
#130712042
#130688162
#130688152
#130688112
#130688072
#130688032
#130688022
#130686502
#130686482
#130686442
#130686382
C11×#18542
#2194511