Finite Group Databasebeta

← #14797479

Subgroups — #14797479

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622658C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic, complemented
3#13071545C211yesmaximal, characteristic, complemented
4#13070137C211yesmaximal, characteristic, complemented
5#13070034C211yesmaximal, characteristic, complemented
6#13069809C211yesmaximal, characteristic, complemented
7#13069802C211yesmaximal, characteristic, complemented
8#13069247C211yesmaximal, characteristic, complemented
9#13069240C211yesmaximal, characteristic, complemented
10#13068939C211yesmaximal, characteristic, complemented
11#13068914C211yesmaximal, characteristic, complemented
12#13068808C211yesmaximal, characteristic, complemented
13#13068647C211yesmaximal, characteristic, complemented
14#13068556C211yesmaximal, characteristic, complemented
15C11×#2407C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C11×#394—21no—
24C11×#392—21no—
25C11×#391C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#386—21no—
28C11×#385—21no—
29C11×#380C2211yescharacteristic
30#10622845—24no—
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35#10622833—21no—
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40#10622825C2211yescharacteristic
41#10622825C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622658—24no—
46#10622594—21no—
47C2×#66872C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622564—21no—
52C22⋊C4×Dic11—21no—
53#10622549C2211yescharacteristic
54C4×C4⋊Dic11C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C22×D4×C11D411yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×Dic11—21no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—41no—
78C11×#121—22no—
79C11×#121—41no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97#66979—22no—
98#66979—41no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—41no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×#4318—22no—
109C2×#4318—22no—
110C2×#4318—41no—
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118#66899—22no—
119#66899—22no—
120#66899—41no—
121#66899D414yescomplemented
122#66896—22no—
123#66896—22no—
124#66896—22no—
125#66896—41no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—22no—
133C22⋊(C11⋊C8)—41no—
134#66872—22no—
135#66872—41no—
136#66872—41no—
137#66871—22no—
138#24891—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C24×C11C2×D411yescharacteristic
142C11×#41—28no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C2×D412yes—
152C2×D4×C11—22no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—41no—
159C2×D4×C11—41no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—81no—
166C2×D4×C11#4112yes—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11#4112yes—
188C22×C4×C11#4112yes—
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—42no—
195C22×Dic11—42no—
196C22×Dic11—81no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—42no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—81no—
209C11×C22⋊C4—81no—
210C42×C11—21no—
211C42×C11—21no—
212C22⋊Dic11—42no—
213C22⋊Dic11—42no—
214C22⋊Dic11—81no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—42no—
223C4⋊Dic11C2×D412yes—
224C4×Dic11—42no—
225C4×Dic11—81no—
226#4318—44no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8C2×D412yes—
239C2×#485—111no—
240C2×#417—111no—
241#2407D1111yescharacteristic
242#2352—111no—
243#2092—111no—
244#2074—111no—
245#2035—111no—
246#2034—111no—
247#1927—111no—
248#1926—111no—
249#1875—111no—
250#1870—111no—
251#1853—111no—
252#1809—111no—
253#1788—111no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—22no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11#12312yes—
275C23×C11C22×D411yescharacteristic
276Q8×C11—22no—
277Q8×C11—22no—
278Q8×C11—41no—
279Q8×C11—41no—
280D4×C11—22no—
281D4×C11—22no—
282D4×C11—44no—
283D4×C11—48no—
284D4×C11—41no—
285D4×C11—41no—
286D4×C11—84no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—48no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11#12312yes—
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×Dic11—22no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—84no—
336C11⋊C8—22no—
337C11⋊C8—41no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340C22×#41C2×D1111yescharacteristic
341C22×M16—111no—
342C2×C22⋊Q8C2×D1111yescharacteristic
343C2×#121C2×D1111yescharacteristic
344C2×C4×D4C2×D1111yescharacteristic
345C2×#117—111no—
346C22×C4⋊C4—111no—
347#485—224no—
348C2×#107—111no—
349C2×#106—111no—
350C2×#106—111no—
351C2×#106—111no—
352#417—224no—
353C2×#103—111no—
354C2×#103—111no—
355C2×#103—111no—
356C2×#103—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×C22⋊C8—111no—
362C2×C22⋊C8—111no—
363C2×C22⋊C8—111no—
364#394—21no—
365#392—21no—
366#391C2×D1111yescharacteristic
367#390C2×D1111yescharacteristic
368#388—221no—
369#387—221no—
370#386—21no—
371#386—221no—
372#385—21no—
373#382—111no—
374#380—111no—
375#380—111no—
376#380C2×D1111yescharacteristic
377C4×C4⋊C4—111no—
378C4×C22⋊C4—221no—
379#340—111no—
380#340—111no—
381#340—111no—
382#340—111no—
383#336—111no—
384#336—111no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—42no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—42no—
400C22×C11—41no—
401C22×C11—42no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11C2×#12311yescharacteristic
407C22×C11D4211yescharacteristic
408C22×C11#54611yescharacteristic
409C22×C11#57511yescharacteristic
410C22×C11#57511yescharacteristic
411C22×C11#57711yescharacteristic
412C22×C11#57711yescharacteristic
413C4×C11—22no—
414C4×C11—41no—
415C4×C11—41no—
416C4×C11—41no—
417C4×C11—42no—
418C4×C11—81no—
419C4×C11—81no—
420C4×C11#52511yescharacteristic
421C4×C11#53811yescharacteristic
422C4×C11#54611yescharacteristic
423C4×C11#55111yescharacteristic
424Dic11—42no—
425Dic11—81no—
426Dic11—81no—
427Dic11—81no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—41no—
433C2×#41—41no—
434C22×Q8C22×D1111yescharacteristic
435C22×D4—21no—
436C22×D4—21no—
437C22×D4C22⋊D1111yescharacteristic
438C22×D4C22×D1111yescharacteristic
439C23×C4—21no—
440C23×C4—221no—
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1111yescharacteristic
443C2×M16—222no—
444C2×M16—222no—
445C2×M16—441no—
446C22×C8—111no—
447C22×C8—111no—
448C22×C8—111no—
449C22×C8—111no—
450C22⋊Q8—22no—
451C22⋊Q8—41no—
452#121—22no—
453#121—41no—
454C4×D4—22no—
455C4×D4—22no—
456#117—222no—
457#117—441no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—111no—
463C2×C4⋊C4—222no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—441no—
466C2×C4⋊C4C22⋊D1111yescharacteristic
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4C22⋊D1111yescharacteristic
478C2×C22⋊C4C22⋊D1111yescharacteristic
479C2×C42—221no—
480C2×C42—221no—
481C2×C42C22×D1111yescharacteristic
482#107—222no—
483#106—222no—
484#106—441no—
485#106—441no—
486#103—114no—
487#103—222no—
488#103—222no—
489#103—441no—
490#102—222no—
491#102—222no—
492#102—222no—
493#102—441no—
494C22⋊C8—222no—
495C22⋊C8—222no—
496C22⋊C8—441no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—221no—
501#95—221no—
502#95—221no—
503#95—221no—
504#95—221no—
505C2×C11—42no—
506C2×C11—81no—
507C2×C11—82no—
508C2×C11#241811yescharacteristic
509C2×C11#309311yescharacteristic
510C2×C11#309911yescharacteristic
511C2×C11#327111yescharacteristic
512C2×C11#327511yescharacteristic
513C2×C11#330711yescharacteristic
514C2×C11#332311yescharacteristic
515C24—21no—
516C24C2×C22⋊D1111yescharacteristic
517C24C2×C22⋊D1111yescharacteristic
518#41—28no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8D4×D1112yes—
528C2×D4—22no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—81no—
542C2×D4#434112yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—442no—
564C22×C4—442no—
565C22×C4—881no—
566C22×C4#434112yes—
567C22×C4#434112yes—
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C2×C22⋊D1111yescharacteristic
572C22×C4C23×D1111yescharacteristic
573M16—444no—
574C2×C8—112no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—112no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—442no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—881no—
611C42—21no—
612C42—21no—
613C42—442no—
614C42—881no—
615C11#2489111yescharacteristic, complemented, Sylow
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23#6698812yes—
637C23C22×C22⋊D1111yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—41no—
641Q8—41no—
642D4—22no—
643D4—22no—
644D4—44no—
645D4—48no—
646D4—41no—
647D4—41no—
648D4—84no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—48no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—222no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—884no—
691C2×C4#6698812yes—
692C2×C4C2×D4×D1111yescharacteristic
693C2×C4C2×#434111yescharacteristic
694C2×C4C2×#434111yescharacteristic
695C2×C4C2×#434111yescharacteristic
696C2×C4#6703711yescharacteristic
697C2×C4#6703711yescharacteristic
698C8—222no—
699C8—441no—
700C8—441no—
701C8—441no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—42no—
711C22—41no—
712C22—42no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22C2×#6698811yescharacteristic
724C22D4×C22⋊D1111yescharacteristic
725C22#1062333711yescharacteristic
726C22#1062335311yescharacteristic
727C22#1062335311yescharacteristic
728C22#1062336711yescharacteristic
729C22#1062336811yescharacteristic
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—81no—
736C4—81no—
737C4—442no—
738C4—881no—
739C4—881no—
740C4—881no—
741C4#1062311711yescharacteristic
742C4#1062311811yescharacteristic
743C4#1062312211yescharacteristic
744C4#1062312411yescharacteristic
745C2—42no—
746C2—81no—
747C2—82no—
748C2#1307207411yescharacteristic
749C2#1307854511yescharacteristic
750C2#1307860111yescharacteristic
751C2#1308019711yescharacteristic
752C2#1308024811yescharacteristic
753C2#1308059211yescharacteristic
754C2#1308083211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2407C2
socleC23×C11C22×D4
hypercenter#2407D11
hypocenterC11#24891
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#10622658C2semidirect
2. C2×#10622845C2semidirect
3. #13071545C2semidirect
4. #13070137C2semidirect
5. #13070034C2semidirect
6. #13069809C2semidirect
7. #13069802C2semidirect
8. #13069247C2semidirect
9. #13069240C2semidirect
10. #13068939C2semidirect
11. #13068914C2semidirect
12. #13068808C2semidirect
13. #13068647C2semidirect
14. #13068556C2semidirect
121. #66899D4semidirect
615. C11#24891semidirect

Maximal subgroups

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

subgroupindex
C2×#106226582
C2×#106228452
#130715452
#130701372
#130700342
#130698092
#130698022
#130692472
#130692402
#130689392
#130689142
#130688082
#130686472
#130685562
C11×#24072
#2489111