Finite Group Databasebeta

← #14814929

Subgroups — #14814929

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622648C211yesmaximal, characteristic, complemented
2C2×#10622656C211yesmaximal, characteristic, complemented
3#13071545C211yesmaximal, characteristic, complemented
4#13069816C211yesmaximal, characteristic, complemented
5#13069809C211yesmaximal, characteristic, complemented
6#13069802C211yesmaximal, characteristic, complemented
7#13069802C211yesmaximal, characteristic, complemented
8#13069549C211yesmaximal, characteristic, complemented
9#13069428C211yesmaximal, characteristic, complemented
10#13069411C211yesmaximal, characteristic, complemented
11#13069384C211yesmaximal, characteristic, complemented
12#13068934C211yesmaximal, characteristic, complemented
13#13068929C211yesmaximal, characteristic, complemented
14C4×#66872C211yesmaximal, characteristic, complemented
15C11×#2540C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C11×#399—21no—
25C11×#392—21no—
26C11×#390—21no—
27C11×#390—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622833—21no—
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622825C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622656—24no—
45#10622648—24no—
46#10622594—21no—
47C2×#66872C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622564—21no—
52C22⋊C4×Dic11—21no—
53#10622549C2211yescharacteristic
54C4×C4⋊Dic11C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11D411yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11—21no—
69C11×#124—22no—
70C11×#124—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—41no—
74C11×C22⋊Q8—41no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—41no—
78C11×#121—41no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C2×C11×C4⋊C4—21no—
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⋊C4—21no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11—21no—
99#66979—22no—
100#66979—41no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—41no—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C11×#95—21no—
115#66899—22no—
116#66899—22no—
117#66899—41no—
118#66899—41no—
119#66896—22no—
120#66896—22no—
121#66896—41no—
122#66896—41no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—41no—
131C22⋊(C11⋊C8)—41no—
132#66872—22no—
133#66872—22no—
134#66872D414yescomplemented
135#66871—22no—
136C4⋊(C11⋊C8)—22no—
137C4×C11⋊C8—22no—
138#26239—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C24×C11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—41no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11—81no—
162C2×D4×C11—81no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—42no—
188C22×Dic11—42no—
189C22×Dic11—81no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—42no—
194C11×C4⋊C4—42no—
195C11×C4⋊C4C2×D412yes—
196C11×C4⋊C4#4112yes—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—42no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—42no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C42×C11—81no—
206C42×C11#4112yes—
207C42×C11#4112yes—
208C22⋊Dic11—42no—
209C22⋊Dic11—42no—
210C22⋊Dic11—81no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—42no—
219C4⋊Dic11C2×D412yes—
220C4×Dic11—42no—
221C4×Dic11—81no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
234C2×#482—111no—
235C2×#483—111no—
236#2540D1111yescharacteristic
237#2352—111no—
238#2036—111no—
239#2035—111no—
240#2034—111no—
241#2034—111no—
242#1983—111no—
243#1958—111no—
244#1954—111no—
245#1949—111no—
246#1874—111no—
247#1873—111no—
248C4×#106—111no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
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—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11#13512yes—
270C23×C11C22×D411yescharacteristic
271Q8×C11—41no—
272Q8×C11—41no—
273Q8×C11—41no—
274Q8×C11—41no—
275D4×C11—44no—
276D4×C11—41no—
277D4×C11—41no—
278D4×C11—41no—
279D4×C11—41no—
280D4×C11—84no—
281D4×C11—84no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11#12312yes—
310C2×C4×C11#12312yes—
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C2×Dic11—22no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—84no—
330C11⋊C8—22no—
331C11⋊C8—41no—
332C11⋊C8—41no—
333C11⋊C8—41no—
334C2×#124C2×D1111yescharacteristic
335C2×C22⋊Q8C2×D1111yescharacteristic
336C2×C22⋊Q8C2×D1111yescharacteristic
337C2×#121C2×D1111yescharacteristic
338C2×#121C2×D1111yescharacteristic
339C2×C4×D4C2×D1111yescharacteristic
340C2×#117—111no—
341C22×C4⋊C4—111no—
342#483—224no—
343#482—224no—
344C2×#107—111no—
345C2×#106—111no—
346C2×#106—111no—
347C2×#106—111no—
348C2×C4⋊C8—111no—
349C2×#103—111no—
350C2×#103—111no—
351C2×#103—111no—
352C2×#103—111no—
353C2×#102—111no—
354C2×#102—111no—
355C2×#102—111no—
356C2×#102—111no—
357C2×C22⋊C8—111no—
358C2×C22⋊C8—111no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×C4×C8—111no—
362#399—21no—
363#392—21no—
364#390—21no—
365#390—21no—
366#388—221no—
367#387—221no—
368#386—221no—
369#382—111no—
370#380—111no—
371#380—111no—
372C4×C4⋊C4—111no—
373C4×C4⋊C4C2×D1111yescharacteristic
374C4×C22⋊C4—221no—
375#340—111no—
376#340—111no—
377#340—111no—
378#340—111no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—81no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11C2×#12311yescharacteristic
401C22×C11D4211yescharacteristic
402C22×C11#54611yescharacteristic
403C22×C11C2×#13511yescharacteristic
404C22×C11#57511yescharacteristic
405C22×C11#57711yescharacteristic
406C22×C11#57711yescharacteristic
407C4×C11—22no—
408C4×C11—22no—
409C4×C11—41no—
410C4×C11—41no—
411C4×C11—42no—
412C4×C11—42no—
413C4×C11—81no—
414C4×C11#53211yescharacteristic
415C4×C11#54011yescharacteristic
416C4×C11#55011yescharacteristic
417C4×C11#55911yescharacteristic
418Dic11—42no—
419Dic11—81no—
420Dic11—81no—
421Dic11—81no—
422C22×Q8C22×D1111yescharacteristic
423C22×D4—21no—
424C22×D4—21no—
425C22×D4C22⋊D1111yescharacteristic
426C22×D4C22×D1111yescharacteristic
427C23×C4—221no—
428C23×C4C22×D1111yescharacteristic
429C23×C4C22×D1111yescharacteristic
430C22×C8—111no—
431C22×C8—111no—
432C22×C8—111no—
433C22×C8—111no—
434#124—22no—
435#124—22no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8—41no—
439C22⋊Q8—41no—
440#121—22no—
441#121—22no—
442#121—41no—
443#121—41no—
444C4×D4—22no—
445C4×D4—22no—
446#117—222no—
447#117—441no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—111no—
451C2×C4⋊C4—111no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—222no—
455C2×C4⋊C4—221no—
456C2×C4⋊C4—441no—
457C2×C4⋊C4C22⋊D1111yescharacteristic
458C2×C4⋊C4C22×D1111yescharacteristic
459C2×C4⋊C4C22×D1111yescharacteristic
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—221no—
467C2×C22⋊C4—221no—
468C2×C22⋊C4—221no—
469C2×C22⋊C4C22⋊D1111yescharacteristic
470C2×C22⋊C4C22⋊D1111yescharacteristic
471C2×C42—21no—
472C2×C42—221no—
473C2×C42—221no—
474C2×C42C22×D1111yescharacteristic
475#107—222no—
476#106—114no—
477#106—222no—
478#106—222no—
479C4⋊C8—222no—
480#103—222no—
481#103—222no—
482#103—441no—
483#103—441no—
484#102—222no—
485#102—222no—
486#102—441no—
487#102—441no—
488C22⋊C8—222no—
489C22⋊C8—222no—
490C22⋊C8—441no—
491C22⋊C8—441no—
492C4×C8—222no—
493#95—21no—
494#95—221no—
495#95—221no—
496#95—221no—
497#95—221no—
498#95—221no—
499C2×C11—42no—
500C2×C11—81no—
501C2×C11—161no—
502C2×C11#244511yescharacteristic
503C2×C11#309111yescharacteristic
504C2×C11#309911yescharacteristic
505C2×C11#327511yescharacteristic
506C2×C11#328211yescharacteristic
507C2×C11#329611yescharacteristic
508C2×C11#332611yescharacteristic
509C24—21no—
510C24C2×C22⋊D1111yescharacteristic
511C24C2×C22⋊D1111yescharacteristic
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—41no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—81no—
532C2×D4—81no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—442no—
553C22×C4—442no—
554C22×C4—881no—
555C22×C4C2×C22⋊D1111yescharacteristic
556C22×C4C2×C22⋊D1111yescharacteristic
557C22×C4C2×C22⋊D1111yescharacteristic
558C22×C4C2×C22⋊D1111yescharacteristic
559C22×C4C23×D1111yescharacteristic
560C2×C8—112no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—221no—
565C2×C8—221no—
566C2×C8—221no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—221no—
572C4⋊C4—22no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—112no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—221no—
581C4⋊C4—221no—
582C4⋊C4—221no—
583C4⋊C4—221no—
584C4⋊C4—221no—
585C4⋊C4—442no—
586C4⋊C4D4×D1112yes—
587C4⋊C4#434112yes—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—442no—
597C22⋊C4—442no—
598C22⋊C4—881no—
599C42—81no—
600C42—442no—
601C42—881no—
602C42#434112yes—
603C42#434112yes—
604C11#2623911yescharacteristic, complemented, Sylow
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23#6700312yes—
626C23C22×C22⋊D1111yescharacteristic
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631D4—44no—
632D4—41no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—84no—
637D4—84no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—222no—
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—441no—
676C2×C4—441no—
677C2×C4—884no—
678C2×C4#6698812yes—
679C2×C4#6698812yes—
680C2×C4C2×D4×D1111yescharacteristic
681C2×C4C2×#434111yescharacteristic
682C2×C4C2×#434111yescharacteristic
683C2×C4C2×#434111yescharacteristic
684C2×C4#6703711yescharacteristic
685C2×C4#6703711yescharacteristic
686C8—222no—
687C8—441no—
688C8—441no—
689C8—441no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×#6698811yescharacteristic
712C22D4×C22⋊D1111yescharacteristic
713C22#1062333711yescharacteristic
714C22C2×#6700311yescharacteristic
715C22#1062335311yescharacteristic
716C22#1062336711yescharacteristic
717C22#1062336811yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—41no—
723C4—41no—
724C4—81no—
725C4—442no—
726C4—881no—
727C4—881no—
728C4—881no—
729C4#1062324411yescharacteristic
730C4#1062324711yescharacteristic
731C4#1062324911yescharacteristic
732C4#1062325011yescharacteristic
733C2—42no—
734C2—81no—
735C2—161no—
736C2#1307237711yescharacteristic
737C2#1307852511yescharacteristic
738C2#1307860111yescharacteristic
739C2#1308024311yescharacteristic
740C2#1308032411yescharacteristic
741C2#1308045111yescharacteristic
742C2#1308086911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2540C2
socleC23×C11C22×D4
hypercenter#2540D11
hypocenterC11#26239
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#10622648C2semidirect
2. C2×#10622656C2semidirect
3. #13071545C2semidirect
4. #13069816C2semidirect
5. #13069809C2semidirect
6. #13069802C2semidirect
7. #13069802C2semidirect
8. #13069549C2semidirect
9. #13069428C2semidirect
10. #13069411C2semidirect
11. #13069384C2semidirect
12. #13068934C2semidirect
13. #13068929C2semidirect
14. C4×#66872C2semidirect
134. #66872D4semidirect
604. C11#26239semidirect

Maximal subgroups

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

subgroupindex
C2×#106226482
C2×#106226562
#130715452
#130698162
#130698092
#130698022
#130695492
#130694282
#130694112
#130693842
#130689342
#130689292
C4×#668722
C11×#25402
#2623911