Finite Group Databasebeta

← #14788327

Subgroups — #14788327

Order 2816.

1086 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×#10622707C211yesmaximal, characteristic, complemented
2C2×#10622667C211yesmaximal, characteristic, complemented
3#13071298C211yesmaximal, characteristic, complemented
4#13069809C211yesmaximal, characteristic, complemented
5#13069802C211yesmaximal, characteristic
6#13069624C211yesmaximal, characteristic, complemented
7#13069619C211yesmaximal, characteristic
8#13069565C211yesmaximal, characteristic, complemented
9#13069549C211yesmaximal, characteristic, complemented
10#13068957C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068884C211yesmaximal, characteristic, complemented
13#13068877C211yesmaximal, characteristic, complemented
14#13068600C211yesmaximal, characteristic, complemented
15C2×C11×#542C211yesmaximal, characteristic
16C11×#542—24no—
17C11×#542—24no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#126—21no—
20C2×C11×#124—21no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622707—24no—
43#10622667—24no—
44#10622591—21no—
45#10622585—21no—
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50#10622558—21no—
51#10622557—21no—
52C4×C4⋊Dic11C2211yescharacteristic
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C22×Dic22C2311yescharacteristic
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8D414yes—
72C11×#126—28no—
73C11×#124—28no—
74C11×#124—22no—
75C11×#124D414yes—
76C11×#123—28no—
77C11×C22⋊Q8—28no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×#121—22no—
81C11×#121—22no—
82C4×Q8×C11—22no—
83C4×Q8×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C11×#117—22no—
87C11×#117—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×#4326—22no—
108C2×#4326—22no—
109C2×#4326—41no—
110C2×#4324—22no—
111C2×#4324—22no—
112C2×#4324—41no—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116#66977—22no—
117#66977—22no—
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×C4×Dic11—21no—
122C2×C4×Dic11—21no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C4×Dic22—22no—
128C4×Dic22—22no—
129#66899—22no—
130#66899—22no—
131#66899—41no—
132#66896—22no—
133#66896—22no—
134#66896—41no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—41no—
141C22⋊(C11⋊C8)—41no—
142#66874—22no—
143#66874—22no—
144#66872—22no—
145#66872—22no—
146C4⋊(C11⋊C8)—22no—
147C4⋊(C11⋊C8)—22no—
148#24169—111nomaximal, Sylow
149C24×C11—21no—
150C24×C11C2×D411yescharacteristic
151C2×Q8×C11—24no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—81no—
158C2×Q8×C11—81no—
159C2×Q8×C11C2×D412yes—
160C2×D4×C11—24no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—81no—
167C2×D4×C11—81no—
168C2×D4×C11C2×D412yes—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—24no—
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—81no—
180C22×C4×C11—81no—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22#4112yes—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4C2×D412yes—
205C11×C4⋊C4C2×D412yes—
206C11×C22⋊C4—24no—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C42×C11—24no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11C2×D412yes—
217C42×C11C2×D412yes—
218C22⋊Dic11—24no—
219C22⋊Dic11—81no—
220#4326—44no—
221#4324—44no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11#4112yes—
228Dic11⋊C4—24no—
229Dic11⋊C4—42no—
230Dic11⋊C4—81no—
231C4×Dic11—42no—
232C4×Dic11—81no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×#542D1111yescharacteristic
246C2×#475—111no—
247C2×#464—111no—
248#2323—111no—
249#2035—111no—
250#2034—111no—
251#2001—111no—
252#2000—111no—
253#1987—111no—
254#1983—111no—
255#1878—111no—
256#1877—111no—
257#1865—111no—
258#1864—111no—
259#1798—111no—
260C23×C11—21no—
261C23×C11—22no—
262C23×C11—21no—
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×C11C22×D411yescharacteristic
275Q8×C11—22no—
276Q8×C11—22no—
277Q8×C11—41no—
278Q8×C11—41no—
279Q8×C11—84no—
280D4×C11—22no—
281D4×C11—22no—
282D4×C11—41no—
283D4×C11—41no—
284D4×C11—84no—
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—21no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
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—41no—
310C2×C4×C11—41no—
311C2×C4×C11—84no—
312C2×C4×C11#12012yes—
313C2×C4×C11#12012yes—
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C112−1+411yescharacteristic
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332Dic22—22no—
333Dic22—22no—
334Dic22—41no—
335Dic22—41no—
336C11⋊C8—41no—
337C11⋊C8—41no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340C22×Q16—111no—
341C22×SD16—111no—
342#542—24no—
343#542—24no—
344C2×C4⋊Q8C2×D1111yescharacteristic
345C2×#126—21no—
346C2×#124—21no—
347C2×#124C2×D1111yescharacteristic
348C2×#123—21no—
349C2×C22⋊Q8—21no—
350C2×C22⋊Q8—111no—
351C2×C22⋊Q8C2×D1111yescharacteristic
352C2×#121C2×D1111yescharacteristic
353C2×C4×Q8—111no—
354C2×C4×Q8C2×D1111yescharacteristic
355C2×C4×D4C2×D1111yescharacteristic
356C2×#117C2×D1111yescharacteristic
357#475—224no—
358#464—224no—
359C2×#106—111no—
360C2×#106—111no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×#103—111no—
364C2×#103—111no—
365C2×#103—111no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8—111no—
373#391—111no—
374#389—111no—
375#389—221no—
376#388—221no—
377#388—221no—
378#387—221no—
379#380—111no—
380C4×C4⋊C4—111no—
381#340—111no—
382#340—111no—
383#340—111no—
384#340—111no—
385#336—111no—
386#336—111no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—42no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—42no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—42no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11C2×#12011yescharacteristic
402C22×C11#52511yescharacteristic
403C22×C11#53711yescharacteristic
404C22×C11#57711yescharacteristic
405C22×C11#57711yescharacteristic
406C22×C11#57711yescharacteristic
407C22×C11#57811yescharacteristic
408C4×C11—22no—
409C4×C11—22no—
410C4×C11—41no—
411C4×C11—42no—
412C4×C11—41no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11—41no—
416C4×C11#54611yescharacteristic
417C4×C11#54711yescharacteristic
418C4×C11#54811yescharacteristic
419C4×C11#55011yescharacteristic
420Dic11—42no—
421Dic11—42no—
422Dic11—81no—
423Dic11—81no—
424C22×Q8—21no—
425C22×Q8—111no—
426C22×Q8C22×D1111yescharacteristic
427C22×D4—21no—
428C22×D4C22×D1111yescharacteristic
429C23×C4—21no—
430C23×C4C22×D1111yescharacteristic
431C2×Q16—222no—
432C2×Q16—222no—
433C2×Q16—441no—
434C2×SD16—222no—
435C2×SD16—222no—
436C2×SD16—441no—
437C22×C8—111no—
438C22×C8—111no—
439C22×C8—111no—
440C22×C8—111no—
441C4⋊Q8—22no—
442C4⋊Q8C22⋊D1114yes—
443#126—28no—
444#124—28no—
445#124—22no—
446#124C22⋊D1114yes—
447#123—28no—
448C22⋊Q8—28no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—222no—
452C22⋊Q8—222no—
453#121—22no—
454#121—22no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8—222no—
458C4×Q8—222no—
459C4×D4—22no—
460C4×D4—22no—
461#117—22no—
462#117—22no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4C22⋊D1111yescharacteristic
473C2×C4⋊C4C22⋊D1111yescharacteristic
474C2×C4⋊C4C22×D1111yescharacteristic
475C2×C4⋊C4C22×D1111yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—221no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4C22⋊D1111yescharacteristic
484C2×C22⋊C4C22⋊D1111yescharacteristic
485C2×C42—21no—
486C2×C42—221no—
487C2×C42—221no—
488C2×C42C22×D1111yescharacteristic
489C2×C42C22×D1111yescharacteristic
490#106—222no—
491#106—222no—
492C4⋊C8—222no—
493C4⋊C8—222no—
494#103—222no—
495#103—222no—
496#103—222no—
497#103—222no—
498#103—441no—
499#102—222no—
500#102—222no—
501#102—441no—
502C22⋊C8—441no—
503C22⋊C8—441no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508#95—221no—
509C2×C11—81no—
510C2×C11—82no—
511C2×C11#240711yescharacteristic
512C2×C11#300911yescharacteristic
513C2×C11#301311yescharacteristic
514C2×C11#312111yescharacteristic
515C2×C11#312511yescharacteristic
516C2×C11#325811yescharacteristic
517C2×C11#326311yescharacteristic
518C24—21no—
519C24C2×C22⋊D1111yescharacteristic
520C2×Q8—24no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—81no—
527C2×Q8—81no—
528C2×Q8—112no—
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—221no—
532C2×Q8—221no—
533C2×Q8—221no—
534C2×Q8C2×C22⋊D1112yes—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—81no—
542C2×D4—81no—
543C2×D4C2×C22⋊D1112yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4C2×C22⋊D1111yescharacteristic
561C22×C4C2×C22⋊D1111yescharacteristic
562C22×C4C2×C22⋊D1111yescharacteristic
563C22×C4C2×C22⋊D1111yescharacteristic
564C22×C4C2×C22⋊D1111yescharacteristic
565C22×C4C23×D1111yescharacteristic
566Q16—444no—
567SD16—444no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—112no—
588C4⋊C4—224no—
589C4⋊C4—221no—
590C4⋊C4—221no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—442no—
595C4⋊C4—881no—
596C4⋊C4C2×C22⋊D1112yes—
597C4⋊C4C2×C22⋊D1112yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—224no—
606C22⋊C4—881no—
607C42—24no—
608C42—21no—
609C42—21no—
610C42—442no—
611C42—881no—
612C42C2×C22⋊D1112yes—
613C42C2×C22⋊D1112yes—
614C11#2416911yescharacteristic, complemented, Sylow
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23C22×C22⋊D1111yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—84no—
635Q8—222no—
636Q8—222no—
637Q8—441no—
638Q8—441no—
639D4—22no—
640D4—22no—
641D4—41no—
642D4—41no—
643D4—84no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—84no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—441no—
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#6700612yes—
684C2×C4#6700612yes—
685C2×C4#41×D1111yescharacteristic
686C2×C4#41×D1111yescharacteristic
687C2×C4#6704211yescharacteristic
688C2×C4#6704311yescharacteristic
689C2×C4C22×C22⋊D1111yescharacteristic
690C2×C4C22×C22⋊D1111yescharacteristic
691C8—441no—
692C8—441no—
693C8—441no—
694C8—441no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—41no—
702C22—41no—
703C22—42no—
704C22—41no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22#1062335911yescharacteristic
710C22#1062336411yescharacteristic
711C22#1062336711yescharacteristic
712C22#1062336711yescharacteristic
713C22#1062336811yescharacteristic
714C22#1062336911yescharacteristic
715C22C2×#6700611yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—42no—
722C4—42no—
723C4—41no—
724C4—442no—
725C4—442no—
726C4—881no—
727C4—881no—
728C4#1062335511yescharacteristic
729C4#1062336011yescharacteristic
730C4#1062336211yescharacteristic
731C4#1062336511yescharacteristic
732C2—81no—
733C2—82no—
734C2#1307195511yescharacteristic
735C2#1307789311yescharacteristic
736C2#1307793111yescharacteristic
737C2#1307883911yescharacteristic
738C2#1307888711yescharacteristic
739C2#1308004211yescharacteristic
740C2#1308008111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#542C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#542D11
hypocenterC11#24169
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#10622707C2semidirect
2. C2×#10622667C2semidirect
3. #13071298C2semidirect
4. #13069809C2semidirect
6. #13069624C2semidirect
8. #13069565C2semidirect
9. #13069549C2semidirect
10. #13068957C2semidirect
11. #13068950C2semidirect
12. #13068884C2semidirect
13. #13068877C2semidirect
14. #13068600C2semidirect
614. C11#24169semidirect

Maximal subgroups

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

subgroupindex
C2×#106227072
C2×#106226672
#130712982
#130698092
#130698022
#130696242
#130696192
#130695652
#130695492
#130689572
#130689502
#130688842
#130688772
#130686002
C2×C11×#5422
#2416911