Finite Group Databasebeta

← #14788207

Subgroups — #14788207

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622676C211yesmaximal, characteristic, complemented
2C2×#10622667C211yesmaximal, characteristic, complemented
3C4×#66977C211yesmaximal, characteristic, complemented
4#13069816C211yesmaximal, characteristic, complemented
5#13069802C211yesmaximal, characteristic
6#13069624C211yesmaximal, characteristic, complemented
7#13069619C211yesmaximal, characteristic
8#13069574C211yesmaximal, characteristic, complemented
9#13069549C211yesmaximal, characteristic, complemented
10#13068957C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068884C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068596C211yesmaximal, characteristic, complemented
15C2×C11×#529C211yesmaximal, characteristic
16C11×#529—24no—
17C11×#529—24no—
18C2×C11×#126—21no—
19C2×C11×#125C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117—21no—
28C22×C42×C11C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622825C2211yescharacteristic
40#10622823—21no—
41C4×C22⋊Dic11—21no—
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622676—24no—
45#10622667—24no—
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C4×C4⋊Dic11C2211yescharacteristic
51#10622546—21no—
52C4×Dic11⋊C4—21no—
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×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11D411yescharacteristic
68C23×C4×C11D411yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×Dic22C2311yescharacteristic
71C11×#126—28no—
72C11×#125—22no—
73C11×#125D414yes—
74C11×#124—22no—
75C11×#124D414yes—
76C11×#123—28no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×#121—22no—
80C11×#121—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×D4×C11—28no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C11×#117—28no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C42×C11—21no—
99C2×C42×C11—22no—
100C2×C42×C11—22no—
101C2×C42×C11D411yescharacteristic
102C2×C42×C11D411yescharacteristic
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#66871—22no—
146C4⋊(C11⋊C8)—22no—
147C4⋊(C11⋊C8)—22no—
148#24161—111nomaximal, Sylow
149C24×C11—21no—
150C24×C11C2×D411yescharacteristic
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11C2×D412yes—
157C2×D4×C11—24no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11C2×D412yes—
166C22×C4×C11—24no—
167C22×C4×C11—22no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
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—41no—
181C22×C4×C11—41no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22#4112yes—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4C2×D412yes—
207C11×C4⋊C4C2×D412yes—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C42×C11—24no—
214C42×C11—22no—
215C42×C11—22no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11C2×D412yes—
219C42×C11C2×D412yes—
220C22⋊Dic11—24no—
221C22⋊Dic11—42no—
222#4326—44no—
223#4324—44no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11#4112yes—
230Dic11⋊C4—24no—
231Dic11⋊C4—42no—
232Dic11⋊C4—42no—
233C4×Dic11—42no—
234C4×Dic11—42no—
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×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×#529D1111yescharacteristic
248C2×#479—111no—
249C2×#464—111no—
250C4×C22⋊Q8—111no—
251#2036—111no—
252#2034—111no—
253#2001—111no—
254#2000—111no—
255#1989—111no—
256#1983—111no—
257#1878—111no—
258#1877—111no—
259#1865—111no—
260#1862—111no—
261#1797—111no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—22no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11#13712yes—
276C23×C11C22×D411yescharacteristic
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—41no—
280Q8×C11—41no—
281D4×C11—22no—
282D4×C11—22no—
283D4×C11—48no—
284D4×C11—41no—
285D4×C11—41no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—44no—
302C2×C4×C11—44no—
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#12012yes—
315C2×C4×C11#12012yes—
316C2×C4×C11#13512yes—
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C112−1+411yescharacteristic
323C2×Dic11—22no—
324C2×Dic11—22no—
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—
335Dic22—22no—
336Dic22—22no—
337Dic22—41no—
338Dic22—41no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C11⋊C8—41no—
342C11⋊C8—41no—
343C22×Q16—111no—
344C22×SD16—111no—
345#529—24no—
346#529—24no—
347C2×#126—21no—
348C2×#125C2×D1111yescharacteristic
349C2×#124C2×D1111yescharacteristic
350C2×#123—21no—
351C2×C22⋊Q8—111no—
352C2×C22⋊Q8C2×D1111yescharacteristic
353C2×#121C2×D1111yescharacteristic
354C2×C4×Q8—111no—
355C2×C4×Q8C2×D1111yescharacteristic
356C2×C4×D4—21no—
357C2×C4×D4C2×D1111yescharacteristic
358C2×#117—21no—
359C22×C42C2×D1111yescharacteristic
360#479—224no—
361#464—224no—
362C2×#107—111no—
363C2×#106—111no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8—111no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#103—111no—
370C2×#103—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×C22⋊C8—111no—
375C2×C22⋊C8—111no—
376#391—111no—
377#389—111no—
378#387—221no—
379#385—221no—
380#380—111no—
381C4×C4⋊C4—111no—
382C4×C4⋊C4—221no—
383C4×C22⋊C4—221no—
384#340—111no—
385#340—111no—
386#340—111no—
387#340—111no—
388#336—111no—
389#336—111no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11C2×#12011yescharacteristic
405C22×C11#52511yescharacteristic
406C22×C11#53711yescharacteristic
407C22×C11C2×#13511yescharacteristic
408C22×C11C2×#13711yescharacteristic
409C22×C11#57511yescharacteristic
410C22×C11#57511yescharacteristic
411C4×C11—22no—
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—41no—
415C4×C11—42no—
416C4×C11—42no—
417C4×C11—41no—
418C4×C11—42no—
419C4×C11#54611yescharacteristic
420C4×C11#54711yescharacteristic
421C4×C11#54811yescharacteristic
422C4×C11#55011yescharacteristic
423Dic11—42no—
424Dic11—42no—
425Dic11—81no—
426Dic11—81no—
427C22×Q8—111no—
428C22×Q8C22×D1111yescharacteristic
429C22×D4—21no—
430C22×D4C22×D1111yescharacteristic
431C23×C4—21no—
432C23×C4C22⋊D1111yescharacteristic
433C23×C4C22⋊D1111yescharacteristic
434C23×C4C22×D1111yescharacteristic
435C2×Q16—222no—
436C2×Q16—222no—
437C2×Q16—441no—
438C2×SD16—222no—
439C2×SD16—222no—
440C2×SD16—441no—
441C22×C8—111no—
442C22×C8—111no—
443C22×C8—111no—
444C22×C8—111no—
445#126—28no—
446#125—22no—
447#125C22⋊D1114yes—
448#124—22no—
449#124C22⋊D1114yes—
450#123—28no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—222no—
454C22⋊Q8—222no—
455#121—22no—
456#121—22no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—222no—
460C4×Q8—222no—
461C4×D4—28no—
462C4×D4—22no—
463C4×D4—22no—
464#117—28no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4C22×D1111yescharacteristic
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4—221no—
484C2×C42—21no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—221no—
488C2×C42—221no—
489C2×C42C22⋊D1111yescharacteristic
490C2×C42C22⋊D1111yescharacteristic
491C2×C42C22×D1111yescharacteristic
492C2×C42C22×D1111yescharacteristic
493#107—222no—
494#106—222no—
495C4⋊C8—222no—
496C4⋊C8—222no—
497#103—222no—
498#103—222no—
499#103—222no—
500#103—222no—
501#103—441no—
502#102—222no—
503#102—222no—
504#102—441no—
505C22⋊C8—441no—
506C22⋊C8—441no—
507#95—221no—
508#95—221no—
509#95—221no—
510#95—221no—
511#95—221no—
512C2×C11—42no—
513C2×C11—82no—
514C2×C11#240711yescharacteristic
515C2×C11#300211yescharacteristic
516C2×C11#300711yescharacteristic
517C2×C11#310211yescharacteristic
518C2×C11#311711yescharacteristic
519C2×C11#324811yescharacteristic
520C2×C11#325611yescharacteristic
521C24—21no—
522C24C2×C22⋊D1111yescharacteristic
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
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—42no—
542C2×D4—42no—
543C2×D4C2×C22⋊D1112yes—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C23×D1111yescharacteristic
572Q16—444no—
573SD16—444no—
574C2×C8—221no—
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—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—112no—
593C4⋊C4—224no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—442no—
600C4⋊C4—442no—
601C4⋊C4C2×C22⋊D1112yes—
602C4⋊C4C2×C22⋊D1112yes—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—224no—
609C22⋊C4—442no—
610C42—24no—
611C42—22no—
612C42—22no—
613C42—21no—
614C42—21no—
615C42—442no—
616C42—442no—
617C42C2×C22⋊D1112yes—
618C42C2×C22⋊D1112yes—
619C11#2416111yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23#6700412yes—
634C23C22×C22⋊D1111yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—41no—
638Q8—41no—
639Q8—222no—
640Q8—222no—
641Q8—441no—
642Q8—441no—
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—44no—
664C2×C4—44no—
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—222no—
677C2×C4—222no—
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×C4—441no—
687C2×C4—441no—
688C2×C4#6700312yes—
689C2×C4#6700612yes—
690C2×C4#6700612yes—
691C2×C4#41×D1111yescharacteristic
692C2×C4#41×D1111yescharacteristic
693C2×C4#6704211yescharacteristic
694C2×C4#6704311yescharacteristic
695C2×C4C22×C22⋊D1111yescharacteristic
696C2×C4C22×C22⋊D1111yescharacteristic
697C8—441no—
698C8—441no—
699C8—441no—
700C8—441no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C2×#6700311yescharacteristic
716C22#1062335311yescharacteristic
717C22#1062335311yescharacteristic
718C22C2×#6700411yescharacteristic
719C22#1062335911yescharacteristic
720C22#1062336411yescharacteristic
721C22C2×#6700611yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—42no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—42no—
730C4—442no—
731C4—442no—
732C4—881no—
733C4—881no—
734C4#1062335511yescharacteristic
735C4#1062336011yescharacteristic
736C4#1062336211yescharacteristic
737C4#1062336511yescharacteristic
738C2—42no—
739C2—82no—
740C2#1307195511yescharacteristic
741C2#1307783411yescharacteristic
742C2#1307787611yescharacteristic
743C2#1307862811yescharacteristic
744C2#1307878311yescharacteristic
745C2#1307995311yescharacteristic
746C2#1308001211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#529D11
hypocenterC11#24161
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#10622676C2semidirect
2. C2×#10622667C2semidirect
3. C4×#66977C2semidirect
4. #13069816C2semidirect
6. #13069624C2semidirect
8. #13069574C2semidirect
9. #13069549C2semidirect
10. #13068957C2semidirect
11. #13068950C2semidirect
12. #13068884C2semidirect
13. #13068863C2semidirect
14. #13068596C2semidirect
619. C11#24161semidirect

Maximal subgroups

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

subgroupindex
C2×#106226762
C2×#106226672
C4×#669772
#130698162
#130698022
#130696242
#130696192
#130695742
#130695492
#130689572
#130689502
#130688842
#130688632
#130685962
C2×C11×#5292
#2416111