Finite Group Databasebeta

← #14810237

Subgroups — #14810237

Order 2816.

1292 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622669C211yesmaximal, characteristic, complemented
2C2×#10622635C211yesmaximal, characteristic, complemented
3#13073782C211yesmaximal, characteristic, complemented
4#13069816C211yesmaximal, characteristic, complemented
5#13069809C211yesmaximal, characteristic, complemented
6#13069802C211yesmaximal, characteristic, complemented
7#13069795C211yesmaximal, characteristic, complemented
8#13069549C211yesmaximal, characteristic, complemented
9#13069411C211yesmaximal, characteristic, complemented
10#13068556C211yesmaximal, characteristic, complemented
11#13068556C211yesmaximal, characteristic, complemented
12#13068551C211yesmaximal, characteristic, complemented
13#13068551C211yesmaximal, characteristic, complemented
14C4×#66899C211yesmaximal, characteristic, complemented
15C2×C11×#548C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C11×#548—24no—
19C11×#548—24no—
20C2×C11×#124—21no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×#66923C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622835—21no—
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic
44#10622825C2211yescharacteristic
45#10622825C2211yescharacteristic
46#10622825C2211yescharacteristic
47C2×C22⋊(C11⋊C8)C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51#10622669—24no—
52#10622635—24no—
53#10622595—21no—
54C2×#66872C2211yescharacteristic
55C2×#66871C2211yescharacteristic
56#10622558—21no—
57#10622558—21no—
58C4×C4⋊Dic11C2211yescharacteristic
59C2×C4⋊(C11⋊C8)C2211yescharacteristic
60C2×C4×C11⋊C8C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C22×Q8×C11—22no—
70C22×Q8×C11—22no—
71C22×Q8×C11—21no—
72C22×Q8×C11—22no—
73C22×Q8×C11—22no—
74C22×Q8×C11—41no—
75C22×Q8×C11—41no—
76C22×Q8×C11C2311yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C11×#124—28no—
87C11×#124—22no—
88C11×#124D414yes—
89C11×C22⋊Q8—28no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—22no—
92C11×#121—28no—
93C11×#121—22no—
94C11×#121—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11D414yes—
97C4×D4×C11—28no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×C4×Dic11—21no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127#66923—22no—
128#66923—22no—
129#66899—22no—
130#66899—22no—
131#66899—22no—
132#66899—22no—
133#66899—22no—
134#66899—22no—
135#66899—41no—
136#66899—41no—
137#66896—22no—
138#66896—22no—
139#66896—41no—
140#66896—41no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C22⋊(C11⋊C8)—41no—
147C22⋊(C11⋊C8)—41no—
148C22⋊(C11⋊C8)—41no—
149C22⋊(C11⋊C8)—41no—
150#66872—22no—
151#66871—22no—
152C4⋊(C11⋊C8)—22no—
153C4×C11⋊C8—22no—
154#25889—111nomaximal, Sylow
155C24×C11—21no—
156C24×C11C2×D411yescharacteristic
157C24×C11C2×D411yescharacteristic
158C11×#41—44no—
159C11×#41—44no—
160C11×#41—44no—
161C11×#41—44no—
162C2×Q8×C11—24no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—42no—
172C2×Q8×C11—42no—
173C2×Q8×C11—44no—
174C2×Q8×C11—44no—
175C2×Q8×C11—44no—
176C2×Q8×C11—44no—
177C2×Q8×C11C2×D412yes—
178C2×Q8×C11C2×D412yes—
179C2×Q8×C11#4112yes—
180C2×Q8×C11#4112yes—
181C2×D4×C11—24no—
182C2×D4×C11—24no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—41no—
191C2×D4×C11—42no—
192C2×D4×C11—42no—
193C2×D4×C11—42no—
194C2×D4×C11—42no—
195C2×D4×C11C2×D412yes—
196C22×C4×C11—21no—
197C22×C4×C11—24no—
198C22×C4×C11—24no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—42no—
214C22×C4×C11—42no—
215C22×C4×C11—42no—
216C22×C4×C11—42no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2411yescharacteristic
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4C2×D412yes—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—22no—
237C42×C11—24no—
238C42×C11C2×D412yes—
239C42×C11C2×D412yes—
240C22⋊Dic11—42no—
241C22⋊Dic11—42no—
242C22⋊Dic11—81no—
243C22⋊Dic11—81no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252Dic11⋊C4—42no—
253Dic11⋊C4—42no—
254C4×Dic11—81no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×#548D1111yescharacteristic
268C2×#488—111no—
269C2×#479—111no—
270#2562—111no—
271#2036—111no—
272#2035—111no—
273#2034—111no—
274#2033—111no—
275#1983—111no—
276#1954—111no—
277#1788—111no—
278#1788—111no—
279#1787—111no—
280#1787—111no—
281C4×#103—111no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—22no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11#13512yes—
303C23×C11C22×D411yescharacteristic
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—48no—
310Q8×C11—41no—
311Q8×C11—41no—
312Q8×C11#12414yes—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—44no—
316D4×C11—48no—
317D4×C11—48no—
318D4×C11—41no—
319D4×C11—41no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—48no—
336C2×C4×C11—48no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11#12012yes—
350C2×C4×C11#12012yes—
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C2×#4111yescharacteristic
354C2×C4×C11C2×#4111yescharacteristic
355C2×C4×C11H(5,𝔽2)11yescharacteristic
356C2×C4×C11H(5,𝔽2)11yescharacteristic
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C11⋊C8—41no—
370C11⋊C8—41no—
371C11⋊C8—41no—
372C11⋊C8—41no—
373C22×#41C2×D1111yescharacteristic
374C23×Q8C2×D1111yescharacteristic
375#548—24no—
376#548—24no—
377C2×#125—111no—
378C2×#124—21no—
379C2×#124C2×D1111yescharacteristic
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8C2×D1111yescharacteristic
382C2×#121—21no—
383C2×#121C2×D1111yescharacteristic
384C2×C4×Q8C2×D1111yescharacteristic
385C2×C4×D4—21no—
386C2×C4×D4C2×D1111yescharacteristic
387#488—224no—
388#479—224no—
389C2×#107—111no—
390C2×#106—111no—
391C2×C4⋊C8—111no—
392C2×#103—111no—
393C2×#103—111no—
394C2×#103—111no—
395C2×#103—111no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#102—111no—
401C2×#102—111no—
402C2×#102—111no—
403C2×#102—111no—
404C2×C22⋊C8—111no—
405C2×C22⋊C8—111no—
406C2×C22⋊C8—111no—
407C2×C22⋊C8—111no—
408C2×C4×C8—111no—
409#400—221no—
410#394—221no—
411#388—221no—
412#388—221no—
413#380—111no—
414#380—111no—
415#380—111no—
416#380—111no—
417C4×C4⋊C4—111no—
418#340—111no—
419#340—111no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—42no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—42no—
431C22×C11—41no—
432C22×C11—42no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—81no—
438C22×C11—81no—
439C22×C11—81no—
440C22×C11—81no—
441C22×C11C2×#12011yescharacteristic
442C22×C11#54611yescharacteristic
443C22×C11#54611yescharacteristic
444C22×C11C2×#13511yescharacteristic
445C22×C11#57511yescharacteristic
446C22×C11#57711yescharacteristic
447C22×C11#57811yescharacteristic
448C4×C11—24no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—41no—
452C4×C11—41no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11C2×#12411yescharacteristic
456C4×C11#53511yescharacteristic
457C4×C11#54611yescharacteristic
458C4×C11#54611yescharacteristic
459Dic11—81no—
460Dic11—81no—
461Dic11—81no—
462Dic11—81no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—22no—
467C2×#41—41no—
468C2×#41—41no—
469C22×Q8—22no—
470C22×Q8—22no—
471C22×Q8—21no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—41no—
475C22×Q8—41no—
476C22×Q8C22×D1111yescharacteristic
477C22×Q8C22×D1111yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4C22⋊D1111yescharacteristic
481C22×D4C22×D1111yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C22×D1111yescharacteristic
485C23×C4C22×D1111yescharacteristic
486C22×C8—111no—
487C22×C8—111no—
488C22×C8—111no—
489C22×C8—111no—
490#125—222no—
491#125—222no—
492#124—28no—
493#124—22no—
494#124C22⋊D1114yes—
495C22⋊Q8—28no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498#121—28no—
499#121—22no—
500#121—22no—
501C4×Q8—22no—
502C4×Q8C22⋊D1114yes—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4C22⋊D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4C22⋊D1111yescharacteristic
525C2×C22⋊C4C22⋊D1111yescharacteristic
526C2×C42—21no—
527C2×C42—221no—
528C2×C42C22×D1111yescharacteristic
529#107—222no—
530#106—222no—
531C4⋊C8—222no—
532#103—222no—
533#103—222no—
534#103—222no—
535#103—222no—
536#103—222no—
537#103—222no—
538#103—441no—
539#103—441no—
540#102—222no—
541#102—222no—
542#102—441no—
543#102—441no—
544C22⋊C8—441no—
545C22⋊C8—441no—
546C22⋊C8—441no—
547C22⋊C8—441no—
548C4×C8—222no—
549#95—221no—
550#95—221no—
551#95—221no—
552#95—221no—
553#95—221no—
554C2×C11—42no—
555C2×C11—81no—
556C2×C11—82no—
557C2×C11#243511yescharacteristic
558C2×C11#300211yescharacteristic
559C2×C11#301311yescharacteristic
560C2×C11#330011yescharacteristic
561C2×C11#330111yescharacteristic
562C2×C11#332611yescharacteristic
563C2×C11#332711yescharacteristic
564C24—21no—
565C24C2×C22⋊D1111yescharacteristic
566C24C2×C22⋊D1111yescharacteristic
567#41—44no—
568#41—44no—
569#41—44no—
570#41—44no—
571C2×Q8—24no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—42no—
581C2×Q8—42no—
582C2×Q8—44no—
583C2×Q8—44no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8#434112yes—
587C2×Q8#434112yes—
588C2×Q8C2×C22⋊D1112yes—
589C2×Q8C2×C22⋊D1112yes—
590C2×D4—24no—
591C2×D4—24no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—41no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4C2×C22⋊D1112yes—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4C2×C22⋊D1111yescharacteristic
631C22×C4C2×C22⋊D1111yescharacteristic
632C22×C4C2×C22⋊D1111yescharacteristic
633C22×C4C2×C22⋊D1111yescharacteristic
634C22×C4C23×D1111yescharacteristic
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—221no—
645C2×C8—221no—
646C2×C8—221no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—221no—
655C4⋊C4—221no—
656C4⋊C4—221no—
657C4⋊C4—221no—
658C4⋊C4—221no—
659C4⋊C4—442no—
660C4⋊C4—442no—
661C4⋊C4C2×C22⋊D1112yes—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—442no—
669C22⋊C4—442no—
670C22⋊C4—881no—
671C22⋊C4—881no—
672C42—24no—
673C42—881no—
674C42C2×C22⋊D1112yes—
675C42C2×C22⋊D1112yes—
676C11#2588911yescharacteristic, complemented, Sylow
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23#6700312yes—
698C23C22×C22⋊D1111yescharacteristic
699Q8—22no—
700Q8—22no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—48no—
705Q8—41no—
706Q8—41no—
707Q8#6698914yes—
708D4—22no—
709D4—22no—
710D4—44no—
711D4—48no—
712D4—48no—
713D4—41no—
714D4—41no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—48no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4#6700612yes—
757C2×C4#6700612yes—
758C2×C4C2×#434111yescharacteristic
759C2×C4C2×#434111yescharacteristic
760C2×C4#6703711yescharacteristic
761C2×C4#6703711yescharacteristic
762C2×C4C22×C22⋊D1111yescharacteristic
763C2×C4C22×C22⋊D1111yescharacteristic
764C8—441no—
765C8—441no—
766C8—441no—
767C8—441no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—41no—
782C22—42no—
783C22—41no—
784C22—41no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22#1062333711yescharacteristic
790C22#1062333711yescharacteristic
791C22C2×#6700311yescharacteristic
792C22#1062335311yescharacteristic
793C22#1062336811yescharacteristic
794C22#1062336911yescharacteristic
795C22C2×#6700611yescharacteristic
796C4—22no—
797C4—24no—
798C4—22no—
799C4—42no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—881no—
804C4—881no—
805C4—881no—
806C4—881no—
807C4C2×#6698911yescharacteristic
808C4#1062333611yescharacteristic
809C4#1062333711yescharacteristic
810C4#1062333711yescharacteristic
811C2—42no—
812C2—81no—
813C2—82no—
814C2#1307226311yescharacteristic
815C2#1307783411yescharacteristic
816C2#1307793111yescharacteristic
817C2#1308050311yescharacteristic
818C2#1308051811yescharacteristic
819C2#1308086911yescharacteristic
820C2#1308088411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#548C2
socleC23×C11C22×D4
hypercenterC2×#548D11
hypocenterC11#25889
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#10622669C2semidirect
2. C2×#10622635C2semidirect
3. #13073782C2semidirect
4. #13069816C2semidirect
5. #13069809C2semidirect
6. #13069802C2semidirect
7. #13069795C2semidirect
8. #13069549C2semidirect
9. #13069411C2semidirect
10. #13068556C2semidirect
11. #13068556C2semidirect
12. #13068551C2semidirect
13. #13068551C2semidirect
14. C4×#66899C2semidirect
676. C11#25889semidirect

Maximal subgroups

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

subgroupindex
C2×#106226692
C2×#106226352
#130737822
#130698162
#130698092
#130698022
#130697952
#130695492
#130694112
#130685562
#130685512
C4×#668992
C2×C11×#5482
#2588911