Finite Group Databasebeta

← #14762906

Subgroups — #14762906

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2#13070999C211yesmaximal, characteristic, complemented
3#13069062C214yesmaximal, complemented
4#13068918C214yesmaximal, complemented
5#13068713C212yesmaximal, complemented
6#13068559C212yesmaximal, complemented
7C2×C11×#407C211yesmaximal, characteristic, complemented
8C24×C4×C11C2211yescharacteristic
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2212yescomplemented
11C2×#67006—21no—
12#10623322—21no—
13#10623322—21no—
14#10623322—21no—
15#10623322—21no—
16#10623322C412yescomplemented
17#10623322C412yescomplemented
18#10623322C2212yes—
19#10623322C2212yes—
20C2×#66983C411yescharacteristic, complemented
21C2×#66983C411yescharacteristic, complemented
22C2×#66982—21no—
23C2×C4×C22⋊D11—21no—
24C2×C4×C22⋊D11—21no—
25C2×#66979C2211yescharacteristic
26C2×#66979C2212yescomplemented
27C2×#66977C411yescharacteristic, complemented
28C2×#66977C411yescharacteristic, complemented
29C11×#407—21no—
30C11×#407—21no—
31C11×#407C2212yes—
32C11×#407C2212yescomplemented
33C2×C11×C22⋊C8—21no—
34C2×C11×C22⋊C8—21no—
35#10622860—21no—
36#10622825—21no—
37#10622825—21no—
38#10622824—21no—
39C4×C22⋊Dic11C2212yes—
40C4×C22⋊Dic11C2212yescomplemented
41C2×#66889C2218yescomplemented
42#10622193C2218yescomplemented
43C25×C11D411yescharacteristic
44C23×C4×C11—44no—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—21no—
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C2×#4339—21no—
63C2×#4339—21no—
64C2×#4339—44no—
65C2×#4339C2×C412yes—
66C2×#4339C2312yes—
67C22×D44C2×C411yescharacteristic
68C22×C4×D11—21no—
69C22×Dic22C2×C411yescharacteristic
70C2×C11×M16—22no—
71C2×C11×M16—44no—
72C2×C11×M16C2314yes—
73C22×C8×C11—22no—
74#67006—22no—
75#67006—22no—
76#67006—22no—
77#67006—22no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84#66983—21no—
85#66983—21no—
86#66983—21no—
87#66983—21no—
88#66983C2×C412yes—
89#66983C2×C412yes—
90#66983C2×C412yes—
91#66983C2×C412yes—
92#66982—22no—
93#66982—22no—
94#66982—22no—
95#66982—22no—
96C4×C22⋊D11—22no—
97C4×C22⋊D11—22no—
98C4×C22⋊D11—22no—
99C4×C22⋊D11—22no—
100C4×C22⋊D11—22no—
101C4×C22⋊D11—22no—
102C4×C22⋊D11—22no—
103C4×C22⋊D11—22no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106#66979—21no—
107#66979—21no—
108#66979—44no—
109#66979C2×C412yes—
110#66979C2312yes—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11C2×C411yescharacteristic
113C2×C4⋊Dic11C2×C411yescharacteristic
114#66977—21no—
115#66977—21no—
116#66977—21no—
117#66977—21no—
118#66977C2×C412yes—
119#66977C2×C412yes—
120#66977C2×C412yes—
121#66977C2×C412yes—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×C4×Dic11—21no—
125C2×C4×Dic11C2314yes—
126C11×C22⋊C8—22no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132#66889—48no—
133#21774—111nomaximal, Sylow
134C24×C11—42no—
135C24×C11—42no—
136C24×C11—42no—
137C24×C11C22⋊C411yescharacteristic
138C24×C11C22⋊C411yescharacteristic
139C24×C11C22⋊C411yescharacteristic
140C24×C11C22⋊C411yescharacteristic
141C24×C11C2×D411yescharacteristic
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C23×D11—21no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11C22⋊C411yescharacteristic
160C22×C4×C11C22⋊C411yescharacteristic
161C22×C4×C11C22⋊C411yescharacteristic
162C22×C4×C11C22⋊C411yescharacteristic
163C22×C4×C11C22⋊C411yescharacteristic
164C22×C4×C11C22⋊C411yescharacteristic
165C22×C4×C11C22⋊C411yescharacteristic
166C22×C4×C11C22⋊C411yescharacteristic
167C22×C4×C11C22⋊C411yescharacteristic
168C22×C4×C11C22⋊C411yescharacteristic
169C22×C4×C11C22⋊C411yescharacteristic
170C22×C4×C11C22⋊C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C2×C22⋊D11—22no—
188C2×C22⋊D11—22no—
189C2×C22⋊D11—22no—
190C2×C22⋊D11—22no—
191C2×C22⋊D11—22no—
192C2×C22⋊D11—22no—
193C2×C22⋊D11—44no—
194C2×C22⋊D11—44no—
195C2×C22⋊D11—44no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—24no—
200#4339—28no—
201#4339—44no—
202#4339—44no—
203#4339—44no—
204C2×D44—21no—
205C2×D44—42no—
206C2×D44C22×C412yes—
207C2×C4×D11—22no—
208C2×C4×D11—22no—
209C2×C4×D11—44no—
210C2×Dic22—21no—
211C2×Dic22—42no—
212C2×Dic22C22×C412yes—
213C11×M16—28no—
214C11×M16—44no—
215C2×C8×C11—24no—
216C2×C8×C11—44no—
217C22⋊Dic11—22no—
218C22⋊Dic11—22no—
219C22⋊Dic11—22no—
220C22⋊Dic11—22no—
221C22⋊Dic11—22no—
222C22⋊Dic11—22no—
223C22⋊Dic11—44no—
224C22⋊Dic11—44no—
225C22⋊Dic11—44no—
226(C2×D11)⋊C4—22no—
227(C2×D11)⋊C4—22no—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4—22no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—44no—
233C4⋊Dic11C22×C412yes—
234C4⋊Dic11C22×C412yes—
235Dic11⋊C4—22no—
236Dic11⋊C4—22no—
237Dic11⋊C4—22no—
238Dic11⋊C4—22no—
239C4×Dic11—22no—
240C4×Dic11—22no—
241C4×Dic11—28no—
242C2×#525—111no—
243C2×#407D1111yescharacteristic, complemented
244#2280—111no—
245#1897—114no—
246#1871—114no—
247#1826—112no—
248#1789—112no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—416no—
271C23×C11C2×C22⋊C411yescharacteristic
272C23×C11C2×C22⋊C411yescharacteristic
273C23×C11C2×C22⋊C411yescharacteristic
274C23×C11C2×C22⋊C411yescharacteristic
275C23×C11C2×C22⋊C411yescharacteristic
276C23×C11C2×C22⋊C411yescharacteristic
277C23×C11C22×D411yescharacteristic
278C22×D11—22no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
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×C11C2×C22⋊C411yescharacteristic
310C2×C4×C11C2×C22⋊C411yescharacteristic
311C2×C4×C11C2×C22⋊C411yescharacteristic
312C2×C4×C11C2×C22⋊C411yescharacteristic
313C2×C4×C11C2×C22⋊C411yescharacteristic
314C2×C4×C11C2×C22⋊C411yescharacteristic
315C2×C4×C11C23×C411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11H(5,𝔽2)14yes—
318C22⋊D11—44no—
319C22⋊D11—44no—
320C22⋊D11—44no—
321C22⋊D11—44no—
322C22⋊D11—44no—
323C22⋊D11—44no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—44no—
331C2×Dic11—44no—
332C2×Dic11—44no—
333D44—24no—
334D44—42no—
335C4×D11—44no—
336C4×D11—44no—
337Dic22—24no—
338Dic22—42no—
339C8×C11—44no—
340C22×#41—111no—
341C24×C4C2×D1111yescharacteristic
342C22×M16C2×D1112yescomplemented
343#525—112no—
344#525—112no—
345#525—112no—
346#525—112no—
347#525—221no—
348#525—221no—
349#525—221no—
350#525—221no—
351C2×#123—221no—
352C2×C22⋊Q8—111no—
353C2×C22⋊Q8—111no—
354C2×#121—111no—
355C2×#121—111no—
356C2×#120—221no—
357C2×C4×D4—221no—
358C2×C4×D4—221no—
359C2×#117—112no—
360C2×#117—111no—
361C2×#104—118no—
362#407—21no—
363#407—21no—
364#407C2×D1112yes—
365#407C2×D1112yescomplemented
366C2×C22⋊C8—21no—
367C2×C22⋊C8—21no—
368#381—221no—
369#380—221no—
370#380—221no—
371#379—221no—
372C4×C22⋊C4—112no—
373C4×C22⋊C4—112no—
374#339—118no—
375C22×C11—21no—
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—21no—
383C22×C11—21no—
384C22×C11—21no—
385C22×C11—21no—
386C22×C11—21no—
387C22×C11—21no—
388C22×C11—21no—
389C22×C11—21no—
390C22×C11—21no—
391C22×C11—21no—
392C22×C11—21no—
393C22×C11—44no—
394C22×C11—44no—
395C22×C11—44no—
396C22×C11—44no—
397C22×C11—44no—
398C22×C11—44no—
399C22×C11—44no—
400C22×C11#42112yes—
401C22×C11#42112yes—
402C22×C11C22×C22⋊C411yescharacteristic
403C22×C11#53412yes—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—84no—
408C4×C11—21no—
409C4×C11—21no—
410C4×C11—21no—
411C4×C11—21no—
412C4×C11—21no—
413C4×C11—21no—
414C4×C11#51812yes—
415C4×C11#53412yes—
416Dic11—42no—
417Dic11—42no—
418Dic11—42no—
419Dic11—84no—
420C25D4411yescharacteristic
421C2×#41—112no—
422C2×#41—112no—
423C2×#41—221no—
424C2×#41—221no—
425C2×#41—444no—
426C22×Q8—111no—
427C22×D4—111no—
428C22×D4—221no—
429C22×D4—221no—
430C22×D4—221no—
431C23×C4—44no—
432C23×C4—221no—
433C23×C4C4×D1111yescharacteristic
434C23×C4C4×D1111yescharacteristic
435C23×C4C4×D1111yescharacteristic
436C23×C4C4×D1111yescharacteristic
437C23×C4D4411yescharacteristic
438C23×C4D4411yescharacteristic
439C23×C4D4411yescharacteristic
440C23×C4C22⋊D1111yescharacteristic
441C23×C4C22⋊D1111yescharacteristic
442C23×C4C22⋊D1111yescharacteristic
443C23×C4C22⋊D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1111yescharacteristic
447C2×M16—22no—
448C2×M16—44no—
449C2×M16C22×D1114yes—
450C22×C8—22no—
451#123—222no—
452#123—222no—
453#123—222no—
454#123—222no—
455C22⋊Q8—112no—
456C22⋊Q8—112no—
457C22⋊Q8—112no—
458C22⋊Q8—112no—
459C22⋊Q8—221no—
460C22⋊Q8—221no—
461C22⋊Q8—221no—
462C22⋊Q8—221no—
463#121—112no—
464#121—112no—
465#121—112no—
466#121—112no—
467#121—221no—
468#121—221no—
469#121—221no—
470#121—221no—
471#120—222no—
472#120—222no—
473#120—222no—
474#120—222no—
475C4×D4—222no—
476C4×D4—222no—
477C4×D4—222no—
478C4×D4—222no—
479C4×D4—222no—
480C4×D4—222no—
481C4×D4—222no—
482C4×D4—222no—
483#117—112no—
484#117—112no—
485#117—221no—
486#117—221no—
487#117—444no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—222no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—222no—
499C2×C22⋊C4—222no—
500C2×C22⋊C4—222no—
501C2×C42—114no—
502C2×C42—221no—
503#104—448no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508#95—222no—
509#95—222no—
510C2×C11—22no—
511C2×C11—22no—
512C2×C11—22no—
513C2×C11—41no—
514C2×C11—41no—
515C2×C11—41no—
516C2×C11—41no—
517C2×C11#230811yescharacteristic
518C2×C11C2×#42111yescharacteristic
519C2×C11C2×#42111yescharacteristic
520D11—82no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24—221no—
525C24(C2×D11)⋊C411yescharacteristic
526C24(C2×D11)⋊C411yescharacteristic
527C24(C2×D11)⋊C411yescharacteristic
528C24(C2×D11)⋊C411yescharacteristic
529C24C2×D4411yescharacteristic
530C24C2×D4411yescharacteristic
531C24C2×D4411yescharacteristic
532#41—228no—
533#41—444no—
534#41—444no—
535#41—444no—
536C2×Q8—112no—
537C2×Q8—221no—
538C2×Q8—442no—
539C2×D4—112no—
540C2×D4—222no—
541C2×D4—222no—
542C2×D4—222no—
543C2×D4—222no—
544C2×D4—222no—
545C2×D4—222no—
546C2×D4—221no—
547C2×D4—442no—
548C2×D4—444no—
549C2×D4—444no—
550C2×D4—444no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—224no—
571C22×C4—444no—
572C22×C4(C2×D11)⋊C411yescharacteristic
573C22×C4(C2×D11)⋊C411yescharacteristic
574C22×C4(C2×D11)⋊C411yescharacteristic
575C22×C4(C2×D11)⋊C411yescharacteristic
576C22×C4(C2×D11)⋊C411yescharacteristic
577C22×C4(C2×D11)⋊C411yescharacteristic
578C22×C4(C2×D11)⋊C411yescharacteristic
579C22×C4(C2×D11)⋊C411yescharacteristic
580C22×C4(C2×D11)⋊C411yescharacteristic
581C22×C4(C2×D11)⋊C411yescharacteristic
582C22×C4(C2×D11)⋊C411yescharacteristic
583C22×C4(C2×D11)⋊C411yescharacteristic
584C22×C4C2×C4×D1111yescharacteristic
585C22×C4C2×C4×D1111yescharacteristic
586C22×C4C2×C4×D1111yescharacteristic
587C22×C4C2×C4×D1111yescharacteristic
588C22×C4C2×C4×D1111yescharacteristic
589C22×C4C2×C4×D1111yescharacteristic
590C22×C4C2×D4411yescharacteristic
591C22×C4C2×D4411yescharacteristic
592C22×C4C2×D4411yescharacteristic
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C2×C22⋊D1111yescharacteristic
597C22×C4C2×C22⋊D1111yescharacteristic
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C23×D1111yescharacteristic
600M16—28no—
601M16—44no—
602C2×C8—24no—
603C2×C8—44no—
604C4⋊C4—112no—
605C4⋊C4—112no—
606C4⋊C4—221no—
607C4⋊C4—221no—
608C4⋊C4—222no—
609C4⋊C4—222no—
610C4⋊C4—222no—
611C4⋊C4—222no—
612C4⋊C4—444no—
613C22⋊C4—222no—
614C22⋊C4—222no—
615C22⋊C4—222no—
616C22⋊C4—222no—
617C22⋊C4—222no—
618C22⋊C4—222no—
619C22⋊C4—222no—
620C22⋊C4—222no—
621C22⋊C4—222no—
622C22⋊C4—222no—
623C22⋊C4—444no—
624C22⋊C4—444no—
625C22⋊C4—444no—
626C42—222no—
627C42—222no—
628C42—228no—
629C11#2177411yescharacteristic, complemented, Sylow
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—416no—
652C23—222no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23C2×(C2×D11)⋊C411yescharacteristic
657C23C2×(C2×D11)⋊C411yescharacteristic
658C23C2×(C2×D11)⋊C411yescharacteristic
659C23C2×(C2×D11)⋊C411yescharacteristic
660C23C2×(C2×D11)⋊C411yescharacteristic
661C23C2×(C2×D11)⋊C411yescharacteristic
662C23C22×D4411yescharacteristic
663Q8—224no—
664Q8—442no—
665D4—224no—
666D4—442no—
667D4—444no—
668D4—444no—
669D4—444no—
670D4—444no—
671D4—444no—
672D4—444no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—444no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—444no—
708C2×C4—444no—
709C2×C4—444no—
710C2×C4—444no—
711C2×C4C2×(C2×D11)⋊C411yescharacteristic
712C2×C4C2×(C2×D11)⋊C411yescharacteristic
713C2×C4C2×(C2×D11)⋊C411yescharacteristic
714C2×C4C2×(C2×D11)⋊C411yescharacteristic
715C2×C4C2×(C2×D11)⋊C411yescharacteristic
716C2×C4C2×(C2×D11)⋊C411yescharacteristic
717C2×C4C22×C4×D1111yescharacteristic
718C2×C4#6703714yes—
719C2×C4C22×C22⋊D1111yescharacteristic
720C8—44no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—884no—
750C22#1062275212yes—
751C22#1062275212yes—
752C22#1062302412yes—
753C22C22×(C2×D11)⋊C411yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—442no—
761C4—442no—
762C4—442no—
763C4—884no—
764C4#1062301712yes—
765C4#1062333512yes—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—41no—
772C2—41no—
773C2—882no—
774C2#1307119111yescharacteristic
775C2C2×#1062275211yescharacteristic
776C2C2×#1062275211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#407C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623322C2
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11#21774
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #13070999C2semidirect
3. #13069062C2semidirect
4. #13068918C2semidirect
5. #13068713C2semidirect
6. #13068559C2semidirect
7. C2×C11×#407C2semidirect
10. C22×C11×M16C22semidirect
16. #10623322C4semidirect
17. #10623322C4semidirect
20. C2×#66983C4semidirect
21. C2×#66983C4semidirect
26. C2×#66979C22semidirect
27. C2×#66977C4semidirect
28. C2×#66977C4semidirect
32. C11×#407C22semidirect
40. C4×C22⋊Dic11C22semidirect
41. C2×#66889C22semidirect
42. #10622193C22semidirect
243. C2×#407D11semidirect
342. C22×M16C2×D11semidirect
365. #407C2×D11semidirect
629. C11#21774semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130709992
#130690622
#130689182
#130687132
#130685592
C2×C11×#4072
#2177411