Finite Group Databasebeta

← C2×#13079665 #15625103

Subgroups — C2×#13079665 #15625103

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623093C211yesmaximal, characteristic, complemented
2C2×#10623246C211yesmaximal, characteristic, complemented
3#13079665C2116yesmaximal, direct product factor
4C2×#10622767C211yesmaximal, characteristic, complemented
5C2×#10622764C211yesmaximal, characteristic, complemented
6C2×#10622377C211yesmaximal, characteristic, complemented
7C2×#10622381C211yesmaximal, characteristic, complemented
8C2×#10622457C211yesmaximal, characteristic, complemented
9C2×#10622629C211yesmaximal, characteristic, complemented
10C2×#10622685C211yesmaximal, characteristic, complemented
11C2×#10622394C211yesmaximal, characteristic, complemented
12C2×#10622771C211yesmaximal, characteristic, complemented
13C2×#10622386C211yesmaximal, characteristic, complemented
14C2×#10622769C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#459C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic, complemented
21C2×C11×#127C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic, complemented
23C2×#66993C2211yescharacteristic
24C2×#66993C2211yescharacteristic, complemented
25C2×#66992—21no—
26C2×#66992—21no—
27C2×#66991C2211yescharacteristic
28C2×#66990—21no—
29C2×#66990—21no—
30C2×#66989C2211yescharacteristic
31C22×#4324C2211yescharacteristic, complemented
32C22×#4323C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C22×#4323C2211yescharacteristic, complemented
35C2×#66983—21no—
36C2×#66982—21no—
37C22×D88C2211yescharacteristic
38C22×#4314C2211yescharacteristic, complemented
39#10623246—24no—
40#10623246C2218yescomplemented
41#10623093—24no—
42#10623093C2218yescomplemented
43C2×#66948C2211yescharacteristic
44C2×#66943C2211yescharacteristic, complemented
45C2×#66937—21no—
46C2×#66936—21no—
47C2×#66928C2211yescharacteristic
48C2×C4×D44C2211yescharacteristic, complemented
49C2×#66925C2211yescharacteristic
50C11×#459C2218yescomplemented
51C2×C11×C4⋊C8C2211yescharacteristic, complemented
52C2×C11×#102C2211yescharacteristic
53C2×C11×#102C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic, complemented
56#10622771C2218yescomplemented
57#10622769C2218yescomplemented
58#10622767C2218yescomplemented
59#10622764C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×#66880C2211yescharacteristic, complemented
64C2×#66879C2211yescharacteristic, complemented
65C2×C8×Dic11C2211yescharacteristic, complemented
66#10622685C2218yescomplemented
67#10622629C2218yescomplemented
68C2×#66874C2211yescharacteristic, complemented
69C2×#66873C2211yescharacteristic
70C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
71#10622457C2218yescomplemented
72#10622453C2218yescomplemented
73#10622394C2218yescomplemented
74#10622386C2218yescomplemented
75#10622381C2218yescomplemented
76#10622377C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C23×Dic11—21no—
92C2×#4341—22no—
93C2×#4341—42no—
94C2×#4341—42no—
95C2×#4341C2314yes—
96C2×D4×D11—22no—
97C2×D4×D11—42no—
98C2×D4×D11—42no—
99C2×D4×D11C2314yes—
100C22×D44—21no—
101C22×D44C2311yescharacteristic
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11C2311yescharacteristic
105C22×Dic22C2311yescharacteristic
106C2×C11×D8—42no—
107C2×C11×D8—42no—
108C2×C11×D8C2314yes—
109C2×C11×D8C2314yescomplemented
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×#127—22no—
113C11×#127C2314yes—
114C4×D4×C11—22no—
115C4×D4×C11C2314yescomplemented
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C42×C11C2311yescharacteristic
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122#66993—22no—
123#66993—22no—
124#66993C2314yes—
125#66993C2314yescomplemented
126#66992—28no—
127#66992—28no—
128#66991—22no—
129#66991C2314yes—
130#66990—28no—
131#66990—28no—
132#66989—22no—
133#66989C2314yes—
134C2×#4324—42no—
135C2×#4324C2314yescomplemented
136C2×#4323—42no—
137C2×#4323—42no—
138C2×#4323—42no—
139C2×#4323C2314yes—
140C2×#4323C2314yes—
141C2×#4323C2314yescomplemented
142#66983—28no—
143#66982—28no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4D411yescharacteristic
149C2×(C2×D11)⋊C4D411yescharacteristic
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11C2311yescharacteristic
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4D411yescharacteristic
154C2×Dic11⋊C4D411yescharacteristic
155C2×C4×Dic11C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C2×D88—42no—
159C2×D88C2314yes—
160C2×#4314—42no—
161C2×#4314C2314yescomplemented
162#66948—22no—
163#66948C2314yes—
164#66943—22no—
165#66943C2314yescomplemented
166#66937—28no—
167#66936—28no—
168#66928—22no—
169#66928C2314yes—
170C4×D44—22no—
171C4×D44C2314yescomplemented
172#66925D414yes—
173#66925C2314yes—
174C11×C4⋊C8C2314yescomplemented
175C11×#102C2314yes—
176C11×#102C2314yescomplemented
177#66896C2314yes—
178#66896C2314yescomplemented
179#66885C2314yes—
180(C2×D11)⋊C8C2314yes—
181(C2×D11)⋊C8C2314yes—
182#66880C2314yescomplemented
183#66879C2314yescomplemented
184C8×Dic11C2314yescomplemented
185#66874C2314yescomplemented
186#66873C2314yes—
187C4⋊(C11⋊C8)C2314yescomplemented
188C2×#3220—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—24no—
195C23×D11—44no—
196C23×D11—82no—
197C23×D11—82no—
198C23×D11C2×D411yescharacteristic
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—24no—
203C2×D4×C11—24no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—82no—
211C2×D4×C11—82no—
212C2×D4×C11C2412yes—
213C2×D4×C11C2412yes—
214C2×D4×C11C2412yes—
215C22×C4×C11—21no—
216C22×C4×C11—24no—
217C22×C4×C11—82no—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2411yescharacteristic
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—82no—
231C2×C22⋊D11—82no—
232C2×C22⋊D11—82no—
233C2×C22⋊D11—82no—
234C2×C22⋊D11—82no—
235C22×Dic11—24no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—44no—
239C22×Dic11C2×D411yescharacteristic
240C22×Dic11C2×D411yescharacteristic
241C22×Dic11C2×D411yescharacteristic
242#4341—44no—
243#4341—44no—
244#4341—48no—
245D4×D11—44no—
246D4×D11—44no—
247D4×D11—48no—
248C2×D44—24no—
249C2×D44—21no—
250C2×D44—21no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44—22no—
254C2×D44—22no—
255C2×D44—82no—
256C2×D44C2412yes—
257C2×D44C2412yes—
258C2×C4×D11—24no—
259C2×C4×D11—22no—
260C2×C4×D11—22no—
261C2×C4×D11—82no—
262C2×C4×D11C2×D412yes—
263C2×C4×D11C2412yes—
264C2×Dic22—21no—
265C2×Dic22—22no—
266C2×Dic22—22no—
267C2×Dic22C2412yes—
268C11×D8—44no—
269C11×D8—44no—
270C2×C8×C11—22no—
271C2×C8×C11—22no—
272C2×C8×C11C2412yes—
273C2×C8×C11C2412yes—
274C11×C4⋊C4—21no—
275C11×C4⋊C4C2412yes—
276C11×C22⋊C4—24no—
277C42×C11C2×D412yes—
278C42×C11C2412yes—
279C22⋊Dic11—24no—
280C22⋊Dic11—24no—
281C22⋊Dic11—24no—
282#4324—44no—
283#4323—44no—
284#4323—44no—
285#4323—44no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288(C2×D11)⋊C4—24no—
289(C2×D11)⋊C4—24no—
290(C2×D11)⋊C4C2×D414yes—
291(C2×D11)⋊C4C2×D414yes—
292C4⋊Dic11—24no—
293C4⋊Dic11—21no—
294C4⋊Dic11C2412yes—
295Dic11⋊C4—24no—
296Dic11⋊C4C2×D414yes—
297Dic11⋊C4C2×D414yes—
298C4×Dic11C2×D412yes—
299C4×Dic11C2412yes—
300C2×C11⋊C8—22no—
301C2×C11⋊C8—22no—
302C2×C11⋊C8C2412yes—
303C2×C11⋊C8C2412yes—
304D88—44no—
305#4314—44no—
306C2×#540—111no—
307C2×#535—111no—
308#3220—1116no—
309C2×#496—111no—
310C2×#493—111no—
311C2×#490—111no—
312C2×#488—111no—
313C2×#463—111no—
314C2×#463—111no—
315C2×#459—111no—
316C2×#459D1111yescharacteristic, complemented
317C2×#449—111no—
318C2×#449—111no—
319C2×#447—111no—
320C2×#447—111no—
321C2×#433—111no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11—42no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11C22×D411yescharacteristic
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—48no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—84no—
348C22×D11—84no—
349C22×D11—816no—
350C22×D11C22×D412yes—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—42no—
358D4×C11—42no—
359D4×C11—42no—
360D4×C11—84no—
361D4×C11—84no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—42no—
366C2×C4×C11—84no—
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11H(5,𝔽2)12yes—
371C2×C4×C11H(5,𝔽2)12yes—
372C2×C4×C11C2511yescharacteristic
373C22⋊D11—48no—
374C22⋊D11—48no—
375C22⋊D11—84no—
376C22⋊D11—84no—
377C22⋊D11—84no—
378C22⋊D11—84no—
379C22⋊D11—84no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—48no—
386C2×Dic11—42no—
387C2×Dic11—42no—
388C2×Dic11C22×D412yes—
389C2×Dic11C22×D412yes—
390C2×Dic11C22×D412yes—
391D44—22no—
392D44—22no—
393D44—22no—
394D44—22no—
395D44—42no—
396D44—42no—
397D44—84no—
398C4×D11—24no—
399C4×D11—22no—
400C4×D11—22no—
401C4×D11—84no—
402Dic22—22no—
403Dic22—22no—
404Dic22—42no—
405C8×C11—22no—
406C8×C11—22no—
407C11⋊C8—22no—
408C11⋊C8—22no—
409C22×#41—111no—
410C23×D4—111no—
411C22×SD16—111no—
412C22×SD16—111no—
413C22×D8—111no—
414C22×D8—111no—
415C22×D8—111no—
416C22×D8—111no—
417C22×D8C2×D1111yescharacteristic
418C22×D8C2×D1111yescharacteristic, complemented
419#540—118no—
420#540—224no—
421#535—118no—
422#535—224no—
423C2×#127—111no—
424C2×#127—111no—
425C2×#127C2×D1111yescharacteristic
426C2×#125—111no—
427C2×#124—111no—
428C2×#124—111no—
429C2×#123—221no—
430C2×#123—221no—
431C2×#121—111no—
432C2×#121—111no—
433C2×#121—221no—
434C2×#121—221no—
435C2×#121—221no—
436C2×#121—221no—
437C2×#120—221no—
438C2×#120—221no—
439C2×C4×D4—111no—
440C2×C4×D4C2×D1111yescharacteristic, complemented
441C2×#117—111no—
442#496—118no—
443#493—118no—
444#490—118no—
445#488—118no—
446#463—118no—
447#463—118no—
448#459—118no—
449#459C2×D1118yescomplemented
450#449—118no—
451#449—118no—
452#447—118no—
453#447—118no—
454#433—118no—
455C2×C4⋊C8—111no—
456C2×C4⋊C8C2×D1111yescharacteristic, complemented
457C2×#103—111no—
458C2×#103—111no—
459C2×#102—111no—
460C2×#102—111no—
461C2×#102—111no—
462C2×#102—111no—
463C2×#102C2×D1111yescharacteristic
464C2×#102C2×D1111yescharacteristic, complemented
465C2×C22⋊C8—111no—
466C2×C22⋊C8—111no—
467C2×#97—111no—
468C2×C4×C8—111no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—84no—
479C22×C11—84no—
480C22×C11—84no—
481C22×C11#53512yes—
482C22×C11#57612yes—
483C22×C11#57612yes—
484C22×C11C23×D411yescharacteristic
485C2×D11—22no—
486C2×D11—22no—
487C2×D11—22no—
488C2×D11—44no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—816no—
496C2×D11—84no—
497C2×D11—84no—
498C4×C11—22no—
499C4×C11—22no—
500C4×C11—42no—
501C4×C11#53512yes—
502C4×C11C2×H(5,𝔽2)11yescharacteristic
503C4×C11C2×H(5,𝔽2)11yescharacteristic
504Dic11—22no—
505Dic11—22no—
506Dic11—22no—
507Dic11—42no—
508Dic11—42no—
509C25—221no—
510C2×#41—114no—
511C2×#41—222no—
512C2×#41—442no—
513C2×#41—442no—
514C22×Q8—111no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—114no—
518C22×D4—111no—
519C22×D4—111no—
520C22×D4—221no—
521C22×D4—222no—
522C22×D4—221no—
523C22×D4—221no—
524C22×D4—221no—
525C22×D4—221no—
526C22×D4—221no—
527C22×D4—221no—
528C22×D4—221no—
529C22×D4—442no—
530C22×D4—442no—
531C22×D4C22×D1111yescharacteristic
532C22×D4C22×D1111yescharacteristic
533C22×D4C22×D1111yescharacteristic
534C23×C4—21no—
535C23×C4—111no—
536C23×C4—221no—
537C23×C4—221no—
538C2×SD16—114no—
539C2×SD16—114no—
540C2×SD16—442no—
541C2×SD16—442no—
542C2×D8—42no—
543C2×D8—42no—
544C2×D8—114no—
545C2×D8—114no—
546C2×D8—114no—
547C2×D8—114no—
548C2×D8—442no—
549C2×D8—442no—
550C2×D8—442no—
551C2×D8—442no—
552C2×D8C22×D1114yes—
553C2×D8C22×D1114yescomplemented
554C22×C8—111no—
555C22×C8—111no—
556C22×C8C22×D1111yescharacteristic
557C22×C8C22×D1111yescharacteristic
558#127—22no—
559#127—114no—
560#127—114no—
561#127—222no—
562#127—222no—
563#127C22×D1114yes—
564#125—114no—
565#125—222no—
566#124—114no—
567#124—114no—
568#124—222no—
569#124—222no—
570#123—228no—
571#123—228no—
572#121—114no—
573#121—114no—
574#121—228no—
575#121—228no—
576#121—222no—
577#121—228no—
578#121—228no—
579#121—222no—
580#120—228no—
581#120—228no—
582C4×D4—22no—
583C4×D4—114no—
584C4×D4—222no—
585C4×D4C22×D1114yescomplemented
586#117—114no—
587#117—114no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—221no—
592C2×C4⋊C4—221no—
593C2×C4⋊C4C22×D1111yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—111no—
596C2×C22⋊C4—111no—
597C2×C22⋊C4—221no—
598C2×C22⋊C4—221no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C42—111no—
605C2×C42C22×D1111yescharacteristic
606C4⋊C8—114no—
607C4⋊C8C22×D1114yescomplemented
608#103—114no—
609#103—114no—
610#102—114no—
611#102—114no—
612#102—114no—
613#102—114no—
614#102C22×D1114yes—
615#102C22×D1114yescomplemented
616C22⋊C8—114no—
617C22⋊C8—114no—
618#97—114no—
619C4×C8—114no—
620C2×C11—82no—
621C2×C11—82no—
622C2×C11—82no—
623C2×C11#322014yescomplemented
624C2×C11C2×#53511yescharacteristic
625C2×C11C2×#57611yescharacteristic
626C2×C11C2×#57611yescharacteristic
627D11—42no—
628D11—82no—
629D11—82no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—111no—
634C24—224no—
635C24—221no—
636C24—221no—
637C24—444no—
638C24—882no—
639C24—882no—
640#41—444no—
641#41—444no—
642#41—448no—
643C2×Q8—112no—
644C2×Q8—221no—
645C2×Q8—222no—
646C2×Q8—222no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—82no—
659C2×D4—82no—
660C2×D4—112no—
661C2×D4—112no—
662C2×D4—224no—
663C2×D4—224no—
664C2×D4—224no—
665C2×D4—224no—
666C2×D4—224no—
667C2×D4—224no—
668C2×D4—224no—
669C2×D4—224no—
670C2×D4—221no—
671C2×D4—221no—
672C2×D4—222no—
673C2×D4—222no—
674C2×D4—222no—
675C2×D4—222no—
676C2×D4—444no—
677C2×D4—444no—
678C2×D4—448no—
679C2×D4—444no—
680C2×D4—444no—
681C2×D4—882no—
682C2×D4—882no—
683C2×D4—882no—
684C2×D4—882no—
685C2×D4—882no—
686C2×D4—882no—
687C2×D4C23×D1112yes—
688C2×D4C23×D1112yes—
689C2×D4C23×D1112yes—
690C22×C4—21no—
691C22×C4—24no—
692C22×C4—82no—
693C22×C4—111no—
694C22×C4—111no—
695C22×C4—111no—
696C22×C4—112no—
697C22×C4—112no—
698C22×C4—224no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—224no—
704C22×C4—444no—
705C22×C4—882no—
706C22×C4D4×D1111yescharacteristic
707C22×C4D4×D1111yescharacteristic
708C22×C4C23×D1111yescharacteristic
709SD16—444no—
710SD16—444no—
711D8—44no—
712D8—44no—
713D8—444no—
714D8—444no—
715D8—444no—
716D8—444no—
717C2×C8—22no—
718C2×C8—22no—
719C2×C8—112no—
720C2×C8—112no—
721C2×C8—222no—
722C2×C8—222no—
723C2×C8C23×D1112yes—
724C2×C8C23×D1112yes—
725C4⋊C4—21no—
726C4⋊C4—114no—
727C4⋊C4—114no—
728C4⋊C4—112no—
729C4⋊C4—224no—
730C4⋊C4—224no—
731C4⋊C4—221no—
732C4⋊C4C23×D1112yes—
733C22⋊C4—24no—
734C22⋊C4—114no—
735C22⋊C4—114no—
736C22⋊C4—224no—
737C22⋊C4—224no—
738C22⋊C4—224no—
739C22⋊C4—224no—
740C22⋊C4—224no—
741C22⋊C4—224no—
742C22⋊C4—224no—
743C42—112no—
744C42—112no—
745C42D4×D1112yes—
746C42C23×D1112yes—
747C11C2×#322011yescharacteristic, complemented, Sylow
748C23—22no—
749C23—22no—
750C23—22no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—112no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—448no—
767C23—442no—
768C23—442no—
769C23—442no—
770C23—442no—
771C23—442no—
772C23—442no—
773C23—884no—
774C23—884no—
775C23—8816no—
776C23C2×D4×D1111yescharacteristic
777Q8—222no—
778Q8—222no—
779Q8—442no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—42no—
787D4—42no—
788D4—42no—
789D4—84no—
790D4—84no—
791D4—222no—
792D4—222no—
793D4—222no—
794D4—222no—
795D4—448no—
796D4—448no—
797D4—442no—
798D4—442no—
799D4—884no—
800D4—884no—
801D4—884no—
802D4—884no—
803D4—884no—
804D4—884no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—42no—
809C2×C4—84no—
810C2×C4—112no—
811C2×C4—112no—
812C2×C4—112no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—224no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—448no—
822C2×C4—442no—
823C2×C4—442no—
824C2×C4—884no—
825C2×C4C2×D4×D1112yes—
826C2×C4C2×D4×D1112yes—
827C2×C4C2×D4×D1111yescharacteristic
828C2×C4#6703712yes—
829C2×C4#6704212yes—
830C2×C4C24×D1111yescharacteristic
831C8—22no—
832C8—22no—
833C8—222no—
834C8—222no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—84no—
845C22—84no—
846C22—84no—
847C22—222no—
848C22—222no—
849C22—222no—
850C22—444no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—442no—
855C22—442no—
856C22—442no—
857C22—8816no—
858C22—884no—
859C22—884no—
860C22#1062313812yes—
861C22#1062328812yes—
862C22#1062330512yes—
863C22C22×D4×D1111yescharacteristic
864C4—22no—
865C4—22no—
866C4—42no—
867C4—222no—
868C4—222no—
869C4—222no—
870C4—442no—
871C4—442no—
872C4#1062313812yes—
873C4C2×#6703711yescharacteristic
874C4C2×#6704211yescharacteristic
875C2—82no—
876C2—82no—
877C2—82no—
878C2—442no—
879C2—882no—
880C2—882no—
881C2#1307966514yesdirect product factor
882C2C2×#1062313811yescharacteristic
883C2C2×#1062328811yescharacteristic
884C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11C2×#3220
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10623093C2semidirect
2. C2×#10623246C2semidirect
3. #13079665C2direct (N × H)
4. C2×#10622767C2semidirect
5. C2×#10622764C2semidirect
6. C2×#10622377C2semidirect
7. C2×#10622381C2semidirect
8. C2×#10622457C2semidirect
9. C2×#10622629C2semidirect
10. C2×#10622685C2semidirect
11. C2×#10622394C2semidirect
12. C2×#10622771C2semidirect
13. C2×#10622386C2semidirect
14. C2×#10622769C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#459C2semidirect
20. C22×C11×D8C22semidirect
22. C2×C4×D4×C11C22semidirect
24. C2×#66993C22semidirect
31. C22×#4324C22semidirect
34. C22×#4323C22semidirect
38. C22×#4314C22semidirect
40. #10623246C22semidirect
42. #10623093C22semidirect
44. C2×#66943C22semidirect
48. C2×C4×D44C22semidirect
50. C11×#459C22semidirect
51. C2×C11×C4⋊C8C22semidirect
53. C2×C11×#102C22semidirect
55. C2×#66896C22semidirect
56. #10622771C22semidirect
57. #10622769C22semidirect
58. #10622767C22semidirect
59. #10622764C22semidirect
63. C2×#66880C22semidirect
64. C2×#66879C22semidirect
65. C2×C8×Dic11C22semidirect
66. #10622685C22semidirect
67. #10622629C22semidirect
68. C2×#66874C22semidirect
70. C2×C4⋊(C11⋊C8)C22semidirect
71. #10622457C22semidirect
72. #10622453C22semidirect
73. #10622394C22semidirect
74. #10622386C22semidirect
75. #10622381C22semidirect
76. #10622377C22semidirect
109. C2×C11×D8C23semidirect
115. C4×D4×C11C23semidirect
125. #66993C23semidirect
135. C2×#4324C23semidirect
141. C2×#4323C23semidirect
161. C2×#4314C23semidirect
165. #66943C23semidirect
171. C4×D44C23semidirect
174. C11×C4⋊C8C23semidirect
176. C11×#102C23semidirect
178. #66896C23semidirect
182. #66880C23semidirect
183. #66879C23semidirect
184. C8×Dic11C23semidirect
185. #66874C23semidirect
187. C4⋊(C11⋊C8)C23semidirect
316. C2×#459D11semidirect
418. C22×D8C2×D11semidirect
440. C2×C4×D4C2×D11semidirect
449. #459C2×D11semidirect
456. C2×C4⋊C8C2×D11semidirect
464. C2×#102C2×D11semidirect
553. C2×D8C22×D11semidirect
585. C4×D4C22×D11semidirect
607. C4⋊C8C22×D11semidirect
615. #102C22×D11semidirect
623. C2×C11#3220semidirect
747. C11C2×#3220semidirect
881. C2#13079665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230932
C2×#106232462
#130796652
C2×#106227672
C2×#106227642
C2×#106223772
C2×#106223812
C2×#106224572
C2×#106226292
C2×#106226852
C2×#106223942
C2×#106227712
C2×#106223862
C2×#106227692
C2×#106224532
C2×C11×#4592
C2×#322011