Finite Group Databasebeta

← C2×#13079662 #15625100

Subgroups — C2×#13079662 #15625100

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×#10623150C211yesmaximal, characteristic, complemented
2C2×#10623336C211yesmaximal, characteristic, complemented
3#13079662C2116yesmaximal, direct product factor
4C2×#10622767C211yesmaximal, characteristic, complemented
5C2×#10622764C211yesmaximal, characteristic, complemented
6C2×#10622377C211yesmaximal, characteristic, complemented
7C2×#10622381C211yesmaximal, characteristic, complemented
8C2×#10622400C211yesmaximal, characteristic, complemented
9C2×#10622766C211yesmaximal, characteristic, complemented
10C2×#10622399C211yesmaximal, characteristic, complemented
11C2×#10622763C211yesmaximal, characteristic, complemented
12C2×#10622347C211yesmaximal, characteristic, complemented
13C2×#10622650C211yesmaximal, characteristic, complemented
14C2×#10622830C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#447C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×#67006—21no—
23C2×#67006—21no—
24#10623336—24no—
25#10623336C2218yescomplemented
26C2×#66993C2211yescharacteristic
27C2×#66993C2211yescharacteristic
28C2×#66993C2211yescharacteristic, complemented
29C2×#66992—21no—
30C2×#66991—21no—
31C2×#66991—21no—
32C2×#66991—21no—
33C2×#66989C2211yescharacteristic
34C2×#66989C2211yescharacteristic
35C2×D4×Dic11C2211yescharacteristic, complemented
36C22×#4324C2211yescharacteristic, complemented
37C22×#4323C2211yescharacteristic
38C22×#4323C2211yescharacteristic
39C22×#4323C2211yescharacteristic, complemented
40C2×#66983C2211yescharacteristic
41C2×#66979C2211yescharacteristic
42C22×D88C2211yescharacteristic, complemented
43C22×#4314C2211yescharacteristic, complemented
44#10623150—24no—
45#10623150C2218yescomplemented
46C2×#66946C2211yescharacteristic, complemented
47C2×#66943C2211yescharacteristic, complemented
48C2×#66939—21no—
49C2×#66936—21no—
50C11×#447C2218yescomplemented
51C2×C11×#102C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54#10622830C2218yescomplemented
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622767C2218yescomplemented
59#10622766C2218yescomplemented
60#10622764C2218yescomplemented
61#10622763C2218yescomplemented
62C2×#66885C2211yescharacteristic, complemented
63C2×#66880C2211yescharacteristic, complemented
64C2×#66879C2211yescharacteristic, complemented
65C2×Dic11⋊C8C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×C8×Dic11C2211yescharacteristic, complemented
68#10622650C2218yescomplemented
69C2×#66874C2211yescharacteristic, complemented
70C2×#66873C2211yescharacteristic, complemented
71#10622400C2218yescomplemented
72#10622399C2218yescomplemented
73#10622381C2218yescomplemented
74#10622377C2218yescomplemented
75#10622347C2218yescomplemented
76#10622333C2218yescomplemented
77C25×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—22no—
81C22×D4×C11—42no—
82C22×D4×C11—42no—
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2314yes—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C23×Dic11—21no—
97C2×#4339—22no—
98C2×#4339—42no—
99C2×#4339—42no—
100C2×#4339C2314yes—
101C22×D44C2311yescharacteristic
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×Dic22C2311yescharacteristic
106C2×C11×D8—42no—
107C2×C11×D8—42no—
108C2×C11×D8C2314yes—
109C2×C11×D8C2314yes—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×#121—22no—
113C11×#121C2314yes—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116#67006—28no—
117#67006—28no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11D411yescharacteristic
124C2×C22⋊Dic11D411yescharacteristic
125#66993—22no—
126#66993—22no—
127#66993—22no—
128#66993C2314yes—
129#66993C2314yes—
130#66993C2314yescomplemented
131#66992—28no—
132#66991—28no—
133#66991—28no—
134#66991—28no—
135#66989—22no—
136#66989—22no—
137#66989C2314yes—
138#66989C2314yes—
139D4×Dic11—22no—
140D4×Dic11C2314yescomplemented
141C2×#4324—42no—
142C2×#4324C2314yescomplemented
143C2×#4323—42no—
144C2×#4323—42no—
145C2×#4323—42no—
146C2×#4323C2314yes—
147C2×#4323C2314yes—
148C2×#4323C2314yescomplemented
149#66983—22no—
150#66983C2314yes—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4—21no—
153#66979D414yes—
154#66979C2314yes—
155C2×C4⋊Dic11—21no—
156C2×C4⋊Dic11D411yescharacteristic
157C2×C4⋊Dic11D411yescharacteristic
158C2×C4⋊Dic11C2311yescharacteristic
159C2×Dic11⋊C4—21no—
160C2×C4×Dic11C2311yescharacteristic
161C2×C4×Dic11C2311yescharacteristic
162C22×C11⋊C8C2311yescharacteristic
163C22×C11⋊C8C2311yescharacteristic
164C2×D88—42no—
165C2×D88C2314yescomplemented
166C2×#4314—42no—
167C2×#4314C2314yescomplemented
168#66946—22no—
169#66946C2314yescomplemented
170#66943—22no—
171#66943C2314yescomplemented
172#66939—28no—
173#66936—28no—
174C11×#102C2314yes—
175C11×#102C2314yes—
176C11×C22⋊C8C2314yes—
177#66896C2314yes—
178#66896C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180#66885C2314yescomplemented
181#66880C2314yescomplemented
182#66879C2314yescomplemented
183Dic11⋊C8C2314yescomplemented
184Dic11⋊C8C2314yescomplemented
185C8×Dic11C2314yescomplemented
186#66874C2314yescomplemented
187#66873C2314yescomplemented
188C2×#3220—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—24no—
193C24×C11—44no—
194C24×C11—82no—
195C24×C11—82no—
196C24×C11C2×D411yescharacteristic
197C23×D11—21no—
198C23×D11—21no—
199C2×D4×C11—24no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
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—44no—
211C2×D4×C11—44no—
212C2×D4×C11—44no—
213C2×D4×C11—48no—
214C2×D4×C11—82no—
215C2×D4×C11C2412yes—
216C2×D4×C11C2412yes—
217C2×D4×C11C2412yes—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—21no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2411yescharacteristic
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—24no—
231C2×C22⋊D11—24no—
232C2×C22⋊D11—24no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—82no—
235C2×C22⋊D11—82no—
236C2×C22⋊D11—82no—
237C2×C22⋊D11—82no—
238C2×C22⋊D11—82no—
239C2×C22⋊D11—82no—
240C2×C22⋊D11—82no—
241C22×Dic11—24no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—82no—
245C22×Dic11C2×D411yescharacteristic
246C22×Dic11C2×D411yescharacteristic
247C22×Dic11C2×D411yescharacteristic
248C22×Dic11C2×D411yescharacteristic
249#4339—44no—
250#4339—44no—
251#4339—48no—
252C2×D44—21no—
253C2×D44—21no—
254C2×D44—22no—
255C2×D44—22no—
256C2×D44—22no—
257C2×D44—22no—
258C2×D44C2412yes—
259C2×D44C2412yes—
260C2×C4×D11—24no—
261C2×C4×D11—24no—
262C2×C4×D11—44no—
263C2×C4×D11—82no—
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—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279C22⋊Dic11—24no—
280C22⋊Dic11—24no—
281C22⋊Dic11—24no—
282C22⋊Dic11C2×D414yes—
283C22⋊Dic11C2×D414yes—
284#4324—44no—
285#4323—44no—
286#4323—44no—
287#4323—44no—
288(C2×D11)⋊C4—24no—
289(C2×D11)⋊C4—24no—
290C4⋊Dic11—24no—
291C4⋊Dic11—21no—
292C4⋊Dic11C2×D414yes—
293C4⋊Dic11C2×D414yes—
294C4⋊Dic11C2412yes—
295Dic11⋊C4—24no—
296C4×Dic11C2×D412yes—
297C4×Dic11C2×D412yes—
298C4×Dic11C2412yes—
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×#459—111no—
317C2×#449—111no—
318C2×#449—111no—
319C2×#447—111no—
320C2×#447D1111yescharacteristic, complemented
321C2×#433—111no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—48no—
329C23×C11—42no—
330C23×C11—42no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—42no—
335C23×C11—42no—
336C23×C11—42no—
337C23×C11—42no—
338C23×C11—84no—
339C23×C11—84no—
340C23×C11—816no—
341C23×C11C22×D412yes—
342C23×C11C22×D411yescharacteristic
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—48no—
358D4×C11—42no—
359D4×C11—42no—
360D4×C11—42no—
361D4×C11—84no—
362C2×C4×C11—22no—
363C2×C4×C11—24no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—42no—
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—84no—
375C22⋊D11—84no—
376C22⋊D11—84no—
377C22⋊D11—84no—
378C22⋊D11—84no—
379C22⋊D11—84no—
380C22⋊D11—84no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389C2×Dic11—84no—
390C2×Dic11C22×D412yes—
391C2×Dic11C22×D412yes—
392C2×Dic11C22×D412yes—
393C2×Dic11C22×D412yes—
394D44—22no—
395D44—22no—
396D44—22no—
397D44—22no—
398D44—42no—
399D44—42no—
400C4×D11—48no—
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×D4C2×D1111yescharacteristic
411C22×SD16—111no—
412C22×SD16—111no—
413C22×D8—111no—
414C22×D8—111no—
415C22×D8—111no—
416C22×D8—111no—
417C22×D8C2×D1111yescharacteristic
418C22×D8C2×D1111yescharacteristic
419#540—118no—
420#540—224no—
421#535—118no—
422#535—224no—
423C2×#127—111no—
424C2×#127—111no—
425C2×#127—111no—
426C2×#125—111no—
427C2×#124—111no—
428C2×#124—111no—
429C2×#123—221no—
430C2×#123—221no—
431C2×#121—111no—
432C2×#121—221no—
433C2×#121—221no—
434C2×#121—221no—
435C2×#121—221no—
436C2×#121C2×D1111yescharacteristic
437C2×#120—221no—
438C2×#120—221no—
439C2×C4×D4—111no—
440C2×C4×D4—111no—
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#459—118no—
450#449—118no—
451#449—118no—
452#447—118no—
453#447C2×D1118yescomplemented
454#433—118no—
455C2×C4⋊C8—111no—
456C2×C4⋊C8—111no—
457C2×#103—111no—
458C2×#103—111no—
459C2×#102—111no—
460C2×#102—111no—
461C2×#102—111no—
462C2×#102—111no—
463C2×#102C2×D1111yescharacteristic
464C2×#102C2×D1111yescharacteristic
465C2×C22⋊C8—111no—
466C2×C22⋊C8C2×D1111yescharacteristic
467C2×#97—111no—
468C2×C4×C8—111no—
469C22×C11—22no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—44no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—816no—
483C22×C11—84no—
484C22×C11—84no—
485C22×C11—84no—
486C22×C11#53512yes—
487C22×C11#57612yes—
488C22×C11#57612yes—
489C22×C11C23×D411yescharacteristic
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—84no—
497C2×D11—84no—
498C4×C11—22no—
499C4×C11—42no—
500C4×C11#53512yes—
501C4×C11C2×H(5,𝔽2)11yescharacteristic
502C4×C11C2×H(5,𝔽2)11yescharacteristic
503Dic11—22no—
504Dic11—22no—
505Dic11—22no—
506Dic11—22no—
507Dic11—42no—
508Dic11—42no—
509C25—21no—
510C2×#41—114no—
511C2×#41—222no—
512C2×#41—442no—
513C2×#41—442no—
514C22×Q8—111no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—42no—
519C22×D4—42no—
520C22×D4—111no—
521C22×D4—111no—
522C22×D4—221no—
523C22×D4—221no—
524C22×D4—221no—
525C22×D4—221no—
526C22×D4—221no—
527C22×D4—221no—
528C22×D4—221no—
529C22×D4—221no—
530C22×D4C22×D1111yescharacteristic
531C22×D4C22×D1111yescharacteristic
532C22×D4C22×D1111yescharacteristic
533C22×D4C22×D1114yes—
534C23×C4—221no—
535C23×C4—221no—
536C23×C4—221no—
537C23×C4C22×D1111yescharacteristic
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×D1114yes—
554C22×C8—111no—
555C22×C8—111no—
556C22×C8C22×D1111yescharacteristic
557C22×C8C22×D1111yescharacteristic
558#127—114no—
559#127—114no—
560#127—114no—
561#127—222no—
562#127—222no—
563#127—222no—
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—22no—
573#121—114no—
574#121—228no—
575#121—228no—
576#121—228no—
577#121—228no—
578#121—222no—
579#121C22×D1114yes—
580#120—228no—
581#120—228no—
582C4×D4—114no—
583C4×D4—114no—
584C4×D4—222no—
585C4×D4—222no—
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×C42—111no—
606C4⋊C8—114no—
607C4⋊C8—114no—
608#103—114no—
609#103—114no—
610#102—114no—
611#102—114no—
612#102—114no—
613#102—114no—
614#102C22×D1114yes—
615#102C22×D1114yes—
616C22⋊C8—114no—
617C22⋊C8C22×D1114yes—
618#97—114no—
619C4×C8—114no—
620C2×C11—42no—
621C2×C11—82no—
622C2×C11—82no—
623C2×C11—82no—
624C2×C11#322014yescomplemented
625C2×C11C2×#53511yescharacteristic
626C2×C11C2×#57611yescharacteristic
627C2×C11C2×#57611yescharacteristic
628D11—82no—
629D11—82no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—24no—
634C24—44no—
635C24—82no—
636C24—82no—
637C24—221no—
638C24—221no—
639C24D4×D1111yescharacteristic
640#41—444no—
641#41—444no—
642#41—448no—
643C2×Q8—112no—
644C2×Q8—221no—
645C2×Q8—222no—
646C2×Q8—222no—
647C2×D4—24no—
648C2×D4—21no—
649C2×D4—24no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—44no—
659C2×D4—44no—
660C2×D4—44no—
661C2×D4—48no—
662C2×D4—82no—
663C2×D4—112no—
664C2×D4—112no—
665C2×D4—224no—
666C2×D4—224no—
667C2×D4—224no—
668C2×D4—224no—
669C2×D4—224no—
670C2×D4—224no—
671C2×D4—224no—
672C2×D4—224no—
673C2×D4—221no—
674C2×D4—221no—
675C2×D4—222no—
676C2×D4—222no—
677C2×D4—222no—
678C2×D4—222no—
679C2×D4—444no—
680C2×D4—882no—
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—22no—
691C22×C4—22no—
692C22×C4—21no—
693C22×C4—111no—
694C22×C4—111no—
695C22×C4—111no—
696C22×C4—111no—
697C22×C4—224no—
698C22×C4—224no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—224no—
702C22×C4—444no—
703C22×C4—882no—
704C22×C4—882no—
705C22×C4D4×D1112yes—
706C22×C4D4×D1111yescharacteristic
707C22×C4C23×D1112yes—
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—
745C42—112no—
746C42—112no—
747C11C2×#322011yescharacteristic, complemented, Sylow
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—48no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—84no—
765C23—84no—
766C23—816no—
767C23—222no—
768C23—222no—
769C23—442no—
770C23—442no—
771C23—442no—
772C23—442no—
773C23—442no—
774C23—442no—
775C23C2×D4×D1112yes—
776C23C2×D4×D1111yescharacteristic
777Q8—222no—
778Q8—222no—
779Q8—442no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—48no—
787D4—42no—
788D4—42no—
789D4—42no—
790D4—84no—
791D4—222no—
792D4—222no—
793D4—222no—
794D4—222no—
795D4—448no—
796D4—442no—
797D4—442no—
798D4—884no—
799D4—884no—
800D4—884no—
801D4—884no—
802D4—884no—
803D4—884no—
804D4—884no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—42no—
811C2×C4—112no—
812C2×C4—112no—
813C2×C4—112no—
814C2×C4—112no—
815C2×C4—222no—
816C2×C4—222no—
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×C4—884no—
826C2×C4C2×D4×D1112yes—
827C2×C4C2×D4×D1111yescharacteristic
828C2×C4#6703712yes—
829C2×C4#6703712yes—
830C2×C4C24×D1111yescharacteristic
831C8—22no—
832C8—22no—
833C8—222no—
834C8—222no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—44no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—816no—
849C22—84no—
850C22—84no—
851C22—84no—
852C22—442no—
853C22—442no—
854C22—442no—
855C22—442no—
856C22—442no—
857C22—442no—
858C22—884no—
859C22—884no—
860C22#1062312312yes—
861C22#1062328812yes—
862C22#1062330512yes—
863C22C22×D4×D1111yescharacteristic
864C4—22no—
865C4—42no—
866C4—222no—
867C4—222no—
868C4—222no—
869C4—222no—
870C4—442no—
871C4—442no—
872C4#1062312312yes—
873C4C2×#6703711yescharacteristic
874C4C2×#6703711yescharacteristic
875C2—42no—
876C2—82no—
877C2—82no—
878C2—82no—
879C2—882no—
880C2—882no—
881C2#1307966214yesdirect product factor
882C2C2×#1062312311yescharacteristic
883C2C2×#1062328811yescharacteristic
884C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#447C2
socleC23×C11C22×D4
hypercenterC2×#447D11
hypocenterC11C2×#3220
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#10623150C2semidirect
2. C2×#10623336C2semidirect
3. #13079662C2direct (N × H)
4. C2×#10622767C2semidirect
5. C2×#10622764C2semidirect
6. C2×#10622377C2semidirect
7. C2×#10622381C2semidirect
8. C2×#10622400C2semidirect
9. C2×#10622766C2semidirect
10. C2×#10622399C2semidirect
11. C2×#10622763C2semidirect
12. C2×#10622347C2semidirect
13. C2×#10622650C2semidirect
14. C2×#10622830C2semidirect
15. C2×#10622333C2semidirect
16. C2×C11×#447C2semidirect
25. #10623336C22semidirect
28. C2×#66993C22semidirect
35. C2×D4×Dic11C22semidirect
36. C22×#4324C22semidirect
39. C22×#4323C22semidirect
42. C22×D88C22semidirect
43. C22×#4314C22semidirect
45. #10623150C22semidirect
46. C2×#66946C22semidirect
47. C2×#66943C22semidirect
50. C11×#447C22semidirect
54. #10622830C22semidirect
58. #10622767C22semidirect
59. #10622766C22semidirect
60. #10622764C22semidirect
61. #10622763C22semidirect
62. C2×#66885C22semidirect
63. C2×#66880C22semidirect
64. C2×#66879C22semidirect
65. C2×Dic11⋊C8C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×C8×Dic11C22semidirect
68. #10622650C22semidirect
69. C2×#66874C22semidirect
70. C2×#66873C22semidirect
71. #10622400C22semidirect
72. #10622399C22semidirect
73. #10622381C22semidirect
74. #10622377C22semidirect
75. #10622347C22semidirect
76. #10622333C22semidirect
130. #66993C23semidirect
140. D4×Dic11C23semidirect
142. C2×#4324C23semidirect
148. C2×#4323C23semidirect
165. C2×D88C23semidirect
167. C2×#4314C23semidirect
169. #66946C23semidirect
171. #66943C23semidirect
180. #66885C23semidirect
181. #66880C23semidirect
182. #66879C23semidirect
183. Dic11⋊C8C23semidirect
184. Dic11⋊C8C23semidirect
185. C8×Dic11C23semidirect
186. #66874C23semidirect
187. #66873C23semidirect
320. C2×#447D11semidirect
453. #447C2×D11semidirect
624. C2×C11#3220semidirect
747. C11C2×#3220semidirect
881. C2#13079662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231502
C2×#106233362
#130796622
C2×#106227672
C2×#106227642
C2×#106223772
C2×#106223812
C2×#106224002
C2×#106227662
C2×#106223992
C2×#106227632
C2×#106223472
C2×#106226502
C2×#106228302
C2×#106223332
C2×C11×#4472
C2×#322011