Finite Group Databasebeta

← C2×#13079487 #15624447

Subgroups — C2×#13079487 #15624447

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623159C211yesmaximal, characteristic, complemented
2C2×#10623056C211yesmaximal, characteristic
3#13079487C2116yesmaximal, direct product factor
4C2×#10622609C211yesmaximal, characteristic, complemented
5C2×#10622498C211yesmaximal, characteristic, complemented
6C2×#10622479C211yesmaximal, characteristic, complemented
7C2×#10622425C211yesmaximal, characteristic, complemented
8C2×#10622499C211yesmaximal, characteristic, complemented
9C2×#10622420C211yesmaximal, characteristic, complemented
10C2×#10622477C211yesmaximal, characteristic, complemented
11C2×#10622419C211yesmaximal, characteristic, complemented
12C2×#10622419C211yesmaximal, characteristic, complemented
13C2×#10622344C211yesmaximal, characteristic, complemented
14C2×#10622659C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#485C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic, complemented
18C22×#4339C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C2×#66999C2211yescharacteristic, complemented
23C22×#4325C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28C22×#4313C2211yescharacteristic, complemented
29C22×C8×D11C2211yescharacteristic, complemented
30#10623159—24no—
31#10623159C2218yescomplemented
32#10623056—24no—
33#10623056C2218yes—
34C2×#66950C2211yescharacteristic, complemented
35C2×#66948C2211yescharacteristic
36C2×#66948C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66948C2211yescharacteristic
39C2×#66947—21no—
40C2×#66945C2211yescharacteristic, complemented
41C2×#66941—21no—
42C2×#66938—21no—
43C2×#66936—21no—
44C2×#66935—21no—
45C2×#66935—21no—
46C2×#66928—21no—
47C2×#66927—21no—
48C11×#485C2218yescomplemented
49C2×C11×#107C2211yescharacteristic, complemented
50C2×C11×#106C2211yescharacteristic, complemented
51C2×C11×#103C2211yescharacteristic, complemented
52C2×C11×#103C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C22⋊(C11⋊C8)C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
58C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
59#10622659C2218yescomplemented
60#10622609C2218yescomplemented
61C2×#66874C2211yescharacteristic, complemented
62C2×#66874C2211yescharacteristic, complemented
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic, complemented
66C2×#66871C2211yescharacteristic, complemented
67#10622499C2218yescomplemented
68#10622498C2218yescomplemented
69#10622479C2218yescomplemented
70#10622477C2218yescomplemented
71#10622425C2218yescomplemented
72#10622420C2218yescomplemented
73#10622419C2218yescomplemented
74#10622419C2218yescomplemented
75#10622344C2218yescomplemented
76#10622340C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11D411yescharacteristic
81C22×C22⋊D11D411yescharacteristic
82C2×Q8×D11—22no—
83C2×Q8×D11—42no—
84C2×Q8×D11—42no—
85C2×Q8×D11C2314yescomplemented
86C2×#4339—42no—
87C2×#4339—42no—
88C2×#4339D414yes—
89C2×#4339C2314yes—
90C22×D44—21no—
91C22×D44—22no—
92C22×D44—21no—
93C22×D44—21no—
94C22×D44—21no—
95C22×D44—21no—
96C22×D44—42no—
97C22×D44—42no—
98C22×D44D411yescharacteristic
99C22×D44C2311yescharacteristic
100C22×D44C2311yescharacteristic
101C22×D44C2314yes—
102C22×C4×D11—21no—
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2311yescharacteristic
105C22×Dic22—21no—
106C22×Dic22D411yescharacteristic
107C22×Dic22C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8C2314yes—
112C11×#117—22no—
113C11×#117C2314yes—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C42×C11—21no—
121C2×C22⋊Dic11—21no—
122#66999—22no—
123#66999C2314yescomplemented
124C2×#4325—42no—
125C2×#4325—42no—
126C2×#4325C2314yes—
127C2×#4325C2314yes—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11C2311yescharacteristic
137#66977—22no—
138#66977C2314yes—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×C4×Dic11—21no—
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C2×#4314—42no—
145C2×#4314—42no—
146C2×#4314C2314yes—
147C2×#4314C2314yes—
148C2×#4313—42no—
149C2×#4313C2314yescomplemented
150C2×C8×D11—42no—
151C2×C8×D11C2314yescomplemented
152#66950—22no—
153#66950C2314yescomplemented
154#66948—22no—
155#66948—22no—
156#66948—22no—
157#66948—22no—
158#66948C2314yes—
159#66948C2314yes—
160#66948C2314yes—
161#66948C2314yes—
162#66947—28no—
163#66945—22no—
164#66945C2314yescomplemented
165#66941—28no—
166#66938—28no—
167#66936—28no—
168#66935—28no—
169#66935—28no—
170#66928—28no—
171#66927—28no—
172C11×#107C2314yescomplemented
173C11×#106C2314yescomplemented
174C11×#103C2314yescomplemented
175C11×#103C2314yescomplemented
176C11×C22⋊C8C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178#66885C2314yes—
179#66885C2314yes—
180(C2×D11)⋊C8C2314yescomplemented
181(C2×D11)⋊C8C2314yescomplemented
182#66874C2314yescomplemented
183#66874C2314yescomplemented
184#66873C2314yes—
185#66873C2314yes—
186#66872C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3200—111nomaximal, Sylow
189C24×C11C2×D411yescharacteristic
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—24no—
193C23×D11—44no—
194C23×D11—82no—
195C23×D11—82no—
196C23×D11C2×D411yescharacteristic
197C23×D11C2×D411yescharacteristic
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11C2412yes—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—42no—
213C2×C22⋊D11—42no—
214C2×C22⋊D11C2×D414yes—
215C2×C22⋊D11C2×D414yes—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220Q8×D11—44no—
221Q8×D11—44no—
222Q8×D11—48no—
223#4339—48no—
224#4339—44no—
225#4339—44no—
226C2×D44—24no—
227C2×D44—24no—
228C2×D44—24no—
229C2×D44—24no—
230C2×D44—24no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44—22no—
236C2×D44—22no—
237C2×D44—42no—
238C2×D44—44no—
239C2×D44—44no—
240C2×D44—44no—
241C2×D44—48no—
242C2×D44—82no—
243C2×D44—82no—
244C2×D44—82no—
245C2×D44—82no—
246C2×D44C2×D414yes—
247C2×D44C2412yes—
248C2×D44C2412yes—
249C2×C4×D11—24no—
250C2×C4×D11—22no—
251C2×C4×D11—22no—
252C2×C4×D11—22no—
253C2×C4×D11—22no—
254C2×C4×D11—44no—
255C2×C4×D11C2×D412yes—
256C2×C4×D11C2×D412yes—
257C2×C4×D11C2412yes—
258C2×C4×D11C2412yes—
259C2×Dic22—24no—
260C2×Dic22—21no—
261C2×Dic22—22no—
262C2×Dic22—22no—
263C2×Dic22—42no—
264C2×Dic22—44no—
265C2×Dic22C2×D414yes—
266C2×Dic22C2412yes—
267C2×C8×C11—22no—
268C2×C8×C11—22no—
269C2×C8×C11C2412yes—
270C2×C8×C11C2412yes—
271C11×C4⋊C4—24no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4C2412yes—
276C11×C4⋊C4C2412yes—
277C11×C4⋊C4C2412yes—
278C11×C22⋊C4—24no—
279C11×C22⋊C4—24no—
280C42×C11—24no—
281C22⋊Dic11—24no—
282#4325—44no—
283#4325—44no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288(C2×D11)⋊C4—24no—
289(C2×D11)⋊C4—24no—
290(C2×D11)⋊C4—24no—
291C4⋊Dic11—24no—
292C4⋊Dic11—21no—
293C4⋊Dic11C2412yes—
294Dic11⋊C4—24no—
295Dic11⋊C4—24no—
296C4×Dic11—24no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8—22no—
299C2×C11⋊C8C2412yes—
300C2×C11⋊C8C2412yes—
301#4314—44no—
302#4314—44no—
303#4313—44no—
304C8×D11—44no—
305C2×#536—111no—
306C2×#535—111no—
307#3200—1116no—
308C2×#485—111no—
309C2×#485D1111yescharacteristic, complemented
310C2×#482—111no—
311C2×#482—111no—
312C2×#468—111no—
313C2×#468—111no—
314C2×#465—111no—
315C2×#465—111no—
316C2×#448—111no—
317C2×#448—111no—
318C2×#450—111no—
319C2×#450—111no—
320C2×#408—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11C22×D412yes—
325C23×C11C22×D411yescharacteristic
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—48no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—42no—
341C22×D11—84no—
342C22×D11—84no—
343C22×D11—816no—
344C22×D11C22×D412yes—
345C22×D11C22×D412yes—
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—42no—
349C2×C4×C11—22no—
350C2×C4×C11—24no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11—42no—
360C2×C4×C11—42no—
361C2×C4×C11C22×D412yes—
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11H(5,𝔽2)12yes—
364C2×C4×C11H(5,𝔽2)12yes—
365C2×C4×C11C2511yescharacteristic
366C22⋊D11—44no—
367C22⋊D11—44no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374C2×Dic11C22×D412yes—
375C2×Dic11C22×D412yes—
376D44—22no—
377D44—22no—
378D44—22no—
379D44—22no—
380D44—44no—
381D44—48no—
382D44—42no—
383D44—42no—
384D44—84no—
385D44—84no—
386D44—84no—
387D44—84no—
388C4×D11—24no—
389C4×D11—24no—
390C4×D11—22no—
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—48no—
395Dic22—22no—
396Dic22—22no—
397Dic22—44no—
398Dic22—48no—
399Dic22—42no—
400C8×C11—22no—
401C8×C11—22no—
402C11⋊C8—22no—
403C11⋊C8—22no—
404C22×#41—111no—
405C23×Q8—111no—
406C23×D4—111no—
407C22×SD16—111no—
408C22×SD16—111no—
409C22×SD16—111no—
410C22×SD16—111no—
411C22×M16—111no—
412C23×C8—111no—
413#536—118no—
414#536—224no—
415#535—118no—
416#535—224no—
417C2×C4⋊Q8—221no—
418C2×#127—221no—
419C2×#124—221no—
420C2×#124—221no—
421C2×#123—221no—
422C2×#123—221no—
423C2×C22⋊Q8—111no—
424C2×C22⋊Q8—111no—
425C2×C22⋊Q8—111no—
426C2×C22⋊Q8C2×D1111yescharacteristic
427C2×#121—111no—
428C2×#121—111no—
429C2×#121—111no—
430C2×#121—111no—
431C2×#120—221no—
432C2×#120—221no—
433C2×#117—111no—
434C2×#117C2×D1111yescharacteristic
435#485—118no—
436#485C2×D1118yescomplemented
437#482—118no—
438#482—118no—
439#468—118no—
440#468—118no—
441#465—118no—
442#465—118no—
443#450—118no—
444#450—118no—
445#448—118no—
446#448—118no—
447C2×#107—111no—
448C2×#107C2×D1111yescharacteristic, complemented
449C2×#106—111no—
450C2×#106C2×D1111yescharacteristic, complemented
451C2×#103—111no—
452C2×#103—111no—
453C2×#103C2×D1111yescharacteristic, complemented
454C2×#103C2×D1111yescharacteristic, complemented
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102—111no—
459#408—118no—
460C2×C22⋊C8—111no—
461C2×C22⋊C8—111no—
462C2×C22⋊C8—111no—
463C2×C22⋊C8C2×D1111yescharacteristic
464C22×C11—22no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—44no—
468C22×C11#53412yes—
469C22×C11#57712yes—
470C22×C11#57712yes—
471C22×C11C23×D411yescharacteristic
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—22no—
475C2×D11—22no—
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—44no—
479C2×D11—44no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—816no—
487C2×D11—84no—
488C2×D11—84no—
489C4×C11—22no—
490C4×C11—42no—
491C4×C11—42no—
492C4×C11—42no—
493C4×C11—42no—
494C4×C11#53412yes—
495C4×C11C2×H(5,𝔽2)11yescharacteristic
496C4×C11C2×H(5,𝔽2)11yescharacteristic
497Dic11—22no—
498Dic11—22no—
499Dic11—42no—
500Dic11—42no—
501C25—221no—
502C2×#41—114no—
503C2×#41—114no—
504C2×#41—442no—
505C2×#41—442no—
506C22×Q8—111no—
507C22×Q8—114no—
508C22×Q8—111no—
509C22×Q8—221no—
510C22×Q8—222no—
511C22×Q8—442no—
512C22×Q8—442no—
513C22×Q8C22×D1111yescharacteristic
514C22×D4—111no—
515C22×D4—111no—
516C22×D4—111no—
517C22×D4—111no—
518C22×D4—111no—
519C22×D4—114no—
520C22×D4—221no—
521C22×D4—221no—
522C22×D4—221no—
523C22×D4—221no—
524C22×D4—221no—
525C22×D4—222no—
526C22×D4—442no—
527C22×D4—442no—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—221no—
531C23×C4C22×D1111yescharacteristic
532C2×SD16—114no—
533C2×SD16—114no—
534C2×SD16—114no—
535C2×SD16—114no—
536C2×SD16—442no—
537C2×SD16—442no—
538C2×SD16—442no—
539C2×SD16—442no—
540C2×M16—114no—
541C2×M16—442no—
542C22×C8—111no—
543C22×C8—111no—
544C22×C8—114no—
545C22×C8—442no—
546C22×C8C22×D1111yescharacteristic
547C22×C8C22×D1111yescharacteristic
548C4⋊Q8—228no—
549#127—228no—
550#124—228no—
551#124—228no—
552#123—228no—
553#123—228no—
554C22⋊Q8—22no—
555C22⋊Q8—114no—
556C22⋊Q8—114no—
557C22⋊Q8—114no—
558C22⋊Q8—222no—
559C22⋊Q8—222no—
560C22⋊Q8—222no—
561C22⋊Q8C22×D1114yes—
562#121—114no—
563#121—114no—
564#121—114no—
565#121—114no—
566#121—222no—
567#121—222no—
568#121—222no—
569#121—222no—
570#120—228no—
571#120—228no—
572#117—22no—
573#117—114no—
574#117—222no—
575#117C22×D1114yes—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—221no—
579C2×C4⋊C4—221no—
580C2×C4⋊C4—221no—
581C2×C4⋊C4C22×D1111yescharacteristic
582C2×C4⋊C4C22×D1111yescharacteristic
583C2×C4⋊C4C22×D1111yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—221no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4—221no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594C2×C42—21no—
595C2×C42—221no—
596#107—114no—
597#107C22×D1114yescomplemented
598#106—114no—
599#106C22×D1114yescomplemented
600#103—114no—
601#103—114no—
602#103C22×D1114yescomplemented
603#103C22×D1114yescomplemented
604#102—114no—
605#102—114no—
606#102—114no—
607#102—114no—
608C22⋊C8—114no—
609C22⋊C8—114no—
610C22⋊C8—114no—
611C22⋊C8C22×D1114yes—
612C2×C11—42no—
613C2×C11#320014yescomplemented
614C2×C11C2×#53411yescharacteristic
615C2×C11C2×#57711yescharacteristic
616C2×C11C2×#57711yescharacteristic
617D11—42no—
618D11—42no—
619D11—82no—
620D11—82no—
621C24—111no—
622C24—111no—
623C24—221no—
624C24—221no—
625C24—224no—
626C24—444no—
627C24—882no—
628C24—882no—
629C24D4×D1111yescharacteristic
630#41—448no—
631#41—444no—
632#41—444no—
633C2×Q8—21no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—114no—
637C2×Q8—112no—
638C2×Q8—224no—
639C2×Q8—221no—
640C2×Q8—222no—
641C2×Q8—222no—
642C2×Q8—442no—
643C2×Q8—444no—
644C2×Q8—444no—
645C2×Q8—444no—
646C2×Q8—448no—
647C2×Q8C23×D1112yes—
648C2×D4—114no—
649C2×D4—114no—
650C2×D4—114no—
651C2×D4—112no—
652C2×D4—112no—
653C2×D4—224no—
654C2×D4—224no—
655C2×D4—224no—
656C2×D4—224no—
657C2×D4—221no—
658C2×D4—221no—
659C2×D4—224no—
660C2×D4—222no—
661C2×D4—222no—
662C2×D4—222no—
663C2×D4—222no—
664C2×D4—444no—
665C2×D4—444no—
666C2×D4—442no—
667C2×D4—444no—
668C2×D4—448no—
669C2×D4—442no—
670C2×D4—442no—
671C2×D4—882no—
672C2×D4—882no—
673C2×D4—882no—
674C2×D4—882no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—111no—
682C22×C4—111no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—224no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—444no—
695C22×C4D4×D1112yes—
696C22×C4D4×D1111yescharacteristic
697C22×C4C23×D1112yes—
698C22×C4C23×D1111yescharacteristic
699SD16—444no—
700SD16—444no—
701SD16—444no—
702SD16—444no—
703M16—444no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—112no—
707C2×C8—112no—
708C2×C8—222no—
709C2×C8—222no—
710C2×C8—444no—
711C2×C8C23×D1112yes—
712C2×C8C23×D1112yes—
713C4⋊C4—24no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—112no—
718C4⋊C4—224no—
719C4⋊C4—224no—
720C4⋊C4—221no—
721C4⋊C4—224no—
722C4⋊C4C23×D1112yes—
723C4⋊C4C23×D1112yes—
724C4⋊C4C23×D1112yes—
725C22⋊C4—24no—
726C22⋊C4—24no—
727C22⋊C4—224no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C42—24no—
736C42—224no—
737C11C2×#320011yescharacteristic, complemented, Sylow
738C23—22no—
739C23—22no—
740C23—22no—
741C23—112no—
742C23—112no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—448no—
752C23—442no—
753C23—442no—
754C23—442no—
755C23—442no—
756C23—442no—
757C23—442no—
758C23—884no—
759C23—884no—
760C23—8816no—
761C23C2×D4×D1112yes—
762C23C2×D4×D1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—222no—
767Q8—222no—
768Q8—444no—
769Q8—448no—
770Q8—442no—
771D4—222no—
772D4—222no—
773D4—222no—
774D4—222no—
775D4—444no—
776D4—448no—
777D4—444no—
778D4—444no—
779D4—442no—
780D4—442no—
781D4—884no—
782D4—884no—
783D4—884no—
784D4—884no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—112no—
798C2×C4—112no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—224no—
802C2×C4—224no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—448no—
810C2×C4—442no—
811C2×C4—442no—
812C2×C4C2×D4×D1112yes—
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4#6704212yes—
815C2×C4#6704212yes—
816C2×C4C24×D1111yescharacteristic
817C8—22no—
818C8—22no—
819C8—222no—
820C8—222no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—222no—
826C22—222no—
827C22—222no—
828C22—222no—
829C22—222no—
830C22—222no—
831C22—444no—
832C22—444no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—442no—
838C22—442no—
839C22—8816no—
840C22—884no—
841C22—884no—
842C22#1062318412yes—
843C22#1062330112yes—
844C22#1062330912yes—
845C22C22×D4×D1111yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—222no—
852C4—222no—
853C4—442no—
854C4—442no—
855C4#1062318412yes—
856C4C2×#6704211yescharacteristic
857C4C2×#6704211yescharacteristic
858C2—42no—
859C2—442no—
860C2—442no—
861C2—882no—
862C2—882no—
863C2#1307948714yesdirect product factor
864C2C2×#1062318411yescharacteristic
865C2C2×#1062330111yescharacteristic
866C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
prime radicalC2×#10623056C2
hypercenterC2×#485D11
hypocenterC11C2×#3200
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#10623159C2semidirect
3. #13079487C2direct (N × H)
4. C2×#10622609C2semidirect
5. C2×#10622498C2semidirect
6. C2×#10622479C2semidirect
7. C2×#10622425C2semidirect
8. C2×#10622499C2semidirect
9. C2×#10622420C2semidirect
10. C2×#10622477C2semidirect
11. C2×#10622419C2semidirect
12. C2×#10622419C2semidirect
13. C2×#10622344C2semidirect
14. C2×#10622659C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#485C2semidirect
17. C22×Q8×D11C22semidirect
22. C2×#66999C22semidirect
28. C22×#4313C22semidirect
29. C22×C8×D11C22semidirect
31. #10623159C22semidirect
34. C2×#66950C22semidirect
40. C2×#66945C22semidirect
48. C11×#485C22semidirect
49. C2×C11×#107C22semidirect
50. C2×C11×#106C22semidirect
51. C2×C11×#103C22semidirect
52. C2×C11×#103C22semidirect
57. C2×(C2×D11)⋊C8C22semidirect
58. C2×(C2×D11)⋊C8C22semidirect
59. #10622659C22semidirect
60. #10622609C22semidirect
61. C2×#66874C22semidirect
62. C2×#66874C22semidirect
65. C2×#66872C22semidirect
66. C2×#66871C22semidirect
67. #10622499C22semidirect
68. #10622498C22semidirect
69. #10622479C22semidirect
70. #10622477C22semidirect
71. #10622425C22semidirect
72. #10622420C22semidirect
73. #10622419C22semidirect
74. #10622419C22semidirect
75. #10622344C22semidirect
76. #10622340C22semidirect
85. C2×Q8×D11C23semidirect
123. #66999C23semidirect
149. C2×#4313C23semidirect
151. C2×C8×D11C23semidirect
153. #66950C23semidirect
164. #66945C23semidirect
172. C11×#107C23semidirect
173. C11×#106C23semidirect
174. C11×#103C23semidirect
175. C11×#103C23semidirect
180. (C2×D11)⋊C8C23semidirect
181. (C2×D11)⋊C8C23semidirect
182. #66874C23semidirect
183. #66874C23semidirect
186. #66872C23semidirect
187. #66871C23semidirect
309. C2×#485D11semidirect
436. #485C2×D11semidirect
448. C2×#107C2×D11semidirect
450. C2×#106C2×D11semidirect
453. C2×#103C2×D11semidirect
454. C2×#103C2×D11semidirect
597. #107C22×D11semidirect
599. #106C22×D11semidirect
602. #103C22×D11semidirect
603. #103C22×D11semidirect
613. C2×C11#3200semidirect
737. C11C2×#3200semidirect
863. C2#13079487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231592
C2×#106230562
#130794872
C2×#106226092
C2×#106224982
C2×#106224792
C2×#106224252
C2×#106224992
C2×#106224202
C2×#106224772
C2×#106224192
C2×#106223442
C2×#106226592
C2×#106223402
C2×C11×#4852
C2×#320011