Finite Group Databasebeta

← C2×#13078567 #15621593

Subgroups — C2×#13078567 #15621593

Order 2816.

2362 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623138C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic, complemented
3#13078567C2116yesmaximal, direct product factor
4C2×#10622581C211yesmaximal, characteristic, complemented
5C2×#10622390C211yesmaximal, characteristic, complemented
6C2×#10622498C211yesmaximal, characteristic, complemented
7C2×#10622350C211yesmaximal, characteristic, complemented
8C2×#10622397C211yesmaximal, characteristic, complemented
9C2×#10622648C211yesmaximal, characteristic, complemented
10C2×#10622495C211yesmaximal, characteristic, complemented
11C2×#10622494C211yesmaximal, characteristic, complemented
12C2×#10622493C211yesmaximal, characteristic, complemented
13C2×#10622383C211yesmaximal, characteristic, complemented
14C2×D11×#102C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#480C211yesmaximal, characteristic, complemented
17C22×D4×D11C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic, complemented
21C2×#66993—21no—
22C2×#66991C2211yescharacteristic
23C2×#66990—21no—
24C2×#66983C2211yescharacteristic
25C2×C4×C22⋊D11—21no—
26C2×C4×C22⋊D11—21no—
27C2×#66979C2211yescharacteristic, complemented
28C22×#4313C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic
30#10623138—24no—
31#10623138C2218yes—
32C2×#66948C2211yescharacteristic
33#10623035—24no—
34#10623035C2218yescomplemented
35C2×#66946—21no—
36C2×#66945C2211yescharacteristic
37C2×#66945C2211yescharacteristic
38C2×#66945C2211yescharacteristic, complemented
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic, complemented
41C2×#66940—21no—
42C2×#66938—21no—
43C2×#66935—21no—
44C11×#480C2218yescomplemented
45C2×C11×#107C2211yescharacteristic, complemented
46C2×C11×#107C2211yescharacteristic, complemented
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic, complemented
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
53C2×#66885C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
56C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
57C2×#66882C2211yescharacteristic, complemented
58C2×#66881C2211yescharacteristic, complemented
59#10622648C2218yescomplemented
60#10622581C2218yescomplemented
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66872C2211yescharacteristic, complemented
64C2×#66872C2211yescharacteristic, complemented
65C2×#66872C2211yescharacteristic, complemented
66C2×#66871C2211yescharacteristic, complemented
67#10622498C2218yescomplemented
68#10622495C2218yescomplemented
69#10622494C2218yescomplemented
70#10622493C2218yescomplemented
71#10622397C2218yescomplemented
72#10622390C2218yescomplemented
73#10622383C2218yescomplemented
74D11×#102C2218yescomplemented
75#10622350C2218yescomplemented
76#10622340C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11D411yescharacteristic
86C22×C22⋊D11D411yescharacteristic
87C2×D4×D11—22no—
88C2×D4×D11—24no—
89C2×D4×D11—24no—
90C2×D4×D11C2314yes—
91C2×#4339—24no—
92C2×#4339—24no—
93C2×#4339D414yes—
94C2×#4339C2314yes—
95C22×D44—21no—
96C22×D44D411yescharacteristic
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11C2311yescharacteristic
101C22×C4×D11C2311yescharacteristic
102C22×Dic22D411yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×#121—22no—
106C11×#121C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2314yescomplemented
113C2×C11×C22⋊C4—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116#66993—28no—
117#66991—22no—
118#66991C2314yes—
119#66990—28no—
120#66983—22no—
121#66983C2314yes—
122C4×C22⋊D11—28no—
123C4×C22⋊D11—28no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129#66979—22no—
130#66979C2314yescomplemented
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11—21no—
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C2×#4313—24no—
143C2×#4313C2314yes—
144C2×C8×D11—24no—
145C2×C8×D11C2314yes—
146#66948—22no—
147#66948C2314yes—
148#66946—28no—
149#66945—22no—
150#66945—22no—
151#66945—22no—
152#66945C2314yes—
153#66945C2314yes—
154#66945C2314yescomplemented
155C4⋊C4×D11—22no—
156C4⋊C4×D11—22no—
157C4⋊C4×D11C2314yes—
158C4⋊C4×D11C2314yescomplemented
159#66940—28no—
160#66938—28no—
161#66935—28no—
162C11×#107C2314yescomplemented
163C11×#107C2314yescomplemented
164C11×#102C2314yes—
165C11×#102C2314yes—
166C11×C22⋊C8C2314yescomplemented
167#66896C2314yes—
168#66896C2314yes—
169C22⋊(C11⋊C8)C2314yescomplemented
170#66885C2314yes—
171#66885C2314yes—
172(C2×D11)⋊C8C2314yescomplemented
173(C2×D11)⋊C8C2314yescomplemented
174#66882C2314yescomplemented
175#66881C2314yescomplemented
176#66873C2314yes—
177#66873C2314yes—
178#66872C2314yescomplemented
179#66872C2314yescomplemented
180#66872C2314yescomplemented
181#66871C2314yescomplemented
182C2×#3096—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11—21no—
186C23×D11—24no—
187C23×D11—44no—
188C23×D11—82no—
189C23×D11—82no—
190C23×D11C2×D411yescharacteristic
191C23×D11C2×D411yescharacteristic
192C2×D4×C11—24no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—82no—
197C2×D4×C11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—24no—
204C22×C4×C11—82no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—82no—
216C2×C22⋊D11—82no—
217C2×C22⋊D11C2×D414yes—
218C2×C22⋊D11C2×D414yes—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224D4×D11—28no—
225D4×D11—28no—
226D4×D11—48no—
227#4339—216no—
228#4339—28no—
229#4339—28no—
230C2×D44—24no—
231C2×D44—24no—
232C2×D44—21no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44—82no—
236C2×D44C2×D414yes—
237C2×D44C2412yes—
238C2×C4×D11—24no—
239C2×C4×D11—24no—
240C2×C4×D11—22no—
241C2×C4×D11—22no—
242C2×C4×D11—82no—
243C2×C4×D11—82no—
244C2×C4×D11C2×D412yes—
245C2×C4×D11C2×D412yes—
246C2×C4×D11#4114yes—
247C2×C4×D11#4114yes—
248C2×C4×D11C2412yes—
249C2×C4×D11C2412yes—
250C2×Dic22—24no—
251C2×Dic22C2×D414yes—
252C2×C8×C11—22no—
253C2×C8×C11—22no—
254C2×C8×C11C2412yes—
255C2×C8×C11C2412yes—
256C11×C4⋊C4—24no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4C2412yes—
261C11×C4⋊C4C2412yes—
262C11×C4⋊C4C2412yes—
263C11×C22⋊C4—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11C2412yes—
275C4⋊Dic11C2412yes—
276C4⋊Dic11C2412yes—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279C4×Dic11—24no—
280C4×Dic11—24no—
281C4×Dic11—24no—
282C4×Dic11—24no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287#4313—28no—
288C8×D11—28no—
289C2×#535—111no—
290C2×#520—111no—
291#3096—1116no—
292C2×#481—111no—
293C2×#481—111no—
294C2×#482—111no—
295C2×#482—111no—
296C2×#482—111no—
297C2×#482—111no—
298C2×#480—111no—
299C2×#480D1111yescharacteristic, complemented
300C2×#428—111no—
301C2×#427—111no—
302C2×#418—111no—
303C22×#102—111no—
304C2×#408—111no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D412yes—
313C23×C11C22×D411yescharacteristic
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11—48no—
324C22×D11—84no—
325C22×D11—84no—
326C22×D11—816no—
327C22×D11#12314yes—
328C22×D11C22×D412yes—
329C22×D11C22×D412yes—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—42no—
333D4×C11—84no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11—84no—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C2×#4112yes—
348C2×C4×C11C2×#4112yes—
349C2×C4×C11C2511yescharacteristic
350C22⋊D11—28no—
351C22⋊D11—28no—
352C22⋊D11—48no—
353C22⋊D11—84no—
354C22⋊D11—84no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11#12314yes—
363C2×Dic11C22×D412yes—
364C2×Dic11C22×D412yes—
365D44—28no—
366D44—22no—
367D44—22no—
368D44—42no—
369D44—84no—
370C4×D11—24no—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—84no—
374C4×D11—84no—
375C4×D11#12318yes—
376C4×D11C2×#4114yes—
377C4×D11C2×#4114yes—
378Dic22—28no—
379C8×C11—22no—
380C8×C11—22no—
381C11⋊C8—22no—
382C11⋊C8—22no—
383C22×#41—111no—
384C23×D4—111no—
385C22×M16—111no—
386C23×C8—111no—
387#535—118no—
388#535—224no—
389C2×#127—221no—
390C2×#124—221no—
391C2×#121—111no—
392C2×#121—111no—
393C2×#121—111no—
394C2×#121C2×D1111yescharacteristic
395C2×#120—221no—
396C2×#120—221no—
397#520—118no—
398#520—224no—
399C2×C4×Q8—221no—
400C2×C4×D4—221no—
401C2×C4×D4—221no—
402C2×C4×D4—221no—
403C2×#117—111no—
404C2×#117—111no—
405C2×#117—111no—
406C2×#117—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4C2×D1111yescharacteristic, complemented
410#482—118no—
411#482—118no—
412#482—118no—
413#482—118no—
414#481—118no—
415#481—118no—
416#480—118no—
417#480C2×D1118yescomplemented
418#428—118no—
419#427—118no—
420C2×#107—111no—
421C2×#107—111no—
422C2×#107C2×D1111yescharacteristic, complemented
423C2×#107C2×D1111yescharacteristic, complemented
424C2×#106—111no—
425C2×#106—111no—
426C2×#106—111no—
427C2×#106—111no—
428#418—118no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—118no—
436C2×#102C2×D1111yescharacteristic
437C2×#102C2×D1111yescharacteristic
438#408—118no—
439C2×C22⋊C8—111no—
440C2×C22⋊C8—111no—
441C2×C22⋊C8—111no—
442C2×C22⋊C8C2×D1111yescharacteristic, complemented
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—44no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—84no—
451C22×C11C2×#12312yes—
452C22×C11#57612yes—
453C22×C11#57712yes—
454C22×C11C23×D411yescharacteristic
455C2×D11—28no—
456C2×D11—22no—
457C2×D11—22no—
458C2×D11—22no—
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—44no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—816no—
466C2×D11—84no—
467C2×D11C2×#12314yes—
468C4×C11—22no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11—42no—
472C4×C11C2×#12312yes—
473C4×C11C22×#4111yescharacteristic
474C4×C11C22×#4111yescharacteristic
475Dic11—22no—
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11C2×#12314yes—
480C25—221no—
481C2×#41—114no—
482C2×#41—114no—
483C2×#41—224no—
484C2×#41—224no—
485C22×Q8—111no—
486C22×D4—21no—
487C22×D4—111no—
488C22×D4—111no—
489C22×D4—114no—
490C22×D4—111no—
491C22×D4—111no—
492C22×D4—221no—
493C22×D4—224no—
494C22×D4—224no—
495C22×D4—222no—
496C22×D4—221no—
497C22×D4—221no—
498C22×D4—221no—
499C22×D4C22×D1111yescharacteristic
500C23×C4—21no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—221no—
504C23×C4—221no—
505C23×C4C22×D1111yescharacteristic
506C2×M16—114no—
507C2×M16—224no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—114no—
511C22×C8—224no—
512C22×C8C22×D1111yescharacteristic
513C22×C8C22×D1111yescharacteristic
514#127—228no—
515#124—228no—
516#121—22no—
517#121—114no—
518#121—114no—
519#121—114no—
520#121—222no—
521#121—222no—
522#121—222no—
523#121C22×D1114yes—
524#120—228no—
525#120—228no—
526C4×Q8—228no—
527C4×D4—228no—
528C4×D4—228no—
529C4×D4—228no—
530#117—114no—
531#117—114no—
532#117—114no—
533#117—114no—
534#117—222no—
535#117—222no—
536#117—222no—
537#117—222no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—114no—
544C2×C4⋊C4—114no—
545C2×C4⋊C4—222no—
546C2×C4⋊C4—222no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C4⋊C4C22×D1114yescomplemented
553C2×C22⋊C4—21no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C42—221no—
562C2×C42—221no—
563C2×C42—221no—
564C2×C42—221no—
565#107—114no—
566#107—114no—
567#107C22×D1114yescomplemented
568#107C22×D1114yescomplemented
569#106—114no—
570#106—114no—
571#106—114no—
572#106—114no—
573#102—114no—
574#102—114no—
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579#102C22×D1114yes—
580#102C22×D1114yes—
581C22⋊C8—114no—
582C22⋊C8—114no—
583C22⋊C8—114no—
584C22⋊C8C22×D1114yescomplemented
585C2×C11—42no—
586C2×C11—82no—
587C2×C11#309614yescomplemented
588C2×C11C22×#12311yescharacteristic
589C2×C11C2×#57611yescharacteristic
590C2×C11C2×#57711yescharacteristic
591D11—24no—
592D11—42no—
593D11—82no—
594C24—21no—
595C24—111no—
596C24—111no—
597C24—224no—
598C24—221no—
599C24—444no—
600C24—882no—
601C24—882no—
602C24D4×D1111yescharacteristic
603#41—2216no—
604#41—228no—
605#41—228no—
606C2×Q8—114no—
607C2×Q8—224no—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—82no—
613C2×D4—114no—
614C2×D4—114no—
615C2×D4—114no—
616C2×D4—112no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—228no—
620C2×D4—228no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—224no—
626C2×D4—221no—
627C2×D4—222no—
628C2×D4—222no—
629C2×D4—448no—
630C2×D4—444no—
631C2×D4—882no—
632C2×D4—882no—
633C2×D4—882no—
634C2×D4C23×D1112yes—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—82no—
642C22×C4—111no—
643C22×C4—112no—
644C22×C4—114no—
645C22×C4—114no—
646C22×C4—112no—
647C22×C4—111no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—224no—
651C22×C4—224no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—882no—
658C22×C4—882no—
659C22×C4D4×D1112yes—
660C22×C4D4×D1111yescharacteristic
661C22×C4C23×D1112yes—
662C22×C4C23×D1111yescharacteristic
663M16—228no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—112no—
667C2×C8—112no—
668C2×C8—228no—
669C2×C8—222no—
670C2×C8—222no—
671C2×C8C23×D1112yes—
672C2×C8C23×D1112yes—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—24no—
676C4⋊C4—21no—
677C4⋊C4—112no—
678C4⋊C4—112no—
679C4⋊C4—112no—
680C4⋊C4—224no—
681C4⋊C4—224no—
682C4⋊C4—221no—
683C4⋊C4—221no—
684C4⋊C4—221no—
685C4⋊C4C23×D1112yes—
686C4⋊C4C23×D1112yes—
687C4⋊C4C23×D1112yes—
688C22⋊C4—24no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—224no—
695C22⋊C4—224no—
696C42—224no—
697C42—224no—
698C42—224no—
699C42—224no—
700C11C2×#309611yescharacteristic, complemented, Sylow
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—114no—
709C23—112no—
710C23—112no—
711C23—222no—
712C23—222no—
713C23—222no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23—448no—
718C23—442no—
719C23—442no—
720C23—442no—
721C23—884no—
722C23—884no—
723C23—8816no—
724C23C2×D4×D1112yes—
725C23C2×D4×D1111yescharacteristic
726Q8—228no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—228no—
732D4—228no—
733D4—228no—
734D4—222no—
735D4—222no—
736D4—448no—
737D4—442no—
738D4—884no—
739D4—884no—
740D4—884no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—114no—
753C2×C4—112no—
754C2×C4—118no—
755C2×C4—114no—
756C2×C4—114no—
757C2×C4—112no—
758C2×C4—222no—
759C2×C4—224no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—442no—
766C2×C4—442no—
767C2×C4—442no—
768C2×C4—884no—
769C2×C4—884no—
770C2×C4C2×D4×D1112yes—
771C2×C4C2×D4×D1111yescharacteristic
772C2×C4#41×D1112yes—
773C2×C4#41×D1112yes—
774C2×C4C24×D1111yescharacteristic
775C8—22no—
776C8—22no—
777C8—222no—
778C8—222no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—114no—
788C22—228no—
789C22—222no—
790C22—222no—
791C22—222no—
792C22—222no—
793C22—222no—
794C22—444no—
795C22—442no—
796C22—442no—
797C22—442no—
798C22—8816no—
799C22—884no—
800C22D11×#12312yes—
801C22#1062328812yes—
802C22#1062330912yes—
803C22C22×D4×D1111yescharacteristic
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—114no—
809C4—222no—
810C4—442no—
811C4—442no—
812C4—442no—
813C4D11×#12312yes—
814C4C2×#41×D1111yescharacteristic
815C4C2×#41×D1111yescharacteristic
816C2—42no—
817C2—82no—
818C2—224no—
819C2—442no—
820C2—882no—
821C2#1307856714yesdirect product factor
822C2C2×D11×#12311yescharacteristic
823C2C2×#1062328811yescharacteristic
824C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#480C2
socleC23×C11C22×D4
prime radicalC2×#10623138C2
hypercenterC2×#480D11
hypocenterC11C2×#3096
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. #13078567C2direct (N × H)
4. C2×#10622581C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622498C2semidirect
7. C2×#10622350C2semidirect
8. C2×#10622397C2semidirect
9. C2×#10622648C2semidirect
10. C2×#10622495C2semidirect
11. C2×#10622494C2semidirect
12. C2×#10622493C2semidirect
13. C2×#10622383C2semidirect
14. C2×D11×#102C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#480C2semidirect
20. C22×C11×C4⋊C4C22semidirect
27. C2×#66979C22semidirect
34. #10623035C22semidirect
38. C2×#66945C22semidirect
40. C2×C4⋊C4×D11C22semidirect
44. C11×#480C22semidirect
45. C2×C11×#107C22semidirect
46. C2×C11×#107C22semidirect
49. C2×C11×C22⋊C8C22semidirect
52. C2×C22⋊(C11⋊C8)C22semidirect
55. C2×(C2×D11)⋊C8C22semidirect
56. C2×(C2×D11)⋊C8C22semidirect
57. C2×#66882C22semidirect
58. C2×#66881C22semidirect
59. #10622648C22semidirect
60. #10622581C22semidirect
63. C2×#66872C22semidirect
64. C2×#66872C22semidirect
65. C2×#66872C22semidirect
66. C2×#66871C22semidirect
67. #10622498C22semidirect
68. #10622495C22semidirect
69. #10622494C22semidirect
70. #10622493C22semidirect
71. #10622397C22semidirect
72. #10622390C22semidirect
73. #10622383C22semidirect
74. D11×#102C22semidirect
75. #10622350C22semidirect
76. #10622340C22semidirect
112. C2×C11×C4⋊C4C23semidirect
130. #66979C23semidirect
154. #66945C23semidirect
158. C4⋊C4×D11C23semidirect
162. C11×#107C23semidirect
163. C11×#107C23semidirect
166. C11×C22⋊C8C23semidirect
169. C22⋊(C11⋊C8)C23semidirect
172. (C2×D11)⋊C8C23semidirect
173. (C2×D11)⋊C8C23semidirect
174. #66882C23semidirect
175. #66881C23semidirect
178. #66872C23semidirect
179. #66872C23semidirect
180. #66872C23semidirect
181. #66871C23semidirect
299. C2×#480D11semidirect
409. C22×C4⋊C4C2×D11semidirect
417. #480C2×D11semidirect
422. C2×#107C2×D11semidirect
423. C2×#107C2×D11semidirect
442. C2×C22⋊C8C2×D11semidirect
552. C2×C4⋊C4C22×D11semidirect
567. #107C22×D11semidirect
568. #107C22×D11semidirect
584. C22⋊C8C22×D11semidirect
587. C2×C11#3096semidirect
700. C11C2×#3096semidirect
821. C2#13078567direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231382
C2×#106230352
#130785672
C2×#106225812
C2×#106223902
C2×#106224982
C2×#106223502
C2×#106223972
C2×#106226482
C2×#106224952
C2×#106224942
C2×#106224932
C2×#106223832
C2×D11×#1022
C2×#106223402
C2×C11×#4802
C2×#309611