Finite Group Databasebeta

← C2×#13079286 #15623643

Subgroups — C2×#13079286 #15623643

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic
2#13079286C2116yesmaximal, direct product factor
3C2×#10622678C211yesmaximal, characteristic, complemented
4C2×#10622699C211yesmaximal, characteristic, complemented
5C2×#10622681C211yesmaximal, characteristic, complemented
6C2×#10622694C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622662C211yesmaximal, characteristic
9C2×#10622664C211yesmaximal, characteristic, complemented
10C2×#10622661C211yesmaximal, characteristic
11C2×#10622643C211yesmaximal, characteristic, complemented
12C2×#10622639C211yesmaximal, characteristic, complemented
13C2×C4×#4326C211yesmaximal, characteristic, complemented
14C2×C4×#4325C211yesmaximal, characteristic, complemented
15C2×#10622610C211yesmaximal, characteristic, complemented
16C2×C11×#541C211yesmaximal, characteristic, complemented
17C11×#541—24no—
18C11×#541C2218yescomplemented
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#126—21no—
21C2×C11×#126—21no—
22C2×C11×#125—21no—
23C2×C11×#125—21no—
24C2×C11×#125C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C22×#4325C2211yescharacteristic
33C22×#4325C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623065—24no—
39#10623065C2218yes—
40C2×#66951—21no—
41C2×#66949—21no—
42C2×#66938—21no—
43C2×#66936—21no—
44C2×#66928C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×#66922C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C2×#66899C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52#10622699C2218yescomplemented
53#10622694C2218yescomplemented
54#10622681C2218yescomplemented
55#10622678C2218yescomplemented
56#10622665C2218yescomplemented
57#10622664C2218yescomplemented
58#10622662C2218yes—
59#10622661C2218yes—
60#10622643C2218yescomplemented
61C4×#4326C2218yescomplemented
62#10622639C2218yescomplemented
63C4×#4325C2218yescomplemented
64#10622610C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×#66867C2211yescharacteristic
74C2×#66867C2211yescharacteristic
75C2×C4×C11⋊C8C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×D44C2311yescharacteristic
82C22×C4×D11—21no—
83C22×Dic22—21no—
84C22×Dic22C2311yescharacteristic
85C11×C4⋊Q8—22no—
86C11×C4⋊Q8C2314yes—
87C11×#126—28no—
88C11×#126—28no—
89C11×#125—28no—
90C11×#125—28no—
91C11×#125—22no—
92C11×#125C2314yes—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8C2314yes—
96C11×C22⋊Q8C2314yes—
97C4×Q8×C11—22no—
98C4×Q8×C11—22no—
99C4×Q8×C11C2314yes—
100C4×Q8×C11C2314yes—
101C11×#117D414yes—
102C11×#117C2314yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C42×C11—21no—
120C2×C42×C11—21no—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C22⋊Dic11—21no—
124C2×#4326—24no—
125C2×#4326—24no—
126C2×#4326C2314yes—
127C2×#4326C2314yes—
128C2×#4325—24no—
129C2×#4325—24no—
130C2×#4325C2314yes—
131C2×#4325C2314yes—
132#66983—22no—
133#66983C2314yes—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141#66977—22no—
142#66977C2314yes—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×C4×Dic11—21no—
146C2×#4318—24no—
147C2×#4318C2314yes—
148C22×C11⋊C8—24no—
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2314yes—
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154#66951—28no—
155#66949—28no—
156#66938—28no—
157#66936—28no—
158#66928—22no—
159#66928C2314yes—
160C4×D44—22no—
161C4×D44C2314yes—
162#66922—22no—
163#66922C2314yes—
164C4×Dic22—22no—
165C4×Dic22C2314yes—
166#66899C2314yes—
167#66899C2314yes—
168#66899C2314yes—
169#66899C2314yes—
170#66874C2314yes—
171#66874C2314yes—
172#66873C2314yes—
173#66873C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178#66867C2314yes—
179#66867C2314yes—
180C4×C11⋊C8C2314yes—
181C4×C11⋊C8C2314yes—
182C2×#3178—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11C2412yes—
192C2×Q8×C11C2412yes—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2412yes—
206C22×C4×C11C2411yescharacteristic
207C2×C22⋊D11—24no—
208C2×C22⋊D11—82no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C2×D44—21no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44C2412yes—
216C2×C4×D11—24no—
217C2×C4×D11—82no—
218C2×Dic22—21no—
219C2×Dic22—24no—
220C2×Dic22—22no—
221C2×Dic22—22no—
222C2×Dic22—82no—
223C2×Dic22C2412yes—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—24no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—24no—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4C2×D414yes—
235C11×C4⋊C4C2×D414yes—
236C11×C4⋊C4C2412yes—
237C11×C4⋊C4C2412yes—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4C2×D414yes—
241C11×C22⋊C4C2×D414yes—
242C42×C11—24no—
243C42×C11—24no—
244C42×C11C2×D412yes—
245C42×C11C2×D412yes—
246C42×C11C2412yes—
247C42×C11C2412yes—
248C22⋊Dic11—24no—
249#4326—28no—
250#4326—28no—
251#4325—28no—
252#4325—28no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—24no—
260C4⋊Dic11C2412yes—
261C4⋊Dic11C2412yes—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264C4×Dic11—24no—
265#4318—28no—
266C2×C11⋊C8—28no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8#4114yes—
270C2×C11⋊C8#4114yes—
271C2×C11⋊C8C2412yes—
272C2×C11⋊C8C2412yes—
273C2×C11⋊C8C2412yes—
274C2×C11⋊C8C2412yes—
275C2×#542—111no—
276C2×#541D1111yescharacteristic, complemented
277#3178—1116no—
278C2×#501—111no—
279C2×#497—111no—
280C2×#488—111no—
281C2×#487—111no—
282C2×#470—111no—
283C2×#468—111no—
284C2×#467—111no—
285C2×#465—111no—
286C2×#441—111no—
287C2×#440—111no—
288C2×C4×Q16—111no—
289C2×C4×SD16—111no—
290C2×#405—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11C22×D412yes—
295C23×C11C22×D411yescharacteristic
296C22×D11—22no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11—42no—
300Q8×C11—22no—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—42no—
305Q8×C11—42no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4112yes—
329C2×C4×C11C2×#4112yes—
330C2×C4×C11C2511yescharacteristic
331C22⋊D11—84no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338D44—22no—
339D44—22no—
340D44—42no—
341C4×D11—84no—
342Dic22—22no—
343Dic22—22no—
344Dic22—42no—
345Dic22—84no—
346C11⋊C8—22no—
347C11⋊C8—22no—
348C11⋊C8C2×#4114yes—
349C11⋊C8C2×#4114yes—
350C22×Q16—111no—
351C22×Q16—111no—
352C22×SD16—111no—
353C22×SD16—111no—
354C22×M16—111no—
355C23×C8—111no—
356#542—118no—
357#542—224no—
358#541—24no—
359#541C2×D1118yescomplemented
360C2×C4⋊Q8—111no—
361C2×C4⋊Q8C2×D1111yescharacteristic
362C2×#126—21no—
363C2×#126—21no—
364C2×#126—221no—
365C2×#125—21no—
366C2×#125—21no—
367C2×#125C2×D1111yescharacteristic
368C2×#124—111no—
369C2×#124—221no—
370C2×#123—221no—
371C2×C22⋊Q8—111no—
372C2×C22⋊Q8—221no—
373C2×C22⋊Q8C2×D1111yescharacteristic
374C2×C22⋊Q8C2×D1111yescharacteristic
375C2×#121—111no—
376C2×C4×Q8—111no—
377C2×C4×Q8C2×D1111yescharacteristic
378C2×C4×Q8C2×D1111yescharacteristic
379C2×C4×D4—111no—
380C2×#117C2×D1111yescharacteristic
381#501—118no—
382#497—118no—
383#488—118no—
384#487—118no—
385#470—118no—
386#468—118no—
387#467—118no—
388#465—118no—
389#441—118no—
390#440—118no—
391C4×Q16—118no—
392C4×SD16—118no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#106—111no—
396C2×#106—111no—
397C2×#103—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103—111no—
403C2×#102—111no—
404C2×#102—111no—
405#405—118no—
406C2×#97—111no—
407C2×#97—111no—
408C2×C4×C8—111no—
409C2×C4×C8—111no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—44no—
414C22×C11#53212yes—
415C22×C11#57712yes—
416C22×C11#57812yes—
417C22×C11C23×D411yescharacteristic
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—84no—
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11#53212yes—
432C4×C11C22×#4111yescharacteristic
433C4×C11C22×#4111yescharacteristic
434Dic11—42no—
435Dic11—42no—
436Dic11—42no—
437C22×Q8—111no—
438C22×Q8—221no—
439C22×Q8C22×D1111yescharacteristic
440C22×Q8C22×D1111yescharacteristic
441C22×D4—111no—
442C22×D4—221no—
443C23×C4—221no—
444C23×C4C22×D1111yescharacteristic
445C2×Q16—114no—
446C2×Q16—114no—
447C2×Q16—224no—
448C2×Q16—224no—
449C2×SD16—114no—
450C2×SD16—114no—
451C2×SD16—224no—
452C2×SD16—224no—
453C2×M16—114no—
454C2×M16—224no—
455C22×C8—111no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—114no—
459C22×C8—111no—
460C22×C8—224no—
461C4⋊Q8—22no—
462C4⋊Q8—114no—
463C4⋊Q8—222no—
464C4⋊Q8C22×D1114yes—
465#126—28no—
466#126—28no—
467#126—228no—
468#125—28no—
469#125—28no—
470#125—22no—
471#125C22×D1114yes—
472#124—114no—
473#124—228no—
474#124—222no—
475#123—228no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—114no—
479C22⋊Q8—222no—
480C22⋊Q8—228no—
481C22⋊Q8C22×D1114yes—
482C22⋊Q8C22×D1114yes—
483#121—114no—
484#121—222no—
485C4×Q8—22no—
486C4×Q8—22no—
487C4×Q8—114no—
488C4×Q8—222no—
489C4×Q8C22×D1114yes—
490C4×Q8C22×D1114yes—
491C4×D4—114no—
492C4×D4—222no—
493#117C22⋊D1114yes—
494#117C22×D1114yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4C22⋊D1111yescharacteristic
509C2×C4⋊C4C22⋊D1111yescharacteristic
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4C22⋊D1111yescharacteristic
520C2×C22⋊C4C22⋊D1111yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—221no—
524C2×C42C22×D1111yescharacteristic
525C2×C42C22×D1111yescharacteristic
526#107—114no—
527#107—114no—
528#106—114no—
529#106—114no—
530#103—114no—
531#103—114no—
532#103—114no—
533#103—114no—
534#103—114no—
535#103—114no—
536#102—114no—
537#102—114no—
538#97—114no—
539#97—114no—
540C4×C8—114no—
541C4×C8—114no—
542C2×C11—42no—
543C2×C11#317814yescomplemented
544C2×C11C2×#53211yescharacteristic
545C2×C11C2×#57711yescharacteristic
546C2×C11C2×#57811yescharacteristic
547D11—82no—
548C24—221no—
549C24C2×C22⋊D1111yescharacteristic
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—112no—
557C2×Q8—221no—
558C2×Q8—224no—
559C2×Q8—222no—
560C2×Q8—222no—
561C2×Q8—882no—
562C2×Q8C23×D1112yes—
563C2×Q8C23×D1112yes—
564C2×D4—112no—
565C2×D4—224no—
566C2×D4—222no—
567C2×D4—222no—
568C2×D4—221no—
569C2×D4—882no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—224no—
580C22×C4—882no—
581C22×C4C2×C22⋊D1112yes—
582C22×C4C2×C22⋊D1111yescharacteristic
583C22×C4C2×C22⋊D1111yescharacteristic
584C22×C4C2×C22⋊D1111yescharacteristic
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C2×C22⋊D1111yescharacteristic
587C22×C4C23×D1112yes—
588C22×C4C23×D1111yescharacteristic
589Q16—228no—
590Q16—228no—
591SD16—228no—
592SD16—228no—
593M16—228no—
594C2×C8—114no—
595C2×C8—114no—
596C2×C8—112no—
597C2×C8—112no—
598C2×C8—112no—
599C2×C8—112no—
600C2×C8—228no—
601C2×C8—222no—
602C2×C8—222no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—112no—
614C4⋊C4—112no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4C2×C22⋊D1114yes—
621C4⋊C4C2×C22⋊D1114yes—
622C4⋊C4C23×D1112yes—
623C4⋊C4C23×D1112yes—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4C2×C22⋊D1114yes—
632C22⋊C4C2×C22⋊D1114yes—
633C42—24no—
634C42—24no—
635C42—224no—
636C42C2×C22⋊D1112yes—
637C42C2×C22⋊D1112yes—
638C42C23×D1112yes—
639C42C23×D1112yes—
640C11C2×#317811yescharacteristic, complemented, Sylow
641C23—22no—
642C23—22no—
643C23—22no—
644C23—222no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23C22×C22⋊D1112yes—
649C23C22×C22⋊D1111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—222no—
657Q8—222no—
658Q8—442no—
659Q8—884no—
660D4—222no—
661D4—222no—
662D4—442no—
663D4—884no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—442no—
684C2×C4—442no—
685C2×C4—442no—
686C2×C4—884no—
687C2×C4#41×D1112yes—
688C2×C4#41×D1112yes—
689C2×C4C22×C22⋊D1112yes—
690C2×C4C22×C22⋊D1112yes—
691C2×C4C22×C22⋊D1112yes—
692C2×C4C22×C22⋊D1112yes—
693C2×C4C22×C22⋊D1112yes—
694C2×C4C22×C22⋊D1111yescharacteristic
695C2×C4C24×D1111yescharacteristic
696C8—114no—
697C8—114no—
698C8—222no—
699C8—222no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—442no—
705C22—442no—
706C22—442no—
707C22—884no—
708C22#1062336312yes—
709C22#1062336812yes—
710C22#1062336912yes—
711C22C23×C22⋊D1111yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—442no—
722C4—442no—
723C4—442no—
724C4#1062336312yes—
725C4C2×#41×D1111yescharacteristic
726C4C2×#41×D1111yescharacteristic
727C2—42no—
728C2—882no—
729C2#1307928614yesdirect product factor
730C2C2×#1062336311yescharacteristic
731C2C2×#1062336811yescharacteristic
732C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#541C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#541D11
hypocenterC11C2×#3178
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #13079286C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622699C2semidirect
5. C2×#10622681C2semidirect
6. C2×#10622694C2semidirect
7. C2×#10622665C2semidirect
9. C2×#10622664C2semidirect
11. C2×#10622643C2semidirect
12. C2×#10622639C2semidirect
13. C2×C4×#4326C2semidirect
14. C2×C4×#4325C2semidirect
15. C2×#10622610C2semidirect
16. C2×C11×#541C2semidirect
18. C11×#541C22semidirect
52. #10622699C22semidirect
53. #10622694C22semidirect
54. #10622681C22semidirect
55. #10622678C22semidirect
56. #10622665C22semidirect
57. #10622664C22semidirect
60. #10622643C22semidirect
61. C4×#4326C22semidirect
62. #10622639C22semidirect
63. C4×#4325C22semidirect
64. #10622610C22semidirect
276. C2×#541D11semidirect
359. #541C2×D11semidirect
543. C2×C11#3178semidirect
640. C11C2×#3178semidirect
729. C2#13079286direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230652
#130792862
C2×#106226782
C2×#106226992
C2×#106226812
C2×#106226942
C2×#106226652
C2×#106226622
C2×#106226642
C2×#106226612
C2×#106226432
C2×#106226392
C2×C4×#43262
C2×C4×#43252
C2×#106226102
C2×C11×#5412
C2×#317811