Finite Group Databasebeta

← C2×#13078719 #15621947

Subgroups — C2×#13078719 #15621947

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic, complemented
2#13078719C2116yesmaximal, direct product factor
3C2×#10622658C211yesmaximal, characteristic, complemented
4C2×#10622648C211yesmaximal, characteristic, complemented
5C2×#10622676C211yesmaximal, characteristic, complemented
6C2×#10622679C211yesmaximal, characteristic, complemented
7C2×#10622667C211yesmaximal, characteristic, complemented
8C2×#10622670C211yesmaximal, characteristic, complemented
9C2×#10622660C211yesmaximal, characteristic, complemented
10C2×#10622650C211yesmaximal, characteristic
11C2×#10622627C211yesmaximal, characteristic, complemented
12C2×#10622643C211yesmaximal, characteristic, complemented
13C2×#10622631C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×#10622539C211yesmaximal, characteristic, complemented
16C2×C11×#529C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C11×#529—24no—
19C11×#529C2218yescomplemented
20C2×C11×#126—21no—
21C2×C11×#125C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117—21no—
30C22×C42×C11C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C22×#4325C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C22×#4323C2211yescharacteristic
35C2×C4×C22⋊D11—21no—
36C2×C4×C22⋊D11—21no—
37C2×#66979C2211yescharacteristic
38C4×#4339—24no—
39C4×#4339C2218yescomplemented
40C2×C4×D44C2211yescharacteristic
41C2×C4×D44C2211yescharacteristic
42C2×#66925—21no—
43C2×C42×D11—21no—
44C2×C4×Dic22C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C2×#66899C2211yescharacteristic
47C2×#66899C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49C2×#66896C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52#10622679C2218yescomplemented
53#10622676C2218yescomplemented
54#10622670C2218yescomplemented
55#10622667C2218yescomplemented
56#10622660C2218yescomplemented
57#10622658C2218yescomplemented
58#10622650C2218yes—
59#10622648C2218yescomplemented
60#10622643C2218yescomplemented
61#10622639C2218yescomplemented
62#10622631C2218yescomplemented
63#10622627C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66874C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72#10622539C2218yescomplemented
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×#66867C2211yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C23×C4×C11D411yescharacteristic
82C23×C4×C11D411yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—21no—
85C2×#4339—22no—
86C2×#4339—24no—
87C2×#4339—24no—
88C2×#4339C2314yes—
89C22×D44C2311yescharacteristic
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×Dic22C2311yescharacteristic
94C11×#126—28no—
95C11×#125—22no—
96C11×#125C2314yes—
97C11×#124—22no—
98C11×#124C2314yes—
99C11×#123—28no—
100C11×C22⋊Q8—22no—
101C11×C22⋊Q8C2314yes—
102C11×#121—22no—
103C11×#121C2314yes—
104C4×Q8×C11—22no—
105C4×Q8×C11C2314yes—
106C4×D4×C11—28no—
107C4×D4×C11—22no—
108C4×D4×C11C2314yes—
109C11×#117—28no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C42×C11—21no—
122C2×C42×C11D411yescharacteristic
123C2×C42×C11D411yescharacteristic
124C2×C42×C11D414yes—
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2314yes—
128C2×C22⋊Dic11—21no—
129C2×#4326—24no—
130C2×#4326C2314yes—
131C2×#4325—24no—
132C2×#4325C2314yes—
133C2×#4324—24no—
134C2×#4324C2314yes—
135C2×#4323—24no—
136C2×#4323C2314yes—
137C4×C22⋊D11—28no—
138C4×C22⋊D11—28no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141#66979—22no—
142#66979C2314yes—
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2311yescharacteristic
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×C4×Dic11—21no—
148C2×C4×Dic11—21no—
149C2×C4×Dic11—21no—
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C4×D44—22no—
155C4×D44—22no—
156C4×D44C2314yes—
157C4×D44C2314yes—
158#66925—28no—
159C42×D11—28no—
160C4×Dic22—22no—
161C4×Dic22—22no—
162C4×Dic22C2314yes—
163C4×Dic22C2314yes—
164#66899C2314yes—
165#66899C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168C22⋊(C11⋊C8)C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170#66874C2314yes—
171#66874C2314yes—
172#66873C2314yes—
173#66873C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180#66867C2314yes—
181#66867C2314yes—
182C2×#3111—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11C2412yes—
190C2×D4×C11—24no—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—44no—
195C2×D4×C11C2412yes—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—24no—
202C22×C4×C11—42no—
203C22×C4×C11—42no—
204C22×C4×C11—44no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D414yes—
212C22×C4×C11C2×D414yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2411yescharacteristic
215C2×C22⋊D11—28no—
216C2×C22⋊D11—24no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220#4339—216no—
221#4339—28no—
222#4339—28no—
223C2×D44—21no—
224C2×D44—22no—
225C2×D44#4114yes—
226C2×D44C2412yes—
227C2×C4×D11—28no—
228C2×C4×D11—24no—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—44no—
232C2×C4×D11—44no—
233C2×Dic22—21no—
234C2×Dic22—22no—
235C2×Dic22#4114yes—
236C2×Dic22C2412yes—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4C2412yes—
244C11×C4⋊C4C2412yes—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—24no—
250C42×C11—24no—
251C42×C11C2×D412yes—
252C42×C11C2×D412yes—
253C42×C11C2×D414yes—
254C42×C11C2×D414yes—
255C42×C11C2412yes—
256C42×C11C2412yes—
257C22⋊Dic11—24no—
258#4326—28no—
259#4325—28no—
260#4324—28no—
261#4323—28no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11C2412yes—
267C4⋊Dic11C2412yes—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11—24no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8—22no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281C2×#529D1111yescharacteristic, complemented
282C2×C4×#41—111no—
283#3111—1116no—
284C2×#485—111no—
285C2×#482—111no—
286C2×#479—111no—
287C2×#478—111no—
288C2×#464—111no—
289C2×#463—111no—
290C2×#452—111no—
291C2×#449—111no—
292C2×#442—111no—
293C2×#441—111no—
294C2×#440—111no—
295C2×#440—111no—
296C2×#432—111no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11C22×D412yes—
305C23×C11C22×D411yescharacteristic
306C22×D11—24no—
307C22×D11—22no—
308C22×D11—42no—
309C22×D11—42no—
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—42no—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—48no—
316D4×C11—42no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—44no—
329C2×C4×C11—44no—
330C2×C4×C11—48no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D412yes—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C2×#4112yes—
341C2×C4×C11C2×#4112yes—
342C2×C4×C11C2511yescharacteristic
343C22⋊D11—216no—
344C2×Dic11—24no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350D44—24no—
351D44—22no—
352D44C2×#4114yes—
353C4×D11—216no—
354C4×D11—48no—
355C4×D11—48no—
356Dic22—24no—
357Dic22—22no—
358Dic22C2×#4114yes—
359C11⋊C8—22no—
360C11⋊C8—22no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C22×#41—111no—
364C22×Q16—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×D8—111no—
368#529—24no—
369#529C2×D1118yescomplemented
370C2×#126—21no—
371C2×#125C2×D1111yescharacteristic
372C2×#124C2×D1111yescharacteristic
373C2×#123—21no—
374C2×C22⋊Q8C2×D1111yescharacteristic
375C2×#121C2×D1111yescharacteristic
376C4×#41—118no—
377C4×#41—224no—
378C2×C4×Q8—111no—
379C2×C4×Q8—111no—
380C2×C4×Q8C2×D1111yescharacteristic
381C2×C4×D4—21no—
382C2×C4×D4—111no—
383C2×C4×D4—111no—
384C2×C4×D4—221no—
385C2×C4×D4—221no—
386C2×C4×D4C2×D1111yescharacteristic
387C2×#117—21no—
388C2×#117—111no—
389C2×#117—221no—
390C22×C42—221no—
391C22×C42C2×D1111yescharacteristic
392#485—118no—
393#482—118no—
394#479—118no—
395#478—118no—
396#464—118no—
397#463—118no—
398#452—118no—
399#449—118no—
400#442—118no—
401#441—118no—
402#440—118no—
403#440—118no—
404#432—118no—
405C2×#107—111no—
406C2×#107—111no—
407C2×#106—111no—
408C2×#106—111no—
409C2×C4⋊C8—111no—
410C2×C4⋊C8—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×C22⋊C8—111no—
420C2×C22⋊C8—111no—
421C2×#97—111no—
422C2×#97—111no—
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—44no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—84no—
431C22×C11#52512yes—
432C22×C11#57512yes—
433C22×C11#57512yes—
434C22×C11C23×D411yescharacteristic
435C2×D11—24no—
436C2×D11—48no—
437C2×D11—42no—
438C2×D11—42no—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—22no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11#52512yes—
448C4×C11C22×#4111yescharacteristic
449C4×C11C22×#4111yescharacteristic
450Dic11—24no—
451Dic11—42no—
452Dic11—42no—
453C2×#41—114no—
454C2×#41—224no—
455C2×#41—224no—
456C2×#41—222no—
457C22×Q8—111no—
458C22×Q8C22×D1111yescharacteristic
459C22×D4—21no—
460C22×D4—111no—
461C22×D4—221no—
462C22×D4C22×D1111yescharacteristic
463C23×C4—21no—
464C23×C4—221no—
465C23×C4—221no—
466C23×C4—221no—
467C23×C4C22⋊D1111yescharacteristic
468C23×C4C22⋊D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470C2×Q16—114no—
471C2×Q16—224no—
472C2×SD16—114no—
473C2×SD16—114no—
474C2×SD16—224no—
475C2×SD16—224no—
476C2×D8—114no—
477C2×D8—224no—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8—111no—
481C22×C8—111no—
482#126—28no—
483#125—22no—
484#125C22×D1114yes—
485#124—22no—
486#124C22×D1114yes—
487#123—28no—
488C22⋊Q8—22no—
489C22⋊Q8C22×D1114yes—
490#121—22no—
491#121C22×D1114yes—
492C4×Q8—22no—
493C4×Q8—114no—
494C4×Q8—114no—
495C4×Q8—222no—
496C4×Q8—222no—
497C4×Q8C22×D1114yes—
498C4×D4—28no—
499C4×D4—22no—
500C4×D4—114no—
501C4×D4—114no—
502C4×D4—228no—
503C4×D4—228no—
504C4×D4—222no—
505C4×D4—222no—
506C4×D4C22×D1114yes—
507#117—28no—
508#117—114no—
509#117—222no—
510#117—228no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C42—21no—
530C2×C42—221no—
531C2×C42—221no—
532C2×C42—221no—
533C2×C42—228no—
534C2×C42C22⋊D1111yescharacteristic
535C2×C42C22⋊D1114yes—
536C2×C42C22⋊D1111yescharacteristic
537C2×C42C22×D1111yescharacteristic
538C2×C42C22×D1111yescharacteristic
539C2×C42C22×D1114yes—
540#107—114no—
541#107—114no—
542#106—114no—
543#106—114no—
544C4⋊C8—114no—
545C4⋊C8—114no—
546#103—114no—
547#103—114no—
548#103—114no—
549#103—114no—
550#102—114no—
551#102—114no—
552#102—114no—
553#102—114no—
554C22⋊C8—114no—
555C22⋊C8—114no—
556#97—114no—
557#97—114no—
558C2×C11—42no—
559C2×C11—82no—
560C2×C11#311114yescomplemented
561C2×C11C2×#52511yescharacteristic
562C2×C11C2×#57511yescharacteristic
563C2×C11C2×#57511yescharacteristic
564D11—44no—
565C24—21no—
566C24—221no—
567C24C2×C22⋊D1111yescharacteristic
568#41—228no—
569#41—228no—
570#41—2216no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—114no—
575C2×Q8—112no—
576C2×Q8—222no—
577C2×Q8—221no—
578C2×Q8C23×D1112yes—
579C2×D4—24no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—44no—
584C2×D4—114no—
585C2×D4—112no—
586C2×D4—228no—
587C2×D4—224no—
588C2×D4—222no—
589C2×D4—221no—
590C2×D4C23×D1112yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—44no—
600C22×C4—228no—
601C22×C4—221no—
602C22×C4—224no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—444no—
608C22×C4—444no—
609C22×C4C2×C22⋊D1112yes—
610C22×C4C2×C22⋊D1111yescharacteristic
611C22×C4C2×C22⋊D1111yescharacteristic
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C2×C22⋊D1111yescharacteristic
615C22×C4C2×C22⋊D1114yes—
616C22×C4C2×C22⋊D1114yes—
617C22×C4C23×D1112yes—
618C22×C4C23×D1111yescharacteristic
619Q16—228no—
620SD16—228no—
621SD16—228no—
622D8—228no—
623C2×C8—112no—
624C2×C8—112no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8—222no—
630C2×C8—222no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—112no—
638C4⋊C4—112no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4C23×D1112yes—
644C4⋊C4C23×D1112yes—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C42—24no—
654C42—224no—
655C42—224no—
656C42—224no—
657C42C2×C22⋊D1114yes—
658C42C2×C22⋊D1114yes—
659C42C2×C22⋊D1112yes—
660C42C2×C22⋊D1112yes—
661C42C23×D1112yes—
662C42C23×D1112yes—
663C11C2×#311111yescharacteristic, complemented, Sylow
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—224no—
672C23—222no—
673C23—442no—
674C23—442no—
675C23C22×C22⋊D1112yes—
676C23C22×C22⋊D1111yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—114no—
681Q8—224no—
682Q8—222no—
683D4—22no—
684D4—22no—
685D4—48no—
686D4—42no—
687D4—114no—
688D4—2216no—
689D4—224no—
690D4—222no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—48no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—2216no—
709C2×C4—224no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—448no—
714C2×C4—448no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4#41×D1112yes—
718C2×C4#41×D1112yes—
719C2×C4C22×C22⋊D1112yes—
720C2×C4C22×C22⋊D1112yes—
721C2×C4C22×C22⋊D1112yes—
722C2×C4C22×C22⋊D1112yes—
723C2×C4C22×C22⋊D1112yes—
724C2×C4C22×C22⋊D1111yescharacteristic
725C2×C4C24×D1111yescharacteristic
726C8—222no—
727C8—222no—
728C8—222no—
729C8—222no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—224no—
739C22—448no—
740C22—442no—
741C22—442no—
742C22#1062335312yes—
743C22#1062335312yes—
744C22#1062335912yes—
745C22C23×C22⋊D1111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—224no—
755C4—442no—
756C4—442no—
757C4#1062335912yes—
758C4C2×#41×D1111yescharacteristic
759C4C2×#41×D1111yescharacteristic
760C2—42no—
761C2—82no—
762C2—444no—
763C2#1307871914yesdirect product factor
764C2C2×#1062335911yescharacteristic
765C2C2×#1062335311yescharacteristic
766C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
prime radicalC2×#10622650C2
hypercenterC2×#529D11
hypocenterC11C2×#3111
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C4×#4339C2semidirect
2. #13078719C2direct (N × H)
3. C2×#10622658C2semidirect
4. C2×#10622648C2semidirect
5. C2×#10622676C2semidirect
6. C2×#10622679C2semidirect
7. C2×#10622667C2semidirect
8. C2×#10622670C2semidirect
9. C2×#10622660C2semidirect
11. C2×#10622627C2semidirect
12. C2×#10622643C2semidirect
13. C2×#10622631C2semidirect
14. C2×#10622639C2semidirect
15. C2×#10622539C2semidirect
16. C2×C11×#529C2semidirect
19. C11×#529C22semidirect
39. C4×#4339C22semidirect
52. #10622679C22semidirect
53. #10622676C22semidirect
54. #10622670C22semidirect
55. #10622667C22semidirect
56. #10622660C22semidirect
57. #10622658C22semidirect
59. #10622648C22semidirect
60. #10622643C22semidirect
61. #10622639C22semidirect
62. #10622631C22semidirect
63. #10622627C22semidirect
72. #10622539C22semidirect
281. C2×#529D11semidirect
369. #529C2×D11semidirect
560. C2×C11#3111semidirect
663. C11C2×#3111semidirect
763. C2#13078719direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130787192
C2×#106226582
C2×#106226482
C2×#106226762
C2×#106226792
C2×#106226672
C2×#106226702
C2×#106226602
C2×#106226502
C2×#106226272
C2×#106226432
C2×#106226312
C2×#106226392
C2×#106225392
C2×C11×#5292
C2×#311111