Finite Group Databasebeta

← C2×#13078893 #15622104

Subgroups — C2×#13078893 #15622104

Order 2816.

2134 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×#10623065C211yesmaximal, characteristic, complemented
2#13078893C2116yesmaximal, direct product factor
3C2×#10622581C211yesmaximal, characteristic, complemented
4C2×#10622584C211yesmaximal, characteristic, complemented
5C2×#10622633C211yesmaximal, characteristic, complemented
6C2×#10622621C211yesmaximal, characteristic, complemented
7C2×#10622641C211yesmaximal, characteristic, complemented
8C2×#10622629C211yesmaximal, characteristic, complemented
9C2×#10622852C211yesmaximal, characteristic, complemented
10C2×#10622851C211yesmaximal, characteristic
11C2×#10622627C211yesmaximal, characteristic, complemented
12C2×#10622643C211yesmaximal, characteristic, complemented
13C2×C4×#4325C211yesmaximal, characteristic, complemented
14C2×C4×#4324C211yesmaximal, characteristic, complemented
15C2×#10622613C211yesmaximal, characteristic, complemented
16C2×C11×#520C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C11×#520—24no—
19C11×#520C2218yescomplemented
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117—21no—
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4—21no—
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C22×#4324C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36#10623065—24no—
37#10623065C2218yescomplemented
38C2×#66951—21no—
39C2×#66949—21no—
40C2×#66938—21no—
41C2×#66936—21no—
42C2×#66928C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46#10622852C2218yescomplemented
47#10622851C2218yes—
48C2×#66899C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622643C2218yescomplemented
55#10622641C2218yescomplemented
56C4×#4325C2218yescomplemented
57#10622633C2218yescomplemented
58C4×#4324C2218yescomplemented
59#10622629C2218yescomplemented
60#10622627C2218yescomplemented
61#10622621C2218yescomplemented
62#10622613C2218yescomplemented
63#10622584C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66874C2211yescharacteristic
66#10622581C2218yescomplemented
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71C2×#66872C2211yescharacteristic
72C2×#66872C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C2×C11×#41—24no—
78C2×C11×#41—24no—
79C2×C11×#41—22no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—21no—
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×Dic22—21no—
93C22×Dic22C2311yescharacteristic
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11C2314yes—
97C4×Q8×C11C2314yes—
98C4×D4×C11—28no—
99C4×D4×C11—28no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11C2314yes—
103C4×D4×C11C2314yes—
104C11×#117—28no—
105C11×#117D414yes—
106C11×#117C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—28no—
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C11×C22⋊C4D411yescharacteristic
121C2×C42×C11—21no—
122C2×C42×C11—21no—
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C2×C22⋊Dic11—21no—
126C2×#4326—24no—
127C2×#4326C2314yes—
128C2×#4325—24no—
129C2×#4325C2314yes—
130C2×#4324—24no—
131C2×#4324C2314yes—
132C2×#4323—24no—
133C2×#4323C2314yes—
134#66983—22no—
135#66983C2314yes—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143#66977—22no—
144#66977C2314yes—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×C4×Dic11—21no—
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152#66951—28no—
153#66949—28no—
154#66938—28no—
155#66936—28no—
156#66928—22no—
157#66928C2314yes—
158C4×D44—22no—
159C4×D44C2314yes—
160#66922—22no—
161#66922C2314yes—
162C4×Dic22—22no—
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#66872C2314yes—
177#66872C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180#66867C2314yes—
181C4×C11⋊C8C2314yes—
182C2×#3125—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11—21no—
186C11×#41—216no—
187C11×#41—28no—
188C11×#41—28no—
189C2×Q8×C11—21no—
190C2×Q8×C11—22no—
191C2×Q8×C11#4114yes—
192C2×Q8×C11C2412yes—
193C2×D4×C11—28no—
194C2×D4×C11—24no—
195C2×D4×C11—21no—
196C2×D4×C11—22no—
197C2×D4×C11#4114yes—
198C2×D4×C11C2412yes—
199C22×C4×C11—28no—
200C22×C4×C11—21no—
201C22×C4×C11—24no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
208C22×C4×C11—24no—
209C22×C4×C11—82no—
210C22×C4×C11—82no—
211C22×C4×C11—82no—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2412yes—
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—24no—
221C2×C22⋊D11—82no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C2×D44—21no—
226C2×D44—22no—
227C2×D44—22no—
228C2×D44C2412yes—
229C2×C4×D11—24no—
230C2×C4×D11—82no—
231C2×Dic22—21no—
232C2×Dic22—24no—
233C2×Dic22—22no—
234C2×Dic22—22no—
235C2×Dic22—82no—
236C2×Dic22C2412yes—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4C2×D414yes—
243C11×C4⋊C4C2×D414yes—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4C2×D414yes—
249C11×C22⋊C4C2×D414yes—
250C42×C11—24no—
251C42×C11—24no—
252C42×C11C2×D412yes—
253C42×C11C2×D412yes—
254C42×C11C2412yes—
255C42×C11C2412yes—
256C22⋊Dic11—24no—
257#4326—28no—
258#4325—28no—
259#4324—28no—
260#4323—28no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—24no—
268C4⋊Dic11C2412yes—
269C4⋊Dic11C2412yes—
270Dic11⋊C4—24no—
271Dic11⋊C4—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×#542—111no—
282C2×#520D1111yescharacteristic, complemented
283#3125—1116no—
284C2×#481—111no—
285C2×#483—111no—
286C2×#475—111no—
287C2×#476—111no—
288C2×#464—111no—
289C2×#463—111no—
290C2×#452—111no—
291C2×#449—111no—
292C2×#442—111no—
293C2×#441—111no—
294C2×C4×SD16—111no—
295C2×C4×SD16—111no—
296C2×#433—111no—
297C23×C11—22no—
298C23×C11—24no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11C22×D412yes—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310Q8×C11—24no—
311Q8×C11—22no—
312Q8×C11C2×#4114yes—
313D4×C11—216no—
314D4×C11—24no—
315D4×C11—22no—
316D4×C11C2×#4114yes—
317C2×C4×C11—216no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—24no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—84no—
333C2×C4×C11—84no—
334C2×C4×C11—84no—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D412yes—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C2×#4112yes—
342C2×C4×C11C2×#4112yes—
343C2×C4×C11C2511yescharacteristic
344C22⋊D11—84no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351D44—22no—
352D44—22no—
353D44—42no—
354C4×D11—84no—
355Dic22—22no—
356Dic22—22no—
357Dic22—42no—
358Dic22—84no—
359C11⋊C8—22no—
360C11⋊C8—22no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C22×#41C2×D1111yescharacteristic
364C22×Q16—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×D8—111no—
368#542—118no—
369#542—224no—
370C2×C4⋊Q8—111no—
371C2×#126—221no—
372C2×#124—111no—
373C2×#124—221no—
374C2×#123—221no—
375C2×C22⋊Q8—111no—
376C2×C22⋊Q8—221no—
377C2×#121—111no—
378#520—24no—
379#520C2×D1118yescomplemented
380C2×C4×Q8—111no—
381C2×C4×Q8C2×D1111yescharacteristic
382C2×C4×Q8C2×D1111yescharacteristic
383C2×C4×D4—21no—
384C2×C4×D4—21no—
385C2×C4×D4—111no—
386C2×C4×D4C2×D1111yescharacteristic
387C2×C4×D4C2×D1111yescharacteristic
388C2×#117—21no—
389C2×#117C2×D1111yescharacteristic
390C22×C4⋊C4—21no—
391C22×C4⋊C4C2×D1111yescharacteristic
392#483—118no—
393#481—118no—
394#476—118no—
395#475—118no—
396#464—118no—
397#463—118no—
398#452—118no—
399#449—118no—
400#442—118no—
401#441—118no—
402C4×SD16—118no—
403C4×SD16—118no—
404#433—118no—
405C2×#106—111no—
406C2×#106—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×C4×C8—111no—
423C22×C11—22no—
424C22×C11—24no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—44no—
428C22×C11—48no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11#52512yes—
432C22×C11#57712yes—
433C22×C11#57712yes—
434C22×C11C23×D411yescharacteristic
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—84no—
439C4×C11—22no—
440C4×C11—24no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—22no—
444C4×C11—22no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11#52512yes—
448C4×C11C22×#4111yescharacteristic
449C4×C11C22×#4111yescharacteristic
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453C2×#41—24no—
454C2×#41—24no—
455C2×#41—22no—
456C2×#41C22×D1114yes—
457C22×Q8—111no—
458C22×Q8—221no—
459C22×Q8C22×D1111yescharacteristic
460C22×D4—21no—
461C22×D4—111no—
462C22×D4—221no—
463C22×D4C22×D1111yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—221no—
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—
482C4⋊Q8—114no—
483C4⋊Q8—222no—
484#126—228no—
485#124—114no—
486#124—228no—
487#124—222no—
488#123—228no—
489C22⋊Q8—114no—
490C22⋊Q8—222no—
491C22⋊Q8—228no—
492#121—114no—
493#121—222no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—114no—
497C4×Q8—222no—
498C4×Q8C22×D1114yes—
499C4×Q8C22×D1114yes—
500C4×D4—28no—
501C4×D4—28no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—114no—
505C4×D4—222no—
506C4×D4C22×D1114yes—
507C4×D4C22×D1114yes—
508#117—28no—
509#117C22⋊D1114yes—
510#117C22×D1114yes—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—28no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—111no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4C22⋊D1111yescharacteristic
522C2×C4⋊C4C22⋊D1111yescharacteristic
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1114yes—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4C22⋊D1111yescharacteristic
534C2×C22⋊C4C22⋊D1111yescharacteristic
535C2×C42—21no—
536C2×C42—21no—
537C2×C42—221no—
538C2×C42C22×D1111yescharacteristic
539C2×C42C22×D1111yescharacteristic
540#106—114no—
541#106—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—
557C4×C8—114no—
558C2×C11—42no—
559C2×C11—44no—
560C2×C11#312514yescomplemented
561C2×C11C2×#52511yescharacteristic
562C2×C11C2×#57711yescharacteristic
563C2×C11C2×#57711yescharacteristic
564D11—82no—
565C24—21no—
566C24—221no—
567C24C2×C22⋊D1111yescharacteristic
568#41—216no—
569#41—28no—
570#41—28no—
571C2×Q8—22no—
572C2×Q8—21no—
573C2×Q8—112no—
574C2×Q8—221no—
575C2×Q8—224no—
576C2×Q8—222no—
577C2×Q8—222no—
578C2×Q8—882no—
579C2×Q8#433914yes—
580C2×Q8C23×D1112yes—
581C2×D4—28no—
582C2×D4—24no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—112no—
586C2×D4—224no—
587C2×D4—222no—
588C2×D4—222no—
589C2×D4—221no—
590C2×D4—882no—
591C2×D4#433914yes—
592C2×D4C23×D1112yes—
593C22×C4—28no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—224no—
610C22×C4—882no—
611C22×C4C2×C22⋊D1112yes—
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C2×C22⋊D1111yescharacteristic
615C22×C4C2×C22⋊D1111yescharacteristic
616C22×C4C2×C22⋊D1111yescharacteristic
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—21no—
635C4⋊C4—21no—
636C4⋊C4—112no—
637C4⋊C4—112no—
638C4⋊C4—221no—
639C4⋊C4—221no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4C2×C22⋊D1114yes—
644C4⋊C4C2×C22⋊D1114yes—
645C4⋊C4C23×D1112yes—
646C4⋊C4C23×D1112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—224no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4C2×C22⋊D1114yes—
655C22⋊C4C2×C22⋊D1114yes—
656C42—24no—
657C42—24no—
658C42—224no—
659C42C2×C22⋊D1112yes—
660C42C2×C22⋊D1112yes—
661C42C23×D1112yes—
662C42C23×D1112yes—
663C11C2×#312511yescharacteristic, complemented, Sylow
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—222no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23C22×C22⋊D1112yes—
676C23C22×C22⋊D1111yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—222no—
680Q8—222no—
681Q8—442no—
682Q8—884no—
683Q8C2×#433914yes—
684D4—216no—
685D4—24no—
686D4—22no—
687D4—222no—
688D4—222no—
689D4—442no—
690D4—884no—
691D4C2×#433914yes—
692C2×C4—216no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—84no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—884no—
717C2×C4C2×#433912yes—
718C2×C4C2×#433912yes—
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—24no—
732C22—22no—
733C22—22no—
734C22—44no—
735C22—48no—
736C22—42no—
737C22—42no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—884no—
742C22#1062332212yes—
743C22#1062336712yes—
744C22#1062336812yes—
745C22C23×C22⋊D1111yescharacteristic
746C4—22no—
747C4—24no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—442no—
755C4—442no—
756C4—442no—
757C4#1062332212yes—
758C4C22×#433911yescharacteristic
759C4C22×#433911yescharacteristic
760C2—42no—
761C2—44no—
762C2—882no—
763C2#1307889314yesdirect product factor
764C2C2×#1062332211yescharacteristic
765C2C2×#1062336811yescharacteristic
766C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#520C2
socleC23×C11C22×D4
prime radicalC2×#10622851C2
hypercenterC2×#520D11
hypocenterC11C2×#3125
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. #13078893C2direct (N × H)
3. C2×#10622581C2semidirect
4. C2×#10622584C2semidirect
5. C2×#10622633C2semidirect
6. C2×#10622621C2semidirect
7. C2×#10622641C2semidirect
8. C2×#10622629C2semidirect
9. C2×#10622852C2semidirect
11. C2×#10622627C2semidirect
12. C2×#10622643C2semidirect
13. C2×C4×#4325C2semidirect
14. C2×C4×#4324C2semidirect
15. C2×#10622613C2semidirect
16. C2×C11×#520C2semidirect
19. C11×#520C22semidirect
37. #10623065C22semidirect
46. #10622852C22semidirect
54. #10622643C22semidirect
55. #10622641C22semidirect
56. C4×#4325C22semidirect
57. #10622633C22semidirect
58. C4×#4324C22semidirect
59. #10622629C22semidirect
60. #10622627C22semidirect
61. #10622621C22semidirect
62. #10622613C22semidirect
63. #10622584C22semidirect
66. #10622581C22semidirect
282. C2×#520D11semidirect
379. #520C2×D11semidirect
560. C2×C11#3125semidirect
663. C11C2×#3125semidirect
763. C2#13078893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230652
#130788932
C2×#106225812
C2×#106225842
C2×#106226332
C2×#106226212
C2×#106226412
C2×#106226292
C2×#106228522
C2×#106228512
C2×#106226272
C2×#106226432
C2×C4×#43252
C2×C4×#43242
C2×#106226132
C2×C11×#5202
C2×#312511