Finite Group Databasebeta

← C2×#13078872 #15622082

Subgroups — C2×#13078872 #15622082

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×#10623054C211yesmaximal, characteristic, complemented
2#13078872C2116yesmaximal, direct product factor
3C2×#10622657C211yesmaximal, characteristic, complemented
4C2×#10622646C211yesmaximal, characteristic, complemented
5C2×#10622704C211yesmaximal, characteristic, complemented
6C2×#10622700C211yesmaximal, characteristic, complemented
7C2×#10622667C211yesmaximal, characteristic, complemented
8C2×#10622670C211yesmaximal, characteristic, complemented
9C2×#10622660C211yesmaximal, characteristic, complemented
10C2×#10622650C211yesmaximal, characteristic
11C2×#10622631C211yesmaximal, characteristic, complemented
12C2×#10622639C211yesmaximal, characteristic, complemented
13C2×C4×#4326C211yesmaximal, characteristic, complemented
14C2×C4×#4323C211yesmaximal, characteristic, complemented
15C2×#10622613C211yesmaximal, characteristic, complemented
16C2×C11×#542C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C11×#542—24no—
19C11×#542C2218yescomplemented
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#126—21no—
22C2×C11×#124—21no—
23C2×C11×#124C2211yescharacteristic
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C22×#4325C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C22×#4323C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36#10623054—24no—
37#10623054C2218yescomplemented
38C2×#66945—21no—
39C2×C4⋊C4×D11—21no—
40C2×(C22⋊D11)⋊C4—21no—
41C2×(C22⋊D11)⋊C4—21no—
42C2×C4×D44C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
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#10622704C2218yescomplemented
53#10622700C2218yescomplemented
54#10622670C2218yescomplemented
55#10622667C2218yescomplemented
56#10622660C2218yescomplemented
57#10622657C2218yescomplemented
58#10622650C2218yes—
59#10622646C2218yescomplemented
60C4×#4326C2218yescomplemented
61#10622639C2218yescomplemented
62#10622631C2218yescomplemented
63C4×#4323C2218yescomplemented
64#10622613C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C23×Dic11—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×C4⋊Q8—22no—
95C11×C4⋊Q8C2314yes—
96C11×#126—28no—
97C11×#124—28no—
98C11×#124—22no—
99C11×#124C2314yes—
100C11×#123—28no—
101C11×C22⋊Q8—22no—
102C11×C22⋊Q8—28no—
103C11×C22⋊Q8C2314yes—
104C11×#121—22no—
105C11×#121C2314yes—
106C4×Q8×C11—22no—
107C4×Q8×C11C2314yes—
108C4×D4×C11—22no—
109C4×D4×C11C2314yes—
110C11×#117D414yes—
111C11×#117C2314yes—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4D411yescharacteristic
116C2×C11×C4⋊C4D411yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4D411yescharacteristic
125C2×C11×C22⋊C4D411yescharacteristic
126C2×C42×C11—21no—
127C2×C42×C11C2311yescharacteristic
128C2×C42×C11C2311yescharacteristic
129C2×#4326—24no—
130C2×#4326C2314yes—
131C2×#4325—24no—
132C2×#4325C2314yes—
133C2×#4324—24no—
134C2×#4324C2314yes—
135C2×#4323—24no—
136C2×#4323C2314yes—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—22no—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2314yes—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×C4×Dic11—21no—
147C2×C4×Dic11—21no—
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152#66945—28no—
153C4⋊C4×D11—28no—
154(C22⋊D11)⋊C4—28no—
155(C22⋊D11)⋊C4—28no—
156C4×D44—22no—
157C4×D44—22no—
158C4×D44C2314yes—
159C4×D44C2314yes—
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#66871C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180#66867C2314yes—
181C4×C11⋊C8C2314yes—
182C2×#3124—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—24no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11—82no—
191C2×Q8×C11C2412yes—
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×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2411yescharacteristic
213C2×C22⋊D11—28no—
214C2×C22⋊D11—24no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—24no—
219C22×Dic11—82no—
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—82no—
232C2×C4×D11—82no—
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—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⋊C4—24no—
249C11×C22⋊C4—24no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4C2×D414yes—
252C11×C22⋊C4C2×D414yes—
253C42×C11—24no—
254C42×C11C2×D412yes—
255C42×C11C2×D412yes—
256C42×C11C2412yes—
257C42×C11C2412yes—
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⋊Dic11—24no—
267C4⋊Dic11C2412yes—
268C4⋊Dic11C2412yes—
269Dic11⋊C4—24no—
270Dic11⋊C4—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×#542D1111yescharacteristic, complemented
282C2×#520—111no—
283#3124—1116no—
284C2×#484—111no—
285C2×#480—111no—
286C2×#477—111no—
287C2×#474—111no—
288C2×#464—111no—
289C2×#463—111no—
290C2×#452—111no—
291C2×#449—111no—
292C2×#440—111no—
293C2×#440—111no—
294C2×C4×Q16—111no—
295C2×C4×D8—111no—
296C2×#433—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—
313Q8×C11—84no—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—42no—
317D4×C11—84no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—84no—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D412yes—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C2×#4112yes—
340C2×C4×C11C2×#4112yes—
341C2×C4×C11C2511yescharacteristic
342C22⋊D11—216no—
343C2×Dic11—24no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—84no—
350D44—24no—
351D44—22no—
352D44C2×#4114yes—
353C4×D11—216no—
354C4×D11—84no—
355C4×D11—84no—
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#542—24no—
369#542C2×D1118yescomplemented
370C2×C4⋊Q8C2×D1111yescharacteristic
371C2×#126—21no—
372C2×#124—21no—
373C2×#124C2×D1111yescharacteristic
374C2×#123—21no—
375C2×C22⋊Q8—21no—
376C2×C22⋊Q8C2×D1111yescharacteristic
377C2×#121C2×D1111yescharacteristic
378#520—118no—
379#520—224no—
380C2×C4×Q8—111no—
381C2×C4×Q8—111no—
382C2×C4×Q8C2×D1111yescharacteristic
383C2×C4×D4—111no—
384C2×C4×D4—111no—
385C2×C4×D4—221no—
386C2×C4×D4—221no—
387C2×C4×D4C2×D1111yescharacteristic
388C2×#117—221no—
389C2×#117C2×D1111yescharacteristic
390C22×C4⋊C4—111no—
391C22×C4⋊C4—221no—
392#484—118no—
393#480—118no—
394#477—118no—
395#474—118no—
396#464—118no—
397#463—118no—
398#452—118no—
399#449—118no—
400#440—118no—
401#440—118no—
402C4×Q16—118no—
403C4×D8—118no—
404#433—118no—
405C2×#107—111no—
406C2×#107—111no—
407C2×#107—111no—
408C2×#107—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—22no—
425C22×C11—22no—
426C22×C11—44no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—84no—
431C22×C11#52512yes—
432C22×C11#57612yes—
433C22×C11#57812yes—
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—21no—
458C22×Q8—111no—
459C22×Q8C22×D1111yescharacteristic
460C22×D4—21no—
461C22×D4—111no—
462C22×D4—221no—
463C22×D4C22×D1111yescharacteristic
464C23×C4—21no—
465C23×C4—221no—
466C23×C4—221no—
467C23×C4—221no—
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—22no—
483C4⋊Q8C22×D1114yes—
484#126—28no—
485#124—28no—
486#124—22no—
487#124C22×D1114yes—
488#123—28no—
489C22⋊Q8—22no—
490C22⋊Q8—28no—
491C22⋊Q8C22×D1114yes—
492#121—22no—
493#121C22×D1114yes—
494C4×Q8—22no—
495C4×Q8—114no—
496C4×Q8—114no—
497C4×Q8—222no—
498C4×Q8—222no—
499C4×Q8C22×D1114yes—
500C4×D4—22no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—228no—
504C4×D4—228no—
505C4×D4—222no—
506C4×D4—222no—
507C4×D4C22×D1114yes—
508#117—228no—
509#117C22⋊D1114yes—
510#117C22×D1114yes—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—222no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—228no—
522C2×C4⋊C4C22⋊D1111yescharacteristic
523C2×C4⋊C4C22⋊D1111yescharacteristic
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4C22⋊D1111yescharacteristic
534C2×C22⋊C4C22⋊D1111yescharacteristic
535C2×C42—21no—
536C2×C42—221no—
537C2×C42—221no—
538C2×C42C22×D1111yescharacteristic
539C2×C42C22×D1111yescharacteristic
540#107—114no—
541#107—114no—
542#107—114no—
543#107—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—82no—
560C2×C11#312414yescomplemented
561C2×C11C2×#52511yescharacteristic
562C2×C11C2×#57611yescharacteristic
563C2×C11C2×#57811yescharacteristic
564D11—44no—
565C24—21no—
566C24—221no—
567C24C2×C22⋊D1111yescharacteristic
568#41—228no—
569#41—228no—
570#41—2216no—
571C2×Q8—21no—
572C2×Q8—24no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—82no—
576C2×Q8—114no—
577C2×Q8—112no—
578C2×Q8—222no—
579C2×Q8—221no—
580C2×Q8C23×D1112yes—
581C2×D4—24no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—82no—
586C2×D4—114no—
587C2×D4—112no—
588C2×D4—228no—
589C2×D4—224no—
590C2×D4—222no—
591C2×D4—221no—
592C2×D4C23×D1112yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—82no—
600C22×C4—228no—
601C22×C4—221no—
602C22×C4—224no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—224no—
608C22×C4—882no—
609C22×C4—882no—
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—224no—
639C4⋊C4—221no—
640C4⋊C4—221no—
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—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4C2×C22⋊D1114yes—
655C22⋊C4C2×C22⋊D1114yes—
656C42—24no—
657C42—224no—
658C42—224no—
659C42C2×C22⋊D1112yes—
660C42C2×C22⋊D1112yes—
661C42C23×D1112yes—
662C42C23×D1112yes—
663C11C2×#312411yescharacteristic, 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—84no—
681Q8—114no—
682Q8—224no—
683Q8—222no—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—84no—
688D4—114no—
689D4—2216no—
690D4—224no—
691D4—222no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—84no—
707C2×C4—2216no—
708C2×C4—224no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—884no—
715C2×C4—884no—
716C2×C4—884no—
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#1062335912yes—
743C22#1062336612yes—
744C22#1062336912yes—
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#1307887214yesdirect product factor
764C2C2×#1062335911yescharacteristic
765C2C2×#1062336611yescharacteristic
766C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#542C2
socleC23×C11C22×D4
prime radicalC2×#10622650C2
hypercenterC2×#542D11
hypocenterC11C2×#3124
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#10623054C2semidirect
2. #13078872C2direct (N × H)
3. C2×#10622657C2semidirect
4. C2×#10622646C2semidirect
5. C2×#10622704C2semidirect
6. C2×#10622700C2semidirect
7. C2×#10622667C2semidirect
8. C2×#10622670C2semidirect
9. C2×#10622660C2semidirect
11. C2×#10622631C2semidirect
12. C2×#10622639C2semidirect
13. C2×C4×#4326C2semidirect
14. C2×C4×#4323C2semidirect
15. C2×#10622613C2semidirect
16. C2×C11×#542C2semidirect
19. C11×#542C22semidirect
37. #10623054C22semidirect
52. #10622704C22semidirect
53. #10622700C22semidirect
54. #10622670C22semidirect
55. #10622667C22semidirect
56. #10622660C22semidirect
57. #10622657C22semidirect
59. #10622646C22semidirect
60. C4×#4326C22semidirect
61. #10622639C22semidirect
62. #10622631C22semidirect
63. C4×#4323C22semidirect
64. #10622613C22semidirect
281. C2×#542D11semidirect
369. #542C2×D11semidirect
560. C2×C11#3124semidirect
663. C11C2×#3124semidirect
763. C2#13078872direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230542
#130788722
C2×#106226572
C2×#106226462
C2×#106227042
C2×#106227002
C2×#106226672
C2×#106226702
C2×#106226602
C2×#106226502
C2×#106226312
C2×#106226392
C2×C4×#43262
C2×C4×#43232
C2×#106226132
C2×C11×#5422
C2×#312411