Finite Group Databasebeta

← C2×#13078891 #15622102

Subgroups — C2×#13078891 #15622102

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×#10623113C211yesmaximal, characteristic, complemented
2C2×#10623105C211yesmaximal, characteristic, complemented
3#13078891C2116yesmaximal, direct product factor
4C2×#10622476C211yesmaximal, characteristic, complemented
5C2×#10622418C211yesmaximal, characteristic, complemented
6C2×#10622404C211yesmaximal, characteristic, complemented
7C2×#10622483C211yesmaximal, characteristic, complemented
8C2×#10622798C211yesmaximal, characteristic, complemented
9C2×#10622432C211yesmaximal, characteristic, complemented
10C2×#10622800C211yesmaximal, characteristic, complemented
11C2×#10622424C211yesmaximal, characteristic
12C2×#10622324C211yesmaximal, characteristic, complemented
13C2×C4×#4325C211yesmaximal, characteristic, complemented
14C2×C4×#4325C211yesmaximal, characteristic, complemented
15C2×#10622322C211yesmaximal, characteristic, complemented
16C2×C11×#441C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C22×#4325C2211yescharacteristic
26C22×D88C2211yescharacteristic
27#10623113—24no—
28#10623113C2218yescomplemented
29#10623105—24no—
30#10623105C2218yescomplemented
31C2×#66949—21no—
32C2×#66948C2211yescharacteristic
33C2×#66947—21no—
34C2×#66946—21no—
35C2×#66946C2211yescharacteristic
36C2×C4⋊C4×D11—21no—
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66941C2211yescharacteristic
39C2×#66929—21no—
40C2×#66928—21no—
41C2×C4×D44—21no—
42C2×C4×D44C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×#66925—21no—
45C2×#66925C2211yescharacteristic
46C11×#441C2218yescomplemented
47C2×C11×#106C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53#10622800C2218yescomplemented
54#10622798C2218yescomplemented
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×#66881C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62C4×#4325C2218yescomplemented
63C4×#4325C2218yescomplemented
64C2×#66873C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×C4×C11⋊C8C2211yescharacteristic
69#10622483C2218yescomplemented
70#10622476C2218yescomplemented
71#10622432C2218yescomplemented
72#10622424C2218yes—
73#10622418C2218yescomplemented
74#10622404C2218yescomplemented
75#10622324C2218yescomplemented
76#10622322C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C2×#4343—24no—
80C2×#4343—24no—
81C2×#4343—22no—
82C2×#4343C2314yes—
83C22×D44—21no—
84C22×D44—21no—
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×C4×D11C2311yescharacteristic
93C22×Dic22—21no—
94C2×C11×Q16—24no—
95C2×C11×Q16C2314yes—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C4×Q8×C11—22no—
99C4×Q8×C11—22no—
100C4×Q8×C11C2314yes—
101C4×Q8×C11C2314yes—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109#67000—22no—
110#67000C2314yes—
111#66999—22no—
112#66999C2314yes—
113Q8×Dic11—22no—
114Q8×Dic11C2314yes—
115C2×#4325—24no—
116C2×#4325—24no—
117C2×#4325C2314yes—
118C2×#4325C2314yes—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4D411yescharacteristic
127C2×(C2×D11)⋊C4D411yescharacteristic
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4D411yescharacteristic
135C2×Dic11⋊C4D411yescharacteristic
136C2×C4×Dic11—21no—
137C2×C4×Dic11C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C2×D88—24no—
141C2×D88C2314yes—
142#66949—28no—
143#66948—22no—
144#66948C2314yes—
145#66947—28no—
146#66946—28no—
147#66946—22no—
148#66946C2314yes—
149C4⋊C4×D11—22no—
150C4⋊C4×D11—28no—
151C4⋊C4×D11C2314yes—
152#66941—22no—
153#66941C2314yes—
154#66929—28no—
155#66928—28no—
156C4×D44—22no—
157C4×D44—22no—
158C4×D44—28no—
159C4×D44C2314yes—
160C4×D44C2314yes—
161#66925—28no—
162#66925D414yes—
163#66925C2314yes—
164C11×#106C2314yes—
165C11×#103C2314yes—
166C11×#103C2314yes—
167C11×#97C2314yes—
168#66899C2314yes—
169#66899C2314yes—
170#66885C2314yes—
171#66885C2314yes—
172(C2×D11)⋊C8C2314yes—
173(C2×D11)⋊C8C2314yes—
174#66881C2314yes—
175Dic11⋊C8C2314yes—
176Dic11⋊C8C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66872C2314yes—
180#66872C2314yes—
181C4×C11⋊C8C2314yes—
182C2×#3125—111nomaximal, Sylow
183C23×D11—21no—
184C23×D11—21no—
185C23×D11C2×D411yescharacteristic
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11#4114yes—
192C2×Q8×C11C2412yes—
193C2×Q8×C11C2412yes—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206#4343—216no—
207#4343—28no—
208#4343—28no—
209C2×D44—28no—
210C2×D44—24no—
211C2×D44—24no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—82no—
218C2×D44#4114yes—
219C2×D44C2412yes—
220C2×D44C2412yes—
221C2×C4×D11—28no—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—24no—
227C2×C4×D11—22no—
228C2×C4×D11—22no—
229C2×C4×D11—82no—
230C2×C4×D11—82no—
231C2×C4×D11—82no—
232C2×C4×D11—82no—
233C2×C4×D11C2×D412yes—
234C2×C4×D11C2412yes—
235C2×Dic22—24no—
236C2×Dic22—82no—
237C11×Q16—28no—
238C2×C8×C11—22no—
239C2×C8×C11—22no—
240C2×C8×C11C2412yes—
241C2×C8×C11C2412yes—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4C2412yes—
247C11×C4⋊C4C2412yes—
248C42×C11—24no—
249C42×C11—24no—
250C42×C11C2×D412yes—
251C42×C11C2412yes—
252#4325—28no—
253#4325—28no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4C2×D414yes—
262(C2×D11)⋊C4C2×D414yes—
263C4⋊Dic11—24no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11C2412yes—
267C4⋊Dic11C2412yes—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271Dic11⋊C4C2×D414yes—
272Dic11⋊C4C2×D414yes—
273C4×Dic11—24no—
274C4×Dic11C2×D412yes—
275C4×Dic11C2412yes—
276C2×C11⋊C8—22no—
277C2×C11⋊C8—22no—
278C2×C11⋊C8C2412yes—
279C2×C11⋊C8C2412yes—
280D88—28no—
281C2×#542—111no—
282C2×#520—111no—
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×#441D1111yescharacteristic, complemented
294C2×C4×SD16—111no—
295C2×C4×SD16—111no—
296C2×#433—111no—
297C23×C11C22×D411yescharacteristic
298C22×D11—22no—
299C22×D11—24no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11C22×D412yes—
310Q8×C11—24no—
311Q8×C11—22no—
312Q8×C11—22no—
313Q8×C11—22no—
314Q8×C11—42no—
315Q8×C11C2×#4114yes—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4112yes—
330C2×C4×C11C2×#4112yes—
331C2×C4×C11C2511yescharacteristic
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11C22×D412yes—
340C2×Dic11C22×D412yes—
341C2×Dic11C22×D412yes—
342D44—216no—
343D44—24no—
344D44—22no—
345D44—22no—
346D44—22no—
347D44—42no—
348D44—84no—
349D44C2×#4114yes—
350C4×D11—216no—
351C4×D11—24no—
352C4×D11—22no—
353C4×D11—22no—
354C4×D11—84no—
355C4×D11—84no—
356C4×D11—84no—
357C4×D11—84no—
358Dic22—84no—
359C8×C11—22no—
360C8×C11—22no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C22×#41—111no—
364C22×Q16C2×D1111yescharacteristic
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—118no—
379#520—224no—
380C2×C4×Q8—111no—
381C2×C4×Q8C2×D1111yescharacteristic
382C2×C4×Q8C2×D1111yescharacteristic
383C2×C4×D4—111no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4—221no—
387C2×C4×D4—221no—
388C2×#117—111no—
389C2×#117—221no—
390C22×C4⋊C4—111no—
391C22×C4⋊C4—221no—
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#441C2×D1118yescomplemented
402C4×SD16—118no—
403C4×SD16—118no—
404#433—118no—
405C2×#106—111no—
406C2×#106—111no—
407C2×#106—111no—
408C2×#106C2×D1111yescharacteristic
409C2×C4⋊C8—111no—
410C2×C4⋊C8—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#103C2×D1111yescharacteristic
414C2×#103C2×D1111yescharacteristic
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×C22⋊C8—111no—
420C2×C22⋊C8—111no—
421C2×#97C2×D1111yescharacteristic
422C2×C4×C8—111no—
423C22×C11#52512yes—
424C22×C11#57712yes—
425C22×C11#57712yes—
426C22×C11C23×D411yescharacteristic
427C2×D11—24no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—22no—
431C2×D11—44no—
432C2×D11—48no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—84no—
439C4×C11—24no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11#52512yes—
446C4×C11C22×#4111yescharacteristic
447C4×C11C22×#4111yescharacteristic
448Dic11—22no—
449Dic11—22no—
450Dic11—22no—
451Dic11—42no—
452Dic11—42no—
453C2×#41—114no—
454C2×#41—222no—
455C2×#41—224no—
456C2×#41—224no—
457C22×Q8—221no—
458C22×Q8C22×D1111yescharacteristic
459C22×Q8C22×D1111yescharacteristic
460C22×D4—111no—
461C22×D4—111no—
462C22×D4—221no—
463C22×D4—221no—
464C23×C4—111no—
465C23×C4—221no—
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4—221no—
470C2×Q16—24no—
471C2×Q16C22×D1114yes—
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×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
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—228no—
491C22⋊Q8—222no—
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—114no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—228no—
504C4×D4—222no—
505C4×D4—228no—
506C4×D4—222no—
507C4×D4—222no—
508#117—114no—
509#117—114no—
510#117—228no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—114no—
518C2×C4⋊C4—228no—
519C2×C4⋊C4—222no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—111no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C42—21no—
536C2×C42—21no—
537C2×C42—111no—
538C2×C42—221no—
539C2×C42C22×D1111yescharacteristic
540#106—114no—
541#106—114no—
542#106—114no—
543#106C22×D1114yes—
544C4⋊C8—114no—
545C4⋊C8—114no—
546#103—114no—
547#103—114no—
548#103C22×D1114yes—
549#103C22×D1114yes—
550#102—114no—
551#102—114no—
552#102—114no—
553#102—114no—
554C22⋊C8—114no—
555C22⋊C8—114no—
556#97C22×D1114yes—
557C4×C8—114no—
558C2×C11#312514yescomplemented
559C2×C11C2×#52511yescharacteristic
560C2×C11C2×#57711yescharacteristic
561C2×C11C2×#57711yescharacteristic
562D11—42no—
563D11—44no—
564D11—82no—
565C24—111no—
566C24—221no—
567C24—221no—
568#41—228no—
569#41—2216no—
570#41—228no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—224no—
577C2×Q8—882no—
578C2×Q8#433914yes—
579C2×Q8C23×D1112yes—
580C2×Q8C23×D1112yes—
581C2×D4—114no—
582C2×D4—112no—
583C2×D4—112no—
584C2×D4—224no—
585C2×D4—228no—
586C2×D4—224no—
587C2×D4—222no—
588C2×D4—222no—
589C2×D4—221no—
590C2×D4—221no—
591C2×D4—222no—
592C2×D4—882no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—224no—
603C22×C4—224no—
604C22×C4—228no—
605C22×C4—224no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—224no—
611C22×C4—224no—
612C22×C4—882no—
613C22×C4—882no—
614C22×C4—882no—
615C22×C4—882no—
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619Q16—28no—
620SD16—228no—
621SD16—228no—
622D8—228no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8C23×D1112yes—
630C2×C8C23×D1112yes—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—114no—
636C4⋊C4—114no—
637C4⋊C4—112no—
638C4⋊C4—112no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4C23×D1112yes—
646C4⋊C4C23×D1112yes—
647C22⋊C4—114no—
648C22⋊C4—114no—
649C22⋊C4—224no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C42—24no—
657C42—24no—
658C42—112no—
659C42—112no—
660C42—224no—
661C42D4×D1112yes—
662C42C23×D1112yes—
663C11C2×#312511yescharacteristic, complemented, Sylow
664C23—112no—
665C23—222no—
666C23—222no—
667C23—224no—
668C23—222no—
669C23—222no—
670C23—222no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23C2×D4×D1111yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—42no—
682Q8—884no—
683Q8C2×#433914yes—
684D4—114no—
685D4—2216no—
686D4—224no—
687D4—222no—
688D4—222no—
689D4—222no—
690D4—442no—
691D4—884no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—112no—
703C2×C4—112no—
704C2×C4—112no—
705C2×C4—2216no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—224no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—884no—
717C2×C4—884no—
718C2×C4—884no—
719C2×C4—884no—
720C2×C4C2×#433912yes—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1112yes—
723C2×C4C2×D4×D1111yescharacteristic
724C2×C4#41×D1112yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—222no—
729C8—222no—
730C22—224no—
731C22—222no—
732C22—222no—
733C22—222no—
734C22—444no—
735C22—448no—
736C22—442no—
737C22—442no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—884no—
742C22#1062307812yes—
743C22#1062330912yes—
744C22#1062330912yes—
745C22C22×D4×D1111yescharacteristic
746C4—24no—
747C4—22no—
748C4—22no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—222no—
753C4—222no—
754C4—222no—
755C4—442no—
756C4—442no—
757C4#1062307812yes—
758C4C22×#433911yescharacteristic
759C4C2×#41×D1111yescharacteristic
760C2—442no—
761C2—444no—
762C2—882no—
763C2#1307889114yesdirect product factor
764C2C2×#1062307811yescharacteristic
765C2C2×#1062330911yescharacteristic
766C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#441C2
socleC23×C11C22×D4
prime radicalC2×#10622424C2
hypercenterC2×#441D11
hypocenterC11C2×#3125
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×#10623113C2semidirect
2. C2×#10623105C2semidirect
3. #13078891C2direct (N × H)
4. C2×#10622476C2semidirect
5. C2×#10622418C2semidirect
6. C2×#10622404C2semidirect
7. C2×#10622483C2semidirect
8. C2×#10622798C2semidirect
9. C2×#10622432C2semidirect
10. C2×#10622800C2semidirect
12. C2×#10622324C2semidirect
13. C2×C4×#4325C2semidirect
14. C2×C4×#4325C2semidirect
15. C2×#10622322C2semidirect
16. C2×C11×#441C2semidirect
28. #10623113C22semidirect
30. #10623105C22semidirect
46. C11×#441C22semidirect
53. #10622800C22semidirect
54. #10622798C22semidirect
62. C4×#4325C22semidirect
63. C4×#4325C22semidirect
69. #10622483C22semidirect
70. #10622476C22semidirect
71. #10622432C22semidirect
73. #10622418C22semidirect
74. #10622404C22semidirect
75. #10622324C22semidirect
76. #10622322C22semidirect
293. C2×#441D11semidirect
401. #441C2×D11semidirect
558. C2×C11#3125semidirect
663. C11C2×#3125semidirect
763. C2#13078891direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231132
C2×#106231052
#130788912
C2×#106224762
C2×#106224182
C2×#106224042
C2×#106224832
C2×#106227982
C2×#106224322
C2×#106228002
C2×#106224242
C2×#106223242
C2×C4×#43252
C2×#106223222
C2×C11×#4412
C2×#312511