Finite Group Databasebeta

← C2×#13078903 #15622115

Subgroups — C2×#13078903 #15622115

Order 2816.

2122 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×#10623150C211yesmaximal, characteristic
2C2×#10623047C211yesmaximal, characteristic, complemented
3#13078903C2116yesmaximal, direct product factor
4C2×#10622616C211yesmaximal, characteristic, complemented
5C2×#10622470C211yesmaximal, characteristic, complemented
6C2×#10622490C211yesmaximal, characteristic, complemented
7C2×#10622375C211yesmaximal, characteristic, complemented
8C2×#10622375C211yesmaximal, characteristic, complemented
9C2×#10622351C211yesmaximal, characteristic, complemented
10C2×#10622653C211yesmaximal, characteristic, complemented
11C2×#10622502C211yesmaximal, characteristic, complemented
12C2×#10622370C211yesmaximal, characteristic, complemented
13C2×#10622371C211yesmaximal, characteristic, complemented
14C2×#10622465C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#482C211yesmaximal, characteristic, complemented
17C23×Dic22C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#66993C2211yescharacteristic
21C2×#66992—21no—
22C2×#66991—21no—
23C2×D4×Dic11C2211yescharacteristic
24C22×#4324C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C2×#66983C2211yescharacteristic
27C2×#66979C2211yescharacteristic
28C22×#4314C2211yescharacteristic
29C22×#4314C2211yescharacteristic
30#10623150—24no—
31#10623150C2218yes—
32#10623047—24no—
33#10623047C2218yescomplemented
34C2×#66946C2211yescharacteristic
35C2×#66943C2211yescharacteristic
36C2×#66940C2211yescharacteristic
37C2×#66940C2211yescharacteristic
38C2×#66940C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66939—21no—
41C2×#66936—21no—
42C2×#66930—21no—
43C2×#66930—21no—
44C2×C4×Dic22—21no—
45C2×C4×Dic22—21no—
46C11×#482C2218yescomplemented
47C2×C11×#107C2211yescharacteristic
48C2×C11×#106C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×#66880C2211yescharacteristic
54C2×#66880C2211yescharacteristic
55C2×#66879C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622653C2218yescomplemented
60#10622616C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622502C2218yescomplemented
68#10622490C2218yescomplemented
69#10622470C2218yescomplemented
70#10622465C2218yescomplemented
71#10622375C2218yescomplemented
72#10622375C2218yescomplemented
73#10622371C2218yescomplemented
74#10622370C2218yescomplemented
75#10622351C2218yescomplemented
76#10622333C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C23×Dic11—21no—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×Dic22—21no—
88C22×Dic22—22no—
89C22×Dic22—24no—
90C22×Dic22—24no—
91C22×Dic22C2314yes—
92C22×Dic22C2311yescharacteristic
93C22×Dic22C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C11×#121—22no—
97C11×#121C2314yes—
98C11×#117—22no—
99C11×#117C2314yes—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C42×C11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11D411yescharacteristic
108C2×C22⋊Dic11D411yescharacteristic
109#66993—22no—
110#66993C2314yes—
111#66992—28no—
112#66991—28no—
113D4×Dic11—22no—
114D4×Dic11C2314yes—
115C2×#4324—24no—
116C2×#4324—24no—
117C2×#4324C2314yes—
118C2×#4324C2314yes—
119#66983—22no—
120#66983C2314yes—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123#66979D414yes—
124#66979C2314yes—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11D411yescharacteristic
127C2×C4⋊Dic11D411yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C2×#4314—24no—
143C2×#4314—24no—
144C2×#4314C2314yes—
145C2×#4314C2314yes—
146#66946—22no—
147#66946C2314yes—
148#66943—22no—
149#66943C2314yes—
150#66940—22no—
151#66940—22no—
152#66940—22no—
153#66940—22no—
154#66940C2314yes—
155#66940C2314yes—
156#66940C2314yes—
157#66940C2314yes—
158#66939—28no—
159#66936—28no—
160#66930—28no—
161#66930—28no—
162C4×Dic22—28no—
163C4×Dic22—28no—
164C11×#107C2314yes—
165C11×#106C2314yes—
166C11×#102C2314yes—
167C11×#102C2314yes—
168C11×C22⋊C8C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170#66880C2314yes—
171#66880C2314yes—
172#66879C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175C8×Dic11C2314yes—
176#66874C2314yes—
177#66874C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182C2×#3126—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11—21no—
186C2×D4×C11—24no—
187C2×D4×C11—21no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—82no—
191C2×D4×C11C2412yes—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—82no—
205C2×C22⋊D11—82no—
206C2×C22⋊D11—82no—
207C22×Dic11—28no—
208C22×Dic11—24no—
209C22×Dic11—24no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—82no—
214C22×Dic11C2×D411yescharacteristic
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218C2×D44—21no—
219C2×D44—22no—
220C2×D44—22no—
221C2×D44C2412yes—
222C2×C4×D11—24no—
223C2×C4×D11—82no—
224C2×Dic22—28no—
225C2×Dic22—216no—
226C2×Dic22—28no—
227C2×Dic22—28no—
228C2×Dic22—24no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—22no—
232C2×Dic22—22no—
233C2×Dic22#4114yes—
234C2×Dic22#4114yes—
235C2×Dic22C2412yes—
236C2×Dic22C2412yes—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11C2412yes—
240C2×C8×C11C2412yes—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C4⋊C4C2412yes—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C42×C11—24no—
250C22⋊Dic11—24no—
251C22⋊Dic11C2×D414yes—
252C22⋊Dic11C2×D414yes—
253#4324—28no—
254#4324—28no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257C4⋊Dic11—24no—
258C4⋊Dic11—21no—
259C4⋊Dic11C2×D414yes—
260C4⋊Dic11C2×D414yes—
261C4⋊Dic11C2412yes—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267C4×Dic11—24no—
268C4×Dic11—24no—
269C4×Dic11—24no—
270C4×Dic11—24no—
271C4×Dic11C2×D412yes—
272C4×Dic11C2×D412yes—
273C4×Dic11C2412yes—
274C4×Dic11C2412yes—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279#4314—28no—
280#4314—28no—
281C2×#540—111no—
282C2×#519—111no—
283#3126—1116no—
284C2×#482—111no—
285C2×#482D1111yescharacteristic, complemented
286C2×#479—111no—
287C2×#479—111no—
288C2×#460—111no—
289C2×#460—111no—
290C2×#448—111no—
291C2×#448—111no—
292C2×#440—111no—
293C2×#440—111no—
294C2×C4×SD16—111no—
295C2×C4×SD16—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—22no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—42no—
313D4×C11—84no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C2×#4112yes—
327C2×C4×C11C2×#4112yes—
328C2×C4×C11C2511yescharacteristic
329C22⋊D11—84no—
330C22⋊D11—84no—
331C22⋊D11—84no—
332C2×Dic11—216no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—42no—
343C2×Dic11—84no—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346C2×Dic11C22×D412yes—
347C2×Dic11C22×D412yes—
348D44—22no—
349D44—22no—
350D44—42no—
351C4×D11—84no—
352Dic22—216no—
353Dic22—24no—
354Dic22—24no—
355Dic22—22no—
356Dic22—22no—
357Dic22C2×#4114yes—
358Dic22C2×#4114yes—
359C8×C11—22no—
360C8×C11—22no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C23×Q8—111no—
364C22×SD16—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×SD16—111no—
368#540—118no—
369#540—224no—
370C2×#127—111no—
371C2×#125—111no—
372C2×#123—221no—
373C2×#123—221no—
374C2×#121—111no—
375C2×#121—221no—
376C2×#121—221no—
377C2×#121C2×D1111yescharacteristic
378#519—118no—
379#519—224no—
380C2×C4×Q8—111no—
381C2×C4×Q8—111no—
382C2×C4×Q8—111no—
383C2×C4×Q8—111no—
384C2×C4×Q8—221no—
385C2×C4×Q8—221no—
386C2×C4×D4—111no—
387C2×C4×D4—111no—
388C2×#117—111no—
389C2×#117—221no—
390C2×#117—221no—
391C2×#117C2×D1111yescharacteristic
392#482—118no—
393#482C2×D1118yescomplemented
394#479—118no—
395#479—118no—
396#460—118no—
397#460—118no—
398#448—118no—
399#448—118no—
400#440—118no—
401#440—118no—
402C4×SD16—118no—
403C4×SD16—118no—
404#433—118no—
405C2×#107—111no—
406C2×#107C2×D1111yescharacteristic
407C2×#106—111no—
408C2×#106C2×D1111yescharacteristic
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×#102C2×D1111yescharacteristic
418C2×#102C2×D1111yescharacteristic
419C2×C22⋊C8—111no—
420C2×C22⋊C8C2×D1111yescharacteristic
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#57712yes—
433C22×C11#57712yes—
434C22×C11C23×D411yescharacteristic
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—84no—
439C4×C11—22no—
440C4×C11—42no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11#52512yes—
444C4×C11C22×#4111yescharacteristic
445C4×C11C22×#4111yescharacteristic
446Dic11—24no—
447Dic11—24no—
448Dic11—22no—
449Dic11—22no—
450Dic11—22no—
451Dic11—22no—
452Dic11—42no—
453C22×Q8—111no—
454C22×Q8—111no—
455C22×Q8—114no—
456C22×Q8—224no—
457C22×Q8—224no—
458C22×Q8—221no—
459C22×Q8—222no—
460C22×D4—21no—
461C22×D4—111no—
462C22×D4—221no—
463C22×D4—221no—
464C22×D4—221no—
465C22×D4C22×D1111yescharacteristic
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4C22×D1111yescharacteristic
470C2×SD16—114no—
471C2×SD16—114no—
472C2×SD16—114no—
473C2×SD16—114no—
474C2×SD16—224no—
475C2×SD16—224no—
476C2×SD16—224no—
477C2×SD16—224no—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482#127—114no—
483#127—222no—
484#125—114no—
485#125—222no—
486#123—228no—
487#123—228no—
488#121—22no—
489#121—114no—
490#121—228no—
491#121—228no—
492#121—222no—
493#121C22×D1114yes—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—114no—
497C4×Q8—114no—
498C4×Q8—228no—
499C4×Q8—228no—
500C4×Q8—222no—
501C4×Q8—222no—
502C4×Q8—222no—
503C4×Q8—222no—
504C4×D4—114no—
505C4×D4—114no—
506C4×D4—222no—
507C4×D4—222no—
508#117—22no—
509#117—114no—
510#117—114no—
511#117—228no—
512#117—228no—
513#117C22×D1114yes—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—111no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C42—21no—
534C2×C42—111no—
535C2×C42—111no—
536C2×C42—221no—
537C2×C42—221no—
538C2×C42—221no—
539C2×C42—221no—
540#107—114no—
541#107C22×D1114yes—
542#106—114no—
543#106C22×D1114yes—
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#102C22×D1114yes—
553#102C22×D1114yes—
554C22⋊C8—114no—
555C22⋊C8C22×D1114yes—
556#97—114no—
557C4×C8—114no—
558C2×C11—42no—
559C2×C11—82no—
560C2×C11#312614yescomplemented
561C2×C11C2×#52511yescharacteristic
562C2×C11C2×#57711yescharacteristic
563C2×C11C2×#57711yescharacteristic
564D11—82no—
565C24—21no—
566C24—221no—
567C24D4×D1111yescharacteristic
568C2×Q8—114no—
569C2×Q8—114no—
570C2×Q8—112no—
571C2×Q8—112no—
572C2×Q8—228no—
573C2×Q8—228no—
574C2×Q8—228no—
575C2×Q8—2216no—
576C2×Q8—224no—
577C2×Q8—221no—
578C2×Q8—221no—
579C2×Q8—222no—
580C2×Q8—222no—
581C2×D4—24no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—82no—
586C2×D4—112no—
587C2×D4—224no—
588C2×D4—224no—
589C2×D4—224no—
590C2×D4—221no—
591C2×D4—222no—
592C2×D4—222no—
593C2×D4—882no—
594C2×D4—882no—
595C2×D4—882no—
596C2×D4C23×D1112yes—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—111no—
606C22×C4—224no—
607C22×C4—224no—
608C22×C4—228no—
609C22×C4—224no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—882no—
614C22×C4—882no—
615C22×C4D4×D1112yes—
616C22×C4D4×D1111yescharacteristic
617C22×C4C23×D1112yes—
618C22×C4C23×D1111yescharacteristic
619SD16—228no—
620SD16—228no—
621SD16—228no—
622SD16—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—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—114no—
635C4⋊C4—114no—
636C4⋊C4—112no—
637C4⋊C4—224no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—221no—
644C4⋊C4C23×D1112yes—
645C4⋊C4C23×D1112yes—
646C4⋊C4C23×D1112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—114no—
650C22⋊C4—114no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C42—24no—
655C42—112no—
656C42—112no—
657C42—112no—
658C42—112no—
659C42—224no—
660C42—224no—
661C42—224no—
662C42—224no—
663C11C2×#312611yescharacteristic, complemented, Sylow
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—222no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23C2×D4×D1112yes—
676C23C2×D4×D1111yescharacteristic
677Q8—114no—
678Q8—114no—
679Q8—2216no—
680Q8—224no—
681Q8—224no—
682Q8—222no—
683Q8—222no—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—84no—
688D4—222no—
689D4—222no—
690D4—442no—
691D4—884no—
692D4—884no—
693D4—884no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—112no—
705C2×C4—112no—
706C2×C4—112no—
707C2×C4—112no—
708C2×C4—2216no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—224no—
714C2×C4—224no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—442no—
719C2×C4—884no—
720C2×C4—884no—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1111yescharacteristic
723C2×C4#41×D1112yes—
724C2×C4#41×D1112yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—222no—
729C8—222no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—884no—
742C22#1062318712yes—
743C22#1062330112yes—
744C22#1062330612yes—
745C22C22×D4×D1111yescharacteristic
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—222no—
751C4—222no—
752C4—222no—
753C4—222no—
754C4—224no—
755C4—224no—
756C4—442no—
757C4#1062318712yes—
758C4C2×#41×D1111yescharacteristic
759C4C2×#41×D1111yescharacteristic
760C2—42no—
761C2—82no—
762C2—882no—
763C2#1307890314yesdirect product factor
764C2C2×#1062318711yescharacteristic
765C2C2×#1062330111yescharacteristic
766C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#482C2
socleC23×C11C22×D4
prime radicalC2×#10623150C2
hypercenterC2×#482D11
hypocenterC11C2×#3126
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#10623047C2semidirect
3. #13078903C2direct (N × H)
4. C2×#10622616C2semidirect
5. C2×#10622470C2semidirect
6. C2×#10622490C2semidirect
7. C2×#10622375C2semidirect
8. C2×#10622375C2semidirect
9. C2×#10622351C2semidirect
10. C2×#10622653C2semidirect
11. C2×#10622502C2semidirect
12. C2×#10622370C2semidirect
13. C2×#10622371C2semidirect
14. C2×#10622465C2semidirect
15. C2×#10622333C2semidirect
16. C2×C11×#482C2semidirect
33. #10623047C22semidirect
46. C11×#482C22semidirect
59. #10622653C22semidirect
60. #10622616C22semidirect
67. #10622502C22semidirect
68. #10622490C22semidirect
69. #10622470C22semidirect
70. #10622465C22semidirect
71. #10622375C22semidirect
72. #10622375C22semidirect
73. #10622371C22semidirect
74. #10622370C22semidirect
75. #10622351C22semidirect
76. #10622333C22semidirect
285. C2×#482D11semidirect
393. #482C2×D11semidirect
560. C2×C11#3126semidirect
663. C11C2×#3126semidirect
763. C2#13078903direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231502
C2×#106230472
#130789032
C2×#106226162
C2×#106224702
C2×#106224902
C2×#106223752
C2×#106223512
C2×#106226532
C2×#106225022
C2×#106223702
C2×#106223712
C2×#106224652
C2×#106223332
C2×C11×#4822
C2×#312611