Finite Group Databasebeta

← C2×#13081670 #15634766

Subgroups — C2×#13081670 #15634766

Order 2816.

1970 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623090C211yesmaximal, characteristic
2C2×#10623098C211yesmaximal, characteristic, complemented
3#13081670C2116yesmaximal, direct product factor
4C2×#10622328C211yesmaximal, characteristic, complemented
5C2×#10622780C211yesmaximal, characteristic, complemented
6C2×#10622788C211yesmaximal, characteristic
7C2×#10622641C211yesmaximal, characteristic, complemented
8C2×#10622380C211yesmaximal, characteristic, complemented
9C2×#10622406C211yesmaximal, characteristic, complemented
10C2×#10622375C211yesmaximal, characteristic
11C2×#10622632C211yesmaximal, characteristic, complemented
12C2×#10622431C211yesmaximal, characteristic, complemented
13C2×#10622314C211yesmaximal, characteristic, complemented
14C2×#10622502C211yesmaximal, characteristic, complemented
15C2×#10622486C211yesmaximal, characteristic, complemented
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66997C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66993C2211yescharacteristic
25C2×#66989C2211yescharacteristic
26C22×#4324C2211yescharacteristic
27C22×#4324C2211yescharacteristic
28C2×#66982—21no—
29C2×C4×C22⋊D11—21no—
30C22×Dic44C2211yescharacteristic
31C22×Dic44C2211yescharacteristic
32C22×#4314C2211yescharacteristic
33C22×#4314C2211yescharacteristic
34#10623098—24no—
35#10623098C2218yescomplemented
36#10623090—24no—
37#10623090C2218yes—
38C2×#66946C2211yescharacteristic
39C2×#66942—21no—
40C2×#66942—21no—
41C2×#66940C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×#66938—21no—
45C2×#66936—21no—
46C2×#66928C2211yescharacteristic
47C2×#66923—21no—
48C2×#66922C2211yescharacteristic
49C2×C4×Dic22—21no—
50C2×C4×Dic22C2211yescharacteristic
51C11×#440C2218yescomplemented
52C2×C11×#107C2211yescharacteristic
53C2×C11×#103C2211yescharacteristic
54C2×C11×#102C2211yescharacteristic
55C2×C11×#97C2211yescharacteristic
56#10622788C2218yes—
57#10622780C2218yescomplemented
58C2×#66879C2211yescharacteristic
59C2×Dic11⋊C8C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×C8×Dic11C2211yescharacteristic
62#10622641C2218yescomplemented
63#10622632C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622502C2218yescomplemented
70#10622486C2218yescomplemented
71#10622431C2218yescomplemented
72#10622406C2218yescomplemented
73#10622380C2218yescomplemented
74#10622375C2218yes—
75#10622328C2218yescomplemented
76#10622314C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×Dic22D411yescharacteristic
85C22×Dic22C2311yescharacteristic
86C22×Dic22C2311yescharacteristic
87C22×Dic22C2311yescharacteristic
88C2×C11×SD16—24no—
89C2×C11×SD16C2314yes—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C4×Q8×C11—22no—
93C4×Q8×C11C2314yes—
94C4×D4×C11—22no—
95C4×D4×C11C2314yes—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104#66997—22no—
105#66997—22no—
106#66997C2314yes—
107#66997C2314yes—
108C2×#4326—42no—
109C2×#4326C2314yes—
110C2×#4325—42no—
111C2×#4325C2314yes—
112#66993—22no—
113#66993C2314yes—
114#66989—22no—
115#66989C2314yes—
116C2×#4324—42no—
117C2×#4324—42no—
118C2×#4324C2314yes—
119C2×#4324C2314yes—
120#66982—28no—
121C4×C22⋊D11—28no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11D411yescharacteristic
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4D411yescharacteristic
136C2×Dic11⋊C4D411yescharacteristic
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11—21no—
140C2×C4×Dic11C2311yescharacteristic
141C2×C4×Dic11C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C2×Dic44—24no—
145C2×Dic44—42no—
146C2×Dic44C2314yes—
147C2×Dic44C2314yes—
148C2×#4314—24no—
149C2×#4314—42no—
150C2×#4314C2314yes—
151C2×#4314C2314yes—
152#66946—22no—
153#66946C2314yes—
154#66942—28no—
155#66942—28no—
156#66940—22no—
157#66940—22no—
158#66940—22no—
159#66940C2314yes—
160#66940C2314yes—
161#66940C2314yes—
162#66938—28no—
163#66936—28no—
164#66928—22no—
165#66928C2314yes—
166#66923—28no—
167#66922—22no—
168#66922C2314yes—
169C4×Dic22—28no—
170C4×Dic22D414yes—
171C4×Dic22C2314yes—
172C11×#107C2314yes—
173C11×#103C2314yes—
174C11×#102C2314yes—
175C11×#97C2314yes—
176#66879C2314yes—
177Dic11⋊C8C2314yes—
178Dic11⋊C8C2314yes—
179C8×Dic11C2314yes—
180#66874C2314yes—
181#66874C2314yes—
182#66874C2314yes—
183#66873C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C2×#3400—111nomaximal, Sylow
186C24×C11—21no—
187C23×D11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11C2412yes—
192C2×D4×C11—21no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11C2412yes—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—24no—
200C22×C4×C11—82no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—82no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215C2×D44—21no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44C2412yes—
219C2×C4×D11—24no—
220C2×C4×D11—82no—
221C2×Dic22—24no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—21no—
225C2×Dic22—22no—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22—22no—
229C2×Dic22—22no—
230C2×Dic22—22no—
231C2×Dic22C2×D414yes—
232C2×Dic22C2412yes—
233C2×Dic22C2412yes—
234C2×Dic22C2412yes—
235C11×SD16—28no—
236C2×C8×C11—22no—
237C2×C8×C11#4114yes—
238C2×C8×C11C2412yes—
239C2×C8×C11C2412yes—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4C2412yes—
244C11×C4⋊C4C2412yes—
245C11×C22⋊C4—24no—
246C42×C11—24no—
247C42×C11C2×D412yes—
248C42×C11C2412yes—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251#4326—44no—
252#4325—44no—
253#4324—44no—
254#4324—44no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258C4⋊Dic11—24no—
259C4⋊Dic11—24no—
260C4⋊Dic11C2×D414yes—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4C2×D414yes—
269Dic11⋊C4C2×D414yes—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11—24no—
273C4×Dic11C2×D412yes—
274C4×Dic11C2×D412yes—
275C4×Dic11C2412yes—
276C4×Dic11C2412yes—
277C2×C11⋊C8—22no—
278C2×C11⋊C8—22no—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281Dic44—28no—
282Dic44—44no—
283#4314—28no—
284#4314—44no—
285C2×#559—111no—
286C2×#557—111no—
287#3400—1116no—
288C2×#497—111no—
289C2×#497—111no—
290C2×#492—111no—
291C2×#464—111no—
292C2×#464—111no—
293C2×#462—111no—
294C2×#460—111no—
295C2×#461—111no—
296C2×#461—111no—
297C2×#446—111no—
298C2×#440—111no—
299C2×#440D1111yescharacteristic, complemented
300C2×C4×Q16—111no—
301C23×C11—22no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—42no—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—42no—
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×C11—84no—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4112yes—
329C2×C4×C11H(5,𝔽2)12yes—
330C2×C4×C11C2511yescharacteristic
331C22⋊D11—48no—
332C22⋊D11—84no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11#13714yes—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346C2×Dic11C22×D412yes—
347D44—22no—
348D44—22no—
349D44—42no—
350C4×D11—84no—
351Dic22—28no—
352Dic22—22no—
353Dic22—22no—
354Dic22—22no—
355Dic22—22no—
356Dic22—22no—
357Dic22—22no—
358Dic22—42no—
359Dic22—42no—
360Dic22—42no—
361C8×C11—22no—
362C8×C11C2×#4114yes—
363C11⋊C8—22no—
364C11⋊C8—22no—
365C22×Q16—111no—
366C22×Q16—111no—
367C22×Q16—111no—
368C22×SD16—111no—
369C22×SD16—111no—
370C22×SD16—111no—
371C22×SD16—111no—
372C22×SD16—111no—
373C22×SD16C2×D1111yescharacteristic
374#559—118no—
375#559—224no—
376#557—118no—
377#557—224no—
378C2×C4⋊Q8—111no—
379C2×C4⋊Q8—111no—
380C2×C4⋊Q8—111no—
381C2×#127—111no—
382C2×#125—221no—
383C2×#125—221no—
384C2×#125—221no—
385C2×#124—111no—
386C2×#124—111no—
387C2×#124—221no—
388C2×#123—221no—
389C2×#123—221no—
390C2×C4×Q8—111no—
391C2×C4×Q8—111no—
392C2×C4×Q8—111no—
393C2×C4×Q8—111no—
394C2×C4×Q8—221no—
395C2×C4×Q8C2×D1111yescharacteristic
396C2×C4×D4—111no—
397C2×C4×D4—221no—
398C2×C4×D4C2×D1111yescharacteristic
399#497—118no—
400#497—118no—
401#492—118no—
402#464—118no—
403#464—118no—
404#462—118no—
405#461—118no—
406#461—118no—
407#460—118no—
408#446—118no—
409#440—118no—
410#440C2×D1118yescomplemented
411C4×Q16—118no—
412C2×#107C2×D1111yescharacteristic
413C2×C4⋊C8—111no—
414C2×C4⋊C8—111no—
415C2×C4⋊C8—111no—
416C2×#103—111no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#103C2×D1111yescharacteristic
420C2×#102—111no—
421C2×#102C2×D1111yescharacteristic
422C2×#97—111no—
423C2×#97C2×D1111yescharacteristic
424C2×C4×C8—111no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—84no—
429C22×C11#55012yes—
430C22×C11C2×#13712yes—
431C22×C11#57712yes—
432C22×C11C23×D411yescharacteristic
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—84no—
437C4×C11—22no—
438C4×C11—22no—
439C4×C11—42no—
440C4×C11—42no—
441C4×C11—42no—
442C4×C11#55012yes—
443C4×C11C22×#4111yescharacteristic
444C4×C11C2×H(5,𝔽2)11yescharacteristic
445Dic11—22no—
446Dic11—22no—
447Dic11—22no—
448Dic11—42no—
449Dic11—42no—
450Dic11—42no—
451Dic11C2×#13714yes—
452C22×Q8—111no—
453C22×Q8—111no—
454C22×Q8—111no—
455C22×Q8—111no—
456C22×Q8C22×D1111yescharacteristic
457C22×D4—111no—
458C22×D4—221no—
459C22×D4—221no—
460C22×D4C22×D1111yescharacteristic
461C23×C4—21no—
462C23×C4—221no—
463C2×Q16—114no—
464C2×Q16—114no—
465C2×Q16—114no—
466C2×Q16—224no—
467C2×Q16—442no—
468C2×Q16—442no—
469C2×SD16—24no—
470C2×SD16—114no—
471C2×SD16—114no—
472C2×SD16—114no—
473C2×SD16—114no—
474C2×SD16—114no—
475C2×SD16—224no—
476C2×SD16—442no—
477C2×SD16—442no—
478C2×SD16—442no—
479C2×SD16—442no—
480C2×SD16C22×D1114yes—
481C22×C8—111no—
482C22×C8—111no—
483C22×C8C22×D1111yescharacteristic
484C22×C8C22×D1111yescharacteristic
485C4⋊Q8—114no—
486C4⋊Q8—114no—
487C4⋊Q8—114no—
488C4⋊Q8—222no—
489C4⋊Q8—222no—
490C4⋊Q8—222no—
491#127—114no—
492#127—222no—
493#125—228no—
494#125—228no—
495#125—228no—
496#124—114no—
497#124—114no—
498#124—222no—
499#124—228no—
500#124—222no—
501#123—228no—
502#123—228no—
503C4×Q8—22no—
504C4×Q8—114no—
505C4×Q8—114no—
506C4×Q8—114no—
507C4×Q8—114no—
508C4×Q8—114no—
509C4×Q8—228no—
510C4×Q8—222no—
511C4×Q8—222no—
512C4×Q8—222no—
513C4×Q8C22×D1114yes—
514C4×D4—22no—
515C4×D4—114no—
516C4×D4—222no—
517C4×D4—228no—
518C4×D4C22×D1114yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—111no—
522C2×C4⋊C4—111no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—221no—
525C2×C4⋊C4—221no—
526C2×C4⋊C4—221no—
527C2×C4⋊C4—221no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4C22×D1111yescharacteristic
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—221no—
536C2×C22⋊C4—221no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C42—21no—
541C2×C42—111no—
542C2×C42—111no—
543C2×C42—221no—
544C2×C42—221no—
545C2×C42—221no—
546C2×C42C22×D1111yescharacteristic
547#107C22×D1114yes—
548C4⋊C8—114no—
549C4⋊C8—114no—
550C4⋊C8—114no—
551#103—114no—
552#103—114no—
553#103—114no—
554#103C22×D1114yes—
555#102—114no—
556#102C22×D1114yes—
557#97—114no—
558#97C22×D1114yes—
559C4×C8—114no—
560C2×C11—82no—
561C2×C11#340014yescomplemented
562C2×C11C2×#55011yescharacteristic
563C2×C11C22×#13711yescharacteristic
564C2×C11C2×#57711yescharacteristic
565D11—82no—
566C24—21no—
567C24—221no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—114no—
572C2×Q8—112no—
573C2×Q8—112no—
574C2×Q8—112no—
575C2×Q8—224no—
576C2×Q8—221no—
577C2×Q8—221no—
578C2×Q8—221no—
579C2×Q8—222no—
580C2×Q8—222no—
581C2×Q8—222no—
582C2×Q8—222no—
583C2×Q8—222no—
584C2×Q8—222no—
585C2×Q8C23×D1112yes—
586C2×D4—22no—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—112no—
590C2×D4—224no—
591C2×D4—224no—
592C2×D4—222no—
593C2×D4—221no—
594C2×D4—222no—
595C2×D4—444no—
596C2×D4—882no—
597C2×D4C23×D1112yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—82no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—111no—
606C22×C4—111no—
607C22×C4—224no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—882no—
612C22×C4D4×D1111yescharacteristic
613C22×C4D4×D1111yescharacteristic
614C22×C4C23×D1111yescharacteristic
615Q16—228no—
616Q16—444no—
617Q16—444no—
618SD16—28no—
619SD16—228no—
620SD16—444no—
621SD16—444no—
622SD16—444no—
623SD16—444no—
624C2×C8—22no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8#433914yes—
630C2×C8C23×D1112yes—
631C2×C8C23×D1112yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—114no—
636C4⋊C4—114no—
637C4⋊C4—114no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—224no—
644C4⋊C4—224no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4C23×D1112yes—
648C4⋊C4C23×D1112yes—
649C22⋊C4—24no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C42—24no—
656C42—112no—
657C42—112no—
658C42—112no—
659C42—112no—
660C42—224no—
661C42—224no—
662C42—224no—
663C42D4×D1112yes—
664C42C23×D1112yes—
665C11C2×#340011yescharacteristic, complemented, Sylow
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—222no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23C2×D4×D1111yescharacteristic
675Q8—22no—
676Q8—22no—
677Q8—42no—
678Q8—228no—
679Q8—222no—
680Q8—222no—
681Q8—222no—
682Q8—222no—
683Q8—222no—
684Q8—222no—
685Q8—442no—
686Q8—442no—
687Q8—442no—
688D4—22no—
689D4—22no—
690D4—42no—
691D4—222no—
692D4—222no—
693D4—448no—
694D4—442no—
695D4—884no—
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—84no—
705C2×C4—114no—
706C2×C4—112no—
707C2×C4—112no—
708C2×C4—112no—
709C2×C4—112no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—884no—
720C2×C4C2×#433912yes—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1112yes—
723C2×C4C2×D4×D1111yescharacteristic
724C2×C4#6704212yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—222no—
728C8—222no—
729C8C2×#433914yes—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—442no—
735C22—442no—
736C22—442no—
737C22—884no—
738C22#1062308412yes—
739C22#1062330612yes—
740C22D11×#13712yes—
741C22C22×D4×D1111yescharacteristic
742C4—22no—
743C4—22no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—114no—
748C4—222no—
749C4—222no—
750C4—222no—
751C4—442no—
752C4—442no—
753C4—442no—
754C4#1062308412yes—
755C4C22×#433911yescharacteristic
756C4C2×#6704211yescharacteristic
757C2—82no—
758C2—882no—
759C2#1308167014yesdirect product factor
760C2C2×#1062308411yescharacteristic
761C2C2×D11×#13711yescharacteristic
762C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC2×#66993C22
hypercenterC2×#440D11
hypocenterC11C2×#3400
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#10623098C2semidirect
3. #13081670C2direct (N × H)
4. C2×#10622328C2semidirect
5. C2×#10622780C2semidirect
7. C2×#10622641C2semidirect
8. C2×#10622380C2semidirect
9. C2×#10622406C2semidirect
11. C2×#10622632C2semidirect
12. C2×#10622431C2semidirect
13. C2×#10622314C2semidirect
14. C2×#10622502C2semidirect
15. C2×#10622486C2semidirect
16. C2×C11×#440C2semidirect
35. #10623098C22semidirect
51. C11×#440C22semidirect
57. #10622780C22semidirect
62. #10622641C22semidirect
63. #10622632C22semidirect
69. #10622502C22semidirect
70. #10622486C22semidirect
71. #10622431C22semidirect
72. #10622406C22semidirect
73. #10622380C22semidirect
75. #10622328C22semidirect
76. #10622314C22semidirect
299. C2×#440D11semidirect
410. #440C2×D11semidirect
561. C2×C11#3400semidirect
665. C11C2×#3400semidirect
759. C2#13081670direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230902
C2×#106230982
#130816702
C2×#106223282
C2×#106227802
C2×#106227882
C2×#106226412
C2×#106223802
C2×#106224062
C2×#106223752
C2×#106226322
C2×#106224312
C2×#106223142
C2×#106225022
C2×#106224862
C2×C11×#4402
C2×#340011