Finite Group Databasebeta

← C2×#13081666 #15634762

Subgroups — C2×#13081666 #15634762

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×#10623212C211yesmaximal, characteristic
2C2×#10623252C211yesmaximal, characteristic, complemented
3#13081666C2116yesmaximal, direct product factor
4C2×#10622803C211yesmaximal, characteristic, complemented
5C2×#10622788C211yesmaximal, characteristic
6C2×#10622798C211yesmaximal, characteristic, complemented
7C2×#10622667C211yesmaximal, characteristic, complemented
8C2×#10622795C211yesmaximal, characteristic, complemented
9C2×#10622776C211yesmaximal, characteristic
10C2×#10622775C211yesmaximal, characteristic, complemented
11C2×#10622696C211yesmaximal, characteristic, complemented
12C2×#10622314C211yesmaximal, characteristic, complemented
13C2×#10622323C211yesmaximal, characteristic, complemented
14C2×#10622777C211yesmaximal, characteristic, complemented
15C2×Q16×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#497C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×#67000C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27C2×#66997C2211yescharacteristic
28C2×#66997C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C2×#66993C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C22×#4324C2211yescharacteristic
35C22×#4314C2211yescharacteristic
36#10623252—24no—
37#10623252C2218yescomplemented
38#10623212—24no—
39#10623212C2218yes—
40C2×#66943—21no—
41C2×#66942—21no—
42C2×#66942—21no—
43C2×#66940—21no—
44C2×#66939—21no—
45C2×#66938—21no—
46C2×#66936—21no—
47C2×(C22⋊D11)⋊C4—21no—
48C2×C4×D44C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C11×#497C2218yescomplemented
52C2×C11×#97C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57#10622803C2218yescomplemented
58#10622798C2218yescomplemented
59Q16×Dic11C2218yescomplemented
60#10622795C2218yescomplemented
61#10622788C2218yes—
62#10622777C2218yescomplemented
63#10622776C2218yes—
64#10622775C2218yescomplemented
65C2×#66885C2211yescharacteristic
66C2×#66882C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66879C2211yescharacteristic
69C2×Dic11⋊C8C2211yescharacteristic
70C2×Dic11⋊C8C2211yescharacteristic
71C2×C8×Dic11C2211yescharacteristic
72#10622696C2218yescomplemented
73#10622667C2218yescomplemented
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75#10622323C2218yescomplemented
76#10622314C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×Dic22D411yescharacteristic
87C22×Dic22C2311yescharacteristic
88C2×C11×Q16—24no—
89C2×C11×Q16—42no—
90C2×C11×Q16C2314yes—
91C2×C11×Q16C2314yes—
92C2×C11×SD16—24no—
93C2×C11×SD16—42no—
94C2×C11×SD16C2314yes—
95C2×C11×SD16C2314yes—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C11×C4⋊Q8—22no—
99C11×C4⋊Q8C2314yes—
100C11×#124—22no—
101C11×#124C2314yes—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108#67000—22no—
109#67000C2314yes—
110Q8×Dic11—22no—
111Q8×Dic11—22no—
112Q8×Dic11—22no—
113Q8×Dic11C2314yes—
114Q8×Dic11C2314yes—
115Q8×Dic11C2314yes—
116#66997—22no—
117#66997—22no—
118#66997C2314yes—
119#66997C2314yes—
120C2×#4326—42no—
121C2×#4326C2314yes—
122C2×#4325—42no—
123C2×#4325—42no—
124C2×#4325C2314yes—
125C2×#4325C2314yes—
126#66993—22no—
127#66993C2314yes—
128D4×Dic11—22no—
129D4×Dic11C2314yes—
130C2×#4324—42no—
131C2×#4324C2314yes—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11D411yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4D411yescharacteristic
147C2×Dic11⋊C4D411yescharacteristic
148C2×C4×Dic11—21no—
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156C2×#4314—24no—
157C2×#4314C2314yes—
158#66943—28no—
159#66942—28no—
160#66942—28no—
161#66940—28no—
162#66939—28no—
163#66938—28no—
164#66936—28no—
165(C22⋊D11)⋊C4—28no—
166C4×D44—22no—
167C4×D44C2314yes—
168C4×Dic22—22no—
169C4×Dic22D414yes—
170C4×Dic22C2314yes—
171C4×Dic22C2314yes—
172C11×#97C2314yes—
173#66899C2314yes—
174#66899C2314yes—
175#66899C2314yes—
176#66896C2314yes—
177#66885C2314yes—
178#66882C2314yes—
179#66880C2314yes—
180#66879C2314yes—
181Dic11⋊C8C2314yes—
182Dic11⋊C8C2314yes—
183C8×Dic11C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C2×#3400—111nomaximal, Sylow
186C24×C11—21no—
187C23×D11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11C2412yes—
198C2×Q8×C11C2412yes—
199C2×Q8×C11C2412yes—
200C2×D4×C11—21no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11C2412yes—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—82no—
214C22×Dic11—24no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—82no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222C22×Dic11C2×D411yescharacteristic
223C2×D44—21no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44C2412yes—
227C2×C4×D11—24no—
228C2×C4×D11—82no—
229C2×Dic22—24no—
230C2×Dic22—21no—
231C2×Dic22—22no—
232C2×Dic22—22no—
233C2×Dic22C2×D414yes—
234C2×Dic22C2412yes—
235C11×Q16—28no—
236C11×Q16—44no—
237C11×SD16—28no—
238C11×SD16—44no—
239C2×C8×C11—22no—
240C2×C8×C11#4114yes—
241C2×C8×C11C2412yes—
242C2×C8×C11C2412yes—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—24no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C42×C11C2×D412yes—
248C42×C11C2412yes—
249C22⋊Dic11—24no—
250#4326—44no—
251#4325—44no—
252#4325—44no—
253#4324—44no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257C4⋊Dic11—24no—
258C4⋊Dic11—24no—
259C4⋊Dic11—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11C2×D414yes—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4C2×D414yes—
271Dic11⋊C4C2×D414yes—
272C4×Dic11—24no—
273C4×Dic11—24no—
274C4×Dic11—24no—
275C4×Dic11—24no—
276C4×Dic11C2×D412yes—
277C4×Dic11C2×D412yes—
278C4×Dic11C2412yes—
279C4×Dic11C2412yes—
280C2×C11⋊C8—22no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8C2412yes—
283C2×C11⋊C8C2412yes—
284#4314—28no—
285C2×#559—111no—
286C2×#557—111no—
287#3400—1116no—
288C2×#497—111no—
289C2×#497D1111yescharacteristic, complemented
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×#440—111no—
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—22no—
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—42no—
317Q8×C11—42no—
318Q8×C11—42no—
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—42no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4112yes—
334C2×C4×C11H(5,𝔽2)12yes—
335C2×C4×C11C2511yescharacteristic
336C22⋊D11—48no—
337C22⋊D11—84no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—84no—
348C2×Dic11#13714yes—
349C2×Dic11C22×D412yes—
350C2×Dic11C22×D412yes—
351C2×Dic11C22×D412yes—
352C2×Dic11C22×D412yes—
353D44—22no—
354D44—22no—
355D44—42no—
356C4×D11—84no—
357Dic22—28no—
358Dic22—22no—
359Dic22—22no—
360Dic22—42no—
361C8×C11—22no—
362C8×C11C2×#4114yes—
363C11⋊C8—22no—
364C11⋊C8—22no—
365C22×Q16—111no—
366C22×Q16C2×D1111yescharacteristic
367C22×Q16C2×D1111yescharacteristic
368C22×SD16—111no—
369C22×SD16—111no—
370C22×SD16—111no—
371C22×SD16—111no—
372C22×SD16C2×D1111yescharacteristic
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⋊Q8C2×D1111yescharacteristic
381C2×#127—111no—
382C2×#125—221no—
383C2×#125—221no—
384C2×#125—221no—
385C2×#124—111no—
386C2×#124—221no—
387C2×#124C2×D1111yescharacteristic
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—111no—
395C2×C4×Q8—221no—
396C2×C4×D4—111no—
397C2×C4×D4—111no—
398C2×C4×D4—221no—
399#497—118no—
400#497C2×D1118yescomplemented
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#440—118no—
411C4×Q16—118no—
412C2×#107—111no—
413C2×C4⋊C8—111no—
414C2×C4⋊C8—111no—
415C2×C4⋊C8—111no—
416C2×#103—111no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#103—111no—
420C2×#102—111no—
421C2×#102—111no—
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×Q8C22×D1111yescharacteristic
455C22×Q8C22×D1111yescharacteristic
456C22×Q8C22×D1111yescharacteristic
457C22×D4—111no—
458C22×D4—221no—
459C22×D4—221no—
460C22×D4C22×D1111yescharacteristic
461C23×C4—221no—
462C23×C4—221no—
463C2×Q16—24no—
464C2×Q16—42no—
465C2×Q16—114no—
466C2×Q16—442no—
467C2×Q16C22×D1114yes—
468C2×Q16C22×D1114yes—
469C2×SD16—24no—
470C2×SD16—42no—
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×SD16C22×D1114yes—
480C2×SD16C22×D1114yes—
481C22×C8—111no—
482C22×C8—111no—
483C22×C8C22×D1111yescharacteristic
484C22×C8C22×D1111yescharacteristic
485C4⋊Q8—22no—
486C4⋊Q8—114no—
487C4⋊Q8—114no—
488C4⋊Q8—222no—
489C4⋊Q8—222no—
490C4⋊Q8C22×D1114yes—
491#127—114no—
492#127—222no—
493#125—228no—
494#125—228no—
495#125—228no—
496#124—22no—
497#124—114no—
498#124—222no—
499#124—228no—
500#124C22×D1114yes—
501#123—228no—
502#123—228no—
503C4×Q8—114no—
504C4×Q8—114no—
505C4×Q8—114no—
506C4×Q8—114no—
507C4×Q8—114no—
508C4×Q8—114no—
509C4×Q8—222no—
510C4×Q8—222no—
511C4×Q8—222no—
512C4×Q8—228no—
513C4×Q8—222no—
514C4×D4—114no—
515C4×D4—114no—
516C4×D4—222no—
517C4×D4—228no—
518C4×D4—222no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—111no—
522C2×C4⋊C4—111no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—111no—
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⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—221no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C42—111no—
541C2×C42—111no—
542C2×C42—221no—
543C2×C42—221no—
544C2×C42—221no—
545C2×C42—221no—
546C2×C42C22×D1111yescharacteristic
547#107—114no—
548C4⋊C8—114no—
549C4⋊C8—114no—
550C4⋊C8—114no—
551#103—114no—
552#103—114no—
553#103—114no—
554#103—114no—
555#102—114no—
556#102—114no—
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—21no—
570C2×Q8—21no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—114no—
578C2×Q8—112no—
579C2×Q8—224no—
580C2×Q8—221no—
581C2×Q8—222no—
582C2×Q8—222no—
583C2×Q8C23×D1112yes—
584C2×Q8C23×D1112yes—
585C2×Q8C23×D1112yes—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—112no—
590C2×D4—224no—
591C2×D4—224no—
592C2×D4—221no—
593C2×D4—222no—
594C2×D4—222no—
595C2×D4—444no—
596C2×D4—882no—
597C2×D4C23×D1112yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—224no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—224no—
610C22×C4—882no—
611C22×C4—882no—
612C22×C4D4×D1111yescharacteristic
613C22×C4D4×D1111yescharacteristic
614C22×C4C23×D1111yescharacteristic
615Q16—28no—
616Q16—44no—
617Q16—444no—
618SD16—28no—
619SD16—44no—
620SD16—228no—
621SD16—444no—
622SD16—444no—
623SD16—444no—
624C2×C8—22no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8#434114yes—
630C2×C8C23×D1112yes—
631C2×C8C23×D1112yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—114no—
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—224no—
644C4⋊C4—224no—
645C4⋊C4—224no—
646C4⋊C4—221no—
647C4⋊C4—221no—
648C4⋊C4—224no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C42—112no—
656C42—112no—
657C42—112no—
658C42—112no—
659C42—224no—
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—22no—
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—42no—
682Q8—42no—
683Q8—42no—
684Q8—228no—
685Q8—222no—
686Q8—222no—
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—114no—
705C2×C4—112no—
706C2×C4—112no—
707C2×C4—112no—
708C2×C4—112no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—884no—
719C2×C4—884no—
720C2×C4C2×D4×D1112yes—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1111yescharacteristic
723C2×C4C2×#434112yes—
724C2×C4#6703712yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—222no—
728C8—222no—
729C8C2×#434114yes—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—442no—
735C22—442no—
736C22—442no—
737C22—884no—
738C22#1062324912yes—
739C22D11×#13712yes—
740C22#1062330912yes—
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#1062324912yes—
755C4C22×#434111yescharacteristic
756C4C2×#6703711yescharacteristic
757C2—82no—
758C2—882no—
759C2#1308166614yesdirect product factor
760C2C2×#1062324911yescharacteristic
761C2C2×D11×#13711yescharacteristic
762C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#497C2
socleC23×C11C22×D4
prime radicalC2×#66993C22
hypercenterC2×#497D11
hypocenterC11C2×#3400
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
2. C2×#10623252C2semidirect
3. #13081666C2direct (N × H)
4. C2×#10622803C2semidirect
6. C2×#10622798C2semidirect
7. C2×#10622667C2semidirect
8. C2×#10622795C2semidirect
10. C2×#10622775C2semidirect
11. C2×#10622696C2semidirect
12. C2×#10622314C2semidirect
13. C2×#10622323C2semidirect
14. C2×#10622777C2semidirect
15. C2×Q16×Dic11C2semidirect
16. C2×C11×#497C2semidirect
37. #10623252C22semidirect
51. C11×#497C22semidirect
57. #10622803C22semidirect
58. #10622798C22semidirect
59. Q16×Dic11C22semidirect
60. #10622795C22semidirect
62. #10622777C22semidirect
64. #10622775C22semidirect
72. #10622696C22semidirect
73. #10622667C22semidirect
75. #10622323C22semidirect
76. #10622314C22semidirect
289. C2×#497D11semidirect
400. #497C2×D11semidirect
561. C2×C11#3400semidirect
665. C11C2×#3400semidirect
759. C2#13081666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232122
C2×#106232522
#130816662
C2×#106228032
C2×#106227882
C2×#106227982
C2×#106226672
C2×#106227952
C2×#106227762
C2×#106227752
C2×#106226962
C2×#106223142
C2×#106223232
C2×#106227772
C2×Q16×Dic112
C2×C11×#4972
C2×#340011