Finite Group Databasebeta

← C2×#13081683 #15634780

Subgroups — C2×#13081683 #15634780

Order 2816.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic, complemented
2C2×#10623099C211yesmaximal, characteristic, complemented
3#13081683C2116yesmaximal, direct product factor
4C2×#10622803C211yesmaximal, characteristic, complemented
5C2×#10622325C211yesmaximal, characteristic
6C2×#10622804C211yesmaximal, characteristic, complemented
7C2×#10622411C211yesmaximal, characteristic, complemented
8C2×#10622641C211yesmaximal, characteristic, complemented
9C2×#10622640C211yesmaximal, characteristic, complemented
10C2×#10622432C211yesmaximal, characteristic, complemented
11C2×#10622432C211yesmaximal, characteristic, complemented
12C2×#10622431C211yesmaximal, characteristic, complemented
13C2×#10622314C211yesmaximal, characteristic, complemented
14C2×#10622482C211yesmaximal, characteristic, complemented
15C2×#10622465C211yesmaximal, characteristic, complemented
16C2×C11×#441C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×#67000C2211yescharacteristic
23C2×#66997C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C22×#4325C2211yescharacteristic
26C22×#4325C2211yescharacteristic
27C22×#4325C2211yescharacteristic
28C22×D88C2211yescharacteristic
29C22×D88C2211yescharacteristic
30C22×#4314C2211yescharacteristic
31C22×#4314C2211yescharacteristic
32#10623116—24no—
33#10623116C2218yescomplemented
34#10623099—24no—
35#10623099C2218yescomplemented
36C2×#66951—21no—
37C2×#66949—21no—
38C2×#66947—21no—
39C2×#66947—21no—
40C2×#66946C2211yescharacteristic
41C2×#66946C2211yescharacteristic
42C2×#66946C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×#66929—21no—
45C2×#66928—21no—
46C2×#66928C2211yescharacteristic
47C2×#66927C2211yescharacteristic
48C2×C4×D44—21no—
49C2×#66925—21no—
50C2×C4×Dic22C2211yescharacteristic
51C11×#441C2218yescomplemented
52C2×C11×#106C2211yescharacteristic
53C2×C11×#103C2211yescharacteristic
54C2×C11×#103C2211yescharacteristic
55C2×C11×#97C2211yescharacteristic
56#10622804C2218yescomplemented
57#10622803C2218yescomplemented
58C2×#66879C2211yescharacteristic
59C2×Dic11⋊C8C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×C8×Dic11C2211yescharacteristic
62#10622641C2218yescomplemented
63#10622640C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622482C2218yescomplemented
70#10622465C2218yescomplemented
71#10622432C2218yescomplemented
72#10622432C2218yescomplemented
73#10622431C2218yescomplemented
74#10622411C2218yescomplemented
75#10622325C2218yes—
76#10622314C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D44—21no—
80C22×D44—21no—
81C22×D44C2311yescharacteristic
82C22×D44C2311yescharacteristic
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×Dic22D411yescharacteristic
88C22×Dic22C2311yescharacteristic
89C2×C11×Q16—24no—
90C2×C11×Q16C2314yes—
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11C2314yes—
96C4×Q8×C11C2314yes—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C42×C11—21no—
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104#67000—22no—
105#67000—22no—
106#67000—22no—
107#67000C2314yes—
108#67000C2314yes—
109#67000C2314yes—
110#66997—22no—
111#66997C2314yes—
112C2×#4326—42no—
113C2×#4326C2314yes—
114C2×#4325—42no—
115C2×#4325—42no—
116C2×#4325—42no—
117C2×#4325C2314yes—
118C2×#4325C2314yes—
119C2×#4325C2314yes—
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)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×C4⋊Dic11D411yescharacteristic
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4D411yescharacteristic
136C2×Dic11⋊C4D411yescharacteristic
137C2×C4×Dic11—21no—
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C2×D88—24no—
143C2×D88—42no—
144C2×D88C2314yes—
145C2×D88C2314yes—
146C2×#4314—24no—
147C2×#4314—42no—
148C2×#4314C2314yes—
149C2×#4314C2314yes—
150#66951—28no—
151#66949—28no—
152#66947—28no—
153#66947—28no—
154#66946—22no—
155#66946—22no—
156#66946—22no—
157#66946C2314yes—
158#66946C2314yes—
159#66946C2314yes—
160#66940—22no—
161#66940C2314yes—
162#66929—28no—
163#66928—28no—
164#66928—22no—
165#66928C2314yes—
166#66927—22no—
167#66927C2314yes—
168C4×D44—28no—
169#66925—28no—
170C4×Dic22D414yes—
171C4×Dic22C2314yes—
172C11×#106C2314yes—
173C11×#103C2314yes—
174C11×#103C2314yes—
175C11×#97C2314yes—
176#66879C2314yes—
177Dic11⋊C8C2314yes—
178Dic11⋊C8C2314yes—
179C8×Dic11C2314yes—
180#66874C2314yes—
181#66873C2314yes—
182#66873C2314yes—
183#66873C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C2×#3401—111nomaximal, Sylow
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—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×C11C2412yes—
196C2×Q8×C11C2412yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C22×Dic11—21no—
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C2×D44—24no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—24no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—22no—
220C2×D44—44no—
221C2×D44—82no—
222C2×D44C2412yes—
223C2×D44C2412yes—
224C2×D44C2412yes—
225C2×C4×D11—24no—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—44no—
229C2×C4×D11—82no—
230C2×C4×D11—82no—
231C2×Dic22—21no—
232C2×Dic22—22no—
233C2×Dic22—22no—
234C2×Dic22—42no—
235C2×Dic22C2×D414yes—
236C2×Dic22C2412yes—
237C11×Q16—28no—
238C2×C8×C11—22no—
239C2×C8×C11#4114yes—
240C2×C8×C11C2412yes—
241C2×C8×C11C2412yes—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4C2412yes—
247C11×C4⋊C4C2412yes—
248C42×C11—24no—
249C42×C11—24no—
250C42×C11C2×D412yes—
251C42×C11C2412yes—
252#4326—44no—
253#4325—44no—
254#4325—44no—
255#4325—44no—
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)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267C4⋊Dic11C2×D414yes—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271Dic11⋊C4C2×D414yes—
272Dic11⋊C4C2×D414yes—
273C4×Dic11—24no—
274C4×Dic11C2×D412yes—
275C4×Dic11C2×D412yes—
276C4×Dic11C2412yes—
277C4×Dic11C2412yes—
278C2×C11⋊C8—22no—
279C2×C11⋊C8—22no—
280C2×C11⋊C8C2412yes—
281C2×C11⋊C8C2412yes—
282D88—28no—
283D88—44no—
284#4314—28no—
285#4314—44no—
286C2×#559—111no—
287C2×#556—111no—
288#3401—1116no—
289C2×#497—111no—
290C2×#496—111no—
291C2×#495—111no—
292C2×#464—111no—
293C2×#464—111no—
294C2×#460—111no—
295C2×#463—111no—
296C2×#463—111no—
297C2×#461—111no—
298C2×#446—111no—
299C2×#442—111no—
300C2×#441D1111yescharacteristic, complemented
301C2×C4×SD16—111no—
302C23×C11C22×D411yescharacteristic
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11—42no—
313C22×D11—42no—
314C22×D11—42no—
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—22no—
318Q8×C11—22no—
319Q8×C11—42no—
320Q8×C11—42no—
321C2×C4×C11—22no—
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×C11—42no—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C2×#4112yes—
335C2×C4×C11H(5,𝔽2)12yes—
336C2×C4×C11C2511yescharacteristic
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—42no—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346C2×Dic11C22×D412yes—
347D44—22no—
348D44—22no—
349D44—22no—
350D44—22no—
351D44—22no—
352D44—22no—
353D44—48no—
354D44—42no—
355D44—42no—
356D44—42no—
357D44—84no—
358C4×D11—48no—
359C4×D11—84no—
360C4×D11—84no—
361Dic22—22no—
362Dic22—22no—
363Dic22—44no—
364Dic22—42no—
365C8×C11—22no—
366C8×C11C2×#4114yes—
367C11⋊C8—22no—
368C11⋊C8—22no—
369C22×Q16—111no—
370C22×Q16C2×D1111yescharacteristic
371C22×SD16—111no—
372C22×SD16—111no—
373C22×SD16—111no—
374C22×SD16—111no—
375C22×SD16—111no—
376C22×D8—111no—
377C22×D8—111no—
378#559—118no—
379#559—224no—
380#556—118no—
381#556—224no—
382C2×C4⋊Q8—111no—
383C2×#127—111no—
384C2×#126—221no—
385C2×#126—221no—
386C2×#124—111no—
387C2×#124—111no—
388C2×#124—111no—
389C2×#124—111no—
390C2×#124—221no—
391C2×#123—221no—
392C2×#123—221no—
393C2×C22⋊Q8—221no—
394C2×C4×Q8—111no—
395C2×C4×Q8—111no—
396C2×C4×Q8C2×D1111yescharacteristic
397C2×C4×Q8C2×D1111yescharacteristic
398C2×C4×D4—111no—
399C2×C4×D4—111no—
400C2×C4×D4—111no—
401C2×C4×D4—221no—
402C2×#117—221no—
403#497—118no—
404#496—118no—
405#495—118no—
406#464—118no—
407#464—118no—
408#463—118no—
409#463—118no—
410#461—118no—
411#460—118no—
412#446—118no—
413#442—118no—
414#441C2×D1118yescomplemented
415C4×SD16—118no—
416C2×#106C2×D1111yescharacteristic
417C2×C4⋊C8—111no—
418C2×C4⋊C8—111no—
419C2×C4⋊C8—111no—
420C2×#103—111no—
421C2×#103C2×D1111yescharacteristic
422C2×#103C2×D1111yescharacteristic
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#97—111no—
427C2×#97C2×D1111yescharacteristic
428C2×C4×C8—111no—
429C22×C11#55012yes—
430C22×C11#57512yes—
431C22×C11#57712yes—
432C22×C11C23×D411yescharacteristic
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—84no—
443C2×D11—84no—
444C2×D11—84no—
445C4×C11—22no—
446C4×C11—22no—
447C4×C11—42no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11#55012yes—
452C4×C11C22×#4111yescharacteristic
453C4×C11C2×H(5,𝔽2)11yescharacteristic
454Dic11—22no—
455Dic11—22no—
456Dic11—22no—
457Dic11—22no—
458Dic11—42no—
459C22×Q8—111no—
460C22×Q8—111no—
461C22×Q8C22×D1111yescharacteristic
462C22×Q8C22×D1111yescharacteristic
463C22×D4—111no—
464C22×D4—111no—
465C22×D4—111no—
466C22×D4—221no—
467C22×D4—221no—
468C23×C4—221no—
469C23×C4—221no—
470C23×C4—221no—
471C2×Q16—24no—
472C2×Q16—114no—
473C2×Q16—442no—
474C2×Q16C22×D1114yes—
475C2×SD16—114no—
476C2×SD16—114no—
477C2×SD16—114no—
478C2×SD16—114no—
479C2×SD16—114no—
480C2×SD16—224no—
481C2×SD16—442no—
482C2×SD16—442no—
483C2×SD16—442no—
484C2×SD16—442no—
485C2×D8—114no—
486C2×D8—114no—
487C2×D8—224no—
488C2×D8—442no—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8C22×D1111yescharacteristic
492C22×C8C22×D1111yescharacteristic
493C4⋊Q8—114no—
494C4⋊Q8—222no—
495#127—114no—
496#127—222no—
497#126—228no—
498#126—228no—
499#124—114no—
500#124—114no—
501#124—114no—
502#124—114no—
503#124—228no—
504#124—222no—
505#124—222no—
506#124—222no—
507#124—222no—
508#123—228no—
509#123—228no—
510C22⋊Q8—228no—
511C4×Q8—22no—
512C4×Q8—22no—
513C4×Q8—114no—
514C4×Q8—114no—
515C4×Q8—114no—
516C4×Q8—222no—
517C4×Q8C22×D1114yes—
518C4×Q8C22×D1114yes—
519C4×D4—114no—
520C4×D4—114no—
521C4×D4—114no—
522C4×D4—228no—
523C4×D4—222no—
524C4×D4—222no—
525C4×D4—222no—
526#117—228no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C42—21no—
549C2×C42—21no—
550C2×C42—111no—
551C2×C42—111no—
552C2×C42—221no—
553C2×C42C22×D1111yescharacteristic
554#106C22×D1114yes—
555C4⋊C8—114no—
556C4⋊C8—114no—
557C4⋊C8—114no—
558#103—114no—
559#103C22×D1114yes—
560#103C22×D1114yes—
561#102—114no—
562#102—114no—
563#102—114no—
564#97—114no—
565#97C22×D1114yes—
566C4×C8—114no—
567C2×C11#340114yescomplemented
568C2×C11C2×#55011yescharacteristic
569C2×C11C2×#57511yescharacteristic
570C2×C11C2×#57711yescharacteristic
571D11—82no—
572D11—82no—
573D11—82no—
574C24—221no—
575C24—221no—
576C24—221no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—114no—
584C2×Q8—112no—
585C2×Q8—221no—
586C2×Q8—222no—
587C2×Q8—222no—
588C2×Q8—442no—
589C2×Q8C23×D1112yes—
590C2×Q8C23×D1112yes—
591C2×D4—112no—
592C2×D4—112no—
593C2×D4—112no—
594C2×D4—222no—
595C2×D4—222no—
596C2×D4—222no—
597C2×D4—221no—
598C2×D4—224no—
599C2×D4—221no—
600C2×D4—221no—
601C2×D4—224no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4—222no—
605C2×D4—444no—
606C2×D4—882no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—111no—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—111no—
615C22×C4—224no—
616C22×C4—224no—
617C22×C4—224no—
618C22×C4—221no—
619C22×C4—444no—
620C22×C4—882no—
621C22×C4—882no—
622C22×C4D4×D1111yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4C23×D1111yescharacteristic
625Q16—28no—
626Q16—444no—
627SD16—228no—
628SD16—444no—
629SD16—444no—
630SD16—444no—
631SD16—444no—
632D8—228no—
633D8—444no—
634C2×C8—22no—
635C2×C8—112no—
636C2×C8—112no—
637C2×C8—222no—
638C2×C8—222no—
639C2×C8#433914yes—
640C2×C8C23×D1112yes—
641C2×C8C23×D1112yes—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—114no—
647C4⋊C4—114no—
648C4⋊C4—114no—
649C4⋊C4—224no—
650C4⋊C4—224no—
651C4⋊C4—224no—
652C4⋊C4C23×D1112yes—
653C4⋊C4C23×D1112yes—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C22⋊C4—224no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C42—24no—
666C42—24no—
667C42—112no—
668C42—112no—
669C42—112no—
670C42—112no—
671C42—224no—
672C42D4×D1112yes—
673C42C23×D1112yes—
674C11C2×#340111yescharacteristic, complemented, Sylow
675C23—222no—
676C23—222no—
677C23—222no—
678C23—442no—
679C23—442no—
680C23—442no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23C2×D4×D1111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—42no—
693Q8—42no—
694Q8—222no—
695Q8—222no—
696Q8—444no—
697Q8—442no—
698D4—222no—
699D4—222no—
700D4—222no—
701D4—222no—
702D4—222no—
703D4—222no—
704D4—448no—
705D4—442no—
706D4—442no—
707D4—442no—
708D4—884no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—112no—
720C2×C4—112no—
721C2×C4—112no—
722C2×C4—112no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—448no—
729C2×C4—442no—
730C2×C4—884no—
731C2×C4—884no—
732C2×C4C2×#433912yes—
733C2×C4C2×D4×D1112yes—
734C2×C4C2×D4×D1112yes—
735C2×C4C2×D4×D1111yescharacteristic
736C2×C4#6704212yes—
737C2×C4C24×D1111yescharacteristic
738C8—22no—
739C8—222no—
740C8—222no—
741C8C2×#433914yes—
742C22—442no—
743C22—442no—
744C22—442no—
745C22—442no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—884no—
752C22—884no—
753C22—884no—
754C22#1062308412yes—
755C22#1062330812yes—
756C22#1062330912yes—
757C22C22×D4×D1111yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—222no—
765C4—222no—
766C4—222no—
767C4—222no—
768C4—442no—
769C4#1062308412yes—
770C4C22×#433911yescharacteristic
771C4C2×#6704211yescharacteristic
772C2—882no—
773C2—882no—
774C2—882no—
775C2#1308168314yesdirect product factor
776C2C2×#1062308411yescharacteristic
777C2C2×#1062330811yescharacteristic
778C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#441C2
socleC23×C11C22×D4
prime radicalC2×#10622325C2
hypercenterC2×#441D11
hypocenterC11C2×#3401
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×#10623116C2semidirect
2. C2×#10623099C2semidirect
3. #13081683C2direct (N × H)
4. C2×#10622803C2semidirect
6. C2×#10622804C2semidirect
7. C2×#10622411C2semidirect
8. C2×#10622641C2semidirect
9. C2×#10622640C2semidirect
10. C2×#10622432C2semidirect
11. C2×#10622432C2semidirect
12. C2×#10622431C2semidirect
13. C2×#10622314C2semidirect
14. C2×#10622482C2semidirect
15. C2×#10622465C2semidirect
16. C2×C11×#441C2semidirect
33. #10623116C22semidirect
35. #10623099C22semidirect
51. C11×#441C22semidirect
56. #10622804C22semidirect
57. #10622803C22semidirect
62. #10622641C22semidirect
63. #10622640C22semidirect
69. #10622482C22semidirect
70. #10622465C22semidirect
71. #10622432C22semidirect
72. #10622432C22semidirect
73. #10622431C22semidirect
74. #10622411C22semidirect
76. #10622314C22semidirect
300. C2×#441D11semidirect
414. #441C2×D11semidirect
567. C2×C11#3401semidirect
674. C11C2×#3401semidirect
775. C2#13081683direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106230992
#130816832
C2×#106228032
C2×#106223252
C2×#106228042
C2×#106224112
C2×#106226412
C2×#106226402
C2×#106224322
C2×#106224312
C2×#106223142
C2×#106224822
C2×#106224652
C2×C11×#4412
C2×#340111