Finite Group Databasebeta

← C2×#13081684 #15634781

Subgroups — C2×#13081684 #15634781

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×#10623115C211yesmaximal, characteristic, complemented
3#13081684C2116yesmaximal, direct product factor
4C2×#10622328C211yesmaximal, characteristic, complemented
5C2×#10622325C211yesmaximal, characteristic
6C2×#10622309C211yesmaximal, characteristic, complemented
7C2×#10622458C211yesmaximal, characteristic, complemented
8C2×#10622458C211yesmaximal, characteristic, complemented
9C2×#10622461C211yesmaximal, characteristic, complemented
10C2×#10622457C211yesmaximal, characteristic, complemented
11C2×#10622457C211yesmaximal, characteristic, complemented
12C2×#10622454C211yesmaximal, characteristic, complemented
13C2×#10622324C211yesmaximal, characteristic, complemented
14C2×#10622329C211yesmaximal, characteristic, complemented
15C2×C4×#4314C211yesmaximal, characteristic, complemented
16C2×C11×#446C211yesmaximal, characteristic, complemented
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#67000—21no—
19C2×#66999—21no—
20C22×Dic44C2211yescharacteristic
21C22×Dic44C2211yescharacteristic
22C22×D88C2211yescharacteristic
23C22×D88C2211yescharacteristic
24C22×#4314C2211yescharacteristic
25C22×#4314C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28C22×#4314C2211yescharacteristic
29#10623116—24no—
30#10623116C2218yescomplemented
31#10623115—24no—
32#10623115C2218yescomplemented
33C2×#66951—21no—
34C2×#66951—21no—
35C2×#66947—21no—
36C2×#66947—21no—
37C2×#66946—21no—
38C2×#66945—21no—
39C2×#66928C2211yescharacteristic
40C2×#66928C2211yescharacteristic
41C2×#66928C2211yescharacteristic
42C2×#66928C2211yescharacteristic
43C2×#66927C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66922C2211yescharacteristic
48C2×C4×Dic22C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C11×#446C2218yescomplemented
52C2×C11×C4⋊C8C2211yescharacteristic
53C2×C11×C4⋊C8C2211yescharacteristic
54C2×C11×C4⋊C8C2211yescharacteristic
55C2×C11×#97C2211yescharacteristic
56C2×C11×#97C2211yescharacteristic
57C2×C4×C8×C11C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66885C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66880C2211yescharacteristic
65#10622461C2218yescomplemented
66#10622458C2218yescomplemented
67#10622458C2218yescomplemented
68#10622457C2218yescomplemented
69#10622457C2218yescomplemented
70#10622454C2218yescomplemented
71#10622329C2218yescomplemented
72#10622328C2218yescomplemented
73#10622325C2218yes—
74#10622324C2218yescomplemented
75#10622309C2218yescomplemented
76C4×#4314C2218yescomplemented
77C22×Q8×C11D411yescharacteristic
78C22×D44—21no—
79C22×D44—21no—
80C22×D44C2311yescharacteristic
81C22×D44C2311yescharacteristic
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×Dic22C2311yescharacteristic
87C22×Dic22C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C4×Q8×C11D414yes—
94C4×Q8×C11C2314yes—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101#67000—28no—
102#66999—28no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×C4×Dic11—21no—
122C2×C4×Dic11—21no—
123C2×C4×Dic11—21no—
124C2×Dic44—24no—
125C2×Dic44—42no—
126C2×Dic44C2314yes—
127C2×Dic44C2314yes—
128C2×D88—24no—
129C2×D88—42no—
130C2×D88C2314yes—
131C2×D88C2314yes—
132C2×#4314—24no—
133C2×#4314—42no—
134C2×#4314—42no—
135C2×#4314—42no—
136C2×#4314—42no—
137C2×#4314C2314yes—
138C2×#4314C2314yes—
139C2×#4314C2314yes—
140C2×#4314C2314yes—
141C2×#4314C2314yes—
142#66951—28no—
143#66951—28no—
144#66947—28no—
145#66947—28no—
146#66946—28no—
147#66945—28no—
148#66928—22no—
149#66928—22no—
150#66928—22no—
151#66928—22no—
152#66928C2314yes—
153#66928C2314yes—
154#66928C2314yes—
155#66928C2314yes—
156#66927—22no—
157#66927C2314yes—
158C4×D44—22no—
159C4×D44—22no—
160C4×D44—22no—
161C4×D44C2314yes—
162C4×D44C2314yes—
163C4×D44C2314yes—
164#66922—22no—
165#66922C2314yes—
166C4×Dic22—22no—
167C4×Dic22—22no—
168C4×Dic22—22no—
169C4×Dic22C2314yes—
170C4×Dic22C2314yes—
171C4×Dic22C2314yes—
172C11×C4⋊C8C2314yes—
173C11×C4⋊C8C2314yes—
174C11×C4⋊C8C2314yes—
175C11×#97C2314yes—
176C11×#97C2314yes—
177C4×C8×C11C2314yes—
178#66885C2314yes—
179#66885C2314yes—
180#66885C2314yes—
181#66881C2314yes—
182#66880C2314yes—
183#66880C2314yes—
184#66880C2314yes—
185C2×#3401—111nomaximal, Sylow
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C2×Q8×C11—42no—
190C2×Q8×C11C2×D414yes—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—24no—
207C2×D44—24no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—22no—
211C2×D44—22no—
212C2×D44—22no—
213C2×D44—22no—
214C2×D44—44no—
215C2×D44—82no—
216C2×D44C2412yes—
217C2×D44C2412yes—
218C2×D44C2412yes—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—44no—
223C2×C4×D11—82no—
224C2×C4×D11—82no—
225C2×Dic22—21no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C2×Dic22—22no—
229C2×Dic22—22no—
230C2×Dic22—22no—
231C2×Dic22—22no—
232C2×Dic22—22no—
233C2×Dic22—22no—
234C2×Dic22C2412yes—
235C2×Dic22C2412yes—
236C2×Dic22C2412yes—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11—22no—
240C2×C8×C11#4114yes—
241C2×C8×C11C2412yes—
242C2×C8×C11C2412yes—
243C2×C8×C11C2412yes—
244C2×C8×C11C2412yes—
245C11×C4⋊C4C2×D414yes—
246C11×C4⋊C4C2×D414yes—
247C11×C4⋊C4C2×D414yes—
248C42×C11C2×D412yes—
249C42×C11C2×D412yes—
250C42×C11C2×D412yes—
251C42×C11C2412yes—
252C42×C11C2412yes—
253C42×C11C2412yes—
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)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—24no—
268C4⋊Dic11—24no—
269C4⋊Dic11C2412yes—
270C4⋊Dic11C2412yes—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274C4×Dic11—24no—
275C4×Dic11—24no—
276C4×Dic11—24no—
277Dic44—28no—
278Dic44—44no—
279D88—28no—
280D88—44no—
281#4314—28no—
282#4314—44no—
283#4314—44no—
284#4314—44no—
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×#446D1111yescharacteristic, complemented
299C2×#442—111no—
300C2×#441—111no—
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—44no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4112yes—
330C2×C4×C11H(5,𝔽2)12yes—
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×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342D44—22no—
343D44—22no—
344D44—22no—
345D44—22no—
346D44—22no—
347D44—22no—
348D44—48no—
349D44—42no—
350D44—42no—
351D44—42no—
352D44—84no—
353C4×D11—48no—
354C4×D11—84no—
355C4×D11—84no—
356Dic22—22no—
357Dic22—22no—
358Dic22—22no—
359Dic22—22no—
360Dic22—22no—
361Dic22—22no—
362Dic22—42no—
363Dic22—42no—
364Dic22—42no—
365C8×C11—22no—
366C8×C11—22no—
367C8×C11—22no—
368C8×C11C2×#4114yes—
369C22×Q16—111no—
370C22×Q16—111no—
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×Q8—111no—
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#446C2×D1118yescomplemented
413#442—118no—
414#441—118no—
415C4×SD16—118no—
416C2×#106—111no—
417C2×C4⋊C8C2×D1111yescharacteristic
418C2×C4⋊C8C2×D1111yescharacteristic
419C2×C4⋊C8C2×D1111yescharacteristic
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#97C2×D1111yescharacteristic
427C2×#97C2×D1111yescharacteristic
428C2×C4×C8C2×D1111yescharacteristic
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—22no—
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11#55012yes—
452C4×C11C22×#4111yescharacteristic
453C4×C11C2×H(5,𝔽2)11yescharacteristic
454Dic11—42no—
455Dic11—42no—
456Dic11—42no—
457Dic11—42no—
458Dic11—42no—
459C22×Q8—111no—
460C22×Q8—111no—
461C22×Q8—111no—
462C22×Q8D4411yescharacteristic
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—114no—
472C2×Q16—114no—
473C2×Q16—224no—
474C2×Q16—442no—
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×C8C22×D1111yescharacteristic
490C22×C8C22×D1111yescharacteristic
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—114no—
512C4×Q8—114no—
513C4×Q8—114no—
514C4×Q8—222no—
515C4×Q8—222no—
516C4×Q8—222no—
517C4×Q8D4414yes—
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—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4D4411yescharacteristic
535C2×C4⋊C4D4411yescharacteristic
536C2×C4⋊C4D4411yescharacteristic
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—221no—
549C2×C42—221no—
550C2×C42—221no—
551C2×C42C22×D1111yescharacteristic
552C2×C42C22×D1111yescharacteristic
553C2×C42C22×D1111yescharacteristic
554#106—114no—
555C4⋊C8C22×D1114yes—
556C4⋊C8C22×D1114yes—
557C4⋊C8C22×D1114yes—
558#103—114no—
559#103—114no—
560#103—114no—
561#102—114no—
562#102—114no—
563#102—114no—
564#97C22×D1114yes—
565#97C22×D1114yes—
566C4×C8C22×D1114yes—
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—42no—
578C2×Q8—112no—
579C2×Q8—112no—
580C2×Q8—112no—
581C2×Q8—221no—
582C2×Q8—221no—
583C2×Q8—221no—
584C2×Q8—222no—
585C2×Q8—222no—
586C2×Q8—222no—
587C2×Q8—222no—
588C2×Q8—222no—
589C2×Q8—222no—
590C2×Q8C2×D4414yes—
591C2×D4—112no—
592C2×D4—112no—
593C2×D4—112no—
594C2×D4—221no—
595C2×D4—224no—
596C2×D4—221no—
597C2×D4—221no—
598C2×D4—224no—
599C2×D4—222no—
600C2×D4—222no—
601C2×D4—222no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4—222no—
605C2×D4—444no—
606C2×D4—882no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—224no—
613C22×C4—224no—
614C22×C4—224no—
615C22×C4—444no—
616C22×C4—882no—
617C22×C4—882no—
618C22×C4C2×D4411yescharacteristic
619C22×C4C2×D4411yescharacteristic
620C22×C4C2×D4411yescharacteristic
621C22×C4C2×D4411yescharacteristic
622C22×C4C2×D4411yescharacteristic
623C22×C4C2×D4411yescharacteristic
624C22×C4C23×D1111yescharacteristic
625Q16—228no—
626Q16—444no—
627SD16—228no—
628SD16—444no—
629SD16—444no—
630SD16—444no—
631SD16—444no—
632D8—228no—
633D8—444no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8#434314yes—
638C2×C8C23×D1112yes—
639C2×C8C23×D1112yes—
640C2×C8C23×D1112yes—
641C2×C8C23×D1112yes—
642C4⋊C4—112no—
643C4⋊C4—112no—
644C4⋊C4—221no—
645C4⋊C4—221no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—224no—
651C4⋊C4C2×D4414yes—
652C4⋊C4C2×D4414yes—
653C4⋊C4C2×D4414yes—
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—224no—
666C42—224no—
667C42—224no—
668C42C2×D4412yes—
669C42C2×D4412yes—
670C42C2×D4412yes—
671C42C23×D1112yes—
672C42C23×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—
687C23C22×D4411yescharacteristic
688Q8—44no—
689Q8—222no—
690Q8—222no—
691Q8—222no—
692Q8—222no—
693Q8—222no—
694Q8—222no—
695Q8—442no—
696Q8—442no—
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—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—448no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—884no—
727C2×C4—884no—
728C2×C4C22×D4412yes—
729C2×C4C22×D4412yes—
730C2×C4C22×D4412yes—
731C2×C4C22×D4412yes—
732C2×C4C22×D4412yes—
733C2×C4C22×D4412yes—
734C2×C4C22×D4411yescharacteristic
735C2×C4C2×#434312yes—
736C2×C4#6704212yes—
737C2×C4C24×D1111yescharacteristic
738C8—22no—
739C8—22no—
740C8—22no—
741C8C2×#434314yes—
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#1062310812yes—
755C22#1062327912yes—
756C22#1062328212yes—
757C22C23×D4411yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—442no—
765C4—442no—
766C4—442no—
767C4—442no—
768C4—442no—
769C4#1062310812yes—
770C4C22×#434311yescharacteristic
771C4C2×#6704211yescharacteristic
772C2—882no—
773C2—882no—
774C2—882no—
775C2#1308168414yesdirect product factor
776C2C2×#1062310811yescharacteristic
777C2C2×#1062327911yescharacteristic
778C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#446C2
socleC23×C11C22×D4
prime radicalC2×#10622325C2
hypercenterC2×#446D11
hypocenterC11C2×#3401
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. C2×#10623115C2semidirect
3. #13081684C2direct (N × H)
4. C2×#10622328C2semidirect
6. C2×#10622309C2semidirect
7. C2×#10622458C2semidirect
8. C2×#10622458C2semidirect
9. C2×#10622461C2semidirect
10. C2×#10622457C2semidirect
11. C2×#10622457C2semidirect
12. C2×#10622454C2semidirect
13. C2×#10622324C2semidirect
14. C2×#10622329C2semidirect
15. C2×C4×#4314C2semidirect
16. C2×C11×#446C2semidirect
30. #10623116C22semidirect
32. #10623115C22semidirect
51. C11×#446C22semidirect
65. #10622461C22semidirect
66. #10622458C22semidirect
67. #10622458C22semidirect
68. #10622457C22semidirect
69. #10622457C22semidirect
70. #10622454C22semidirect
71. #10622329C22semidirect
72. #10622328C22semidirect
74. #10622324C22semidirect
75. #10622309C22semidirect
76. C4×#4314C22semidirect
298. C2×#446D11semidirect
412. #446C2×D11semidirect
567. C2×C11#3401semidirect
674. C11C2×#3401semidirect
775. C2#13081684direct (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×#106231152
#130816842
C2×#106223282
C2×#106223252
C2×#106223092
C2×#106224582
C2×#106224612
C2×#106224572
C2×#106224542
C2×#106223242
C2×#106223292
C2×C4×#43142
C2×C11×#4462
C2×#340111