Finite Group Databasebeta

← C2×#13080029 #15626685

Subgroups — C2×#13080029 #15626685

Order 2816.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic, complemented
2C2×#10623066C211yesmaximal, characteristic, complemented
3#13080029C2116yesmaximal, direct product factor
4C2×#10622442C211yesmaximal, characteristic, complemented
5C2×#10622460C211yesmaximal, characteristic, complemented
6C2×#10622455C211yesmaximal, characteristic, complemented
7C2×#10622459C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622747C211yesmaximal, characteristic, complemented
10C2×#10622728C211yesmaximal, characteristic, complemented
11C2×#10622727C211yesmaximal, characteristic, complemented
12C2×#10622461C211yesmaximal, characteristic, complemented
13C2×#10622457C211yesmaximal, characteristic, complemented
14C2×#10622457C211yesmaximal, characteristic, complemented
15C2×#10622456C211yesmaximal, characteristic, complemented
16C2×C11×#424C211yesmaximal, characteristic, complemented
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×D88C2211yescharacteristic
25C22×D88C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28#10623066—24no—
29#10623066C2218yescomplemented
30#10623065—24no—
31#10623065C2218yescomplemented
32C2×#66951—21no—
33C2×#66949—21no—
34C2×#66947—21no—
35C2×#66947—21no—
36C2×#66938—21no—
37C2×#66937—21no—
38C2×#66937—21no—
39C2×#66936—21no—
40C2×#66928C2211yescharacteristic
41C2×#66927C2211yescharacteristic
42C2×C4×D44C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×#66923C2211yescharacteristic
46C2×#66922C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C11×#424C2218yescomplemented
49C2×C11×C4⋊C8C2211yescharacteristic
50C2×C11×C4⋊C8C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×C4⋊C8C2211yescharacteristic
53#10622748C2218yescomplemented
54#10622747C2218yescomplemented
55#10622728C2218yescomplemented
56#10622727C2218yescomplemented
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic
62C2×#66885C2211yescharacteristic
63C2×#66882C2211yescharacteristic
64C2×#66882C2211yescharacteristic
65C2×#66881C2211yescharacteristic
66C2×#66881C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66880C2211yescharacteristic
69#10622461C2218yescomplemented
70#10622460C2218yescomplemented
71#10622459C2218yescomplemented
72#10622457C2218yescomplemented
73#10622457C2218yescomplemented
74#10622456C2218yescomplemented
75#10622455C2218yescomplemented
76#10622442C2218yescomplemented
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—21no—
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C22×D44—21no—
82C22×D44—21no—
83C22×D44C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×Dic22—21no—
90C22×Dic22C2311yescharacteristic
91C2×C11×M16—42no—
92C2×C11×M16C2314yes—
93C22×C8×C11—42no—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2314yes—
99C11×#117D414yes—
100C11×#117C2314yes—
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108#66983—22no—
109#66983—22no—
110#66983—22no—
111#66983C2314yes—
112#66983C2314yes—
113#66983C2314yes—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127#66977—22no—
128#66977C2314yes—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×C4×Dic11—21no—
134C2×D88—42no—
135C2×D88—42no—
136C2×D88C2314yes—
137C2×D88C2314yes—
138C2×#4314—42no—
139C2×#4314—42no—
140C2×#4314C2314yes—
141C2×#4314C2314yes—
142#66951—28no—
143#66949—28no—
144#66947—28no—
145#66947—28no—
146#66938—28no—
147#66937—28no—
148#66937—28no—
149#66936—28no—
150#66928—22no—
151#66928C2314yes—
152#66927—22no—
153#66927C2314yes—
154C4×D44—22no—
155C4×D44—22no—
156C4×D44—22no—
157C4×D44C2314yes—
158C4×D44C2314yes—
159C4×D44C2314yes—
160#66923—22no—
161#66923C2314yes—
162#66922—22no—
163#66922C2314yes—
164C4×Dic22—22no—
165C4×Dic22C2314yes—
166C11×C4⋊C8C2314yes—
167C11×C4⋊C8C2314yes—
168C11×C4⋊C8C2314yes—
169C11×C4⋊C8C2314yes—
170#66885C2314yes—
171#66885C2314yes—
172#66885C2314yes—
173#66885C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176#66882C2314yes—
177#66882C2314yes—
178#66881C2314yes—
179#66881C2314yes—
180#66880C2314yes—
181#66880C2314yes—
182C2×#3257—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2412yes—
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—82no—
201C2×C22⋊D11—82no—
202C2×C22⋊D11—82no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—24no—
212C2×D44—24no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—82no—
220C2×D44—82no—
221C2×D44C2412yes—
222C2×D44C2412yes—
223C2×D44C2412yes—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—24no—
227C2×C4×D11—82no—
228C2×C4×D11—82no—
229C2×C4×D11—82no—
230C2×Dic22—21no—
231C2×Dic22—24no—
232C2×Dic22—22no—
233C2×Dic22—22no—
234C2×Dic22—82no—
235C2×Dic22C2412yes—
236C11×M16—44no—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11—22no—
240C2×C8×C11—22no—
241C2×C8×C11—44no—
242C2×C8×C11C2412yes—
243C2×C8×C11C2412yes—
244C2×C8×C11C2412yes—
245C2×C8×C11C2412yes—
246C11×C4⋊C4C2×D414yes—
247C11×C4⋊C4C2×D414yes—
248C11×C22⋊C4C2×D414yes—
249C11×C22⋊C4C2×D414yes—
250C42×C11C2×D412yes—
251C42×C11C2×D412yes—
252C42×C11C2412yes—
253C42×C11C2412yes—
254C22⋊Dic11—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—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—24no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11C2412yes—
269C4⋊Dic11C2412yes—
270C4⋊Dic11C2412yes—
271C4⋊Dic11C2412yes—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276C4×Dic11—24no—
277D88—44no—
278D88—44no—
279#4314—44no—
280#4314—44no—
281C2×#542—111no—
282C2×#540—111no—
283#3257—1116no—
284C2×#479—111no—
285C2×#478—111no—
286C2×#476—111no—
287C2×#474—111no—
288C2×#469—111no—
289C2×#468—111no—
290C2×#466—111no—
291C2×#465—111no—
292C2×#460—111no—
293C2×#463—111no—
294C2×#463—111no—
295C2×#459—111no—
296C2×#424D1111yescharacteristic, complemented
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11C22×D412yes—
301C23×C11C22×D411yescharacteristic
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11—42no—
313C22×D11—42no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
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×D411yescharacteristic
328C2×C4×C11H(5,𝔽2)12yes—
329C2×C4×C112−1+412yes—
330C2×C4×C11C2511yescharacteristic
331C22⋊D11—84no—
332C22⋊D11—84no—
333C22⋊D11—84no—
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—42no—
343C2×Dic11—42no—
344D44—22no—
345D44—22no—
346D44—22no—
347D44—22no—
348D44—22no—
349D44—22no—
350D44—42no—
351D44—42no—
352D44—42no—
353D44—84no—
354D44—84no—
355C4×D11—84no—
356C4×D11—84no—
357C4×D11—84no—
358Dic22—22no—
359Dic22—22no—
360Dic22—42no—
361Dic22—84no—
362C8×C11—22no—
363C8×C11—22no—
364C8×C11—22no—
365C8×C11—22no—
366C22×SD16—111no—
367C22×SD16—111no—
368C22×D8—111no—
369C22×D8—111no—
370C22×M16C2×D1111yescharacteristic
371C23×C8C2×D1111yescharacteristic
372#542—118no—
373#542—224no—
374#540—118no—
375#540—224no—
376C2×C4⋊Q8—111no—
377C2×#127—111no—
378C2×#126—221no—
379C2×#125—111no—
380C2×#124—111no—
381C2×#124—221no—
382C2×#123—221no—
383C2×#123—221no—
384C2×#123—221no—
385C2×C22⋊Q8—111no—
386C2×C22⋊Q8—221no—
387C2×#121—111no—
388C2×#121—111no—
389C2×#121—111no—
390C2×#121—221no—
391C2×#121—221no—
392C2×C4×Q8—111no—
393C2×C4×D4—111no—
394C2×C4×D4—111no—
395C2×C4×D4—111no—
396C2×#117C2×D1111yescharacteristic
397#479—118no—
398#478—118no—
399#476—118no—
400#474—118no—
401#469—118no—
402#468—118no—
403#466—118no—
404#465—118no—
405#463—118no—
406#463—118no—
407#460—118no—
408#459—118no—
409C2×#107—111no—
410C2×#107—111no—
411C2×#106—111no—
412C2×#106—111no—
413#424C2×D1118yescomplemented
414C2×C4⋊C8C2×D1111yescharacteristic
415C2×C4⋊C8C2×D1111yescharacteristic
416C2×C4⋊C8C2×D1111yescharacteristic
417C2×C4⋊C8C2×D1111yescharacteristic
418C2×#103—111no—
419C2×#103—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—44no—
430C22×C11#53712yes—
431C22×C11#57612yes—
432C22×C11#57712yes—
433C22×C11C23×D411yescharacteristic
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—42no—
443C2×D11—84no—
444C2×D11—84no—
445C2×D11—84no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11#53712yes—
452C4×C11C2×H(5,𝔽2)11yescharacteristic
453C4×C11C2×2−1+411yescharacteristic
454Dic11—42no—
455Dic11—42no—
456Dic11—42no—
457Dic11—42no—
458Dic11—42no—
459C22×Q8—111no—
460C22×Q8—221no—
461C22×D4—111no—
462C22×D4—111no—
463C22×D4—111no—
464C22×D4—221no—
465C22×D4—221no—
466C22×D4—221no—
467C22×D4—221no—
468C22×D4—221no—
469C23×C4—221no—
470C23×C4—221no—
471C23×C4—221no—
472C23×C4C22×D1111yescharacteristic
473C2×SD16—114no—
474C2×SD16—114no—
475C2×SD16—442no—
476C2×SD16—442no—
477C2×D8—114no—
478C2×D8—114no—
479C2×D8—442no—
480C2×D8—442no—
481C2×M16—42no—
482C2×M16C22×D1114yes—
483C22×C8—42no—
484C22×C8C22×D1111yescharacteristic
485C22×C8C22×D1111yescharacteristic
486C22×C8C22×D1111yescharacteristic
487C22×C8C22×D1111yescharacteristic
488C22×C8C22×D1114yes—
489C4⋊Q8—114no—
490C4⋊Q8—222no—
491#127—114no—
492#127—222no—
493#126—228no—
494#125—114no—
495#125—222no—
496#124—114no—
497#124—228no—
498#124—222no—
499#123—228no—
500#123—228no—
501#123—228no—
502C22⋊Q8—114no—
503C22⋊Q8—222no—
504C22⋊Q8—228no—
505#121—114no—
506#121—114no—
507#121—114no—
508#121—222no—
509#121—222no—
510#121—222no—
511#121—228no—
512#121—228no—
513C4×Q8—114no—
514C4×Q8—222no—
515C4×D4—114no—
516C4×D4—114no—
517C4×D4—114no—
518C4×D4—222no—
519C4×D4—222no—
520C4×D4—222no—
521#117D4414yes—
522#117C22×D1114yes—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—221no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4D4411yescharacteristic
533C2×C4⋊C4D4411yescharacteristic
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C22⋊C4—221no—
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⋊C4D4411yescharacteristic
544C2×C22⋊C4D4411yescharacteristic
545C2×C42—221no—
546C2×C42C22×D1111yescharacteristic
547C2×C42C22×D1111yescharacteristic
548#107—114no—
549#107—114no—
550#106—114no—
551#106—114no—
552C4⋊C8C22×D1114yes—
553C4⋊C8C22×D1114yes—
554C4⋊C8C22×D1114yes—
555C4⋊C8C22×D1114yes—
556#103—114no—
557#103—114no—
558#102—114no—
559#102—114no—
560#102—114no—
561#102—114no—
562#102—114no—
563#102—114no—
564C2×C11—42no—
565C2×C11#325714yescomplemented
566C2×C11C2×#53711yescharacteristic
567C2×C11C2×#57611yescharacteristic
568C2×C11C2×#57711yescharacteristic
569D11—82no—
570D11—82no—
571D11—82no—
572C24—221no—
573C24—221no—
574C24—221no—
575C24C2×D4411yescharacteristic
576C2×Q8—112no—
577C2×Q8—221no—
578C2×Q8—224no—
579C2×Q8—222no—
580C2×Q8—222no—
581C2×Q8—882no—
582C2×D4—112no—
583C2×D4—112no—
584C2×D4—112no—
585C2×D4—224no—
586C2×D4—224no—
587C2×D4—224no—
588C2×D4—221no—
589C2×D4—221no—
590C2×D4—221no—
591C2×D4—224no—
592C2×D4—224no—
593C2×D4—222no—
594C2×D4—222no—
595C2×D4—222no—
596C2×D4—222no—
597C2×D4—222no—
598C2×D4—222no—
599C2×D4—882no—
600C2×D4—882no—
601C2×D4—882no—
602C2×D4—882no—
603C2×D4—882no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—224no—
612C22×C4—224no—
613C22×C4—224no—
614C22×C4—882no—
615C22×C4—882no—
616C22×C4—882no—
617C22×C4C2×D4412yes—
618C22×C4C2×D4411yescharacteristic
619C22×C4C2×D4411yescharacteristic
620C22×C4C2×D4411yescharacteristic
621C22×C4C2×D4411yescharacteristic
622C22×C4C2×D4411yescharacteristic
623C22×C4C23×D1112yes—
624C22×C4C23×D1111yescharacteristic
625SD16—444no—
626SD16—444no—
627D8—444no—
628D8—444no—
629M16—44no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—44no—
635C2×C8C23×D1112yes—
636C2×C8C23×D1112yes—
637C2×C8C23×D1112yes—
638C2×C8C23×D1112yes—
639C4⋊C4—112no—
640C4⋊C4—112no—
641C4⋊C4—112no—
642C4⋊C4—112no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4—221no—
646C4⋊C4—221no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—224no—
651C4⋊C4—224no—
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⋊C4C2×D4414yes—
664C22⋊C4C2×D4414yes—
665C42—224no—
666C42C2×D4412yes—
667C42C2×D4412yes—
668C42C23×D1112yes—
669C42C23×D1112yes—
670C11C2×#325711yescharacteristic, complemented, Sylow
671C23—22no—
672C23—22no—
673C23—22no—
674C23—222no—
675C23—222no—
676C23—222no—
677C23—442no—
678C23—442no—
679C23—442no—
680C23—442no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23C22×D4412yes—
687C23C22×D4411yescharacteristic
688Q8—222no—
689Q8—222no—
690Q8—442no—
691Q8—884no—
692D4—222no—
693D4—222no—
694D4—222no—
695D4—222no—
696D4—222no—
697D4—222no—
698D4—442no—
699D4—442no—
700D4—442no—
701D4—884no—
702D4—884no—
703D4—884no—
704D4—884no—
705D4—884no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—884no—
725C2×C4—884no—
726C2×C4—884no—
727C2×C4C22×D4412yes—
728C2×C4C22×D4412yes—
729C2×C4C22×D4412yes—
730C2×C4C22×D4412yes—
731C2×C4C22×D4412yes—
732C2×C4C22×D4411yescharacteristic
733C2×C4#6703712yes—
734C2×C4#6704012yes—
735C2×C4C24×D1111yescharacteristic
736C8—22no—
737C8—22no—
738C8—22no—
739C8—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—442no—
745C22—442no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—884no—
754C22—884no—
755C22—884no—
756C22#1062304112yes—
757C22#1062328212yes—
758C22#1062328312yes—
759C22C23×D4411yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—442no—
766C4—442no—
767C4—442no—
768C4—442no—
769C4—442no—
770C4#1062304112yes—
771C4C2×#6703711yescharacteristic
772C4C2×#6704011yescharacteristic
773C2—42no—
774C2—882no—
775C2—882no—
776C2—882no—
777C2#1308002914yesdirect product factor
778C2C2×#1062304111yescharacteristic
779C2C2×#1062328311yescharacteristic
780C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#424C2
socleC23×C11C22×D4
hypercenterC2×#424D11
hypocenterC11C2×#3257
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. C2×#10623066C2semidirect
3. #13080029C2direct (N × H)
4. C2×#10622442C2semidirect
5. C2×#10622460C2semidirect
6. C2×#10622455C2semidirect
7. C2×#10622459C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622747C2semidirect
10. C2×#10622728C2semidirect
11. C2×#10622727C2semidirect
12. C2×#10622461C2semidirect
13. C2×#10622457C2semidirect
14. C2×#10622457C2semidirect
15. C2×#10622456C2semidirect
16. C2×C11×#424C2semidirect
29. #10623066C22semidirect
31. #10623065C22semidirect
48. C11×#424C22semidirect
53. #10622748C22semidirect
54. #10622747C22semidirect
55. #10622728C22semidirect
56. #10622727C22semidirect
69. #10622461C22semidirect
70. #10622460C22semidirect
71. #10622459C22semidirect
72. #10622457C22semidirect
73. #10622457C22semidirect
74. #10622456C22semidirect
75. #10622455C22semidirect
76. #10622442C22semidirect
296. C2×#424D11semidirect
413. #424C2×D11semidirect
565. C2×C11#3257semidirect
670. C11C2×#3257semidirect
777. C2#13080029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230652
C2×#106230662
#130800292
C2×#106224422
C2×#106224602
C2×#106224552
C2×#106224592
C2×#106227482
C2×#106227472
C2×#106227282
C2×#106227272
C2×#106224612
C2×#106224572
C2×#106224562
C2×C11×#4242
C2×#325711