Finite Group Databasebeta

← C2×#13080794 #15630402

Subgroups — C2×#13080794 #15630402

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623089C211yesmaximal, characteristic
2C2×#10623258C211yesmaximal, characteristic, complemented
3#13080794C2116yesmaximal, direct product factor
4C2×#10622695C211yesmaximal, characteristic, complemented
5C2×#10622422C211yesmaximal, characteristic, complemented
6C2×#10622428C211yesmaximal, characteristic, complemented
7C2×#10622442C211yesmaximal, characteristic, complemented
8C2×#10622787C211yesmaximal, characteristic, complemented
9C2×#10622784C211yesmaximal, characteristic, complemented
10C2×#10622783C211yesmaximal, characteristic, complemented
11C2×#10622783C211yesmaximal, characteristic, complemented
12C2×#10622631C211yesmaximal, characteristic, complemented
13C2×#10622449C211yesmaximal, characteristic, complemented
14C2×#10622415C211yesmaximal, characteristic, complemented
15C2×D11×#103C211yesmaximal, characteristic, complemented
16C2×C11×#461C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C2×#66991C2211yescharacteristic
26C2×#66991C2211yescharacteristic
27C22×#4324C2211yescharacteristic
28C2×#66982—21no—
29C2×C4×C22⋊D11—21no—
30C22×#4313C2211yescharacteristic
31C22×C8×D11C2211yescharacteristic
32#10623258—24no—
33#10623258C2218yescomplemented
34#10623089—24no—
35#10623089C2218yes—
36C2×#66949—21no—
37C2×#66949—21no—
38C2×#66946—21no—
39C2×#66945C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×#66941—21no—
42C2×#66937—21no—
43C2×#66932—21no—
44C2×C4×D44C2211yescharacteristic
45C2×#66923C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C11×#461C2218yescomplemented
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56#10622787C2218yescomplemented
57#10622784C2218yescomplemented
58#10622783C2218yescomplemented
59#10622783C2218yescomplemented
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×#66882C2211yescharacteristic
63C2×#66881C2211yescharacteristic
64C2×#66880C2211yescharacteristic
65C2×#66880C2211yescharacteristic
66#10622695C2218yescomplemented
67#10622631C2218yescomplemented
68C2×#66874C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66867C2211yescharacteristic
71#10622449C2218yescomplemented
72#10622442C2218yescomplemented
73#10622428C2218yescomplemented
74#10622422C2218yescomplemented
75#10622415C2218yescomplemented
76D11×#103C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C2×Q8×D11—22no—
84C2×Q8×D11—22no—
85C2×Q8×D11—24no—
86C2×Q8×D11—24no—
87C2×Q8×D11—42no—
88C2×Q8×D11—42no—
89C2×Q8×D11C2314yes—
90C2×Q8×D11C2314yes—
91C22×D44D411yescharacteristic
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11—21no—
95C22×C4×D11C2311yescharacteristic
96C22×C4×D11C2311yescharacteristic
97C22×Dic22—21no—
98C22×Dic22—21no—
99C22×Dic22C2311yescharacteristic
100C2×C11×SD16—42no—
101C2×C11×SD16—42no—
102C2×C11×SD16C2314yes—
103C2×C11×SD16C2314yes—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×C4⋊Q8—22no—
107C11×C4⋊Q8C2314yes—
108C4×D4×C11—22no—
109C4×D4×C11C2314yes—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#66999—22no—
118#66999—22no—
119#66999C2314yes—
120#66999C2314yes—
121#66991—22no—
122#66991—22no—
123#66991C2314yes—
124#66991C2314yes—
125C2×#4324—24no—
126C2×#4324C2314yes—
127#66982—28no—
128C4×C22⋊D11—28no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4D411yescharacteristic
133C2×(C2×D11)⋊C4D411yescharacteristic
134C2×C4⋊Dic11D411yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×C4×Dic11—21no—
145C2×C4×Dic11—21no—
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148C2×#4313—42no—
149C2×#4313C2314yes—
150C2×C8×D11—42no—
151C2×C8×D11C2314yes—
152#66949—28no—
153#66949—28no—
154#66946—28no—
155#66945—22no—
156#66945C2314yes—
157C4⋊C4×D11—22no—
158C4⋊C4×D11C2314yes—
159#66941—28no—
160#66937—28no—
161#66932—28no—
162C4×D44D414yes—
163C4×D44C2314yes—
164#66923—22no—
165#66923C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168C11×C4⋊C8C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171#66899C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174#66899C2314yes—
175#66896C2314yes—
176(C2×D11)⋊C8C2314yes—
177(C2×D11)⋊C8C2314yes—
178#66882C2314yes—
179#66881C2314yes—
180#66880C2314yes—
181#66880C2314yes—
182#66874C2314yes—
183#66871C2314yes—
184#66867C2314yes—
185C2×#3320—111nomaximal, Sylow
186C24×C11—21no—
187C23×D11C2×D411yescharacteristic
188C23×D11C2×D411yescharacteristic
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—
197C2×D4×C11—21no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11C2412yes—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—24no—
205C22×C4×C11—82no—
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—82no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219Q8×D11—28no—
220Q8×D11—28no—
221Q8×D11—44no—
222Q8×D11—44no—
223Q8×D11—48no—
224Q8×D11—48no—
225C2×D44—24no—
226C2×D44C2×D414yes—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—24no—
230C2×C4×D11—22no—
231C2×C4×D11—22no—
232C2×C4×D11—22no—
233C2×C4×D11—22no—
234C2×C4×D11—44no—
235C2×C4×D11—44no—
236C2×C4×D11—82no—
237C2×C4×D11C2×D412yes—
238C2×C4×D11C2×D412yes—
239C2×C4×D11C2412yes—
240C2×C4×D11C2412yes—
241C2×Dic22—24no—
242C2×Dic22—24no—
243C2×Dic22—21no—
244C2×Dic22—22no—
245C2×Dic22—44no—
246C2×Dic22—44no—
247C2×Dic22#4114yes—
248C2×Dic22C2412yes—
249C11×SD16—44no—
250C11×SD16—44no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11C2412yes—
254C2×C8×C11C2412yes—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4C2412yes—
259C11×C22⋊C4—24no—
260C42×C11C2×D412yes—
261C42×C11C2412yes—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264#4324—28no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4C2×D414yes—
269(C2×D11)⋊C4C2×D414yes—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11C2×D414yes—
274C4⋊Dic11C2412yes—
275C4⋊Dic11C2412yes—
276C4⋊Dic11C2412yes—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283C4×Dic11—24no—
284C4×Dic11—24no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8C2412yes—
288C2×C11⋊C8C2412yes—
289#4313—44no—
290C8×D11—44no—
291C2×#553—111no—
292C2×D4×Q8—111no—
293#3320—1116no—
294C2×#491—111no—
295C2×#484—111no—
296C2×#485—111no—
297C2×#479—111no—
298C2×#468—111no—
299C2×#465—111no—
300C2×#461D1111yescharacteristic, complemented
301C2×#448—111no—
302C2×#448—111no—
303C2×#440—111no—
304C2×#435—111no—
305C2×#419—111no—
306C22×#103—111no—
307C23×C11—22no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11#13714yes—
318C22×D11C22×D412yes—
319C22×D11C22×D412yes—
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11—22no—
324Q8×C11—42no—
325Q8×C11—42no—
326D4×C11—22no—
327D4×C11—22no—
328D4×C11—42no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—84no—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C2×#4112yes—
342C2×C4×C11H(5,𝔽2)12yes—
343C2×C4×C11C2511yescharacteristic
344C22⋊D11—48no—
345C22⋊D11—84no—
346C2×Dic11—24no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358D44—28no—
359C4×D11—24no—
360C4×D11—24no—
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—22no—
365C4×D11—48no—
366C4×D11—48no—
367C4×D11—84no—
368Dic22—24no—
369Dic22—22no—
370Dic22—48no—
371Dic22—48no—
372Dic22C2×#4114yes—
373C8×C11—22no—
374C8×C11—22no—
375C11⋊C8—22no—
376C11⋊C8—22no—
377C23×Q8—111no—
378C23×Q8—111no—
379C22×SD16—111no—
380C22×SD16C2×D1111yescharacteristic
381C22×SD16C2×D1111yescharacteristic
382C22×M16—111no—
383C23×C8—111no—
384#553—118no—
385#553—224no—
386D4×Q8—118no—
387D4×Q8—224no—
388C2×C4⋊Q8—221no—
389C2×C4⋊Q8C2×D1111yescharacteristic
390C2×#126—221no—
391C2×#125—111no—
392C2×#123—221no—
393C2×C22⋊Q8—111no—
394C2×C22⋊Q8—111no—
395C2×C22⋊Q8—221no—
396C2×C22⋊Q8—221no—
397C2×#121—111no—
398C2×#121—111no—
399C2×#121—221no—
400C2×C4×Q8—111no—
401C2×C4×D4—111no—
402C2×C4×D4—221no—
403C2×C4×D4—221no—
404C2×C4×D4C2×D1111yescharacteristic
405C2×#117—111no—
406C22×C4⋊C4—111no—
407#491—118no—
408#485—118no—
409#484—118no—
410#479—118no—
411#468—118no—
412#465—118no—
413#461C2×D1118yescomplemented
414#448—118no—
415#448—118no—
416#440—118no—
417#435—118no—
418C2×#107—111no—
419C2×#107—111no—
420C2×#106—111no—
421C2×C4⋊C8C2×D1111yescharacteristic
422#419—118no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—118no—
431C2×#103C2×D1111yescharacteristic
432C2×#103C2×D1111yescharacteristic
433C2×#102—111no—
434C2×C22⋊C8—111no—
435C2×C22⋊C8—111no—
436C2×#97—111no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—84no—
441C22×C11#54612yes—
442C22×C11C2×#13712yes—
443C22×C11#57712yes—
444C22×C11C23×D411yescharacteristic
445C2×D11—22no—
446C2×D11—28no—
447C2×D11—22no—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11—22no—
451C2×D11—44no—
452C2×D11C2×#13714yes—
453C4×C11—22no—
454C4×C11—22no—
455C4×C11—42no—
456C4×C11—42no—
457C4×C11—42no—
458C4×C11#54612yes—
459C4×C11C22×#4111yescharacteristic
460C4×C11C2×H(5,𝔽2)11yescharacteristic
461Dic11—24no—
462Dic11—22no—
463Dic11—22no—
464Dic11—42no—
465Dic11—42no—
466Dic11—42no—
467C22×Q8—114no—
468C22×Q8—114no—
469C22×Q8—111no—
470C22×Q8—221no—
471C22×Q8—221no—
472C22×Q8—222no—
473C22×Q8—222no—
474C22×Q8—224no—
475C22×Q8—224no—
476C22×Q8—442no—
477C22×Q8—442no—
478C22×Q8C22×D1111yescharacteristic
479C22×Q8C22×D1111yescharacteristic
480C22×D4—111no—
481C22×D4—221no—
482C22×D4—221no—
483C22×D4C22×D1111yescharacteristic
484C23×C4—21no—
485C23×C4—111no—
486C23×C4—111no—
487C23×C4—221no—
488C23×C4—221no—
489C23×C4—221no—
490C2×SD16—42no—
491C2×SD16—42no—
492C2×SD16—114no—
493C2×SD16—224no—
494C2×SD16C22×D1114yes—
495C2×SD16C22×D1114yes—
496C2×M16—114no—
497C2×M16—442no—
498C22×C8—111no—
499C22×C8—111no—
500C22×C8—114no—
501C22×C8—442no—
502C22×C8C22×D1111yescharacteristic
503C22×C8C22×D1111yescharacteristic
504C4⋊Q8—22no—
505C4⋊Q8—228no—
506C4⋊Q8C22×D1114yes—
507#126—228no—
508#125—114no—
509#125—222no—
510#123—228no—
511C22⋊Q8—114no—
512C22⋊Q8—114no—
513C22⋊Q8—228no—
514C22⋊Q8—228no—
515C22⋊Q8—222no—
516C22⋊Q8—222no—
517#121—114no—
518#121—114no—
519#121—228no—
520#121—222no—
521#121—222no—
522C4×Q8—114no—
523C4×Q8—222no—
524C4×D4—22no—
525C4×D4—114no—
526C4×D4—114no—
527C4×D4—228no—
528C4×D4—228no—
529C4×D4C22×D1114yes—
530#117—114no—
531#117—222no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—111no—
535C2×C4⋊C4—111no—
536C2×C4⋊C4—111no—
537C2×C4⋊C4—111no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—222no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4—221no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4—221no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4C22×D1111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—111no—
549C2×C22⋊C4—111no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C42—221no—
556C2×C42—221no—
557C2×C42C22×D1111yescharacteristic
558#107—114no—
559#107—114no—
560#106—114no—
561C4⋊C8C22×D1114yes—
562#103—114no—
563#103—114no—
564#103—114no—
565#103—114no—
566#103—114no—
567#103—114no—
568#103—114no—
569#103C22×D1114yes—
570#103C22×D1114yes—
571#102—114no—
572C22⋊C8—114no—
573C22⋊C8—114no—
574#97—114no—
575C2×C11—82no—
576C2×C11#332014yescomplemented
577C2×C11C2×#54611yescharacteristic
578C2×C11C22×#13711yescharacteristic
579C2×C11C2×#57711yescharacteristic
580D11—24no—
581D11—42no—
582C24—21no—
583C24—111no—
584C24—111no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—114no—
592C2×Q8—112no—
593C2×Q8—224no—
594C2×Q8—224no—
595C2×Q8—221no—
596C2×Q8—222no—
597C2×Q8—228no—
598C2×Q8—228no—
599C2×Q8—444no—
600C2×Q8—444no—
601C2×Q8—444no—
602C2×Q8—444no—
603C2×Q8—448no—
604C2×Q8—448no—
605C2×Q8C23×D1112yes—
606C2×Q8C23×D1112yes—
607C2×D4—21no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—114no—
611C2×D4—224no—
612C2×D4—224no—
613C2×D4—224no—
614C2×D4—444no—
615C2×D4—882no—
616C2×D4C23×D1112yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—24no—
621C22×C4—82no—
622C22×C4—111no—
623C22×C4—111no—
624C22×C4—112no—
625C22×C4—112no—
626C22×C4—112no—
627C22×C4—112no—
628C22×C4—224no—
629C22×C4—224no—
630C22×C4—224no—
631C22×C4—221no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—444no—
640C22×C4—444no—
641C22×C4—882no—
642C22×C4D4×D1111yescharacteristic
643C22×C4D4×D1111yescharacteristic
644C22×C4C23×D1111yescharacteristic
645SD16—44no—
646SD16—44no—
647SD16—228no—
648M16—444no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—112no—
652C2×C8—112no—
653C2×C8—222no—
654C2×C8—222no—
655C2×C8—444no—
656C2×C8C23×D1112yes—
657C2×C8C23×D1112yes—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—114no—
662C4⋊C4—112no—
663C4⋊C4—112no—
664C4⋊C4—112no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—221no—
669C4⋊C4—221no—
670C4⋊C4—221no—
671C4⋊C4—224no—
672C4⋊C4—224no—
673C4⋊C4—224no—
674C4⋊C4C23×D1112yes—
675C22⋊C4—24no—
676C22⋊C4—114no—
677C22⋊C4—114no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—224no—
683C42—224no—
684C42—224no—
685C42D4×D1112yes—
686C42C23×D1112yes—
687C11C2×#332011yescharacteristic, complemented, Sylow
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—114no—
693C23—112no—
694C23—112no—
695C23—222no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23—222no—
700C23C2×D4×D1111yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—42no—
706Q8—42no—
707Q8—114no—
708Q8—224no—
709Q8—222no—
710Q8—448no—
711Q8—448no—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—228no—
716D4—448no—
717D4—884no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—84no—
727C2×C4—112no—
728C2×C4—112no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—224no—
732C2×C4—222no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—448no—
743C2×C4—448no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—884no—
748C2×C4C2×D4×D1112yes—
749C2×C4C2×D4×D1112yes—
750C2×C4C2×D4×D1111yescharacteristic
751C2×C4#6703712yes—
752C2×C4#41×D1112yes—
753C2×C4C24×D1111yescharacteristic
754C8—22no—
755C8—22no—
756C8—222no—
757C8—222no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22—114no—
763C22—222no—
764C22—228no—
765C22—222no—
766C22—222no—
767C22—222no—
768C22—222no—
769C22—444no—
770C22#1062314312yes—
771C22#1062329312yes—
772C22D11×#13712yes—
773C22C22×D4×D1111yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—222no—
780C4—222no—
781C4—224no—
782C4—442no—
783C4—442no—
784C4—442no—
785C4#1062314312yes—
786C4C2×#6703711yescharacteristic
787C4C2×#41×D1111yescharacteristic
788C2—82no—
789C2—224no—
790C2—442no—
791C2#1308079414yesdirect product factor
792C2C2×#1062314311yescharacteristic
793C2C2×D11×#13711yescharacteristic
794C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC2×#10623089C2
hypercenterC2×#461D11
hypocenterC11C2×#3320
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. C2×#10623258C2semidirect
3. #13080794C2direct (N × H)
4. C2×#10622695C2semidirect
5. C2×#10622422C2semidirect
6. C2×#10622428C2semidirect
7. C2×#10622442C2semidirect
8. C2×#10622787C2semidirect
9. C2×#10622784C2semidirect
10. C2×#10622783C2semidirect
11. C2×#10622783C2semidirect
12. C2×#10622631C2semidirect
13. C2×#10622449C2semidirect
14. C2×#10622415C2semidirect
15. C2×D11×#103C2semidirect
16. C2×C11×#461C2semidirect
33. #10623258C22semidirect
47. C11×#461C22semidirect
56. #10622787C22semidirect
57. #10622784C22semidirect
58. #10622783C22semidirect
59. #10622783C22semidirect
66. #10622695C22semidirect
67. #10622631C22semidirect
71. #10622449C22semidirect
72. #10622442C22semidirect
73. #10622428C22semidirect
74. #10622422C22semidirect
75. #10622415C22semidirect
76. D11×#103C22semidirect
300. C2×#461D11semidirect
413. #461C2×D11semidirect
576. C2×C11#3320semidirect
687. C11C2×#3320semidirect
791. C2#13080794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230892
C2×#106232582
#130807942
C2×#106226952
C2×#106224222
C2×#106224282
C2×#106224422
C2×#106227872
C2×#106227842
C2×#106227832
C2×#106226312
C2×#106224492
C2×#106224152
C2×D11×#1032
C2×C11×#4612
C2×#332011