Finite Group Databasebeta

← C2×#13080905 #15630665

Subgroups — C2×#13080905 #15630665

Order 2816.

2146 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×#10623147C211yesmaximal, characteristic
2C2×#10623163C211yesmaximal, characteristic, complemented
3#13080905C2116yesmaximal, direct product factor
4C2×#10622405C211yesmaximal, characteristic, complemented
5C2×#10622501C211yesmaximal, characteristic, complemented
6C2×#10622658C211yesmaximal, characteristic, complemented
7C2×#10622488C211yesmaximal, characteristic, complemented
8C2×#10622393C211yesmaximal, characteristic, complemented
9C2×#10622775C211yesmaximal, characteristic, complemented
10C2×#10622653C211yesmaximal, characteristic, complemented
11C2×#10622783C211yesmaximal, characteristic, complemented
12C2×#10622371C211yesmaximal, characteristic, complemented
13C2×#10622741C211yesmaximal, characteristic, complemented
14C2×#10622733C211yesmaximal, characteristic, complemented
15C2×#10622415C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×#66997C2211yescharacteristic
24C2×#66992—21no—
25C2×#66991C2211yescharacteristic
26C2×#66989—21no—
27C2×D4×Dic11C2211yescharacteristic
28C22×#4324C2211yescharacteristic
29C22×#4324C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C22×#4313C2211yescharacteristic
33#10623163—24no—
34#10623163C2218yescomplemented
35#10623147—24no—
36#10623147C2218yes—
37C2×#66950C2211yescharacteristic
38C2×#66949—21no—
39C2×#66945C2211yescharacteristic
40C2×#66941—21no—
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66938—21no—
44C2×(C22⋊D11)⋊C4—21no—
45C2×#66931—21no—
46C2×#66930—21no—
47C11×#468C2218yescomplemented
48C2×C11×#107C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622783C2218yescomplemented
55#10622775C2218yescomplemented
56#10622741C2218yescomplemented
57#10622733C2218yescomplemented
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×C8×Dic11C2211yescharacteristic
65#10622658C2218yescomplemented
66#10622653C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66874C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622501C2218yescomplemented
72#10622488C2218yescomplemented
73#10622415C2218yescomplemented
74#10622405C2218yescomplemented
75#10622393C2218yescomplemented
76#10622371C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11D411yescharacteristic
83C23×Dic11—21no—
84C23×Dic11—21no—
85C2×Q8×D11—22no—
86C2×Q8×D11—24no—
87C2×Q8×D11—42no—
88C2×Q8×D11C2314yes—
89C22×C4×D11—21no—
90C22×C4×D11C2311yescharacteristic
91C22×Dic22—24no—
92C22×Dic22—21no—
93C22×Dic22—22no—
94C22×Dic22—21no—
95C22×Dic22—21no—
96C22×Dic22—42no—
97C22×Dic22C2311yescharacteristic
98C22×Dic22C2314yes—
99C22×Dic22C2311yescharacteristic
100C2×C11×SD16—42no—
101C2×C11×SD16C2314yes—
102C2×C11×M16—42no—
103C2×C11×M16C2314yes—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×C22⋊Q8—22no—
107C11×C22⋊Q8C2314yes—
108C11×#121—22no—
109C11×#121C2314yes—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11D411yescharacteristic
119#66997—22no—
120#66997C2314yes—
121#66992—28no—
122#66991—22no—
123#66991C2314yes—
124#66989—28no—
125D4×Dic11—22no—
126D4×Dic11C2314yes—
127C2×#4324—24no—
128C2×#4324—42no—
129C2×#4324C2314yes—
130C2×#4324C2314yes—
131C4×C22⋊D11D414yes—
132C4×C22⋊D11C2314yes—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4D411yescharacteristic
136#66979—22no—
137#66979C2314yes—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4D411yescharacteristic
146C2×C4×Dic11—21no—
147C2×C4×Dic11—21no—
148C2×C4×Dic11—21no—
149C2×C4×Dic11C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C2×#4313—42no—
153C2×#4313C2314yes—
154#66950—22no—
155#66950C2314yes—
156#66949—28no—
157#66945—22no—
158#66945C2314yes—
159#66941—28no—
160#66941—22no—
161#66941C2314yes—
162#66940—22no—
163#66940C2314yes—
164#66938—28no—
165(C22⋊D11)⋊C4—28no—
166#66931—28no—
167#66930—28no—
168C11×#107C2314yes—
169C11×#103C2314yes—
170C11×#102C2314yes—
171#66899C2314yes—
172#66899C2314yes—
173C22⋊(C11⋊C8)C2314yes—
174(C2×D11)⋊C8C2314yes—
175#66880C2314yes—
176#66880C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179Dic11⋊C8C2314yes—
180C8×Dic11C2314yes—
181#66874C2314yes—
182#66874C2314yes—
183#66872C2314yes—
184#66871C2314yes—
185C2×#3329—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C23×D11C2×D411yescharacteristic
189C2×Q8×C11—21no—
190C2×Q8×C11—22no—
191C2×Q8×C11—22no—
192C2×Q8×C11C2412yes—
193C2×D4×C11—24no—
194C2×D4×C11—21no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—82no—
198C2×D4×C11C2412yes—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2411yescharacteristic
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—82no—
211C2×C22⋊D11C2×D414yes—
212C22×Dic11—24no—
213C22×Dic11—21no—
214C22×Dic11—24no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—44no—
219C22×Dic11—44no—
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222C22×Dic11C2×D411yescharacteristic
223Q8×D11—28no—
224Q8×D11—44no—
225Q8×D11—48no—
226C2×C4×D11—24no—
227C2×C4×D11—22no—
228C2×C4×D11—22no—
229C2×C4×D11—44no—
230C2×C4×D11C2×D412yes—
231C2×C4×D11C2412yes—
232C2×Dic22—28no—
233C2×Dic22—24no—
234C2×Dic22—24no—
235C2×Dic22—21no—
236C2×Dic22—24no—
237C2×Dic22—21no—
238C2×Dic22—22no—
239C2×Dic22—22no—
240C2×Dic22—22no—
241C2×Dic22—44no—
242C2×Dic22—48no—
243C2×Dic22—44no—
244C2×Dic22—44no—
245C2×Dic22—82no—
246C2×Dic22#4114yes—
247C2×Dic22C2412yes—
248C2×Dic22C2412yes—
249C11×SD16—44no—
250C11×M16—44no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11C2412yes—
254C2×C8×C11C2412yes—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4C2412yes—
259C11×C4⋊C4C2412yes—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11C2×D414yes—
266#4324—28no—
267#4324—44no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4C2×D414yes—
271C4⋊Dic11—24no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11C2412yes—
275C4⋊Dic11C2412yes—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4C2×D414yes—
281C4×Dic11—24no—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11C2×D412yes—
285C4×Dic11C2412yes—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290#4313—44no—
291C2×#555—111no—
292C2×D4×Q8—111no—
293#3329—1116no—
294C2×#487—111no—
295C2×#485—111no—
296C2×#485—111no—
297C2×#477—111no—
298C2×#468—111no—
299C2×#468D1111yescharacteristic, complemented
300C2×#461—111no—
301C2×#448—111no—
302C2×#448—111no—
303C2×C4×SD16—111no—
304C2×#436—111no—
305C2×#419—111no—
306C2×#419—111no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—42no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11C22×D412yes—
315C23×C11C22×D411yescharacteristic
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11C22×D412yes—
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—42no—
323D4×C11—22no—
324D4×C11—22no—
325D4×C11—42no—
326D4×C11—84no—
327C2×C4×C11—22no—
328C2×C4×C11—24no—
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×C11C22×D412yes—
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C2×#4112yes—
340C2×C4×C11H(5,𝔽2)12yes—
341C2×C4×C11C2511yescharacteristic
342C22⋊D11—28no—
343C22⋊D11—84no—
344C2×Dic11—24no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—48no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—48no—
356C2×Dic11#13714yes—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359C2×Dic11C22×D412yes—
360C4×D11—24no—
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—48no—
364Dic22—24no—
365Dic22—22no—
366Dic22—22no—
367Dic22—22no—
368Dic22—48no—
369Dic22—48no—
370Dic22—42no—
371Dic22—84no—
372Dic22C2×#4114yes—
373C8×C11—22no—
374C8×C11—22no—
375C11⋊C8—22no—
376C11⋊C8—22no—
377C23×Q8—111no—
378C23×Q8—111no—
379C22×SD16—111no—
380C22×SD16—111no—
381C22×SD16C2×D1111yescharacteristic
382C22×M16—111no—
383C22×M16C2×D1111yescharacteristic
384#555—118no—
385#555—224no—
386D4×Q8—118no—
387D4×Q8—224no—
388C2×C4⋊Q8—111no—
389C2×C4⋊Q8—111no—
390C2×C4⋊Q8—221no—
391C2×#124—221no—
392C2×#124—221no—
393C2×C22⋊Q8—111no—
394C2×C22⋊Q8—221no—
395C2×C22⋊Q8—221no—
396C2×C22⋊Q8C2×D1111yescharacteristic
397C2×#121—111no—
398C2×#121—221no—
399C2×#121C2×D1111yescharacteristic
400C2×C4×Q8—111no—
401C2×C4×D4—111no—
402C2×C4×D4—111no—
403C2×C4×D4—221no—
404C2×#117—111no—
405C2×#117—111no—
406C2×#117—221no—
407#487—118no—
408#485—118no—
409#485—118no—
410#477—118no—
411#468—118no—
412#468C2×D1118yescomplemented
413#461—118no—
414#448—118no—
415#448—118no—
416C4×SD16—118no—
417#436—118no—
418C2×#107—111no—
419C2×#107C2×D1111yescharacteristic
420C2×#106—111no—
421C2×C4⋊C8—111no—
422#419—118no—
423#419—118no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103C2×D1111yescharacteristic
433C2×#102C2×D1111yescharacteristic
434C2×C22⋊C8—111no—
435C2×C22⋊C8—111no—
436C2×C4×C8—111no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—44no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—84no—
445C22×C11#54612yes—
446C22×C11C2×#13712yes—
447C22×C11#57712yes—
448C22×C11C23×D411yescharacteristic
449C2×D11—22no—
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—44no—
453C4×C11—22no—
454C4×C11—42no—
455C4×C11—42no—
456C4×C11—42no—
457C4×C11#54612yes—
458C4×C11C22×#4111yescharacteristic
459C4×C11C2×H(5,𝔽2)11yescharacteristic
460Dic11—24no—
461Dic11—22no—
462Dic11—22no—
463Dic11—42no—
464Dic11—42no—
465Dic11—42no—
466Dic11C2×#13714yes—
467C22×Q8—114no—
468C22×Q8—111no—
469C22×Q8—111no—
470C22×Q8—114no—
471C22×Q8—221no—
472C22×Q8—221no—
473C22×Q8—224no—
474C22×Q8—222no—
475C22×Q8—221no—
476C22×Q8—222no—
477C22×Q8—224no—
478C22×Q8—442no—
479C22×Q8—442no—
480C22×Q8C22×D1111yescharacteristic
481C22×D4—21no—
482C22×D4—111no—
483C22×D4—221no—
484C22×D4C22×D1111yescharacteristic
485C23×C4—111no—
486C23×C4—221no—
487C23×C4—221no—
488C23×C4—221no—
489C23×C4C22×D1111yescharacteristic
490C2×SD16—42no—
491C2×SD16—114no—
492C2×SD16—114no—
493C2×SD16—224no—
494C2×SD16—442no—
495C2×SD16C22×D1114yes—
496C2×M16—42no—
497C2×M16—114no—
498C2×M16—442no—
499C2×M16C22×D1114yes—
500C22×C8—111no—
501C22×C8—111no—
502C22×C8C22×D1111yescharacteristic
503C22×C8C22×D1111yescharacteristic
504C4⋊Q8—114no—
505C4⋊Q8—114no—
506C4⋊Q8—222no—
507C4⋊Q8—222no—
508C4⋊Q8—228no—
509#124—228no—
510#124—228no—
511C22⋊Q8—22no—
512C22⋊Q8—114no—
513C22⋊Q8—228no—
514C22⋊Q8—228no—
515C22⋊Q8—222no—
516C22⋊Q8C22×D1114yes—
517#121—22no—
518#121—114no—
519#121—222no—
520#121—228no—
521#121C22×D1114yes—
522C4×Q8—114no—
523C4×Q8—222no—
524C4×D4—114no—
525C4×D4—114no—
526C4×D4—114no—
527C4×D4—222no—
528C4×D4—228no—
529#117—114no—
530#117—114no—
531#117—228no—
532#117—222no—
533#117—222no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—111no—
536C2×C4⋊C4—111no—
537C2×C4⋊C4—111no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4—221no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4C22×D1111yescharacteristic
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—111no—
548C2×C22⋊C4—111no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C42—111no—
555C2×C42—221no—
556C2×C42—221no—
557C2×C42—221no—
558#107—114no—
559#107C22×D1114yes—
560#106—114no—
561C4⋊C8—114no—
562#103—114no—
563#103—114no—
564#103—114no—
565#103—114no—
566#103—114no—
567#103—114no—
568#103—114no—
569#103—114no—
570#103C22×D1114yes—
571#102C22×D1114yes—
572C22⋊C8—114no—
573C22⋊C8—114no—
574C4×C8—114no—
575C2×C11—42no—
576C2×C11—82no—
577C2×C11#332914yescomplemented
578C2×C11C2×#54611yescharacteristic
579C2×C11C22×#13711yescharacteristic
580C2×C11C2×#57711yescharacteristic
581D11—42no—
582C24—21no—
583C24—111no—
584C24D4×D1111yescharacteristic
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—114no—
589C2×Q8—112no—
590C2×Q8—112no—
591C2×Q8—224no—
592C2×Q8—224no—
593C2×Q8—228no—
594C2×Q8—221no—
595C2×Q8—224no—
596C2×Q8—221no—
597C2×Q8—222no—
598C2×Q8—228no—
599C2×Q8—222no—
600C2×Q8—222no—
601C2×Q8—444no—
602C2×Q8—444no—
603C2×Q8—448no—
604C2×Q8—444no—
605C2×Q8—444no—
606C2×Q8—448no—
607C2×Q8—882no—
608C2×Q8C23×D1112yes—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—82no—
614C2×D4—114no—
615C2×D4—224no—
616C2×D4—224no—
617C2×D4—882no—
618C2×D4C23×D1112yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—111no—
625C22×C4—111no—
626C22×C4—111no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—224no—
630C22×C4—224no—
631C22×C4—221no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—224no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—444no—
639C22×C4—444no—
640C22×C4—444no—
641C22×C4D4×D1112yes—
642C22×C4D4×D1111yescharacteristic
643C22×C4C23×D1112yes—
644C22×C4C23×D1111yescharacteristic
645SD16—44no—
646SD16—228no—
647SD16—444no—
648M16—44no—
649M16—444no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—112no—
653C2×C8—112no—
654C2×C8—222no—
655C2×C8—222no—
656C2×C8C23×D1112yes—
657C2×C8C23×D1112yes—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—114no—
662C4⋊C4—112no—
663C4⋊C4—112no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—224no—
669C4⋊C4—221no—
670C4⋊C4—221no—
671C4⋊C4C23×D1112yes—
672C4⋊C4C23×D1112yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—114no—
676C22⋊C4—114no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C42—112no—
683C42—112no—
684C42—224no—
685C42—224no—
686C42—224no—
687C11C2×#332911yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—112no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23C2×D4×D1112yes—
700C23C2×D4×D1111yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—114no—
705Q8—224no—
706Q8—222no—
707Q8—222no—
708Q8—222no—
709Q8—448no—
710Q8—448no—
711Q8—442no—
712Q8—884no—
713D4—22no—
714D4—22no—
715D4—42no—
716D4—84no—
717D4—228no—
718D4—884no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—114no—
730C2×C4—112no—
731C2×C4—112no—
732C2×C4—112no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—224no—
736C2×C4—222no—
737C2×C4—224no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—448no—
744C2×C4—448no—
745C2×C4—448no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
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—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—222no—
767C22—222no—
768C22—222no—
769C22—444no—
770C22#1062314112yes—
771C22#1062330612yes—
772C22D11×#13712yes—
773C22C22×D4×D1111yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—114no—
779C4—222no—
780C4—224no—
781C4—222no—
782C4—442no—
783C4—442no—
784C4—442no—
785C4#1062314112yes—
786C4C2×#6703711yescharacteristic
787C4C2×#41×D1111yescharacteristic
788C2—42no—
789C2—82no—
790C2—442no—
791C2#1308090514yesdirect product factor
792C2C2×#1062314111yescharacteristic
793C2C2×D11×#13711yescharacteristic
794C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
prime radicalC2×#10623147C2
hypercenterC2×#468D11
hypocenterC11C2×#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#10623163C2semidirect
3. #13080905C2direct (N × H)
4. C2×#10622405C2semidirect
5. C2×#10622501C2semidirect
6. C2×#10622658C2semidirect
7. C2×#10622488C2semidirect
8. C2×#10622393C2semidirect
9. C2×#10622775C2semidirect
10. C2×#10622653C2semidirect
11. C2×#10622783C2semidirect
12. C2×#10622371C2semidirect
13. C2×#10622741C2semidirect
14. C2×#10622733C2semidirect
15. C2×#10622415C2semidirect
16. C2×C11×#468C2semidirect
34. #10623163C22semidirect
47. C11×#468C22semidirect
54. #10622783C22semidirect
55. #10622775C22semidirect
56. #10622741C22semidirect
57. #10622733C22semidirect
65. #10622658C22semidirect
66. #10622653C22semidirect
71. #10622501C22semidirect
72. #10622488C22semidirect
73. #10622415C22semidirect
74. #10622405C22semidirect
75. #10622393C22semidirect
76. #10622371C22semidirect
299. C2×#468D11semidirect
412. #468C2×D11semidirect
577. C2×C11#3329semidirect
687. C11C2×#3329semidirect
791. C2#13080905direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231472
C2×#106231632
#130809052
C2×#106224052
C2×#106225012
C2×#106226582
C2×#106224882
C2×#106223932
C2×#106227752
C2×#106226532
C2×#106227832
C2×#106223712
C2×#106227412
C2×#106227332
C2×#106224152
C2×C11×#4682
C2×#332911