Finite Group Databasebeta

← C2×#13080678 #15630503

Subgroups — C2×#13080678 #15630503

Order 2816.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623064C211yesmaximal, characteristic, complemented
2C2×#10623362C211yesmaximal, characteristic
3#13080678C2116yesmaximal, direct product factor
4C2×#10622378C211yesmaximal, characteristic, complemented
5C2×#10622609C211yesmaximal, characteristic, complemented
6C2×#10622397C211yesmaximal, characteristic, complemented
7C2×#10622407C211yesmaximal, characteristic, complemented
8C2×#10622393C211yesmaximal, characteristic, complemented
9C2×#10622729C211yesmaximal, characteristic, complemented
10C2×#10622380C211yesmaximal, characteristic, complemented
11C2×#10622852C211yesmaximal, characteristic, complemented
12C2×#10622421C211yesmaximal, characteristic, complemented
13C2×#10622402C211yesmaximal, characteristic, complemented
14C2×#10622724C211yesmaximal, characteristic, complemented
15C2×#10622415C211yesmaximal, characteristic, complemented
16C2×C11×#416C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21#10623362—24no—
22#10623362C2218yes—
23C2×Q8×Dic11C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C2×#66991—21no—
26C2×#66991C2211yescharacteristic
27C2×#66989—21no—
28C2×#66989C2211yescharacteristic
29C22×#4324C2211yescharacteristic
30C2×C4×C22⋊D11—21no—
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×#66977—21no—
33C2×#66977C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C22×Dic44C2211yescharacteristic
36C22×#4313C2211yescharacteristic
37#10623064—24no—
38#10623064C2218yescomplemented
39C2×#66950C2211yescharacteristic
40C2×#66945C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66938—21no—
44C2×#66932—21no—
45C2×#66929—21no—
46C2×C4×Dic22—21no—
47C11×#416C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52#10622852C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622729C2218yescomplemented
57#10622724C2218yescomplemented
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64#10622609C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69#10622421C2218yescomplemented
70#10622415C2218yescomplemented
71#10622407C2218yescomplemented
72#10622402C2218yescomplemented
73#10622397C2218yescomplemented
74#10622393C2218yescomplemented
75#10622380C2218yescomplemented
76#10622378C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—24no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—21no—
87C22×C22⋊D11D411yescharacteristic
88C2×Q8×D11—22no—
89C2×Q8×D11—24no—
90C2×Q8×D11—42no—
91C2×Q8×D11C2314yes—
92C22×C4×D11—21no—
93C22×C4×D11C2311yescharacteristic
94C22×Dic22—21no—
95C22×Dic22—21no—
96C22×Dic22C2311yescharacteristic
97C22×Dic22C2311yescharacteristic
98C22×C8×C11—42no—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2314yes—
102C11×#117—22no—
103C11×#117C2314yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C42×C11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11D411yescharacteristic
114Q8×Dic11—22no—
115Q8×Dic11C2314yes—
116C2×#4326—24no—
117C2×#4326C2314yes—
118#66991—28no—
119#66991—22no—
120#66991C2314yes—
121#66989—28no—
122#66989—22no—
123#66989C2314yes—
124C2×#4324—42no—
125C2×#4324C2314yes—
126C4×C22⋊D11—28no—
127C4×C22⋊D11D414yes—
128C4×C22⋊D11C2314yes—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4D411yescharacteristic
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11—21no—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136#66977—22no—
137#66977—22no—
138#66977—28no—
139#66977C2314yes—
140#66977C2314yes—
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×Dic44—42no—
153C2×Dic44C2314yes—
154C2×#4313—42no—
155C2×#4313C2314yes—
156#66950—22no—
157#66950C2314yes—
158#66945—22no—
159#66945C2314yes—
160#66941—22no—
161#66941C2314yes—
162#66940—22no—
163#66940C2314yes—
164#66938—28no—
165#66932—28no—
166#66929—28no—
167C4×Dic22—28no—
168C11×#103C2314yes—
169C11×#103C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yes—
172#66899C2314yes—
173#66896C2314yes—
174C22⋊(C11⋊C8)C2314yes—
175(C2×D11)⋊C8C2314yes—
176#66882C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179#66879C2314yes—
180Dic11⋊C8C2314yes—
181#66874C2314yes—
182#66874C2314yes—
183#66872C2314yes—
184#66871C2314yes—
185C2×#3313—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C23×D11C2×D411yescharacteristic
189C11×#41—28no—
190C11×#41—44no—
191C11×#41—48no—
192C2×Q8×C11—21no—
193C2×Q8×C11—22no—
194C2×Q8×C11#4114yes—
195C2×Q8×C11C2412yes—
196C2×D4×C11—24no—
197C2×D4×C11—21no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—44no—
201C2×D4×C11C2412yes—
202C22×C4×C11—21no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—24no—
208C22×C4×C11—44no—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2411yescharacteristic
213C2×C22⋊D11—24no—
214C2×C22⋊D11—42no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11C2×D414yes—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11C2×D411yescharacteristic
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224Q8×D11—28no—
225Q8×D11—44no—
226Q8×D11—48no—
227C2×C4×D11—24no—
228C2×C4×D11—22no—
229C2×C4×D11—22no—
230C2×C4×D11—44no—
231C2×C4×D11C2×D412yes—
232C2×C4×D11C2412yes—
233C2×Dic22—24no—
234C2×Dic22—24no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—22no—
238C2×Dic22—22no—
239C2×Dic22—22no—
240C2×Dic22—22no—
241C2×Dic22—44no—
242C2×Dic22—44no—
243C2×Dic22C2412yes—
244C2×Dic22C2412yes—
245C2×C8×C11—22no—
246C2×C8×C11—22no—
247C2×C8×C11—44no—
248C2×C8×C11C2412yes—
249C2×C8×C11C2412yes—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4C2412yes—
253C11×C4⋊C4C2412yes—
254C11×C22⋊C4—24no—
255C42×C11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11C2×D414yes—
262#4326—28no—
263#4324—44no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4C2×D414yes—
267C4⋊Dic11—24no—
268C4⋊Dic11—24no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11C2412yes—
272C4⋊Dic11C2412yes—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4C2×D414yes—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C4×Dic11—24no—
281C4×Dic11C2×D412yes—
282C4×Dic11C2412yes—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287Dic44—44no—
288#4313—44no—
289C2×#556—111no—
290C2×#548—111no—
291#3313—1116no—
292C2×#489—111no—
293C2×#485—111no—
294C2×#482—111no—
295C2×#477—111no—
296C2×#468—111no—
297C2×#467—111no—
298C2×#464—111no—
299C2×#452—111no—
300C2×#451—111no—
301C2×#441—111no—
302C2×#435—111no—
303C2×#419—111no—
304C2×#416D1111yescharacteristic, complemented
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D412yes—
313C23×C11C22×D411yescharacteristic
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11C22×D412yes—
318Q8×C11—24no—
319Q8×C11—22no—
320Q8×C11C2×#4114yes—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—48no—
324D4×C11—42no—
325C2×C4×C11—24no—
326C2×C4×C11—22no—
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—48no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11C22×D412yes—
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C2×#4112yes—
339C2×C4×C11H(5,𝔽2)12yes—
340C2×C4×C11C2511yescharacteristic
341C22⋊D11—44no—
342C22⋊D11—48no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11C22×D412yes—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357C4×D11—24no—
358C4×D11—22no—
359C4×D11—22no—
360C4×D11—48no—
361Dic22—22no—
362Dic22—22no—
363Dic22—22no—
364Dic22—22no—
365Dic22—48no—
366Dic22—48no—
367Dic22—42no—
368Dic22—42no—
369C8×C11—22no—
370C8×C11—22no—
371C11⋊C8—22no—
372C11⋊C8—22no—
373C22×#41C2×D1111yescharacteristic
374C23×Q8—111no—
375C22×Q16—111no—
376C22×Q16—111no—
377C22×SD16—111no—
378C22×M16—111no—
379C23×C8C2×D1111yescharacteristic
380#556—118no—
381#556—224no—
382#548—118no—
383#548—224no—
384C2×C4⋊Q8—111no—
385C2×#126—221no—
386C2×#126—221no—
387C2×#124—111no—
388C2×#124—221no—
389C2×#124—221no—
390C2×C22⋊Q8—111no—
391C2×C22⋊Q8—111no—
392C2×C22⋊Q8—111no—
393C2×C22⋊Q8—221no—
394C2×#121—111no—
395C2×#121—221no—
396C2×C4×Q8—111no—
397C2×C4×Q8—111no—
398C2×C4×Q8—221no—
399C2×C4×D4—111no—
400C2×C4×D4—221no—
401C2×#117—111no—
402C2×#117C2×D1111yescharacteristic
403#489—118no—
404#485—118no—
405#482—118no—
406#477—118no—
407#468—118no—
408#467—118no—
409#464—118no—
410#452—118no—
411#451—118no—
412#441—118no—
413#435—118no—
414C2×#107—111no—
415C2×#107—111no—
416C2×#106—111no—
417C2×C4⋊C8—111no—
418#419—118no—
419#416C2×D1118yescomplemented
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#103C2×D1111yescharacteristic
426C2×#103C2×D1111yescharacteristic
427C2×#102—111no—
428C2×#102C2×D1111yescharacteristic
429C2×#102C2×D1111yescharacteristic
430C2×C22⋊C8—111no—
431C2×C22⋊C8—111no—
432C2×#97—111no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—44no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—84no—
441C22×C11#54612yes—
442C22×C11#57512yes—
443C22×C11#57812yes—
444C22×C11C23×D411yescharacteristic
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—22no—
448C2×D11—44no—
449C4×C11—22no—
450C4×C11—24no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11#54612yes—
454C4×C11C22×#4111yescharacteristic
455C4×C11C2×H(5,𝔽2)11yescharacteristic
456Dic11—22no—
457Dic11—22no—
458Dic11—22no—
459Dic11—42no—
460Dic11—42no—
461Dic11—42no—
462Dic11—42no—
463C2×#41—22no—
464C2×#41—24no—
465C2×#41—42no—
466C2×#41C22×D1114yes—
467C22×Q8—114no—
468C22×Q8—111no—
469C22×Q8—111no—
470C22×Q8—221no—
471C22×Q8—221no—
472C22×Q8—222no—
473C22×Q8—224no—
474C22×Q8—442no—
475C22×Q8C22×D1111yescharacteristic
476C22×D4—21no—
477C22×D4—111no—
478C22×D4—221no—
479C22×D4C22×D1111yescharacteristic
480C23×C4—21no—
481C23×C4—111no—
482C23×C4—221no—
483C23×C4C22×D1111yescharacteristic
484C2×Q16—114no—
485C2×Q16—114no—
486C2×Q16—224no—
487C2×Q16—442no—
488C2×SD16—114no—
489C2×SD16—442no—
490C2×M16—114no—
491C2×M16—442no—
492C22×C8—42no—
493C22×C8—111no—
494C22×C8—111no—
495C22×C8C22×D1111yescharacteristic
496C22×C8C22×D1111yescharacteristic
497C22×C8C22×D1114yes—
498C4⋊Q8—114no—
499C4⋊Q8—222no—
500#126—228no—
501#126—228no—
502#124—114no—
503#124—222no—
504#124—228no—
505#124—228no—
506C22⋊Q8—114no—
507C22⋊Q8—114no—
508C22⋊Q8—114no—
509C22⋊Q8—222no—
510C22⋊Q8—228no—
511C22⋊Q8—222no—
512C22⋊Q8—222no—
513#121—114no—
514#121—222no—
515#121—228no—
516C4×Q8—114no—
517C4×Q8—114no—
518C4×Q8—228no—
519C4×Q8—222no—
520C4×Q8—222no—
521C4×D4—114no—
522C4×D4—114no—
523C4×D4—228no—
524#117—22no—
525#117—114no—
526#117—222no—
527#117C22×D1114yes—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—111no—
541C2×C22⋊C4—111no—
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×C22⋊C4—221no—
549C2×C42—21no—
550C2×C42—111no—
551C2×C42—221no—
552C2×C42—221no—
553C2×C42—221no—
554#107—114no—
555#107—114no—
556#106—114no—
557C4⋊C8—114no—
558#103—114no—
559#103—114no—
560#103—114no—
561#103—114no—
562#103—114no—
563#103C22×D1114yes—
564#103C22×D1114yes—
565#102—114no—
566#102C22×D1114yes—
567#102C22×D1114yes—
568C22⋊C8—114no—
569C22⋊C8—114no—
570#97—114no—
571C2×C11—42no—
572C2×C11—82no—
573C2×C11#331314yescomplemented
574C2×C11C2×#54611yescharacteristic
575C2×C11C2×#57511yescharacteristic
576C2×C11C2×#57811yescharacteristic
577D11—42no—
578C24—21no—
579C24—111no—
580C24D4×D1111yescharacteristic
581#41—28no—
582#41—44no—
583#41—48no—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—112no—
587C2×Q8—112no—
588C2×Q8—224no—
589C2×Q8—224no—
590C2×Q8—221no—
591C2×Q8—221no—
592C2×Q8—228no—
593C2×Q8—222no—
594C2×Q8—222no—
595C2×Q8—222no—
596C2×Q8—222no—
597C2×Q8—444no—
598C2×Q8—444no—
599C2×Q8—444no—
600C2×Q8—448no—
601C2×Q8#433914yes—
602C2×Q8C23×D1112yes—
603C2×D4—24no—
604C2×D4—22no—
605C2×D4—21no—
606C2×D4—22no—
607C2×D4—44no—
608C2×D4—114no—
609C2×D4—224no—
610C2×D4—442no—
611C2×D4—444no—
612C2×D4C23×D1112yes—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—44no—
620C22×C4—111no—
621C22×C4—111no—
622C22×C4—111no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—224no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—444no—
633C22×C4D4×D1112yes—
634C22×C4D4×D1111yescharacteristic
635C22×C4C23×D1112yes—
636C22×C4C23×D1111yescharacteristic
637Q16—228no—
638Q16—444no—
639SD16—444no—
640M16—444no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—44no—
644C2×C8—112no—
645C2×C8—112no—
646C2×C8—222no—
647C2×C8—222no—
648C2×C8C23×D1112yes—
649C2×C8C23×D1112yes—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—114no—
653C4⋊C4—112no—
654C4⋊C4—112no—
655C4⋊C4—224no—
656C4⋊C4—224no—
657C4⋊C4—224no—
658C4⋊C4—224no—
659C4⋊C4—221no—
660C4⋊C4—221no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4C23×D1112yes—
664C4⋊C4C23×D1112yes—
665C22⋊C4—24no—
666C22⋊C4—114no—
667C22⋊C4—114no—
668C22⋊C4—224no—
669C22⋊C4—224no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C42—24no—
676C42—112no—
677C42—112no—
678C42—224no—
679C42—224no—
680C42—224no—
681C11C2×#331311yescharacteristic, complemented, Sylow
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—112no—
690C23—222no—
691C23—222no—
692C23—222no—
693C23C2×D4×D1112yes—
694C23C2×D4×D1111yescharacteristic
695Q8—24no—
696Q8—22no—
697Q8—222no—
698Q8—222no—
699Q8—222no—
700Q8—222no—
701Q8—448no—
702Q8—448no—
703Q8—442no—
704Q8—442no—
705Q8C2×#433914yes—
706D4—22no—
707D4—22no—
708D4—48no—
709D4—42no—
710D4—444no—
711D4—448no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—112no—
724C2×C4—112no—
725C2×C4—112no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—224no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—448no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4C2×#433912yes—
742C2×C4C2×D4×D1112yes—
743C2×C4C2×D4×D1111yescharacteristic
744C2×C4#6703712yes—
745C2×C4C24×D1111yescharacteristic
746C8—22no—
747C8—22no—
748C8—222no—
749C8—222no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—222no—
759C22—222no—
760C22—222no—
761C22—444no—
762C22#1062302112yes—
763C22#1062329912yes—
764C22#1062330212yes—
765C22C22×D4×D1111yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—222no—
771C4—222no—
772C4—222no—
773C4—442no—
774C4—442no—
775C4—442no—
776C4—442no—
777C4#1062302112yes—
778C4C22×#433911yescharacteristic
779C4C2×#6703711yescharacteristic
780C2—42no—
781C2—82no—
782C2—442no—
783C2#1308067814yesdirect product factor
784C2C2×#1062302111yescharacteristic
785C2C2×#1062329911yescharacteristic
786C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC2×#10623362C2
hypercenterC2×#416D11
hypocenterC11C2×#3313
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#10623064C2semidirect
3. #13080678C2direct (N × H)
4. C2×#10622378C2semidirect
5. C2×#10622609C2semidirect
6. C2×#10622397C2semidirect
7. C2×#10622407C2semidirect
8. C2×#10622393C2semidirect
9. C2×#10622729C2semidirect
10. C2×#10622380C2semidirect
11. C2×#10622852C2semidirect
12. C2×#10622421C2semidirect
13. C2×#10622402C2semidirect
14. C2×#10622724C2semidirect
15. C2×#10622415C2semidirect
16. C2×C11×#416C2semidirect
38. #10623064C22semidirect
47. C11×#416C22semidirect
52. #10622852C22semidirect
56. #10622729C22semidirect
57. #10622724C22semidirect
64. #10622609C22semidirect
69. #10622421C22semidirect
70. #10622415C22semidirect
71. #10622407C22semidirect
72. #10622402C22semidirect
73. #10622397C22semidirect
74. #10622393C22semidirect
75. #10622380C22semidirect
76. #10622378C22semidirect
304. C2×#416D11semidirect
419. #416C2×D11semidirect
573. C2×C11#3313semidirect
681. C11C2×#3313semidirect
783. C2#13080678direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230642
C2×#106233622
#130806782
C2×#106223782
C2×#106226092
C2×#106223972
C2×#106224072
C2×#106223932
C2×#106227292
C2×#106223802
C2×#106228522
C2×#106224212
C2×#106224022
C2×#106227242
C2×#106224152
C2×C11×#4162
C2×#331311