Finite Group Databasebeta

← C2×#13079461 #15624419

Subgroups — C2×#13079461 #15624419

Order 2816.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623139C211yesmaximal, characteristic, complemented
2C2×#10623138C211yesmaximal, characteristic, complemented
3#13079461C2116yesmaximal, direct product factor
4C2×#10622390C211yesmaximal, characteristic, complemented
5C2×#10622501C211yesmaximal, characteristic, complemented
6C2×#10622392C211yesmaximal, characteristic, complemented
7C2×#10622495C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622655C211yesmaximal, characteristic, complemented
10C2×#10622727C211yesmaximal, characteristic, complemented
11C2×#10622394C211yesmaximal, characteristic, complemented
12C2×#10622771C211yesmaximal, characteristic, complemented
13C2×#10622389C211yesmaximal, characteristic, complemented
14C2×#10622769C211yesmaximal, characteristic, complemented
15C2×#10622723C211yesmaximal, characteristic, complemented
16C2×C11×#466C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic, complemented
18C22×D4×D11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic, complemented
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic, complemented
24C2×#66993—21no—
25C2×#66992—21no—
26C2×#66991—21no—
27C2×#66991C2211yescharacteristic
28C2×#66991C2211yescharacteristic
29C2×#66990—21no—
30C22×#4324C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32C2×#66983C2211yescharacteristic
33C2×#66977C2211yescharacteristic, complemented
34C22×#4318C2211yescharacteristic, complemented
35C22×#4314C2211yescharacteristic
36#10623139—24no—
37#10623139C2218yescomplemented
38#10623138—24no—
39#10623138C2218yescomplemented
40C2×#66950C2211yescharacteristic
41C2×#66948C2211yescharacteristic
42C2×#66945C2211yescharacteristic
43C2×C4⋊C4×D11C2211yescharacteristic, complemented
44C2×#66938—21no—
45C2×#66937—21no—
46C2×#66935—21no—
47C2×#66931—21no—
48C11×#466C2218yescomplemented
49C2×C11×#107C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic, complemented
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic, complemented
54#10622771C2218yescomplemented
55#10622769C2218yescomplemented
56#10622727C2218yescomplemented
57C2×#66885C2211yescharacteristic
58#10622723C2218yescomplemented
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×#66881C2211yescharacteristic, complemented
64C2×#66880C2211yescharacteristic, complemented
65#10622655C2218yescomplemented
66#10622652C2218yescomplemented
67C2×#66874C2211yescharacteristic, complemented
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622501C2218yescomplemented
72#10622495C2218yescomplemented
73#10622394C2218yescomplemented
74#10622392C2218yescomplemented
75#10622390C2218yescomplemented
76#10622389C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C22×C22⋊D11D411yescharacteristic
89C22×C22⋊D11D411yescharacteristic
90C23×Dic11—21no—
91C2×#4341—22no—
92C2×#4341—42no—
93C2×#4341—42no—
94C2×#4341C2314yescomplemented
95C2×D4×D11—22no—
96C2×D4×D11—42no—
97C2×D4×D11—42no—
98C2×D4×D11C2314yes—
99C2×#4339—42no—
100C2×#4339—42no—
101C2×#4339D414yes—
102C2×#4339C2314yes—
103C22×D44—21no—
104C22×D44D411yescharacteristic
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C22×C4×D11C2311yescharacteristic
108C22×C4×D11C2311yescharacteristic
109C22×Dic22D411yescharacteristic
110C22×Dic22C2311yescharacteristic
111C2×C11×D8—42no—
112C2×C11×D8C2314yes—
113C22×C8×C11—42no—
114C22×C8×C11C2311yescharacteristic
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2314yescomplemented
117C11×#121—22no—
118C11×#121—22no—
119C11×#121C2314yes—
120C11×#121C2314yescomplemented
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11—21no—
128#66993—28no—
129#66992—28no—
130#66991—28no—
131#66991—22no—
132#66991—22no—
133#66991C2314yes—
134#66991C2314yes—
135#66990—28no—
136C2×#4324—42no—
137C2×#4324C2314yes—
138C2×#4323—42no—
139C2×#4323C2314yes—
140#66983—22no—
141#66983C2314yes—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149#66977—22no—
150#66977C2314yescomplemented
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×C4×Dic11—21no—
154C2×#4318—42no—
155C2×#4318C2314yescomplemented
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C2×#4314—42no—
159C2×#4314C2314yes—
160#66950—22no—
161#66950C2314yes—
162#66948—22no—
163#66948C2314yes—
164#66945—22no—
165#66945C2314yes—
166C4⋊C4×D11—22no—
167C4⋊C4×D11C2314yescomplemented
168#66938—28no—
169#66937—28no—
170#66935—28no—
171#66931—28no—
172C11×#107C2314yescomplemented
173C11×#102C2314yes—
174C11×#102C2314yescomplemented
175#66896C2314yes—
176#66896C2314yescomplemented
177#66885C2314yes—
178(C2×D11)⋊C8C2314yes—
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yescomplemented
181(C2×D11)⋊C8C2314yescomplemented
182#66881C2314yescomplemented
183#66880C2314yescomplemented
184#66874C2314yescomplemented
185#66873C2314yes—
186#66872C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3198—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C24×C11C2×D411yescharacteristic
192C23×D11—21no—
193C23×D11—24no—
194C23×D11—44no—
195C23×D11—82no—
196C23×D11—82no—
197C23×D11C2×D411yescharacteristic
198C23×D11C2×D411yescharacteristic
199C2×D4×C11—24no—
200C2×D4×C11—24no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—82no—
208C2×D4×C11—82no—
209C2×D4×C11C2412yes—
210C2×D4×C11C2412yes—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2411yescharacteristic
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—42no—
225C2×C22⋊D11—42no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—82no—
229C2×C22⋊D11—82no—
230C2×C22⋊D11—82no—
231C2×C22⋊D11C2×D414yes—
232C2×C22⋊D11C2×D414yes—
233C22×Dic11—24no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—44no—
238C22×Dic11C2×D411yescharacteristic
239C22×Dic11C2×D411yescharacteristic
240#4341—44no—
241#4341—44no—
242#4341—48no—
243D4×D11—44no—
244D4×D11—44no—
245D4×D11—48no—
246#4339—48no—
247#4339—44no—
248#4339—44no—
249C2×D44—24no—
250C2×D44—21no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44—42no—
254C2×D44—82no—
255C2×D44C2×D414yes—
256C2×D44C2412yes—
257C2×C4×D11—24no—
258C2×C4×D11—22no—
259C2×C4×D11—22no—
260C2×C4×D11—22no—
261C2×C4×D11—22no—
262C2×C4×D11—82no—
263C2×C4×D11C2×D412yes—
264C2×C4×D11C2×D412yes—
265C2×C4×D11C2412yes—
266C2×C4×D11C2412yes—
267C2×Dic22—21no—
268C2×Dic22—22no—
269C2×Dic22—22no—
270C2×Dic22—42no—
271C2×Dic22C2×D414yes—
272C2×Dic22C2412yes—
273C11×D8—44no—
274C2×C8×C11—22no—
275C2×C8×C11—22no—
276C2×C8×C11—44no—
277C2×C8×C11C2412yes—
278C2×C8×C11C2412yes—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4C2412yes—
282C11×C4⋊C4C2412yes—
283C11×C22⋊C4—24no—
284C11×C22⋊C4—24no—
285C22⋊Dic11—24no—
286C22⋊Dic11—24no—
287C22⋊Dic11—24no—
288#4324—44no—
289#4323—44no—
290(C2×D11)⋊C4—24no—
291(C2×D11)⋊C4—24no—
292(C2×D11)⋊C4—24no—
293(C2×D11)⋊C4—24no—
294C4⋊Dic11—24no—
295C4⋊Dic11—21no—
296C4⋊Dic11—21no—
297C4⋊Dic11C2412yes—
298C4⋊Dic11C2412yes—
299Dic11⋊C4—24no—
300Dic11⋊C4—24no—
301C4×Dic11—24no—
302#4318—44no—
303C2×C11⋊C8—22no—
304C2×C11⋊C8—22no—
305C2×C11⋊C8C2412yes—
306C2×C11⋊C8C2412yes—
307#4314—44no—
308C2×#537—111no—
309C2×#535—111no—
310#3198—1116no—
311C2×#481—111no—
312C2×#485—111no—
313C2×#482—111no—
314C2×#480—111no—
315C2×#469—111no—
316C2×#468—111no—
317C2×#466D1111yescharacteristic, complemented
318C2×#465—111no—
319C2×#449—111no—
320C2×#449—111no—
321C2×#450—111no—
322C2×#447—111no—
323C2×#408—111no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—42no—
330C23×C11—42no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—42no—
335C23×C11C22×D412yes—
336C23×C11C22×D411yescharacteristic
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—48no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—84no—
349C22×D11—84no—
350C22×D11—816no—
351C22×D11C22×D412yes—
352C22×D11C22×D412yes—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—42no—
358D4×C11—42no—
359D4×C11—84no—
360D4×C11—84no—
361C2×C4×C11—22no—
362C2×C4×C11—24no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11H(5,𝔽2)12yes—
372C2×C4×C11H(5,𝔽2)12yes—
373C2×C4×C11C2511yescharacteristic
374C22⋊D11—44no—
375C22⋊D11—44no—
376C22⋊D11—48no—
377C22⋊D11—48no—
378C22⋊D11—84no—
379C22⋊D11—84no—
380C22⋊D11—84no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—48no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11C22×D412yes—
391C2×Dic11C22×D412yes—
392D44—22no—
393D44—22no—
394D44—44no—
395D44—42no—
396D44—84no—
397C4×D11—24no—
398C4×D11—24no—
399C4×D11—22no—
400C4×D11—22no—
401C4×D11—22no—
402C4×D11—22no—
403C4×D11—84no—
404Dic22—22no—
405Dic22—22no—
406Dic22—44no—
407Dic22—42no—
408C8×C11—22no—
409C8×C11—22no—
410C11⋊C8—22no—
411C11⋊C8—22no—
412C22×#41—111no—
413C22×#41—111no—
414C23×D4—111no—
415C22×SD16—111no—
416C22×SD16—111no—
417C22×D8—111no—
418C22×D8C2×D1111yescharacteristic
419C22×M16—111no—
420C23×C8C2×D1111yescharacteristic, complemented
421#537—118no—
422#537—224no—
423#535—118no—
424#535—224no—
425C2×#127—221no—
426C2×#124—221no—
427C2×C22⋊Q8—111no—
428C2×C22⋊Q8—111no—
429C2×C22⋊Q8—221no—
430C2×#121—111no—
431C2×#121—111no—
432C2×#121—111no—
433C2×#121—111no—
434C2×#121—221no—
435C2×#121—221no—
436C2×#121—221no—
437C2×#121C2×D1111yescharacteristic
438C2×#121C2×D1111yescharacteristic, complemented
439C2×#120—221no—
440C2×#120—221no—
441C2×#117—111no—
442C22×C4⋊C4—111no—
443#485—118no—
444#482—118no—
445#481—118no—
446#480—118no—
447#469—118no—
448#468—118no—
449#466C2×D1118yescomplemented
450#465—118no—
451#450—118no—
452#449—118no—
453#449—118no—
454#447—118no—
455C2×#107—111no—
456C2×#107C2×D1111yescharacteristic, complemented
457C2×#106—111no—
458C2×#106—111no—
459C2×#103—111no—
460C2×#103—111no—
461C2×#102—111no—
462C2×#102—111no—
463C2×#102—111no—
464C2×#102—111no—
465C2×#102C2×D1111yescharacteristic
466C2×#102C2×D1111yescharacteristic, complemented
467#408—118no—
468C2×C22⋊C8—111no—
469C2×C22⋊C8—111no—
470C2×C22⋊C8—111no—
471C2×C22⋊C8—111no—
472C22×C11—22no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—44no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—84no—
483C22×C11—84no—
484C22×C11#53412yes—
485C22×C11#57612yes—
486C22×C11#57712yes—
487C22×C11C23×D411yescharacteristic
488C2×D11—22no—
489C2×D11—22no—
490C2×D11—22no—
491C2×D11—22no—
492C2×D11—22no—
493C2×D11—22no—
494C2×D11—44no—
495C2×D11—44no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—816no—
500C2×D11—84no—
501C4×C11—22no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11#53412yes—
505C4×C11C2×H(5,𝔽2)11yescharacteristic
506C4×C11C2×H(5,𝔽2)11yescharacteristic
507Dic11—22no—
508Dic11—22no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512C25—221no—
513C2×#41—114no—
514C2×#41—114no—
515C2×#41—114no—
516C2×#41—222no—
517C2×#41—442no—
518C2×#41—442no—
519C2×#41—442no—
520C2×#41—442no—
521C22×Q8—111no—
522C22×Q8—111no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—111no—
526C22×D4—111no—
527C22×D4—114no—
528C22×D4—111no—
529C22×D4—111no—
530C22×D4—221no—
531C22×D4—222no—
532C22×D4—221no—
533C22×D4—221no—
534C22×D4—221no—
535C22×D4—221no—
536C22×D4—221no—
537C22×D4—442no—
538C22×D4—442no—
539C22×D4C22×D1111yescharacteristic
540C22×D4C22×D1111yescharacteristic
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—221no—
544C23×C4—221no—
545C23×C4C22×D1111yescharacteristic
546C2×SD16—114no—
547C2×SD16—114no—
548C2×SD16—442no—
549C2×SD16—442no—
550C2×D8—42no—
551C2×D8—114no—
552C2×D8—442no—
553C2×D8C22×D1114yes—
554C2×M16—114no—
555C2×M16—442no—
556C22×C8—42no—
557C22×C8—111no—
558C22×C8—111no—
559C22×C8C22×D1111yescharacteristic
560C22×C8C22×D1111yescharacteristic
561C22×C8C22×D1114yescomplemented
562#127—228no—
563#124—228no—
564C22⋊Q8—114no—
565C22⋊Q8—114no—
566C22⋊Q8—228no—
567C22⋊Q8—222no—
568C22⋊Q8—222no—
569#121—22no—
570#121—22no—
571#121—114no—
572#121—114no—
573#121—114no—
574#121—114no—
575#121—228no—
576#121—222no—
577#121—222no—
578#121—222no—
579#121—228no—
580#121—228no—
581#121—222no—
582#121C22×D1114yes—
583#121C22×D1114yescomplemented
584#120—228no—
585#120—228no—
586#117—114no—
587#117—222no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—114no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—221no—
593C2×C4⋊C4—221no—
594C2×C4⋊C4—221no—
595C2×C4⋊C4C22×D1111yescharacteristic
596C2×C4⋊C4C22×D1111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C22⋊C4—221no—
605C2×C22⋊C4—221no—
606C2×C42—221no—
607#107—114no—
608#107C22×D1114yescomplemented
609#106—114no—
610#106—114no—
611#103—114no—
612#103—114no—
613#102—114no—
614#102—114no—
615#102—114no—
616#102—114no—
617#102C22×D1114yes—
618#102C22×D1114yescomplemented
619C22⋊C8—114no—
620C22⋊C8—114no—
621C22⋊C8—114no—
622C22⋊C8—114no—
623C2×C11—42no—
624C2×C11—82no—
625C2×C11—82no—
626C2×C11#319814yescomplemented
627C2×C11C2×#53411yescharacteristic
628C2×C11C2×#57611yescharacteristic
629C2×C11C2×#57711yescharacteristic
630D11—42no—
631D11—42no—
632D11—82no—
633C24—21no—
634C24—21no—
635C24—111no—
636C24—111no—
637C24—224no—
638C24—221no—
639C24—444no—
640C24—882no—
641C24—882no—
642C24D4×D1111yescharacteristic
643#41—448no—
644#41—444no—
645#41—444no—
646#41—444no—
647#41—444no—
648#41—448no—
649C2×Q8—114no—
650C2×Q8—112no—
651C2×Q8—221no—
652C2×Q8—222no—
653C2×Q8—222no—
654C2×Q8—442no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—82no—
664C2×D4—82no—
665C2×D4—114no—
666C2×D4—114no—
667C2×D4—114no—
668C2×D4—112no—
669C2×D4—224no—
670C2×D4—224no—
671C2×D4—224no—
672C2×D4—224no—
673C2×D4—224no—
674C2×D4—224no—
675C2×D4—221no—
676C2×D4—222no—
677C2×D4—222no—
678C2×D4—442no—
679C2×D4—444no—
680C2×D4—444no—
681C2×D4—448no—
682C2×D4—442no—
683C2×D4—442no—
684C2×D4—444no—
685C2×D4—444no—
686C2×D4—882no—
687C2×D4—882no—
688C2×D4—882no—
689C2×D4—882no—
690C2×D4C23×D1112yes—
691C2×D4C23×D1112yes—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—111no—
697C22×C4—111no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—224no—
703C22×C4—224no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—444no—
712C22×C4—882no—
713C22×C4D4×D1112yes—
714C22×C4D4×D1111yescharacteristic
715C22×C4C23×D1112yes—
716C22×C4C23×D1111yescharacteristic
717SD16—444no—
718SD16—444no—
719D8—44no—
720D8—444no—
721M16—444no—
722C2×C8—22no—
723C2×C8—22no—
724C2×C8—44no—
725C2×C8—112no—
726C2×C8—112no—
727C2×C8—222no—
728C2×C8—222no—
729C2×C8C23×D1112yes—
730C2×C8C23×D1112yes—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—112no—
734C4⋊C4—112no—
735C4⋊C4—224no—
736C4⋊C4—224no—
737C4⋊C4—221no—
738C4⋊C4—221no—
739C4⋊C4—224no—
740C4⋊C4C23×D1112yes—
741C4⋊C4C23×D1112yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—224no—
745C22⋊C4—224no—
746C22⋊C4—224no—
747C22⋊C4—224no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C42—224no—
752C11C2×#319811yescharacteristic, complemented, Sylow
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—112no—
765C23—112no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—448no—
774C23—442no—
775C23—442no—
776C23—442no—
777C23—884no—
778C23—884no—
779C23—8816no—
780C23C2×D4×D1112yes—
781C23C2×D4×D1111yescharacteristic
782Q8—222no—
783Q8—222no—
784Q8—444no—
785Q8—442no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—42no—
791D4—42no—
792D4—84no—
793D4—84no—
794D4—222no—
795D4—222no—
796D4—444no—
797D4—444no—
798D4—444no—
799D4—448no—
800D4—448no—
801D4—442no—
802D4—884no—
803D4—884no—
804D4—884no—
805D4—884no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—112no—
815C2×C4—112no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—224no—
819C2×C4—224no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—448no—
828C2×C4—442no—
829C2×C4—442no—
830C2×C4—442no—
831C2×C4—884no—
832C2×C4C2×D4×D1112yes—
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4#6703712yes—
835C2×C4#6704212yes—
836C2×C4C24×D1111yescharacteristic
837C8—22no—
838C8—22no—
839C8—222no—
840C8—222no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—84no—
852C22—84no—
853C22—222no—
854C22—222no—
855C22—222no—
856C22—222no—
857C22—222no—
858C22—222no—
859C22—444no—
860C22—444no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—8816no—
865C22—884no—
866C22#1062313612yes—
867C22#1062328812yes—
868C22#1062330112yes—
869C22C22×D4×D1111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—222no—
874C4—222no—
875C4—442no—
876C4—442no—
877C4—442no—
878C4#1062313612yes—
879C4C2×#6703711yescharacteristic
880C4C2×#6704211yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—442no—
885C2—442no—
886C2—882no—
887C2#1307946114yesdirect product factor
888C2C2×#1062313611yescharacteristic
889C2C2×#1062328811yescharacteristic
890C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#466C2
socleC23×C11C22×D4
hypercenterC2×#466D11
hypocenterC11C2×#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#10623139C2semidirect
2. C2×#10623138C2semidirect
3. #13079461C2direct (N × H)
4. C2×#10622390C2semidirect
5. C2×#10622501C2semidirect
6. C2×#10622392C2semidirect
7. C2×#10622495C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622655C2semidirect
10. C2×#10622727C2semidirect
11. C2×#10622394C2semidirect
12. C2×#10622771C2semidirect
13. C2×#10622389C2semidirect
14. C2×#10622769C2semidirect
15. C2×#10622723C2semidirect
16. C2×C11×#466C2semidirect
17. C22×#4341C22semidirect
21. C23×C8×C11C22semidirect
23. C2×C11×#121C22semidirect
33. C2×#66977C22semidirect
34. C22×#4318C22semidirect
37. #10623139C22semidirect
39. #10623138C22semidirect
43. C2×C4⋊C4×D11C22semidirect
48. C11×#466C22semidirect
49. C2×C11×#107C22semidirect
51. C2×C11×#102C22semidirect
53. C2×#66896C22semidirect
54. #10622771C22semidirect
55. #10622769C22semidirect
56. #10622727C22semidirect
58. #10622723C22semidirect
61. C2×(C2×D11)⋊C8C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×#66881C22semidirect
64. C2×#66880C22semidirect
65. #10622655C22semidirect
66. #10622652C22semidirect
67. C2×#66874C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622501C22semidirect
72. #10622495C22semidirect
73. #10622394C22semidirect
74. #10622392C22semidirect
75. #10622390C22semidirect
76. #10622389C22semidirect
94. C2×#4341C23semidirect
116. C22×C8×C11C23semidirect
120. C11×#121C23semidirect
150. #66977C23semidirect
155. C2×#4318C23semidirect
167. C4⋊C4×D11C23semidirect
172. C11×#107C23semidirect
174. C11×#102C23semidirect
176. #66896C23semidirect
180. (C2×D11)⋊C8C23semidirect
181. (C2×D11)⋊C8C23semidirect
182. #66881C23semidirect
183. #66880C23semidirect
184. #66874C23semidirect
186. #66872C23semidirect
187. #66871C23semidirect
317. C2×#466D11semidirect
420. C23×C8C2×D11semidirect
438. C2×#121C2×D11semidirect
449. #466C2×D11semidirect
456. C2×#107C2×D11semidirect
466. C2×#102C2×D11semidirect
561. C22×C8C22×D11semidirect
583. #121C22×D11semidirect
608. #107C22×D11semidirect
618. #102C22×D11semidirect
626. C2×C11#3198semidirect
752. C11C2×#3198semidirect
887. C2#13079461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231392
C2×#106231382
#130794612
C2×#106223902
C2×#106225012
C2×#106223922
C2×#106224952
C2×#106226522
C2×#106226552
C2×#106227272
C2×#106223942
C2×#106227712
C2×#106223892
C2×#106227692
C2×#106227232
C2×C11×#4662
C2×#319811