Finite Group Databasebeta

← #14769333

Subgroups — #14769333

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623085C211yesmaximal, characteristic
2C2×#10622319C211yesmaximal, characteristic, complemented
3C2×#10622383C211yesmaximal, characteristic, complemented
4C2×#10622385C211yesmaximal, characteristic, complemented
5#13071563C211yesmaximal, characteristic, complemented
6#13069548C211yesmaximal, characteristic, complemented
7#13069432C211yesmaximal, characteristic, complemented
8#13069048C211yesmaximal, characteristic, complemented
9#13069043C211yesmaximal, characteristic, complemented
10#13068937C211yesmaximal, characteristic, complemented
11#13068927C211yesmaximal, characteristic, complemented
12#13068616C211yesmaximal, characteristic, complemented
13#13068553C211yesmaximal, characteristic, complemented
14#13068545C211yesmaximal, characteristic, complemented
15C11×#1762C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66983—21no—
20C22×(C2×D11)⋊C4—21no—
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic, complemented
23#10623085—24no—
24#10623085C418yescomplemented
25C2×#66950C2211yescharacteristic
26C2×#66948C2211yescharacteristic
27C2×#66945C2211yescharacteristic
28C2×#66945C2211yescharacteristic, complemented
29C2×#66939—21no—
30C2×#66935—21no—
31C2×#66928C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#97C2211yescharacteristic, complemented
36C4×C11×C4⋊C4C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
43C2×#66880C2211yescharacteristic, complemented
44C2×#66880C2211yescharacteristic, complemented
45#10622600C2211yescharacteristic
46#10622600C2211yescharacteristic, complemented
47C2×#66874C2211yescharacteristic, complemented
48C2×#66874C2211yescharacteristic, complemented
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51#10622552—21no—
52#10622548C2211yescharacteristic, complemented
53C4×C4⋊Dic11—21no—
54C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
55#10622385—24no—
56#10622383—24no—
57#10622319—24no—
58#10622283—21no—
59#10622283—21no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C2×#4341—22no—
71C2×#4341—22no—
72C2×#4341—22no—
73C2×#4341—41no—
74C2×#4341—41no—
75C2×#4341C2×C414yes—
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—22no—
79C2×D4×D11—41no—
80C2×D4×D11—41no—
81C2×D4×D11C2×C414yes—
82C22×D44—21no—
83C22×D44D411yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×Dic22C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C4×D4×C11—22no—
91C4×D4×C11C2×C414yes—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98#66983—28no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—28no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4D411yescharacteristic
109C2×(C2×D11)⋊C4D411yescharacteristic
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11D411yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C2×#4313—22no—
121C2×#4313—22no—
122C2×#4313—41no—
123C2×C8×D11—22no—
124C2×C8×D11—22no—
125C2×C8×D11—41no—
126#66950—22no—
127#66950C2×C414yes—
128#66948—22no—
129#66948C2×C414yes—
130#66945—22no—
131#66945—22no—
132#66945—41no—
133#66945—41no—
134#66939—28no—
135#66935—28no—
136#66928—22no—
137#66928C2×C414yes—
138C4×D44C2×C414yes—
139C4×D44D414yes—
140C11×#102—22no—
141C11×#102D414yescomplemented
142C11×#97—22no—
143C11×#95—21no—
144#66896—22no—
145#66896—22no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148#66885—22no—
149#66885—41no—
150(C2×D11)⋊C8—22no—
151(C2×D11)⋊C8—22no—
152#66880—22no—
153#66880—41no—
154#66874—22no—
155#66874—41no—
156#66873—22no—
157#66873—41no—
158C4⋊(C11⋊C8)—22no—
159#22424—111nomaximal, Sylow
160C24×C11—21no—
161C23×D11—21no—
162C23×D11—24no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—81no—
168C23×D11—81no—
169C23×D11C2×D411yescharacteristic
170C23×D11C2×D411yescharacteristic
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11C22×C412yes—
175C2×D4×C11C2×D412yes—
176C2×D4×C11#4112yes—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—24no—
180C22×C4×C11—21no—
181C22×C4×C11—81no—
182C22×C4×C11—81no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C2×C22⋊D11—24no—
187C2×C22⋊D11—24no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11—42no—
190C2×C22⋊D11—42no—
191C2×C22⋊D11—42no—
192C22×Dic11—24no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200#4341—28no—
201#4341—44no—
202#4341—44no—
203#4341—44no—
204D4×D11—28no—
205D4×D11—44no—
206D4×D11—44no—
207D4×D11—44no—
208C2×D44—24no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—41no—
215C2×D44—41no—
216C2×D44—81no—
217C2×D44—81no—
218C2×D44C22⋊C414yes—
219C2×D44C22×C412yes—
220C2×C4×D11—21no—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—21no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11C22×C412yes—
229C2×C4×D11C22×C412yes—
230C2×C4×D11C2×D412yes—
231C2×C4×D11C2×D412yes—
232C2×Dic22—21no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22C22×C412yes—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11C2×D412yes—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4C22×C412yes—
249C11×C4⋊C4C2×D412yes—
250C11×C22⋊C4—24no—
251C42×C11—42no—
252C42×C11C22×C412yes—
253C42×C11C2×D412yes—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—42no—
259(C2×D11)⋊C4—42no—
260(C2×D11)⋊C4—81no—
261(C2×D11)⋊C4—81no—
262(C2×D11)⋊C4C22⋊C414yes—
263(C2×D11)⋊C4C22⋊C414yes—
264C4⋊Dic11—24no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—42no—
270C4⋊Dic11—81no—
271C4⋊Dic11C22⋊C414yes—
272C4×Dic11—42no—
273C4×Dic11—42no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280#4313—44no—
281C8×D11—44no—
282C2×#546—111no—
283C2×#435—111no—
284C2×#418—111no—
285C2×#416—111no—
286#2354—111no—
287#1983—111no—
288#1959—111no—
289#1894—111no—
290#1893—111no—
291#1875—111no—
292#1873—111no—
293#1802—111no—
294#1788—111no—
295#1786—111no—
296#1762D1111yescharacteristic, complemented
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11C22×D411yescharacteristic
305C22×D11—21no—
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—22no—
318C22×D11—48no—
319C22×D11—48no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11C2×C22⋊C412yes—
332C22×D11C2×C22⋊C412yes—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11C4×D414yes—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—84no—
351C2×C4×C11C2×C22⋊C412yes—
352C2×C4×C11C2×C22⋊C412yes—
353C2×C4×C11C23×C411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C22⋊D11—48no—
360C22⋊D11—48no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—22no—
366C2×Dic11—48no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11C2×C22⋊C412yes—
376C2×Dic11C2×C22⋊C412yes—
377D44—22no—
378D44—22no—
379D44—44no—
380D44—41no—
381D44—41no—
382D44—84no—
383C4×D11—22no—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—22no—
391Dic22—22no—
392Dic22—22no—
393Dic22—41no—
394Dic22—41no—
395C8×C11—22no—
396C8×C11—41no—
397C11⋊C8—41no—
398C11⋊C8—41no—
399C22×#41—111no—
400C23×D4—111no—
401C22×M16—111no—
402C23×C8—111no—
403#546—118no—
404#546—224no—
405C2×#124—111no—
406C2×#123—221no—
407C2×C22⋊Q8—111no—
408C2×#121—111no—
409C2×#121—221no—
410C2×#120—221no—
411C2×C4×D4—111no—
412C2×C4×D4C2×D1111yescharacteristic
413C2×#117—111no—
414C2×#117—111no—
415C22×C22⋊C4—221no—
416#435—224no—
417C2×C4⋊C8—111no—
418#418—224no—
419#416—224no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102C2×D1111yescharacteristic
431C2×#102C2×D1111yescharacteristic
432C2×C22⋊C8—111no—
433C2×C22⋊C8—111no—
434C2×#97C2×D1111yescharacteristic, complemented
435#390—221no—
436#388—221no—
437#388—221no—
438#384—111no—
439#380—111no—
440#380—111no—
441C4×C4⋊C4—221no—
442C4×C4⋊C4C2×D1111yescharacteristic, complemented
443#340—111no—
444#340—111no—
445#340C2×D1111yescharacteristic, complemented
446#340C2×D1111yescharacteristic, complemented
447C22×C11—24no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11C22×C22⋊C411yescharacteristic
455C22×C11D4211yescharacteristic
456C22×C11#54611yescharacteristic
457C22×C11#57511yescharacteristic
458C22×C11#57511yescharacteristic
459C22×C11#57611yescharacteristic
460C22×C11#57711yescharacteristic
461C2×D11—22no—
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—41no—
468C2×D11—41no—
469C2×D11—41no—
470C2×D11—41no—
471C2×D11—41no—
472C2×D11—41no—
473C2×D11—41no—
474C2×D11—41no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—816no—
479C2×D11—81no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C4×C11—22no—
484C4×C11—22no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—81no—
488C4×C11C2×C4×D411yescharacteristic
489C4×C11#51811yescharacteristic
490C4×C11D4211yescharacteristic
491C4×C11#54611yescharacteristic
492Dic11—22no—
493Dic11—22no—
494Dic11—42no—
495Dic11—81no—
496Dic11—81no—
497C25—221no—
498C2×#41—114no—
499C2×#41—222no—
500C2×#41—222no—
501C2×#41—222no—
502C2×#41—441no—
503C2×#41—441no—
504C22×Q8—111no—
505C22×D4—114no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—221no—
509C22×D4—222no—
510C22×D4—221no—
511C22×D4—222no—
512C22×D4—222no—
513C22×D4—221no—
514C22×D4—441no—
515C22×D4—441no—
516C22×D4C22×D1111yescharacteristic
517C23×C4—21no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—221no—
521C2×M16—222no—
522C2×M16—222no—
523C2×M16—441no—
524C22×C8—111no—
525C22×C8—111no—
526C22×C8—222no—
527C22×C8—222no—
528C22×C8—441no—
529C22×C8C22×D1111yescharacteristic
530C22×C8C22×D1111yescharacteristic
531#124—114no—
532#124—222no—
533#123—228no—
534C22⋊Q8—114no—
535C22⋊Q8—222no—
536#121—114no—
537#121—228no—
538#121—222no—
539#120—228no—
540C4×D4—22no—
541C4×D4—114no—
542C4×D4—114no—
543C4×D4C4×D1114yes—
544#117—222no—
545#117—222no—
546#117—441no—
547#117—441no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—111no—
559C2×C22⋊C4—111no—
560C2×C22⋊C4—228no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C42—21no—
570C2×C42—221no—
571C2×C42—221no—
572C2×C42C22×D1111yescharacteristic
573C4⋊C8—222no—
574#103—222no—
575#103—222no—
576#103—441no—
577#103—441no—
578#102—22no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—222no—
583#102—441no—
584#102—441no—
585#102D4414yescomplemented
586C22⋊C8—222no—
587C22⋊C8—222no—
588#97—22no—
589#95—21no—
590#95—221no—
591#95—221no—
592C2×C11—44no—
593C2×C11D4×C22⋊C411yescharacteristic
594C2×C11#289611yescharacteristic
595C2×C11#289711yescharacteristic
596C2×C11#326711yescharacteristic
597C2×C11#326811yescharacteristic
598C2×C11#331111yescharacteristic
599C2×C11#331911yescharacteristic
600D11—42no—
601D11—42no—
602D11—82no—
603C24—21no—
604C24—111no—
605C24—111no—
606C24—224no—
607C24—221no—
608C24—442no—
609C24—442no—
610C24—442no—
611C24—442no—
612C24—881no—
613C24—881no—
614#41—228no—
615#41—444no—
616#41—444no—
617#41—444no—
618C2×Q8—112no—
619C2×Q8—221no—
620C2×Q8—221no—
621C2×Q8—221no—
622C2×Q8—221no—
623C2×Q8—221no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—114no—
628C2×D4—112no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—228no—
632C2×D4—224no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—441no—
639C2×D4—441no—
640C2×D4—444no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—442no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—881no—
648C2×D4—881no—
649C2×D4C2×C4×D1112yes—
650C2×D4C2×D4412yes—
651C2×D4#433912yes—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—81no—
657C22×C4—81no—
658C22×C4—111no—
659C22×C4—111no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—224no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—442no—
677C22×C4—442no—
678C22×C4D4×D1111yescharacteristic
679C22×C4D4×D1111yescharacteristic
680C22×C4C23×D1111yescharacteristic
681M16—444no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—444no—
694C2×C8C2×D4412yes—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—114no—
700C4⋊C4—224no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—442no—
706C4⋊C4—881no—
707C4⋊C4C2×C4×D1112yes—
708C4⋊C4C2×D4412yes—
709C22⋊C4—24no—
710C22⋊C4—114no—
711C22⋊C4—114no—
712C22⋊C4—224no—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—442no—
717C22⋊C4—442no—
718C22⋊C4—881no—
719C22⋊C4—881no—
720C42—42no—
721C42—442no—
722C42—442no—
723C42C2×C4×D1112yes—
724C42D4×D1112yes—
725C11#2242411yescharacteristic, complemented, Sylow
726C23—22no—
727C23—22no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—112no—
734C23—112no—
735C23—221no—
736C23—221no—
737C23—221no—
738C23—221no—
739C23—221no—
740C23—221no—
741C23—221no—
742C23—221no—
743C23—221no—
744C23—221no—
745C23—221no—
746C23—221no—
747C23—222no—
748C23—448no—
749C23—448no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—884no—
757C23—884no—
758C23—884no—
759C23—884no—
760C23—884no—
761C23C2×D4×D1111yescharacteristic
762Q8—222no—
763Q8—222no—
764Q8—441no—
765Q8—441no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—222no—
770D4—222no—
771D4—444no—
772D4—448no—
773D4—448no—
774D4—441no—
775D4—441no—
776D4—884no—
777D4C4×D4414yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—84no—
792C2×C4—112no—
793C2×C4—112no—
794C2×C4—221no—
795C2×C4—221no—
796C2×C4—221no—
797C2×C4—221no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—448no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4C22⋊C4×D1112yes—
817C2×C4C22⋊C4×D1112yes—
818C2×C4C22×C4×D1111yescharacteristic
819C2×C4C22×D4411yescharacteristic
820C2×C4C2×#433911yescharacteristic
821C2×C4C2×D4×D1111yescharacteristic
822C2×C4#6704211yescharacteristic
823C2×C4#6704211yescharacteristic
824C8—22no—
825C8—41no—
826C8—441no—
827C8—441no—
828C22—24no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—222no—
836C22—222no—
837C22—222no—
838C22—222no—
839C22—222no—
840C22—222no—
841C22—441no—
842C22—441no—
843C22—441no—
844C22—441no—
845C22—441no—
846C22—441no—
847C22—441no—
848C22—441no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—8816no—
853C22—881no—
854C22—881no—
855C22—881no—
856C22—881no—
857C22C2×C22⋊C4×D1111yescharacteristic
858C22D4×D4411yescharacteristic
859C22#1062308111yescharacteristic
860C22#1062330411yescharacteristic
861C22#1062330511yescharacteristic
862C22#1062330611yescharacteristic
863C22#1062330811yescharacteristic
864C4—22no—
865C4—22no—
866C4—42no—
867C4—42no—
868C4—81no—
869C4—222no—
870C4—222no—
871C4—442no—
872C4—881no—
873C4—881no—
874C4C2×C4×D4411yescharacteristic
875C4#1062305211yescharacteristic
876C4D4×D4411yescharacteristic
877C4#1062308111yescharacteristic
878C2—44no—
879C2—442no—
880C2—442no—
881C2—882no—
882C2C22⋊C4×D4411yescharacteristic
883C2#1307713211yescharacteristic
884C2#1307714111yescharacteristic
885C2#1308014311yescharacteristic
886C2#1308015811yescharacteristic
887C2#1308065711yescharacteristic
888C2#1308077711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1762C2
socleC23×C11C22×D4
prime radicalC2×#10623085C2
cosocleC22×C4×C11C24
hypercenter#1762D11
hypocenterC11#22424
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#10622319C2semidirect
3. C2×#10622383C2semidirect
4. C2×#10622385C2semidirect
5. #13071563C2semidirect
6. #13069548C2semidirect
7. #13069432C2semidirect
8. #13069048C2semidirect
9. #13069043C2semidirect
10. #13068937C2semidirect
11. #13068927C2semidirect
12. #13068616C2semidirect
13. #13068553C2semidirect
14. #13068545C2semidirect
15. C11×#1762C2semidirect
22. C22×C8×D11C22semidirect
24. #10623085C4semidirect
28. C2×#66945C22semidirect
35. C2×C11×#97C22semidirect
36. C4×C11×C4⋊C4C22semidirect
42. C2×(C2×D11)⋊C8C22semidirect
43. C2×#66880C22semidirect
44. C2×#66880C22semidirect
46. #10622600C22semidirect
47. C2×#66874C22semidirect
48. C2×#66874C22semidirect
52. #10622548C22semidirect
54. C2×C4⋊(C11⋊C8)C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
141. C11×#102D4semidirect
296. #1762D11semidirect
434. C2×#97C2×D11semidirect
442. C4×C4⋊C4C2×D11semidirect
445. #340C2×D11semidirect
446. #340C2×D11semidirect
585. #102D44semidirect
725. C11#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#106230852
C2×#106223192
C2×#106223832
C2×#106223852
#130715632
#130695482
#130694322
#130690482
#130690432
#130689372
#130689272
#130686162
#130685532
#130685452
C11×#17622
#2242411