Finite Group Databasebeta

← #14763590

Subgroups — #14763590

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623091C211yesmaximal, characteristic
2#13071229C211yesmaximal, characteristic, complemented
3#13071213C211yesmaximal, characteristic, complemented
4#13069599C212yesmaximal, complemented
5#13069450C212yesmaximal, complemented
6#13069068C212yesmaximal, complemented
7#13069066C212yesmaximal, complemented
8#13068604C211yesmaximal, characteristic, complemented
9#13068601C211yesmaximal, characteristic, complemented
10#13068601C211yesmaximal, characteristic, complemented
11C11×#1799C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66992C2211yescharacteristic
14C2×#66990C2211yescharacteristic
15C2×#66983C411yescharacteristic, complemented
16C2×#66982C411yescharacteristic, complemented
17C2×C4×C22⋊D11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19#10623091—22no—
20#10623091—22no—
21#10623091—22no—
22#10623091—22no—
23C2×#66951C411yescharacteristic, complemented
24C2×#66947C411yescharacteristic, complemented
25C2×#66938C411yescharacteristic, complemented
26C2×#66937C411yescharacteristic, complemented
27C2×#66935C2211yescharacteristic
28C2×C22⋊C4×D11C2212yes—
29C2×#66931C2211yescharacteristic
30C2×#66929C411yescharacteristic, complemented
31C2×#66928C411yescharacteristic, complemented
32C2×C11×#99C2212yes—
33C11×#380C2211yescharacteristic
34C11×#380C2211yescharacteristic
35C2×#66898C2212yes—
36#10622825C2211yescharacteristic
37#10622825C2211yescharacteristic
38#10622603—22no—
39#10622602—22no—
40#10622568C2212yes—
41C2×#66870C2212yes—
42C2×#66870C2212yes—
43#10622555C2212yes—
44C22⋊C4×Dic11C2212yes—
45#10622283—22no—
46#10622281—22no—
47C11×#342C2212yes—
48#10622165C2212yes—
49#10622165C2212yes—
50#10622164C2212yes—
51C24×D11C2311yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11C2×C411yescharacteristic, complemented
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11C2×C411yescharacteristic
56C22×C22⋊D11C2×C411yescharacteristic
57C22×C22⋊D11C2×C411yescharacteristic, complemented
58C22×C22⋊D11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C22×D44C2×C411yescharacteristic
61C22×D44C2×C411yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11C2×C411yescharacteristic, complemented
64C22×Dic22C2×C411yescharacteristic, complemented
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
72C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
73C2×C11×C22⋊C4C2312yes—
74C2×C11×C22⋊C4C2312yes—
75C2×C11×C22⋊C4C2311yescharacteristic
76C2×C42×C11C2×C411yescharacteristic, complemented
77C2×C22⋊Dic11C2×C411yescharacteristic, complemented
78C2×C22⋊Dic11C2312yes—
79C2×C22⋊Dic11C2312yes—
80C2×C22⋊Dic11C2311yescharacteristic
81#66992—22no—
82#66992—22no—
83#66990—22no—
84#66990—22no—
85#66983—22no—
86#66983—22no—
87#66982—22no—
88#66982—22no—
89C4×C22⋊D11—21no—
90C4×C22⋊D11—21no—
91C4×C22⋊D11—21no—
92C4×C22⋊D11—21no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×(C2×D11)⋊C4C2×C411yescharacteristic
102C2×(C2×D11)⋊C4C2×C411yescharacteristic
103C2×(C2×D11)⋊C4C2×C411yescharacteristic
104C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
105C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
106C2×(C2×D11)⋊C4D412yes—
107C2×(C2×D11)⋊C4D412yes—
108C2×(C2×D11)⋊C4D412yes—
109C2×(C2×D11)⋊C4D412yes—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11C2×C411yescharacteristic, complemented
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4C2×C411yescharacteristic, complemented
115C2×Dic11⋊C4C2×C411yescharacteristic, complemented
116C2×Dic11⋊C4C2×C411yescharacteristic, complemented
117C2×Dic11⋊C4C2×C411yescharacteristic, complemented
118C2×C4×Dic11—22no—
119C2×C4×Dic11C2×C411yescharacteristic, complemented
120#66951—22no—
121#66951—22no—
122#66947—22no—
123#66947—22no—
124#66938—22no—
125#66938—22no—
126#66937—22no—
127#66937—22no—
128#66935—22no—
129#66935—22no—
130C22⋊C4×D11—42no—
131C22⋊C4×D11—42no—
132#66931—22no—
133#66931—22no—
134#66929—22no—
135#66929—22no—
136#66928—22no—
137#66928—22no—
138C11×#99—42no—
139C11×#95—21no—
140C11×#95—21no—
141#66898—42no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146#66870—42no—
147#66870—42no—
148#21876—111nomaximal, Sylow
149C24×C11C22×C411yescharacteristic
150C24×C11C2411yescharacteristic
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—81no—
156C23×D11—81no—
157C23×D11C22×C411yescharacteristic
158C23×D11C22×C411yescharacteristic
159C23×D11C22×C411yescharacteristic
160C23×D11C2×D412yes—
161C23×D11C2×D412yes—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—81no—
173C22×C4×C11—81no—
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C2×C22⋊D11—22no—
184C2×C22⋊D11—21no—
185C2×C22⋊D11—21no—
186C2×C22⋊D11—21no—
187C2×C22⋊D11—21no—
188C2×C22⋊D11—21no—
189C2×C22⋊D11—21no—
190C2×C22⋊D11—22no—
191C2×C22⋊D11—22no—
192C2×C22⋊D11—81no—
193C2×C22⋊D11—81no—
194C2×C22⋊D11—81no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—81no—
198C22×Dic11C22×C411yescharacteristic
199C22×Dic11C22×C411yescharacteristic
200C22×Dic11C22×C411yescharacteristic
201C22×Dic11C22×C411yescharacteristic
202C22×Dic11C22×C411yescharacteristic
203C22×Dic11C2×D412yes—
204C22×Dic11C2×D412yes—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44—81no—
208C2×D44—81no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—44no—
212C2×C4×D11—82no—
213C2×C4×D11—82no—
214C2×C4×D11—81no—
215C2×Dic22—22no—
216C2×Dic22—81no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—81no—
220C11×C4⋊C4—81no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—21no—
223C11×C22⋊C4—21no—
224C11×C22⋊C4—21no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—22no—
229C42×C11—21no—
230C42×C11—21no—
231C22⋊Dic11—22no—
232C22⋊Dic11—21no—
233C22⋊Dic11—21no—
234C22⋊Dic11—22no—
235C22⋊Dic11—22no—
236C22⋊Dic11—22no—
237C22⋊Dic11—22no—
238(C2×D11)⋊C4—22no—
239(C2×D11)⋊C4—22no—
240(C2×D11)⋊C4—22no—
241(C2×D11)⋊C4—22no—
242(C2×D11)⋊C4—22no—
243(C2×D11)⋊C4—21no—
244(C2×D11)⋊C4—21no—
245(C2×D11)⋊C4—44no—
246(C2×D11)⋊C4—82no—
247(C2×D11)⋊C4—82no—
248(C2×D11)⋊C4C22⋊C412yes—
249(C2×D11)⋊C4C22⋊C412yes—
250(C2×D11)⋊C4C22⋊C412yes—
251(C2×D11)⋊C4C22⋊C412yes—
252(C2×D11)⋊C4C22⋊C412yes—
253(C2×D11)⋊C4C22⋊C412yes—
254(C2×D11)⋊C4C22⋊C412yes—
255(C2×D11)⋊C4C22⋊C412yes—
256C4⋊Dic11—22no—
257C4⋊Dic11—81no—
258C4⋊Dic11—81no—
259Dic11⋊C4—22no—
260Dic11⋊C4—22no—
261Dic11⋊C4—22no—
262Dic11⋊C4—21no—
263Dic11⋊C4—21no—
264Dic11⋊C4—82no—
265C4×Dic11—21no—
266C4×Dic11—21no—
267C4×Dic11—82no—
268C2×#538—111no—
269#2315—111no—
270#2312—111no—
271#1996—112no—
272#1964—112no—
273#1898—112no—
274#1898—112no—
275#1799—111no—
276#1799—111no—
277#1799—111no—
278#1799D1111yescharacteristic, complemented
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11C23×C411yescharacteristic
287C23×C11C22×D411yescharacteristic
288C23×C11C22×D411yescharacteristic
289C23×C11H(5,𝔽2)11yescharacteristic
290C23×C11H(5,𝔽2)11yescharacteristic
291C23×C112−1+411yescharacteristic
292C23×C112−1+411yescharacteristic
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—82no—
315C22×D11—82no—
316C22×D11—82no—
317C22×D11—82no—
318C22×D11C2×C22⋊C412yes—
319C22×D11C2×C22⋊C412yes—
320D4×C11—41no—
321D4×C11—41no—
322D4×C11—41no—
323D4×C11—41no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—81no—
344C2×C4×C11—81no—
345C2×C4×C11C2×C22⋊C411yescharacteristic
346C2×C4×C11C2×C22⋊C411yescharacteristic
347C2×C4×C11C2×C22⋊C411yescharacteristic
348C2×C4×C11C2×C22⋊C411yescharacteristic
349C22⋊D11—41no—
350C22⋊D11—41no—
351C22⋊D11—41no—
352C22⋊D11—41no—
353C22⋊D11—82no—
354C22⋊D11—82no—
355C22⋊D11—82no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—21no—
359C2×Dic11—21no—
360C2×Dic11—21no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—42no—
368C2×Dic11—42no—
369C2×Dic11—42no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11C2×C22⋊C412yes—
374C2×Dic11C2×C22⋊C412yes—
375D44—82no—
376D44—82no—
377C4×D11—81no—
378C4×D11—81no—
379C4×D11—88no—
380Dic22—82no—
381#538—222no—
382#538—222no—
383#538—222no—
384#538—222no—
385C2×#126—111no—
386C2×#126—111no—
387C2×#124—111no—
388C2×#124—111no—
389C2×#123—111no—
390C2×#123—111no—
391C2×C22⋊Q8—111no—
392C2×#121—111no—
393C2×#121—111no—
394C2×#121—111no—
395C2×#120—111no—
396C2×#120—111no—
397C2×C4×D4—111no—
398C2×C4×D4C2×D1111yescharacteristic
399C22×C22⋊C4—111no—
400C22×C22⋊C4—112no—
401C2×#99—112no—
402C2×#99—112no—
403C2×#99—112no—
404C2×#99C2×D1112yes—
405#388—222no—
406#388—222no—
407#385—222no—
408#385—222no—
409#380—111no—
410#380—111no—
411#380—112no—
412#380C2×D1111yescharacteristic
413#380C2×D1111yescharacteristic
414#379—112no—
415C4×C22⋊C4—112no—
416#342—112no—
417#342—112no—
418#342—112no—
419#342C2×D1112yes—
420C22×C11—21no—
421C22×C11—21no—
422C22×C11—21no—
423C22×C11—21no—
424C22×C11—21no—
425C22×C11—21no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—81no—
434C22×C11—81no—
435C22×C11C22×C22⋊C411yescharacteristic
436C22×C11#52011yescharacteristic
437C22×C11#52011yescharacteristic
438C22×C11#53511yescharacteristic
439C22×C11#53611yescharacteristic
440C22×C11#53711yescharacteristic
441C22×C11#53711yescharacteristic
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—22no—
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—22no—
448C2×D11—44no—
449C2×D11—44no—
450C2×D11—41no—
451C2×D11—41no—
452C2×D11—41no—
453C2×D11—82no—
454C2×D11—82no—
455C2×D11—81no—
456C2×D11—81no—
457C2×D11—81no—
458C2×D11—81no—
459C2×D11—81no—
460C2×D11—81no—
461C4×C11—21no—
462C4×C11—21no—
463C4×C11—21no—
464C4×C11—21no—
465C4×C11—41no—
466C4×C11—41no—
467C4×C11—41no—
468C4×C11—82no—
469C4×C11—82no—
470Dic11—22no—
471Dic11—22no—
472Dic11—41no—
473Dic11—41no—
474Dic11—41no—
475Dic11—82no—
476Dic11—82no—
477C25—111no—
478C22×Q8—111no—
479C22×D4—111no—
480C22×D4—111no—
481C22×D4—111no—
482C22×D4—111no—
483C22×D4—111no—
484C22×D4—111no—
485C22×D4C22×D1111yescharacteristic
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—222no—
489C23×C4C4×D1111yescharacteristic, complemented
490C23×C4C22×D1111yescharacteristic
491#126—222no—
492#126—222no—
493#126—222no—
494#126—222no—
495#124—222no—
496#124—222no—
497#124—222no—
498#124—222no—
499#123—222no—
500#123—222no—
501#123—222no—
502#123—222no—
503C22⋊Q8—222no—
504C22⋊Q8—222no—
505#121—222no—
506#121—222no—
507#121—222no—
508#121—222no—
509#121—222no—
510#121—222no—
511#120—222no—
512#120—222no—
513#120—222no—
514#120—222no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—221no—
520C4×D4—221no—
521C4×D4—221no—
522C4×D4—221no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—222no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4C4×D1111yescharacteristic, complemented
534C2×C22⋊C4—111no—
535C2×C22⋊C4—111no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—111no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—112no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—111no—
543C2×C22⋊C4—111no—
544C2×C22⋊C4—111no—
545C2×C22⋊C4—111no—
546C2×C22⋊C4—111no—
547C2×C22⋊C4—111no—
548C2×C22⋊C4—111no—
549C2×C22⋊C4—111no—
550C2×C22⋊C4—112no—
551C2×C22⋊C4—112no—
552C2×C22⋊C4—222no—
553C2×C22⋊C4—222no—
554C2×C22⋊C4—222no—
555C2×C22⋊C4—442no—
556C2×C22⋊C4—442no—
557C2×C22⋊C4C4×D1111yescharacteristic, complemented
558C2×C22⋊C4C22×D1112yes—
559C2×C22⋊C4C22×D1112yes—
560C2×C22⋊C4C22×D1111yescharacteristic
561C2×C42—111no—
562C2×C42—222no—
563C2×C42C4×D1111yescharacteristic, complemented
564#99—42no—
565#99—442no—
566#99—442no—
567#99—442no—
568#95—21no—
569#95—21no—
570#95—222no—
571#95—222no—
572#95—221no—
573#95—221no—
574C2×C11—21no—
575C2×C11—21no—
576C2×C11—21no—
577C2×C11—21no—
578C2×C11—21no—
579C2×C11—21no—
580C2×C11—81no—
581C2×C11#231111yescharacteristic
582C2×C11#288311yescharacteristic
583C2×C11#288311yescharacteristic
584D11—42no—
585D11—42no—
586D11—81no—
587C24—111no—
588C24—111no—
589C24—112no—
590C24—112no—
591C24—111no—
592C24—221no—
593C24—221no—
594C24—221no—
595C24—221no—
596C24—881no—
597C24—881no—
598C24C2×C4×D1111yescharacteristic
599C24C23×D1111yescharacteristic
600C2×Q8—222no—
601C2×Q8—881no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—222no—
609C2×D4—222no—
610C2×D4—222no—
611C2×D4—221no—
612C2×D4—221no—
613C2×D4—221no—
614C2×D4—221no—
615C2×D4—221no—
616C2×D4—221no—
617C2×D4—222no—
618C2×D4—222no—
619C2×D4—881no—
620C2×D4—881no—
621C2×D4—881no—
622C2×D4—881no—
623C2×D4—881no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4—111no—
631C22×C4—111no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—111no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—444no—
642C22×C4—882no—
643C22×C4—882no—
644C22×C4—881no—
645C22×C4—881no—
646C22×C4C2×C4×D1111yescharacteristic
647C22×C4C2×C4×D1111yescharacteristic
648C22×C4C2×C4×D1111yescharacteristic
649C22×C4C2×C4×D1111yescharacteristic
650C22×C4C2×C4×D1111yescharacteristic
651C22×C4D4×D1111yescharacteristic
652C22×C4D4×D1111yescharacteristic
653C22×C4D4×D1111yescharacteristic
654C22×C4D4×D1111yescharacteristic
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—81no—
658C4⋊C4—81no—
659C4⋊C4—222no—
660C4⋊C4—222no—
661C4⋊C4—222no—
662C4⋊C4—222no—
663C4⋊C4—221no—
664C4⋊C4—221no—
665C4⋊C4—882no—
666C4⋊C4—881no—
667C4⋊C4—881no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—112no—
677C22⋊C4—112no—
678C22⋊C4—112no—
679C22⋊C4—112no—
680C22⋊C4—112no—
681C22⋊C4—112no—
682C22⋊C4—112no—
683C22⋊C4—112no—
684C22⋊C4—222no—
685C22⋊C4—222no—
686C22⋊C4—222no—
687C22⋊C4—222no—
688C22⋊C4—222no—
689C22⋊C4—222no—
690C22⋊C4—221no—
691C22⋊C4—221no—
692C22⋊C4—221no—
693C22⋊C4—221no—
694C22⋊C4—222no—
695C22⋊C4—222no—
696C22⋊C4—222no—
697C22⋊C4—222no—
698C22⋊C4—444no—
699C22⋊C4—882no—
700C22⋊C4—882no—
701C42—21no—
702C42—21no—
703C42—221no—
704C42—221no—
705C42—882no—
706C11#2187611yescharacteristic, complemented, Sylow
707C23—21no—
708C23—21no—
709C23—21no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—112no—
715C23—112no—
716C23—222no—
717C23—222no—
718C23—221no—
719C23—221no—
720C23—221no—
721C23—221no—
722C23—222no—
723C23—222no—
724C23—221no—
725C23—221no—
726C23—221no—
727C23—442no—
728C23—442no—
729C23—442no—
730C23—442no—
731C23—441no—
732C23—441no—
733C23—441no—
734C23—441no—
735C23—441no—
736C23—441no—
737C23—882no—
738C23—882no—
739C23—882no—
740C23—882no—
741C23C22×C4×D1111yescharacteristic
742C23C2×D4×D1111yescharacteristic
743C23C2×D4×D1111yescharacteristic
744C23#6703711yescharacteristic
745C23#6704011yescharacteristic
746C23#6704211yescharacteristic
747C23#6704311yescharacteristic
748Q8—882no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—441no—
754D4—441no—
755D4—441no—
756D4—441no—
757D4—882no—
758D4—882no—
759D4—882no—
760D4—882no—
761D4—882no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—112no—
784C2×C4—112no—
785C2×C4—221no—
786C2×C4—221no—
787C2×C4—221no—
788C2×C4—221no—
789C2×C4—221no—
790C2×C4—442no—
791C2×C4—442no—
792C2×C4—441no—
793C2×C4—441no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—442no—
797C2×C4—442no—
798C2×C4—442no—
799C2×C4—442no—
800C2×C4—442no—
801C2×C4—442no—
802C2×C4—881no—
803C2×C4—881no—
804C2×C4—888no—
805C2×C4C22⋊C4×D1111yescharacteristic
806C2×C4C22⋊C4×D1111yescharacteristic
807C2×C4C22⋊C4×D1111yescharacteristic
808C2×C4C22⋊C4×D1111yescharacteristic
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—81no—
823C22—81no—
824C22—222no—
825C22—222no—
826C22—222no—
827C22—222no—
828C22—222no—
829C22—222no—
830C22—444no—
831C22—444no—
832C22—441no—
833C22—441no—
834C22—441no—
835C22—882no—
836C22—882no—
837C22—881no—
838C22—881no—
839C22—881no—
840C22—881no—
841C22—881no—
842C22—881no—
843C22C2×C22⋊C4×D1111yescharacteristic
844C22#1062303511yescharacteristic
845C22#1062305411yescharacteristic
846C22#1062313811yescharacteristic
847C22#1062313911yescharacteristic
848C22#1062315911yescharacteristic
849C22#1062316011yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—82no—
858C4—82no—
859C4—222no—
860C4—222no—
861C4—441no—
862C4—441no—
863C4—441no—
864C4—882no—
865C4—882no—
866C2—21no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—81no—
873C2—442no—
874C2—442no—
875C2—881no—
876C2#1307120511yescharacteristic
877C2#1307707411yescharacteristic
878C2#1307707511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1799C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623091C2
cosocleC24×C11C24
hypercenter#1799D11
hypocenterC11#21876
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #13071229C2semidirect
3. #13071213C2semidirect
4. #13069599C2semidirect
5. #13069450C2semidirect
6. #13069068C2semidirect
7. #13069066C2semidirect
8. #13068604C2semidirect
9. #13068601C2semidirect
10. #13068601C2semidirect
11. C11×#1799C2semidirect
15. C2×#66983C4semidirect
16. C2×#66982C4semidirect
23. C2×#66951C4semidirect
24. C2×#66947C4semidirect
25. C2×#66938C4semidirect
26. C2×#66937C4semidirect
30. C2×#66929C4semidirect
31. C2×#66928C4semidirect
53. C23×C4×C11C2×C4semidirect
57. C22×C22⋊D11C2×C4semidirect
63. C22×C4×D11C2×C4semidirect
64. C22×Dic22C2×C4semidirect
71. C2×C11×C4⋊C4C2×C4semidirect
72. C2×C11×C22⋊C4C2×C4semidirect
76. C2×C42×C11C2×C4semidirect
77. C2×C22⋊Dic11C2×C4semidirect
104. C2×(C2×D11)⋊C4C2×C4semidirect
105. C2×(C2×D11)⋊C4C2×C4semidirect
112. C2×C4⋊Dic11C2×C4semidirect
114. C2×Dic11⋊C4C2×C4semidirect
115. C2×Dic11⋊C4C2×C4semidirect
116. C2×Dic11⋊C4C2×C4semidirect
117. C2×Dic11⋊C4C2×C4semidirect
119. C2×C4×Dic11C2×C4semidirect
278. #1799D11semidirect
489. C23×C4C4×D11semidirect
533. C2×C4⋊C4C4×D11semidirect
557. C2×C22⋊C4C4×D11semidirect
563. C2×C42C4×D11semidirect
706. C11#21876semidirect

Maximal subgroups

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

subgroupindex
C2×#106230912
#130712292
#130712132
#130695992
#130694502
#130690682
#130690662
#130686042
#130686012
C11×#17992
#2187611