Finite Group Databasebeta

← #14761635

Subgroups — #14761635

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622443C211yesmaximal, characteristic, complemented
2C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic
3C4×#66938C211yesmaximal, characteristic
4#13069550C211yesmaximal, characteristic, complemented
5#13069408C211yesmaximal, characteristic
6#13069225C211yesmaximal, characteristic, complemented
7#13069222C211yesmaximal, characteristic, complemented
8#13069221C211yesmaximal, characteristic, complemented
9#13068731C211yesmaximal, characteristic, complemented
10#13068390C211yesmaximal, characteristic, complemented
11C22⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
12#13068386C211yesmaximal, characteristic, complemented
13#13068386C211yesmaximal, characteristic, complemented
14C4×C8×Dic11C211yesmaximal, characteristic, complemented
15C11×#1923C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D11C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×#66938C411yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622570C411yescharacteristic
40#10622564C411yescharacteristic
41#10622557C411yescharacteristic
42C4×(C2×D11)⋊C4C2211yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C42×Dic11C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622443—24no—
48(C22⋊D11)⋊C8—24no—
49#10622283C411yescharacteristic
50#10622282C411yescharacteristic
51#10622263C411yescharacteristic
52#10622259C411yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11C2×C411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2×C411yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11C2×C411yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76C4×C22⋊D11—22no—
77C4×C22⋊D11—22no—
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×(C2×D11)⋊C4C2×C411yescharacteristic
82C2×(C2×D11)⋊C4C2×C411yescharacteristic
83C2×C4⋊Dic11C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2×C411yescharacteristic
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8—22no—
95C22×C11⋊C8—22no—
96C22×C11⋊C8—22no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×C8×D11—22no—
102C2×C8×D11—22no—
103C2×C8×D11—22no—
104#66938C818yescomplemented
105C4×Dic22—22no—
106C4×Dic22—22no—
107C11×C4⋊C8—22no—
108C11×C22⋊C8—22no—
109C11×C22⋊C8—22no—
110C4×C8×C11—22no—
111C11×#95C2×C411yescharacteristic
112C11×#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C11⋊#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C22⋊(C11⋊C8)—22no—
120(C2×D11)⋊C8—22no—
121(C2×D11)⋊C8—22no—
122(C2×D11)⋊C8—22no—
123Dic11⋊C8—22no—
124Dic11⋊C8—22no—
125Dic11⋊C8—22no—
126C8×Dic11—22no—
127C8×Dic11—22no—
128C8×Dic11—22no—
129C8×Dic11—22no—
130C8×Dic11D414yes—
131C4×C11⋊C8—22no—
132C4×C11⋊C8—22no—
133C8×#124—111nomaximal, Sylow
134C24×C11C22×C411yescharacteristic
135C23×D11C22×C411yescharacteristic
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—22no—
149C2×C22⋊D11—22no—
150C2×C22⋊D11C2×C814yes—
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×Dic22—22no—
165C2×Dic22—22no—
166C2×Dic22C2×C814yescomplemented
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D412yes—
178C2×C8×C11#4112yes—
179C11×C22⋊C4—22no—
180C11×C22⋊C4C2×C814yescomplemented
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C22⋊Dic11—22no—
186C22⋊Dic11—22no—
187C22⋊Dic11C2×C814yescomplemented
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4C2×C814yescomplemented
192(C2×D11)⋊C4C2×C814yescomplemented
193C4⋊Dic11—22no—
194Dic11⋊C4—22no—
195Dic11⋊C4—22no—
196Dic11⋊C4—22no—
197C4×Dic11—22no—
198C4×Dic11—22no—
199C4×Dic11—22no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11C2×C814yescomplemented
205C4×Dic11C2×D412yes—
206C4×Dic11#4112yes—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—44no—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8#4112yes—
218C2×C11⋊C8#4112yes—
219C2×C11⋊C8#4112yes—
220C8×D11—44no—
221C2×C8×Q8—111no—
222C2×C8×D4—111no—
223C4×#124—111no—
224#1984—111no—
225#1954—111no—
226#1923—111no—
227#1923—111no—
228#1923—111no—
229#1923D1111yescharacteristic, complemented
230#1831—111no—
231C8×C22⋊C4—111no—
232C8×C22⋊C4—111no—
233C8×C22⋊C4—111no—
234C8×C22⋊C4—111no—
235C42×C8—111no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11C22×C812yes—
243C23×C11C23×C411yescharacteristic
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11C22×C812yes—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11C22×C812yes—
268C2×C4×C11C22×C812yes—
269C2×C4×C11#13112yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C22⋊D11—28no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11C4×D412yes—
292C2×Dic11C4×D412yes—
293C2×Dic11C22×C812yes—
294C2×Dic11C22×C812yes—
295C2×Dic11C22×C812yes—
296C2×Dic11#13112yes—
297C2×Dic11#13112yes—
298C4×D11—41no—
299C4×D11—41no—
300C4×D11—41no—
301C4×D11—41no—
302Dic22—28no—
303C8×C11—22no—
304C8×C11—22no—
305C8×C11—41no—
306C8×C11—41no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C11⋊C8#12414yescomplemented
311C23×C8—111no—
312C23×C8—111no—
313C2×#124—111no—
314C2×C4×Q8—111no—
315C2×C4×D4—111no—
316C8×Q8—224no—
317C8×D4—224no—
318C2×C4⋊C8—111no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8—111no—
321C2×C4⋊C8C2×D1111yescharacteristic
322C2×C22⋊C8—111no—
323C2×C22⋊C8—111no—
324C2×C22⋊C8—111no—
325C2×C22⋊C8—111no—
326C2×C22⋊C8C2×D1111yescharacteristic
327C2×C22⋊C8C2×D1111yescharacteristic
328C2×C4×C8—111no—
329C2×C4×C8—111no—
330C2×C4×C8—111no—
331C2×C4×C8—111no—
332C2×C4×C8—111no—
333C2×C4×C8—111no—
334C2×C4×C8—111no—
335C2×C4×C8C2×D1111yescharacteristic
336#391—111no—
337#390—111no—
338#388—111no—
339#388—111no—
340#388—111no—
341#388—111no—
342#382—111no—
343C4×C22⋊C4—111no—
344C4×C22⋊C4—111no—
345C4×C22⋊C4—111no—
346C4×C22⋊C4C2×D1111yescharacteristic
347C43—111no—
348#336—111no—
349#336—111no—
350#336—111no—
351#336—111no—
352#336—111no—
353#336—111no—
354#336C2×D1111yescharacteristic
355#336C2×D1111yescharacteristic
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11C2×C4×D411yescharacteristic
364C22×C11C4×#4111yescharacteristic
365C22×C11C4×#4111yescharacteristic
366C22×C11C23×C811yescharacteristic
367C22×C11C2×#13111yescharacteristic
368C22×C11C2×#13111yescharacteristic
369C22×C11C2×#13111yescharacteristic
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C4×C11—22no—
378C4×C11—22no—
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11C2×#12411yescharacteristic
383C4×C11#52911yescharacteristic
384C4×C11#52911yescharacteristic
385C4×C11#53211yescharacteristic
386Dic11—22no—
387Dic11—22no—
388Dic11—22no—
389Dic11—22no—
390Dic11—41no—
391Dic11—41no—
392Dic11C8×D414yes—
393C22×Q8—111no—
394C22×D4—111no—
395C23×C4—111no—
396C23×C4C22×D1111yescharacteristic
397C22×C8—111no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8—111no—
401C22×C8—222no—
402C22×C8—222no—
403C22×C8—222no—
404C22×C8—222no—
405C22×C8—222no—
406C22×C8—222no—
407C22×C8C22×D1111yescharacteristic
408C22×C8C22×D1111yescharacteristic
409C22×C8C22×D1111yescharacteristic
410C22×C8C22×D1111yescharacteristic
411#124—118no—
412C4×Q8—222no—
413C4×Q8—222no—
414C4×D4—222no—
415C4×D4—222no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C22⋊C4—111no—
421C2×C22⋊C4—111no—
422C2×C22⋊C4—111no—
423C2×C22⋊C4—111no—
424C2×C22⋊C4—111no—
425C2×C22⋊C4—111no—
426C2×C22⋊C4—111no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4C4×D1111yescharacteristic
429C2×C22⋊C4C4×D1111yescharacteristic
430C2×C42—111no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—111no—
436C2×C42—111no—
437C2×C42C22×D1111yescharacteristic
438C2×C42C22×D1111yescharacteristic
439C4⋊C8—22no—
440C4⋊C8—222no—
441C4⋊C8—222no—
442C4⋊C8—222no—
443C22⋊C8—22no—
444C22⋊C8—22no—
445C22⋊C8—222no—
446C22⋊C8—222no—
447C22⋊C8—222no—
448C22⋊C8—222no—
449C4×C8—22no—
450C4×C8—114no—
451C4×C8—222no—
452C4×C8—222no—
453C4×C8—222no—
454C4×C8—222no—
455C4×C8—222no—
456C4×C8—222no—
457#95—111no—
458#95—111no—
459#95—111no—
460#95—111no—
461#95—111no—
462#95—111no—
463#95C4×D1111yescharacteristic
464#95C4×D1111yescharacteristic
465C2×C11—42no—
466C2×C11C4×#12411yescharacteristic
467C2×C11C2×C8×D411yescharacteristic
468C2×C11#293111yescharacteristic
469C2×C11C8×#4111yescharacteristic
470C2×C11C8×#4111yescharacteristic
471C2×C11#296611yescharacteristic
472C2×C11#296611yescharacteristic
473D11—42no—
474C24—111no—
475C24C2×C4×D1111yescharacteristic
476C2×Q8—114no—
477C2×Q8—222no—
478C2×Q8—222no—
479C2×D4—114no—
480C2×D4—222no—
481C2×D4—222no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4C2×C4×D1111yescharacteristic
502C22×C4C2×C4×D1111yescharacteristic
503C22×C4C2×C4×D1111yescharacteristic
504C22×C4C2×C4×D1111yescharacteristic
505C22×C4C2×C4×D1111yescharacteristic
506C22×C4C23×D1111yescharacteristic
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—112no—
518C2×C8—112no—
519C2×C8—112no—
520C2×C8—112no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—444no—
530C2×C8—444no—
531C2×C8D4×D1112yes—
532C2×C8#434112yes—
533C4⋊C4—222no—
534C4⋊C4—222no—
535C4⋊C4—222no—
536C4⋊C4—222no—
537C22⋊C4—22no—
538C22⋊C4—114no—
539C22⋊C4—114no—
540C22⋊C4—114no—
541C22⋊C4—222no—
542C22⋊C4—222no—
543C22⋊C4—222no—
544C22⋊C4—222no—
545C22⋊C4—222no—
546C22⋊C4C8×D1114yescomplemented
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—114no—
552C42—112no—
553C42—112no—
554C42—222no—
555C42—222no—
556C42—222no—
557C42—221no—
558C42—221no—
559C42—221no—
560C42—221no—
561C11C8×#12411yescharacteristic, complemented, Sylow
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—112no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23—221no—
574C23—221no—
575C23C2×C8×D1112yes—
576C23C22×C4×D1111yescharacteristic
577Q8—228no—
578D4—228no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—112no—
596C2×C4—112no—
597C2×C4—112no—
598C2×C4—112no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—112no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4C2×C8×D1112yes—
621C2×C4C2×C8×D1112yes—
622C2×C4#6696012yes—
623C2×C4C2×D4×D1111yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C2×C4#41×D1111yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C8—22no—
630C8—22no—
631C8—41no—
632C8—41no—
633C8—114no—
634C8—222no—
635C8—441no—
636C8—441no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—222no—
645C22—222no—
646C22—222no—
647C22—441no—
648C22—441no—
649C22—441no—
650C22—441no—
651C22#1062305311yescharacteristic
652C22C4×#434111yescharacteristic
653C22C4×D4×D1111yescharacteristic
654C22C22×C8×D1111yescharacteristic
655C22C2×#6696011yescharacteristic
656C22D11×#13111yescharacteristic
657C22D11×#13111yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—41no—
662C4—41no—
663C4—114no—
664C4—222no—
665C4—222no—
666C4—222no—
667C4—222no—
668C4—441no—
669C4—441no—
670C4#1062312711yescharacteristic
671C4#1062318011yescharacteristic
672C4D11×#12411yescharacteristic
673C4#1062323711yescharacteristic
674C2—42no—
675C2—442no—
676C2#1307115711yescharacteristic
677C2C8×D4×D1111yescharacteristic
678C2#1307732511yescharacteristic
679C2C8×#434111yescharacteristic
680C2#1307757211yescharacteristic
681C2#1307758611yescharacteristic
682C2#1307758911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC11×#1923C2
socleC23×C11C23×C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1923D11
hypocenterC11C8×#124
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#10622443C2semidirect
4. #13069550C2semidirect
6. #13069225C2semidirect
7. #13069222C2semidirect
8. #13069221C2semidirect
9. #13068731C2semidirect
10. #13068390C2semidirect
11. C22⋊C4×C11⋊C8C2semidirect
12. #13068386C2semidirect
13. #13068386C2semidirect
14. C4×C8×Dic11C2semidirect
15. C11×#1923C2semidirect
104. #66938C8semidirect
166. C2×Dic22C2×C8semidirect
180. C11×C22⋊C4C2×C8semidirect
187. C22⋊Dic11C2×C8semidirect
191. (C2×D11)⋊C4C2×C8semidirect
192. (C2×D11)⋊C4C2×C8semidirect
204. C4×Dic11C2×C8semidirect
229. #1923D11semidirect
310. C11⋊C8#124semidirect
546. C22⋊C4C8×D11semidirect
561. C11C8×#124semidirect

Maximal subgroups

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

subgroupindex
C2×#106224432
C2×(C22⋊D11)⋊C82
C4×#669382
#130695502
#130694082
#130692252
#130692222
#130692212
#130687312
#130683902
C22⋊C4×C11⋊C82
#130683862
C4×C8×Dic112
C11×#19232
C8×#12411