Finite Group Databasebeta

← #14775883

Subgroups — #14775883

Order 2816.

1084 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2C2×#10622740C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4C2×#10622731C211yesmaximal, characteristic, complemented
5C4×#66992C211yesmaximal, characteristic
6#13069408C211yesmaximal, characteristic, complemented
7#13069333C211yesmaximal, characteristic, complemented
8#13069232C211yesmaximal, characteristic, complemented
9#13069227C211yesmaximal, characteristic, complemented
10#13068911C211yesmaximal, characteristic, complemented
11#13068795C211yesmaximal, characteristic, complemented
12#13068793C211yesmaximal, characteristic, complemented
13#13068482C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66992C411yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C22×C8×D11C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28#10622833C411yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622740—24no—
33#10622731—24no—
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44C2×C8×Dic11C2211yescharacteristic
45#10622624—24no—
46#10622603C411yescharacteristic
47#10622585C411yescharacteristic
48#10622571C411yescharacteristic
49#10622570C411yescharacteristic
50#10622558C411yescharacteristic
51#10622555C411yescharacteristic
52C4×(C2×D11)⋊C4C2211yescharacteristic
53C4×Dic11⋊C4C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×#66867C2211yescharacteristic
56(C22⋊D11)⋊C8—24no—
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C23×Dic11C2×C411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16—41no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C2×C11×C4⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88#66992—24no—
89C4×C22⋊D11—22no—
90C4×C22⋊D11—22no—
91C4×C22⋊D11—22no—
92C4×C22⋊D11—22no—
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×Dic11⋊C4C2×C411yescharacteristic
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11C2×C411yescharacteristic
104C2×C4×Dic11C2×C411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C2×#4318—22no—
109C2×#4318—22no—
110C2×#4318—41no—
111C22×C11⋊C8—22no—
112C22×C11⋊C8—22no—
113C22×C11⋊C8—41no—
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C2×C8×D11—22no—
119C2×C8×D11—22no—
120C2×C8×D11—41no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C11×C22⋊C8—41no—
124C11⋊#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)D414yescomplemented
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8—41no—
135#66879—22no—
136Dic11⋊C8—22no—
137Dic11⋊C8—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8D414yescomplemented
141C8×Dic11—22no—
142C8×Dic11—22no—
143C4⋊(C11⋊C8)—22no—
144#66867—22no—
145#22986—111nomaximal, Sylow
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C23×D11C22×C411yescharacteristic
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—41no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4112yes—
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—22no—
170C2×C22⋊D11—22no—
171C2×C22⋊D11—22no—
172C2×C22⋊D11—22no—
173C2×C22⋊D11—41no—
174C2×C22⋊D11M1614yescomplemented
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—41no—
181C22×Dic11C22×C411yescharacteristic
182C22×Dic11C22×C411yescharacteristic
183C22×Dic11C22×C411yescharacteristic
184C22×Dic11C22×C411yescharacteristic
185C22×Dic11C22×C411yescharacteristic
186C22×Dic11C22×C411yescharacteristic
187C22×Dic11C22×C411yescharacteristic
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C11×M16—44no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C42×C11—21no—
211C42×C11—21no—
212C22⋊Dic11—22no—
213C22⋊Dic11—22no—
214C22⋊Dic11—22no—
215C22⋊Dic11—22no—
216(C2×D11)⋊C4—22no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—22no—
219(C2×D11)⋊C4—22no—
220Dic11⋊C4—22no—
221Dic11⋊C4—22no—
222Dic11⋊C4—22no—
223Dic11⋊C4—22no—
224C4×Dic11—22no—
225C4×Dic11—22no—
226C4×Dic11—21no—
227C4×Dic11—21no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11C2×D412yes—
231C4×Dic11#4112yes—
232#4318—44no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—44no—
243C2×C11⋊C8C2×D412yes—
244C2×C11⋊C8C2×D412yes—
245C2×C11⋊C8C2×D412yes—
246C8×D11—44no—
247C2×#435—111no—
248C2×#435—111no—
249C2×C8×D4—111no—
250C2×#423—111no—
251C4×#121—111no—
252#1954—111no—
253#1939—111no—
254#1924—111no—
255#1924—111no—
256#1870—111no—
257#1870D1111yescharacteristic, complemented
258#1850—111no—
259#1850—111no—
260#1770—111no—
261C4×C22⋊C8—111no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11C4×D412yes—
275C23×C11C2×M1612yes—
276C23×C11C23×C411yescharacteristic
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11C2×M1612yes—
284D4×C11—44no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11C4×D412yes—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C112−1+411yescharacteristic
311C22⋊D11—28no—
312C22⋊D11—44no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—44no—
330C2×Dic11—44no—
331C2×Dic11C4×D412yes—
332C2×Dic11C4×D412yes—
333C2×Dic11C2×M1612yes—
334C2×Dic11#13112yes—
335C2×Dic11#13112yes—
336C4×D11—41no—
337C4×D11—41no—
338C4×D11—41no—
339C4×D11—41no—
340C8×C11—22no—
341C8×C11—41no—
342C8×C11—41no—
343C8×C11—41no—
344C11⋊C8—22no—
345C11⋊C8—22no—
346C11⋊C8—22no—
347C11⋊C8—41no—
348C22×M16—111no—
349C22×M16C2×D1111yescharacteristic
350C23×C8—111no—
351C23×C8—111no—
352C2×#121—111no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C2×C4×D4C2×D1111yescharacteristic
356C22×C42—111no—
357#435—224no—
358#435—224no—
359C8×D4—224no—
360#423—224no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×C4⋊C8—111no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8—111no—
366C2×C4⋊C8—111no—
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370C2×C22⋊C8—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8C2×D1111yescharacteristic
373C2×C22⋊C8C2×D1111yescharacteristic
374C2×C22⋊C8C2×D1111yescharacteristic
375C2×#97—111no—
376C2×#97—111no—
377C2×C4×C8—111no—
378C2×C4×C8—111no—
379#390—111no—
380#389—111no—
381#388—111no—
382#388—111no—
383#386—111no—
384#386—111no—
385#380—111no—
386C4×C4⋊C4—111no—
387C4×C22⋊C4—111no—
388C4×C22⋊C4—111no—
389#336—111no—
390#336—111no—
391#336—111no—
392#336—111no—
393#336C2×D1111yescharacteristic
394#336C2×D1111yescharacteristic
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11C2×C4×D411yescharacteristic
410C22×C11C2×C4×D411yescharacteristic
411C22×C11#52011yescharacteristic
412C22×C11C22×M1611yescharacteristic
413C22×C11C2×#13111yescharacteristic
414C22×C11C2×#13111yescharacteristic
415C22×C11#56811yescharacteristic
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—22no—
419C2×D11—41no—
420C2×D11—41no—
421C2×D11—41no—
422C2×D11—41no—
423C4×C11—22no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11D4211yescharacteristic
428C4×C11#54711yescharacteristic
429C4×C11#54811yescharacteristic
430C4×C11#55311yescharacteristic
431Dic11—22no—
432Dic11—22no—
433Dic11—41no—
434Dic11—41no—
435Dic11—41no—
436Dic11—41no—
437Dic11#43514yescomplemented
438C22×D4—111no—
439C22×D4—111no—
440C22×D4C4×D1111yescharacteristic
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—41no—
449C2×M16—222no—
450C2×M16—222no—
451C2×M16—441no—
452C22×C8—111no—
453C22×C8—111no—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8—222no—
457C22×C8—222no—
458C22×C8—222no—
459C22×C8—222no—
460C22×C8—441no—
461C22×C8—441no—
462C22×C8C22×D1111yescharacteristic
463C22×C8C22×D1111yescharacteristic
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466#121—224no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—222no—
470C4×D4—222no—
471C4×D4—222no—
472C4×D4—222no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4C4×D1111yescharacteristic
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—111no—
484C2×C22⋊C4—111no—
485C2×C22⋊C4—111no—
486C2×C22⋊C4C4×D1111yescharacteristic
487C2×C22⋊C4C4×D1111yescharacteristic
488C2×C42—111no—
489C2×C42—111no—
490C2×C42—111no—
491C2×C42—111no—
492C2×C42—111no—
493C2×C42—222no—
494C2×C42—222no—
495C2×C42C22×D1111yescharacteristic
496C4⋊C8—114no—
497C4⋊C8—222no—
498C4⋊C8—222no—
499C4⋊C8—222no—
500C4⋊C8—222no—
501C4⋊C8—222no—
502C22⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8—41no—
505C22⋊C8—114no—
506C22⋊C8—222no—
507C22⋊C8—222no—
508C22⋊C8—222no—
509C22⋊C8—441no—
510#97—222no—
511#97—222no—
512C4×C8—222no—
513C4×C8—222no—
514#95—111no—
515#95—111no—
516#95—111no—
517#95—111no—
518#95—111no—
519#95—111no—
520C2×C11—42no—
521C2×C11—42no—
522C2×C11#236111yescharacteristic
523C2×C11C2×#43511yescharacteristic
524C2×C11#293111yescharacteristic
525C2×C11#293311yescharacteristic
526C2×C11D4×M1611yescharacteristic
527C2×C11#299011yescharacteristic
528C2×C11#299311yescharacteristic
529D11—42no—
530C24—111no—
531C24C2×C4×D1111yescharacteristic
532C24C2×C4×D1111yescharacteristic
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—41no—
536C2×D4—114no—
537C2×D4—222no—
538C2×D4—222no—
539C2×D4—222no—
540C2×D4—222no—
541C2×D4—441no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—111no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—441no—
571C22×C4C2×C4×D1111yescharacteristic
572C22×C4C2×C4×D1111yescharacteristic
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×C4×D1111yescharacteristic
575C22×C4D4×D1112yes—
576C22×C4#434112yes—
577C22×C4C23×D1111yescharacteristic
578M16—44no—
579M16—444no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—112no—
592C2×C8—112no—
593C2×C8—112no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—444no—
604C2×C8—444no—
605C2×C8D4×D1112yes—
606C4⋊C4—22no—
607C4⋊C4—222no—
608C4⋊C4—222no—
609C4⋊C4—222no—
610C4⋊C4—222no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—222no—
614C22⋊C4—222no—
615C22⋊C4—222no—
616C22⋊C4—222no—
617C22⋊C4—222no—
618C22⋊C4—222no—
619C22⋊C4—222no—
620C22⋊C4—222no—
621C42—21no—
622C42—21no—
623C42—112no—
624C42—112no—
625C42—222no—
626C42—222no—
627C42—221no—
628C42—221no—
629C42—221no—
630C42—221no—
631C11#2298611yescharacteristic, complemented, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—112no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23(C22⋊D11)⋊C412yes—
652C23M16×D1112yes—
653C23C22×C4×D1111yescharacteristic
654D4—44no—
655D4—228no—
656D4—444no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—221no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—221no—
693C2×C4—221no—
694C2×C4—221no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—444no—
698C2×C4—444no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4(C22⋊D11)⋊C412yes—
704C2×C4C2×D4×D1111yescharacteristic
705C2×C4C2×D4×D1111yescharacteristic
706C2×C4C2×#434111yescharacteristic
707C2×C4#6703711yescharacteristic
708C2×C4#41×D1111yescharacteristic
709C2×C4#6704311yescharacteristic
710C8—22no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—222no—
715C8—222no—
716C8—222no—
717C8—441no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—222no—
733C22—222no—
734C22—222no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22—441no—
739C22C2×(C22⋊D11)⋊C411yescharacteristic
740C22C4×D4×D1111yescharacteristic
741C22#1062307711yescharacteristic
742C22C2×M16×D1111yescharacteristic
743C22#1062327611yescharacteristic
744C22D11×#13111yescharacteristic
745C22D11×#13111yescharacteristic
746C4—22no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—114no—
751C4—222no—
752C4—222no—
753C4—441no—
754C4—441no—
755C4—441no—
756C4—441no—
757C4#1062312111yescharacteristic
758C4#1062312911yescharacteristic
759C4#1062313211yescharacteristic
760C4#1062318611yescharacteristic
761C2—42no—
762C2—42no—
763C2—442no—
764C2#1307162711yescharacteristic
765C2D11×#43511yescharacteristic
766C2#1307732411yescharacteristic
767C2#1307734511yescharacteristic
768C2#1307734811yescharacteristic
769C2#1307773611yescharacteristic
770C2#1307776211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC2×#66992C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#22986
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C2×#10622740C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
4. C2×#10622731C2semidirect
6. #13069408C2semidirect
7. #13069333C2semidirect
8. #13069232C2semidirect
9. #13069227C2semidirect
10. #13068911C2semidirect
11. #13068795C2semidirect
12. #13068793C2semidirect
13. #13068482C2semidirect
14. C22⋊C8×Dic11C2semidirect
15. C11×#1870C2semidirect
131. C22⋊(C11⋊C8)D4semidirect
140. Dic11⋊C8D4semidirect
174. C2×C22⋊D11M16semidirect
257. #1870D11semidirect
437. Dic11#435semidirect
631. C11#22986semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C2×#106227402
C2×(C22⋊D11)⋊C82
C2×#106227312
C4×#669922
#130694082
#130693332
#130692322
#130692272
#130689112
#130687952
#130687932
#130684822
C22⋊C8×Dic112
C11×#18702
#2298611