Finite Group Databasebeta

← #14676351

Subgroups — #14676351

Order 2816.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic
2C2×#10622594C211yesmaximal, characteristic, complemented
3#13066885C211yesmaximal, characteristic, complemented
4#13066883C211yesmaximal, characteristic, complemented
5#13066862C211yesmaximal, characteristic
6#13066858C211yesmaximal, characteristic
7#13066854C211yesmaximal, characteristic
8#13066852C211yesmaximal, characteristic
9#13066845C211yesmaximal, characteristic, complemented
10#13066840C211yesmaximal, characteristic, complemented
11#13066840C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic
13(C2×D11)⋊#95C211yesmaximal, characteristic
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#387C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66945—24no—
32C2×#66945—24no—
33C2×#66945C418yescomplemented
34C11×#387—24no—
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622594—24no—
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11C2×C414yes—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4C2×C414yes—
82C2×C11×C4⋊C4D414yes—
83C2×C11×C4⋊C4D414yes—
84C2×C42×C11—22no—
85C2×C42×C11—22no—
86C2×C42×C11—41no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—41no—
100C2×(C2×D11)⋊C4—41no—
101C2×(C2×D11)⋊C4—41no—
102C2×(C2×D11)⋊C4—41no—
103C2×(C2×D11)⋊C4C2×C414yes—
104C2×(C2×D11)⋊C4C2×C414yes—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—41no—
110C2×C4⋊Dic11C2×C414yes—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—41no—
118C2×C4×Dic11C2×C414yes—
119C2×C4×Dic11C2×C414yes—
120#66945—232no—
121C11×#95—22no—
122C11×#95—22no—
123C11×#95—22no—
124C11×#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141#13944—111nomaximal, Sylow
142C24×C11C2411yescharacteristic
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11C22×C412yes—
156C23×D11#4112yes—
157C23×D11#4112yes—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2×D412yes—
205C22×C4×C11#4112yes—
206C22×C4×C11#4112yes—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C22×C412yes—
252C22×Dic11#4112yes—
253C22×Dic11#4112yes—
254C22×Dic11#4112yes—
255C22×Dic11#4112yes—
256C2×C4×D11—28no—
257C2×C4×D11—28no—
258C2×C4×D11—28no—
259C2×C4×D11—28no—
260C2×C4×D11—28no—
261C2×C4×D11—28no—
262C2×C4×D11—28no—
263C11×C4⋊C4—44no—
264C11×C4⋊C4C22⋊C4116yescomplemented
265C42×C11—44no—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—44no—
272C4⋊Dic11—28no—
273C4⋊Dic11—44no—
274C4×Dic11—28no—
275C4×Dic11—28no—
276C4×Dic11—44no—
277C22×#117—111no—
278C2×#387—111no—
279C2×#387D1111yescharacteristic, complemented
280#1445—111no—
281#1445—111no—
282#1439—111no—
283#1439—111no—
284#1437—111no—
285#1437—111no—
286C4⋊#95—111no—
287#1434—111no—
288#1434—111no—
289C22⋊#95—111no—
290C22⋊#95—111no—
291C4×#95—111no—
292C23×C11C23×C411yescharacteristic
293C23×C11C22×D411yescharacteristic
294C23×C11C22×D411yescharacteristic
295C23×C11C2×#4111yescharacteristic
296C23×C11C2×#4111yescharacteristic
297C23×C11C2×#4111yescharacteristic
298C23×C11C2×#4111yescharacteristic
299C23×C11C2×#4111yescharacteristic
300C23×C11C2×#4111yescharacteristic
301C23×C11C2×#4111yescharacteristic
302C23×C11C2×#4111yescharacteristic
303C23×C11H(5,𝔽2)11yescharacteristic
304C23×C11H(5,𝔽2)11yescharacteristic
305C23×C112−1+411yescharacteristic
306C23×C112−1+411yescharacteristic
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11#11714yes—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11C2×C22⋊C414yes—
389C2×C4×C11C2×C22⋊C414yes—
390C2×C4×C11C2×C22⋊C414yes—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11#11714yes—
440C4×D11—232no—
441C24×C4—111no—
442C2×#117—118no—
443C2×#117—224no—
444C2×#117—224no—
445C22×C4⋊C4—111no—
446C22×C4⋊C4—111no—
447C22×C4⋊C4C2×D1111yescharacteristic
448C22×C4⋊C4C2×D1111yescharacteristic
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4—111no—
454C22×C22⋊C4—111no—
455C22×C42—111no—
456C22×C42—111no—
457C22×C42—111no—
458C22×C42C2×D1111yescharacteristic
459#387—24no—
460#387—224no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95—111no—
468C2×#95—111no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95C2×D1111yescharacteristic
478C2×#95C2×D1111yescharacteristic
479C2×#95C2×D1111yescharacteristic
480C2×#95C2×D1111yescharacteristic
481C22×C11C22×C22⋊C411yescharacteristic
482C22×C11C2×#11711yescharacteristic
483C22×C11C2×#11711yescharacteristic
484C22×C11C4×#4111yescharacteristic
485C22×C11C4×#4111yescharacteristic
486C22×C11#52011yescharacteristic
487C22×C11#52011yescharacteristic
488C22×C11#52511yescharacteristic
489C22×C11#52511yescharacteristic
490C22×C11#52511yescharacteristic
491C22×C11#52511yescharacteristic
492C22×C11#52911yescharacteristic
493C22×C11#52911yescharacteristic
494C22×C11#52911yescharacteristic
495C22×C11#52911yescharacteristic
496C22×C11#54011yescharacteristic
497C22×C11#54111yescharacteristic
498C22×C11#54211yescharacteristic
499C22×C11#54211yescharacteristic
500C22×C11#54611yescharacteristic
501C22×C11#54611yescharacteristic
502C22×C11#54711yescharacteristic
503C22×C11#54711yescharacteristic
504C22×C11#54811yescharacteristic
505C22×C11#54811yescharacteristic
506C22×C11#55011yescharacteristic
507C22×C11#55011yescharacteristic
508C22×C11#55111yescharacteristic
509C22×C11#55111yescharacteristic
510C22×C11#55111yescharacteristic
511C22×C11#55111yescharacteristic
512C22×C11#55211yescharacteristic
513C22×C11#55211yescharacteristic
514C22×C11#55211yescharacteristic
515C22×C11#55211yescharacteristic
516C2×D11—24no—
517C2×D11—24no—
518C2×D11—24no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C4×C11—24no—
532C4×C11—24no—
533C4×C11—24no—
534C4×C11—42no—
535C4×C11—42no—
536C4×C11—81no—
537C4×C11—81no—
538Dic11—24no—
539Dic11—42no—
540Dic11—42no—
541Dic11—42no—
542Dic11—42no—
543Dic11—81no—
544Dic11—81no—
545C25—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—114no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—222no—
555C23×C4—222no—
556C23×C4—222no—
557C23×C4—222no—
558C23×C4—222no—
559C23×C4—222no—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C23×C4C22×D1111yescharacteristic
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1111yescharacteristic
566C23×C4C22×D1111yescharacteristic
567#117—2232no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4—114no—
572C2×C4⋊C4—222no—
573C2×C4⋊C4—222no—
574C2×C4⋊C4—222no—
575C2×C4⋊C4—222no—
576C2×C4⋊C4—441no—
577C2×C4⋊C4C4×D1114yes—
578C2×C4⋊C4D4414yes—
579C2×C4⋊C4C22⋊D1114yes—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—222no—
583C2×C22⋊C4—222no—
584C2×C22⋊C4—222no—
585C2×C22⋊C4—222no—
586C2×C22⋊C4—222no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—222no—
589C2×C22⋊C4—222no—
590C2×C22⋊C4—222no—
591C2×C22⋊C4—222no—
592C2×C22⋊C4—222no—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—441no—
595C2×C22⋊C4—441no—
596C2×C22⋊C4—441no—
597C2×C22⋊C4—441no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—41no—
601C2×C42—114no—
602C2×C42—114no—
603C2×C42—222no—
604C2×C42—222no—
605C2×C42—222no—
606C2×C42—222no—
607C2×C42—222no—
608C2×C42—222no—
609C2×C42—441no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—222no—
615#95—222no—
616#95—222no—
617#95—222no—
618#95—222no—
619#95—222no—
620#95—222no—
621#95—222no—
622#95—222no—
623#95—222no—
624#95—222no—
625#95—222no—
626#95—441no—
627#95—441no—
628#95—441no—
629#95—441no—
630C2×C11#228011yescharacteristic
631C2×C11#229811yescharacteristic
632C2×C11#231411yescharacteristic
633C2×C11#233911yescharacteristic
634C2×C11#234111yescharacteristic
635C2×C11#234311yescharacteristic
636C2×C11#234311yescharacteristic
637C2×C11#247111yescharacteristic
638C2×C11#247111yescharacteristic
639C2×C11#247511yescharacteristic
640C2×C11#247511yescharacteristic
641C2×C11#247711yescharacteristic
642C2×C11#247711yescharacteristic
643C2×C11#247911yescharacteristic
644C2×C11#247911yescharacteristic
645D11—44no—
646C24—112no—
647C24—112no—
648C24—112no—
649C24—221no—
650C24—221no—
651C24—221no—
652C24—221no—
653C24—221no—
654C24—221no—
655C24—221no—
656C24—221no—
657C24—221no—
658C24—221no—
659C24—221no—
660C24—221no—
661C24C23×D1111yescharacteristic
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—228no—
708C22×C4—228no—
709C22×C4—228no—
710C22×C4—228no—
711C22×C4—228no—
712C22×C4—228no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—228no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4C2×C4×D1112yes—
757C22×C4C2×C4×D1112yes—
758C22×C4C2×C4×D1112yes—
759C22×C4C2×D4412yes—
760C22×C4C2×D4412yes—
761C22×C4C2×D4412yes—
762C22×C4#434112yes—
763C22×C4#434312yes—
764C22×C4C2×C22⋊D1112yes—
765C22×C4C2×C22⋊D1112yes—
766C22×C4C2×C22⋊D1112yes—
767C4⋊C4—44no—
768C4⋊C4—228no—
769C4⋊C4—444no—
770C4⋊C4(C2×D11)⋊C4116yescomplemented
771C22⋊C4—228no—
772C22⋊C4—228no—
773C22⋊C4—444no—
774C22⋊C4—444no—
775C22⋊C4—444no—
776C22⋊C4—444no—
777C42—44no—
778C42—228no—
779C42—228no—
780C42—444no—
781C11#1394411yescharacteristic, complemented, Sylow
782C23—114no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—222no—
789C23—222no—
790C23—222no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23—441no—
807C23—441no—
808C23—441no—
809C23—441no—
810C23—441no—
811C23—441no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23—441no—
816C23—441no—
817C23C22×C4×D1111yescharacteristic
818C23C22×D4411yescharacteristic
819C23C2×#434111yescharacteristic
820C23#6703711yescharacteristic
821C23C2×#434311yescharacteristic
822C23#6704011yescharacteristic
823C23#41×D1111yescharacteristic
824C23#41×D1111yescharacteristic
825C23#41×D1111yescharacteristic
826C23#41×D1111yescharacteristic
827C23#41×D1111yescharacteristic
828C23#41×D1111yescharacteristic
829C23#6704211yescharacteristic
830C23#6704311yescharacteristic
831C23C22×C22⋊D1111yescharacteristic
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—114no—
879C2×C4—2232no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4—441no—
918C2×C4—441no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4C2×(C2×D11)⋊C414yes—
929C2×C4C2×(C2×D11)⋊C414yes—
930C2×C4C2×(C2×D11)⋊C414yes—
931C22—224no—
932C22—224no—
933C22—224no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22D11×#11711yescharacteristic
947C22D11×#11711yescharacteristic
948C22#1062305511yescharacteristic
949C22#1062305511yescharacteristic
950C22C4×#434111yescharacteristic
951C22#1062307711yescharacteristic
952C22#1062308511yescharacteristic
953C22#1062308611yescharacteristic
954C22C4×#434311yescharacteristic
955C22#1062310511yescharacteristic
956C22#1062310711yescharacteristic
957C22#1062310811yescharacteristic
958C22#1062315511yescharacteristic
959C22#1062316811yescharacteristic
960C22#1062317011yescharacteristic
961C22#1062317111yescharacteristic
962C22#1062318011yescharacteristic
963C22#1062318911yescharacteristic
964C22#1062319011yescharacteristic
965C22#1062319411yescharacteristic
966C22#1062322211yescharacteristic
967C22#1062322411yescharacteristic
968C22#1062322511yescharacteristic
969C22#1062322711yescharacteristic
970C22#1062323611yescharacteristic
971C22#1062323711yescharacteristic
972C22#1062323911yescharacteristic
973C22#1062324111yescharacteristic
974C22C22×(C2×D11)⋊C411yescharacteristic
975C22#1062333711yescharacteristic
976C22#1062334811yescharacteristic
977C22#1062335511yescharacteristic
978C22#1062335911yescharacteristic
979C22#1062335911yescharacteristic
980C22#1062336511yescharacteristic
981C4—24no—
982C4—24no—
983C4—24no—
984C4—42no—
985C4—42no—
986C4—81no—
987C4—81no—
988C4—224no—
989C4—442no—
990C4—442no—
991C4—442no—
992C4—442no—
993C4—881no—
994C4—881no—
995C2—444no—
996C2#1307099511yescharacteristic
997C2#1307110811yescharacteristic
998C2#1307122211yescharacteristic
999C2#1307144111yescharacteristic
1000C2#1307145411yescharacteristic
1001C2#1307147111yescharacteristic
1002C2#1307147511yescharacteristic
1003C2#1307272311yescharacteristic
1004C2#1307272511yescharacteristic
1005C2#1307278311yescharacteristic
1006C2#1307278511yescharacteristic
1007C2#1307281311yescharacteristic
1008C2#1307281511yescharacteristic
1009C2#1307284311yescharacteristic
1010C2#1307284511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#387C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#387D11
hypocenterC11#13944
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C2×#10622594C2semidirect
3. #13066885C2semidirect
4. #13066883C2semidirect
9. #13066845C2semidirect
10. #13066840C2semidirect
11. #13066840C2semidirect
14. C4×C11⋊#95C2semidirect
15. C2×C11×#387C2semidirect
33. C2×#66945C4semidirect
264. C11×C4⋊C4C22⋊C4semidirect
279. C2×#387D11semidirect
770. C4⋊C4(C2×D11)⋊C4semidirect
781. C11#13944semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
C2×#106225942
#130668852
#130668832
#130668622
#130668582
#130668542
#130668522
#130668452
#130668402
(C2×D11)⋊#952
C4×C11⋊#952
C2×C11×#3872
#1394411