Finite Group Databasebeta

← #14676338

Subgroups — #14676338

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×#66930C211yesmaximal, characteristic
2C2×#10622564C211yesmaximal, characteristic
3#13066870C211yesmaximal, characteristic, complemented
4#13066866C211yesmaximal, characteristic, complemented
5#13066863C211yesmaximal, characteristic
6#13066863C211yesmaximal, characteristic
7#13066851C211yesmaximal, characteristic, complemented
8#13066849C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066840C211yesmaximal, characteristic, complemented
11#13066840C211yesmaximal, characteristic, complemented
12#13066838C211yesmaximal, characteristic
13#13066838C211yesmaximal, characteristic
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#388C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66930—24no—
32C2×#66930—24no—
33C2×#66930C418yescomplemented
34C11×#388—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#10622564—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11C2×C414yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4—41no—
87C2×C11×C22⋊C4C2×C414yes—
88C2×C11×C22⋊C4D414yes—
89C2×C11×C22⋊C4D414yes—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11—41no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11—41no—
101C2×C22⋊Dic11C2×C414yes—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—41no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4C2×C414yes—
110C2×Dic11⋊C4C2×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#66930—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#13943—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11C22×C412yes—
155C24×C11C2×D412yes—
156C24×C11C2×D412yes—
157C24×C11C2411yescharacteristic
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×C11C22×C412yes—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D412yes—
198C22×C4×C11#4112yes—
199C22×C4×C11#4112yes—
200C22×Dic11—28no—
201C22×Dic11—28no—
202C22×Dic11—28no—
203C22×Dic11—28no—
204C22×Dic11—28no—
205C22×Dic11—28no—
206C22×Dic11—28no—
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×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11C22×C412yes—
254C22×Dic11C22×C412yes—
255C22×Dic11C22×C412yes—
256C22×Dic11C22×C412yes—
257C22×Dic11#4112yes—
258C22×Dic11#4112yes—
259C22×Dic11#4112yes—
260C22×Dic11#4112yes—
261C22×Dic11#4112yes—
262C22×Dic11#4112yes—
263C11×C4⋊C4—44no—
264C11×C22⋊C4—44no—
265C11×C22⋊C4—44no—
266C11×C22⋊C4C22⋊C4116yes—
267C42×C11—44no—
268C22⋊Dic11—28no—
269C22⋊Dic11—44no—
270C22⋊Dic11—44no—
271C4⋊Dic11—44no—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274C4×Dic11—28no—
275C4×Dic11—28no—
276C4×Dic11—44no—
277C22×#117—111no—
278C2×#388—111no—
279C2×#388D1111yescharacteristic
280#1441—111no—
281#1441—111no—
282#1440—111no—
283#1440—111no—
284#1436—111no—
285#1436—111no—
286C4⋊#95—111no—
287#1434—111no—
288#1434—111no—
289C22⋊#95—111no—
290C22⋊#95—111no—
291C4×#95—111no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11C2×C22⋊C414yes—
327C23×C11C23×C411yescharacteristic
328C23×C11C22×D411yescharacteristic
329C23×C11C22×D411yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11C2×#4111yescharacteristic
334C23×C11C2×#4111yescharacteristic
335C23×C11C2×#4111yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11H(5,𝔽2)11yescharacteristic
339C23×C11H(5,𝔽2)11yescharacteristic
340C23×C112−1+411yescharacteristic
341C23×C112−1+411yescharacteristic
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—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
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×C11C2×C22⋊C414yes—
383C2×C4×C11C2×C22⋊C414yes—
384C2×Dic11—232no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
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—
440C2×Dic11#11714yes—
441C24×C4—111no—
442C2×#117—118no—
443C2×#117—224no—
444C2×#117—224no—
445C22×C4⋊C4—111no—
446C22×C4⋊C4—111no—
447C22×C4⋊C4—111no—
448C22×C4⋊C4C2×D1111yescharacteristic
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4C2×D1111yescharacteristic
453C22×C22⋊C4C2×D1111yescharacteristic
454C22×C22⋊C4C2×D1111yescharacteristic
455C22×C42—111no—
456C22×C42—111no—
457C22×C42—111no—
458C22×C42C2×D1111yescharacteristic
459#388—24no—
460#388—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×#95—111no—
478C2×#95—111no—
479C2×#95C2×D1111yescharacteristic
480C2×#95C2×D1111yescharacteristic
481C22×C11—24no—
482C22×C11—24no—
483C22×C11—24no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11C22×C22⋊C411yescharacteristic
497C22×C11C2×#11711yescharacteristic
498C22×C11C2×#11711yescharacteristic
499C22×C11C4×#4111yescharacteristic
500C22×C11C4×#4111yescharacteristic
501C22×C11#52011yescharacteristic
502C22×C11#52011yescharacteristic
503C22×C11#52511yescharacteristic
504C22×C11#52511yescharacteristic
505C22×C11#52511yescharacteristic
506C22×C11#52511yescharacteristic
507C22×C11#52911yescharacteristic
508C22×C11#52911yescharacteristic
509C22×C11#52911yescharacteristic
510C22×C11#52911yescharacteristic
511C22×C11#54011yescharacteristic
512C22×C11#54111yescharacteristic
513C22×C11#54211yescharacteristic
514C22×C11#54211yescharacteristic
515C22×C11#54611yescharacteristic
516C22×C11#54611yescharacteristic
517C22×C11#54611yescharacteristic
518C22×C11#54611yescharacteristic
519C22×C11#54711yescharacteristic
520C22×C11#54711yescharacteristic
521C22×C11#54711yescharacteristic
522C22×C11#54711yescharacteristic
523C22×C11#55211yescharacteristic
524C22×C11#55211yescharacteristic
525C22×C11#55311yescharacteristic
526C22×C11#55311yescharacteristic
527C22×C11#55511yescharacteristic
528C22×C11#55511yescharacteristic
529C22×C11#55611yescharacteristic
530C22×C11#55611yescharacteristic
531C4×C11—24no—
532C4×C11—24no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—81no—
536C4×C11—81no—
537Dic11—24no—
538Dic11—24no—
539Dic11—42no—
540Dic11—42no—
541Dic11—42no—
542Dic11—42no—
543Dic11—81no—
544Dic11—81no—
545C25C22×D1111yescharacteristic
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—114no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—222no—
556C23×C4—222no—
557C23×C4—222no—
558C23×C4—222no—
559C23×C4—222no—
560C23×C4—222no—
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—114no—
573C2×C4⋊C4—222no—
574C2×C4⋊C4—222no—
575C2×C4⋊C4—222no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—222no—
578C2×C4⋊C4—222no—
579C2×C4⋊C4—441no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—114no—
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—441no—
594C2×C22⋊C4—441no—
595C2×C22⋊C4C4×D1114yes—
596C2×C22⋊C4D4414yes—
597C2×C22⋊C4C22⋊D1114yes—
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—222no—
613#95—222no—
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—44no—
631C2×C11#228011yescharacteristic
632C2×C11#229811yescharacteristic
633C2×C11#231411yescharacteristic
634C2×C11#233911yescharacteristic
635C2×C11#233911yescharacteristic
636C2×C11#234611yescharacteristic
637C2×C11#234711yescharacteristic
638C2×C11#247011yescharacteristic
639C2×C11#247011yescharacteristic
640C2×C11#247411yescharacteristic
641C2×C11#247411yescharacteristic
642C2×C11#247611yescharacteristic
643C2×C11#247611yescharacteristic
644C2×C11#247811yescharacteristic
645C2×C11#247811yescharacteristic
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24C2×C4×D1112yes—
659C24C2×D4412yes—
660C24C2×C22⋊D1112yes—
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—112no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—228no—
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—221no—
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×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4C2×C4×D1112yes—
760C22×C4C2×C4×D1112yes—
761C22×C4C2×D4412yes—
762C22×C4C2×D4412yes—
763C22×C4#434112yes—
764C22×C4#434112yes—
765C22×C4C2×C22⋊D1112yes—
766C22×C4C2×C22⋊D1112yes—
767C4⋊C4—44no—
768C4⋊C4—228no—
769C4⋊C4—228no—
770C4⋊C4—444no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4—228no—
774C22⋊C4—444no—
775C22⋊C4—444no—
776C22⋊C4(C2×D11)⋊C4116yes—
777C42—44no—
778C42—228no—
779C42—228no—
780C42—444no—
781C11#1394311yescharacteristic, complemented, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23C2×(C2×D11)⋊C414yes—
817C23C22×C4×D1111yescharacteristic
818C23C22×D4411yescharacteristic
819C23C2×#434111yescharacteristic
820C23C2×#434111yescharacteristic
821C23#6703711yescharacteristic
822C23#6703711yescharacteristic
823C23#41×D1111yescharacteristic
824C23#41×D1111yescharacteristic
825C23#41×D1111yescharacteristic
826C23#41×D1111yescharacteristic
827C23#41×D1111yescharacteristic
828C23#41×D1111yescharacteristic
829C23#6704311yescharacteristic
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—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
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—114no—
873C2×C4—114no—
874C2×C4—2232no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
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—222no—
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×C4—441no—
929C2×C4C2×(C2×D11)⋊C414yes—
930C2×C4C2×(C2×D11)⋊C414yes—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22D11×#11711yescharacteristic
947C22D11×#11711yescharacteristic
948C22#1062305511yescharacteristic
949C22#1062305511yescharacteristic
950C22C4×#434111yescharacteristic
951C22C4×#434111yescharacteristic
952C22#1062307711yescharacteristic
953C22#1062307711yescharacteristic
954C22#1062308511yescharacteristic
955C22#1062308511yescharacteristic
956C22#1062308611yescharacteristic
957C22#1062308611yescharacteristic
958C22#1062313111yescharacteristic
959C22#1062313211yescharacteristic
960C22#1062314611yescharacteristic
961C22#1062314711yescharacteristic
962C22#1062318011yescharacteristic
963C22#1062318111yescharacteristic
964C22#1062319211yescharacteristic
965C22#1062319311yescharacteristic
966C22#1062320011yescharacteristic
967C22#1062320111yescharacteristic
968C22#1062320211yescharacteristic
969C22#1062321111yescharacteristic
970C22#1062323211yescharacteristic
971C22#1062323311yescharacteristic
972C22#1062323711yescharacteristic
973C22#1062323911yescharacteristic
974C22C22×(C2×D11)⋊C411yescharacteristic
975C22#1062333711yescharacteristic
976C22#1062333711yescharacteristic
977C22#1062335511yescharacteristic
978C22#1062335511yescharacteristic
979C22#1062335911yescharacteristic
980C22#1062335911yescharacteristic
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C4—224no—
988C4—224no—
989C4—442no—
990C4—442no—
991C4—442no—
992C4—442no—
993C4—881no—
994C4—881no—
995C2—44no—
996C2#1307099511yescharacteristic
997C2#1307111011yescharacteristic
998C2#1307122011yescharacteristic
999C2#1307144111yescharacteristic
1000C2#1307144111yescharacteristic
1001C2#1307149811yescharacteristic
1002C2#1307150611yescharacteristic
1003C2#1307270811yescharacteristic
1004C2#1307271011yescharacteristic
1005C2#1307276811yescharacteristic
1006C2#1307277011yescharacteristic
1007C2#1307279811yescharacteristic
1008C2#1307280011yescharacteristic
1009C2#1307282811yescharacteristic
1010C2#1307283011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#388D11
hypocenterC11#13943
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. #13066870C2semidirect
4. #13066866C2semidirect
7. #13066851C2semidirect
8. #13066849C2semidirect
9. #13066845C2semidirect
10. #13066840C2semidirect
11. #13066840C2semidirect
14. C4×C11⋊#95C2semidirect
33. C2×#66930C4semidirect
781. C11#13943semidirect

Maximal subgroups

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

subgroupindex
C22×#669302
C2×#106225642
#130668702
#130668662
#130668632
#130668512
#130668492
#130668452
#130668402
#130668382
C4×C11⋊#952
C2×C11×#3882
#1394311