Finite Group Databasebeta

← #14681702

Subgroups — #14681702

Order 2816.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622260C211yesmaximal, characteristic, complemented
2C2×#10622585C211yesmaximal, characteristic, complemented
3C2×#10622558C211yesmaximal, characteristic
4C2×#10622557C211yesmaximal, characteristic
5C2×#10622823C211yesmaximal, characteristic
6C2×#10622825C211yesmaximal, characteristic
7#13066880C211yesmaximal, characteristic, complemented
8#13066879C211yesmaximal, characteristic, complemented
9#13066870C211yesmaximal, characteristic, complemented
10#13066866C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic
12#13066859C211yesmaximal, characteristic
13#13066850C211yesmaximal, characteristic, complemented
14#13066848C211yesmaximal, characteristic, complemented
15C2×C11×#380C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C11×#380—24no—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38#10622825—24no—
39#10622823C418yescomplemented
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
54#10622585—24no—
55#10622558—24no—
56#10622557—24no—
57#10622260—24no—
58C25×C11C2311yescharacteristic
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—41no—
64C23×C4×C11—41no—
65C23×C4×C11C2×C414yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—41no—
85C2×C11×C4⋊C4—41no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4—41no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11C2×C414yes—
101C2×C22⋊Dic11C2×C414yes—
102C2×C22⋊Dic11D414yes—
103C2×C22⋊Dic11Q814yes—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—41no—
109C2×C4⋊Dic11—41no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—41no—
121C2×Dic11⋊C4—41no—
122C2×Dic11⋊C4—41no—
123C2×Dic11⋊C4—41no—
124C2×Dic11⋊C4—41no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4C2×C414yes—
127C2×Dic11⋊C4C2×C414yes—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—41no—
133C2×C4×Dic11—41no—
134C11×#95—22no—
135C11×#95D414yes—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95C2×C414yes—
148C11⋊#95C2×C414yes—
149C11⋊#95D414yes—
150#14402—111nomaximal, Sylow
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11C22×C412yes—
164C24×C11C2×D412yes—
165C24×C11C2×Q812yes—
166C24×C11C2411yescharacteristic
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—28no—
188C22×C4×C11—28no—
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×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—44no—
204C22×C4×C11—44no—
205C22×C4×C11—44no—
206C22×C4×C11—44no—
207C22×C4×C11—44no—
208C22×C4×C11C22×C412yes—
209C22×C4×C11C22×C412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D412yes—
214C22×C4×C11#4112yes—
215C22×C4×C11#4112yes—
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×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11C22×C412yes—
263C22×Dic11C22×C412yes—
264C22×Dic11C22×C412yes—
265C22×Dic11C22×C412yes—
266C22×Dic11C2×D412yes—
267C22×Dic11C2×D412yes—
268C22×Dic11C2×D412yes—
269C22×Dic11C2×D412yes—
270C22×Dic11C2×Q812yes—
271C22×Dic11C2×Q812yes—
272C11×C4⋊C4—44no—
273C11×C4⋊C4—44no—
274C11×C22⋊C4—44no—
275C11×C22⋊C4—44no—
276C22⋊Dic11—44no—
277C22⋊Dic11—44no—
278C22⋊Dic11—44no—
279C22⋊Dic11C4⋊C4116yescomplemented
280C4⋊Dic11—44no—
281C4⋊Dic11—44no—
282Dic11⋊C4—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4—44no—
285Dic11⋊C4—44no—
286Dic11⋊C4—44no—
287Dic11⋊C4—44no—
288C4×Dic11—44no—
289C4×Dic11—44no—
290C2×#389—111no—
291C2×#389—111no—
292C2×#388—111no—
293C2×#388—111no—
294C2×#385—111no—
295C2×#380—111no—
296C2×#380D1111yescharacteristic
297#1444—111no—
298#1444—111no—
299#1441—111no—
300#1441—111no—
301#1439—111no—
302#1439—111no—
303#1436—111no—
304#1436—111no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11C2×C4⋊C414yes—
340C23×C11C23×C411yescharacteristic
341C23×C11C22×D411yescharacteristic
342C23×C11C22×D411yescharacteristic
343C23×C11C22×D411yescharacteristic
344C23×C11C22×Q811yescharacteristic
345C23×C11C2×#4111yescharacteristic
346C23×C11C2×#4111yescharacteristic
347C23×C11H(5,𝔽2)11yescharacteristic
348C23×C11H(5,𝔽2)11yescharacteristic
349C23×C11H(5,𝔽2)11yescharacteristic
350C23×C11H(5,𝔽2)11yescharacteristic
351C23×C112−1+411yescharacteristic
352C23×C112−1+411yescharacteristic
353C23×C112−1+411yescharacteristic
354C23×C112−1+411yescharacteristic
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—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—416no—
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×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11C4×D414yes—
397C2×C4×C11C4×D414yes—
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—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
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—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11C2×C4⋊C414yes—
453C2×Dic11C2×C4⋊C414yes—
454C24×C4C2×D1111yescharacteristic
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4C2×D1111yescharacteristic
464C22×C4⋊C4C2×D1111yescharacteristic
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4C2×D1111yescharacteristic
470C22×C22⋊C4C2×D1111yescharacteristic
471C22×C42—111no—
472C22×C42—111no—
473#389—224no—
474#389—224no—
475#388—224no—
476#388—224no—
477#385—118no—
478#380—24no—
479#380—224no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C2×#95—111no—
494C2×#95C2×D1111yescharacteristic
495C2×#95C2×D1111yescharacteristic
496C22×C11—24no—
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11C22×C4⋊C411yescharacteristic
512C22×C11C2×C4×D411yescharacteristic
513C22×C11C2×C4×D411yescharacteristic
514C22×C11#51811yescharacteristic
515C22×C11#51911yescharacteristic
516C22×C11#52011yescharacteristic
517C22×C11#52011yescharacteristic
518C22×C11#53611yescharacteristic
519C22×C11#53611yescharacteristic
520C22×C11#53711yescharacteristic
521C22×C11#53711yescharacteristic
522C22×C11#53711yescharacteristic
523C22×C11#53711yescharacteristic
524C22×C11#54111yescharacteristic
525C22×C11#54111yescharacteristic
526C22×C11#54211yescharacteristic
527C22×C11#54211yescharacteristic
528C22×C11#54411yescharacteristic
529C22×C11#54411yescharacteristic
530C22×C11D4211yescharacteristic
531C22×C11D4211yescharacteristic
532C22×C11D4211yescharacteristic
533C22×C11#54611yescharacteristic
534C22×C11#54611yescharacteristic
535C22×C11#54711yescharacteristic
536C22×C11#54711yescharacteristic
537C22×C11D4×Q811yescharacteristic
538C22×C11D4×Q811yescharacteristic
539C22×C11#55111yescharacteristic
540C22×C11#55411yescharacteristic
541C22×C11#55411yescharacteristic
542C22×C11#56011yescharacteristic
543C22×C11#56211yescharacteristic
544C22×C11#56211yescharacteristic
545C22×C11#56311yescharacteristic
546C4×C11—24no—
547C4×C11—24no—
548C4×C11—42no—
549C4×C11—42no—
550C4×C11—81no—
551C4×C11—81no—
552Dic11—24no—
553Dic11—24no—
554Dic11—42no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558Dic11—81no—
559Dic11—81no—
560C25C22×D1111yescharacteristic
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—41no—
566C23×C4—41no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—111no—
575C23×C4C4×D1114yes—
576C23×C4C22×D1111yescharacteristic
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—114no—
589C2×C4⋊C4—114no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—222no—
596C2×C4⋊C4—222no—
597C2×C4⋊C4—222no—
598C2×C4⋊C4—222no—
599C2×C4⋊C4—222no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—222no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4—222no—
604C2×C4⋊C4—441no—
605C2×C4⋊C4—441no—
606C2×C4⋊C4—441no—
607C2×C4⋊C4—441no—
608C2×C4⋊C4—441no—
609C2×C4⋊C4—441no—
610C2×C4⋊C4—441no—
611C2×C4⋊C4—441no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—114no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—222no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—441no—
627C2×C22⋊C4—441no—
628C2×C22⋊C4—441no—
629C2×C22⋊C4—441no—
630C2×C42—222no—
631C2×C42—222no—
632C2×C42—222no—
633C2×C42—222no—
634C2×C42—441no—
635C2×C42—441no—
636#95—22no—
637#95—114no—
638#95—114no—
639#95—114no—
640#95—222no—
641#95—222no—
642#95—222no—
643#95—222no—
644#95—222no—
645#95—222no—
646#95—222no—
647#95—441no—
648#95—441no—
649#95—441no—
650#95—441no—
651#95C22⋊D1114yes—
652C2×C11—44no—
653C2×C11#231611yescharacteristic
654C2×C11#232311yescharacteristic
655C2×C11#232311yescharacteristic
656C2×C11D4×C4⋊C411yescharacteristic
657C2×C11D4×C4⋊C411yescharacteristic
658C2×C11#235811yescharacteristic
659C2×C11#237611yescharacteristic
660C2×C11#267211yescharacteristic
661C2×C11#267211yescharacteristic
662C2×C11#267511yescharacteristic
663C2×C11#267711yescharacteristic
664C2×C11#270411yescharacteristic
665C2×C11#270411yescharacteristic
666C2×C11#272211yescharacteristic
667C2×C11#274211yescharacteristic
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C2×C4×D1112yes—
681C24D4×D1112yes—
682C24Q8×D1112yes—
683C24C23×D1111yescharacteristic
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—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
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×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4C2×C4×D1112yes—
782C22×C4C2×C4×D1112yes—
783C22×C4#433912yes—
784C22×C4D4×D1112yes—
785C22×C4#434112yes—
786C22×C4C2×C22⋊D1112yes—
787C22×C4C2×C22⋊D1112yes—
788C22×C4C2×C22⋊D1112yes—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—228no—
792C4⋊C4—228no—
793C4⋊C4—444no—
794C4⋊C4—444no—
795C4⋊C4—444no—
796C4⋊C4—444no—
797C4⋊C4—444no—
798C4⋊C4—444no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—1116no—
802C22⋊C4—444no—
803C22⋊C4—444no—
804C22⋊C4—444no—
805C42—444no—
806C42—444no—
807C11#1440211yescharacteristic, complemented, Sylow
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C4⋊C4×D1114yes—
843C23C22×C4×D1111yescharacteristic
844C23C2×#433911yescharacteristic
845C23C2×D4×D1111yescharacteristic
846C23C2×D4×D1111yescharacteristic
847C23C2×#434111yescharacteristic
848C23#6703711yescharacteristic
849C23#6703711yescharacteristic
850C23#6703711yescharacteristic
851C23C2×Q8×D1111yescharacteristic
852C23#6704011yescharacteristic
853C23#6704211yescharacteristic
854C23#6704311yescharacteristic
855C23#6704311yescharacteristic
856C23#6704311yescharacteristic
857C23C22×C22⋊D1111yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—416no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—114no—
900C2×C4—114no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4(C22⋊D11)⋊C414yes—
956C2×C4C4×C22⋊D1114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C2×(C22⋊D11)⋊C411yescharacteristic
973C22#1062301711yescharacteristic
974C22#1062302111yescharacteristic
975C22#1062302611yescharacteristic
976C22C2×C4⋊C4×D1111yescharacteristic
977C22#1062303511yescharacteristic
978C22#1062303811yescharacteristic
979C22#1062304211yescharacteristic
980C22#1062304711yescharacteristic
981C22#1062304911yescharacteristic
982C22#1062305411yescharacteristic
983C22#1062306511yescharacteristic
984C22#1062312811yescharacteristic
985C22#1062312811yescharacteristic
986C22#1062313411yescharacteristic
987C22#1062313911yescharacteristic
988C22#1062314011yescharacteristic
989C22#1062314211yescharacteristic
990C22#1062315111yescharacteristic
991C22#1062315211yescharacteristic
992C22#1062315411yescharacteristic
993C22#1062315411yescharacteristic
994C22#1062315611yescharacteristic
995C22#1062315911yescharacteristic
996C22#1062316311yescharacteristic
997C22#1062316611yescharacteristic
998C22#1062317711yescharacteristic
999C22#1062317811yescharacteristic
1000C22C2×C4×C22⋊D1111yescharacteristic
1001C22D4×C22⋊D1111yescharacteristic
1002C22D4×C22⋊D1111yescharacteristic
1003C22#1062333711yescharacteristic
1004C22Q8×C22⋊D1111yescharacteristic
1005C22#1062335611yescharacteristic
1006C22#1062336411yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—224no—
1014C4—224no—
1015C4—442no—
1016C4—442no—
1017C4—442no—
1018C4—442no—
1019C4—881no—
1020C4—881no—
1021C2—44no—
1022C2#1307123311yescharacteristic
1023C2#1307129411yescharacteristic
1024C2#1307129811yescharacteristic
1025C2#1307151211yescharacteristic
1026C2C4⋊C4×C22⋊D1111yescharacteristic
1027C2#1307159511yescharacteristic
1028C2#1307176011yescharacteristic
1029C2#1307486111yescharacteristic
1030C2#1307486811yescharacteristic
1031C2#1307490611yescharacteristic
1032C2#1307492711yescharacteristic
1033C2#1307527011yescharacteristic
1034C2#1307527411yescharacteristic
1035C2#1307552111yescharacteristic
1036C2#1307574111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#14402
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#10622260C2semidirect
2. C2×#10622585C2semidirect
7. #13066880C2semidirect
8. #13066879C2semidirect
9. #13066870C2semidirect
10. #13066866C2semidirect
13. #13066850C2semidirect
14. #13066848C2semidirect
39. #10622823C4semidirect
279. C22⋊Dic11C4⋊C4semidirect
807. C11#14402semidirect

Maximal subgroups

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

subgroupindex
C2×#106222602
C2×#106225852
C2×#106225582
C2×#106225572
C2×#106228232
C2×#106228252
#130668802
#130668792
#130668702
#130668662
#130668592
#130668502
#130668482
C2×C11×#3802
#1440211