Finite Group Databasebeta

← #14677860

Subgroups — #14677860

Order 2816.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C211yesmaximal, characteristic
2C2×#10622260C211yesmaximal, characteristic, complemented
3C2×#10622557C211yesmaximal, characteristic
4C2×#10622265C211yesmaximal, characteristic, complemented
5C2×#10622823C211yesmaximal, characteristic
6#13066872C211yesmaximal, characteristic, complemented
7#13066870C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic
9#13066859C211yesmaximal, characteristic
10#13066853C211yesmaximal, characteristic
11#13066851C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C2×#66979—24no—
24C2×#66979—24no—
25C2×#66979—24no—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40#10622823C418yescomplemented
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#10622557—24no—
56#10622265—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—22no—
64C23×C4×C11—22no—
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×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—41no—
85C2×C11×C22⋊C4—41no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11C2×C414yes—
96C2×C22⋊Dic11C2×C414yes—
97C2×C22⋊Dic11D414yes—
98#66979—232no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11D414yes—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—41no—
115C2×Dic11⋊C4C2×C414yes—
116C2×Dic11⋊C4C2×C414yes—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—41no—
127C2×C4×Dic11—41no—
128C2×C4×Dic11D414yes—
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—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—41no—
145C11⋊#95C2×C414yes—
146C11⋊#95C2×C414yes—
147#14072—111nomaximal, Sylow
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
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×C11C22×C412yes—
161C24×C11C2×D412yes—
162C24×C11#4112yes—
163C24×C11C2411yescharacteristic
164C22×C4×C11—28no—
165C22×C4×C11—28no—
166C22×C4×C11—28no—
167C22×C4×C11—28no—
168C22×C4×C11—28no—
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—28no—
178C22×C4×C11—28no—
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×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—21no—
204C22×C4×C11—21no—
205C22×C4×C11C22×C412yes—
206C22×C4×C11C22×C412yes—
207C22×C4×C11C2×D412yes—
208C22×C4×C11C2×D412yes—
209C22×C4×C11#4112yes—
210C22×C4×C11#4112yes—
211C22×C4×C11#4112yes—
212C22×C4×C11#4112yes—
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×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11C2×D412yes—
265C22×Dic11C2×D412yes—
266C22×Dic11C2×D412yes—
267C22×Dic11#4112yes—
268C22×Dic11#4112yes—
269C11×C22⋊C4—44no—
270C11×C22⋊C4—44no—
271C22⋊Dic11—28no—
272C22⋊Dic11—28no—
273C22⋊Dic11—28no—
274C22⋊Dic11—28no—
275C4⋊Dic11—28no—
276C4⋊Dic11—28no—
277Dic11⋊C4—28no—
278Dic11⋊C4—28no—
279Dic11⋊C4—44no—
280Dic11⋊C4—44no—
281C4×Dic11—28no—
282C4×Dic11—28no—
283C4×Dic11—44no—
284C4×Dic11—44no—
285C22×#117—111no—
286C2×#389—111no—
287C2×#388—111no—
288C2×#387—111no—
289C2×#385—111no—
290#1442—111no—
291#1441—111no—
292#1440—111no—
293#1439—111no—
294#1437—111no—
295#1436—111no—
296#1436—111no—
297#1436—111no—
298C22⋊#95D1111yescharacteristic
299C4×#95—111no—
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—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
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×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11C4×D414yes—
335C23×C11C23×C411yescharacteristic
336C23×C11C22×D411yescharacteristic
337C23×C11C22×D411yescharacteristic
338C23×C11C22×D411yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11C2×#4111yescharacteristic
344C23×C11C2×#4111yescharacteristic
345C23×C11C2×#4111yescharacteristic
346C23×C11H(5,𝔽2)11yescharacteristic
347C23×C112−1+411yescharacteristic
348C23×C112−1+411yescharacteristic
349C23×C112−1+411yescharacteristic
350C2×C4×C11—232no—
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—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
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×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11C4×D414yes—
392C2×C4×C11C4×D414yes—
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—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—22no—
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#11714yescomplemented
448C2×Dic11#12014yes—
449C24×C4C2×D1111yescharacteristic
450C2×#117—224no—
451C2×#117—224no—
452C2×#117—224no—
453C22×C4⋊C4—111no—
454C22×C4⋊C4—111no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4C2×D1111yescharacteristic
464C22×C22⋊C4C2×D1111yescharacteristic
465C22×C42—111no—
466C22×C42—111no—
467C22×C42—111no—
468C22×C42—111no—
469#389—224no—
470#388—224no—
471#387—224no—
472#385—118no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95C2×D1111yescharacteristic
488C2×#95C2×D1111yescharacteristic
489C2×#95C2×D1111yescharacteristic
490C2×#95C2×D1111yescharacteristic
491C22×C11—24no—
492C22×C11—24no—
493C22×C11—24no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11C2×#11711yescharacteristic
507C22×C11C2×C4×D411yescharacteristic
508C22×C11C2×C4×D411yescharacteristic
509C22×C11C2×C4×D411yescharacteristic
510C22×C11C4×#4111yescharacteristic
511C22×C11#51911yescharacteristic
512C22×C11#52011yescharacteristic
513C22×C11C2×#12011yescharacteristic
514C22×C11#52511yescharacteristic
515C22×C11#52511yescharacteristic
516C22×C11#52511yescharacteristic
517C22×C11#52911yescharacteristic
518C22×C11#52911yescharacteristic
519C22×C11#53211yescharacteristic
520C22×C11#53211yescharacteristic
521C22×C11#53611yescharacteristic
522C22×C11#53711yescharacteristic
523C22×C11#54111yescharacteristic
524C22×C11#54211yescharacteristic
525C22×C11#54611yescharacteristic
526C22×C11#54611yescharacteristic
527C22×C11#54711yescharacteristic
528C22×C11#54711yescharacteristic
529C22×C11#54711yescharacteristic
530C22×C11#54711yescharacteristic
531C22×C11#54811yescharacteristic
532C22×C11#54811yescharacteristic
533C22×C11#55111yescharacteristic
534C22×C11#55211yescharacteristic
535C22×C11#55211yescharacteristic
536C22×C11#55211yescharacteristic
537C22×C11#55211yescharacteristic
538C22×C11#55211yescharacteristic
539C22×C11#55311yescharacteristic
540C22×C11#55611yescharacteristic
541C4×C11—24no—
542C4×C11—24no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—81no—
546C4×C11—81no—
547Dic11—24no—
548Dic11—24no—
549Dic11—42no—
550Dic11—42no—
551Dic11—42no—
552Dic11—42no—
553Dic11—42no—
554Dic11—42no—
555C25C22×D1111yescharacteristic
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4C4×D1114yes—
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577#117—2232no—
578C2×C4⋊C4—114no—
579C2×C4⋊C4—114no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4—222no—
583C2×C4⋊C4—222no—
584C2×C4⋊C4—222no—
585C2×C4⋊C4—222no—
586C2×C4⋊C4—222no—
587C2×C4⋊C4—222no—
588C2×C4⋊C4—222no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—441no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—222no—
606C2×C22⋊C4—222no—
607C2×C22⋊C4—222no—
608C2×C22⋊C4—222no—
609C2×C22⋊C4—222no—
610C2×C22⋊C4—222no—
611C2×C22⋊C4—222no—
612C2×C22⋊C4—222no—
613C2×C22⋊C4—222no—
614C2×C42—114no—
615C2×C42—222no—
616C2×C42—222no—
617C2×C42—222no—
618C2×C42—222no—
619C2×C42—222no—
620C2×C42—222no—
621C2×C42—222no—
622C2×C42—222no—
623C2×C42—222no—
624C2×C42—441no—
625C2×C42—441no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—114no—
631#95—114no—
632#95—222no—
633#95—222no—
634#95—222no—
635#95—222no—
636#95—222no—
637#95—222no—
638#95—222no—
639#95—222no—
640#95—222no—
641#95—222no—
642#95—222no—
643#95—441no—
644C2×C11—44no—
645C2×C11#229311yescharacteristic
646C2×C11C4×#12011yescharacteristic
647C2×C11#232311yescharacteristic
648C2×C11#234411yescharacteristic
649C2×C11#235211yescharacteristic
650C2×C11#235911yescharacteristic
651C2×C11#236211yescharacteristic
652C2×C11#243011yescharacteristic
653C2×C11#243211yescharacteristic
654C2×C11#247011yescharacteristic
655C2×C11#247511yescharacteristic
656C2×C11#247711yescharacteristic
657C2×C11#247811yescharacteristic
658C2×C11#260111yescharacteristic
659C2×C11#261111yescharacteristic
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24C2×C4×D1112yes—
673C24D4×D1112yes—
674C24#434112yes—
675C24C23×D1111yescharacteristic
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
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—28no—
690C22×C4—28no—
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—21no—
705C22×C4—21no—
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—112no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
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×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×C4C2×C4×D1112yes—
774C22×C4C2×C4×D1112yes—
775C22×C4#433912yes—
776C22×C4#433912yes—
777C22×C4D4×D1112yes—
778C22×C4D4×D1112yes—
779C22×C4#434112yes—
780C22×C4#434112yes—
781C4⋊C4—228no—
782C4⋊C4—228no—
783C4⋊C4—228no—
784C4⋊C4—228no—
785C4⋊C4—444no—
786C4⋊C4—444no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—228no—
792C22⋊C4—228no—
793C42—228no—
794C42—228no—
795C42—444no—
796C42—444no—
797C11#1407211yescharacteristic, complemented, Sylow
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23(C22⋊D11)⋊C414yes—
833C23C22×C4×D1111yescharacteristic
834C23C2×#433911yescharacteristic
835C23C2×#433911yescharacteristic
836C23C2×D4×D1111yescharacteristic
837C23C2×D4×D1111yescharacteristic
838C23C2×D4×D1111yescharacteristic
839C23C2×#434111yescharacteristic
840C23C2×#434111yescharacteristic
841C23C2×#434111yescharacteristic
842C23#6703711yescharacteristic
843C23#6704011yescharacteristic
844C23#41×D1111yescharacteristic
845C23#41×D1111yescharacteristic
846C23#6704311yescharacteristic
847C23#6704311yescharacteristic
848C2×C4—232no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
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—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—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—114no—
890C2×C4—114no—
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—222no—
900C2×C4—222no—
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—441no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
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(C22⋊D11)⋊C414yes—
946C2×C4(C22⋊D11)⋊C414yes—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22C4×#433911yescharacteristic
963C22C2×(C22⋊D11)⋊C411yescharacteristic
964C22C2×(C22⋊D11)⋊C411yescharacteristic
965C22C2×(C22⋊D11)⋊C411yescharacteristic
966C22#1062302111yescharacteristic
967C22#1062302611yescharacteristic
968C22#1062303511yescharacteristic
969C22#1062303811yescharacteristic
970C22#1062304411yescharacteristic
971C22#1062304711yescharacteristic
972C22D11×#11711yescharacteristic
973C22#1062306911yescharacteristic
974C22#1062306911yescharacteristic
975C22#1062307211yescharacteristic
976C22#1062307311yescharacteristic
977C22#1062307911yescharacteristic
978C22#1062307911yescharacteristic
979C22#1062308211yescharacteristic
980C22#1062308311yescharacteristic
981C22#1062311711yescharacteristic
982C22#1062311711yescharacteristic
983C22#1062311711yescharacteristic
984C22D11×#12011yescharacteristic
985C22#1062313411yescharacteristic
986C22#1062313911yescharacteristic
987C22#1062314311yescharacteristic
988C22#1062314511yescharacteristic
989C22#1062315611yescharacteristic
990C22#1062315911yescharacteristic
991C22#1062316411yescharacteristic
992C22#1062317011yescharacteristic
993C22#1062318111yescharacteristic
994C22#1062318111yescharacteristic
995C22#1062318611yescharacteristic
996C22#1062318611yescharacteristic
997C4—24no—
998C4—24no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4—224no—
1004C4—224no—
1005C4—442no—
1006C4—442no—
1007C4—442no—
1008C4—442no—
1009C4—442no—
1010C4—442no—
1011C2—44no—
1012C2#1307107911yescharacteristic
1013C2#1307111511yescharacteristic
1014C2#1307129411yescharacteristic
1015C2#1307148011yescharacteristic
1016C2#1307153811yescharacteristic
1017C2#1307160411yescharacteristic
1018C2#1307164111yescharacteristic
1019C2#1307222311yescharacteristic
1020C2#1307224211yescharacteristic
1021C2#1307270911yescharacteristic
1022C2#1307278411yescharacteristic
1023C2#1307281411yescharacteristic
1024C2#1307282911yescharacteristic
1025C2#1307420911yescharacteristic
1026C2#1307431011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#14072
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622260C2semidirect
4. C2×#10622265C2semidirect
6. #13066872C2semidirect
7. #13066870C2semidirect
11. #13066851C2semidirect
12. #13066850C2semidirect
13. #13066847C2semidirect
14. #95×Dic11C2semidirect
40. #10622823C4semidirect
447. C2×Dic11#117semidirect
797. C11#14072semidirect

Maximal subgroups

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

subgroupindex
C22×#669792
C2×#106222602
C2×#106225572
C2×#106222652
C2×#106228232
#130668722
#130668702
#130668632
#130668592
#130668532
#130668512
#130668502
#130668472
#95×Dic112
C11×C22⋊#952
#1407211