Finite Group Databasebeta

← #14680356

Subgroups — #14680356

Order 2816.

1202 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622586C211yesmaximal, characteristic
2C2×#10622268C211yesmaximal, characteristic
3C2×#10622591C211yesmaximal, characteristic
4#13066885C211yesmaximal, characteristic
5#13066883C211yesmaximal, characteristic
6#13066877C211yesmaximal, characteristic
7#13066876C211yesmaximal, characteristic
8#13066875C211yesmaximal, characteristic
9#13066872C211yesmaximal, characteristic
10#13066869C211yesmaximal, characteristic
11#13066847C211yesmaximal, characteristic
12#13066847C211yesmaximal, characteristic
13#13066841C211yesmaximal, characteristic
14#95×Dic11C211yesmaximal, characteristic
15C11×#1441C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
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
51#10622591—24no—
52#10622586C418yescomplemented
53#10622268—24no—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—41no—
71C2×C11×C4⋊C4—41no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2×C414yes—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—41no—
79C2×C4⋊Dic11—41no—
80C2×C4⋊Dic11C2×C414yes—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4C2×C414yes—
86C2×Dic11⋊C4C2×C414yes—
87C2×C4×Dic11—22no—
88C2×C4×Dic11—41no—
89C2×C4×Dic11—41no—
90C2×C4×Dic11—41no—
91C2×C4×Dic11—41no—
92C2×C4×Dic11—41no—
93C2×C4×Dic11—41no—
94C2×C4×Dic11C2×C414yes—
95C2×C4×Dic11D414yes—
96C11×#95—22no—
97C11×#95—22no—
98C11×#95—22no—
99C11×#95—41no—
100C11×#95—41no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106C11⋊#95—22no—
107C11⋊#95—22no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—41no—
117C11⋊#95—41no—
118C11⋊#95—41no—
119C11⋊#95—41no—
120C11⋊#95C2×C414yes—
121C11⋊#95C2×C414yes—
122#14280—111nomaximal, Sylow
123C24×C11C2411yescharacteristic
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C22×C412yes—
167C22×C4×C11C22×C412yes—
168C22×C4×C11C22×C412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11#4112yes—
171C22×C4×C11#4112yes—
172C22×C4×C11#4112yes—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
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×Dic11C22×C412yes—
222C22×Dic11C22×C412yes—
223C22×Dic11C22×C412yes—
224C22×Dic11C22×C412yes—
225C22×Dic11C2×D412yes—
226C22×Dic11C2×D412yes—
227C22×Dic11#4112yes—
228C22×Dic11#4112yes—
229C11×C4⋊C4—44no—
230C11×C4⋊C4—44no—
231C4⋊Dic11—28no—
232C4⋊Dic11—44no—
233Dic11⋊C4—28no—
234Dic11⋊C4—28no—
235C4×Dic11—44no—
236C4×Dic11—44no—
237C4×Dic11—44no—
238C2×#389—111no—
239C2×#387—111no—
240C2×#387—111no—
241#1445—111no—
242#1445—111no—
243#1443—111no—
244#1443—111no—
245#1442—111no—
246#1442—111no—
247#1441—111no—
248#1441D1111yescharacteristic
249#1436—111no—
250#1436—111no—
251#1434—111no—
252C4×#95—111no—
253C23×C11C23×C411yescharacteristic
254C23×C11C22×D411yescharacteristic
255C23×C11C2×#4111yescharacteristic
256C23×C11C2×#4111yescharacteristic
257C23×C11C2×#4111yescharacteristic
258C23×C11C2×#4111yescharacteristic
259C23×C11C2×#4111yescharacteristic
260C23×C11H(5,𝔽2)11yescharacteristic
261C23×C11H(5,𝔽2)11yescharacteristic
262C23×C11H(5,𝔽2)11yescharacteristic
263C23×C112−1+411yescharacteristic
264C23×C112−1+411yescharacteristic
265C23×C112−1+411yescharacteristic
266C23×C112−1+411yescharacteristic
267C23×C112−1+411yescharacteristic
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11#11714yes—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11C4×D414yes—
373C22×C4⋊C4—111no—
374C22×C4⋊C4—111no—
375C22×C4⋊C4—111no—
376C22×C4⋊C4—111no—
377C22×C4⋊C4C2×D1111yescharacteristic
378C22×C4⋊C4C2×D1111yescharacteristic
379C22×C42—111no—
380C22×C42—111no—
381C22×C42—111no—
382#389—118no—
383#387—224no—
384#387—224no—
385C2×#95—111no—
386C2×#95—111no—
387C2×#95—111no—
388C2×#95—111no—
389C2×#95—111no—
390C2×#95—111no—
391C2×#95—111no—
392C2×#95—111no—
393C2×#95—111no—
394C2×#95—111no—
395C2×#95—111no—
396C2×#95—111no—
397C2×#95—111no—
398C2×#95—111no—
399C2×#95—111no—
400C2×#95—111no—
401C2×#95—111no—
402C2×#95—111no—
403C2×#95—111no—
404C2×#95—111no—
405C2×#95—111no—
406C2×#95C2×D1111yescharacteristic
407C2×#95C2×D1111yescharacteristic
408C2×#95C2×D1111yescharacteristic
409C2×#95C2×D1111yescharacteristic
410C2×#95C2×D1111yescharacteristic
411C22×C11C2×#11711yescharacteristic
412C22×C11C2×C4×D411yescharacteristic
413C22×C11C4×#4111yescharacteristic
414C22×C11#51811yescharacteristic
415C22×C11#51911yescharacteristic
416C22×C11#51911yescharacteristic
417C22×C11#52011yescharacteristic
418C22×C11#52911yescharacteristic
419C22×C11#52911yescharacteristic
420C22×C11#53211yescharacteristic
421C22×C11#53211yescharacteristic
422C22×C11#53411yescharacteristic
423C22×C11#53611yescharacteristic
424C22×C11#53611yescharacteristic
425C22×C11#53711yescharacteristic
426C22×C11#53811yescharacteristic
427C22×C11#53911yescharacteristic
428C22×C11#53911yescharacteristic
429C22×C11#53911yescharacteristic
430C22×C11#53911yescharacteristic
431C22×C11#53911yescharacteristic
432C22×C11#53911yescharacteristic
433C22×C11#53911yescharacteristic
434C22×C11#53911yescharacteristic
435C22×C11#53911yescharacteristic
436C22×C11#54111yescharacteristic
437C22×C11#54111yescharacteristic
438C22×C11#54111yescharacteristic
439C22×C11#54111yescharacteristic
440C22×C11#54111yescharacteristic
441C22×C11#54111yescharacteristic
442C22×C11#54211yescharacteristic
443C22×C11#54211yescharacteristic
444C22×C11#54211yescharacteristic
445C22×C11#54211yescharacteristic
446C4×C11—24no—
447C4×C11—42no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11—81no—
452C4×C11—81no—
453Dic11—24no—
454Dic11—42no—
455Dic11—42no—
456Dic11—42no—
457Dic11—42no—
458Dic11—42no—
459Dic11—81no—
460Dic11—81no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4C22×D1111yescharacteristic
470C23×C4C22×D1111yescharacteristic
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C2×C4⋊C4—22no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—222no—
485C2×C4⋊C4—222no—
486C2×C4⋊C4—222no—
487C2×C4⋊C4—222no—
488C2×C4⋊C4—222no—
489C2×C4⋊C4—222no—
490C2×C4⋊C4—222no—
491C2×C4⋊C4—441no—
492C2×C4⋊C4—441no—
493C2×C4⋊C4C4×D1114yes—
494C2×C42—114no—
495C2×C42—114no—
496C2×C42—222no—
497C2×C42—441no—
498C2×C42—441no—
499C2×C42—441no—
500C2×C42—441no—
501C2×C42—441no—
502C2×C42—441no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—41no—
507#95—41no—
508#95—114no—
509#95—114no—
510#95—222no—
511#95—222no—
512#95—222no—
513#95—222no—
514#95—222no—
515#95—222no—
516#95—222no—
517#95—222no—
518#95—222no—
519#95—222no—
520#95—222no—
521#95—222no—
522#95—222no—
523#95—222no—
524#95—222no—
525#95—441no—
526#95—441no—
527#95—441no—
528#95—441no—
529C2×C11#229311yescharacteristic
530C2×C11#231311yescharacteristic
531C2×C11#232011yescharacteristic
532C2×C11#232511yescharacteristic
533C2×C11#232711yescharacteristic
534C2×C11#233211yescharacteristic
535C2×C11#233611yescharacteristic
536C2×C11#265211yescharacteristic
537C2×C11#265211yescharacteristic
538C2×C11#265511yescharacteristic
539C2×C11#265511yescharacteristic
540C2×C11#266311yescharacteristic
541C2×C11#266311yescharacteristic
542C2×C11#266411yescharacteristic
543C2×C11#266411yescharacteristic
544C24C23×D1111yescharacteristic
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4C2×C4×D1112yes—
644C22×C4C2×C4×D1112yes—
645C22×C4C2×C4×D1112yes—
646C22×C4D4×D1112yes—
647C22×C4#434112yes—
648C22×C4#434312yes—
649C22×C4#434312yes—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—228no—
653C4⋊C4—228no—
654C4⋊C4—228no—
655C4⋊C4—444no—
656C42—444no—
657C42—444no—
658C42—444no—
659C11#1428011yescharacteristic, complemented, Sylow
660C23C22×C4×D1111yescharacteristic
661C23C2×D4×D1111yescharacteristic
662C23C2×#434111yescharacteristic
663C23#6703711yescharacteristic
664C23#6703711yescharacteristic
665C23#6703711yescharacteristic
666C23C2×#434311yescharacteristic
667C23C2×#434311yescharacteristic
668C23#6704011yescharacteristic
669C23#41×D1111yescharacteristic
670C23#41×D1111yescharacteristic
671C23#6704311yescharacteristic
672C23#6704311yescharacteristic
673C23#6704311yescharacteristic
674C23#6704311yescharacteristic
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—114no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—441no—
763C2×C4—441no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4#6694514yes—
780C22#1062301711yescharacteristic
781C22C2×#6694511yescharacteristic
782C22#1062304711yescharacteristic
783C22C4×D4×D1111yescharacteristic
784C22#1062307711yescharacteristic
785C22#1062310311yescharacteristic
786C22C4×#434311yescharacteristic
787C22#1062312011yescharacteristic
788C22#1062312711yescharacteristic
789C22#1062313311yescharacteristic
790C22#1062313311yescharacteristic
791C22#1062313411yescharacteristic
792C22#1062313911yescharacteristic
793C22#1062314411yescharacteristic
794C22#1062315511yescharacteristic
795C22#1062315611yescharacteristic
796C22#1062315911yescharacteristic
797C22#1062316911yescharacteristic
798C22#1062317611yescharacteristic
799C22#1062317611yescharacteristic
800C22#1062317611yescharacteristic
801C22#1062317611yescharacteristic
802C22#1062317911yescharacteristic
803C22#1062319111yescharacteristic
804C22#1062319111yescharacteristic
805C22#1062320011yescharacteristic
806C22#1062322211yescharacteristic
807C22#1062322711yescharacteristic
808C22#1062322811yescharacteristic
809C22#1062322811yescharacteristic
810C22#1062323211yescharacteristic
811C22#1062323211yescharacteristic
812C22#1062325611yescharacteristic
813C22#1062326411yescharacteristic
814C22#1062326411yescharacteristic
815C4—24no—
816C4—42no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—81no—
821C4—81no—
822C4—224no—
823C4—442no—
824C4—442no—
825C4—442no—
826C4—442no—
827C4—442no—
828C4—881no—
829C4—881no—
830C2#1307107411yescharacteristic
831C2#1307121811yescharacteristic
832C2#1307126311yescharacteristic
833C2#1307131811yescharacteristic
834C2#1307133111yescharacteristic
835C2#1307137111yescharacteristic
836C2#1307141911yescharacteristic
837C2#1307466311yescharacteristic
838C2#1307466711yescharacteristic
839C2#1307470811yescharacteristic
840C2#1307471211yescharacteristic
841C2#1307476311yescharacteristic
842C2#1307477111yescharacteristic
843C2#1307477611yescharacteristic
844C2#1307478211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1441D11
hypocenterC11#14280
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
52. #10622586C4semidirect
659. C11#14280semidirect

Maximal subgroups

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

subgroupindex
C2×#106225862
C2×#106222682
C2×#106225912
#130668852
#130668832
#130668772
#130668762
#130668752
#130668722
#130668692
#130668472
#130668412
#95×Dic112
C11×#14412
#1428011