Finite Group Databasebeta

← #14683895

Subgroups — #14683895

Order 2816.

1390 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622562C211yesmaximal, characteristic
2C2×#10622557C211yesmaximal, characteristic
3C2×#10622265C211yesmaximal, characteristic, complemented
4#13066874C211yesmaximal, characteristic, complemented
5#13066868C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic
7#13066859C211yesmaximal, characteristic
8#13066853C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066851C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14#13066842C211yesmaximal, characteristic, complemented
15C11×#1440C211yesmaximal, characteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
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#10622562C418yescomplemented
52#10622557—24no—
53#10622265—24no—
54C25×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×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—41no—
72C2×C11×C22⋊C4—41no—
73C2×C11×C22⋊C4—41no—
74C2×C11×C22⋊C4—41no—
75C2×C11×C22⋊C4—41no—
76C2×C11×C22⋊C4—41no—
77C2×C11×C22⋊C4C2×C414yes—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—41no—
85C2×C22⋊Dic11—41no—
86C2×C22⋊Dic11—41no—
87C2×C22⋊Dic11—41no—
88C2×C22⋊Dic11C2×C414yes—
89C2×C22⋊Dic11C2×C414yes—
90C2×C4⋊Dic11—41no—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11C2×C414yes—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—41no—
99C2×Dic11⋊C4—41no—
100C2×Dic11⋊C4—41no—
101C2×Dic11⋊C4—41no—
102C2×Dic11⋊C4—41no—
103C2×Dic11⋊C4C2×C414yes—
104C2×Dic11⋊C4C2×C414yes—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—41no—
110C2×C4×Dic11—41no—
111C2×C4×Dic11—41no—
112C2×C4×Dic11—41no—
113C2×C4×Dic11—41no—
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—41no—
117C11×#95—41no—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—41no—
127C11⋊#95—41no—
128C11⋊#95—41no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95C2×C414yes—
133C11⋊#95D414yes—
134#14578—111nomaximal, Sylow
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11C22×C412yes—
150C24×C11C2411yescharacteristic
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×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×C11C22×C412yes—
190C22×C4×C11C22×C412yes—
191C22×C4×C11C2×D412yes—
192C22×C4×C11#4112yes—
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×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×Dic11C22×C412yes—
240C22×Dic11C22×C412yes—
241C22×Dic11C22×C412yes—
242C22×Dic11C22×C412yes—
243C22×Dic11C2×D412yes—
244C22×Dic11C2×D412yes—
245C22×Dic11#4112yes—
246C22×Dic11#4112yes—
247C22×Dic11#4112yes—
248C22×Dic11#4112yes—
249C11×C22⋊C4—44no—
250C11×C22⋊C4—44no—
251C11×C22⋊C4—44no—
252C22⋊Dic11—28no—
253C22⋊Dic11—44no—
254C22⋊Dic11—44no—
255C22⋊Dic11—44no—
256C4⋊Dic11—44no—
257Dic11⋊C4—28no—
258Dic11⋊C4—44no—
259Dic11⋊C4—44no—
260Dic11⋊C4—44no—
261C4×Dic11—44no—
262C4×Dic11—44no—
263C4×Dic11—44no—
264C2×#399—111no—
265C2×#388—111no—
266C2×#387—111no—
267#1442—111no—
268#1441—111no—
269#1440—111no—
270#1440D1111yescharacteristic
271#1439—111no—
272#1437—111no—
273#1437—111no—
274#1436—111no—
275#1436—111no—
276#1436—111no—
277C4⋊#95—111no—
278#1434—111no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11C23×C411yescharacteristic
315C23×C11C22×D411yescharacteristic
316C23×C11C2×#4111yescharacteristic
317C23×C11C2×#4111yescharacteristic
318C23×C11C2×#4111yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11H(5,𝔽2)11yescharacteristic
322C23×C11H(5,𝔽2)11yescharacteristic
323C23×C11H(5,𝔽2)11yescharacteristic
324C23×C11H(5,𝔽2)11yescharacteristic
325C23×C11H(5,𝔽2)11yescharacteristic
326C23×C112−1+411yescharacteristic
327C23×C112−1+411yescharacteristic
328C23×C112−1+411yescharacteristic
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
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×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
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—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
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×Dic11C4×D414yes—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—111no—
430C22×C4⋊C4—111no—
431C22×C4⋊C4—111no—
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4C2×D1111yescharacteristic
437C22×C22⋊C4C2×D1111yescharacteristic
438C22×C22⋊C4C2×D1111yescharacteristic
439C22×C42—111no—
440C22×C42—111no—
441C22×C42—111no—
442#399—118no—
443#388—224no—
444#387—224no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95C2×D1111yescharacteristic
462C2×#95C2×D1111yescharacteristic
463C2×#95C2×D1111yescharacteristic
464C2×#95C2×D1111yescharacteristic
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—81no—
473C22×C11—81no—
474C22×C11—81no—
475C22×C11—81no—
476C22×C11—81no—
477C22×C11—81no—
478C22×C11—81no—
479C22×C11—81no—
480C22×C11C2×C4×D411yescharacteristic
481C22×C11C4×#4111yescharacteristic
482C22×C11C4×#4111yescharacteristic
483C22×C11#51811yescharacteristic
484C22×C11#51811yescharacteristic
485C22×C11#51911yescharacteristic
486C22×C11#52011yescharacteristic
487C22×C11#53511yescharacteristic
488C22×C11#53511yescharacteristic
489C22×C11#53811yescharacteristic
490C22×C11#53911yescharacteristic
491C22×C11#53911yescharacteristic
492C22×C11#53911yescharacteristic
493C22×C11#54011yescharacteristic
494C22×C11#54011yescharacteristic
495C22×C11#54011yescharacteristic
496C22×C11#54211yescharacteristic
497C22×C11#54211yescharacteristic
498C22×C11#54211yescharacteristic
499C22×C11#54611yescharacteristic
500C22×C11#54711yescharacteristic
501C22×C11#54711yescharacteristic
502C22×C11#54811yescharacteristic
503C22×C11#55111yescharacteristic
504C22×C11#55111yescharacteristic
505C22×C11#55211yescharacteristic
506C22×C11#55211yescharacteristic
507C22×C11#55311yescharacteristic
508C22×C11#55311yescharacteristic
509C22×C11#55611yescharacteristic
510C22×C11#55911yescharacteristic
511C22×C11#56211yescharacteristic
512C22×C11#56211yescharacteristic
513C22×C11#56311yescharacteristic
514C22×C11#56311yescharacteristic
515C4×C11—42no—
516C4×C11—42no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11—81no—
520C4×C11—81no—
521Dic11—24no—
522Dic11—42no—
523Dic11—42no—
524Dic11—42no—
525Dic11—42no—
526Dic11—42no—
527Dic11—42no—
528Dic11—42no—
529C25C22×D1111yescharacteristic
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C2×C4⋊C4—114no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—222no—
548C2×C4⋊C4—222no—
549C2×C4⋊C4—222no—
550C2×C4⋊C4—222no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—441no—
553C2×C4⋊C4—441no—
554C2×C4⋊C4—441no—
555C2×C4⋊C4—441no—
556C2×C4⋊C4—441no—
557C2×C4⋊C4—441no—
558C2×C4⋊C4—441no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—222no—
570C2×C22⋊C4—222no—
571C2×C22⋊C4—222no—
572C2×C22⋊C4—222no—
573C2×C22⋊C4—222no—
574C2×C22⋊C4—222no—
575C2×C22⋊C4—441no—
576C2×C22⋊C4—441no—
577C2×C22⋊C4—441no—
578C2×C22⋊C4—441no—
579C2×C22⋊C4C4×D1114yes—
580C2×C42—222no—
581C2×C42—222no—
582C2×C42—222no—
583C2×C42—222no—
584C2×C42—441no—
585C2×C42—441no—
586C2×C42—441no—
587C2×C42—441no—
588C2×C42—441no—
589#95—22no—
590#95—22no—
591#95—41no—
592#95—41no—
593#95—114no—
594#95—114no—
595#95—222no—
596#95—222no—
597#95—222no—
598#95—222no—
599#95—222no—
600#95—222no—
601#95—222no—
602#95—222no—
603#95—441no—
604#95—441no—
605#95—441no—
606#95—441no—
607#95—441no—
608#95—441no—
609C2×C11—82no—
610C2×C11#232811yescharacteristic
611C2×C11#233211yescharacteristic
612C2×C11#233511yescharacteristic
613C2×C11#235911yescharacteristic
614C2×C11#236211yescharacteristic
615C2×C11#237411yescharacteristic
616C2×C11#237811yescharacteristic
617C2×C11#271011yescharacteristic
618C2×C11#271111yescharacteristic
619C2×C11#271811yescharacteristic
620C2×C11#272311yescharacteristic
621C2×C11#274011yescharacteristic
622C2×C11#274111yescharacteristic
623C2×C11#277311yescharacteristic
624C2×C11#277711yescharacteristic
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C2×C4×D1112yes—
640C24C23×D1111yescharacteristic
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
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—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—112no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
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×C4C2×C4×D1112yes—
736C22×C4C2×C4×D1112yes—
737C22×C4D4×D1112yes—
738C22×C4#434112yes—
739C4⋊C4—228no—
740C4⋊C4—444no—
741C4⋊C4—444no—
742C4⋊C4—444no—
743C4⋊C4—444no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—228no—
748C22⋊C4—444no—
749C22⋊C4—444no—
750C22⋊C4—444no—
751C42—444no—
752C42—444no—
753C42—444no—
754C11#1457811yescharacteristic, complemented, Sylow
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23C22×C4×D1111yescharacteristic
791C23C2×D4×D1111yescharacteristic
792C23C2×#434111yescharacteristic
793C23#6703711yescharacteristic
794C23#6703711yescharacteristic
795C23#6703711yescharacteristic
796C23#6703711yescharacteristic
797C23#41×D1111yescharacteristic
798C23#41×D1111yescharacteristic
799C23#41×D1111yescharacteristic
800C23#41×D1111yescharacteristic
801C23#6704211yescharacteristic
802C23#6704311yescharacteristic
803C23#6704311yescharacteristic
804C23#6704311yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—114no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—441no—
880C2×C4—441no—
881C2×C4—441no—
882C2×C4—441no—
883C2×C4—441no—
884C2×C4—441no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22#1062301711yescharacteristic
919C22#1062304711yescharacteristic
920C22#1062305311yescharacteristic
921C22C4×#434111yescharacteristic
922C22C4×D4×D1111yescharacteristic
923C22#1062307611yescharacteristic
924C22#1062307711yescharacteristic
925C22#1062312311yescharacteristic
926C22#1062312411yescharacteristic
927C22#1062313211yescharacteristic
928C22#1062313411yescharacteristic
929C22#1062313811yescharacteristic
930C22#1062314211yescharacteristic
931C22#1062314311yescharacteristic
932C22#1062314611yescharacteristic
933C22#1062314611yescharacteristic
934C22#1062315211yescharacteristic
935C22#1062318111yescharacteristic
936C22#1062318611yescharacteristic
937C22#1062319111yescharacteristic
938C22#1062319111yescharacteristic
939C22#1062319111yescharacteristic
940C22#1062319211yescharacteristic
941C22#1062319311yescharacteristic
942C22#1062319311yescharacteristic
943C22#1062319411yescharacteristic
944C22#1062319811yescharacteristic
945C22#1062320311yescharacteristic
946C22#1062320811yescharacteristic
947C22#1062321011yescharacteristic
948C22#1062321211yescharacteristic
949C22#1062323311yescharacteristic
950C22#1062323611yescharacteristic
951C22#1062323911yescharacteristic
952C22#1062324311yescharacteristic
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—81no—
958C4—81no—
959C4—224no—
960C4—442no—
961C4—442no—
962C4—442no—
963C4—442no—
964C4—442no—
965C4—442no—
966C4—442no—
967C2—82no—
968C2#1307133711yescharacteristic
969C2#1307136911yescharacteristic
970C2#1307140711yescharacteristic
971C2#1307160511yescharacteristic
972C2#1307164011yescharacteristic
973C2#1307174411yescharacteristic
974C2#1307177611yescharacteristic
975C2#1307536511yescharacteristic
976C2#1307538011yescharacteristic
977C2#1307546811yescharacteristic
978C2#1307553711yescharacteristic
979C2#1307570911yescharacteristic
980C2#1307572411yescharacteristic
981C2#1307615211yescharacteristic
982C2#1307621211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1440D11
hypocenterC11#14578
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
3. C2×#10622265C2semidirect
4. #13066874C2semidirect
5. #13066868C2semidirect
10. #13066851C2semidirect
11. #13066850C2semidirect
12. #13066847C2semidirect
13. Dic11⋊#95C2semidirect
14. #13066842C2semidirect
51. #10622562C4semidirect
754. C11#14578semidirect

Maximal subgroups

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

subgroupindex
C2×#106225622
C2×#106225572
C2×#106222652
#130668742
#130668682
#130668632
#130668592
#130668532
#130668512
#130668502
#130668472
Dic11⋊#952
#130668422
C11×#14402
#1457811