Finite Group Databasebeta

← #29609282

Subgroups — #29609282

Order 15616.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839663C211yesmaximal, characteristic
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839640C211yesmaximal, characteristic
4#21444078C211yesmaximal, characteristic, complemented
5#21444065C211yesmaximal, characteristic, complemented
6#21444065C211yesmaximal, characteristic, complemented
7#21444063C211yesmaximal, characteristic, complemented
8#21444063C211yesmaximal, characteristic, complemented
9#21444053C211yesmaximal, characteristic, complemented
10#21444050C211yesmaximal, characteristic, complemented
11#21444040C211yesmaximal, characteristic, complemented
12#21444040C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1442C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839663—24no—
33#16839640—24no—
34#16839640C418yescomplemented
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C22×C4⋊C4×C61C2211yescharacteristic
48C2×#95×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C24×D61C2311yescharacteristic
55C24×D61C2311yescharacteristic
56C22×D244—41no—
57C22×D244—41no—
58C22×D244—41no—
59C22×D244—41no—
60C22×D244C2×C414yes—
61C22×D244D414yes—
62C22×D244Q814yes—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61—41no—
73C22×C4×D61—41no—
74C22×C4×D61—41no—
75C22×C4×D61—41no—
76C22×C4×D61—41no—
77C22×C4×D61—41no—
78C22×C4×D61—41no—
79C22×C4×D61—41no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61C2×C414yescomplemented
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—41no—
85C2×C4⋊Dic61—41no—
86C2×#11758196—22no—
87C2×#11758196—41no—
88C2×#11758196—41no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—41no—
103C2×#11758198—41no—
104C2×#11758198—41no—
105C2×#11758198—41no—
106C2×#11758198—41no—
107C2×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198—41no—
116C2×#11758198C2×C414yes—
117C2×#11758198C2×C414yes—
118C2×#11758198C2×C414yescomplemented
119C2×C4×Dic61—22no—
120C2×C4×Dic61—41no—
121C2×C4×Dic61—41no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—41no—
126#14519684—41no—
127#14519684—41no—
128#14519684—41no—
129#14519684—41no—
130#14519684—41no—
131#14519684—41no—
132#14519684—41no—
133#14519684C2×C414yescomplemented
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61—41no—
143C2×C4⋊C4×C61—41no—
144#95×C61—22no—
145#95×C61—41no—
146#95×C61—41no—
147#95×C61—41no—
148#95×C61—41no—
149#95×C61C2×C414yescomplemented
150C24×C61C2411yescharacteristic
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—21no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—21no—
157C23×D61—21no—
158C23×D61—21no—
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61C22×C412yes—
176C23×D61C22×C412yes—
177C23×D61C2×D412yes—
178C23×D61C2×D412yes—
179C23×D61C2×Q812yes—
180C23×D61C2×Q812yes—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61C22×C412yes—
225C22×C4×C61C22×C412yes—
226C22×C4×C61C22×C412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×Q812yes—
229C22×C4×C61#4112yes—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61C22×C412yes—
268C22×Dic61C22×C412yes—
269C22×Dic61#4112yes—
270C22×Dic61#4112yes—
271C22×Dic61#4112yes—
272C2×D244—44no—
273C2×D244—44no—
274C2×D244—44no—
275C2×D244—44no—
276C2×D244—44no—
277C2×D244—44no—
278C2×D244C4⋊C4116yescomplemented
279C2×C4×D61—44no—
280C2×C4×D61—44no—
281C2×C4×D61—44no—
282C2×C4×D61—44no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61—44no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C2×C4×D61—44no—
289C2×C4×D61—44no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C4⋊C4×C61—44no—
294#11758198—44no—
295#11758198—44no—
296#11758198—44no—
297#11758198—44no—
298#11758198—44no—
299#11758198—44no—
300#11758198—44no—
301#11758198—44no—
302#11758198—44no—
303#11758198—44no—
304C4⋊Dic61—44no—
305#11758196—44no—
306C4×Dic61—44no—
307C23×C61C23×C411yescharacteristic
308C23×C61C22×D411yescharacteristic
309C23×C61C22×Q811yescharacteristic
310C23×C61C2×#4111yescharacteristic
311C23×C61C2×#4111yescharacteristic
312C23×C61C2×#4111yescharacteristic
313C23×C61C2×#4111yescharacteristic
314C23×C61H(5,𝔽2)11yescharacteristic
315C23×C61H(5,𝔽2)11yescharacteristic
316C23×C61H(5,𝔽2)11yescharacteristic
317C23×C61H(5,𝔽2)11yescharacteristic
318C23×C61H(5,𝔽2)11yescharacteristic
319C23×C61H(5,𝔽2)11yescharacteristic
320C23×C61H(5,𝔽2)11yescharacteristic
321C23×C61H(5,𝔽2)11yescharacteristic
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61C2×C4⋊C414yes—
391C22×D61C2×C4⋊C414yes—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—22no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61C2×C4⋊C414yes—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—22no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—41no—
457C2×Dic61—41no—
458C2×Dic61—41no—
459C2×Dic61—41no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—41no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—41no—
482C2×Dic61—41no—
483D244—416no—
484C4×D61—416no—
485C4×D61—416no—
486#14513—611nomaximal, Sylow
487C22×C61C22×C4⋊C411yescharacteristic
488C22×C61C4×#4111yescharacteristic
489C22×C61C4×#4111yescharacteristic
490C22×C61#51811yescharacteristic
491C22×C61#51811yescharacteristic
492C22×C61#51811yescharacteristic
493C22×C61#51811yescharacteristic
494C22×C61#53411yescharacteristic
495C22×C61#53411yescharacteristic
496C22×C61#53811yescharacteristic
497C22×C61#53811yescharacteristic
498C22×C61#53811yescharacteristic
499C22×C61#53811yescharacteristic
500C22×C61#54011yescharacteristic
501C22×C61#54011yescharacteristic
502C22×C61#54011yescharacteristic
503C22×C61#54011yescharacteristic
504C22×C61#54311yescharacteristic
505C22×C61#54311yescharacteristic
506C22×C61#54611yescharacteristic
507C22×C61#54611yescharacteristic
508C22×C61#54611yescharacteristic
509C22×C61#54611yescharacteristic
510C22×C61#55111yescharacteristic
511C22×C61#55311yescharacteristic
512C22×C61#55311yescharacteristic
513C22×C61#55411yescharacteristic
514C22×C61#55411yescharacteristic
515C22×C61#55411yescharacteristic
516C22×C61#55411yescharacteristic
517C22×C61#55911yescharacteristic
518C22×C61#56011yescharacteristic
519C22×C61#56011yescharacteristic
520C22×C61#56011yescharacteristic
521C22×C61H(3,𝔽4)11yescharacteristic
522C2×D61—24no—
523C2×D61—24no—
524C2×D61—24no—
525C2×D61—24no—
526C2×D61—24no—
527C2×D61—24no—
528C2×D61—42no—
529C2×D61—42no—
530C2×D61—42no—
531C2×D61—42no—
532C2×D61—42no—
533C2×D61—42no—
534C2×D61—42no—
535C2×D61—42no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—42no—
550C2×D61—42no—
551C2×D61—42no—
552C4×C61—24no—
553C4×C61—42no—
554C4×C61—42no—
555C4×C61—42no—
556C4×C61—81no—
557C4×C61—81no—
558C4×C61—81no—
559Dic61—42no—
560Dic61—42no—
561Dic61—42no—
562Dic61—42no—
563Dic61—42no—
564Dic61—81no—
565C2×#390—611no—
566C2×#386—611no—
567C2×#386—611no—
568#1442—611no—
569#1442D6111yescharacteristic, complemented
570#1439—611no—
571#1439—611no—
572#1439—611no—
573#1439—611no—
574#1436—611no—
575#1436—611no—
576C22⋊#95—611no—
577C22⋊#95—611no—
578C22⋊#95—611no—
579C22⋊#95—611no—
580C2×C61#231511yescharacteristic
581C2×C61#233311yescharacteristic
582C2×C61#233311yescharacteristic
583C2×C61#234911yescharacteristic
584C2×C61#234911yescharacteristic
585C2×C61#237411yescharacteristic
586C2×C61#237511yescharacteristic
587C2×C61#268411yescharacteristic
588C2×C61#268811yescharacteristic
589C2×C61#268811yescharacteristic
590C2×C61#270911yescharacteristic
591C2×C61#274811yescharacteristic
592C2×C61#278011yescharacteristic
593C2×C61#278011yescharacteristic
594C2×C61#280411yescharacteristic
595D61—44no—
596D61—44no—
597C23×D4—611no—
598C24×C4—611no—
599C24×C4—611no—
600C22×C4⋊C4—611no—
601C22×C4⋊C4—611no—
602C22×C4⋊C4C2×D6111yescharacteristic
603C22×C22⋊C4—611no—
604C22×C22⋊C4—611no—
605C22×C22⋊C4—611no—
606C22×C22⋊C4—611no—
607C22×C22⋊C4—611no—
608C22×C22⋊C4—611no—
609C22×C22⋊C4—611no—
610C22×C22⋊C4—611no—
611C22×C22⋊C4—611no—
612C22×C22⋊C4—611no—
613C22×C42—611no—
614#390—1224no—
615#386—618no—
616#386—1224no—
617C2×#95—611no—
618C2×#95—611no—
619C2×#95—611no—
620C2×#95—611no—
621C2×#95—611no—
622C2×#95—611no—
623C2×#95—611no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95—611no—
629C2×#95C2×D6111yescharacteristic
630C2×#95C2×D6111yescharacteristic
631C2×#95C2×D6111yescharacteristic
632C2×#95C2×D6111yescharacteristic
633C2×#95C2×D6111yescharacteristic
634C2×#95C2×D6111yescharacteristic
635C61#1451311yescharacteristic, complemented, Sylow
636C25—611no—
637C25—611no—
638C22×D4—614no—
639C22×D4—614no—
640C22×D4—614no—
641C22×D4—2441no—
642C22×D4—2441no—
643C22×D4—2441no—
644C22×D4—2441no—
645C23×C4—611no—
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—611no—
650C23×C4—614no—
651C23×C4—611no—
652C23×C4—1222no—
653C23×C4—1222no—
654C23×C4—1222no—
655C23×C4—2441no—
656C23×C4—2441no—
657C23×C4—2441no—
658C23×C4—2441no—
659C23×C4—2441no—
660C23×C4—2441no—
661C23×C4—2441no—
662C23×C4—2441no—
663C23×C4—2441no—
664C23×C4—2441no—
665C23×C4C22×D6111yescharacteristic
666C23×C4C22×D6111yescharacteristic
667C23×C4C22×D6111yescharacteristic
668C23×C4C22×D6111yescharacteristic
669C23×C4C22×D6111yescharacteristic
670C23×C4C22×D6111yescharacteristic
671C23×C4C22×D6111yescharacteristic
672C2×C4⋊C4—22no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—1222no—
676C2×C4⋊C4—1222no—
677C2×C4⋊C4—2441no—
678C2×C4⋊C4—2441no—
679C2×C4⋊C4—2441no—
680C2×C4⋊C4—2441no—
681C2×C22⋊C4—614no—
682C2×C22⋊C4—614no—
683C2×C22⋊C4—614no—
684C2×C22⋊C4—1222no—
685C2×C22⋊C4—1222no—
686C2×C22⋊C4—1222no—
687C2×C22⋊C4—1222no—
688C2×C22⋊C4—1222no—
689C2×C22⋊C4—1222no—
690C2×C22⋊C4—1222no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4—1222no—
695C2×C22⋊C4—1222no—
696C2×C22⋊C4—1222no—
697C2×C22⋊C4—2441no—
698C2×C22⋊C4—2441no—
699C2×C22⋊C4—2441no—
700C2×C22⋊C4—2441no—
701C2×C22⋊C4—2441no—
702C2×C22⋊C4—2441no—
703C2×C22⋊C4—2441no—
704C2×C22⋊C4—2441no—
705C2×C22⋊C4—2441no—
706C2×C22⋊C4—2441no—
707C2×C22⋊C4—2441no—
708C2×C22⋊C4—2441no—
709C2×C22⋊C4—2441no—
710C2×C22⋊C4—2441no—
711C2×C42—1222no—
712C2×C42—2441no—
713C2×C42—2441no—
714#95—22no—
715#95—41no—
716#95—41no—
717#95—41no—
718#95—41no—
719#95—614no—
720#95—1222no—
721#95—1222no—
722#95—1222no—
723#95—2441no—
724#95—2441no—
725#95—2441no—
726#95—2441no—
727#95—2441no—
728#95—2441no—
729#95—2441no—
730#95—2441no—
731#95C4×D6114yescomplemented
732C24—612no—
733C24—612no—
734C24—612no—
735C24—612no—
736C24—612no—
737C24—612no—
738C24—1221no—
739C24—1221no—
740C24—1221no—
741C24—1221no—
742C24—1221no—
743C24—1221no—
744C24—1221no—
745C24—1221no—
746C24—1221no—
747C24—1221no—
748C24—1221no—
749C24—1221no—
750C24—1221no—
751C24—1221no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24C23×D6111yescharacteristic
763C2×D4—6116no—
764C2×D4—2444no—
765C2×D4—2444no—
766C2×D4—2444no—
767C2×D4—2444no—
768C2×D4—2444no—
769C2×D4—2444no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—612no—
814C22×C4—612no—
815C22×C4—612no—
816C22×C4—612no—
817C22×C4—612no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—2444no—
856C22×C4—2444no—
857C22×C4—2444no—
858C22×C4—2444no—
859C22×C4—2444no—
860C22×C4—2444no—
861C22×C4—2444no—
862C22×C4—2444no—
863C22×C4—2444no—
864C22×C4—2444no—
865C22×C4—2444no—
866C22×C4—2444no—
867C22×C4—2444no—
868C22×C4—2444no—
869C22×C4C2×C4×D6112yes—
870C22×C4C2×C4×D6112yes—
871C22×C4C2×C4×D6112yes—
872C22×C4D4×D6112yes—
873C22×C4Q8×D6112yes—
874C22×C4#1175822612yes—
875C4⋊C4—44no—
876C4⋊C4—2444no—
877C4⋊C4—2444no—
878C22⋊C4—2444no—
879C22⋊C4—2444no—
880C22⋊C4—2444no—
881C22⋊C4—2444no—
882C22⋊C4—2444no—
883C22⋊C4—2444no—
884C22⋊C4—2444no—
885C22⋊C4—2444no—
886C22⋊C4—2444no—
887C22⋊C4—2444no—
888C42—2444no—
889C23—614no—
890C23—614no—
891C23—1222no—
892C23—1222no—
893C23—1222no—
894C23—1222no—
895C23—1222no—
896C23—1222no—
897C23—1222no—
898C23—1222no—
899C23—1222no—
900C23—1222no—
901C23—1222no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—1222no—
909C23—1222no—
910C23—1222no—
911C23—1222no—
912C23—1222no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1222no—
917C23—1222no—
918C23—1222no—
919C23—1222no—
920C23—1222no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—1222no—
927C23—2441no—
928C23—2441no—
929C23—2441no—
930C23—2441no—
931C23—2441no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23—2441no—
936C23—2441no—
937C23—2441no—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23—2441no—
947C23—2441no—
948C23—2441no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23C22×C4×D6111yescharacteristic
960C23C2×D4×D6111yescharacteristic
961C23C2×Q8×D6111yescharacteristic
962C23#41×D6111yescharacteristic
963C23#41×D6111yescharacteristic
964C23#41×D6111yescharacteristic
965C23C2×#1175822611yescharacteristic
966C23#1451982211yescharacteristic
967C23#1451982211yescharacteristic
968C23#1451982211yescharacteristic
969C23#1451982311yescharacteristic
970C23#1451982311yescharacteristic
971C23#1451982311yescharacteristic
972C23#1451982311yescharacteristic
973C23#1451982311yescharacteristic
974D4—24416no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—1222no—
1037C2×C4—1222no—
1038C2×C4—24416no—
1039C2×C4—24416no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4C4⋊C4×D6114yes—
1068C22—1224no—
1069C22—1224no—
1070C22—1224no—
1071C22—1224no—
1072C22—1224no—
1073C22—1224no—
1074C22—2442no—
1075C22—2442no—
1076C22—2442no—
1077C22—2442no—
1078C22—2442no—
1079C22—2442no—
1080C22—2442no—
1081C22—2442no—
1082C22—2442no—
1083C22—2442no—
1084C22—2442no—
1085C22—2442no—
1086C22—2442no—
1087C22—2442no—
1088C22—2442no—
1089C22—2442no—
1090C22—2442no—
1091C22—2442no—
1092C22—2442no—
1093C22—2442no—
1094C22—2442no—
1095C22—2442no—
1096C22—2442no—
1097C22—2442no—
1098C22C2×C4⋊C4×D6111yescharacteristic
1099C22#1684023011yescharacteristic
1100C22C4×#1175822611yescharacteristic
1101C22#1684023411yescharacteristic
1102C22#1684023411yescharacteristic
1103C22#1684023411yescharacteristic
1104C22#1684023611yescharacteristic
1105C22#1684032211yescharacteristic
1106C22#1684032311yescharacteristic
1107C22#1684034611yescharacteristic
1108C22#1684035111yescharacteristic
1109C22#1684035111yescharacteristic
1110C22#1684035211yescharacteristic
1111C22#1684036211yescharacteristic
1112C22#1684036411yescharacteristic
1113C22#1684036411yescharacteristic
1114C22#1684036811yescharacteristic
1115C22#1684038711yescharacteristic
1116C22#1684038711yescharacteristic
1117C22#1684040311yescharacteristic
1118C22#1684040511yescharacteristic
1119C22#1684040511yescharacteristic
1120C22#1684040911yescharacteristic
1121C22#1684043911yescharacteristic
1122C22#1684046311yescharacteristic
1123C22#1684046511yescharacteristic
1124C22#1684046811yescharacteristic
1125C22#1684046811yescharacteristic
1126C22#1684046811yescharacteristic
1127C22#1684047311yescharacteristic
1128C22#1684049611yescharacteristic
1129C22#1684050011yescharacteristic
1130C22#1684050211yescharacteristic
1131C22#1684050311yescharacteristic
1132C22#1684050411yescharacteristic
1133C4—24no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—4881no—
1141C4—2442no—
1142C4—2442no—
1143C4—2442no—
1144C4—2442no—
1145C4—2442no—
1146C2—2444no—
1147C2—2444no—
1148C2#2144843011yescharacteristic
1149C2#2144858211yescharacteristic
1150C2#2144858311yescharacteristic
1151C2#2144872711yescharacteristic
1152C2#2144872811yescharacteristic
1153C2#2144895111yescharacteristic
1154C2#2144895911yescharacteristic
1155C2#2145220211yescharacteristic
1156C2#2145226011yescharacteristic
1157C2#2145226211yescharacteristic
1158C2#2145255311yescharacteristic
1159C2#2145303111yescharacteristic
1160C2#2145346611yescharacteristic
1161C2#2145347311yescharacteristic
1162C2#2145376411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1442C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1442D61
hypocenterC61#14513
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
4. #21444078C2semidirect
5. #21444065C2semidirect
6. #21444065C2semidirect
7. #21444063C2semidirect
8. #21444063C2semidirect
9. #21444053C2semidirect
10. #21444050C2semidirect
11. #21444040C2semidirect
12. #21444040C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1442C2semidirect
34. #16839640C4semidirect
82. C22×C4×D61C2×C4semidirect
118. C2×#11758198C2×C4semidirect
133. #14519684C2×C4semidirect
149. #95×C61C2×C4semidirect
278. C2×D244C4⋊C4semidirect
569. #1442D61semidirect
635. C61#14513semidirect
731. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396632
C2×#168396402
#214440782
#214440652
#214440632
#214440532
#214440502
#214440402
C61×#14422
#1451361