Finite Group Databasebeta

← #29601518

Subgroups — #29601518

Order 15616.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839636C211yesmaximal, characteristic
2C2×#16839633C211yesmaximal, characteristic
3C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
4C2×C4×#11758198C211yesmaximal, characteristic
5C2×#16839609C211yesmaximal, characteristic
6C2×#16839609C211yesmaximal, characteristic
7C2×#95×D61C211yesmaximal, characteristic
8#21444054C211yesmaximal, characteristic, complemented
9#21444053C211yesmaximal, characteristic, complemented
10#21444050C211yesmaximal, characteristic, complemented
11#21444047C211yesmaximal, characteristic, complemented
12#21444044C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic
14C4×#14519684C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31#16839636C418yescomplemented
32#16839633C418yescomplemented
33C4⋊C4×Dic61—24no—
34C4×#11758198—24no—
35#16839609—24no—
36#16839609C418yescomplemented
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50#95×D61—24no—
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—41no—
79C22×C4×D61—41no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C22×C4×D61—41no—
84C22×C4×D61C2×C414yes—
85C22×C4×D61C2×C414yes—
86C22×C4×D61C2×C414yes—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61C2×C414yescomplemented
90C2×#11758196—41no—
91C2×#11758196—41no—
92C2×#11758196—41no—
93C2×#11758196—41no—
94C2×#11758196C2×C414yescomplemented
95C2×#11758196C2×C414yescomplemented
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198C2×C414yes—
101C2×#11758198C2×C414yes—
102C2×#11758198C2×C414yes—
103C2×#11758198C2×C414yes—
104C2×#11758198C2×C414yes—
105C2×#11758198C2×C414yes—
106C2×#11758198D414yes—
107C2×#11758198Q814yes—
108C2×C4×Dic61—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—22no—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—22no—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—41no—
117C2×C4×Dic61—41no—
118C2×C4×Dic61—41no—
119C2×C4×Dic61—41no—
120C2×C4×Dic61—41no—
121C2×C4×Dic61C2×C414yescomplemented
122C2×C4×Dic61C2×C414yescomplemented
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—41no—
131#14519684C2×C414yescomplemented
132#14519684C2×C414yescomplemented
133#14519684C2×C414yescomplemented
134#14519684C2×C414yescomplemented
135#14519684D414yes—
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61—22no—
144C2×C4⋊C4×C61—22no—
145C2×C4⋊C4×C61C2×C414yescomplemented
146C2×C42×C61—22no—
147C2×C42×C61—22no—
148C2×C42×C61—41no—
149#95×C61—22no—
150#95×C61—22no—
151#95×C61—41no—
152#95×C61C2×C414yescomplemented
153#95×C61C2×C414yescomplemented
154C24×C61C2411yescharacteristic
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×D61C22×C412yes—
164C23×D61C22×C412yes—
165C23×D61C22×C412yes—
166C23×D61C2×D412yes—
167C23×D61C2×Q812yes—
168C23×D61#4112yes—
169C23×D61#4112yes—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
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×C61C22×C412yes—
207C22×C4×C61C22×C412yes—
208C22×C4×C61C22×C412yes—
209C22×C4×C61C22×C412yes—
210C22×C4×C61C22×C412yes—
211C22×C4×C61C22×C412yes—
212C22×C4×C61C22×C412yes—
213C22×C4×C61C22×C412yes—
214C22×C4×C61C22×C412yes—
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2×Q812yes—
218C22×C4×C61#4112yes—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
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×Dic61C22×C412yes—
254C22×Dic61C22×C412yes—
255C22×Dic61C22×C412yes—
256C22×Dic61C22×C412yes—
257C22×Dic61C22×C412yes—
258C22×Dic61C22×C412yes—
259C22×Dic61C22×C412yes—
260C22×Dic61C22×C412yes—
261C22×Dic61C22×C412yes—
262C22×Dic61C2×D412yes—
263C22×Dic61C2×D412yes—
264C22×Dic61C2×D412yes—
265C22×Dic61C2×Q812yes—
266C22×Dic61#4112yes—
267C22×Dic61#4112yes—
268C2×C4×D61—28no—
269C2×C4×D61—28no—
270C2×C4×D61—28no—
271C2×C4×D61—28no—
272C2×C4×D61—28no—
273C2×C4×D61—28no—
274C2×C4×D61—44no—
275C2×C4×D61—44no—
276C2×C4×D61—44no—
277C2×C4×D61—44no—
278C2×C4×D61—44no—
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—
289C4⋊C4×C61—28no—
290C42×C61—44no—
291#11758198—28no—
292#11758198—28no—
293#11758198C42116yescomplemented
294#11758198C4⋊C4116yescomplemented
295C4⋊Dic61—28no—
296#11758196—44no—
297#11758196—44no—
298C4×Dic61—28no—
299C4×Dic61—44no—
300C4×Dic61—44no—
301C4×Dic61—44no—
302C4×Dic61—44no—
303C23×C61C23×C411yescharacteristic
304C23×C61C23×C411yescharacteristic
305C23×C61C23×C411yescharacteristic
306C23×C61C22×D411yescharacteristic
307C23×C61C22×D411yescharacteristic
308C23×C61C22×Q811yescharacteristic
309C23×C61C2×#4111yescharacteristic
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×C612−1+411yescharacteristic
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
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×D61C2×C4214yes—
347C22×D61C2×C4⋊C414yes—
348C22×D61#11714yes—
349C22×D61C4×D414yes—
350C22×D61C4×D414yes—
351C22×D61C4×Q814yes—
352C22×D61C4×Q814yes—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—22no—
381C2×C4×C61—22no—
382C2×C4×C61—22no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61C2×C4214yes—
400C2×C4×C61C2×C4⋊C414yes—
401C2×C4×C61C4×D414yes—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—22no—
408C2×Dic61—22no—
409C2×Dic61—22no—
410C2×Dic61—22no—
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—22no—
416C2×Dic61—22no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—22no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—22no—
423C2×Dic61—22no—
424C2×Dic61—22no—
425C2×Dic61—22no—
426C2×Dic61—22no—
427C2×Dic61—22no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438C2×Dic61—41no—
439C2×Dic61—41no—
440C2×Dic61—41no—
441C2×Dic61—41no—
442C2×Dic61—41no—
443C2×Dic61—41no—
444C2×Dic61—41no—
445C2×Dic61—41no—
446C2×Dic61—41no—
447C2×Dic61C2×C4214yes—
448C2×Dic61C2×C4⋊C414yes—
449C2×Dic61C4×D414yes—
450C2×Dic61C4×D414yes—
451C4×D61—416no—
452C4×D61—416no—
453C4×D61—416no—
454#13814—611nomaximal, Sylow
455C22×C61C22×C4211yescharacteristic
456C22×C61C22×C4⋊C411yescharacteristic
457C22×C61C2×#11711yescharacteristic
458C22×C61C2×C4×D411yescharacteristic
459C22×C61C2×C4×D411yescharacteristic
460C22×C61C2×C4×D411yescharacteristic
461C22×C61C2×C4×D411yescharacteristic
462C22×C61C2×C4×D411yescharacteristic
463C22×C61C2×C4×Q811yescharacteristic
464C22×C61C2×C4×Q811yescharacteristic
465C22×C61C4×#4111yescharacteristic
466C22×C61C4×#4111yescharacteristic
467C22×C61C4×#4111yescharacteristic
468C22×C61#51811yescharacteristic
469C22×C61#51811yescharacteristic
470C22×C61#51811yescharacteristic
471C22×C61#52011yescharacteristic
472C22×C61#52011yescharacteristic
473C22×C61#52011yescharacteristic
474C22×C61D4211yescharacteristic
475C22×C61#54611yescharacteristic
476C22×C61#54611yescharacteristic
477C22×C61#54611yescharacteristic
478C22×C61#54611yescharacteristic
479C22×C61#54711yescharacteristic
480C22×C61D4×Q811yescharacteristic
481C22×C61#55111yescharacteristic
482C22×C61#55111yescharacteristic
483C22×C61#55111yescharacteristic
484C22×C61#55111yescharacteristic
485C22×C61#55211yescharacteristic
486C22×C61#55211yescharacteristic
487C22×C61#55411yescharacteristic
488C22×C61#55411yescharacteristic
489C22×C61#55411yescharacteristic
490C2×D61—24no—
491C2×D61—24no—
492C2×D61—24no—
493C2×D61—24no—
494C2×D61—24no—
495C2×D61—24no—
496C2×D61—24no—
497C2×D61—24no—
498C2×D61—24no—
499C2×D61—24no—
500C2×D61—24no—
501C2×D61—24no—
502C2×D61—24no—
503C2×D61—24no—
504C2×D61C4×C4⋊C418yescomplemented
505C4×C61—24no—
506C4×C61—24no—
507C4×C61—24no—
508C4×C61—42no—
509C4×C61—42no—
510C4×C61—42no—
511C4×C61—42no—
512Dic61—24no—
513Dic61—24no—
514Dic61—24no—
515Dic61—24no—
516Dic61—42no—
517Dic61—42no—
518Dic61—42no—
519C2×#385—611no—
520C2×#385—611no—
521C2×C4×C4⋊C4—611no—
522C2×C4×C22⋊C4—611no—
523C2×C4×C22⋊C4—611no—
524C2×C4×C22⋊C4—611no—
525C22×#95—611no—
526#1436—611no—
527#1436—611no—
528#1436—611no—
529#1436D6111yescharacteristic, complemented
530C4⋊#95—611no—
531#1434—611no—
532C22⋊#95—611no—
533C4×#95—611no—
534C2×C61C2×C4×C4⋊C411yescharacteristic
535C2×C61C42×D411yescharacteristic
536C2×C61#227511yescharacteristic
537C2×C61#234211yescharacteristic
538C2×C61#234311yescharacteristic
539C2×C61D4×C4⋊C411yescharacteristic
540C2×C61#234911yescharacteristic
541C2×C61#235811yescharacteristic
542C2×C61#235811yescharacteristic
543C2×C61#235911yescharacteristic
544C2×C61#235911yescharacteristic
545C2×C61#236011yescharacteristic
546C2×C61#236011yescharacteristic
547C2×C61#236811yescharacteristic
548C2×C61#236811yescharacteristic
549D61—28no—
550C24×C4—611no—
551C24×C4—611no—
552C24×C4—611no—
553C22×C4⋊C4—611no—
554C22×C4⋊C4—611no—
555C22×C4⋊C4—611no—
556C22×C4⋊C4C2×D6111yescharacteristic
557C22×C22⋊C4—611no—
558C22×C22⋊C4—611no—
559C22×C22⋊C4—611no—
560C22×C22⋊C4—611no—
561C22×C42—611no—
562C22×C42—611no—
563C22×C42—611no—
564C22×C42—611no—
565C22×C42—611no—
566C22×C42C2×D6111yescharacteristic
567#385—618no—
568#385—618no—
569C4×C4⋊C4—1224no—
570C4×C22⋊C4—618no—
571C4×C22⋊C4—1224no—
572C4×C22⋊C4—1224no—
573C2×#95—611no—
574C2×#95—611no—
575C2×#95—611no—
576C2×#95—611no—
577C2×#95—611no—
578C2×#95—611no—
579C2×#95—611no—
580C2×#95—611no—
581C2×#95—611no—
582C2×#95—611no—
583C2×#95—611no—
584C2×#95—611no—
585C2×#95—611no—
586C2×#95—1224no—
587C2×#95C2×D6111yescharacteristic
588C2×#95C2×D6111yescharacteristic
589C2×#95C2×D6111yescharacteristic
590C2×#95C2×D6111yescharacteristic
591C2×#95C2×D6111yescharacteristic
592C61#1381411yescharacteristic, complemented, Sylow
593C25—611no—
594C23×C4—611no—
595C23×C4—611no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—611no—
600C23×C4—611no—
601C23×C4—614no—
602C23×C4—614no—
603C23×C4—614no—
604C23×C4—1222no—
605C23×C4—1222no—
606C23×C4—1222no—
607C23×C4—1222no—
608C23×C4—1222no—
609C23×C4—1222no—
610C23×C4—1222no—
611C23×C4—1222no—
612C23×C4—1222no—
613C23×C4—1222no—
614C23×C4—1222no—
615C23×C4—1222no—
616C23×C4—2441no—
617C23×C4—2441no—
618C23×C4—2441no—
619C23×C4—2441no—
620C23×C4—2441no—
621C23×C4—2441no—
622C23×C4C22×D6111yescharacteristic
623C23×C4C22×D6111yescharacteristic
624C23×C4C22×D6111yescharacteristic
625C23×C4C22×D6111yescharacteristic
626C23×C4C22×D6111yescharacteristic
627C23×C4C22×D6111yescharacteristic
628C23×C4C22×D6111yescharacteristic
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—614no—
632C2×C4⋊C4—614no—
633C2×C4⋊C4—614no—
634C2×C4⋊C4—1222no—
635C2×C4⋊C4—1222no—
636C2×C4⋊C4—2441no—
637C2×C4⋊C4—2441no—
638C2×C4⋊C4—2441no—
639C2×C4⋊C4—2441no—
640C2×C4⋊C4C4×D6114yescomplemented
641C2×C22⋊C4—614no—
642C2×C22⋊C4—614no—
643C2×C22⋊C4—614no—
644C2×C22⋊C4—614no—
645C2×C22⋊C4—614no—
646C2×C22⋊C4—614no—
647C2×C22⋊C4—614no—
648C2×C22⋊C4—614no—
649C2×C22⋊C4—1222no—
650C2×C22⋊C4—1222no—
651C2×C22⋊C4—1222no—
652C2×C22⋊C4—1222no—
653C2×C42—22no—
654C2×C42—22no—
655C2×C42—41no—
656C2×C42—614no—
657C2×C42—614no—
658C2×C42—1222no—
659C2×C42—1222no—
660C2×C42—1222no—
661C2×C42—1222no—
662C2×C42—1222no—
663C2×C42—1222no—
664C2×C42—1222no—
665C2×C42—1222no—
666C2×C42—2441no—
667C2×C42—2441no—
668C2×C42—2441no—
669C2×C42—2441no—
670C2×C42—2441no—
671#95—22no—
672#95—22no—
673#95—41no—
674#95—614no—
675#95—614no—
676#95—614no—
677#95—614no—
678#95—614no—
679#95—1222no—
680#95—1222no—
681#95—1222no—
682#95—1222no—
683#95—1222no—
684#95—1222no—
685#95—1222no—
686#95—2441no—
687#95C4×D6114yescomplemented
688#95C4×D6114yescomplemented
689C24—612no—
690C24—612no—
691C24—612no—
692C24—612no—
693C24—612no—
694C24—612no—
695C24—612no—
696C24—1221no—
697C24—1221no—
698C24—1221no—
699C24—1221no—
700C24—1221no—
701C24—1221no—
702C24—1221no—
703C24—1221no—
704C24C23×D6111yescharacteristic
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—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—612no—
742C22×C4—612no—
743C22×C4—612no—
744C22×C4—612no—
745C22×C4—612no—
746C22×C4—612no—
747C22×C4—612no—
748C22×C4—612no—
749C22×C4—612no—
750C22×C4—612no—
751C22×C4—612no—
752C22×C4—612no—
753C22×C4—612no—
754C22×C4—612no—
755C22×C4—612no—
756C22×C4—1228no—
757C22×C4—1228no—
758C22×C4—1228no—
759C22×C4—1228no—
760C22×C4—1228no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1228no—
796C22×C4—2444no—
797C22×C4—2444no—
798C22×C4—2444no—
799C22×C4—2444no—
800C22×C4—2444no—
801C22×C4—2444no—
802C22×C4—2444no—
803C22×C4—2444no—
804C22×C4—2444no—
805C22×C4—2444no—
806C22×C4—2444no—
807C22×C4—2444no—
808C22×C4—2444no—
809C22×C4—2444no—
810C22×C4—2444no—
811C22×C4C2×C4×D6112yes—
812C22×C4C2×C4×D6112yes—
813C22×C4C2×C4×D6112yes—
814C22×C4C2×C4×D6112yes—
815C22×C4C2×C4×D6112yes—
816C22×C4C2×C4×D6112yes—
817C22×C4C2×C4×D6112yes—
818C22×C4C2×C4×D6112yes—
819C22×C4C2×C4×D6112yes—
820C22×C4D4×D6112yes—
821C22×C4D4×D6112yes—
822C22×C4#1175822412yes—
823C22×C4Q8×D6112yes—
824C4⋊C4—28no—
825C4⋊C4—1228no—
826C4⋊C4—2444no—
827C4⋊C4—2444no—
828C22⋊C4—6116no—
829C22⋊C4—6116no—
830C22⋊C4—1228no—
831C22⋊C4—1228no—
832C42—44no—
833C42—1228no—
834C42—2444no—
835C42—2444no—
836C42—2444no—
837C42—2444no—
838C23—614no—
839C23—614no—
840C23—614no—
841C23—614no—
842C23—614no—
843C23—614no—
844C23—614no—
845C23—1222no—
846C23—1222no—
847C23—1222no—
848C23—1222no—
849C23—1222no—
850C23—1222no—
851C23—1222no—
852C23—1222no—
853C23—1222no—
854C23—1222no—
855C23—1222no—
856C23—1222no—
857C23—1222no—
858C23—1222no—
859C23—1222no—
860C23—1222no—
861C23—1222no—
862C23—1222no—
863C23—1222no—
864C23—1222no—
865C23—1222no—
866C23—1222no—
867C23—1222no—
868C23—1222no—
869C23—1222no—
870C23—1222no—
871C23—1222no—
872C23—1222no—
873C23C22×C4×D6111yescharacteristic
874C23C22×C4×D6111yescharacteristic
875C23C22×C4×D6111yescharacteristic
876C23C2×D4×D6111yescharacteristic
877C23C2×D4×D6111yescharacteristic
878C23C2×Q8×D6111yescharacteristic
879C23#41×D6111yescharacteristic
880C23#41×D6111yescharacteristic
881C23#41×D6111yescharacteristic
882C23#41×D6111yescharacteristic
883C23C2×#1175822411yescharacteristic
884C23#1451982211yescharacteristic
885C23#1451982311yescharacteristic
886C23#1451982311yescharacteristic
887C23#1451982511yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—614no—
935C2×C4—614no—
936C2×C4—614no—
937C2×C4—614no—
938C2×C4—1222no—
939C2×C4—1222no—
940C2×C4—1222no—
941C2×C4—1222no—
942C2×C4—1222no—
943C2×C4—1222no—
944C2×C4—1222no—
945C2×C4—1222no—
946C2×C4—1222no—
947C2×C4—1222no—
948C2×C4—1222no—
949C2×C4—1222no—
950C2×C4—1222no—
951C2×C4—1222no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—1222no—
955C2×C4—1222no—
956C2×C4—1222no—
957C2×C4—1222no—
958C2×C4—1222no—
959C2×C4—1222no—
960C2×C4—1222no—
961C2×C4—1222no—
962C2×C4—1222no—
963C2×C4—1222no—
964C2×C4—1222no—
965C2×C4—1222no—
966C2×C4—1222no—
967C2×C4—1222no—
968C2×C4—1222no—
969C2×C4—1222no—
970C2×C4—1222no—
971C2×C4—24416no—
972C2×C4—24416no—
973C2×C4—24416no—
974C2×C4—2441no—
975C2×C4—2441no—
976C2×C4—2441no—
977C2×C4—2441no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4C42×D6114yes—
987C2×C4C4⋊C4×D6114yes—
988C2×C4#1451973714yes—
989C22—618no—
990C22—1224no—
991C22—1224no—
992C22—1224no—
993C22—1224no—
994C22—1224no—
995C22—1224no—
996C22—1224no—
997C22—1224no—
998C22—1224no—
999C22—1224no—
1000C22—1224no—
1001C22—1224no—
1002C22—1224no—
1003C22—1224no—
1004C22C2×C42×D6111yescharacteristic
1005C22C2×C4⋊C4×D6111yescharacteristic
1006C22#117×D6111yescharacteristic
1007C22C4×D4×D6111yescharacteristic
1008C22C4×D4×D6111yescharacteristic
1009C22C4×D4×D6111yescharacteristic
1010C22C4×D4×D6111yescharacteristic
1011C22C2×#1451973711yescharacteristic
1012C22C4×Q8×D6111yescharacteristic
1013C22C4×Q8×D6111yescharacteristic
1014C22C4×#1175822411yescharacteristic
1015C22C4×#1175822411yescharacteristic
1016C22#1684023011yescharacteristic
1017C22#1684023411yescharacteristic
1018C22#1684023411yescharacteristic
1019C22#1684023611yescharacteristic
1020C22#1684024311yescharacteristic
1021C22#1684024411yescharacteristic
1022C22#1684024411yescharacteristic
1023C22#1684039611yescharacteristic
1024C22#1684039911yescharacteristic
1025C22#1684040111yescharacteristic
1026C22#1684040411yescharacteristic
1027C22#1684040511yescharacteristic
1028C22#1684041411yescharacteristic
1029C22#1684042711yescharacteristic
1030C22#1684043511yescharacteristic
1031C22#1684043711yescharacteristic
1032C22#1684043711yescharacteristic
1033C22#1684044011yescharacteristic
1034C22#1684044411yescharacteristic
1035C22#1684044611yescharacteristic
1036C22#1684046611yescharacteristic
1037C22#1684046811yescharacteristic
1038C22#1684047011yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—1224no—
1047C4—1224no—
1048C4—1224no—
1049C4—1224no—
1050C4—2442no—
1051C4—2442no—
1052C4—2442no—
1053C2—1228no—
1054C2C4×C4⋊C4×D6111yescharacteristic
1055C2C4×#1451973711yescharacteristic
1056C2#2144817911yescharacteristic
1057C2#2144866711yescharacteristic
1058C2#2144867411yescharacteristic
1059C2#2144872011yescharacteristic
1060C2#2144872511yescharacteristic
1061C2#2144879711yescharacteristic
1062C2#2144879911yescharacteristic
1063C2#2144880411yescharacteristic
1064C2#2144881411yescharacteristic
1065C2#2144882111yescharacteristic
1066C2#2144882911yescharacteristic
1067C2#2144889611yescharacteristic
1068C2#2144890111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1436D61
hypocenterC61#13814
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic61C2semidirect
8. #21444054C2semidirect
9. #21444053C2semidirect
10. #21444050C2semidirect
11. #21444047C2semidirect
12. #21444044C2semidirect
14. C4×#14519684C2semidirect
15. C61×#1436C2semidirect
31. #16839636C4semidirect
32. #16839633C4semidirect
36. #16839609C4semidirect
89. C2×C4⋊Dic61C2×C4semidirect
94. C2×#11758196C2×C4semidirect
95. C2×#11758196C2×C4semidirect
121. C2×C4×Dic61C2×C4semidirect
122. C2×C4×Dic61C2×C4semidirect
131. #14519684C2×C4semidirect
132. #14519684C2×C4semidirect
133. #14519684C2×C4semidirect
134. #14519684C2×C4semidirect
145. C2×C4⋊C4×C61C2×C4semidirect
152. #95×C61C2×C4semidirect
153. #95×C61C2×C4semidirect
293. #11758198C42semidirect
294. #11758198C4⋊C4semidirect
504. C2×D61C4×C4⋊C4semidirect
529. #1436D61semidirect
592. C61#13814semidirect
640. C2×C4⋊C4C4×D61semidirect
687. #95C4×D61semidirect
688. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396362
C2×#168396332
C2×C4⋊C4×Dic612
C2×C4×#117581982
C2×#168396092
C2×#95×D612
#214440542
#214440532
#214440502
#214440472
#214440442
#214440402
C4×#145196842
C61×#14362
#1381461