Finite Group Databasebeta

← #29608409

Subgroups — #29608409

Order 15616.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839665C211yesmaximal, characteristic
2C2×#16839642C211yesmaximal, characteristic
3C2×#16839635C211yesmaximal, characteristic, complemented
4C2×#16839634C211yesmaximal, characteristic, complemented
5#21444071C211yesmaximal, characteristic, complemented
6#21444071C211yesmaximal, characteristic, complemented
7#21444062C211yesmaximal, characteristic, complemented
8#21444062C211yesmaximal, characteristic, complemented
9#21444062C211yesmaximal, characteristic, complemented
10#21444062C211yesmaximal, characteristic, complemented
11#21444047C211yesmaximal, characteristic, complemented
12#21444045C211yesmaximal, characteristic, complemented
13#21444042C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C2×C61×#386C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30#16839665C418yescomplemented
31#16839642—24no—
32#16839635—24no—
33#16839634—24no—
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C23×D4×C61C2211yescharacteristic
49C24×C4×C61C2211yescharacteristic
50C22×C22⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C61×#386—24no—
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C23×Dic61—22no—
57C23×Dic61—22no—
58C23×Dic61—22no—
59C23×Dic61—41no—
60C23×Dic61—41no—
61C23×Dic61—41no—
62C23×Dic61—41no—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C2×C4⋊Dic61—41no—
72C2×C4⋊Dic61—41no—
73C2×C4⋊Dic61C2×C414yescomplemented
74C2×#11758196—22no—
75C2×#11758196—22no—
76C2×#11758196—22no—
77C2×#11758196—22no—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196—41no—
81C2×#11758196—41no—
82C2×#11758196—41no—
83C2×#11758196—41no—
84C2×#11758196—41no—
85C2×#11758196—41no—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—22no—
91C2×C22⋊Dic61—22no—
92C2×C22⋊Dic61—22no—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—41no—
96C2×C22⋊Dic61—41no—
97C2×C22⋊Dic61—41no—
98C2×C22⋊Dic61—41no—
99C2×C22⋊Dic61—41no—
100C2×C22⋊Dic61—41no—
101C2×C22⋊Dic61—41no—
102C2×C22⋊Dic61—41no—
103C2×C22⋊Dic61C2×C414yescomplemented
104C2×C22⋊Dic61C2×C414yescomplemented
105C2×C22⋊Dic61C2×C414yescomplemented
106C2×C22⋊Dic61C2×C414yescomplemented
107C2×C4×Dic61—41no—
108C2×C4×Dic61—41no—
109C2×C4×Dic61C2×C414yescomplemented
110#14519684—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115#14519684—41no—
116#14519684—41no—
117#14519684—41no—
118#14519684—41no—
119#14519684—41no—
120#14519684—41no—
121#14519684—41no—
122#14519684—41no—
123#14519684D414yescomplemented
124C25×C61C2311yescharacteristic
125C25×C61C2311yescharacteristic
126C22×D4×C61—41no—
127C22×D4×C61—41no—
128C22×D4×C61—41no—
129C22×D4×C61—41no—
130C22×D4×C61C2×C414yes—
131C22×D4×C61D414yes—
132C22×D4×C61Q814yes—
133C23×C4×C61—22no—
134C23×C4×C61—22no—
135C23×C4×C61—22no—
136C23×C4×C61—41no—
137C23×C4×C61—41no—
138C23×C4×C61—41no—
139C23×C4×C61—41no—
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C2×C22⋊C4×C61—22no—
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61—41no—
151C2×C22⋊C4×C61—41no—
152C2×C22⋊C4×C61—41no—
153C2×C22⋊C4×C61—41no—
154#95×C61—22no—
155#95×C61—22no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61C22×C412yes—
181C24×C61C22×C412yes—
182C24×C61C2×D412yes—
183C24×C61C2×D412yes—
184C24×C61C2×Q812yes—
185C24×C61C2×Q812yes—
186C24×C61C2411yescharacteristic
187C2×D4×C61—44no—
188C2×D4×C61—44no—
189C2×D4×C61—44no—
190C2×D4×C61—44no—
191C2×D4×C61—44no—
192C2×D4×C61—44no—
193C2×D4×C61C4⋊C4116yescomplemented
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×C61—44no—
225C22×C4×C61—44no—
226C22×C4×C61—44no—
227C22×C4×C61—44no—
228C22×C4×C61—44no—
229C22×C4×C61—44no—
230C22×C4×C61—44no—
231C22×C4×C61C22×C412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2×Q812yes—
235C22×C4×C61#4112yes—
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×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—44no—
285C22×Dic61—44no—
286C22×Dic61—44no—
287C22×Dic61—44no—
288C22×Dic61—44no—
289C22×Dic61—44no—
290C22×Dic61—44no—
291C22×Dic61C22×C412yes—
292C22×Dic61C22×C412yes—
293C22×Dic61C22×C412yes—
294C22×Dic61C22×C412yes—
295C22×Dic61C2×D412yes—
296C22×Dic61C2×D412yes—
297C22×Dic61#4112yes—
298C22×Dic61#4112yes—
299C22⋊C4×C61—44no—
300C22⋊C4×C61—44no—
301C22⋊C4×C61—44no—
302C22⋊Dic61—28no—
303C22⋊Dic61—28no—
304C22⋊Dic61—44no—
305C22⋊Dic61—44no—
306C22⋊Dic61—44no—
307C22⋊Dic61—44no—
308C22⋊Dic61—44no—
309C4⋊Dic61—44no—
310#11758196—44no—
311#11758196—44no—
312#11758196—44no—
313#11758196—44no—
314C4×Dic61—44no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61C2×C4⋊C414yes—
384C23×C61C2×C4⋊C414yes—
385C23×C61C23×C411yescharacteristic
386C23×C61C22×D411yescharacteristic
387C23×C61C22×D411yescharacteristic
388C23×C61C22×Q811yescharacteristic
389C23×C61C2×#4111yescharacteristic
390C23×C61C2×#4111yescharacteristic
391C23×C61C2×#4111yescharacteristic
392C23×C61H(5,𝔽2)11yescharacteristic
393C23×C61H(5,𝔽2)11yescharacteristic
394C23×C61H(5,𝔽2)11yescharacteristic
395C23×C61H(5,𝔽2)11yescharacteristic
396C23×C61H(5,𝔽2)11yescharacteristic
397C23×C61H(5,𝔽2)11yescharacteristic
398C23×C61H(5,𝔽2)11yescharacteristic
399C23×C612−1+411yescharacteristic
400D4×C61—416no—
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—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—416no—
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×C61C2×C4⋊C414yes—
437C2×Dic61—22no—
438C2×Dic61—22no—
439C2×Dic61—22no—
440C2×Dic61—22no—
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—22no—
457C2×Dic61—22no—
458C2×Dic61—416no—
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—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61C4×D414yes—
494#14438—611nomaximal, Sylow
495C22×C61—24no—
496C22×C61—24no—
497C22×C61—24no—
498C22×C61—24no—
499C22×C61—24no—
500C22×C61—24no—
501C22×C61—42no—
502C22×C61—42no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61—42no—
506C22×C61—42no—
507C22×C61—42no—
508C22×C61—42no—
509C22×C61—42no—
510C22×C61—42no—
511C22×C61—42no—
512C22×C61—42no—
513C22×C61—42no—
514C22×C61—42no—
515C22×C61—42no—
516C22×C61—42no—
517C22×C61—42no—
518C22×C61—42no—
519C22×C61—42no—
520C22×C61—42no—
521C22×C61—42no—
522C22×C61—42no—
523C22×C61—42no—
524C22×C61—42no—
525C22×C61C22×C4⋊C411yescharacteristic
526C22×C61C2×C4×D411yescharacteristic
527C22×C61C4×#4111yescharacteristic
528C22×C61#51811yescharacteristic
529C22×C61#51811yescharacteristic
530C22×C61#51811yescharacteristic
531C22×C61#52011yescharacteristic
532C22×C61#53411yescharacteristic
533C22×C61#53411yescharacteristic
534C22×C61#53511yescharacteristic
535C22×C61#53511yescharacteristic
536C22×C61#53811yescharacteristic
537C22×C61#53811yescharacteristic
538C22×C61#54011yescharacteristic
539C22×C61#54011yescharacteristic
540C22×C61#54211yescharacteristic
541C22×C61#54211yescharacteristic
542C22×C61#54311yescharacteristic
543C22×C61#54311yescharacteristic
544C22×C61D4211yescharacteristic
545C22×C61#54611yescharacteristic
546C22×C61#54611yescharacteristic
547C22×C61#54611yescharacteristic
548C22×C61#54611yescharacteristic
549C22×C61#54711yescharacteristic
550C22×C61D4×Q811yescharacteristic
551C22×C61#55311yescharacteristic
552C22×C61#55311yescharacteristic
553C22×C61#55411yescharacteristic
554C22×C61#55411yescharacteristic
555C22×C61#55411yescharacteristic
556C22×C61#56011yescharacteristic
557C22×C61#56011yescharacteristic
558C22×C61#56211yescharacteristic
559C22×C61#56211yescharacteristic
560C4×C61—24no—
561C4×C61—42no—
562C4×C61—42no—
563C4×C61—81no—
564C4×C61—81no—
565Dic61—24no—
566Dic61—42no—
567Dic61—42no—
568Dic61—42no—
569Dic61—42no—
570Dic61—42no—
571Dic61—81no—
572Dic61—81no—
573C2×#390—611no—
574C2×#386—611no—
575C2×#386D6111yescharacteristic
576C2×#385—611no—
577C2×#385—611no—
578#1441—611no—
579#1441—611no—
580#1439—611no—
581#1439—611no—
582#1439—611no—
583#1439—611no—
584C4⋊#95—611no—
585#1434—611no—
586C22⋊#95—611no—
587C22⋊#95—611no—
588C2×C61—44no—
589C2×C61—44no—
590C2×C61#231511yescharacteristic
591C2×C61#232811yescharacteristic
592C2×C61#233711yescharacteristic
593C2×C61D4×C4⋊C411yescharacteristic
594C2×C61#234911yescharacteristic
595C2×C61#236411yescharacteristic
596C2×C61#237711yescharacteristic
597C2×C61#267811yescharacteristic
598C2×C61#267811yescharacteristic
599C2×C61#269211yescharacteristic
600C2×C61#269211yescharacteristic
601C2×C61#270111yescharacteristic
602C2×C61#270111yescharacteristic
603C2×C61#278011yescharacteristic
604C2×C61#278011yescharacteristic
605C23×D4C2×D6111yescharacteristic
606C24×C4—611no—
607C24×C4C2×D6111yescharacteristic
608C22×C4⋊C4—611no—
609C22×C4⋊C4—611no—
610C22×C4⋊C4—611no—
611C22×C4⋊C4—611no—
612C22×C4⋊C4—611no—
613C22×C22⋊C4—611no—
614C22×C22⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C22⋊C4—611no—
620C22×C22⋊C4C2×D6111yescharacteristic
621C22×C22⋊C4C2×D6111yescharacteristic
622C22×C22⋊C4C2×D6111yescharacteristic
623C22×C42—611no—
624#390—618no—
625#386—24no—
626#386—1224no—
627#385—1224no—
628#385—1224no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95C2×D6111yescharacteristic
644C2×#95C2×D6111yescharacteristic
645C61#1443811yescharacteristic, complemented, Sylow
646C25C22×D6111yescharacteristic
647C25C22×D6111yescharacteristic
648C22×D4—41no—
649C22×D4—41no—
650C22×D4—41no—
651C22×D4—41no—
652C22×D4Dic12214yes—
653C22×D4C4×D6114yes—
654C22×D4C22⋊D6114yes—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—41no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4—41no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—611no—
665C23×C4—611no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—611no—
670C23×C4—1222no—
671C23×C4—1222no—
672C23×C4—1222no—
673C23×C4—2441no—
674C23×C4—2441no—
675C23×C4—2441no—
676C23×C4—2441no—
677C23×C4C22×D6111yescharacteristic
678C23×C4C22×D6111yescharacteristic
679C23×C4C22×D6111yescharacteristic
680C23×C4C22×D6111yescharacteristic
681C23×C4C22×D6111yescharacteristic
682C2×C4⋊C4—614no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—1222no—
685C2×C4⋊C4—1222no—
686C2×C4⋊C4—1222no—
687C2×C4⋊C4—1222no—
688C2×C4⋊C4—1222no—
689C2×C4⋊C4—2441no—
690C2×C4⋊C4—2441no—
691C2×C4⋊C4—2441no—
692C2×C4⋊C4—2441no—
693C2×C4⋊C4—2441no—
694C2×C4⋊C4—2441no—
695C2×C4⋊C4—2441no—
696C2×C4⋊C4—2441no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—614no—
707C2×C22⋊C4—614no—
708C2×C22⋊C4—614no—
709C2×C22⋊C4—614no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—1222no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4—2441no—
724C2×C22⋊C4—2441no—
725C2×C22⋊C4—2441no—
726C2×C22⋊C4—2441no—
727C2×C42—614no—
728C2×C42—2441no—
729C2×C42—2441no—
730#95—22no—
731#95—22no—
732#95—614no—
733#95—1222no—
734#95—1222no—
735#95—1222no—
736#95—1222no—
737#95—1222no—
738#95—2441no—
739#95—2441no—
740#95—2441no—
741#95—2441no—
742#95—2441no—
743#95—2441no—
744#95—2441no—
745#95—2441no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24C2×Dic12212yes—
771C24C2×Dic12212yes—
772C24C2×C4×D6112yes—
773C24C2×C4×D6112yes—
774C24C2×C22⋊D6112yes—
775C24C2×C22⋊D6112yes—
776C24C23×D6111yescharacteristic
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4#11758196116yescomplemented
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—21no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—612no—
822C22×C4—612no—
823C22×C4—612no—
824C22×C4—612no—
825C22×C4—612no—
826C22×C4—612no—
827C22×C4—612no—
828C22×C4—612no—
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—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—2444no—
878C22×C4—2444no—
879C22×C4—2444no—
880C22×C4—2444no—
881C22×C4—2444no—
882C22×C4—2444no—
883C22×C4—2444no—
884C22×C4C2×Dic12212yes—
885C22×C4C2×C4×D6112yes—
886C22×C4D4×D6112yes—
887C22×C4#1175822412yes—
888C22×C4C2×C22⋊D6112yes—
889C4⋊C4—2444no—
890C4⋊C4—2444no—
891C4⋊C4—2444no—
892C4⋊C4—2444no—
893C4⋊C4—2444no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—1228no—
898C22⋊C4—1228no—
899C22⋊C4—2444no—
900C22⋊C4—2444no—
901C22⋊C4—2444no—
902C22⋊C4—2444no—
903C22⋊C4—2444no—
904C42—2444no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23C2×#1175819614yes—
974C23C2×#1175819614yes—
975C23C22×C4×D6111yescharacteristic
976C23C2×D4×D6111yescharacteristic
977C23C22×C22⋊D6111yescharacteristic
978C23C22×Dic12211yescharacteristic
979C23#41×D6111yescharacteristic
980C23#41×D6111yescharacteristic
981C23C2×#1175822411yescharacteristic
982C23#1451982211yescharacteristic
983C23#1451982211yescharacteristic
984C23#1451982211yescharacteristic
985C23#1451982211yescharacteristic
986C23#1451982211yescharacteristic
987C23#1451982211yescharacteristic
988C23#1451982311yescharacteristic
989C23#1451982411yescharacteristic
990D4—416no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—416no—
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—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—614no—
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—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
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—24416no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4C2×#1175819614yes—
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22C22×#1175819611yescharacteristic
1115C22C4×D4×D6111yescharacteristic
1116C22C4×#1175822411yescharacteristic
1117C22#1684023411yescharacteristic
1118C22#1684023511yescharacteristic
1119C22#1684023511yescharacteristic
1120C22#1684024111yescharacteristic
1121C22#1684032111yescharacteristic
1122C22#1684032111yescharacteristic
1123C22#1684032711yescharacteristic
1124C22#1684032811yescharacteristic
1125C22#1684034411yescharacteristic
1126C22#1684034711yescharacteristic
1127C22#1684036211yescharacteristic
1128C22#1684036411yescharacteristic
1129C22#1684037911yescharacteristic
1130C22#1684038011yescharacteristic
1131C22#1684038811yescharacteristic
1132C22#1684038811yescharacteristic
1133C22D4×C22⋊D6111yescharacteristic
1134C22#1684039911yescharacteristic
1135C22#1684040011yescharacteristic
1136C22#1684040611yescharacteristic
1137C22#1684040911yescharacteristic
1138C22#1684041111yescharacteristic
1139C22D4×Dic12211yescharacteristic
1140C22#1684045711yescharacteristic
1141C22#1684045911yescharacteristic
1142C22#1684046911yescharacteristic
1143C22#1684047111yescharacteristic
1144C22#1684047111yescharacteristic
1145C22#1684050011yescharacteristic
1146C22#1684050111yescharacteristic
1147C22#1684050711yescharacteristic
1148C22#1684050911yescharacteristic
1149C4—24no—
1150C4—42no—
1151C4—42no—
1152C4—81no—
1153C4—81no—
1154C4—1224no—
1155C4—4881no—
1156C4—4881no—
1157C4—2442no—
1158C4—2442no—
1159C4—2442no—
1160C4—2442no—
1161C4—2442no—
1162C2—44no—
1163C2—44no—
1164C2#2144843111yescharacteristic
1165C2#2144854011yescharacteristic
1166C2#2144862811yescharacteristic
1167C2D4×#1175819611yescharacteristic
1168C2#2144872411yescharacteristic
1169C2#2144886811yescharacteristic
1170C2#2144897111yescharacteristic
1171C2#2145214411yescharacteristic
1172C2#2145214711yescharacteristic
1173C2#2145231611yescharacteristic
1174C2#2145231911yescharacteristic
1175C2#2145242611yescharacteristic
1176C2#2145242811yescharacteristic
1177C2#2145346411yescharacteristic
1178C2#2145347111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#386C2
socle, cosocleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC2×#386D61
hypocenterC61#14438
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#16839635C2semidirect
4. C2×#16839634C2semidirect
5. #21444071C2semidirect
6. #21444071C2semidirect
7. #21444062C2semidirect
8. #21444062C2semidirect
9. #21444062C2semidirect
10. #21444062C2semidirect
11. #21444047C2semidirect
12. #21444045C2semidirect
13. #21444042C2semidirect
14. #21444041C2semidirect
30. #16839665C4semidirect
73. C2×C4⋊Dic61C2×C4semidirect
103. C2×C22⋊Dic61C2×C4semidirect
104. C2×C22⋊Dic61C2×C4semidirect
105. C2×C22⋊Dic61C2×C4semidirect
106. C2×C22⋊Dic61C2×C4semidirect
109. C2×C4×Dic61C2×C4semidirect
123. #14519684D4semidirect
193. C2×D4×C61C4⋊C4semidirect
645. C61#14438semidirect
783. C2×D4#11758196semidirect

Maximal subgroups

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

subgroupindex
C2×#168396652
C2×#168396422
C2×#168396352
C2×#168396342
#214440712
#214440622
#214440472
#214440452
#214440422
#214440412
C2×C61×#3862
#1443861