Finite Group Databasebeta

← #29601524

Subgroups — #29601524

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×#16839637C211yesmaximal, characteristic
2C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic61C211yesmaximal, characteristic
4C2×C22⋊C4×Dic61C211yesmaximal, characteristic
5C2×C4×C22⋊Dic61C211yesmaximal, characteristic
6C22×#14519684C211yesmaximal, characteristic
7#21444053C211yesmaximal, characteristic, complemented
8#21444053C211yesmaximal, characteristic, complemented
9#21444051C211yesmaximal, characteristic, complemented
10#21444051C211yesmaximal, characteristic, complemented
11#21444048C211yesmaximal, characteristic, complemented
12#21444044C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic
14#95×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#385C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28#16839637C418yescomplemented
29C4⋊C4×Dic61—24no—
30C22⋊C4×Dic61—24no—
31C22⋊C4×Dic61C418yescomplemented
32C4×C22⋊Dic61—24no—
33C2×#14519684—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
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C24×C4×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C61×#385C418yescomplemented
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61—22no—
61C23×Dic61—22no—
62C23×Dic61—22no—
63C23×Dic61—22no—
64C23×Dic61—22no—
65C23×Dic61—22no—
66C23×Dic61—41no—
67C23×Dic61—41no—
68C23×Dic61—41no—
69C23×Dic61—41no—
70C23×Dic61C2×C414yes—
71C23×Dic61C2×C414yes—
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—41no—
83C2×C4⋊Dic61—41no—
84C2×C4⋊Dic61C2×C414yescomplemented
85C2×C4⋊Dic61C2×C414yescomplemented
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61C2×C414yes—
89C2×C22⋊Dic61C2×C414yes—
90C2×C22⋊Dic61D414yes—
91C2×C22⋊Dic61Q814yes—
92C2×C4×Dic61—22no—
93C2×C4×Dic61—22no—
94C2×C4×Dic61—22no—
95C2×C4×Dic61—22no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61—22no—
98C2×C4×Dic61—22no—
99C2×C4×Dic61—22no—
100C2×C4×Dic61—22no—
101C2×C4×Dic61—22no—
102C2×C4×Dic61—41no—
103C2×C4×Dic61—41no—
104C2×C4×Dic61—41no—
105C2×C4×Dic61—41no—
106C2×C4×Dic61—41no—
107C2×C4×Dic61—41no—
108C2×C4×Dic61C2×C414yescomplemented
109C2×C4×Dic61C2×C414yescomplemented
110#14519684—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117#14519684—22no—
118#14519684—22no—
119#14519684—41no—
120#14519684—41no—
121#14519684C2×C414yescomplemented
122#14519684C2×C414yescomplemented
123#14519684C2×C414yescomplemented
124#14519684C2×C414yescomplemented
125#14519684D414yes—
126C25×C61C2311yescharacteristic
127C23×C4×C61—22no—
128C23×C4×C61—22no—
129C23×C4×C61—22no—
130C23×C4×C61—22no—
131C23×C4×C61—41no—
132C23×C4×C61—41no—
133C23×C4×C61C2×C414yes—
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61—41no—
143C2×C4⋊C4×C61—41no—
144C2×C4⋊C4×C61C2×C414yescomplemented
145C2×C4⋊C4×C61C2×C414yescomplemented
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61C2×C414yes—
149C2×C22⋊C4×C61C2×C414yes—
150C2×C22⋊C4×C61C2×C414yes—
151C2×C22⋊C4×C61C2×C414yes—
152#95×C61C2×C414yescomplemented
153#95×C61C2×C414yescomplemented
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61C22×C412yes—
163C24×C61C22×C412yes—
164C24×C61C22×C412yes—
165C24×C61C2×D412yes—
166C24×C61C2×Q812yes—
167C24×C61#4112yes—
168C24×C61#4112yes—
169C24×C61C2411yescharacteristic
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—28no—
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—28no—
202C22×C4×C61—44no—
203C22×C4×C61—44no—
204C22×C4×C61—44no—
205C22×C4×C61—44no—
206C22×C4×C61—44no—
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×C61C22×C412yes—
216C22×C4×C61C22×C412yes—
217C22×C4×C61C2×D412yes—
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—28no—
236C22×Dic61—28no—
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—28no—
262C22×Dic61—28no—
263C22×Dic61—44no—
264C22×Dic61—44no—
265C22×Dic61—44no—
266C22×Dic61—44no—
267C22×Dic61—44no—
268C22×Dic61—44no—
269C22×Dic61—44no—
270C22×Dic61—44no—
271C22×Dic61—44no—
272C22×Dic61—44no—
273C22×Dic61C22×C412yes—
274C22×Dic61C22×C412yes—
275C22×Dic61C22×C412yes—
276C22×Dic61C22×C412yes—
277C22×Dic61C22×C412yes—
278C22×Dic61C22×C412yes—
279C22×Dic61C22×C412yes—
280C22×Dic61C22×C412yes—
281C22×Dic61C2×D412yes—
282C22×Dic61C2×D412yes—
283C22×Dic61C2×D412yes—
284C22×Dic61C2×D412yes—
285C22×Dic61C2×Q812yes—
286C22×Dic61C2×Q812yes—
287C22×Dic61#4112yes—
288C22×Dic61#4112yes—
289C4⋊C4×C61—28no—
290C4⋊C4×C61—44no—
291C22⋊C4×C61—28no—
292C22⋊C4×C61C42116yescomplemented
293C22⋊Dic61—28no—
294C22⋊Dic61C4⋊C4116yescomplemented
295C4⋊Dic61—28no—
296C4⋊Dic61—44no—
297C4×Dic61—28no—
298C4×Dic61—44no—
299C4×Dic61—44no—
300C4×Dic61—44no—
301C4×Dic61—44no—
302C4×Dic61—44no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
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×C61C2×C4214yes—
332C23×C61C2×C4⋊C414yes—
333C23×C61#11714yes—
334C23×C61C4×D414yes—
335C23×C61C4×D414yes—
336C23×C61C4×Q814yes—
337C23×C61C4×Q814yes—
338C23×C61C23×C411yescharacteristic
339C23×C61C23×C411yescharacteristic
340C23×C61C23×C411yescharacteristic
341C23×C61C22×D411yescharacteristic
342C23×C61C22×D411yescharacteristic
343C23×C61C22×Q811yescharacteristic
344C23×C61C2×#4111yescharacteristic
345C23×C61C2×#4111yescharacteristic
346C23×C61C2×#4111yescharacteristic
347C23×C61C2×#4111yescharacteristic
348C23×C61C2×#4111yescharacteristic
349C23×C61H(5,𝔽2)11yescharacteristic
350C23×C61H(5,𝔽2)11yescharacteristic
351C23×C61H(5,𝔽2)11yescharacteristic
352C23×C612−1+411yescharacteristic
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—416no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
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×C61C2×C4214yes—
394C2×C4×C61C2×C4214yes—
395C2×C4×C61C4×D414yes—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
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—416no—
433C2×Dic61—416no—
434C2×Dic61—41no—
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×Dic61—41no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61C2×C4⋊C414yes—
451C2×Dic61C2×C4⋊C414yes—
452C2×Dic61C4×D414yes—
453C2×Dic61C4×D414yes—
454#13814—611nomaximal, Sylow
455C22×C61—24no—
456C22×C61—24no—
457C22×C61—24no—
458C22×C61—24no—
459C22×C61—24no—
460C22×C61—24no—
461C22×C61—24no—
462C22×C61—24no—
463C22×C61—24no—
464C22×C61—24no—
465C22×C61—24no—
466C22×C61—24no—
467C22×C61—24no—
468C22×C61—24no—
469C22×C61C4×C4⋊C418yescomplemented
470C22×C61C22×C4211yescharacteristic
471C22×C61C22×C4⋊C411yescharacteristic
472C22×C61C2×#11711yescharacteristic
473C22×C61C2×C4×D411yescharacteristic
474C22×C61C2×C4×D411yescharacteristic
475C22×C61C2×C4×D411yescharacteristic
476C22×C61C2×C4×D411yescharacteristic
477C22×C61C2×C4×D411yescharacteristic
478C22×C61C2×C4×Q811yescharacteristic
479C22×C61C2×C4×Q811yescharacteristic
480C22×C61C4×#4111yescharacteristic
481C22×C61C4×#4111yescharacteristic
482C22×C61C4×#4111yescharacteristic
483C22×C61#51811yescharacteristic
484C22×C61#51811yescharacteristic
485C22×C61#51811yescharacteristic
486C22×C61#52011yescharacteristic
487C22×C61#52011yescharacteristic
488C22×C61#52011yescharacteristic
489C22×C61D4211yescharacteristic
490C22×C61#54611yescharacteristic
491C22×C61#54611yescharacteristic
492C22×C61#54611yescharacteristic
493C22×C61#54611yescharacteristic
494C22×C61#54711yescharacteristic
495C22×C61D4×Q811yescharacteristic
496C22×C61#55111yescharacteristic
497C22×C61#55111yescharacteristic
498C22×C61#55111yescharacteristic
499C22×C61#55111yescharacteristic
500C22×C61#55211yescharacteristic
501C22×C61#55211yescharacteristic
502C22×C61#55411yescharacteristic
503C22×C61#55411yescharacteristic
504C22×C61#55411yescharacteristic
505C4×C61—24no—
506C4×C61—24no—
507C4×C61—24no—
508C4×C61—42no—
509C4×C61—42no—
510C4×C61—42no—
511Dic61—24no—
512Dic61—24no—
513Dic61—24no—
514Dic61—24no—
515Dic61—42no—
516Dic61—42no—
517Dic61—42no—
518Dic61—42no—
519C2×#385—611no—
520C2×#385D6111yescharacteristic
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#1436—611no—
530C4⋊#95—611no—
531#1434—611no—
532C22⋊#95—611no—
533C4×#95—611no—
534C2×C61—28no—
535C2×C61C2×C4×C4⋊C411yescharacteristic
536C2×C61C42×D411yescharacteristic
537C2×C61#227511yescharacteristic
538C2×C61#234211yescharacteristic
539C2×C61#234311yescharacteristic
540C2×C61D4×C4⋊C411yescharacteristic
541C2×C61#234911yescharacteristic
542C2×C61#235811yescharacteristic
543C2×C61#235811yescharacteristic
544C2×C61#235911yescharacteristic
545C2×C61#235911yescharacteristic
546C2×C61#236011yescharacteristic
547C2×C61#236011yescharacteristic
548C2×C61#236811yescharacteristic
549C2×C61#236811yescharacteristic
550C24×C4—611no—
551C24×C4—611no—
552C24×C4C2×D6111yescharacteristic
553C22×C4⋊C4—611no—
554C22×C4⋊C4—611no—
555C22×C4⋊C4C2×D6111yescharacteristic
556C22×C4⋊C4C2×D6111yescharacteristic
557C22×C22⋊C4—611no—
558C22×C22⋊C4—611no—
559C22×C22⋊C4C2×D6111yescharacteristic
560C22×C22⋊C4C2×D6111yescharacteristic
561C22×C42—611no—
562C22×C42—611no—
563C22×C42—611no—
564C22×C42—611no—
565C22×C42—611no—
566C22×C42—611no—
567#385—618no—
568#385Dic6118yescomplemented
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—611no—
587C2×#95—611no—
588C2×#95—611no—
589C2×#95—1224no—
590C2×#95C2×D6111yescharacteristic
591C2×#95C2×D6111yescharacteristic
592C61#1381411yescharacteristic, complemented, Sylow
593C25C22×D6111yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—41no—
599C23×C4—41no—
600C23×C4—611no—
601C23×C4—611no—
602C23×C4—611no—
603C23×C4—611no—
604C23×C4—611no—
605C23×C4—611no—
606C23×C4—611no—
607C23×C4—611no—
608C23×C4—614no—
609C23×C4—614no—
610C23×C4—1222no—
611C23×C4—1222no—
612C23×C4—1222no—
613C23×C4—1222no—
614C23×C4—1222no—
615C23×C4—1222no—
616C23×C4—1222no—
617C23×C4—1222no—
618C23×C4—2441no—
619C23×C4—2441no—
620C23×C4—2441no—
621C23×C4—2441no—
622C23×C4C2×Dic6114yes—
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—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—614no—
634C2×C4⋊C4—614no—
635C2×C4⋊C4—1222no—
636C2×C4⋊C4—1222no—
637C2×C4⋊C4—2441no—
638C2×C4⋊C4—2441no—
639C2×C4⋊C4C2×Dic6114yescomplemented
640C2×C4⋊C4C2×Dic6114yescomplemented
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—614no—
644C2×C22⋊C4—614no—
645C2×C22⋊C4—614no—
646C2×C22⋊C4—614no—
647C2×C22⋊C4—1222no—
648C2×C22⋊C4—1222no—
649C2×C22⋊C4C4×D6114yes—
650C2×C22⋊C4C4×D6114yes—
651C2×C22⋊C4C2×Dic6114yes—
652C2×C22⋊C4C2×Dic6114yes—
653C2×C42—614no—
654C2×C42—614no—
655C2×C42—1222no—
656C2×C42—1222no—
657C2×C42—1222no—
658C2×C42—1222no—
659C2×C42—1222no—
660C2×C42—1222no—
661C2×C42—1222no—
662C2×C42—1222no—
663C2×C42—1222no—
664C2×C42—1222no—
665C2×C42—2441no—
666C2×C42—2441no—
667C2×C42—2441no—
668C2×C42—2441no—
669C2×C42—2441no—
670C2×C42—2441no—
671#95—614no—
672#95—614no—
673#95—614no—
674#95—614no—
675#95—614no—
676#95—1222no—
677#95—1222no—
678#95—1222no—
679#95—1222no—
680#95—1222no—
681#95—1222no—
682#95—1222no—
683#95—1222no—
684#95—1222no—
685#95—2441no—
686#95—2441no—
687#95C2×Dic6114yescomplemented
688#95C2×Dic6114yescomplemented
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×C4×D6112yes—
698C24C2×C4×D6112yes—
699C24D4×D6112yes—
700C24#1175822412yes—
701C24Q8×D6112yes—
702C24#1175822612yes—
703C24C22×Dic6112yes—
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—28no—
736C22×C4—28no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
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—612no—
757C22×C4—612no—
758C22×C4—1228no—
759C22×C4—1228no—
760C22×C4—1221no—
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—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1228no—
801C22×C4—1228no—
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×C4—2444no—
812C22×C4C2×C4×D6112yes—
813C22×C4C2×C4×D6112yes—
814C22×C4C2×C4×D6112yes—
815C22×C4C2×C4×D6112yes—
816C22×C4D4×D6112yes—
817C22×C4#1175822412yes—
818C22×C4C22×Dic6112yes—
819C22×C4C22×Dic6112yes—
820C22×C4C22×Dic6112yes—
821C22×C4C22×Dic6112yes—
822C22×C4C22×Dic6112yes—
823C22×C4C22×Dic6112yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—1228no—
827C4⋊C4—2444no—
828C22⋊C4—28no—
829C22⋊C4—6116no—
830C22⋊C4—1228no—
831C22⋊C4C4×Dic61116yescomplemented
832C42—1228no—
833C42—2444no—
834C42—2444no—
835C42—2444no—
836C42—2444no—
837C42—2444no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C2×C4×Dic6114yes—
867C23C4⋊C4×D6114yes—
868C23#1451973514yes—
869C23#1451973914yes—
870C23D4×Dic6114yes—
871C23#1451974214yes—
872C23Q8×Dic6114yes—
873C23C22×C4×D6111yescharacteristic
874C23C22×C4×D6111yescharacteristic
875C23C23×Dic6111yescharacteristic
876C23C2×D4×D6111yescharacteristic
877C23C2×D4×D6111yescharacteristic
878C23C2×Q8×D6111yescharacteristic
879C23#41×D6111yescharacteristic
880C23#41×D6111yescharacteristic
881C23C2×#1175822411yescharacteristic
882C23C2×#1175822411yescharacteristic
883C23C2×#1175822611yescharacteristic
884C23#1451982211yescharacteristic
885C23#1451982211yescharacteristic
886C23#1451982311yescharacteristic
887C23#1451982411yescharacteristic
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—416no—
916C2×C4—41no—
917C2×C4—41no—
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—614no—
929C2×C4—614no—
930C2×C4—614no—
931C2×C4—614no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—1222no—
935C2×C4—1222no—
936C2×C4—1222no—
937C2×C4—1222no—
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—24416no—
969C2×C4—24416no—
970C2×C4—2441no—
971C2×C4—2441no—
972C2×C4—2441no—
973C2×C4—2441no—
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×C4C2×C4×Dic6114yes—
987C2×C4C2×C4×Dic6114yes—
988C2×C4D4×Dic6114yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22C4⋊C4×Dic6118yescomplemented
1004C22C22×C4×Dic6111yescharacteristic
1005C22C2×C4⋊C4×D6111yescharacteristic
1006C22C2×#1451973511yescharacteristic
1007C22C4×D4×D6111yescharacteristic
1008C22C4×D4×D6111yescharacteristic
1009C22C2×#1451973911yescharacteristic
1010C22C2×D4×Dic6111yescharacteristic
1011C22C2×D4×Dic6111yescharacteristic
1012C22C2×#1451974211yescharacteristic
1013C22C2×Q8×Dic6111yescharacteristic
1014C22C4×#1175822411yescharacteristic
1015C22C4×#1175822411yescharacteristic
1016C22#41×Dic6111yescharacteristic
1017C22#1684023411yescharacteristic
1018C22#1684023411yescharacteristic
1019C22#1684023711yescharacteristic
1020C22#1684024111yescharacteristic
1021C22#1684024111yescharacteristic
1022C22#1684024511yescharacteristic
1023C22#1684039411yescharacteristic
1024C22#1684039911yescharacteristic
1025C22#1684039911yescharacteristic
1026C22#1684040311yescharacteristic
1027C22#1684040411yescharacteristic
1028C22#1684041011yescharacteristic
1029C22#1684042511yescharacteristic
1030C22#1684043511yescharacteristic
1031C22#1684043911yescharacteristic
1032C22#1684043911yescharacteristic
1033C22#1684044311yescharacteristic
1034C22#1684044911yescharacteristic
1035C22#1684045411yescharacteristic
1036C22#1684046611yescharacteristic
1037C22#1684046611yescharacteristic
1038C22#1684047011yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—1224no—
1046C4—1224no—
1047C4—1224no—
1048C4—1224no—
1049C4—2442no—
1050C4—2442no—
1051C4—2442no—
1052C4—2442no—
1053C2—28no—
1054C2C2×C4⋊C4×Dic6111yescharacteristic
1055C2C4×D4×Dic6111yescharacteristic
1056C2#2144818011yescharacteristic
1057C2#2144866611yescharacteristic
1058C2#2144867711yescharacteristic
1059C2#2144871711yescharacteristic
1060C2#2144872511yescharacteristic
1061C2#2144879511yescharacteristic
1062C2#2144880311yescharacteristic
1063C2#2144880911yescharacteristic
1064C2#2144881511yescharacteristic
1065C2#2144881911yescharacteristic
1066C2#2144882811yescharacteristic
1067C2#2144890011yescharacteristic
1068C2#2144890411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C61×#385C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#385D61
hypocenterC61#13814
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic61C2semidirect
7. #21444053C2semidirect
8. #21444053C2semidirect
9. #21444051C2semidirect
10. #21444051C2semidirect
11. #21444048C2semidirect
12. #21444044C2semidirect
14. #95×Dic61C2semidirect
28. #16839637C4semidirect
31. C22⋊C4×Dic61C4semidirect
55. C61×#385C4semidirect
84. C2×C4⋊Dic61C2×C4semidirect
85. C2×C4⋊Dic61C2×C4semidirect
108. C2×C4×Dic61C2×C4semidirect
109. C2×C4×Dic61C2×C4semidirect
121. #14519684C2×C4semidirect
122. #14519684C2×C4semidirect
123. #14519684C2×C4semidirect
124. #14519684C2×C4semidirect
144. C2×C4⋊C4×C61C2×C4semidirect
145. C2×C4⋊C4×C61C2×C4semidirect
152. #95×C61C2×C4semidirect
153. #95×C61C2×C4semidirect
292. C22⋊C4×C61C42semidirect
294. C22⋊Dic61C4⋊C4semidirect
469. C22×C61C4×C4⋊C4semidirect
568. #385Dic61semidirect
592. C61#13814semidirect
639. C2×C4⋊C4C2×Dic61semidirect
640. C2×C4⋊C4C2×Dic61semidirect
687. #95C2×Dic61semidirect
688. #95C2×Dic61semidirect
831. C22⋊C4C4×Dic61semidirect
1003. C22C4⋊C4×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396372
C2×C4⋊C4×Dic612
C2×C22⋊C4×Dic612
C2×C4×C22⋊Dic612
C22×#145196842
#214440532
#214440512
#214440482
#214440442
#214440412
#95×Dic612
C2×C61×#3852
#1381461