Finite Group Databasebeta

← #29601600

Subgroups — #29601600

Order 15616.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839655C211yesmaximal, characteristic
2C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic61C211yesmaximal, characteristic
4C2×C22⋊C4×Dic61C211yesmaximal, characteristic
5#21444056C211yesmaximal, characteristic
6#21444056C211yesmaximal, characteristic
7#21444053C211yesmaximal, characteristic, complemented
8#21444051C211yesmaximal, characteristic, complemented
9#21444044C211yesmaximal, characteristic, complemented
10#21444044C211yesmaximal, characteristic, complemented
11#21444041C211yesmaximal, characteristic
12C4×#14519684C211yesmaximal, characteristic, complemented
13C4×#14519684C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28#16839655C418yescomplemented
29C4⋊C4×Dic61—24no—
30C22⋊C4×Dic61—24no—
31C22⋊C4×Dic61C418yescomplemented
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
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
48C22×C4⋊C4×C61C2211yescharacteristic
49C22×C22⋊C4×C61C2211yescharacteristic
50C22×C22⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C61×#388C418yescomplemented
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C23×Dic61—22no—
57C23×Dic61—22no—
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61—41no—
61C23×Dic61—41no—
62C23×Dic61C2×C414yes—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—22no—
73C2×C4⋊Dic61C2×C414yescomplemented
74C2×C22⋊Dic61—22no—
75C2×C22⋊Dic61—22no—
76C2×C22⋊Dic61—22no—
77C2×C22⋊Dic61—22no—
78C2×C22⋊Dic61—41no—
79C2×C22⋊Dic61—41no—
80C2×C22⋊Dic61C2×C414yes—
81C2×C22⋊Dic61C2×C414yes—
82C2×C22⋊Dic61C2×C414yes—
83C2×C4×Dic61—22no—
84C2×C4×Dic61—22no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61—22no—
87C2×C4×Dic61—22no—
88C2×C4×Dic61—22no—
89C2×C4×Dic61—22no—
90C2×C4×Dic61—22no—
91C2×C4×Dic61—22no—
92C2×C4×Dic61—22no—
93C2×C4×Dic61—41no—
94C2×C4×Dic61—41no—
95C2×C4×Dic61—41no—
96C2×C4×Dic61—41no—
97C2×C4×Dic61—41no—
98C2×C4×Dic61—41no—
99C2×C4×Dic61—41no—
100C2×C4×Dic61—41no—
101C2×C4×Dic61C2×C414yes—
102C2×C4×Dic61C2×C414yes—
103C2×C4×Dic61C2×C414yescomplemented
104#14519684—22no—
105#14519684—22no—
106#14519684—22no—
107#14519684—22no—
108#14519684—22no—
109#14519684—22no—
110#14519684—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—41no—
114#14519684—41no—
115#14519684C2×C414yes—
116#14519684C2×C414yes—
117#14519684C2×C414yescomplemented
118#14519684C2×C414yescomplemented
119#14519684D414yes—
120C25×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61—22no—
128C2×C4⋊C4×C61—22no—
129C2×C4⋊C4×C61C2×C414yescomplemented
130C2×C22⋊C4×C61—22no—
131C2×C22⋊C4×C61—22no—
132C2×C22⋊C4×C61—41no—
133C2×C22⋊C4×C61—41no—
134C2×C22⋊C4×C61C2×C414yes—
135C2×C22⋊C4×C61C2×C414yes—
136C2×C22⋊C4×C61C2×C414yes—
137C2×C22⋊C4×C61C2×C414yes—
138C2×C22⋊C4×C61C2×C414yes—
139C2×C42×C61—41no—
140C2×C42×C61—41no—
141C2×C42×C61C2×C414yescomplemented
142#95×C61C2×C414yescomplemented
143#95×C61C2×C414yescomplemented
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61C22×C412yes—
157C24×C61C22×C412yes—
158C24×C61C22×C412yes—
159C24×C61C2411yescharacteristic
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
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×C61C22×C412yes—
191C22×C4×C61C22×C412yes—
192C22×C4×C61C22×C412yes—
193C22×C4×C61C22×C412yes—
194C22×C4×C61C22×C412yes—
195C22×C4×C61C22×C412yes—
196C22×C4×C61C22×C412yes—
197C22×C4×C61C22×C412yes—
198C22×C4×C61C22×C412yes—
199C22×C4×C61C22×C412yes—
200C22×C4×C61C2×D412yes—
201C22×C4×C61#4112yes—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
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—28no—
243C22×Dic61—28no—
244C22×Dic61—44no—
245C22×Dic61—44no—
246C22×Dic61—44no—
247C22×Dic61—44no—
248C22×Dic61—44no—
249C22×Dic61C22×C412yes—
250C22×Dic61C22×C412yes—
251C22×Dic61C22×C412yes—
252C22×Dic61C22×C412yes—
253C22×Dic61C22×C412yes—
254C22×Dic61C22×C412yes—
255C22×Dic61C22×C412yes—
256C22×Dic61C22×C412yes—
257C22×Dic61C2×D412yes—
258C22×Dic61C2×D412yes—
259C22×Dic61#4112yes—
260C22×Dic61#4112yes—
261C22×Dic61#4112yes—
262C22×Dic61#4112yes—
263C22×Dic61#4112yes—
264C22×Dic61#4112yes—
265C4⋊C4×C61—28no—
266C22⋊C4×C61—28no—
267C22⋊C4×C61—44no—
268C22⋊C4×C61C42116yescomplemented
269C42×C61—44no—
270C22⋊Dic61—28no—
271C22⋊Dic61—28no—
272C22⋊Dic61—44no—
273C4⋊Dic61—28no—
274C4×Dic61—28no—
275C4×Dic61—44no—
276C4×Dic61—44no—
277C4×Dic61—44no—
278C4×Dic61—44no—
279C4×Dic61—44no—
280C4×Dic61—44no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61C2×C4214yes—
316C23×C61C23×C411yescharacteristic
317C23×C61C23×C411yescharacteristic
318C23×C61C23×C411yescharacteristic
319C23×C61C22×D411yescharacteristic
320C23×C61C2×#4111yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61C2×#4111yescharacteristic
324C23×C61C2×#4111yescharacteristic
325C23×C61C2×#4111yescharacteristic
326C23×C61C2×#4111yescharacteristic
327C23×C61H(5,𝔽2)11yescharacteristic
328C23×C61H(5,𝔽2)11yescharacteristic
329C23×C61H(5,𝔽2)11yescharacteristic
330C23×C612−1+411yescharacteristic
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61C2×C4214yes—
371C2×C4×C61C2×C4214yes—
372C2×C4×C61C4×D414yes—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—22no—
395C2×Dic61—22no—
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—416no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61#11714yes—
427C2×Dic61#11714yes—
428C2×Dic61C4×D414yes—
429C2×Dic61C4×D414yes—
430#13822—611nomaximal, Sylow
431C22×C61—24no—
432C22×C61—24no—
433C22×C61—24no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—42no—
437C22×C61—42no—
438C22×C61—42no—
439C22×C61—42no—
440C22×C61—42no—
441C22×C61—42no—
442C22×C61—42no—
443C22×C61—42no—
444C22×C61—42no—
445C22×C61—42no—
446C22×C61C22×C4211yescharacteristic
447C22×C61C2×#11711yescharacteristic
448C22×C61C2×#11711yescharacteristic
449C22×C61C2×C4×D411yescharacteristic
450C22×C61C2×C4×D411yescharacteristic
451C22×C61C2×C4×D411yescharacteristic
452C22×C61C4×#4111yescharacteristic
453C22×C61C4×#4111yescharacteristic
454C22×C61C4×#4111yescharacteristic
455C22×C61C4×#4111yescharacteristic
456C22×C61C4×#4111yescharacteristic
457C22×C61C4×#4111yescharacteristic
458C22×C61C4×#4111yescharacteristic
459C22×C61#51811yescharacteristic
460C22×C61#51811yescharacteristic
461C22×C61#51811yescharacteristic
462C22×C61#52011yescharacteristic
463C22×C61#52011yescharacteristic
464C22×C61#52011yescharacteristic
465C22×C61#54611yescharacteristic
466C22×C61#54611yescharacteristic
467C22×C61#54611yescharacteristic
468C22×C61#54811yescharacteristic
469C22×C61#55111yescharacteristic
470C22×C61#55111yescharacteristic
471C22×C61#55211yescharacteristic
472C22×C61#55311yescharacteristic
473C22×C61#55311yescharacteristic
474C22×C61#55311yescharacteristic
475C22×C61#55311yescharacteristic
476C22×C61#55311yescharacteristic
477C22×C61#55611yescharacteristic
478C22×C61#55611yescharacteristic
479C22×C61#55911yescharacteristic
480C22×C61#55911yescharacteristic
481C4×C61—24no—
482C4×C61—24no—
483C4×C61—24no—
484C4×C61—42no—
485C4×C61—42no—
486C4×C61—42no—
487Dic61—24no—
488Dic61—24no—
489Dic61—24no—
490Dic61—24no—
491Dic61—42no—
492Dic61—42no—
493Dic61—42no—
494Dic61—42no—
495C2×#388—611no—
496C2×#388D6111yescharacteristic
497C2×C4×C4⋊C4—611no—
498C2×C4×C22⋊C4—611no—
499C2×C4×C22⋊C4—611no—
500#1437—611no—
501#1437—611no—
502#1436—611no—
503#1436—611no—
504#1434—611no—
505#1434—611no—
506C22⋊#95—611no—
507C4×#95—611no—
508C4×#95—611no—
509C4×#95—611no—
510C2×C61—44no—
511C2×C61C4×#11711yescharacteristic
512C2×C61C42×D411yescharacteristic
513C2×C61#227511yescharacteristic
514C2×C61#234211yescharacteristic
515C2×C61#234711yescharacteristic
516C2×C61#235211yescharacteristic
517C2×C61#235711yescharacteristic
518C2×C61#236411yescharacteristic
519C2×C61#236411yescharacteristic
520C2×C61#236711yescharacteristic
521C2×C61#236711yescharacteristic
522C2×C61#237311yescharacteristic
523C2×C61#237311yescharacteristic
524C2×C61#237411yescharacteristic
525C2×C61#237411yescharacteristic
526C24×C4—611no—
527C22×C4⋊C4—611no—
528C22×C4⋊C4C2×D6111yescharacteristic
529C22×C22⋊C4—611no—
530C22×C22⋊C4—611no—
531C22×C22⋊C4—611no—
532C22×C22⋊C4C2×D6111yescharacteristic
533C22×C22⋊C4C2×D6111yescharacteristic
534C22×C22⋊C4C2×D6111yescharacteristic
535C22×C42—611no—
536C22×C42—611no—
537C22×C42—611no—
538C22×C42—611no—
539C22×C42—611no—
540C22×C42—611no—
541C22×C42—611no—
542C22×C42C2×D6111yescharacteristic
543#388—618no—
544#388Dic6118yescomplemented
545C4×C4⋊C4—1224no—
546C4×C22⋊C4—618no—
547C4×C22⋊C4—1224no—
548C2×#95—611no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95—611no—
555C2×#95—611no—
556C2×#95—611no—
557C2×#95—611no—
558C2×#95—611no—
559C2×#95—611no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95C2×D6111yescharacteristic
565C2×#95C2×D6111yescharacteristic
566C61#1382211yescharacteristic, complemented, Sylow
567C25C22×D6111yescharacteristic
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—614no—
577C23×C4—1222no—
578C23×C4—1222no—
579C23×C4—1222no—
580C23×C4—1222no—
581C23×C4—2441no—
582C23×C4—2441no—
583C23×C4C22×D6111yescharacteristic
584C23×C4C22×D6111yescharacteristic
585C23×C4C22×D6111yescharacteristic
586C23×C4C22×D6111yescharacteristic
587C23×C4C22×D6111yescharacteristic
588C23×C4C22×D6111yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—614no—
592C2×C4⋊C4—1222no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4C2×Dic6114yescomplemented
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—614no—
600C2×C22⋊C4—614no—
601C2×C22⋊C4—614no—
602C2×C22⋊C4—1222no—
603C2×C22⋊C4—1222no—
604C2×C22⋊C4—1222no—
605C2×C22⋊C4—1222no—
606C2×C22⋊C4—2441no—
607C2×C22⋊C4—2441no—
608C2×C22⋊C4C4×D6114yes—
609C2×C22⋊C4C4×D6114yes—
610C2×C22⋊C4C2×Dic6114yes—
611C2×C22⋊C4C2×Dic6114yes—
612C2×C22⋊C4C2×Dic6114yes—
613C2×C42—41no—
614C2×C42—41no—
615C2×C42—614no—
616C2×C42—614no—
617C2×C42—614no—
618C2×C42—1222no—
619C2×C42—1222no—
620C2×C42—1222no—
621C2×C42—1222no—
622C2×C42—1222no—
623C2×C42—1222no—
624C2×C42—1222no—
625C2×C42—1222no—
626C2×C42—1222no—
627C2×C42—1222no—
628C2×C42—2441no—
629C2×C42—2441no—
630C2×C42—2441no—
631C2×C42—2441no—
632C2×C42—2441no—
633C2×C42—2441no—
634C2×C42—2441no—
635C2×C42—2441no—
636C2×C42C2×Dic6114yescomplemented
637#95—614no—
638#95—614no—
639#95—614no—
640#95—614no—
641#95—614no—
642#95—1222no—
643#95—1222no—
644#95—1222no—
645#95—1222no—
646#95—1222no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650#95—1222no—
651#95—2441no—
652#95—2441no—
653#95C2×Dic6114yescomplemented
654#95C2×Dic6114yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×C4×D6112yes—
668C24C2×C4×D6112yes—
669C24C22×Dic6112yes—
670C24C23×D6111yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—612no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4—612no—
710C22×C4—612no—
711C22×C4—612no—
712C22×C4—612no—
713C22×C4—612no—
714C22×C4—612no—
715C22×C4—612no—
716C22×C4—612no—
717C22×C4—1228no—
718C22×C4—1228no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—2444no—
760C22×C4—2444no—
761C22×C4—2444no—
762C22×C4—2444no—
763C22×C4—2444no—
764C22×C4C2×C4×D6112yes—
765C22×C4C2×C4×D6112yes—
766C22×C4C2×C4×D6112yes—
767C22×C4C2×C4×D6112yes—
768C22×C4D4×D6112yes—
769C22×C4#1175822412yes—
770C22×C4C22×Dic6112yes—
771C22×C4C22×Dic6112yes—
772C22×C4C22×Dic6112yes—
773C22×C4C22×Dic6112yes—
774C22×C4C22×Dic6112yes—
775C22×C4C22×Dic6112yes—
776C4⋊C4—28no—
777C4⋊C4—1228no—
778C22⋊C4—28no—
779C22⋊C4—44no—
780C22⋊C4—1228no—
781C22⋊C4—1228no—
782C22⋊C4—2444no—
783C22⋊C4C4×Dic61116yescomplemented
784C42—44no—
785C42—1228no—
786C42—2444no—
787C42—2444no—
788C42—2444no—
789C42—2444no—
790C42—2444no—
791C42—2444no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4×Dic6114yes—
827C23C22×C4×D6111yescharacteristic
828C23C22×C4×D6111yescharacteristic
829C23C23×Dic6111yescharacteristic
830C23C2×D4×D6111yescharacteristic
831C23#41×D6111yescharacteristic
832C23#41×D6111yescharacteristic
833C23#41×D6111yescharacteristic
834C23#41×D6111yescharacteristic
835C23#41×D6111yescharacteristic
836C23#41×D6111yescharacteristic
837C23C2×#1175822411yescharacteristic
838C23#1451982211yescharacteristic
839C23#1451982211yescharacteristic
840C23#1451982311yescharacteristic
841C23#1451982411yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—614no—
882C2×C4—614no—
883C2×C4—614no—
884C2×C4—614no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1222no—
907C2×C4—1222no—
908C2×C4—1222no—
909C2×C4—1222no—
910C2×C4—1222no—
911C2×C4—1222no—
912C2×C4—1222no—
913C2×C4—1222no—
914C2×C4—1222no—
915C2×C4—1222no—
916C2×C4—1222no—
917C2×C4—1222no—
918C2×C4—1222no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—24416no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4C2×C4×Dic6114yes—
939C2×C4C2×C4×Dic6114yes—
940C2×C4D4×Dic6114yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4×Dic6111yescharacteristic
957C22#117×D6111yescharacteristic
958C22#117×D6111yescharacteristic
959C22C4×D4×D6111yescharacteristic
960C22C4×D4×D6111yescharacteristic
961C22C2×D4×Dic6111yescharacteristic
962C22C4×#1175822411yescharacteristic
963C22C4×#1175822411yescharacteristic
964C22#1684023011yescharacteristic
965C22#1684023011yescharacteristic
966C22#41×Dic6111yescharacteristic
967C22#41×Dic6111yescharacteristic
968C22#41×Dic6111yescharacteristic
969C22#1684023411yescharacteristic
970C22#1684023411yescharacteristic
971C22#1684023711yescharacteristic
972C22#1684024111yescharacteristic
973C22#1684024111yescharacteristic
974C22#1684024511yescharacteristic
975C22#1684040111yescharacteristic
976C22#1684040111yescharacteristic
977C22#1684040511yescharacteristic
978C22#1684042011yescharacteristic
979C22#1684043711yescharacteristic
980C22#1684044011yescharacteristic
981C22#1684044811yescharacteristic
982C22#1684045511yescharacteristic
983C22#1684045511yescharacteristic
984C22#1684045711yescharacteristic
985C22#1684045711yescharacteristic
986C22#1684046311yescharacteristic
987C22#1684047911yescharacteristic
988C22#1684048111yescharacteristic
989C22#1684049411yescharacteristic
990C22#1684049611yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—1224no—
998C4—1224no—
999C4—1224no—
1000C4—1224no—
1001C4—2442no—
1002C4—2442no—
1003C4—2442no—
1004C4—2442no—
1005C2—44no—
1006C2#117×Dic6111yescharacteristic
1007C2C4×D4×Dic6111yescharacteristic
1008C2#2144818011yescharacteristic
1009C2#2144866711yescharacteristic
1010C2#2144870911yescharacteristic
1011C2#2144874711yescharacteristic
1012C2#2144878911yescharacteristic
1013C2#2144886311yescharacteristic
1014C2#2144887111yescharacteristic
1015C2#2144888511yescharacteristic
1016C2#2144889411yescharacteristic
1017C2#2144893711yescharacteristic
1018C2#2144894311yescharacteristic
1019C2#2144894711yescharacteristic
1020C2#2144895511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#388D61
hypocenterC61#13822
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic61C2semidirect
7. #21444053C2semidirect
8. #21444051C2semidirect
9. #21444044C2semidirect
10. #21444044C2semidirect
12. C4×#14519684C2semidirect
13. C4×#14519684C2semidirect
14. #95×Dic61C2semidirect
28. #16839655C4semidirect
31. C22⋊C4×Dic61C4semidirect
53. C61×#388C4semidirect
73. C2×C4⋊Dic61C2×C4semidirect
103. C2×C4×Dic61C2×C4semidirect
117. #14519684C2×C4semidirect
118. #14519684C2×C4semidirect
129. C2×C4⋊C4×C61C2×C4semidirect
141. C2×C42×C61C2×C4semidirect
142. #95×C61C2×C4semidirect
143. #95×C61C2×C4semidirect
268. C22⋊C4×C61C42semidirect
544. #388Dic61semidirect
566. C61#13822semidirect
594. C2×C4⋊C4C2×Dic61semidirect
636. C2×C42C2×Dic61semidirect
653. #95C2×Dic61semidirect
654. #95C2×Dic61semidirect
783. C22⋊C4C4×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396552
C2×C4⋊C4×Dic612
C2×C22⋊C4×Dic612
#214440562
#214440532
#214440512
#214440442
#214440412
C4×#145196842
#95×Dic612
C2×C61×#3882
#1382261