Finite Group Databasebeta

← #29601344

Subgroups — #29601344

Order 15616.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839655C211yesmaximal, characteristic
2C2×C22⋊C4×Dic61C211yesmaximal, characteristic
3#21444056C211yesmaximal, characteristic
4#21444056C211yesmaximal, characteristic
5#21444053C211yesmaximal, characteristic, complemented
6#21444051C211yesmaximal, characteristic, complemented
7#21444048C211yesmaximal, characteristic, complemented
8#21444046C211yesmaximal, characteristic, complemented
9#21444044C211yesmaximal, characteristic, complemented
10#21444044C211yesmaximal, characteristic, complemented
11#21444041C211yesmaximal, characteristic
12#21444041C211yesmaximal, characteristic
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
26#16839655C418yescomplemented
27C22⋊C4×Dic61C418yescomplemented
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
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
46C22×C4⋊C4×C61C2211yescharacteristic
47C22×C22⋊C4×C61C2211yescharacteristic
48C22×C22⋊C4×C61C2211yescharacteristic
49C22×C22⋊C4×C61C2211yescharacteristic
50C22×C42×C61C2211yescharacteristic
51C61×#388C418yescomplemented
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C23×Dic61—22no—
55C23×Dic61—22no—
56C23×Dic61—41no—
57C23×Dic61—41no—
58C23×Dic61—41no—
59C23×Dic61—41no—
60C23×Dic61C2×C414yes—
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C2×C4⋊Dic61—41no—
70C2×C4⋊Dic61—41no—
71C2×C4⋊Dic61C2×C414yescomplemented
72C2×C22⋊Dic61—22no—
73C2×C22⋊Dic61—22no—
74C2×C22⋊Dic61—41no—
75C2×C22⋊Dic61—41no—
76C2×C22⋊Dic61—41no—
77C2×C22⋊Dic61—41no—
78C2×C22⋊Dic61C2×C414yes—
79C2×C22⋊Dic61C2×C414yes—
80C2×C22⋊Dic61C2×C414yes—
81C2×C4×Dic61—22no—
82C2×C4×Dic61—22no—
83C2×C4×Dic61—41no—
84C2×C4×Dic61—41no—
85C2×C4×Dic61—41no—
86C2×C4×Dic61—41no—
87C2×C4×Dic61—41no—
88C2×C4×Dic61—41no—
89C2×C4×Dic61—41no—
90C2×C4×Dic61—41no—
91C2×C4×Dic61—41no—
92C2×C4×Dic61—41no—
93C2×C4×Dic61C2×C414yes—
94C2×C4×Dic61C2×C414yes—
95C2×C4×Dic61C2×C414yescomplemented
96#14519684—22no—
97#14519684—22no—
98#14519684—22no—
99#14519684—22no—
100#14519684—22no—
101#14519684—22no—
102#14519684—41no—
103#14519684—41no—
104#14519684—41no—
105#14519684—41no—
106#14519684—41no—
107#14519684—41no—
108#14519684—41no—
109#14519684—41no—
110#14519684C2×C414yes—
111#14519684C2×C414yes—
112#14519684C2×C414yescomplemented
113#14519684C2×C414yescomplemented
114C25×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C23×C4×C61C2311yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61—41no—
122C2×C4⋊C4×C61—41no—
123C2×C4⋊C4×C61C2×C414yescomplemented
124C2×C22⋊C4×C61—41no—
125C2×C22⋊C4×C61—41no—
126C2×C22⋊C4×C61—41no—
127C2×C22⋊C4×C61—41no—
128C2×C22⋊C4×C61C2×C414yes—
129C2×C22⋊C4×C61C2×C414yes—
130C2×C22⋊C4×C61C2×C414yes—
131C2×C22⋊C4×C61C2×C414yes—
132C2×C22⋊C4×C61C2×C414yes—
133C2×C42×C61—41no—
134C2×C42×C61—41no—
135C2×C42×C61C2×C414yescomplemented
136#95×C61C2×C414yescomplemented
137#95×C61C2×C414yescomplemented
138C24×C61—21no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—21no—
142C24×C61—21no—
143C24×C61—21no—
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61C22×C412yes—
151C24×C61C22×C412yes—
152C24×C61C22×C412yes—
153C24×C61C2411yescharacteristic
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
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×C61C22×C412yes—
187C22×C4×C61C22×C412yes—
188C22×C4×C61C22×C412yes—
189C22×C4×C61C22×C412yes—
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×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
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—28no—
241C22×Dic61—44no—
242C22×Dic61—44no—
243C22×Dic61—44no—
244C22×Dic61—44no—
245C22×Dic61—44no—
246C22×Dic61—44no—
247C22×Dic61C22×C412yes—
248C22×Dic61C22×C412yes—
249C22×Dic61C22×C412yes—
250C22×Dic61C22×C412yes—
251C22×Dic61C22×C412yes—
252C22×Dic61C22×C412yes—
253C22×Dic61C22×C412yes—
254C22×Dic61C22×C412yes—
255C22×Dic61#4112yes—
256C22×Dic61#4112yes—
257C22×Dic61#4112yes—
258C22×Dic61#4112yes—
259C4⋊C4×C61—44no—
260C22⋊C4×C61—44no—
261C22⋊C4×C61—44no—
262C22⋊C4×C61C42116yescomplemented
263C42×C61—44no—
264C22⋊Dic61—28no—
265C22⋊Dic61—44no—
266C22⋊Dic61—44no—
267C4⋊Dic61—44no—
268C4×Dic61—44no—
269C4×Dic61—44no—
270C4×Dic61—44no—
271C4×Dic61—44no—
272C4×Dic61—44no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
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—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
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×C61C2×C4214yes—
308C23×C61C23×C411yescharacteristic
309C23×C61C23×C411yescharacteristic
310C23×C61C23×C411yescharacteristic
311C23×C61C2×#4111yescharacteristic
312C23×C61C2×#4111yescharacteristic
313C23×C61C2×#4111yescharacteristic
314C23×C61C2×#4111yescharacteristic
315C23×C61H(5,𝔽2)11yescharacteristic
316C23×C61H(5,𝔽2)11yescharacteristic
317C23×C61H(5,𝔽2)11yescharacteristic
318C23×C61H(5,𝔽2)11yescharacteristic
319C23×C61H(5,𝔽2)11yescharacteristic
320C23×C61H(5,𝔽2)11yescharacteristic
321C23×C612−1+411yescharacteristic
322C23×C612−1+411yescharacteristic
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
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—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61C2×C4214yes—
364C2×C4×C61C2×C4214yes—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
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—416no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
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#11714yes—
421C2×Dic61#11714yes—
422#13788—611nomaximal, Sylow
423C22×C61—24no—
424C22×C61—24no—
425C22×C61—24no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—42no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—42no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—42no—
437C22×C61—42no—
438C22×C61C22×C4211yescharacteristic
439C22×C61C2×#11711yescharacteristic
440C22×C61C2×#11711yescharacteristic
441C22×C61C4×#4111yescharacteristic
442C22×C61C4×#4111yescharacteristic
443C22×C61C4×#4111yescharacteristic
444C22×C61C4×#4111yescharacteristic
445C22×C61#51811yescharacteristic
446C22×C61#51811yescharacteristic
447C22×C61#51811yescharacteristic
448C22×C61#51811yescharacteristic
449C22×C61#51811yescharacteristic
450C22×C61#51811yescharacteristic
451C22×C61#52011yescharacteristic
452C22×C61#52011yescharacteristic
453C22×C61#52011yescharacteristic
454C22×C61#52011yescharacteristic
455C22×C61#52011yescharacteristic
456C22×C61#52011yescharacteristic
457C22×C61#53811yescharacteristic
458C22×C61#53811yescharacteristic
459C22×C61#53811yescharacteristic
460C22×C61#53811yescharacteristic
461C22×C61#53811yescharacteristic
462C22×C61#53811yescharacteristic
463C22×C61#53911yescharacteristic
464C22×C61#53911yescharacteristic
465C22×C61#54011yescharacteristic
466C22×C61#54011yescharacteristic
467C22×C61#54011yescharacteristic
468C22×C61#54111yescharacteristic
469C22×C61#54211yescharacteristic
470C22×C61#54211yescharacteristic
471C22×C61#54211yescharacteristic
472C22×C61#54211yescharacteristic
473C4×C61—24no—
474C4×C61—24no—
475C4×C61—42no—
476C4×C61—42no—
477C4×C61—42no—
478C4×C61—42no—
479Dic61—24no—
480Dic61—24no—
481Dic61—42no—
482Dic61—42no—
483Dic61—42no—
484Dic61—42no—
485Dic61—42no—
486Dic61—42no—
487C2×#388—611no—
488C2×#388D6111yescharacteristic
489C2×C4×C22⋊C4—611no—
490#1437—611no—
491#1437—611no—
492#1436—611no—
493#1436—611no—
494C4⋊#95—611no—
495#1434—611no—
496#1434—611no—
497#1434—611no—
498C22⋊#95—611no—
499C22⋊#95—611no—
500C4×#95—611no—
501C4×#95—611no—
502C2×C61—44no—
503C2×C61C4×#11711yescharacteristic
504C2×C61#227511yescharacteristic
505C2×C61#227511yescharacteristic
506C2×C61#231211yescharacteristic
507C2×C61#231411yescharacteristic
508C2×C61#231811yescharacteristic
509C2×C61#231911yescharacteristic
510C2×C61#233311yescharacteristic
511C2×C61#233311yescharacteristic
512C2×C61#233411yescharacteristic
513C2×C61#233411yescharacteristic
514C2×C61#233511yescharacteristic
515C2×C61#233511yescharacteristic
516C2×C61#233711yescharacteristic
517C2×C61#233711yescharacteristic
518C24×C4—611no—
519C22×C4⋊C4—611no—
520C22×C4⋊C4C2×D6111yescharacteristic
521C22×C22⋊C4—611no—
522C22×C22⋊C4—611no—
523C22×C22⋊C4—611no—
524C22×C22⋊C4C2×D6111yescharacteristic
525C22×C22⋊C4C2×D6111yescharacteristic
526C22×C22⋊C4C2×D6111yescharacteristic
527C22×C42—611no—
528C22×C42—611no—
529C22×C42—611no—
530C22×C42—611no—
531C22×C42—611no—
532C22×C42C2×D6111yescharacteristic
533#388—618no—
534#388Dic6118yescomplemented
535C4×C22⋊C4—618no—
536C2×#95—611no—
537C2×#95—611no—
538C2×#95—611no—
539C2×#95—611no—
540C2×#95—611no—
541C2×#95—611no—
542C2×#95—611no—
543C2×#95—611no—
544C2×#95—611no—
545C2×#95—611no—
546C2×#95—611no—
547C2×#95—611no—
548C2×#95—611no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95C2×D6111yescharacteristic
555C2×#95C2×D6111yescharacteristic
556C61#1378811yescharacteristic, complemented, Sylow
557C25C22×D6111yescharacteristic
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—611no—
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—614no—
567C23×C4—1222no—
568C23×C4—1222no—
569C23×C4—2441no—
570C23×C4—2441no—
571C23×C4—2441no—
572C23×C4—2441no—
573C23×C4C22×D6111yescharacteristic
574C23×C4C22×D6111yescharacteristic
575C23×C4C22×D6111yescharacteristic
576C23×C4C22×D6111yescharacteristic
577C23×C4C22×D6111yescharacteristic
578C23×C4C22×D6111yescharacteristic
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—614no—
582C2×C4⋊C4—2441no—
583C2×C4⋊C4—2441no—
584C2×C4⋊C4C2×Dic6114yescomplemented
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—614no—
590C2×C22⋊C4—614no—
591C2×C22⋊C4—614no—
592C2×C22⋊C4—1222no—
593C2×C22⋊C4—1222no—
594C2×C22⋊C4—2441no—
595C2×C22⋊C4—2441no—
596C2×C22⋊C4—2441no—
597C2×C22⋊C4—2441no—
598C2×C22⋊C4C4×D6114yes—
599C2×C22⋊C4C4×D6114yes—
600C2×C22⋊C4C2×Dic6114yes—
601C2×C22⋊C4C2×Dic6114yes—
602C2×C22⋊C4C2×Dic6114yes—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—614no—
606C2×C42—614no—
607C2×C42—614no—
608C2×C42—1222no—
609C2×C42—1222no—
610C2×C42—2441no—
611C2×C42—2441no—
612C2×C42—2441no—
613C2×C42—2441no—
614C2×C42—2441no—
615C2×C42—2441no—
616C2×C42—2441no—
617C2×C42—2441no—
618C2×C42—2441no—
619C2×C42—2441no—
620C2×C42C2×Dic6114yescomplemented
621#95—614no—
622#95—614no—
623#95—614no—
624#95—614no—
625#95—1222no—
626#95—1222no—
627#95—1222no—
628#95—1222no—
629#95—1222no—
630#95—1222no—
631#95—2441no—
632#95—2441no—
633#95—2441no—
634#95—2441no—
635#95—2441no—
636#95—2441no—
637#95—2441no—
638#95—2441no—
639#95C2×Dic6114yescomplemented
640#95C2×Dic6114yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C4×D6112yes—
654C24C2×C4×D6112yes—
655C24C22×Dic6112yes—
656C24C23×D6111yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
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—612no—
690C22×C4—612no—
691C22×C4—612no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—612no—
695C22×C4—612no—
696C22×C4—612no—
697C22×C4—612no—
698C22×C4—612no—
699C22×C4—612no—
700C22×C4—612no—
701C22×C4—1228no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
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—2444no—
747C22×C4—2444no—
748C22×C4—2444no—
749C22×C4—2444no—
750C22×C4—2444no—
751C22×C4—2444no—
752C22×C4C2×C4×D6112yes—
753C22×C4C2×C4×D6112yes—
754C22×C4C2×C4×D6112yes—
755C22×C4C2×C4×D6112yes—
756C22×C4C22×Dic6112yes—
757C22×C4C22×Dic6112yes—
758C22×C4C22×Dic6112yes—
759C22×C4C22×Dic6112yes—
760C22×C4C22×Dic6112yes—
761C22×C4C22×Dic6112yes—
762C4⋊C4—44no—
763C4⋊C4—2444no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—1228no—
767C22⋊C4—2444no—
768C22⋊C4—2444no—
769C22⋊C4C4×Dic61116yescomplemented
770C42—44no—
771C42—2444no—
772C42—2444no—
773C42—2444no—
774C42—2444no—
775C42—2444no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4×Dic6114yes—
811C23C22×C4×D6111yescharacteristic
812C23C22×C4×D6111yescharacteristic
813C23C23×Dic6111yescharacteristic
814C23#41×D6111yescharacteristic
815C23#41×D6111yescharacteristic
816C23#41×D6111yescharacteristic
817C23#41×D6111yescharacteristic
818C23#1451982211yescharacteristic
819C23#1451982211yescharacteristic
820C23#1451982211yescharacteristic
821C23#1451982211yescharacteristic
822C23#1451982311yescharacteristic
823C23#1451982311yescharacteristic
824C23#1451982411yescharacteristic
825C23#1451982411yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
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—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—614no—
867C2×C4—614no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
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—24416no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4C2×C4×Dic6114yes—
924C2×C4C2×C4×Dic6114yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4×Dic6111yescharacteristic
941C22#117×D6111yescharacteristic
942C22#117×D6111yescharacteristic
943C22#1684023011yescharacteristic
944C22#1684023011yescharacteristic
945C22#41×Dic6111yescharacteristic
946C22#41×Dic6111yescharacteristic
947C22#1684023411yescharacteristic
948C22#1684023411yescharacteristic
949C22#1684023411yescharacteristic
950C22#1684023411yescharacteristic
951C22#1684023711yescharacteristic
952C22#1684023711yescharacteristic
953C22#1684024111yescharacteristic
954C22#1684024111yescharacteristic
955C22#1684024111yescharacteristic
956C22#1684024111yescharacteristic
957C22#1684024511yescharacteristic
958C22#1684024511yescharacteristic
959C22#1684034411yescharacteristic
960C22#1684034411yescharacteristic
961C22#1684034611yescharacteristic
962C22#1684034611yescharacteristic
963C22#1684034811yescharacteristic
964C22#1684035111yescharacteristic
965C22#1684035311yescharacteristic
966C22#1684035511yescharacteristic
967C22#1684036211yescharacteristic
968C22#1684036211yescharacteristic
969C22#1684036411yescharacteristic
970C22#1684036911yescharacteristic
971C22#1684037611yescharacteristic
972C22#1684037611yescharacteristic
973C22#1684037811yescharacteristic
974C22#1684038011yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—1224no—
982C4—1224no—
983C4—2442no—
984C4—2442no—
985C4—2442no—
986C4—2442no—
987C4—2442no—
988C4—2442no—
989C2—44no—
990C2#117×Dic6111yescharacteristic
991C2#2144818011yescharacteristic
992C2#2144818011yescharacteristic
993C2#2144841311yescharacteristic
994C2#2144842311yescharacteristic
995C2#2144844911yescharacteristic
996C2#2144846011yescharacteristic
997C2#2144858211yescharacteristic
998C2#2144858611yescharacteristic
999C2#2144859211yescharacteristic
1000C2#2144859811yescharacteristic
1001C2#2144860711yescharacteristic
1002C2#2144861311yescharacteristic
1003C2#2144863011yescharacteristic
1004C2#2144863411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#388D61
hypocenterC61#13788
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
5. #21444053C2semidirect
6. #21444051C2semidirect
7. #21444048C2semidirect
8. #21444046C2semidirect
9. #21444044C2semidirect
10. #21444044C2semidirect
13. C4×#14519684C2semidirect
14. #95×Dic61C2semidirect
26. #16839655C4semidirect
27. C22⋊C4×Dic61C4semidirect
51. C61×#388C4semidirect
71. C2×C4⋊Dic61C2×C4semidirect
95. C2×C4×Dic61C2×C4semidirect
112. #14519684C2×C4semidirect
113. #14519684C2×C4semidirect
123. C2×C4⋊C4×C61C2×C4semidirect
135. C2×C42×C61C2×C4semidirect
136. #95×C61C2×C4semidirect
137. #95×C61C2×C4semidirect
262. C22⋊C4×C61C42semidirect
534. #388Dic61semidirect
556. C61#13788semidirect
584. C2×C4⋊C4C2×Dic61semidirect
620. C2×C42C2×Dic61semidirect
639. #95C2×Dic61semidirect
640. #95C2×Dic61semidirect
769. 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×C22⋊C4×Dic612
#214440562
#214440532
#214440512
#214440482
#214440462
#214440442
#214440412
C4×#145196842
#95×Dic612
C2×C61×#3882
#1378861