Finite Group Databasebeta

← #29609362

Subgroups — #29609362

Order 15616.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839670C211yesmaximal, characteristic
2C2×#16839665C211yesmaximal, characteristic, complemented
3C2×#16839654C211yesmaximal, characteristic, complemented
4C2×#16839641C211yesmaximal, characteristic, complemented
5#21444075C211yesmaximal, characteristic, complemented
6#21444066C211yesmaximal, characteristic, complemented
7#21444058C211yesmaximal, characteristic, complemented
8#21444058C211yesmaximal, characteristic, complemented
9#21444058C211yesmaximal, characteristic, complemented
10#21444056C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444044C211yesmaximal, characteristic, complemented
14#21444042C211yesmaximal, characteristic, complemented
15C2×C61×#386C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839670C418yescomplemented
33#16839665—24no—
34#16839654—24no—
35#16839641—24no—
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
56C24×D61C2311yescharacteristic
57C22×C22⋊D61—22no—
58C22×C22⋊D61—22no—
59C22×C22⋊D61—41no—
60C22×C22⋊D61—41no—
61C22×C22⋊D61—41no—
62C22×C22⋊D61—41no—
63C22×C22⋊D61—41no—
64C22×C22⋊D61—41no—
65C22×C22⋊D61—41no—
66C22×C22⋊D61—41no—
67C22×C22⋊D61—41no—
68C22×C22⋊D61—41no—
69C22×C22⋊D61C2×C414yes—
70C22×C22⋊D61C2×C414yescomplemented
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C2×C4⋊Dic61—22no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61—41no—
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—22no—
86C2×C22⋊Dic61—41no—
87C2×C22⋊Dic61—41no—
88C2×C22⋊Dic61—41no—
89C2×C22⋊Dic61—41no—
90C2×C22⋊Dic61—41no—
91C2×C22⋊Dic61—41no—
92C2×C22⋊Dic61—41no—
93C2×C22⋊Dic61—41no—
94C2×C22⋊Dic61—41no—
95C2×C22⋊Dic61—41no—
96C2×C22⋊Dic61C2×C414yes—
97C2×C22⋊Dic61C2×C414yescomplemented
98C2×C22⋊Dic61D414yescomplemented
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198C2×C414yescomplemented
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—41no—
118C2×C4×Dic61—41no—
119C2×C4×Dic61—41no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—41no—
124#14519684—41no—
125#14519684—41no—
126#14519684—41no—
127#14519684—41no—
128#14519684—41no—
129#14519684—41no—
130#14519684—41no—
131#14519684C2×C414yescomplemented
132C25×C61C2311yescharacteristic
133C25×C61C2311yescharacteristic
134C22×D4×C61—22no—
135C22×D4×C61—22no—
136C22×D4×C61—22no—
137C22×D4×C61—22no—
138C22×D4×C61—41no—
139C22×D4×C61—41no—
140C22×D4×C61C2×C414yes—
141C23×C4×C61—22no—
142C23×C4×C61—22no—
143C23×C4×C61—22no—
144C23×C4×C61—41no—
145C23×C4×C61—41no—
146C23×C4×C61—41no—
147C23×C4×C61—41no—
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—22no—
154C2×C22⋊C4×C61—22no—
155C2×C22⋊C4×C61—22no—
156C2×C22⋊C4×C61—22no—
157C2×C22⋊C4×C61—22no—
158C2×C22⋊C4×C61—41no—
159C2×C22⋊C4×C61—41no—
160C2×C22⋊C4×C61—41no—
161C2×C22⋊C4×C61—41no—
162#95×C61—22no—
163#95×C61D414yescomplemented
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×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61C22×C412yes—
191C24×C61C22×C412yes—
192C24×C61C2×D412yes—
193C24×C61#4112yes—
194C24×C61C2411yescharacteristic
195C23×D61—21no—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—21no—
206C23×D61—21no—
207C23×D61—21no—
208C23×D61—21no—
209C23×D61C22×C412yes—
210C2×D4×C61—28no—
211C2×D4×C61—28no—
212C2×D4×C61—44no—
213C2×D4×C61—44no—
214C2×D4×C61—44no—
215C2×D4×C61—44no—
216C2×D4×C61—44no—
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—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—44no—
247C22×C4×C61—44no—
248C22×C4×C61—44no—
249C22×C4×C61—44no—
250C22×C4×C61—44no—
251C22×C4×C61—44no—
252C22×C4×C61—44no—
253C22×C4×C61C22×C412yes—
254C22×C4×C61C2×D412yes—
255C22×C4×C61C2×D412yes—
256C22×C4×C61C2×D412yes—
257C22×C4×C61#4112yes—
258C22×C4×C61#4112yes—
259C2×C22⋊D61—28no—
260C2×C22⋊D61—44no—
261C2×C22⋊D61—44no—
262C2×C22⋊D61—44no—
263C2×C22⋊D61—44no—
264C2×C22⋊D61—44no—
265C2×C22⋊D61—44no—
266C2×C22⋊D61—44no—
267C2×C22⋊D61—44no—
268C2×C22⋊D61—44no—
269C2×C22⋊D61—44no—
270C2×C22⋊D61—44no—
271C2×C22⋊D61—44no—
272C2×C22⋊D61—44no—
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—21no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61—21no—
291C22×Dic61—21no—
292C22×Dic61—21no—
293C22×Dic61—21no—
294C22×Dic61—21no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61—21no—
312C22×Dic61—21no—
313C22×Dic61—21no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61C22×C412yes—
317C22×Dic61C22×C412yes—
318C22×Dic61C22×C412yes—
319C22×Dic61C2×D412yes—
320C22×Dic61C2×D412yes—
321C22×Dic61#4112yes—
322C22⋊C4×C61—44no—
323C22⋊C4×C61—44no—
324C22⋊C4×C61—44no—
325C22⋊Dic61—44no—
326C22⋊Dic61—44no—
327C22⋊Dic61—44no—
328C22⋊Dic61—44no—
329C22⋊Dic61—44no—
330C22⋊Dic61—44no—
331#11758198—28no—
332#11758198—44no—
333#11758198—44no—
334#11758198—44no—
335#11758198—44no—
336C4⋊Dic61—44no—
337C4×Dic61—44no—
338C4×Dic61—44no—
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—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
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×C61—41no—
384C23×C61—41no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61—41no—
388C23×C61—41no—
389C23×C61—41no—
390C23×C61—41no—
391C23×C61—41no—
392C23×C61—41no—
393C23×C61—41no—
394C23×C61—41no—
395C23×C61—41no—
396C23×C61—41no—
397C23×C61—41no—
398C23×C61—41no—
399C23×C61—41no—
400C23×C61—41no—
401C23×C61—41no—
402C23×C61—41no—
403C23×C61—41no—
404C23×C61—41no—
405C23×C61—41no—
406C23×C61—41no—
407C23×C61—41no—
408C23×C61C4×D414yes—
409C23×C61C23×C411yescharacteristic
410C23×C61C22×D411yescharacteristic
411C23×C61C22×D411yescharacteristic
412C23×C61C2×#4111yescharacteristic
413C23×C61C2×#4111yescharacteristic
414C23×C61C2×#4111yescharacteristic
415C23×C61C2×#4111yescharacteristic
416C23×C61H(5,𝔽2)11yescharacteristic
417C23×C61H(5,𝔽2)11yescharacteristic
418C23×C61H(5,𝔽2)11yescharacteristic
419C23×C61H(5,𝔽2)11yescharacteristic
420C23×C61H(5,𝔽2)11yescharacteristic
421C23×C61H(5,𝔽2)11yescharacteristic
422C23×C61H(5,𝔽2)11yescharacteristic
423C23×C61H(5,𝔽2)11yescharacteristic
424C22×D61—22no—
425C22×D61—22no—
426C22×D61—22no—
427C22×D61—22no—
428C22×D61—22no—
429C22×D61—22no—
430C22×D61—22no—
431C22×D61—41no—
432C22×D61—41no—
433C22×D61—41no—
434C22×D61—41no—
435C22×D61—41no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—41no—
439C22×D61—41no—
440C22×D61—41no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61—41no—
451C22×D61—41no—
452C22×D61—41no—
453C22×D61—41no—
454C22×D61—41no—
455C22×D61—41no—
456C22×D61—41no—
457C22×D61—41no—
458C22×D61—41no—
459D4×C61—416no—
460C2×C4×C61—22no—
461C2×C4×C61—22no—
462C2×C4×C61—22no—
463C2×C4×C61—22no—
464C2×C4×C61—22no—
465C2×C4×C61—22no—
466C2×C4×C61—22no—
467C2×C4×C61—22no—
468C2×C4×C61—22no—
469C2×C4×C61—22no—
470C2×C4×C61—22no—
471C2×C4×C61—22no—
472C2×C4×C61—22no—
473C2×C4×C61—22no—
474C2×C4×C61—22no—
475C2×C4×C61—416no—
476C2×C4×C61—41no—
477C2×C4×C61—41no—
478C2×C4×C61—41no—
479C2×C4×C61—41no—
480C2×C4×C61—41no—
481C2×C4×C61—41no—
482C2×C4×C61—41no—
483C2×C4×C61—41no—
484C2×C4×C61—41no—
485C2×C4×C61—41no—
486C2×C4×C61—41no—
487C2×C4×C61—41no—
488C2×C4×C61—41no—
489C2×C4×C61—41no—
490C2×C4×C61—41no—
491C2×C4×C61—41no—
492C2×C4×C61—41no—
493C2×C4×C61—41no—
494C2×C4×C61—41no—
495C2×C4×C61C4×D414yes—
496C22⋊D61—416no—
497C22⋊D61—416no—
498C2×Dic61—22no—
499C2×Dic61—22no—
500C2×Dic61—22no—
501C2×Dic61—22no—
502C2×Dic61—22no—
503C2×Dic61—22no—
504C2×Dic61—22no—
505C2×Dic61—22no—
506C2×Dic61—22no—
507C2×Dic61—22no—
508C2×Dic61—22no—
509C2×Dic61—22no—
510C2×Dic61—22no—
511C2×Dic61—22no—
512C2×Dic61—22no—
513C2×Dic61—22no—
514C2×Dic61—22no—
515C2×Dic61—22no—
516C2×Dic61—41no—
517C2×Dic61—41no—
518C2×Dic61—41no—
519C2×Dic61—41no—
520C2×Dic61—41no—
521C2×Dic61—41no—
522C2×Dic61—41no—
523C2×Dic61—41no—
524C2×Dic61—41no—
525C2×Dic61—41no—
526C2×Dic61—41no—
527C2×Dic61—41no—
528C2×Dic61—41no—
529C2×Dic61—41no—
530C2×Dic61—41no—
531C2×Dic61—41no—
532C2×Dic61—41no—
533C2×Dic61—41no—
534C2×Dic61—41no—
535C2×Dic61—41no—
536C2×Dic61—41no—
537C2×Dic61—41no—
538C2×Dic61—41no—
539C2×Dic61—41no—
540C2×Dic61—41no—
541C2×Dic61—41no—
542C2×Dic61—41no—
543C2×Dic61—41no—
544C2×Dic61—41no—
545C2×Dic61—41no—
546C2×Dic61—41no—
547#14520—611nomaximal, Sylow
548C22×C61—24no—
549C22×C61—24no—
550C22×C61—24no—
551C22×C61—42no—
552C22×C61—42no—
553C22×C61—42no—
554C22×C61—42no—
555C22×C61—42no—
556C22×C61—42no—
557C22×C61—42no—
558C22×C61—42no—
559C22×C61—42no—
560C22×C61—42no—
561C22×C61—42no—
562C22×C61—42no—
563C22×C61—42no—
564C22×C61—42no—
565C22×C61—42no—
566C22×C61—42no—
567C22×C61—42no—
568C22×C61—42no—
569C22×C61—42no—
570C22×C61—81no—
571C22×C61—81no—
572C22×C61—81no—
573C22×C61—81no—
574C22×C61—81no—
575C22×C61—81no—
576C22×C61—81no—
577C22×C61—81no—
578C22×C61C2×C4×D411yescharacteristic
579C22×C61C2×C4×D411yescharacteristic
580C22×C61C4×#4111yescharacteristic
581C22×C61#51811yescharacteristic
582C22×C61#51811yescharacteristic
583C22×C61#51811yescharacteristic
584C22×C61#51811yescharacteristic
585C22×C61#53411yescharacteristic
586C22×C61#53511yescharacteristic
587C22×C61#53511yescharacteristic
588C22×C61#53511yescharacteristic
589C22×C61#53811yescharacteristic
590C22×C61#53811yescharacteristic
591C22×C61#53811yescharacteristic
592C22×C61#53811yescharacteristic
593C22×C61#54011yescharacteristic
594C22×C61#54011yescharacteristic
595C22×C61#54011yescharacteristic
596C22×C61#54011yescharacteristic
597C22×C61D4211yescharacteristic
598C22×C61#54611yescharacteristic
599C22×C61#54611yescharacteristic
600C22×C61#54611yescharacteristic
601C22×C61#54611yescharacteristic
602C22×C61#54611yescharacteristic
603C22×C61#55011yescharacteristic
604C22×C61#55111yescharacteristic
605C22×C61#55311yescharacteristic
606C22×C61#55311yescharacteristic
607C22×C61#55311yescharacteristic
608C22×C61#55511yescharacteristic
609C22×C61#56011yescharacteristic
610C22×C61#56011yescharacteristic
611C22×C61#56011yescharacteristic
612C22×C61H(3,𝔽4)11yescharacteristic
613C2×D61—42no—
614C2×D61—42no—
615C2×D61—42no—
616C2×D61—42no—
617C2×D61—42no—
618C2×D61—42no—
619C2×D61—42no—
620C2×D61—81no—
621C2×D61—81no—
622C2×D61—81no—
623C2×D61—81no—
624C2×D61—81no—
625C2×D61—81no—
626C2×D61—81no—
627C2×D61—81no—
628C4×C61—24no—
629C4×C61—42no—
630C4×C61—42no—
631C4×C61—42no—
632C4×C61—81no—
633Dic61—42no—
634Dic61—42no—
635Dic61—42no—
636Dic61—42no—
637Dic61—42no—
638Dic61—42no—
639Dic61—81no—
640C2×#392—611no—
641C2×#390—611no—
642C2×#388—611no—
643C2×#386—611no—
644C2×#386D6111yescharacteristic, complemented
645#1442—611no—
646#1440—611no—
647#1438—611no—
648#1438—611no—
649#1438—611no—
650#1437—611no—
651#1437—611no—
652#1437—611no—
653#1434—611no—
654C22⋊#95—611no—
655C2×C61—44no—
656C2×C61—82no—
657C2×C61#232111yescharacteristic
658C2×C61#232811yescharacteristic
659C2×C61#233311yescharacteristic
660C2×C61#235811yescharacteristic
661C2×C61#236311yescharacteristic
662C2×C61#236411yescharacteristic
663C2×C61#237511yescharacteristic
664C2×C61#267011yescharacteristic
665C2×C61#267311yescharacteristic
666C2×C61#269911yescharacteristic
667C2×C61#270311yescharacteristic
668C2×C61#270311yescharacteristic
669C2×C61#271411yescharacteristic
670C2×C61#275311yescharacteristic
671C2×C61#275611yescharacteristic
672D61—82no—
673C23×D4—611no—
674C23×D4—611no—
675C23×D4C2×D6111yescharacteristic
676C24×C4C2×D6111yescharacteristic
677C22×C4⋊C4—611no—
678C22×C22⋊C4—611no—
679C22×C22⋊C4—611no—
680C22×C22⋊C4—611no—
681C22×C22⋊C4—611no—
682C22×C22⋊C4—611no—
683C22×C22⋊C4—611no—
684C22×C22⋊C4—611no—
685C22×C22⋊C4—611no—
686C22×C22⋊C4—611no—
687C22×C22⋊C4—611no—
688C22×C22⋊C4—611no—
689C22×C22⋊C4C2×D6111yescharacteristic
690C22×C22⋊C4C2×D6111yescharacteristic
691C22×C22⋊C4C2×D6111yescharacteristic
692C22×C42—611no—
693C22×C42—611no—
694#392—618no—
695#390—1224no—
696#388—1224no—
697#386—24no—
698#386—1224no—
699C2×#95—611no—
700C2×#95—611no—
701C2×#95—611no—
702C2×#95—611no—
703C2×#95—611no—
704C2×#95—611no—
705C2×#95—611no—
706C2×#95—611no—
707C2×#95—611no—
708C2×#95—611no—
709C2×#95—611no—
710C2×#95—611no—
711C2×#95C2×D6111yescharacteristic
712C2×#95C2×D6111yescharacteristic
713C61#1452011yescharacteristic, complemented, Sylow
714C25—611no—
715C25C22×D6111yescharacteristic
716C25C22×D6111yescharacteristic
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—614no—
724C22×D4—614no—
725C22×D4—1222no—
726C22×D4—1222no—
727C22×D4—2441no—
728C22×D4—2441no—
729C22×D4—2441no—
730C22×D4—2441no—
731C22×D4—2441no—
732C22×D4—2441no—
733C22×D4—2441no—
734C22×D4—2441no—
735C22×D4—2441no—
736C22×D4—2441no—
737C22×D4C4×D6114yes—
738C23×C4—22no—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—41no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—611no—
746C23×C4—611no—
747C23×C4—611no—
748C23×C4—611no—
749C23×C4—611no—
750C23×C4—611no—
751C23×C4—611no—
752C23×C4C22×D6111yescharacteristic
753C23×C4C22×D6111yescharacteristic
754C23×C4C22×D6111yescharacteristic
755C23×C4C22×D6111yescharacteristic
756C23×C4C22×D6111yescharacteristic
757C2×C4⋊C4—1222no—
758C2×C4⋊C4—1222no—
759C2×C4⋊C4—2441no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—614no—
770C2×C22⋊C4—614no—
771C2×C22⋊C4—614no—
772C2×C22⋊C4—614no—
773C2×C22⋊C4—1222no—
774C2×C22⋊C4—1222no—
775C2×C22⋊C4—1222no—
776C2×C22⋊C4—1222no—
777C2×C22⋊C4—1222no—
778C2×C22⋊C4—1222no—
779C2×C22⋊C4—1222no—
780C2×C22⋊C4—1222no—
781C2×C22⋊C4—1222no—
782C2×C22⋊C4—1222no—
783C2×C22⋊C4—1222no—
784C2×C22⋊C4—1222no—
785C2×C22⋊C4—1222no—
786C2×C22⋊C4—2441no—
787C2×C22⋊C4—2441no—
788C2×C22⋊C4—2441no—
789C2×C22⋊C4—2441no—
790C2×C22⋊C4—2441no—
791C2×C22⋊C4—2441no—
792C2×C22⋊C4—2441no—
793C2×C22⋊C4—2441no—
794C2×C22⋊C4—2441no—
795C2×C22⋊C4—2441no—
796C2×C22⋊C4—2441no—
797C2×C22⋊C4—2441no—
798C2×C22⋊C4—2441no—
799C2×C22⋊C4—2441no—
800C2×C22⋊C4—2441no—
801C2×C22⋊C4—2441no—
802C2×C42—1222no—
803C2×C42—1222no—
804C2×C42—1222no—
805C2×C42—2441no—
806C2×C42—2441no—
807C2×C42—2441no—
808#95—22no—
809#95—614no—
810#95—1222no—
811#95—1222no—
812#95—1222no—
813#95—2441no—
814#95—2441no—
815#95—2441no—
816#95—2441no—
817#95—2441no—
818#95—2441no—
819#95—2441no—
820#95—2441no—
821#95C22⋊D6114yescomplemented
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—612no—
849C24—1221no—
850C24—1221no—
851C24—1221no—
852C24—1221no—
853C24—1221no—
854C24—1221no—
855C24—1221no—
856C24—1221no—
857C24—1221no—
858C24—1221no—
859C24—1221no—
860C24—1221no—
861C24—1221no—
862C24—1221no—
863C24C2×C4×D6112yes—
864C24C2×C4×D6112yes—
865C24D4×D6112yes—
866C24#1175822412yes—
867C24C23×D6111yescharacteristic
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—1228no—
876C2×D4—2444no—
877C2×D4—2444no—
878C2×D4—2444no—
879C2×D4—2444no—
880C2×D4—2444no—
881C2×D4—2444no—
882C2×D4—2444no—
883C2×D4—2444no—
884C2×D4—2444no—
885C2×D4—2444no—
886C2×D4—2444no—
887C2×D4—2444no—
888C2×D4—2444no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—612no—
926C22×C4—612no—
927C22×C4—612no—
928C22×C4—612no—
929C22×C4—612no—
930C22×C4—612no—
931C22×C4—1221no—
932C22×C4—1221no—
933C22×C4—1221no—
934C22×C4—1221no—
935C22×C4—1221no—
936C22×C4—1221no—
937C22×C4—1221no—
938C22×C4—1221no—
939C22×C4—1221no—
940C22×C4—1221no—
941C22×C4—1221no—
942C22×C4—1221no—
943C22×C4—1221no—
944C22×C4—1221no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—1221no—
966C22×C4—1221no—
967C22×C4—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4C2×C4×D6112yes—
975C22×C4#1175822212yes—
976C22×C4#1175822412yes—
977C22×C4C2×C22⋊D6112yes—
978C22×C4C2×C22⋊D6112yes—
979C22×C4C2×C22⋊D6112yes—
980C4⋊C4—2444no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—1228no—
985C22⋊C4—2444no—
986C22⋊C4—2444no—
987C22⋊C4—2444no—
988C22⋊C4—2444no—
989C22⋊C4—2444no—
990C22⋊C4—2444no—
991C22⋊C4—2444no—
992C22⋊C4—2444no—
993C22⋊C4—2444no—
994C22⋊C4—2444no—
995C42—2444no—
996C42—2444no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—1222no—
1067C23—1222no—
1068C23—1222no—
1069C23—1222no—
1070C23—1222no—
1071C23—1222no—
1072C23—1222no—
1073C23—2441no—
1074C23—2441no—
1075C23—2441no—
1076C23—2441no—
1077C23—2441no—
1078C23—2441no—
1079C23—2441no—
1080C23—2441no—
1081C23—2441no—
1082C23—2441no—
1083C23—2441no—
1084C23—2441no—
1085C23—2441no—
1086C23—2441no—
1087C23—2441no—
1088C23—2441no—
1089C23—2441no—
1090C23—2441no—
1091C23—2441no—
1092C23—2441no—
1093C23—2441no—
1094C23—2441no—
1095C23—2441no—
1096C23—2441no—
1097C23—2441no—
1098C23—2441no—
1099C23—2441no—
1100C23—2441no—
1101C23#1451973714yes—
1102C23C22×C4×D6111yescharacteristic
1103C23C2×D4×D6111yescharacteristic
1104C23C22×C22⋊D6111yescharacteristic
1105C23#41×D6111yescharacteristic
1106C23C2×#1175822411yescharacteristic
1107C23C2×#1175822411yescharacteristic
1108C23C2×#1175822211yescharacteristic
1109C23#1451982211yescharacteristic
1110C23#1451982211yescharacteristic
1111C23#1451982211yescharacteristic
1112C23#1451982211yescharacteristic
1113C23#1451982211yescharacteristic
1114C23#1451982311yescharacteristic
1115C23#1451982311yescharacteristic
1116C23#1451982311yescharacteristic
1117D4—416no—
1118D4—24416no—
1119D4—24416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—416no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—1222no—
1156C2×C4—1222no—
1157C2×C4—1222no—
1158C2×C4—1222no—
1159C2×C4—1222no—
1160C2×C4—1222no—
1161C2×C4—1222no—
1162C2×C4—1222no—
1163C2×C4—1222no—
1164C2×C4—1222no—
1165C2×C4—1222no—
1166C2×C4—1222no—
1167C2×C4—1222no—
1168C2×C4—1222no—
1169C2×C4—1222no—
1170C2×C4—1222no—
1171C2×C4—1222no—
1172C2×C4—1222no—
1173C2×C4—2441no—
1174C2×C4—2441no—
1175C2×C4—2441no—
1176C2×C4—2441no—
1177C2×C4—2441no—
1178C2×C4—2441no—
1179C2×C4—2441no—
1180C2×C4—2441no—
1181C2×C4—2441no—
1182C2×C4—2441no—
1183C2×C4—2441no—
1184C2×C4—2441no—
1185C2×C4—2441no—
1186C2×C4—2441no—
1187C2×C4—2441no—
1188C2×C4—2441no—
1189C2×C4—2441no—
1190C2×C4—2441no—
1191C2×C4—2441no—
1192C2×C4—2441no—
1193C2×C4—2441no—
1194C2×C4—2441no—
1195C2×C4—2441no—
1196C2×C4—2441no—
1197C2×C4—2441no—
1198C2×C4—2441no—
1199C2×C4—2441no—
1200C2×C4—2441no—
1201C2×C4—2441no—
1202C2×C4—2441no—
1203C2×C4—2441no—
1204C2×C4C4×C22⋊D6114yes—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—4881no—
1236C22—4881no—
1237C22—4881no—
1238C22—4881no—
1239C22—4881no—
1240C22—4881no—
1241C22—4881no—
1242C22—4881no—
1243C22—2442no—
1244C22—2442no—
1245C22—2442no—
1246C22—2442no—
1247C22—2442no—
1248C22—2442no—
1249C22—2442no—
1250C22C2×#1451973711yescharacteristic
1251C22C2×C4×C22⋊D6111yescharacteristic
1252C22C4×#1175822411yescharacteristic
1253C22#1684023411yescharacteristic
1254C22#1684023411yescharacteristic
1255C22#1684023411yescharacteristic
1256C22#1684023511yescharacteristic
1257C22#1684032311yescharacteristic
1258C22#1684032611yescharacteristic
1259C22#1684032711yescharacteristic
1260C22#1684032911yescharacteristic
1261C22#1684034411yescharacteristic
1262C22#1684034711yescharacteristic
1263C22#1684034911yescharacteristic
1264C22#1684034911yescharacteristic
1265C22#1684036311yescharacteristic
1266C22#1684036311yescharacteristic
1267C22#1684036411yescharacteristic
1268C22#1684036511yescharacteristic
1269C22D4×C22⋊D6111yescharacteristic
1270C22#1684039911yescharacteristic
1271C22#1684040211yescharacteristic
1272C22#1684040411yescharacteristic
1273C22#1684040611yescharacteristic
1274C22#1684040611yescharacteristic
1275C22#1684043111yescharacteristic
1276C22#1684043811yescharacteristic
1277C22#1684045511yescharacteristic
1278C22#1684046211yescharacteristic
1279C22#1684046411yescharacteristic
1280C22#1684047711yescharacteristic
1281C22#1684050011yescharacteristic
1282C22#1684050011yescharacteristic
1283C22#1684050211yescharacteristic
1284C22#1684050511yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—81no—
1290C4—4881no—
1291C4—2442no—
1292C4—2442no—
1293C4—2442no—
1294C4—2442no—
1295C4—2442no—
1296C4—2442no—
1297C2—44no—
1298C2—82no—
1299C2—4882no—
1300C2#2144848211yescharacteristic
1301C2#2144854111yescharacteristic
1302C2#2144858511yescharacteristic
1303C2#2144879811yescharacteristic
1304C2#2144885311yescharacteristic
1305C2#2144886711yescharacteristic
1306C2#2144895711yescharacteristic
1307C2#2145204111yescharacteristic
1308C2#2145208511yescharacteristic
1309C2#2145240811yescharacteristic
1310C2#2145245811yescharacteristic
1311C2#2145246511yescharacteristic
1312C2#2145260911yescharacteristic
1313C2#2145309011yescharacteristic
1314C2#2145313511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#386C2
socle, cosocleC24×C61C24
prime radicalC2×#16839670C2
hypercenterC2×#386D61
hypocenterC61#14520
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#16839665C2semidirect
3. C2×#16839654C2semidirect
4. C2×#16839641C2semidirect
5. #21444075C2semidirect
6. #21444066C2semidirect
7. #21444058C2semidirect
8. #21444058C2semidirect
9. #21444058C2semidirect
10. #21444056C2semidirect
11. #21444056C2semidirect
12. #21444055C2semidirect
13. #21444044C2semidirect
14. #21444042C2semidirect
15. C2×C61×#386C2semidirect
32. #16839670C4semidirect
70. C22×C22⋊D61C2×C4semidirect
97. C2×C22⋊Dic61C2×C4semidirect
98. C2×C22⋊Dic61D4semidirect
113. C2×#11758198C2×C4semidirect
131. #14519684C2×C4semidirect
163. #95×C61D4semidirect
644. C2×#386D61semidirect
713. C61#14520semidirect
821. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396702
C2×#168396652
C2×#168396542
C2×#168396412
#214440752
#214440662
#214440582
#214440562
#214440552
#214440442
#214440422
C2×C61×#3862
#1452061