Finite Group Databasebeta

← #29601613

Subgroups — #29601613

Order 15616.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839662C211yesmaximal, characteristic
2C2×#16839641C211yesmaximal, characteristic
3C2×#16839638C211yesmaximal, characteristic
4C2×C4×#11758198C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
6C2×#16839609C211yesmaximal, characteristic, complemented
7#21444057C211yesmaximal, characteristic, complemented
8#21444056C211yesmaximal, characteristic, complemented
9#21444056C211yesmaximal, characteristic, complemented
10#21444055C211yesmaximal, characteristic, complemented
11#21444052C211yesmaximal, characteristic, complemented
12#21444050C211yesmaximal, characteristic, complemented
13C4×#14519684C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839662C418yescomplemented
33#16839641C418yescomplemented
34#16839638C418yescomplemented
35C4×#11758198—24no—
36C4×C22⋊Dic61—24no—
37#16839609—24no—
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×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C42×C61C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C4×C22⋊C4×C61—24no—
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C22×C22⋊D61—41no—
60C22×C22⋊D61—41no—
61C22×C22⋊D61—41no—
62C22×C22⋊D61—41no—
63C22×C22⋊D61C2×C414yes—
64C22×C22⋊D61C2×C414yes—
65C22×C22⋊D61C2×C414yes—
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—41no—
78C22×C4×D61—41no—
79C22×C4×D61C2×C414yescomplemented
80C2×#11758196—41no—
81C2×#11758196—41no—
82C2×#11758196C2×C414yescomplemented
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—22no—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—41no—
88C2×C22⋊Dic61—41no—
89C2×C22⋊Dic61C2×C414yes—
90C2×C22⋊Dic61C2×C414yescomplemented
91C2×C22⋊Dic61C2×C414yescomplemented
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—41no—
101C2×#11758198—41no—
102C2×#11758198C2×C414yes—
103C2×#11758198C2×C414yes—
104C2×#11758198C2×C414yescomplemented
105C2×#11758198C2×C414yescomplemented
106C2×#11758198C2×C414yescomplemented
107C2×C4×Dic61—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—22no—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—22no—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—41no—
116C2×C4×Dic61—41no—
117C2×C4×Dic61—41no—
118C2×C4×Dic61—41no—
119C2×C4×Dic61—41no—
120C2×C4×Dic61—41no—
121C2×C4×Dic61C2×C414yescomplemented
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—41no—
128#14519684—41no—
129#14519684C2×C414yescomplemented
130#14519684C2×C414yescomplemented
131#14519684C2×C414yescomplemented
132#14519684C2×C414yescomplemented
133#14519684D414yescomplemented
134C25×C61C2311yescharacteristic
135C23×C4×C61—22no—
136C23×C4×C61—22no—
137C23×C4×C61—22no—
138C23×C4×C61—22no—
139C23×C4×C61—41no—
140C23×C4×C61—41no—
141C23×C4×C61C2×C414yescomplemented
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61—22no—
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61C2×C414yes—
153C2×C22⋊C4×C61C2×C414yescomplemented
154C2×C42×C61—22no—
155C2×C42×C61—22no—
156C2×C42×C61—22no—
157C2×C42×C61—22no—
158C2×C42×C61—41no—
159C2×C42×C61—41no—
160#95×C61—22no—
161#95×C61D414yescomplemented
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61C22×C412yes—
175C24×C61C22×C412yes—
176C24×C61C22×C412yes—
177C24×C61C2411yescharacteristic
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61C22×C412yes—
191C23×D61C22×C412yes—
192C23×D61C22×C412yes—
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—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—28no—
222C22×C4×C61—28no—
223C22×C4×C61—44no—
224C22×C4×C61—44no—
225C22×C4×C61—44no—
226C22×C4×C61—44no—
227C22×C4×C61—44no—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C22×C412yes—
231C22×C4×C61C22×C412yes—
232C22×C4×C61C22×C412yes—
233C22×C4×C61C22×C412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D412yes—
236C22×C4×C61C2×D412yes—
237C22×C4×C61C2×D412yes—
238C22×C4×C61#4112yes—
239C22×C4×C61#4112yes—
240C22×C4×C61#4112yes—
241C22×C4×C61#4112yes—
242C2×C22⋊D61—44no—
243C2×C22⋊D61—44no—
244C2×C22⋊D61—44no—
245C2×C22⋊D61—44no—
246C2×C22⋊D61—44no—
247C2×C22⋊D61—44no—
248C2×C22⋊D61C42116yescomplemented
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61C22×C412yes—
286C22×Dic61C22×C412yes—
287C22×Dic61C22×C412yes—
288C22×Dic61C22×C412yes—
289C22×Dic61C22×C412yes—
290C22×Dic61C22×C412yes—
291C22×Dic61C22×C412yes—
292C22×Dic61C22×C412yes—
293C22×Dic61C22×C412yes—
294C22×Dic61C2×D412yes—
295C22×Dic61C2×D412yes—
296C22×Dic61#4112yes—
297C22×Dic61#4112yes—
298C2×C4×D61—28no—
299C2×C4×D61—28no—
300C2×C4×D61—44no—
301C2×C4×D61—44no—
302C2×C4×D61—44no—
303C2×C4×D61—44no—
304C2×C4×D61—44no—
305C22⋊C4×C61—28no—
306C22⋊C4×C61—28no—
307C42×C61—44no—
308C42×C61—44no—
309C22⋊Dic61—28no—
310C22⋊Dic61—28no—
311C22⋊Dic61—44no—
312#11758198—28no—
313#11758198—28no—
314#11758198—28no—
315#11758198—28no—
316#11758198—44no—
317#11758196—44no—
318C4×Dic61—44no—
319C4×Dic61—44no—
320C4×Dic61—44no—
321C4×Dic61—44no—
322C4×Dic61—44no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61C2×C4214yes—
358C23×C61C23×C411yescharacteristic
359C23×C61C23×C411yescharacteristic
360C23×C61C23×C411yescharacteristic
361C23×C61C22×D411yescharacteristic
362C23×C61C22×D411yescharacteristic
363C23×C61C2×#4111yescharacteristic
364C23×C61C2×#4111yescharacteristic
365C23×C61C2×#4111yescharacteristic
366C23×C61C2×#4111yescharacteristic
367C23×C61C2×#4111yescharacteristic
368C23×C61C2×#4111yescharacteristic
369C23×C61H(5,𝔽2)11yescharacteristic
370C23×C61H(5,𝔽2)11yescharacteristic
371C23×C61H(5,𝔽2)11yescharacteristic
372C23×C61H(5,𝔽2)11yescharacteristic
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—22no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—41no—
392C22×D61—41no—
393C22×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61—41no—
407C22×D61C2×C4214yes—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—22no—
435C2×C4×C61—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—416no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61C4×D414yes—
448C2×C4×C61C4×D414yes—
449C2×C4×C61C4×D414yes—
450C2×C4×C61C4×D414yes—
451C22⋊D61—416no—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—22no—
471C2×Dic61—22no—
472C2×Dic61—22no—
473C2×Dic61—22no—
474C2×Dic61—22no—
475C2×Dic61—22no—
476C2×Dic61—22no—
477C2×Dic61—22no—
478C2×Dic61—22no—
479C2×Dic61—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498C2×Dic61C2×C4214yes—
499C2×Dic61C4×D414yes—
500C2×Dic61C4×D414yes—
501C4×D61—416no—
502#13824—611nomaximal, Sylow
503C22×C61—24no—
504C22×C61—24no—
505C22×C61—24no—
506C22×C61—42no—
507C22×C61—42no—
508C22×C61—42no—
509C22×C61—42no—
510C22×C61—42no—
511C22×C61—42no—
512C22×C61—42no—
513C22×C61—42no—
514C22×C61—42no—
515C22×C61—42no—
516C22×C61—42no—
517C22×C61—42no—
518C22×C61C22×C4211yescharacteristic
519C22×C61C2×C4×D411yescharacteristic
520C22×C61C2×C4×D411yescharacteristic
521C22×C61C2×C4×D411yescharacteristic
522C22×C61C2×C4×D411yescharacteristic
523C22×C61C2×C4×D411yescharacteristic
524C22×C61C2×C4×D411yescharacteristic
525C22×C61C4×#4111yescharacteristic
526C22×C61C4×#4111yescharacteristic
527C22×C61C4×#4111yescharacteristic
528C22×C61C4×#4111yescharacteristic
529C22×C61C4×#4111yescharacteristic
530C22×C61C4×#4111yescharacteristic
531C22×C61#51811yescharacteristic
532C22×C61#51811yescharacteristic
533C22×C61#51811yescharacteristic
534C22×C61#51811yescharacteristic
535C22×C61#51811yescharacteristic
536C22×C61#51811yescharacteristic
537C22×C61D4211yescharacteristic
538C22×C61#54611yescharacteristic
539C22×C61#54611yescharacteristic
540C22×C61#54611yescharacteristic
541C22×C61#54611yescharacteristic
542C22×C61#55011yescharacteristic
543C22×C61#55011yescharacteristic
544C22×C61#55111yescharacteristic
545C22×C61#55111yescharacteristic
546C22×C61#55311yescharacteristic
547C22×C61#55311yescharacteristic
548C22×C61#55311yescharacteristic
549C22×C61#55311yescharacteristic
550C22×C61#55511yescharacteristic
551C22×C61#55511yescharacteristic
552C22×C61#55911yescharacteristic
553C2×D61—24no—
554C2×D61—24no—
555C2×D61—24no—
556C2×D61—42no—
557C2×D61—42no—
558C2×D61—42no—
559C2×D61—42no—
560C2×D61—42no—
561C2×D61—42no—
562C2×D61—42no—
563C2×D61—42no—
564C2×D61—42no—
565C2×D61—42no—
566C2×D61—42no—
567C2×D61—42no—
568C4×C61—24no—
569C4×C61—24no—
570C4×C61—24no—
571C4×C61—24no—
572C4×C61—42no—
573C4×C61—42no—
574Dic61—24no—
575Dic61—24no—
576Dic61—24no—
577Dic61—42no—
578Dic61—42no—
579Dic61—42no—
580Dic61—42no—
581C2×#390—611no—
582C2×#386—611no—
583C2×#386—611no—
584C2×C4×C22⋊C4—611no—
585C2×C4×C22⋊C4—611no—
586C2×C4×C22⋊C4—611no—
587C2×C4×C22⋊C4D6111yescharacteristic, complemented
588#1437—611no—
589#1437—611no—
590#1437—611no—
591#1437—611no—
592#1436—611no—
593#1436—611no—
594C4×#95—611no—
595C4×#95—611no—
596C2×C61—44no—
597C2×C61C42×D411yescharacteristic
598C2×C61C42×D411yescharacteristic
599C2×C61#227311yescharacteristic
600C2×C61#235811yescharacteristic
601C2×C61#235811yescharacteristic
602C2×C61#236311yescharacteristic
603C2×C61#236311yescharacteristic
604C2×C61#236311yescharacteristic
605C2×C61#236311yescharacteristic
606C2×C61#236411yescharacteristic
607C2×C61#236411yescharacteristic
608C2×C61#236611yescharacteristic
609C2×C61#237211yescharacteristic
610C2×C61#237411yescharacteristic
611C2×C61#237411yescharacteristic
612D61—44no—
613C23×D4—611no—
614C24×C4—611no—
615C24×C4C2×D6111yescharacteristic
616C22×C4⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C22⋊C4—611no—
622C22×C22⋊C4—611no—
623C22×C22⋊C4—611no—
624C22×C22⋊C4—611no—
625C22×C22⋊C4C2×D6111yescharacteristic
626C22×C22⋊C4C2×D6111yescharacteristic
627C22×C42—611no—
628C22×C42—611no—
629C22×C42—611no—
630C22×C42—611no—
631C22×C42—611no—
632C22×C42C2×D6111yescharacteristic
633C22×C42C2×D6111yescharacteristic
634#390—618no—
635#386—618no—
636#386—618no—
637C4×C22⋊C4—24no—
638C4×C22⋊C4—1224no—
639C4×C22⋊C4—1224no—
640C4×C22⋊C4—1224no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95—611no—
647C2×#95—611no—
648C2×#95—611no—
649C2×#95—611no—
650C2×#95—611no—
651C2×#95—611no—
652C2×#95—611no—
653C2×#95C2×D6111yescharacteristic
654C2×#95C2×D6111yescharacteristic
655C61#1382411yescharacteristic, complemented, Sylow
656C25—611no—
657C25C22×D6111yescharacteristic
658C22×D4—614no—
659C22×D4—614no—
660C22×D4—614no—
661C22×D4—2441no—
662C22×D4—2441no—
663C22×D4—2441no—
664C22×D4—2441no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—41no—
670C23×C4—41no—
671C23×C4—611no—
672C23×C4—611no—
673C23×C4—611no—
674C23×C4—611no—
675C23×C4—611no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—614no—
679C23×C4—1222no—
680C23×C4—1222no—
681C23×C4—1222no—
682C23×C4—1222no—
683C23×C4—2441no—
684C23×C4—2441no—
685C23×C4C4×D6114yescomplemented
686C23×C4C22×D6111yescharacteristic
687C23×C4C22×D6111yescharacteristic
688C23×C4C22×D6111yescharacteristic
689C23×C4C22×D6111yescharacteristic
690C23×C4C22×D6111yescharacteristic
691C23×C4C22×D6111yescharacteristic
692C2×C4⋊C4—614no—
693C2×C4⋊C4—2441no—
694C2×C4⋊C4—2441no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—614no—
700C2×C22⋊C4—614no—
701C2×C22⋊C4—614no—
702C2×C22⋊C4—614no—
703C2×C22⋊C4—614no—
704C2×C22⋊C4—614no—
705C2×C22⋊C4—614no—
706C2×C22⋊C4—614no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—1222no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4C4×D6114yes—
724C2×C22⋊C4C4×D6114yescomplemented
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—41no—
730C2×C42—41no—
731C2×C42—614no—
732C2×C42—1222no—
733C2×C42—1222no—
734C2×C42—1222no—
735C2×C42—1222no—
736C2×C42—1222no—
737C2×C42—1222no—
738C2×C42—1222no—
739C2×C42—1222no—
740C2×C42—2441no—
741C2×C42—2441no—
742C2×C42—2441no—
743C2×C42—2441no—
744C2×C42—2441no—
745C2×C42—2441no—
746#95—22no—
747#95—614no—
748#95—614no—
749#95—614no—
750#95—614no—
751#95—614no—
752#95—1222no—
753#95—1222no—
754#95—1222no—
755#95—1222no—
756#95—1222no—
757#95—2441no—
758#95—2441no—
759#95C22⋊D6114yescomplemented
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—612no—
773C24—612no—
774C24—612no—
775C24—1221no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24—1221no—
783C24—1221no—
784C24—1221no—
785C24—1221no—
786C24—1221no—
787C24C2×C4×D6112yes—
788C24C2×C4×D6112yes—
789C24C2×C4×D6112yes—
790C24C23×D6111yescharacteristic
791C2×D4—6116no—
792C2×D4—2444no—
793C2×D4—2444no—
794C2×D4—2444no—
795C2×D4—2444no—
796C2×D4—2444no—
797C2×D4—2444no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—28no—
827C22×C4—28no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—612no—
834C22×C4—612no—
835C22×C4—612no—
836C22×C4—612no—
837C22×C4—612no—
838C22×C4—612no—
839C22×C4—612no—
840C22×C4—612no—
841C22×C4—612no—
842C22×C4—612no—
843C22×C4—612no—
844C22×C4—612no—
845C22×C4—612no—
846C22×C4—1228no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1228no—
884C22×C4—2444no—
885C22×C4—2444no—
886C22×C4—2444no—
887C22×C4—2444no—
888C22×C4—2444no—
889C22×C4C2×C4×D6112yes—
890C22×C4C2×C4×D6112yes—
891C22×C4C2×C4×D6112yes—
892C22×C4C2×C4×D6112yes—
893C22×C4C2×C4×D6112yes—
894C22×C4C2×C4×D6112yes—
895C22×C4#1175822212yes—
896C22×C4#1175822212yes—
897C22×C4#1175822212yes—
898C22×C4D4×D6112yes—
899C22×C4#1175822412yes—
900C22×C4C2×C22⋊D6112yes—
901C22×C4C2×C22⋊D6112yes—
902C22×C4C2×C22⋊D6112yes—
903C4⋊C4—2444no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—1228no—
907C22⋊C4—1228no—
908C22⋊C4—1228no—
909C22⋊C4—1228no—
910C22⋊C4—1228no—
911C22⋊C4—1228no—
912C22⋊C4—2444no—
913C22⋊C4—2444no—
914C42—44no—
915C42—44no—
916C42—2444no—
917C42—2444no—
918C42—2444no—
919C42—2444no—
920C42—2444no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—614no—
956C23—1222no—
957C23—1222no—
958C23—1222no—
959C23—1222no—
960C23—1222no—
961C23—1222no—
962C23—1222no—
963C23—1222no—
964C23—1222no—
965C23—1222no—
966C23—1222no—
967C23—1222no—
968C23—1222no—
969C23—1222no—
970C23—1222no—
971C23—1222no—
972C23—1222no—
973C23—1222no—
974C23—2441no—
975C23—2441no—
976C23—2441no—
977C23—2441no—
978C23—2441no—
979C23—2441no—
980C23—2441no—
981C23—2441no—
982C23—2441no—
983C23—2441no—
984C23—2441no—
985C23—2441no—
986C23—2441no—
987C23—2441no—
988C23—2441no—
989C23—2441no—
990C23C42×D6114yes—
991C23C22×C4×D6111yescharacteristic
992C23C22×C4×D6111yescharacteristic
993C23C22×C4×D6111yescharacteristic
994C23C2×D4×D6111yescharacteristic
995C23C22×C22⋊D6111yescharacteristic
996C23#41×D6111yescharacteristic
997C23#41×D6111yescharacteristic
998C23C2×#1175822411yescharacteristic
999C23C2×#1175822211yescharacteristic
1000C23C2×#1175822211yescharacteristic
1001C23C2×#1175822211yescharacteristic
1002C23#1451982211yescharacteristic
1003C23#1451982211yescharacteristic
1004C23#1451982311yescharacteristic
1005C23#1451982311yescharacteristic
1006D4—24416no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—416no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—614no—
1047C2×C4—614no—
1048C2×C4—614no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—1222no—
1064C2×C4—1222no—
1065C2×C4—1222no—
1066C2×C4—1222no—
1067C2×C4—1222no—
1068C2×C4—1222no—
1069C2×C4—1222no—
1070C2×C4—1222no—
1071C2×C4—1222no—
1072C2×C4—1222no—
1073C2×C4—1222no—
1074C2×C4—1222no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1222no—
1078C2×C4—1222no—
1079C2×C4—24416no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4—2441no—
1090C2×C4—2441no—
1091C2×C4—2441no—
1092C2×C4—2441no—
1093C2×C4—2441no—
1094C2×C4—2441no—
1095C2×C4—2441no—
1096C2×C4#1451973714yes—
1097C2×C4C4×C22⋊D6114yes—
1098C2×C4C4×C22⋊D6114yes—
1099C2×C4C4×C22⋊D6114yes—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—1224no—
1116C22—1224no—
1117C22—1224no—
1118C22—2442no—
1119C22—2442no—
1120C22—2442no—
1121C22—2442no—
1122C22—2442no—
1123C22—2442no—
1124C22—2442no—
1125C22—2442no—
1126C22—2442no—
1127C22—2442no—
1128C22—2442no—
1129C22—2442no—
1130C22C2×C42×D6111yescharacteristic
1131C22C4×D4×D6111yescharacteristic
1132C22C4×D4×D6111yescharacteristic
1133C22C2×#1451973711yescharacteristic
1134C22C2×C4×C22⋊D6111yescharacteristic
1135C22C2×C4×C22⋊D6111yescharacteristic
1136C22C2×C4×C22⋊D6111yescharacteristic
1137C22C4×#1175822411yescharacteristic
1138C22C4×#1175822411yescharacteristic
1139C22#1684023011yescharacteristic
1140C22C4×#1175822211yescharacteristic
1141C22C4×#1175822211yescharacteristic
1142C22C4×#1175822211yescharacteristic
1143C22#1684023411yescharacteristic
1144C22#1684023411yescharacteristic
1145C22#1684023411yescharacteristic
1146C22#1684023411yescharacteristic
1147C22#1684023511yescharacteristic
1148C22#1684023611yescharacteristic
1149C22D4×C22⋊D6111yescharacteristic
1150C22#1684040011yescharacteristic
1151C22#1684040211yescharacteristic
1152C22#1684040611yescharacteristic
1153C22#1684040811yescharacteristic
1154C22#1684043111yescharacteristic
1155C22#1684043311yescharacteristic
1156C22#1684043811yescharacteristic
1157C22#1684044111yescharacteristic
1158C22#1684045611yescharacteristic
1159C22#1684045811yescharacteristic
1160C22#1684046111yescharacteristic
1161C22#1684046211yescharacteristic
1162C22#1684047511yescharacteristic
1163C22#1684047711yescharacteristic
1164C22#1684049511yescharacteristic
1165C4—24no—
1166C4—24no—
1167C4—24no—
1168C4—24no—
1169C4—42no—
1170C4—42no—
1171C4—1224no—
1172C4—1224no—
1173C4—1224no—
1174C4—2442no—
1175C4—2442no—
1176C4—2442no—
1177C4—2442no—
1178C2—44no—
1179C2—2444no—
1180C2C4×#1451973711yescharacteristic
1181C2C42×C22⋊D6111yescharacteristic
1182C2#2144817111yescharacteristic
1183C2#2144879611yescharacteristic
1184C2#2144879811yescharacteristic
1185C2#2144885311yescharacteristic
1186C2#2144885511yescharacteristic
1187C2#2144885711yescharacteristic
1188C2#2144885811yescharacteristic
1189C2#2144886411yescharacteristic
1190C2#2144887011yescharacteristic
1191C2#2144888111yescharacteristic
1192C2#2144892711yescharacteristic
1193C2#2144895011yescharacteristic
1194C2#2144895311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#13824
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4×#11758198C2semidirect
5. C2×C4×C22⋊Dic61C2semidirect
6. C2×#16839609C2semidirect
7. #21444057C2semidirect
8. #21444056C2semidirect
9. #21444056C2semidirect
10. #21444055C2semidirect
11. #21444052C2semidirect
12. #21444050C2semidirect
13. C4×#14519684C2semidirect
14. #95×Dic61C2semidirect
15. C2×C4×C22⋊C4×C61C2semidirect
32. #16839662C4semidirect
33. #16839641C4semidirect
34. #16839638C4semidirect
79. C22×C4×D61C2×C4semidirect
82. C2×#11758196C2×C4semidirect
90. C2×C22⋊Dic61C2×C4semidirect
91. C2×C22⋊Dic61C2×C4semidirect
104. C2×#11758198C2×C4semidirect
105. C2×#11758198C2×C4semidirect
106. C2×#11758198C2×C4semidirect
121. C2×C4×Dic61C2×C4semidirect
129. #14519684C2×C4semidirect
130. #14519684C2×C4semidirect
131. #14519684C2×C4semidirect
132. #14519684C2×C4semidirect
133. #14519684D4semidirect
141. C23×C4×C61C2×C4semidirect
153. C2×C22⋊C4×C61C2×C4semidirect
161. #95×C61D4semidirect
248. C2×C22⋊D61C42semidirect
587. C2×C4×C22⋊C4D61semidirect
655. C61#13824semidirect
685. C23×C4C4×D61semidirect
724. C2×C22⋊C4C4×D61semidirect
759. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396622
C2×#168396412
C2×#168396382
C2×C4×#117581982
C2×C4×C22⋊Dic612
C2×#168396092
#214440572
#214440562
#214440552
#214440522
#214440502
C4×#145196842
#95×Dic612
C2×C4×C22⋊C4×C612
#1382461