Finite Group Databasebeta

← #29609178

Subgroups — #29609178

Order 15616.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519759C211yesmaximal, characteristic
2C2×#16839662C211yesmaximal, characteristic
3C2×#16839639C211yesmaximal, characteristic
4#21444071C211yesmaximal, characteristic, complemented
5#21444070C211yesmaximal, characteristic, complemented
6#21444067C211yesmaximal, characteristic, complemented
7#21444067C211yesmaximal, characteristic, complemented
8#21444066C211yesmaximal, characteristic, complemented
9#21444053C211yesmaximal, characteristic, complemented
10#21444050C211yesmaximal, characteristic, complemented
11#21444041C211yesmaximal, characteristic, complemented
12#21444041C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519759—24no—
20C2×#14519759—24no—
21C2×#14519759C418yescomplemented
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839662—24no—
34#16839639—24no—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C22×C22⋊C4×C61C2211yescharacteristic
50C22×C22⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C24×D61C2311yescharacteristic
57C22×C22⋊D61—41no—
58C22×C22⋊D61—41no—
59C22×C22⋊D61—41no—
60C22×C22⋊D61—41no—
61C22×C22⋊D61C2×C414yes—
62C22×C22⋊D61D414yes—
63C22×C22⋊D61D414yes—
64C23×Dic61—22no—
65C23×Dic61—22no—
66C23×Dic61—22no—
67C23×Dic61—41no—
68C23×Dic61—41no—
69C23×Dic61—41no—
70C23×Dic61—41no—
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C22×C4×D61—41no—
84C22×C4×D61C2×C414yescomplemented
85#14519759—232no—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61C2×C414yescomplemented
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196—41no—
93C2×#11758196—41no—
94C2×#11758196C2×C414yescomplemented
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—41no—
100C2×C22⋊Dic61C2×C414yes—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198C2×C414yescomplemented
116C2×C4×Dic61—22no—
117C2×C4×Dic61—41no—
118C2×C4×Dic61—41no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—41no—
125#14519684—41no—
126#14519684—41no—
127#14519684—41no—
128#14519684—41no—
129#14519684—41no—
130#14519684—41no—
131#14519684—41no—
132#14519684—41no—
133C25×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—22no—
141C2×C22⋊C4×C61—22no—
142C2×C22⋊C4×C61—22no—
143C2×C22⋊C4×C61—22no—
144C2×C22⋊C4×C61—22no—
145C2×C22⋊C4×C61—41no—
146C2×C22⋊C4×C61—41no—
147C2×C22⋊C4×C61—41no—
148C2×C22⋊C4×C61C2×C414yes—
149#95×C61—22no—
150#95×C61—41no—
151#95×C61—41no—
152#95×C61—41no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61C22×C412yes—
166C24×C61C2×D412yes—
167C24×C61C2×D412yes—
168C24×C61C2411yescharacteristic
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61C22×C412yes—
182C23×D61C2×D412yes—
183C23×D61C2×D412yes—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—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—21no—
222C22×C4×C61—21no—
223C22×C4×C61C22×C412yes—
224C22×C4×C61C22×C412yes—
225C22×C4×C61#4112yes—
226C2×C22⋊D61—44no—
227C2×C22⋊D61—44no—
228C2×C22⋊D61—44no—
229C2×C22⋊D61—44no—
230C2×C22⋊D61—44no—
231C2×C22⋊D61—44no—
232C2×C22⋊D61C22⋊C4116yes—
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—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—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—44no—
275C22×Dic61—44no—
276C22×Dic61—44no—
277C22×Dic61—44no—
278C22×Dic61—44no—
279C22×Dic61—44no—
280C22×Dic61—44no—
281C22×Dic61C22×C412yes—
282C22×Dic61C22×C412yes—
283C22×Dic61C22×C412yes—
284C22×Dic61C2×D412yes—
285C22×Dic61C2×D412yes—
286C22×Dic61#4112yes—
287C22×Dic61#4112yes—
288C22×Dic61#4112yes—
289C2×C4×D61—28no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C2×C4×D61—44no—
296C22⋊C4×C61—28no—
297C22⋊C4×C61—44no—
298C22⋊C4×C61—44no—
299C22⋊Dic61—28no—
300C22⋊Dic61—44no—
301#11758198—28no—
302#11758198—44no—
303#11758198—44no—
304#11758198—44no—
305#11758198—44no—
306C4⋊Dic61—28no—
307#11758196—28no—
308#11758196—44no—
309C4×Dic61—44no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61C2×C22⋊C414yes—
345C23×C61C23×C411yescharacteristic
346C23×C61C22×D411yescharacteristic
347C23×C61C22×D411yescharacteristic
348C23×C61C2×#4111yescharacteristic
349C23×C61C2×#4111yescharacteristic
350C23×C61C2×#4111yescharacteristic
351C23×C61C2×#4111yescharacteristic
352C23×C61H(5,𝔽2)11yescharacteristic
353C23×C61H(5,𝔽2)11yescharacteristic
354C23×C61H(5,𝔽2)11yescharacteristic
355C23×C61H(5,𝔽2)11yescharacteristic
356C23×C61H(5,𝔽2)11yescharacteristic
357C23×C61H(5,𝔽2)11yescharacteristic
358C23×C612−1+411yescharacteristic
359C23×C612−1+411yescharacteristic
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61—41no—
393C22×D61—41no—
394C22×D61C2×C22⋊C414yes—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C22⋊D61—416no—
438C2×Dic61—22no—
439C2×Dic61—22no—
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—22no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—416no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—41no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—41no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61C2×C22⋊C414yes—
488C4×D61—416no—
489#14505—611nomaximal, Sylow
490C22×C61—24no—
491C22×C61—24no—
492C22×C61—24no—
493C22×C61—42no—
494C22×C61—42no—
495C22×C61—42no—
496C22×C61—42no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—42no—
500C22×C61—42no—
501C22×C61—42no—
502C22×C61—42no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61C22×C22⋊C411yescharacteristic
506C22×C61C4×#4111yescharacteristic
507C22×C61C4×#4111yescharacteristic
508C22×C61#51811yescharacteristic
509C22×C61#51811yescharacteristic
510C22×C61#52011yescharacteristic
511C22×C61#52011yescharacteristic
512C22×C61#53411yescharacteristic
513C22×C61#53411yescharacteristic
514C22×C61#53411yescharacteristic
515C22×C61#53411yescharacteristic
516C22×C61#53811yescharacteristic
517C22×C61#53811yescharacteristic
518C22×C61#53911yescharacteristic
519C22×C61#53911yescharacteristic
520C22×C61#54011yescharacteristic
521C22×C61#54011yescharacteristic
522C22×C61#54211yescharacteristic
523C22×C61#54211yescharacteristic
524C22×C61#54611yescharacteristic
525C22×C61#54611yescharacteristic
526C22×C61#54611yescharacteristic
527C22×C61#54611yescharacteristic
528C22×C61#54711yescharacteristic
529C22×C61#54711yescharacteristic
530C22×C61#54711yescharacteristic
531C22×C61#54711yescharacteristic
532C22×C61#55111yescharacteristic
533C22×C61#55311yescharacteristic
534C22×C61#55311yescharacteristic
535C22×C61#55911yescharacteristic
536C22×C61#56011yescharacteristic
537C22×C61#56211yescharacteristic
538C22×C61#56211yescharacteristic
539C22×C61#56311yescharacteristic
540C2×D61—24no—
541C2×D61—24no—
542C2×D61—24no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—42no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—42no—
555C4×C61—42no—
556C4×C61—42no—
557C4×C61—42no—
558C4×C61—81no—
559C4×C61—81no—
560C4×C61—81no—
561Dic61—24no—
562Dic61—42no—
563Dic61—42no—
564Dic61—42no—
565Dic61—42no—
566Dic61—42no—
567Dic61—81no—
568C22×#123—611no—
569C2×#390—611no—
570C2×#386—611no—
571#1441—611no—
572#1441—611no—
573#1440—611no—
574#1440—611no—
575#1440—611no—
576#1440D6111yescharacteristic, complemented
577#1436—611no—
578#1436—611no—
579C22⋊#95—611no—
580C22⋊#95—611no—
581C22⋊#95—611no—
582C22⋊#95—611no—
583C2×C61—44no—
584C2×C61#230811yescharacteristic
585C2×C61#233511yescharacteristic
586C2×C61#233511yescharacteristic
587C2×C61#233911yescharacteristic
588C2×C61#233911yescharacteristic
589C2×C61#237411yescharacteristic
590C2×C61#237611yescharacteristic
591C2×C61#269711yescharacteristic
592C2×C61#270111yescharacteristic
593C2×C61#270111yescharacteristic
594C2×C61#270811yescharacteristic
595C2×C61#270811yescharacteristic
596C2×C61#270911yescharacteristic
597C2×C61#271711yescharacteristic
598C2×C61#272411yescharacteristic
599D61—44no—
600C23×D4—611no—
601C24×C4—611no—
602C24×C4—611no—
603C2×#123—618no—
604C2×#123—1224no—
605C2×#123—1224no—
606C22×C4⋊C4—611no—
607C22×C4⋊C4—611no—
608C22×C4⋊C4—611no—
609C22×C22⋊C4—611no—
610C22×C22⋊C4—611no—
611C22×C22⋊C4—611no—
612C22×C22⋊C4—611no—
613C22×C22⋊C4—611no—
614C22×C22⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4C2×D6111yescharacteristic
617C22×C22⋊C4C2×D6111yescharacteristic
618C22×C22⋊C4C2×D6111yescharacteristic
619C22×C42—611no—
620#390—1224no—
621#386—1224no—
622C2×#95—611no—
623C2×#95—611no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95—611no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95C2×D6111yescharacteristic
637C2×#95C2×D6111yescharacteristic
638C2×#95C2×D6111yescharacteristic
639C2×#95C2×D6111yescharacteristic
640C61#1450511yescharacteristic, complemented, Sylow
641C25—611no—
642C25C22×D6111yescharacteristic
643C22×D4—614no—
644C22×D4—614no—
645C22×D4—614no—
646C22×D4—2441no—
647C22×D4—2441no—
648C22×D4—2441no—
649C22×D4—2441no—
650C23×C4—611no—
651C23×C4—611no—
652C23×C4—611no—
653C23×C4—611no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—614no—
657C23×C4—611no—
658C23×C4—1222no—
659C23×C4—1222no—
660C23×C4—1222no—
661C23×C4—1222no—
662C23×C4—1222no—
663C23×C4—2441no—
664C23×C4—2441no—
665C23×C4—2441no—
666C23×C4—2441no—
667C23×C4—2441no—
668C23×C4—2441no—
669C23×C4—2441no—
670C23×C4—2441no—
671C23×C4C22×D6111yescharacteristic
672C23×C4C22×D6111yescharacteristic
673C23×C4C22×D6111yescharacteristic
674C23×C4C22×D6111yescharacteristic
675C23×C4C22×D6111yescharacteristic
676C23×C4C22×D6111yescharacteristic
677#123—12232no—
678C2×C4⋊C4—614no—
679C2×C4⋊C4—614no—
680C2×C4⋊C4—1222no—
681C2×C4⋊C4—1222no—
682C2×C4⋊C4—1222no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—1222no—
685C2×C4⋊C4—2441no—
686C2×C4⋊C4—2441no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—614no—
696C2×C22⋊C4—614no—
697C2×C22⋊C4—1222no—
698C2×C22⋊C4—1222no—
699C2×C22⋊C4—1222no—
700C2×C22⋊C4—1222no—
701C2×C22⋊C4—1222no—
702C2×C22⋊C4—1222no—
703C2×C22⋊C4—1222no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—2441no—
712C2×C22⋊C4—2441no—
713C2×C22⋊C4—2441no—
714C2×C22⋊C4—2441no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4C4×D6114yes—
717C2×C42—1222no—
718C2×C42—2441no—
719C2×C42—2441no—
720#95—22no—
721#95—41no—
722#95—41no—
723#95—41no—
724#95—1222no—
725#95—1222no—
726#95—1222no—
727#95—1222no—
728#95—1222no—
729#95—2441no—
730#95—2441no—
731#95—2441no—
732#95—2441no—
733#95—2441no—
734#95—2441no—
735#95—2441no—
736#95—2441no—
737#95—2441no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—612no—
751C24—612no—
752C24—612no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24C2×C4×D6112yes—
766C24D4×D6112yes—
767C24D4×D6112yes—
768C24C23×D6111yescharacteristic
769C2×D4—6116no—
770C2×D4—2444no—
771C2×D4—2444no—
772C2×D4—2444no—
773C2×D4—2444no—
774C2×D4—2444no—
775C2×D4—2444no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
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—612no—
816C22×C4—612no—
817C22×C4—612no—
818C22×C4—612no—
819C22×C4—612no—
820C22×C4—612no—
821C22×C4—612no—
822C22×C4—612no—
823C22×C4—1228no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
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—2444no—
866C22×C4—2444no—
867C22×C4—2444no—
868C22×C4—2444no—
869C22×C4—2444no—
870C22×C4—2444no—
871C22×C4—2444no—
872C22×C4—2444no—
873C22×C4—2444no—
874C22×C4—2444no—
875C22×C4—2444no—
876C22×C4—2444no—
877C22×C4—2444no—
878C22×C4C2×C4×D6112yes—
879C22×C4C2×C4×D6112yes—
880C22×C4#1175822412yes—
881C4⋊C4—1228no—
882C4⋊C4—1228no—
883C4⋊C4—2444no—
884C22⋊C4—28no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—1228no—
888C22⋊C4—1228no—
889C22⋊C4—2444no—
890C22⋊C4—2444no—
891C22⋊C4—2444no—
892C22⋊C4—2444no—
893C22⋊C4—2444no—
894C42—2444no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—614no—
930C23—1222no—
931C23—1222no—
932C23—1222no—
933C23—1222no—
934C23—1222no—
935C23—1222no—
936C23—1222no—
937C23—1222no—
938C23—1222no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
943C23—1222no—
944C23—1222no—
945C23—1222no—
946C23—1222no—
947C23—1222no—
948C23—2441no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23C22⋊C4×D6114yes—
965C23C22×C4×D6111yescharacteristic
966C23C2×D4×D6111yescharacteristic
967C23C2×D4×D6111yescharacteristic
968C23#41×D6111yescharacteristic
969C23#41×D6111yescharacteristic
970C23#41×D6111yescharacteristic
971C23C2×#1175822411yescharacteristic
972C23#1451982211yescharacteristic
973C23#1451982211yescharacteristic
974C23#1451982211yescharacteristic
975C23#1451982311yescharacteristic
976C23#1451982311yescharacteristic
977C23#1451982311yescharacteristic
978C23#1451982411yescharacteristic
979C23#1451982411yescharacteristic
980D4—24416no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—614no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—1222no—
1037C2×C4—1222no—
1038C2×C4—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—24416no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—24416no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—1224no—
1090C22—1224no—
1091C22—1224no—
1092C22—2442no—
1093C22—2442no—
1094C22—2442no—
1095C22—2442no—
1096C22—2442no—
1097C22—2442no—
1098C22—2442no—
1099C22—2442no—
1100C22—2442no—
1101C22—2442no—
1102C22—2442no—
1103C22—2442no—
1104C22C2×C22⋊C4×D6111yescharacteristic
1105C22C4×#1175822411yescharacteristic
1106C22#1684023011yescharacteristic
1107C22#1684023411yescharacteristic
1108C22#1684023411yescharacteristic
1109C22#1684024111yescharacteristic
1110C22#1684024211yescharacteristic
1111C22#1684032011yescharacteristic
1112C22#1684032011yescharacteristic
1113C22#1684032211yescharacteristic
1114C22#1684032311yescharacteristic
1115C22#1684034611yescharacteristic
1116C22#1684035111yescharacteristic
1117C22#1684035311yescharacteristic
1118C22#1684035611yescharacteristic
1119C22#1684036211yescharacteristic
1120C22#1684036511yescharacteristic
1121C22#1684037611yescharacteristic
1122C22#1684038011yescharacteristic
1123C22#1684039911yescharacteristic
1124C22#1684040111yescharacteristic
1125C22#1684040411yescharacteristic
1126C22#1684040411yescharacteristic
1127C22#1684041011yescharacteristic
1128C22#1684041011yescharacteristic
1129C22#1684041011yescharacteristic
1130C22#1684041211yescharacteristic
1131C22#1684043711yescharacteristic
1132C22#1684045511yescharacteristic
1133C22#1684045711yescharacteristic
1134C22#1684049411yescharacteristic
1135C22#1684050211yescharacteristic
1136C22#1684050611yescharacteristic
1137C22#1684050711yescharacteristic
1138C22#1684051411yescharacteristic
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—1224no—
1146C4—4881no—
1147C4—2442no—
1148C4—2442no—
1149C4—2442no—
1150C4—2442no—
1151C4—2442no—
1152C2—44no—
1153C2—2444no—
1154C2#2144839311yescharacteristic
1155C2#2144860711yescharacteristic
1156C2#2144861611yescharacteristic
1157C2#2144864311yescharacteristic
1158C2#2144864511yescharacteristic
1159C2#2144894711yescharacteristic
1160C2#2144896111yescharacteristic
1161C2#2145238411yescharacteristic
1162C2#2145243411yescharacteristic
1163C2#2145243811yescharacteristic
1164C2#2145253011yescharacteristic
1165C2#2145253611yescharacteristic
1166C2#2145254511yescharacteristic
1167C2#2145265311yescharacteristic
1168C2#2145275111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1440C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1440D61
hypocenterC61#14505
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
4. #21444071C2semidirect
5. #21444070C2semidirect
6. #21444067C2semidirect
7. #21444067C2semidirect
8. #21444066C2semidirect
9. #21444053C2semidirect
10. #21444050C2semidirect
11. #21444041C2semidirect
12. #21444041C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1440C2semidirect
21. C2×#14519759C4semidirect
84. C22×C4×D61C2×C4semidirect
88. C2×C4⋊Dic61C2×C4semidirect
94. C2×#11758196C2×C4semidirect
115. C2×#11758198C2×C4semidirect
576. #1440D61semidirect
640. C61#14505semidirect

Maximal subgroups

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

subgroupindex
C22×#145197592
C2×#168396622
C2×#168396392
#214440712
#214440702
#214440672
#214440662
#214440532
#214440502
#214440412
#214440402
C61×#14402
#1450561