Finite Group Databasebeta

← #29609182

Subgroups — #29609182

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×#14519762C211yesmaximal, characteristic
2C2×#16839664C211yesmaximal, characteristic
3C2×#16839640C211yesmaximal, characteristic
4#21444073C211yesmaximal, characteristic, complemented
5#21444072C211yesmaximal, characteristic, complemented
6#21444067C211yesmaximal, characteristic, complemented
7#21444067C211yesmaximal, characteristic, complemented
8#21444067C211yesmaximal, characteristic, complemented
9#21444067C211yesmaximal, characteristic, complemented
10#21444052C211yesmaximal, characteristic, complemented
11#21444040C211yesmaximal, characteristic, complemented
12#21444040C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519762—24no—
20C2×#14519762—24no—
21C2×#14519762C418yescomplemented
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34#16839664—24no—
35#16839640—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
48C2×#14519684C2211yescharacteristic
49C22×C4⋊C4×C61C2211yescharacteristic
50C22×C42×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C24×D61C2311yescharacteristic
57C24×D61C2311yescharacteristic
58C22×D244—41no—
59C22×D244—41no—
60C22×D244—41no—
61C22×D244—41no—
62C22×D244C2×C414yes—
63C22×D244D414yes—
64C22×D244D414yes—
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—41no—
77C22×C4×D61—41no—
78C22×C4×D61—41no—
79C22×C4×D61—41no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C22×C4×D61—41no—
84C22×C4×D61C2×C414yescomplemented
85#14519762—232no—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61—41no—
88C2×C4⋊Dic61—41no—
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196C2×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—22no—
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×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198—41no—
119C2×#11758198C2×C414yes—
120C2×#11758198C2×C414yes—
121C2×#11758198C2×C414yescomplemented
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—41no—
126#14519684—41no—
127#14519684—41no—
128#14519684—41no—
129#14519684—41no—
130#14519684—41no—
131#14519684—41no—
132#14519684—41no—
133#14519684—41no—
134#14519684—41no—
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61—22no—
143C2×C4⋊C4×C61—22no—
144C2×C4⋊C4×C61C2×C414yescomplemented
145C2×C42×C61—22no—
146C2×C42×C61—41no—
147C2×C42×C61—41no—
148#95×C61—22no—
149#95×C61—22no—
150#95×C61—22no—
151#95×C61—41no—
152#95×C61—41no—
153C24×C61C2411yescharacteristic
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—21no—
157C23×D61—21no—
158C23×D61—21no—
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
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×D61C22×C412yes—
179C23×D61C22×C412yes—
180C23×D61C2×D412yes—
181C23×D61C2×D412yes—
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×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61C22×C412yes—
226C22×C4×C61C22×C412yes—
227C22×C4×C61C22×C412yes—
228C22×C4×C61C2×D412yes—
229C22×C4×C61C2×D412yes—
230C22×C4×C61#4112yes—
231C22×C4×C61#4112yes—
232C22×C4×C61#4112yes—
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×Dic61C22×C412yes—
273C22×Dic61C22×C412yes—
274C22×Dic61#4112yes—
275C2×D244—44no—
276C2×D244—44no—
277C2×D244—44no—
278C2×D244—44no—
279C2×D244—44no—
280C2×D244—44no—
281C2×D244C22⋊C4116yes—
282C2×C4×D61—28no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61—44no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C2×C4×D61—44no—
289C2×C4×D61—44no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C2×C4×D61—44no—
296C4⋊C4×C61—28no—
297C42×C61—44no—
298#11758198—28no—
299#11758198—28no—
300#11758198—28no—
301#11758198—44no—
302#11758198—44no—
303#11758198—44no—
304#11758198—44no—
305#11758198—44no—
306#11758198—44no—
307#11758198—44no—
308C4⋊Dic61—44no—
309#11758196—28no—
310C23×C61C23×C411yescharacteristic
311C23×C61C22×D411yescharacteristic
312C23×C61C22×D411yescharacteristic
313C23×C61C2×#4111yescharacteristic
314C23×C61C2×#4111yescharacteristic
315C23×C61C2×#4111yescharacteristic
316C23×C61C2×#4111yescharacteristic
317C23×C61H(5,𝔽2)11yescharacteristic
318C23×C61H(5,𝔽2)11yescharacteristic
319C23×C61H(5,𝔽2)11yescharacteristic
320C23×C61H(5,𝔽2)11yescharacteristic
321C23×C61H(5,𝔽2)11yescharacteristic
322C23×C61H(5,𝔽2)11yescharacteristic
323C23×C612−1+411yescharacteristic
324C23×C612−1+411yescharacteristic
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
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×D61C2×C22⋊C414yes—
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—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
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—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—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61C2×C22⋊C414yes—
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—41no—
454C2×Dic61—41no—
455C2×Dic61—41no—
456C2×Dic61—41no—
457C2×Dic61—41no—
458C2×Dic61—41no—
459C2×Dic61—41no—
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—
486D244—416no—
487C4×D61—416no—
488C4×D61—416no—
489#14505—611nomaximal, Sylow
490C22×C61C22×C22⋊C411yescharacteristic
491C22×C61C4×#4111yescharacteristic
492C22×C61C4×#4111yescharacteristic
493C22×C61#51811yescharacteristic
494C22×C61#51811yescharacteristic
495C22×C61#52011yescharacteristic
496C22×C61#52011yescharacteristic
497C22×C61#53411yescharacteristic
498C22×C61#53411yescharacteristic
499C22×C61#53411yescharacteristic
500C22×C61#53411yescharacteristic
501C22×C61#53811yescharacteristic
502C22×C61#53811yescharacteristic
503C22×C61#53911yescharacteristic
504C22×C61#53911yescharacteristic
505C22×C61#54011yescharacteristic
506C22×C61#54011yescharacteristic
507C22×C61#54211yescharacteristic
508C22×C61#54211yescharacteristic
509C22×C61#54611yescharacteristic
510C22×C61#54611yescharacteristic
511C22×C61#54611yescharacteristic
512C22×C61#54611yescharacteristic
513C22×C61#54711yescharacteristic
514C22×C61#54711yescharacteristic
515C22×C61#54711yescharacteristic
516C22×C61#54711yescharacteristic
517C22×C61#55111yescharacteristic
518C22×C61#55311yescharacteristic
519C22×C61#55311yescharacteristic
520C22×C61#55911yescharacteristic
521C22×C61#56011yescharacteristic
522C22×C61#56211yescharacteristic
523C22×C61#56211yescharacteristic
524C22×C61#56311yescharacteristic
525C2×D61—24no—
526C2×D61—24no—
527C2×D61—24no—
528C2×D61—24no—
529C2×D61—24no—
530C2×D61—24no—
531C2×D61—42no—
532C2×D61—42no—
533C2×D61—42no—
534C2×D61—42no—
535C2×D61—42no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
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—24no—
556C4×C61—42no—
557C4×C61—42no—
558C4×C61—42no—
559C4×C61—42no—
560C4×C61—42no—
561C4×C61—81no—
562Dic61—42no—
563Dic61—42no—
564Dic61—42no—
565Dic61—81no—
566Dic61—81no—
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#1440—611no—
577#1436—611no—
578#1436D6111yescharacteristic, complemented
579C22⋊#95—611no—
580C22⋊#95—611no—
581C22⋊#95—611no—
582C22⋊#95—611no—
583C2×C61#230811yescharacteristic
584C2×C61#233511yescharacteristic
585C2×C61#233511yescharacteristic
586C2×C61#233911yescharacteristic
587C2×C61#233911yescharacteristic
588C2×C61#237411yescharacteristic
589C2×C61#237611yescharacteristic
590C2×C61#269711yescharacteristic
591C2×C61#270111yescharacteristic
592C2×C61#270111yescharacteristic
593C2×C61#270811yescharacteristic
594C2×C61#270811yescharacteristic
595C2×C61#270911yescharacteristic
596C2×C61#271711yescharacteristic
597C2×C61#272411yescharacteristic
598D61—44no—
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⋊C4C2×D6111yescharacteristic
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⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C42C2×D6111yescharacteristic
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×#95C2×D6111yescharacteristic
636C2×#95C2×D6111yescharacteristic
637C2×#95C2×D6111yescharacteristic
638C2×#95C2×D6111yescharacteristic
639C2×#95C2×D6111yescharacteristic
640C61#1450511yescharacteristic, complemented, Sylow
641C25—611no—
642C25—611no—
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—614no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—1222no—
658C23×C4—1222no—
659C23×C4—1222no—
660C23×C4—1222no—
661C23×C4—1222no—
662C23×C4—2441no—
663C23×C4—2441no—
664C23×C4—2441no—
665C23×C4—2441no—
666C23×C4—2441no—
667C23×C4—2441no—
668C23×C4—2441no—
669C23×C4—2441no—
670C23×C4C22×D6111yescharacteristic
671C23×C4C22×D6111yescharacteristic
672C23×C4C22×D6111yescharacteristic
673C23×C4C22×D6111yescharacteristic
674C23×C4C22×D6111yescharacteristic
675C23×C4C22×D6111yescharacteristic
676C23×C4C22×D6111yescharacteristic
677#123—12232no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—614no—
681C2×C4⋊C4—1222no—
682C2×C4⋊C4—1222no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—2441no—
685C2×C4⋊C4—2441no—
686C2×C4⋊C4C4×D6114yescomplemented
687C2×C22⋊C4—614no—
688C2×C22⋊C4—614no—
689C2×C22⋊C4—614no—
690C2×C22⋊C4—1222no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4—1222no—
695C2×C22⋊C4—1222no—
696C2×C22⋊C4—1222no—
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—2441no—
710C2×C22⋊C4—2441no—
711C2×C22⋊C4—2441no—
712C2×C22⋊C4—2441no—
713C2×C22⋊C4—2441no—
714C2×C22⋊C4—2441no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4—2441no—
717C2×C42—22no—
718C2×C42—41no—
719C2×C42—41no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—41no—
724#95—41no—
725#95—1222no—
726#95—1222no—
727#95—1222no—
728#95—2441no—
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—612no—
739C24—612no—
740C24—612no—
741C24—612no—
742C24—612no—
743C24—612no—
744C24—1221no—
745C24—1221no—
746C24—1221no—
747C24—1221no—
748C24—1221no—
749C24—1221no—
750C24—1221no—
751C24—1221no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24—1221no—
767C24—1221no—
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—21no—
816C22×C4—21no—
817C22×C4—612no—
818C22×C4—612no—
819C22×C4—612no—
820C22×C4—1228no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
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—2444no—
861C22×C4—2444no—
862C22×C4—2444no—
863C22×C4—2444no—
864C22×C4—2444no—
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×C4C2×C4×D6112yes—
874C22×C4C2×C4×D6112yes—
875C22×C4C2×C4×D6112yes—
876C22×C4#1175822212yes—
877C22×C4#1175822212yes—
878C22×C4D4×D6112yes—
879C22×C4D4×D6112yes—
880C22×C4#1175822612yes—
881C4⋊C4—28no—
882C4⋊C4—1228no—
883C4⋊C4—2444no—
884C22⋊C4—1228no—
885C22⋊C4—1228no—
886C22⋊C4—1228no—
887C22⋊C4—2444no—
888C22⋊C4—2444no—
889C22⋊C4—2444no—
890C22⋊C4—2444no—
891C22⋊C4—2444no—
892C22⋊C4—2444no—
893C22⋊C4—2444no—
894C42—44no—
895C23—614no—
896C23—614no—
897C23—1222no—
898C23—1222no—
899C23—1222no—
900C23—1222no—
901C23—1222no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—1222no—
909C23—1222no—
910C23—1222no—
911C23—1222no—
912C23—1222no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1222no—
917C23—1222no—
918C23—1222no—
919C23—1222no—
920C23—1222no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—1222no—
927C23—1222no—
928C23—1222no—
929C23—1222no—
930C23—1222no—
931C23—1222no—
932C23—1222no—
933C23—2441no—
934C23—2441no—
935C23—2441no—
936C23—2441no—
937C23—2441no—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23—2441no—
947C23—2441no—
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—
964C23—2441no—
965C23C22×C4×D6111yescharacteristic
966C23C2×D4×D6111yescharacteristic
967C23C2×D4×D6111yescharacteristic
968C23#41×D6111yescharacteristic
969C23C2×#1175822211yescharacteristic
970C23C2×#1175822211yescharacteristic
971C23C2×#1175822611yescharacteristic
972C23#1451982211yescharacteristic
973C23#1451982211yescharacteristic
974C23#1451982311yescharacteristic
975C23#1451982311yescharacteristic
976C23#1451982311yescharacteristic
977C23#1451982311yescharacteristic
978C23#1451982411yescharacteristic
979C23#1451982511yescharacteristic
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—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
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—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
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—24416no—
1039C2×C4—24416no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
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×C4C22⋊C4×D6114yes—
1074C22—1224no—
1075C22—1224no—
1076C22—1224no—
1077C22—1224no—
1078C22—1224no—
1079C22—1224no—
1080C22—2442no—
1081C22—2442no—
1082C22—2442no—
1083C22—2442no—
1084C22—2442no—
1085C22—2442no—
1086C22—2442no—
1087C22—2442no—
1088C22—2442no—
1089C22—2442no—
1090C22—2442no—
1091C22—2442no—
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×#1175822211yescharacteristic
1106C22C4×#1175822611yescharacteristic
1107C22#1684023411yescharacteristic
1108C22#1684023411yescharacteristic
1109C22#1684024211yescharacteristic
1110C22#1684024411yescharacteristic
1111C22#1684032011yescharacteristic
1112C22#1684032011yescharacteristic
1113C22#1684032211yescharacteristic
1114C22#1684032311yescharacteristic
1115C22#1684034511yescharacteristic
1116C22#1684034811yescharacteristic
1117C22#1684035911yescharacteristic
1118C22#1684036111yescharacteristic
1119C22#1684036711yescharacteristic
1120C22#1684036811yescharacteristic
1121C22#1684037811yescharacteristic
1122C22#1684038411yescharacteristic
1123C22#1684040311yescharacteristic
1124C22#1684040511yescharacteristic
1125C22#1684040811yescharacteristic
1126C22#1684040811yescharacteristic
1127C22#1684041411yescharacteristic
1128C22#1684041511yescharacteristic
1129C22#1684041711yescharacteristic
1130C22#1684041711yescharacteristic
1131C22#1684043611yescharacteristic
1132C22#1684046011yescharacteristic
1133C22#1684046111yescharacteristic
1134C22#1684049711yescharacteristic
1135C22#1684050311yescharacteristic
1136C22#1684050811yescharacteristic
1137C22#1684050911yescharacteristic
1138C22#1684051611yescharacteristic
1139C4—24no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—81no—
1146C4—4881no—
1147C4—4881no—
1148C4—4881no—
1149C4—2442no—
1150C4—2442no—
1151C4—2442no—
1152C2—2444no—
1153C2—2444no—
1154C2#2144839311yescharacteristic
1155C2#2144860311yescharacteristic
1156C2#2144860811yescharacteristic
1157C2#2144864811yescharacteristic
1158C2#2144865011yescharacteristic
1159C2#2144894811yescharacteristic
1160C2#2144896611yescharacteristic
1161C2#2145237911yescharacteristic
1162C2#2145242711yescharacteristic
1163C2#2145242911yescharacteristic
1164C2#2145253811yescharacteristic
1165C2#2145254011yescharacteristic
1166C2#2145255111yescharacteristic
1167C2#2145265911yescharacteristic
1168C2#2145274811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1436D61
hypocenterC61#14505
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. #21444073C2semidirect
5. #21444072C2semidirect
6. #21444067C2semidirect
7. #21444067C2semidirect
8. #21444067C2semidirect
9. #21444067C2semidirect
10. #21444052C2semidirect
11. #21444040C2semidirect
12. #21444040C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1436C2semidirect
21. C2×#14519762C4semidirect
84. C22×C4×D61C2×C4semidirect
91. C2×#11758196C2×C4semidirect
121. C2×#11758198C2×C4semidirect
144. C2×C4⋊C4×C61C2×C4semidirect
578. #1436D61semidirect
640. C61#14505semidirect
686. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197622
C2×#168396642
C2×#168396402
#214440732
#214440722
#214440672
#214440522
#214440402
C61×#14362
#1450561