Finite Group Databasebeta

← #29608021

Subgroups — #29608021

Order 15616.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839663C211yesmaximal, characteristic
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839640C211yesmaximal, characteristic
4C2×#16839636C211yesmaximal, characteristic, complemented
5C2×#16839619C211yesmaximal, characteristic, complemented
6#21444078C211yesmaximal, characteristic, complemented
7#21444063C211yesmaximal, characteristic, complemented
8#21444061C211yesmaximal, characteristic, complemented
9#21444061C211yesmaximal, characteristic, complemented
10#21444061C211yesmaximal, characteristic, complemented
11#21444053C211yesmaximal, characteristic, complemented
12#21444050C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1444C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839663—24no—
33#16839640—24no—
34#16839640C418yescomplemented
35#16839636—24no—
36#16839619—24no—
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×C4⋊C4×C61C2211yescharacteristic
51C22×C4⋊C4×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×D244Q814yes—
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
85C2×C4⋊Dic61—41no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61D414yescomplemented
88C2×#11758196—22no—
89C2×#11758196—22no—
90C2×#11758196—41no—
91C2×#11758198—22no—
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—41no—
107C2×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198C2×C414yes—
119C2×#11758198C2×C414yes—
120C2×#11758198C2×C414yescomplemented
121C2×C4×Dic61—22no—
122C2×C4×Dic61—41no—
123C2×C4×Dic61—41no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—41no—
131#14519684—41no—
132#14519684—41no—
133#14519684—41no—
134#14519684—41no—
135#14519684C2×C414yescomplemented
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61—22no—
144C2×C4⋊C4×C61—22no—
145C2×C4⋊C4×C61—41no—
146C2×C4⋊C4×C61—41no—
147C2×C4⋊C4×C61—41no—
148C2×C4⋊C4×C61—41no—
149C2×C4⋊C4×C61—41no—
150C2×C4⋊C4×C61—41no—
151C2×C4⋊C4×C61—41no—
152#95×C61—22no—
153#95×C61—22no—
154#95×C61—41no—
155#95×C61C2×C414yescomplemented
156C24×C61C2411yescharacteristic
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×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61C22×C412yes—
182C23×D61C22×C412yes—
183C23×D61C2×D412yes—
184C23×D61C2×D412yes—
185C23×D61C2×Q812yes—
186C23×D61C2×Q812yes—
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×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C22×C412yes—
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×Q812yes—
234C22×C4×C61#4112yes—
235C22×C4×C61#4112yes—
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×Dic61C22×C412yes—
274C22×Dic61C22×C412yes—
275C22×Dic61C2×D412yes—
276C22×Dic61C2×D412yes—
277C22×Dic61#4112yes—
278C2×D244—44no—
279C2×D244—44no—
280C2×D244—44no—
281C2×D244—44no—
282C2×D244—44no—
283C2×D244—44no—
284C2×D244C4⋊C4116yescomplemented
285C2×C4×D61—28no—
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—
296C2×C4×D61—44no—
297C2×C4×D61—44no—
298C2×C4×D61—44no—
299C4⋊C4×C61—44no—
300C4⋊C4×C61—44no—
301C4⋊C4×C61—44no—
302#11758198—28no—
303#11758198—44no—
304#11758198—44no—
305#11758198—44no—
306#11758198—44no—
307#11758198—44no—
308#11758198—44no—
309#11758198—44no—
310#11758198—44no—
311#11758198—44no—
312C4⋊Dic61—44no—
313#11758196—44no—
314C4×Dic61—44no—
315C23×C61C23×C411yescharacteristic
316C23×C61C22×D411yescharacteristic
317C23×C61C22×D411yescharacteristic
318C23×C61C22×Q811yescharacteristic
319C23×C61C2×#4111yescharacteristic
320C23×C61C2×#4111yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C23×C61H(5,𝔽2)11yescharacteristic
323C23×C61H(5,𝔽2)11yescharacteristic
324C23×C61H(5,𝔽2)11yescharacteristic
325C23×C61H(5,𝔽2)11yescharacteristic
326C23×C61H(5,𝔽2)11yescharacteristic
327C23×C61H(5,𝔽2)11yescharacteristic
328C23×C61H(5,𝔽2)11yescharacteristic
329C23×C612−1+411yescharacteristic
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—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—22no—
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×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61C2×C4⋊C414yes—
399C22×D61C2×C4⋊C414yes—
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—22no—
417C2×C4×C61—22no—
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×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61C2×C4⋊C414yes—
448C2×C4×C61C4×D414yes—
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—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
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×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491D244—416no—
492C4×D61—416no—
493C4×D61—416no—
494#14407—611nomaximal, Sylow
495C22×C61C22×C4⋊C411yescharacteristic
496C22×C61C2×C4×D411yescharacteristic
497C22×C61C4×#4111yescharacteristic
498C22×C61#51811yescharacteristic
499C22×C61#51811yescharacteristic
500C22×C61#51811yescharacteristic
501C22×C61#52011yescharacteristic
502C22×C61#53411yescharacteristic
503C22×C61#53411yescharacteristic
504C22×C61#53411yescharacteristic
505C22×C61#53511yescharacteristic
506C22×C61#53811yescharacteristic
507C22×C61#53811yescharacteristic
508C22×C61#53811yescharacteristic
509C22×C61#53911yescharacteristic
510C22×C61#54011yescharacteristic
511C22×C61#54211yescharacteristic
512C22×C61#54311yescharacteristic
513C22×C61#54311yescharacteristic
514C22×C61D4211yescharacteristic
515C22×C61#54611yescharacteristic
516C22×C61#54611yescharacteristic
517C22×C61#54611yescharacteristic
518C22×C61#54711yescharacteristic
519C22×C61D4×Q811yescharacteristic
520C22×C61#55011yescharacteristic
521C22×C61#55311yescharacteristic
522C22×C61#55411yescharacteristic
523C22×C61#55411yescharacteristic
524C22×C61#55411yescharacteristic
525C22×C61#55511yescharacteristic
526C22×C61#56011yescharacteristic
527C22×C61#56011yescharacteristic
528C22×C61#56211yescharacteristic
529C22×C61#56211yescharacteristic
530C2×D61—24no—
531C2×D61—24no—
532C2×D61—24no—
533C2×D61—24no—
534C2×D61—24no—
535C2×D61—24no—
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—
555C2×D61—42no—
556C2×D61—42no—
557C2×D61—42no—
558C2×D61—42no—
559C2×D61—42no—
560C4×C61—24no—
561C4×C61—24no—
562C4×C61—42no—
563C4×C61—42no—
564C4×C61—81no—
565C4×C61—81no—
566C4×C61—81no—
567Dic61—42no—
568Dic61—42no—
569Dic61—42no—
570Dic61—42no—
571Dic61—42no—
572Dic61—81no—
573C2×#390—611no—
574C2×#386—611no—
575C2×#386—611no—
576C2×#385—611no—
577C2×#380—611no—
578#1444D6111yescharacteristic, complemented
579#1442—611no—
580#1439—611no—
581#1439—611no—
582#1439—611no—
583#1439—611no—
584#1436—611no—
585#1436—611no—
586C22⋊#95—611no—
587C22⋊#95—611no—
588C2×C61#231511yescharacteristic
589C2×C61#232111yescharacteristic
590C2×C61#233511yescharacteristic
591C2×C61D4×C4⋊C411yescharacteristic
592C2×C61#234911yescharacteristic
593C2×C61#236311yescharacteristic
594C2×C61#237711yescharacteristic
595C2×C61#266811yescharacteristic
596C2×C61#267311yescharacteristic
597C2×C61#268611yescharacteristic
598C2×C61#269211yescharacteristic
599C2×C61#270811yescharacteristic
600C2×C61#273211yescharacteristic
601C2×C61#278011yescharacteristic
602C2×C61#278411yescharacteristic
603D61—44no—
604D61—44no—
605C23×D4—611no—
606C24×C4—611no—
607C24×C4—611no—
608C22×C4⋊C4—611no—
609C22×C4⋊C4—611no—
610C22×C4⋊C4C2×D6111yescharacteristic
611C22×C4⋊C4C2×D6111yescharacteristic
612C22×C4⋊C4C2×D6111yescharacteristic
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×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C22⋊C4—611no—
622C22×C22⋊C4—611no—
623C22×C42—611no—
624#390—1224no—
625#386—618no—
626#386—1224no—
627#385—1224no—
628#380—1224no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95C2×D6111yescharacteristic
642C2×#95C2×D6111yescharacteristic
643C2×#95C2×D6111yescharacteristic
644C2×#95C2×D6111yescharacteristic
645C61#1440711yescharacteristic, complemented, Sylow
646C25—611no—
647C25—611no—
648C22×D4—614no—
649C22×D4—614no—
650C22×D4—614no—
651C22×D4—2441no—
652C22×D4—2441no—
653C22×D4—2441no—
654C22×D4—2441no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—611no—
660C23×C4—614no—
661C23×C4—611no—
662C23×C4—1222no—
663C23×C4—1222no—
664C23×C4—1222no—
665C23×C4—1222no—
666C23×C4—1222no—
667C23×C4—2441no—
668C23×C4—2441no—
669C23×C4—2441no—
670C23×C4—2441no—
671C23×C4—2441no—
672C23×C4—2441no—
673C23×C4—2441no—
674C23×C4—2441no—
675C23×C4C22×D6111yescharacteristic
676C23×C4C22×D6111yescharacteristic
677C23×C4C22×D6111yescharacteristic
678C23×C4C22×D6111yescharacteristic
679C23×C4C22×D6111yescharacteristic
680C23×C4C22×D6111yescharacteristic
681C23×C4C22×D6111yescharacteristic
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4—41no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—614no—
692C2×C4⋊C4—1222no—
693C2×C4⋊C4—1222no—
694C2×C4⋊C4—2441no—
695C2×C4⋊C4—2441no—
696C2×C4⋊C4—2441no—
697C2×C22⋊C4—614no—
698C2×C22⋊C4—614no—
699C2×C22⋊C4—614no—
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—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4—2441no—
717C2×C22⋊C4—2441no—
718C2×C22⋊C4—2441no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4—2441no—
724C2×C22⋊C4—2441no—
725C2×C22⋊C4—2441no—
726C2×C22⋊C4—2441no—
727C2×C42—1222no—
728C2×C42—2441no—
729C2×C42—2441no—
730#95—22no—
731#95—22no—
732#95—41no—
733#95—614no—
734#95—1222no—
735#95—1222no—
736#95—1222no—
737#95—1222no—
738#95—1222no—
739#95—1222no—
740#95—2441no—
741#95—2441no—
742#95—2441no—
743#95—2441no—
744#95—2441no—
745#95C4×D6114yescomplemented
746C24—612no—
747C24—612no—
748C24—612no—
749C24—612no—
750C24—612no—
751C24—612no—
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—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24—1221no—
774C24—1221no—
775C24—1221no—
776C24C23×D6111yescharacteristic
777C2×D4—6116no—
778C2×D4—2444no—
779C2×D4—2444no—
780C2×D4—2444no—
781C2×D4—2444no—
782C2×D4—2444no—
783C2×D4—2444no—
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—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—612no—
826C22×C4—612no—
827C22×C4—612no—
828C22×C4—612no—
829C22×C4—612no—
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—1228no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
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×C4—2444no—
879C22×C4—2444no—
880C22×C4—2444no—
881C22×C4C2×C4×D6112yes—
882C22×C4C2×C4×D6112yes—
883C22×C4C2×C4×D6112yes—
884C22×C4D4×D6112yes—
885C22×C4D4×D6112yes—
886C22×C4Q8×D6112yes—
887C22×C4#1175822612yes—
888C22×C4#1175822612yes—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—2444no—
893C4⋊C4—2444no—
894C22⋊C4—1228no—
895C22⋊C4—2444no—
896C22⋊C4—2444no—
897C22⋊C4—2444no—
898C22⋊C4—2444no—
899C22⋊C4—2444no—
900C22⋊C4—2444no—
901C22⋊C4—2444no—
902C22⋊C4—2444no—
903C22⋊C4—2444no—
904C42—2444no—
905C23—614no—
906C23—614no—
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—1222no—
934C23—1222no—
935C23—1222no—
936C23—1222no—
937C23—1222no—
938C23—1222no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
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—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23—2441no—
971C23—2441no—
972C23—2441no—
973C23—2441no—
974C23—2441no—
975C23C22×C4×D6111yescharacteristic
976C23C2×D4×D6111yescharacteristic
977C23C2×D4×D6111yescharacteristic
978C23C2×Q8×D6111yescharacteristic
979C23#41×D6111yescharacteristic
980C23C2×#1175822611yescharacteristic
981C23C2×#1175822611yescharacteristic
982C23#1451982211yescharacteristic
983C23#1451982211yescharacteristic
984C23#1451982211yescharacteristic
985C23#1451982211yescharacteristic
986C23#1451982311yescharacteristic
987C23#1451982311yescharacteristic
988C23#1451982311yescharacteristic
989C23#1451982511yescharacteristic
990D4—24416no—
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—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
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—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—24416no—
1054C2×C4—24416no—
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—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4C4⋊C4×D6114yes—
1083C2×C4#1451973914yes—
1084C22—1224no—
1085C22—1224no—
1086C22—1224no—
1087C22—1224no—
1088C22—1224no—
1089C22—1224no—
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—
1104C22—2442no—
1105C22—2442no—
1106C22—2442no—
1107C22—2442no—
1108C22—2442no—
1109C22—2442no—
1110C22—2442no—
1111C22—2442no—
1112C22—2442no—
1113C22—2442no—
1114C22C2×C4⋊C4×D6111yescharacteristic
1115C22C2×#1451973911yescharacteristic
1116C22C4×#1175822611yescharacteristic
1117C22#1684023411yescharacteristic
1118C22#1684023411yescharacteristic
1119C22#1684023411yescharacteristic
1120C22#1684024311yescharacteristic
1121C22#1684032211yescharacteristic
1122C22#1684032311yescharacteristic
1123C22#1684032311yescharacteristic
1124C22#1684032711yescharacteristic
1125C22#1684035211yescharacteristic
1126C22#1684035211yescharacteristic
1127C22#1684035211yescharacteristic
1128C22#1684036011yescharacteristic
1129C22#1684036211yescharacteristic
1130C22#1684038611yescharacteristic
1131C22#1684038711yescharacteristic
1132C22#1684038711yescharacteristic
1133C22#1684039711yescharacteristic
1134C22#1684040311yescharacteristic
1135C22#1684040311yescharacteristic
1136C22#1684040911yescharacteristic
1137C22#1684041511yescharacteristic
1138C22#1684042711yescharacteristic
1139C22#1684043011yescharacteristic
1140C22#1684046511yescharacteristic
1141C22#1684046811yescharacteristic
1142C22#1684047311yescharacteristic
1143C22#1684047311yescharacteristic
1144C22#1684047811yescharacteristic
1145C22#1684050111yescharacteristic
1146C22#1684050211yescharacteristic
1147C22#1684050811yescharacteristic
1148C22#1684050811yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—4881no—
1157C4—2442no—
1158C4—2442no—
1159C4—2442no—
1160C4—2442no—
1161C4—2442no—
1162C2—2444no—
1163C2—2444no—
1164C2#2144843011yescharacteristic
1165C2#2144847611yescharacteristic
1166C2#2144861211yescharacteristic
1167C2#2144871911yescharacteristic
1168C2#2144872811yescharacteristic
1169C2#2144885611yescharacteristic
1170C2#2144897511yescharacteristic
1171C2#2145202811yescharacteristic
1172C2#2145209011yescharacteristic
1173C2#2145223211yescharacteristic
1174C2#2145232211yescharacteristic
1175C2#2145254411yescharacteristic
1176C2#2145284011yescharacteristic
1177C2#2145347311yescharacteristic
1178C2#2145352211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1444C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1444D61
hypocenterC61#14407
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. C2×#16839636C2semidirect
5. C2×#16839619C2semidirect
6. #21444078C2semidirect
7. #21444063C2semidirect
8. #21444061C2semidirect
9. #21444061C2semidirect
10. #21444061C2semidirect
11. #21444053C2semidirect
12. #21444050C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1444C2semidirect
34. #16839640C4semidirect
84. C22×C4×D61C2×C4semidirect
87. C2×C4⋊Dic61D4semidirect
120. C2×#11758198C2×C4semidirect
135. #14519684C2×C4semidirect
155. #95×C61C2×C4semidirect
284. C2×D244C4⋊C4semidirect
578. #1444D61semidirect
645. C61#14407semidirect
745. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396632
C2×#168396402
C2×#168396362
C2×#168396192
#214440782
#214440632
#214440612
#214440532
#214440502
#214440402
C61×#14442
#1440761