Finite Group Databasebeta

← #29607934

Subgroups — #29607934

Order 15616.

2118 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×#16839664C211yesmaximal, characteristic
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839640C211yesmaximal, characteristic
4C2×#16839636C211yesmaximal, characteristic, complemented
5C2×#16839636C211yesmaximal, characteristic, complemented
6C2×#16839621C211yesmaximal, characteristic, complemented
7C2×#16839619C211yesmaximal, characteristic, complemented
8#21444084C211yesmaximal, characteristic, complemented
9#21444083C211yesmaximal, characteristic, complemented
10#21444065C211yesmaximal, characteristic, complemented
11#21444063C211yesmaximal, characteristic, complemented
12#21444063C211yesmaximal, characteristic, complemented
13#21444061C211yesmaximal, characteristic, complemented
14#21444052C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35#16839664—24no—
36#16839640—24no—
37#16839640C418yescomplemented
38#16839636—24no—
39#16839636—24no—
40#16839621—24no—
41#16839619—24no—
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C24×D61C2311yescharacteristic
60C22×D244—41no—
61C22×D244—41no—
62C22×D244—41no—
63C22×D244—41no—
64C22×D244C2×C414yes—
65C22×D244D414yes—
66C22×D244Q814yes—
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—22no—
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×D61—41no—
85C22×C4×D61—41no—
86C22×C4×D61C2×C414yescomplemented
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—41no—
92C2×C4⋊Dic61—41no—
93C2×C4⋊Dic61—41no—
94C2×C4⋊Dic61—41no—
95C2×C4⋊Dic61—41no—
96C2×#11758196—22no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196—22no—
100C2×#11758196—22no—
101C2×#11758196—41no—
102C2×#11758196—41no—
103C2×#11758196—41no—
104C2×#11758196—41no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198—22no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×#11758198—22no—
122C2×#11758198—41no—
123C2×#11758198—41no—
124C2×#11758198—41no—
125C2×#11758198—41no—
126C2×#11758198—41no—
127C2×#11758198—41no—
128C2×#11758198—41no—
129C2×#11758198—41no—
130C2×#11758198—41no—
131C2×#11758198—41no—
132C2×#11758198C2×C414yes—
133C2×#11758198C2×C414yes—
134C2×#11758198C2×C414yescomplemented
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139#14519684—41no—
140#14519684—41no—
141#14519684—41no—
142#14519684C2×C414yescomplemented
143#14519684D414yescomplemented
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61—22no—
152C2×C4⋊C4×C61—22no—
153C2×C4⋊C4×C61—41no—
154C2×C42×C61—22no—
155C2×C42×C61—41no—
156C2×C42×C61—41no—
157#95×C61—22no—
158#95×C61—22no—
159#95×C61—41no—
160#95×C61C2×C414yescomplemented
161#95×C61D414yescomplemented
162C24×C61C2411yescharacteristic
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×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61C22×C412yes—
188C23×D61C22×C412yes—
189C23×D61C2×D412yes—
190C23×D61C2×D412yes—
191C23×D61C2×Q812yes—
192C23×D61C2×Q812yes—
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×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61C22×C412yes—
233C22×C4×C61C22×C412yes—
234C22×C4×C61C22×C412yes—
235C22×C4×C61C2×D412yes—
236C22×C4×C61C2×D412yes—
237C22×C4×C61C2×D412yes—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2×Q812yes—
241C22×C4×C61#4112yes—
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—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61C22×C412yes—
280C22×Dic61C22×C412yes—
281C22×Dic61C2×D412yes—
282C22×Dic61C2×D412yes—
283C22×Dic61#4112yes—
284C2×D244—44no—
285C2×D244—44no—
286C2×D244—44no—
287C2×D244—44no—
288C2×D244—44no—
289C2×D244—44no—
290C2×D244C4⋊C4116yescomplemented
291C2×C4×D61—28no—
292C2×C4×D61—28no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C2×C4×D61—44no—
296C2×C4×D61—44no—
297C2×C4×D61—44no—
298C2×C4×D61—44no—
299C2×C4×D61—44no—
300C2×C4×D61—44no—
301C2×C4×D61—44no—
302C2×C4×D61—44no—
303C2×C4×D61—44no—
304C2×C4×D61—44no—
305C4⋊C4×C61—44no—
306C42×C61—44no—
307#11758198—28no—
308#11758198—28no—
309#11758198—44no—
310#11758198—44no—
311#11758198—44no—
312#11758198—44no—
313#11758198—44no—
314#11758198—44no—
315#11758198—44no—
316#11758198—44no—
317C4⋊Dic61—44no—
318C4⋊Dic61—44no—
319C4⋊Dic61—44no—
320#11758196—44no—
321#11758196—44no—
322#11758196—44no—
323C23×C61C23×C411yescharacteristic
324C23×C61C22×D411yescharacteristic
325C23×C61C22×D411yescharacteristic
326C23×C61C22×D411yescharacteristic
327C23×C61C22×Q811yescharacteristic
328C23×C61C2×#4111yescharacteristic
329C23×C61C2×#4111yescharacteristic
330C23×C61H(5,𝔽2)11yescharacteristic
331C23×C61H(5,𝔽2)11yescharacteristic
332C23×C61H(5,𝔽2)11yescharacteristic
333C23×C61H(5,𝔽2)11yescharacteristic
334C23×C61H(5,𝔽2)11yescharacteristic
335C23×C61H(5,𝔽2)11yescharacteristic
336C23×C612−1+411yescharacteristic
337C23×C612−1+411yescharacteristic
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—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
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×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61C2×C4⋊C414yes—
407C22×D61C2×C4⋊C414yes—
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—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×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61C2×C4⋊C414yes—
456C2×C4×C61C4×D414yes—
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—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—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498C2×Dic61C4×D414yes—
499D244—416no—
500C4×D61—416no—
501C4×D61—416no—
502#14401—611nomaximal, Sylow
503C22×C61C22×C4⋊C411yescharacteristic
504C22×C61C2×C4×D411yescharacteristic
505C22×C61C2×C4×D411yescharacteristic
506C22×C61#51811yescharacteristic
507C22×C61#51811yescharacteristic
508C22×C61#52011yescharacteristic
509C22×C61#52011yescharacteristic
510C22×C61#53411yescharacteristic
511C22×C61#53411yescharacteristic
512C22×C61#53511yescharacteristic
513C22×C61#53511yescharacteristic
514C22×C61#53711yescharacteristic
515C22×C61#53711yescharacteristic
516C22×C61#54011yescharacteristic
517C22×C61#54011yescharacteristic
518C22×C61#54211yescharacteristic
519C22×C61#54211yescharacteristic
520C22×C61#54311yescharacteristic
521C22×C61#54311yescharacteristic
522C22×C61D4211yescharacteristic
523C22×C61D4211yescharacteristic
524C22×C61D4211yescharacteristic
525C22×C61#54611yescharacteristic
526C22×C61#54611yescharacteristic
527C22×C61#54711yescharacteristic
528C22×C61#54711yescharacteristic
529C22×C61D4×Q811yescharacteristic
530C22×C61D4×Q811yescharacteristic
531C22×C61#55111yescharacteristic
532C22×C61#55411yescharacteristic
533C22×C61#55411yescharacteristic
534C22×C61#56011yescharacteristic
535C22×C61#56211yescharacteristic
536C22×C61#56211yescharacteristic
537C22×C61#56311yescharacteristic
538C2×D61—24no—
539C2×D61—24no—
540C2×D61—24no—
541C2×D61—24no—
542C2×D61—24no—
543C2×D61—24no—
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—
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—42no—
571C4×C61—42no—
572C4×C61—42no—
573C4×C61—42no—
574C4×C61—81no—
575Dic61—24no—
576Dic61—42no—
577Dic61—42no—
578Dic61—81no—
579Dic61—81no—
580Dic61—81no—
581C2×#390—611no—
582C2×#386—611no—
583C2×#386—611no—
584C2×#385—611no—
585C2×#385—611no—
586C2×#380—611no—
587C2×#380—611no—
588#1444—611no—
589#1444—611no—
590#1439—611no—
591#1439—611no—
592#1439—611no—
593#1439—611no—
594#1436—611no—
595#1436D6111yescharacteristic, complemented
596C2×C61#231511yescharacteristic
597C2×C61#232411yescharacteristic
598C2×C61#232411yescharacteristic
599C2×C61D4×C4⋊C411yescharacteristic
600C2×C61D4×C4⋊C411yescharacteristic
601C2×C61#235811yescharacteristic
602C2×C61#237611yescharacteristic
603C2×C61#266911yescharacteristic
604C2×C61#267111yescharacteristic
605C2×C61#267111yescharacteristic
606C2×C61#268311yescharacteristic
607C2×C61#269211yescharacteristic
608C2×C61#269211yescharacteristic
609C2×C61#271711yescharacteristic
610C2×C61#274811yescharacteristic
611D61—44no—
612D61—44no—
613C23×D4—611no—
614C24×C4—611no—
615C24×C4—611no—
616C22×C4⋊C4—611no—
617C22×C4⋊C4—611no—
618C22×C4⋊C4—611no—
619C22×C4⋊C4—611no—
620C22×C4⋊C4—611no—
621C22×C4⋊C4—611no—
622C22×C4⋊C4C2×D6111yescharacteristic
623C22×C22⋊C4—611no—
624C22×C22⋊C4—611no—
625C22×C22⋊C4—611no—
626C22×C22⋊C4—611no—
627C22×C22⋊C4—611no—
628C22×C22⋊C4—611no—
629C22×C22⋊C4—611no—
630C22×C22⋊C4—611no—
631C22×C22⋊C4—611no—
632C22×C22⋊C4—611no—
633C22×C42C2×D6111yescharacteristic
634#390—1224no—
635#386—618no—
636#386—1224no—
637#385—1224no—
638#385—1224no—
639#380—1224no—
640#380—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×#95C2×D6111yescharacteristic
651C2×#95C2×D6111yescharacteristic
652C2×#95C2×D6111yescharacteristic
653C2×#95C2×D6111yescharacteristic
654C2×#95C2×D6111yescharacteristic
655C61#1440111yescharacteristic, complemented, Sylow
656C25—611no—
657C25—611no—
658C22×D4—614no—
659C22×D4—614no—
660C22×D4—614no—
661C22×D4—2441no—
662C22×D4—2441no—
663C22×D4—2441no—
664C22×D4—2441no—
665C23×C4—611no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4—614no—
669C23×C4—611no—
670C23×C4—611no—
671C23×C4—611no—
672C23×C4—1222no—
673C23×C4—1222no—
674C23×C4—1222no—
675C23×C4—1222no—
676C23×C4—1222no—
677C23×C4—1222no—
678C23×C4—1222no—
679C23×C4—2441no—
680C23×C4—2441no—
681C23×C4—2441no—
682C23×C4—2441no—
683C23×C4—2441no—
684C23×C4—2441no—
685C23×C4C22×D6111yescharacteristic
686C23×C4C22×D6111yescharacteristic
687C23×C4C22×D6111yescharacteristic
688C23×C4C22×D6111yescharacteristic
689C23×C4C22×D6111yescharacteristic
690C23×C4C22×D6111yescharacteristic
691C23×C4C22×D6111yescharacteristic
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—1222no—
696C2×C4⋊C4—1222no—
697C2×C4⋊C4—1222no—
698C2×C4⋊C4—1222no—
699C2×C4⋊C4—1222no—
700C2×C4⋊C4—1222no—
701C2×C4⋊C4—1222no—
702C2×C4⋊C4—1222no—
703C2×C4⋊C4—1222no—
704C2×C4⋊C4—2441no—
705C2×C4⋊C4—2441no—
706C2×C4⋊C4—2441no—
707C2×C4⋊C4—2441no—
708C2×C4⋊C4—2441no—
709C2×C4⋊C4—2441no—
710C2×C4⋊C4—2441no—
711C2×C4⋊C4—2441no—
712C2×C4⋊C4—2441no—
713C2×C22⋊C4—614no—
714C2×C22⋊C4—614no—
715C2×C22⋊C4—614no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—1222no—
719C2×C22⋊C4—1222no—
720C2×C22⋊C4—1222no—
721C2×C22⋊C4—1222no—
722C2×C22⋊C4—1222no—
723C2×C22⋊C4—1222no—
724C2×C22⋊C4—1222no—
725C2×C22⋊C4—1222no—
726C2×C22⋊C4—1222no—
727C2×C22⋊C4—1222no—
728C2×C22⋊C4—1222no—
729C2×C22⋊C4—1222no—
730C2×C22⋊C4—1222no—
731C2×C22⋊C4—1222no—
732C2×C22⋊C4—1222no—
733C2×C22⋊C4—2441no—
734C2×C22⋊C4—2441no—
735C2×C22⋊C4—2441no—
736C2×C22⋊C4—2441no—
737C2×C22⋊C4—2441no—
738C2×C22⋊C4—2441no—
739C2×C22⋊C4—2441no—
740C2×C22⋊C4—2441no—
741C2×C22⋊C4—2441no—
742C2×C22⋊C4—2441no—
743C2×C42—22no—
744C2×C42—41no—
745C2×C42—41no—
746#95—22no—
747#95—22no—
748#95—41no—
749#95—614no—
750#95—614no—
751#95—1222no—
752#95—1222no—
753#95—1222no—
754#95—1222no—
755#95—2441no—
756#95—2441no—
757#95—2441no—
758#95C4×D6114yescomplemented
759#95D24414yescomplemented
760C24—612no—
761C24—612no—
762C24—612no—
763C24—612no—
764C24—612no—
765C24—612no—
766C24—1221no—
767C24—1221no—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24—1221no—
774C24—1221no—
775C24—1221no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24—1221no—
783C24—1221no—
784C24—1221no—
785C24—1221no—
786C24—1221no—
787C24—1221no—
788C24—1221no—
789C24—1221no—
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—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—612no—
838C22×C4—612no—
839C22×C4—612no—
840C22×C4—612no—
841C22×C4—612no—
842C22×C4—1228no—
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—1228no—
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—2444no—
882C22×C4—2444no—
883C22×C4—2444no—
884C22×C4—2444no—
885C22×C4—2444no—
886C22×C4—2444no—
887C22×C4—2444no—
888C22×C4—2444no—
889C22×C4—2444no—
890C22×C4—2444no—
891C22×C4—2444no—
892C22×C4—2444no—
893C22×C4C2×C4×D6112yes—
894C22×C4C2×C4×D6112yes—
895C22×C4C2×C4×D6112yes—
896C22×C4C2×D24412yes—
897C22×C4C2×D24412yes—
898C22×C4C2×D24412yes—
899C22×C4#1175822212yes—
900C22×C4D4×D6112yes—
901C22×C4D4×D6112yes—
902C22×C4Q8×D6112yes—
903C4⋊C4—44no—
904C4⋊C4—2444no—
905C4⋊C4—2444no—
906C4⋊C4—2444no—
907C4⋊C4—2444no—
908C4⋊C4—2444no—
909C4⋊C4—2444no—
910C22⋊C4—1228no—
911C22⋊C4—1228no—
912C22⋊C4—2444no—
913C22⋊C4—2444no—
914C22⋊C4—2444no—
915C22⋊C4—2444no—
916C22⋊C4—2444no—
917C22⋊C4—2444no—
918C22⋊C4—2444no—
919C22⋊C4—2444no—
920C42—44no—
921C23—614no—
922C23—614no—
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—1222no—
944C23—1222no—
945C23—1222no—
946C23—1222no—
947C23—1222no—
948C23—1222no—
949C23—1222no—
950C23—1222no—
951C23—1222no—
952C23—1222no—
953C23—1222no—
954C23—1222no—
955C23—1222no—
956C23—1222no—
957C23—1222no—
958C23—1222no—
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—
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—
990C23—2441no—
991C23C22×C4×D6111yescharacteristic
992C23C2×D4×D6111yescharacteristic
993C23C2×D4×D6111yescharacteristic
994C23C22×D24411yescharacteristic
995C23C2×Q8×D6111yescharacteristic
996C23#41×D6111yescharacteristic
997C23C2×#1175822211yescharacteristic
998C23#1451982211yescharacteristic
999C23#1451982211yescharacteristic
1000C23#1451982311yescharacteristic
1001C23#1451982311yescharacteristic
1002C23#1451982311yescharacteristic
1003C23#1451982311yescharacteristic
1004C23#1451982411yescharacteristic
1005C23#1451982511yescharacteristic
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—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
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—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—614no—
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—24416no—
1068C2×C4—24416no—
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×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—2441no—
1097C2×C4—2441no—
1098C2×C4C4⋊C4×D6114yes—
1099C2×C4C4×D24414yes—
1100C22—1224no—
1101C22—1224no—
1102C22—1224no—
1103C22—1224no—
1104C22—1224no—
1105C22—1224no—
1106C22—2442no—
1107C22—2442no—
1108C22—2442no—
1109C22—2442no—
1110C22—2442no—
1111C22—2442no—
1112C22—2442no—
1113C22—2442no—
1114C22—2442no—
1115C22—2442no—
1116C22—2442no—
1117C22—2442no—
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×C4⋊C4×D6111yescharacteristic
1131C22C4×D4×D6111yescharacteristic
1132C22C2×C4×D24411yescharacteristic
1133C22#1684023411yescharacteristic
1134C22#1684023411yescharacteristic
1135C22#1684024211yescharacteristic
1136C22#1684024411yescharacteristic
1137C22#1684032211yescharacteristic
1138C22#1684032311yescharacteristic
1139C22#1684033011yescharacteristic
1140C22#1684033111yescharacteristic
1141C22#1684033911yescharacteristic
1142C22#1684034311yescharacteristic
1143C22#1684036311yescharacteristic
1144C22#1684036411yescharacteristic
1145C22#1684037811yescharacteristic
1146C22#1684038411yescharacteristic
1147C22#1684038711yescharacteristic
1148C22#1684038711yescharacteristic
1149C22#1684039611yescharacteristic
1150C22D4×D24411yescharacteristic
1151C22D4×D24411yescharacteristic
1152C22#1684040211yescharacteristic
1153C22#1684040711yescharacteristic
1154C22#1684041411yescharacteristic
1155C22#1684041711yescharacteristic
1156C22#1684042711yescharacteristic
1157C22Q8×D24411yescharacteristic
1158C22#1684043611yescharacteristic
1159C22#1684046811yescharacteristic
1160C22#1684047211yescharacteristic
1161C22#1684050311yescharacteristic
1162C22#1684050811yescharacteristic
1163C22#1684050911yescharacteristic
1164C22#1684051611yescharacteristic
1165C4—24no—
1166C4—24no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—81no—
1172C4—1224no—
1173C4—4881no—
1174C4—4881no—
1175C4—4881no—
1176C4—2442no—
1177C4—2442no—
1178C2—2444no—
1179C2—2444no—
1180C2#2144843011yescharacteristic
1181C2#2144850711yescharacteristic
1182C2#2144851311yescharacteristic
1183C2#2144872011yescharacteristic
1184C2C4⋊C4×D24411yescharacteristic
1185C2#2144880111yescharacteristic
1186C2#2144896611yescharacteristic
1187C2#2145203411yescharacteristic
1188C2#2145205611yescharacteristic
1189C2#2145205811yescharacteristic
1190C2#2145219011yescharacteristic
1191C2#2145231011yescharacteristic
1192C2#2145231311yescharacteristic
1193C2#2145265911yescharacteristic
1194C2#2145302711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1436D61
hypocenterC61#14401
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×#16839636C2semidirect
5. C2×#16839636C2semidirect
6. C2×#16839621C2semidirect
7. C2×#16839619C2semidirect
8. #21444084C2semidirect
9. #21444083C2semidirect
10. #21444065C2semidirect
11. #21444063C2semidirect
12. #21444063C2semidirect
13. #21444061C2semidirect
14. #21444052C2semidirect
15. C61×#1436C2semidirect
37. #16839640C4semidirect
86. C22×C4×D61C2×C4semidirect
134. C2×#11758198C2×C4semidirect
142. #14519684C2×C4semidirect
143. #14519684D4semidirect
160. #95×C61C2×C4semidirect
161. #95×C61D4semidirect
290. C2×D244C4⋊C4semidirect
595. #1436D61semidirect
655. C61#14401semidirect
758. #95C4×D61semidirect
759. #95D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168396642
C2×#168396402
C2×#168396362
C2×#168396212
C2×#168396192
#214440842
#214440832
#214440652
#214440632
#214440612
#214440522
C61×#14362
#1440161