Finite Group Databasebeta

← #29603387

Subgroups — #29603387

Order 15616.

2590 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C2×#16839638C211yesmaximal, characteristic
3C2×#16839638C211yesmaximal, characteristic
4C2×#16839633C211yesmaximal, characteristic, complemented
5C2×#95×D61C211yesmaximal, characteristic, complemented
6#21444077C211yesmaximal, characteristic, complemented
7#21444074C211yesmaximal, characteristic, complemented
8#21444062C211yesmaximal, characteristic, complemented
9#21444054C211yesmaximal, characteristic, complemented
10#21444051C211yesmaximal, characteristic, complemented
11#21444041C211yesmaximal, characteristic, complemented
12#21444041C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519737—24no—
22C2×#14519737—24no—
23C2×#14519737—24no—
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839638—24no—
33#16839638C418yescomplemented
34#16839633—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
49C2×#14519684C2211yescharacteristic
50#95×D61—24no—
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C22×C22⋊D61—22no—
60C22×C22⋊D61—22no—
61C22×C22⋊D61—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61C2×C414yes—
64C22×C22⋊D61D414yes—
65C22×C22⋊D61Q814yes—
66C23×Dic61—22no—
67C23×Dic61—22no—
68C23×Dic61—22no—
69C23×Dic61—22no—
70C23×Dic61—22no—
71C23×Dic61—41no—
72C23×Dic61—41no—
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—41no—
92C22×C4×D61—41no—
93C22×C4×D61—41no—
94C22×C4×D61—41no—
95C22×C4×D61—41no—
96C22×C4×D61—41no—
97C22×C4×D61—41no—
98C22×C4×D61—41no—
99C22×C4×D61C2×C414yescomplemented
100C22×C4×D61D414yes—
101#14519737—232no—
102C2×#11758196—22no—
103C2×#11758196—22no—
104C2×#11758196—22no—
105C2×#11758196—22no—
106C2×#11758196—22no—
107C2×#11758196—41no—
108C2×C22⋊Dic61—22no—
109C2×C22⋊Dic61—22no—
110C2×C22⋊Dic61—41no—
111C2×C22⋊Dic61—41no—
112C2×C22⋊Dic61—41no—
113C2×C22⋊Dic61C2×C414yescomplemented
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198—22no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×#11758198C2×C414yescomplemented
122C2×#11758198D414yes—
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—41no—
136#14519684—41no—
137#14519684—41no—
138#14519684—41no—
139#14519684C2×C414yescomplemented
140#14519684C2×C414yescomplemented
141C25×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61—22no—
149C2×C4⋊C4×C61—22no—
150C2×C4⋊C4×C61—41no—
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61—22no—
153C2×C22⋊C4×C61—22no—
154C2×C22⋊C4×C61—22no—
155C2×C22⋊C4×C61—22no—
156C2×C22⋊C4×C61—41no—
157C2×C22⋊C4×C61—41no—
158C2×C22⋊C4×C61—41no—
159C2×C22⋊C4×C61C2×C414yescomplemented
160#95×C61—22no—
161#95×C61—41no—
162#95×C61—41no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61C22×C412yes—
176C24×C61C2×D412yes—
177C24×C61C2×Q812yes—
178C24×C61C2411yescharacteristic
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×D61C2×D412yes—
189C23×D61C2×D412yes—
190C23×D61C2×D412yes—
191C23×D61C2×Q812yes—
192C23×D61#4112yes—
193C23×D61#4112yes—
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×C61C22×C412yes—
232C22×C4×C61C22×C412yes—
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61#4112yes—
236C2×C22⋊D61—28no—
237C2×C22⋊D61—28no—
238C2×C22⋊D61—28no—
239C2×C22⋊D61—28no—
240C2×C22⋊D61—28no—
241C2×C22⋊D61—28no—
242C2×C22⋊D61C4⋊C4116yescomplemented
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—28no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—44no—
284C22×Dic61—44no—
285C22×Dic61—44no—
286C22×Dic61—44no—
287C22×Dic61—44no—
288C22×Dic61—44no—
289C22×Dic61C22×C412yes—
290C22×Dic61C22×C412yes—
291C22×Dic61C22×C412yes—
292C22×Dic61C2×D412yes—
293C22×Dic61C2×D412yes—
294C22×Dic61C2×D412yes—
295C22×Dic61C2×Q812yes—
296C22×Dic61#4112yes—
297C22×Dic61#4112yes—
298C22×Dic61#4112yes—
299C2×C4×D61—28no—
300C2×C4×D61—28no—
301C2×C4×D61—28no—
302C2×C4×D61—28no—
303C2×C4×D61—44no—
304C2×C4×D61—44no—
305C2×C4×D61—44no—
306C2×C4×D61—44no—
307C2×C4×D61—44no—
308C2×C4×D61—44no—
309C2×C4×D61—44no—
310C2×C4×D61—44no—
311C2×C4×D61—44no—
312C2×C4×D61—44no—
313C2×C4×D61—44no—
314C2×C4×D61—44no—
315C2×C4×D61—44no—
316C2×C4×D61—44no—
317C2×C4×D61—44no—
318C2×C4×D61—44no—
319C2×C4×D61—44no—
320C4⋊C4×C61—44no—
321C22⋊C4×C61—28no—
322C22⋊C4×C61—44no—
323C22⋊C4×C61—44no—
324C22⋊Dic61—44no—
325C22⋊Dic61—44no—
326#11758198—28no—
327#11758198—28no—
328#11758198—44no—
329#11758196—28no—
330#11758196—44no—
331C4×Dic61—28no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61C2×C4⋊C414yes—
367C23×C61C23×C411yescharacteristic
368C23×C61C22×D411yescharacteristic
369C23×C61C22×D411yescharacteristic
370C23×C61C22×D411yescharacteristic
371C23×C61C22×Q811yescharacteristic
372C23×C61C2×#4111yescharacteristic
373C23×C61C2×#4111yescharacteristic
374C23×C61C2×#4111yescharacteristic
375C23×C61C2×#4111yescharacteristic
376C23×C61C2×#4111yescharacteristic
377C23×C61C2×#4111yescharacteristic
378C23×C61H(5,𝔽2)11yescharacteristic
379C23×C61H(5,𝔽2)11yescharacteristic
380C23×C61H(5,𝔽2)11yescharacteristic
381C23×C61H(5,𝔽2)11yescharacteristic
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—22no—
401C22×D61—22no—
402C22×D61—22no—
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
408C22×D61—22no—
409C22×D61—22no—
410C22×D61C2×C4⋊C414yes—
411C22×D61C4×D414yes—
412C22×D61C4×D414yes—
413C22×D61#12014yes—
414C22×D61C22⋊Q814yes—
415C22×D61C22⋊Q814yes—
416C22×D61#12314yes—
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×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C22⋊D61—232no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—22no—
471C2×Dic61—22no—
472C2×Dic61—22no—
473C2×Dic61—22no—
474C2×Dic61—22no—
475C2×Dic61—22no—
476C2×Dic61—22no—
477C2×Dic61—22no—
478C2×Dic61—22no—
479C2×Dic61—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—22no—
483C2×Dic61—22no—
484C2×Dic61—416no—
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×Dic61—41no—
499C2×Dic61—41no—
500C2×Dic61—41no—
501C2×Dic61—41no—
502C2×Dic61—41no—
503C2×Dic61—41no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506C2×Dic61—41no—
507C2×Dic61—41no—
508C2×Dic61C2×C4⋊C414yes—
509C2×Dic61#12314yes—
510C4×D61—416no—
511C4×D61—416no—
512C4×D61—416no—
513#14016—611nomaximal, Sylow
514C22×C61—24no—
515C22×C61—24no—
516C22×C61—24no—
517C22×C61—42no—
518C22×C61—42no—
519C22×C61—42no—
520C22×C61—42no—
521C22×C61—42no—
522C22×C61—42no—
523C22×C61—42no—
524C22×C61—42no—
525C22×C61—42no—
526C22×C61—42no—
527C22×C61—42no—
528C22×C61—42no—
529C22×C61C22×C4⋊C411yescharacteristic
530C22×C61C2×C4×D411yescharacteristic
531C22×C61C2×C4×D411yescharacteristic
532C22×C61C4×#4111yescharacteristic
533C22×C61C4×#4111yescharacteristic
534C22×C61#51811yescharacteristic
535C22×C61#51811yescharacteristic
536C22×C61C2×#12011yescharacteristic
537C22×C61C2×C22⋊Q811yescharacteristic
538C22×C61C2×C22⋊Q811yescharacteristic
539C22×C61C2×#12311yescharacteristic
540C22×C61C2×#12311yescharacteristic
541C22×C61#52511yescharacteristic
542C22×C61#52911yescharacteristic
543C22×C61#52911yescharacteristic
544C22×C61#53411yescharacteristic
545C22×C61#53511yescharacteristic
546C22×C61#53811yescharacteristic
547C22×C61#53811yescharacteristic
548C22×C61#54611yescharacteristic
549C22×C61#54611yescharacteristic
550C22×C61#54611yescharacteristic
551C22×C61#54611yescharacteristic
552C22×C61#54611yescharacteristic
553C22×C61#54611yescharacteristic
554C22×C61#54611yescharacteristic
555C22×C61#54611yescharacteristic
556C22×C61#55311yescharacteristic
557C22×C61#55311yescharacteristic
558C22×C61#55311yescharacteristic
559C22×C61#55311yescharacteristic
560C22×C61#55411yescharacteristic
561C22×C61#55411yescharacteristic
562C22×C61#55411yescharacteristic
563C22×C61#55411yescharacteristic
564C2×D61—24no—
565C2×D61—24no—
566C2×D61—24no—
567C2×D61—24no—
568C2×D61—24no—
569C2×D61—24no—
570C2×D61—24no—
571C2×D61—24no—
572C2×D61—24no—
573C2×D61—24no—
574C2×D61—24no—
575C2×D61—24no—
576C2×D61—24no—
577C2×D61—24no—
578C2×D61#38518yes—
579C4×C61—42no—
580C4×C61—42no—
581C4×C61—42no—
582C4×C61—42no—
583C4×C61—42no—
584C4×C61—81no—
585Dic61—24no—
586Dic61—24no—
587Dic61—42no—
588Dic61—42no—
589Dic61—42no—
590Dic61—42no—
591Dic61—81no—
592C22×C4×D4—611no—
593C2×#386—611no—
594C2×#386—611no—
595C2×#385—611no—
596C22×#95—611no—
597#1442—611no—
598#1442—611no—
599#1439—611no—
600#1439D6111yescharacteristic, complemented
601#1436—611no—
602#1436—611no—
603C22⋊#95—611no—
604C22⋊#95—611no—
605C22⋊#95—611no—
606C22⋊#95—611no—
607C2×C61—44no—
608C2×C61C2×#38511yescharacteristic
609C2×C61C4×#12311yescharacteristic
610C2×C61#232111yescharacteristic
611C2×C61#234911yescharacteristic
612C2×C61#234911yescharacteristic
613C2×C61#236411yescharacteristic
614C2×C61#236411yescharacteristic
615C2×C61#240411yescharacteristic
616C2×C61#240511yescharacteristic
617C2×C61#244411yescharacteristic
618C2×C61#244411yescharacteristic
619C2×C61#245011yescharacteristic
620C2×C61#245011yescharacteristic
621C2×C61#248711yescharacteristic
622C2×C61#257911yescharacteristic
623D61—28no—
624C23×D4—611no—
625C24×C4—611no—
626C24×C4—611no—
627C24×C4—611no—
628C24×C4—611no—
629C2×C4×D4—1224no—
630C2×C4×D4—1224no—
631C2×C4×D4—1224no—
632C22×C4⋊C4—611no—
633C22×C4⋊C4—611no—
634C22×C4⋊C4C2×D6111yescharacteristic
635C22×C22⋊C4—611no—
636C22×C22⋊C4—611no—
637C22×C22⋊C4—611no—
638C22×C22⋊C4—611no—
639C22×C22⋊C4—611no—
640C22×C22⋊C4C2×D6111yescharacteristic
641C22×C22⋊C4C2×D6111yescharacteristic
642C22×C22⋊C4C2×D6111yescharacteristic
643C22×C42—611no—
644#386—618no—
645#386—1224no—
646#385—1224no—
647C2×#95—611no—
648C2×#95—611no—
649C2×#95—611no—
650C2×#95—611no—
651C2×#95—611no—
652C2×#95—611no—
653C2×#95—611no—
654C2×#95—611no—
655C2×#95—611no—
656C2×#95—611no—
657C2×#95—611no—
658C2×#95—611no—
659C2×#95—611no—
660C2×#95—611no—
661C2×#95—611no—
662C2×#95—1224no—
663C2×#95C2×D6111yescharacteristic
664C2×#95C2×D6111yescharacteristic
665C2×#95C2×D6111yescharacteristic
666C61#1401611yescharacteristic, complemented, Sylow
667C25—611no—
668C25C22×D6111yescharacteristic
669C22×D4—614no—
670C22×D4—614no—
671C22×D4—614no—
672C22×D4—1222no—
673C22×D4—1222no—
674C22×D4—1222no—
675C22×D4—1222no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—611no—
680C23×C4—611no—
681C23×C4—611no—
682C23×C4—614no—
683C23×C4—614no—
684C23×C4—611no—
685C23×C4—1222no—
686C23×C4—1222no—
687C23×C4—1222no—
688C23×C4—1222no—
689C23×C4—1222no—
690C23×C4—1222no—
691C23×C4—1222no—
692C23×C4—1222no—
693C23×C4—1222no—
694C23×C4—1222no—
695C23×C4—1222no—
696C23×C4—1222no—
697C23×C4—1222no—
698C23×C4—1222no—
699C23×C4—1222no—
700C23×C4—1222no—
701C23×C4—2441no—
702C23×C4—2441no—
703C23×C4—2441no—
704C23×C4—2441no—
705C23×C4—2441no—
706C23×C4—2441no—
707C23×C4—2441no—
708C23×C4—2441no—
709C23×C4—2441no—
710C23×C4—2441no—
711C23×C4C22×D6111yescharacteristic
712C23×C4C22×D6111yescharacteristic
713C23×C4C22×D6111yescharacteristic
714C23×C4C22×D6111yescharacteristic
715C23×C4C22×D6111yescharacteristic
716C23×C4C22×D6111yescharacteristic
717C4×D4—12232no—
718C2×C4⋊C4—22no—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—41no—
721C2×C4⋊C4—1222no—
722C2×C4⋊C4—1222no—
723C2×C4⋊C4—1222no—
724C2×C4⋊C4—1222no—
725C2×C4⋊C4—1222no—
726C2×C4⋊C4—2441no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C22⋊C4—41no—
735C2×C22⋊C4—614no—
736C2×C22⋊C4—614no—
737C2×C22⋊C4—614no—
738C2×C22⋊C4—1222no—
739C2×C22⋊C4—1222no—
740C2×C22⋊C4—1222no—
741C2×C22⋊C4—1222no—
742C2×C22⋊C4—1222no—
743C2×C22⋊C4—1222no—
744C2×C22⋊C4—1222no—
745C2×C22⋊C4—1222no—
746C2×C22⋊C4—1222no—
747C2×C22⋊C4—2441no—
748C2×C22⋊C4—2441no—
749C2×C22⋊C4—2441no—
750C2×C22⋊C4C4×D6114yescomplemented
751C2×C42—1222no—
752C2×C42—1222no—
753C2×C42—1222no—
754#95—22no—
755#95—41no—
756#95—41no—
757#95—614no—
758#95—614no—
759#95—1222no—
760#95—1222no—
761#95—1222no—
762#95—1222no—
763#95—1222no—
764#95—1222no—
765#95—1222no—
766#95—1222no—
767#95—1222no—
768#95—2441no—
769#95—2441no—
770#95—2441no—
771#95—2441no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—612no—
785C24—612no—
786C24—612no—
787C24—612no—
788C24—612no—
789C24—612no—
790C24—612no—
791C24—1221no—
792C24—1221no—
793C24—1221no—
794C24—1221no—
795C24—1221no—
796C24—1221no—
797C24—1221no—
798C24—1221no—
799C24C2×C4×D6112yes—
800C24D4×D6112yes—
801C24Q8×D6112yes—
802C24C23×D6111yescharacteristic
803C2×D4—6116no—
804C2×D4—1228no—
805C2×D4—1228no—
806C2×D4—1228no—
807C2×D4—1228no—
808C2×D4—1228no—
809C2×D4—1228no—
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—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—612no—
848C22×C4—612no—
849C22×C4—612no—
850C22×C4—612no—
851C22×C4—612no—
852C22×C4—612no—
853C22×C4—612no—
854C22×C4—612no—
855C22×C4—612no—
856C22×C4—612no—
857C22×C4—1228no—
858C22×C4—1228no—
859C22×C4—1228no—
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—1221no—
869C22×C4—1228no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—1221no—
890C22×C4—1221no—
891C22×C4—1221no—
892C22×C4—1221no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—2444no—
902C22×C4—2444no—
903C22×C4—2444no—
904C22×C4—2444no—
905C22×C4—2444no—
906C22×C4—2444no—
907C22×C4—2444no—
908C22×C4—2444no—
909C22×C4—2444no—
910C22×C4—2444no—
911C22×C4—2444no—
912C22×C4—2444no—
913C22×C4—2444no—
914C22×C4—2444no—
915C22×C4—2444no—
916C22×C4—2444no—
917C22×C4—2444no—
918C22×C4—2444no—
919C22×C4—2444no—
920C22×C4—2444no—
921C22×C4—2444no—
922C22×C4—2444no—
923C22×C4—2444no—
924C22×C4C2×C4×D6112yes—
925C22×C4C2×C4×D6112yes—
926C22×C4D4×D6112yes—
927C22×C4D4×D6112yes—
928C22×C4#1175822412yes—
929C4⋊C4—44no—
930C4⋊C4—1228no—
931C4⋊C4—2444no—
932C22⋊C4—28no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—1228no—
936C22⋊C4—1228no—
937C22⋊C4—2444no—
938C22⋊C4—2444no—
939C22⋊C4—2444no—
940C42—1228no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—614no—
976C23—614no—
977C23—614no—
978C23—614no—
979C23—614no—
980C23—614no—
981C23—614no—
982C23—1222no—
983C23—1222no—
984C23—1222no—
985C23—1222no—
986C23—1222no—
987C23—1222no—
988C23—1222no—
989C23—1222no—
990C23—1222no—
991C23—1222no—
992C23—1222no—
993C23—1222no—
994C23—1222no—
995C23—1222no—
996C23—1222no—
997C23—1222no—
998C23—1222no—
999C23—1222no—
1000C23—1222no—
1001C23—1222no—
1002C23—1222no—
1003C23—1222no—
1004C23—1222no—
1005C23—1222no—
1006C23—1222no—
1007C23—1222no—
1008C23—1222no—
1009C23—1222no—
1010C23C4⋊C4×D6114yes—
1011C23C22×C4×D6111yescharacteristic
1012C23C2×D4×D6111yescharacteristic
1013C23C2×D4×D6111yescharacteristic
1014C23C2×D4×D6111yescharacteristic
1015C23C2×Q8×D6111yescharacteristic
1016C23#41×D6111yescharacteristic
1017C23#41×D6111yescharacteristic
1018C23#41×D6111yescharacteristic
1019C23#41×D6111yescharacteristic
1020C23#41×D6111yescharacteristic
1021C23C2×#1175822411yescharacteristic
1022C23#1451982211yescharacteristic
1023C23#1451982211yescharacteristic
1024C23#1451982211yescharacteristic
1025C23#1451982311yescharacteristic
1026D4—12232no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
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—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—614no—
1070C2×C4—614no—
1071C2×C4—1222no—
1072C2×C4—1222no—
1073C2×C4—1222no—
1074C2×C4—1222no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1222no—
1078C2×C4—1222no—
1079C2×C4—1222no—
1080C2×C4—1222no—
1081C2×C4—1222no—
1082C2×C4—1222no—
1083C2×C4—1222no—
1084C2×C4—1222no—
1085C2×C4—1222no—
1086C2×C4—1222no—
1087C2×C4—1222no—
1088C2×C4—1222no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—1222no—
1094C2×C4—1222no—
1095C2×C4—24416no—
1096C2×C4—24416no—
1097C2×C4—24416no—
1098C2×C4—24416no—
1099C2×C4—2441no—
1100C2×C4—2441no—
1101C2×C4—2441no—
1102C2×C4—2441no—
1103C2×C4—2441no—
1104C2×C4—2441no—
1105C2×C4—2441no—
1106C2×C4—2441no—
1107C2×C4—2441no—
1108C2×C4—2441no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4—2441no—
1112C2×C4—2441no—
1113C2×C4—2441no—
1114C2×C4—2441no—
1115C2×C4—2441no—
1116C2×C4—2441no—
1117C2×C4—2441no—
1118C2×C4—2441no—
1119C2×C4—2441no—
1120C2×C4—2441no—
1121C2×C4—2441no—
1122C22—24no—
1123C22—24no—
1124C22—24no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—618no—
1138C22—1224no—
1139C22—1224no—
1140C22—1224no—
1141C22—1224no—
1142C22—1224no—
1143C22—1224no—
1144C22—1224no—
1145C22—1224no—
1146C22—1224no—
1147C22—1224no—
1148C22—1224no—
1149C22—1224no—
1150C22—1224no—
1151C22—1224no—
1152C22C2×C4⋊C4×D6111yescharacteristic
1153C22C4×D4×D6111yescharacteristic
1154C22C4×D4×D6111yescharacteristic
1155C22C4×#1175822411yescharacteristic
1156C22#1684023011yescharacteristic
1157C22#1684023411yescharacteristic
1158C22#1684023511yescharacteristic
1159C22#120×D6111yescharacteristic
1160C22C22⋊Q8×D6111yescharacteristic
1161C22C22⋊Q8×D6111yescharacteristic
1162C22#123×D6111yescharacteristic
1163C22#123×D6111yescharacteristic
1164C22#1684027211yescharacteristic
1165C22#1684029111yescharacteristic
1166C22#1684029511yescharacteristic
1167C22#1684032011yescharacteristic
1168C22#1684032511yescharacteristic
1169C22#1684034411yescharacteristic
1170C22#1684034611yescharacteristic
1171C22#1684039911yescharacteristic
1172C22#1684039911yescharacteristic
1173C22#1684040111yescharacteristic
1174C22#1684040111yescharacteristic
1175C22#1684040111yescharacteristic
1176C22#1684040411yescharacteristic
1177C22#1684040511yescharacteristic
1178C22#1684040911yescharacteristic
1179C22#1684045711yescharacteristic
1180C22#1684045711yescharacteristic
1181C22#1684045911yescharacteristic
1182C22#1684046311yescharacteristic
1183C22#1684046611yescharacteristic
1184C22#1684046611yescharacteristic
1185C22#1684046611yescharacteristic
1186C22#1684047011yescharacteristic
1187C4—42no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—81no—
1193C4—1224no—
1194C4—1224no—
1195C4—4881no—
1196C4—2442no—
1197C4—2442no—
1198C4—2442no—
1199C4—2442no—
1200C2—44no—
1201C2—1228no—
1202C2#385×D6111yescharacteristic
1203C2#2144834611yescharacteristic
1204C2#2144847811yescharacteristic
1205C2#2144872311yescharacteristic
1206C2#2144872511yescharacteristic
1207C2#2144886311yescharacteristic
1208C2#2144886811yescharacteristic
1209C2#2144913311yescharacteristic
1210C2#2144914111yescharacteristic
1211C2#2144956211yescharacteristic
1212C2#2144956411yescharacteristic
1213C2#2144963611yescharacteristic
1214C2#2144963811yescharacteristic
1215C2#2145012911yescharacteristic
1216C2#2145116111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#14016
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
4. C2×#16839633C2semidirect
5. C2×#95×D61C2semidirect
6. #21444077C2semidirect
7. #21444074C2semidirect
8. #21444062C2semidirect
9. #21444054C2semidirect
10. #21444051C2semidirect
11. #21444041C2semidirect
12. #21444041C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1439C2semidirect
33. #16839638C4semidirect
99. C22×C4×D61C2×C4semidirect
113. C2×C22⋊Dic61C2×C4semidirect
121. C2×#11758198C2×C4semidirect
139. #14519684C2×C4semidirect
140. #14519684C2×C4semidirect
159. C2×C22⋊C4×C61C2×C4semidirect
242. C2×C22⋊D61C4⋊C4semidirect
600. #1439D61semidirect
666. C61#14016semidirect
750. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C2×#168396382
C2×#168396332
C2×#95×D612
#214440772
#214440742
#214440622
#214440542
#214440512
#214440412
#214440402
C61×#14392
#1401661