Finite Group Databasebeta

← #29695488

Subgroups — #29695488

Order 15616.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840409C211yesmaximal, characteristic
2C2×#16839831C211yesmaximal, characteristic, complemented
3C2×#16839764C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic, complemented
5#21448715C211yesmaximal, characteristic, complemented
6#21446750C211yesmaximal, characteristic, complemented
7#21446634C211yesmaximal, characteristic, complemented
8#21446241C211yesmaximal, characteristic, complemented
9#21446137C211yesmaximal, characteristic, complemented
10#21446125C211yesmaximal, characteristic, complemented
11#21445818C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445643C211yesmaximal, characteristic, complemented
15C61×#1895C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840409—24no—
20#16840409C418yescomplemented
21C2×#14519764C2211yescharacteristic
22C2×#14519759—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519748—21no—
25C2×#14519745—21no—
26C2×#14519739C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519737—21no—
29C22×C4⋊Dic61C2211yescharacteristic, complemented
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C22⋊C4×D61—21no—
32#16839831—24no—
33C2×#14519706C2211yescharacteristic, complemented
34#16839764—24no—
35C2×#14519702C2211yescharacteristic, complemented
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45#102×D61—24no—
46C2×C22⋊#92418C2211yescharacteristic, complemented
47C2×#14519689C2211yescharacteristic
48C2×#14519687C2211yescharacteristic, complemented
49#16839659—21no—
50#16839636—21no—
51#16839634—21no—
52#16839631C2211yescharacteristic, complemented
53#16839619C2211yescharacteristic
54C4⋊C4×Dic61C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C22×M16×C61C2211yescharacteristic, complemented
58C2×#121×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222C2×C414yescomplemented
71C22×Dic122C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C22⋊D61D411yescharacteristic
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—41no—
80C2×D4×D61—41no—
81C2×D4×D61C2×C414yescomplemented
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C2×C8×D61—22no—
90C2×C8×D61—22no—
91C2×C8×D61—41no—
92#14519764—22no—
93#14519764C2×C414yescomplemented
94#14519759—28no—
95#14519757—22no—
96#14519757C2×C414yescomplemented
97#14519748—28no—
98#14519745—28no—
99#14519739—22no—
100#14519739C2×C414yescomplemented
101C4×C22⋊D61C2×C414yes—
102C4×C22⋊D61D414yes—
103#14519737—44no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—22no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196D411yescharacteristic
114C4⋊C4×D61—22no—
115C4⋊C4×D61—41no—
116C2×C22⋊Dic61—21no—
117C2×C22⋊Dic61—21no—
118C2×C22⋊Dic61D411yescharacteristic
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C22⋊C4×D61—28no—
124C2×C4×Dic61—21no—
125C2×C4×Dic61C2311yescharacteristic
126#14519706—22no—
127#14519702—22no—
128#14519702—22no—
129#14519700—41no—
130#14519700—41no—
131#14519699—22no—
132#14519699D414yescomplemented
133#14519698—22no—
134#14519698—41no—
135#14519697—22no—
136#14519697—22no—
137C22⋊#92418—22no—
138#14519689—22no—
139#14519687—22no—
140#14519684—21no—
141#14519684—21no—
142C22×D4×C61—21no—
143C22×D4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C2×M16×C61—22no—
146C2×M16×C61—22no—
147C2×M16×C61—41no—
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150#121×C61—22no—
151#121×C61C2×C414yescomplemented
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—21no—
157#102×C61—22no—
158#102×C61—41no—
159#95×C61—21no—
160C24×C61—21no—
161C24×C61C2×D411yescharacteristic
162C23×D61—21no—
163C23×D61—24no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—81no—
169C23×D61—81no—
170C23×D61C2×D411yescharacteristic
171C2×D4×C61—24no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—81no—
178C2×D4×C61—81no—
179C2×D4×C61C22×C412yes—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61C22×C412yes—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D412yes—
190C22×C4×C61C2411yescharacteristic
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—24no—
194C2×C22⋊D61—24no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61C22⋊C414yes—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—42no—
204C22×Dic61—42no—
205C22×Dic61—81no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209D4×D61—28no—
210D4×D61—44no—
211D4×D61—44no—
212D4×D61—44no—
213#11758222—28no—
214#11758222—44no—
215#11758222—44no—
216#11758222—44no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244C22×C412yes—
221C2×D244C2×D412yes—
222C2×D244#4112yes—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—24no—
228C2×C4×D61—24no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—81no—
234C2×C4×D61—81no—
235C2×C4×D61—81no—
236C2×C4×D61C22×C412yes—
237C2×C4×D61C2×D412yes—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122C22×C412yes—
244M16×C61—44no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61C2×D412yes—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C22×C412yes—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—42no—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261C22⋊Dic61C22⋊C414yes—
262#11758198—24no—
263#11758198—24no—
264#11758198—42no—
265#11758198C22⋊C414yes—
266C4⋊Dic61—21no—
267C4⋊Dic61—24no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—42no—
271C4⋊Dic61C2×D412yes—
272#11758196—42no—
273#11758196—42no—
274#11758196—81no—
275#11758196C22⋊C414yes—
276C4×Dic61—42no—
277C4×Dic61C22×C412yes—
278C4×Dic61C2×D412yes—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C8×D61—44no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—22no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61C2×C22⋊C412yes—
300C23×C61C22×D411yescharacteristic
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—48no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—48no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61—84no—
317C22×D61—84no—
318C22×D61—84no—
319C22×D61C2×C22⋊C412yes—
320C22×D61AGL(1,ℤ/8)12yes—
321C22×D61#13712yes—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—41no—
325D4×C61—41no—
326D4×C61—84no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61C2×C22⋊C412yes—
343C2×C4×C61C23×C411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C2×#4111yescharacteristic
347C2×C4×C61H(5,𝔽2)11yescharacteristic
348C2×C4×C61H(5,𝔽2)11yescharacteristic
349C22⋊D61—28no—
350C22⋊D61—48no—
351C22⋊D61—48no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—84no—
368C2×Dic61C2×C22⋊C412yes—
369C2×Dic61C2×C22⋊C412yes—
370C2×Dic61C2×C22⋊C412yes—
371D244—22no—
372D244—22no—
373D244—22no—
374D244C4×D414yescomplemented
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—48no—
380C4×D61—84no—
381C4×D61—84no—
382Dic122—22no—
383Dic122—22no—
384Dic122—41no—
385Dic122—41no—
386C8×C61—22no—
387C8×C61—41no—
388#92418—41no—
389#92418—41no—
390#22419—611nomaximal, Sylow
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61C22×C22⋊C411yescharacteristic
406C22×C61D4211yescharacteristic
407C22×C61#54611yescharacteristic
408C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C61C2×#13711yescharacteristic
410C22×C61#57611yescharacteristic
411C22×C61#57711yescharacteristic
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—24no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—816no—
426C2×D61#41714yescomplemented
427C4×C61—22no—
428C4×C61—42no—
429C4×C61—81no—
430C4×C61—81no—
431C4×C61C2×C4×D411yescharacteristic
432C4×C61#51811yescharacteristic
433C4×C61D4211yescharacteristic
434C4×C61#54611yescharacteristic
435Dic61—22no—
436Dic61—22no—
437Dic61—22no—
438Dic61—42no—
439Dic61—42no—
440Dic61—81no—
441C2×#546—611no—
442C2×#435—611no—
443C2×#417—611no—
444C22×#102—611no—
445D4×C4⋊C4—611no—
446#1983—611no—
447#1959—611no—
448#1895D6111yescharacteristic, complemented
449#1892—611no—
450#1874—611no—
451#1872—611no—
452#1802—611no—
453#1788—611no—
454#1786—611no—
455#1762—611no—
456C2×C61—42no—
457C2×C61—82no—
458C2×C61D4×C22⋊C411yescharacteristic
459C2×C61C2×#41711yescharacteristic
460C2×C61#289711yescharacteristic
461C2×C61#326411yescharacteristic
462C2×C61#326611yescharacteristic
463C2×C61#330611yescharacteristic
464C2×C61#331411yescharacteristic
465D61—24no—
466D61—44no—
467C22×#41—611no—
468C23×D4—611no—
469C22×M16C2×D6111yescharacteristic, complemented
470C23×C8—611no—
471#546—618no—
472#546—1224no—
473C2×#124—611no—
474C2×#123—1221no—
475C2×C22⋊Q8—611no—
476C2×#121—1221no—
477C2×#121C2×D6111yescharacteristic
478C2×#120—1221no—
479C2×C4×D4—611no—
480C2×C4×D4—611no—
481C2×C4×D4—1221no—
482C22×C4⋊C4—611no—
483C22×C4⋊C4—611no—
484C22×C22⋊C4—1221no—
485#435—1224no—
486C2×C4⋊C8—611no—
487#417—1224no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102—611no—
498C2×#102—1224no—
499C2×#102C2×D6111yescharacteristic
500C2×#102C2×D6111yescharacteristic
501C2×C22⋊C8—611no—
502C2×C22⋊C8—611no—
503C2×#97—611no—
504#389—1221no—
505#385—1221no—
506#385—1221no—
507#384—611no—
508#380—611no—
509#380C2×D6111yescharacteristic, complemented
510C4×C4⋊C4—611no—
511#340—611no—
512#340—611no—
513#340C2×D6111yescharacteristic, complemented
514#340C2×D6111yescharacteristic, complemented
515C61#2241911yescharacteristic, complemented, Sylow
516C25—1221no—
517C2×#41—614no—
518C2×#41—1222no—
519C2×#41—1222no—
520C2×#41—1222no—
521C2×#41—2441no—
522C2×#41—2441no—
523C22×Q8—611no—
524C22×D4—21no—
525C22×D4—611no—
526C22×D4—614no—
527C22×D4—611no—
528C22×D4—1222no—
529C22×D4—1221no—
530C22×D4—1222no—
531C22×D4—1222no—
532C22×D4—1221no—
533C22×D4—2441no—
534C22×D4—2441no—
535C22×D4C22×D6111yescharacteristic
536C23×C4—611no—
537C23×C4—1221no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4—1221no—
541C23×C4C22×D6111yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—1222no—
548C22×C8—1222no—
549C22×C8—2441no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#124—614no—
553#124—1222no—
554#123—1228no—
555C22⋊Q8—614no—
556C22⋊Q8—1222no—
557#121—22no—
558#121—1228no—
559#121C4×D6114yescomplemented
560#120—1228no—
561C4×D4—614no—
562C4×D4—614no—
563C4×D4—614no—
564C4×D4—1222no—
565C4×D4—2444no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—1222no—
570C2×C4⋊C4—1222no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—2441no—
577C2×C4⋊C4—2441no—
578C2×C4⋊C4C22×D6111yescharacteristic
579C2×C4⋊C4C22×D6111yescharacteristic
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—611no—
584C2×C22⋊C4—611no—
585C2×C22⋊C4—1228no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C42—611no—
592C2×C42—1221no—
593C4⋊C8—1222no—
594#103—1222no—
595#103—1222no—
596#103—2441no—
597#103—2441no—
598#102—22no—
599#102—41no—
600#102—614no—
601#102—1222no—
602#102—1222no—
603#102—1222no—
604#102—1222no—
605#102—2441no—
606C22⋊C8—1222no—
607C22⋊C8—1222no—
608#97—1222no—
609#95—21no—
610#95—1221no—
611#95—1221no—
612C24—21no—
613C24—611no—
614C24—1224no—
615C24—1221no—
616C24—4881no—
617C24—4881no—
618C24—2442no—
619C24—2442no—
620C24—2442no—
621C24—2442no—
622C24D4×D6111yescharacteristic
623#41—1228no—
624#41—2444no—
625#41—2444no—
626#41—2444no—
627C2×Q8—612no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—1221no—
631C2×Q8—1221no—
632C2×Q8—1221no—
633C2×D4—24no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—614no—
642C2×D4—612no—
643C2×D4—612no—
644C2×D4—612no—
645C2×D4—1224no—
646C2×D4—1228no—
647C2×D4—1222no—
648C2×D4—1222no—
649C2×D4—1224no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—2444no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4—2442no—
657C2×D4—2442no—
658C2×D4—2442no—
659C2×D4—2442no—
660C2×D4C2×C4×D6112yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—1224no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1224no—
681C22×C4—1221no—
682C22×C4—4881no—
683C22×C4—4881no—
684C22×C4—4881no—
685C22×C4—4881no—
686C22×C4—2442no—
687C22×C4—2442no—
688C22×C4—2442no—
689C22×C4—2442no—
690C22×C4—2442no—
691C22×C4—2442no—
692C22×C4C2×C4×D6112yes—
693C22×C4D4×D6112yes—
694C22×C4D4×D6111yescharacteristic
695C22×C4C23×D6111yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—2444no—
709C2×C8D4×D6112yes—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—614no—
716C4⋊C4—612no—
717C4⋊C4—1224no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—4881no—
722C4⋊C4—2442no—
723C4⋊C4—2442no—
724C4⋊C4—2442no—
725C4⋊C4C2×C4×D6112yes—
726C22⋊C4—24no—
727C22⋊C4—42no—
728C22⋊C4—614no—
729C22⋊C4—614no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—2442no—
735C42—612no—
736C42—612no—
737C42—2442no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—612no—
752C23—612no—
753C23—612no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1222no—
759C23—1222no—
760C23—1222no—
761C23—4884no—
762C23—4884no—
763C23—4884no—
764C23—4884no—
765C23—4884no—
766C23—2448no—
767C23—2448no—
768C23—2441no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23C22⋊C4×D6112yes—
773C23C2×D4×D6111yescharacteristic
774Q8—1222no—
775Q8—1222no—
776Q8—2441no—
777Q8—2441no—
778D4—22no—
779D4—22no—
780D4—41no—
781D4—41no—
782D4—84no—
783D4—614no—
784D4—1228no—
785D4—1222no—
786D4—1222no—
787D4—1222no—
788D4—2448no—
789D4—2448no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—612no—
806C2×C4—612no—
807C2×C4—612no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—4884no—
821C2×C4—4884no—
822C2×C4—4884no—
823C2×C4—2448no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4C22⋊C4×D6112yes—
832C2×C4C22×C4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C2×D4×D6111yescharacteristic
835C2×C4#41×D6111yescharacteristic
836C2×C4#1451982211yescharacteristic
837C2×C4#1451982311yescharacteristic
838C8—22no—
839C8—41no—
840C8—2441no—
841C8—2441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—614no—
857C22—1222no—
858C22—1222no—
859C22—1222no—
860C22—1222no—
861C22—1222no—
862C22—1222no—
863C22—1224no—
864C22—48816no—
865C22—2442no—
866C22—2442no—
867C22—2442no—
868C22—2442no—
869C22—2442no—
870C22—2442no—
871C22C2×C22⋊C4×D6111yescharacteristic
872C22#1684039611yescharacteristic
873C22#1684040111yescharacteristic
874C22AGL(1,ℤ/8)×D6111yescharacteristic
875C22#137×D6111yescharacteristic
876C22#1684056611yescharacteristic
877C22#1684057211yescharacteristic
878C4—22no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4—1222no—
883C4—1222no—
884C4—1222no—
885C4—4881no—
886C4—2442no—
887C4—2442no—
888C4C4×D4×D6111yescharacteristic
889C4#1684023411yescharacteristic
890C4#1684039411yescharacteristic
891C4#1684040411yescharacteristic
892C2—42no—
893C2—82no—
894C2—1224no—
895C2—2444no—
896C2#2144863711yescharacteristic
897C2#417×D6111yescharacteristic
898C2#2145434411yescharacteristic
899C2#2145730611yescharacteristic
900C2#2145733611yescharacteristic
901C2#2145777511yescharacteristic
902C2#2145789511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1895C2
socleC23×C61C22×D4
prime radicalC2×#16840409C2
cosocleC22×C4×C61C24
hypercenter#1895D61
hypocenterC61#22419
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#16839831C2semidirect
3. C2×#16839764C2semidirect
4. C2×#102×D61C2semidirect
5. #21448715C2semidirect
6. #21446750C2semidirect
7. #21446634C2semidirect
8. #21446241C2semidirect
9. #21446137C2semidirect
10. #21446125C2semidirect
11. #21445818C2semidirect
12. #21445757C2semidirect
13. #21445748C2semidirect
14. #21445643C2semidirect
15. C61×#1895C2semidirect
20. #16840409C4semidirect
29. C22×C4⋊Dic61C22semidirect
33. C2×#14519706C22semidirect
35. C2×#14519702C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519700C22semidirect
38. C2×#14519700C22semidirect
46. C2×C22⋊#92418C22semidirect
48. C2×#14519687C22semidirect
52. #16839631C22semidirect
54. C4⋊C4×Dic61C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
57. C22×M16×C61C22semidirect
61. C61×#380C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
70. C2×#11758222C2×C4semidirect
81. C2×D4×D61C2×C4semidirect
93. #14519764C2×C4semidirect
96. #14519757C2×C4semidirect
100. #14519739C2×C4semidirect
132. #14519699D4semidirect
151. #121×C61C2×C4semidirect
374. D244C4×D4semidirect
426. C2×D61#417semidirect
448. #1895D61semidirect
469. C22×M16C2×D61semidirect
509. #380C2×D61semidirect
513. #340C2×D61semidirect
514. #340C2×D61semidirect
515. C61#22419semidirect
559. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404092
C2×#168398312
C2×#168397642
C2×#102×D612
#214487152
#214467502
#214466342
#214462412
#214461372
#214461252
#214458182
#214457572
#214457482
#214456432
C61×#18952
#2241961