Finite Group Databasebeta

← #29738242

Subgroups — #29738242

Order 15616.

736 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450840C211yesmaximal, characteristic, complemented
2#21448766C211yesmaximal, characteristic
3#21447192C211yesmaximal, characteristic
4#21447192C211yesmaximal, characteristic
5#21446966C211yesmaximal, characteristic
6#21446956C211yesmaximal, characteristic
7#21446774C211yesmaximal, characteristic, complemented
8#21446770C211yesmaximal, characteristic, complemented
9#21446583C211yesmaximal, characteristic, complemented
10#21446405C211yesmaximal, characteristic, complemented
11#21446398C211yesmaximal, characteristic, complemented
12#21445953C211yesmaximal, characteristic, complemented
13#21445830C211yesmaximal, characteristic
14#21445645C211yesmaximal, characteristic
15C61×#1940C211yesmaximal, characteristic, complemented
16C2×#14519777C2211yescharacteristic
17C2×#14519769C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519735—21no—
20C2×#14519709C2211yescharacteristic
21C2×#14519709C2211yescharacteristic
22C2×#14519699C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26#16839695—21no—
27#16839682—21no—
28#16839666—21no—
29#16839664C2211yescharacteristic
30#16839664C2211yescharacteristic
31#16839660C2211yescharacteristic
32#16839660C2211yescharacteristic
33#16839659—21no—
34#16839654—21no—
35#16839654—21no—
36#16839632C2211yescharacteristic
37#16839628C2211yescharacteristic
38#16839619—21no—
39C4×C4⋊Dic61C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122—21no—
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62#14519777—22no—
63#14519777—41no—
64#14519769—22no—
65#14519769—41no—
66C4×D244—22no—
67C4×D244Q814yescomplemented
68#14519735—44no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91#14519709—22no—
92#14519709—22no—
93#14519699—22no—
94#14519699—22no—
95#14519699—41no—
96#14519699—41no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C2×C4⋊C4×C61D411yescharacteristic
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C42×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113C4⋊C8×C61—22no—
114C4⋊C8×C61—41no—
115C4⋊C8×C61—41no—
116#97×C61—22no—
117#95×C61D411yescharacteristic
118#95×C61D411yescharacteristic
119C23×D61—21no—
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2411yescharacteristic
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C2×D244—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244C2×Q812yes—
140C2×C4×D61—24no—
141C2×C4×D61—42no—
142C2×C4×D61—42no—
143C2×Dic122—42no—
144C2×Dic122—42no—
145C2×Dic122—81no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C4⋊C4×C61—22no—
159C4⋊C4×C61—41no—
160C42×C61—21no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61—21no—
164C42×C61C2×Q812yes—
165C42×C61#4112yes—
166#11758198—24no—
167#11758198—42no—
168#11758198—42no—
169#11758198—81no—
170#11758198—81no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—42no—
183C4⋊Dic61—42no—
184C4⋊Dic61—81no—
185C4⋊Dic61C2×Q812yes—
186C4⋊Dic61#4112yes—
187C4⋊Dic61#4112yes—
188#11758196—42no—
189#11758196—42no—
190#11758196—42no—
191#11758196—81no—
192C4×Dic61—42no—
193C4×Dic61—42no—
194C4×Dic61—81no—
195C23×C61C22×D411yescharacteristic
196C22×D61—22no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—41no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61C22⋊Q812yes—
219C2×C4×C61C22⋊Q812yes—
220C2×C4×C61AGL(1,ℤ/8)12yes—
221C2×C4×C61C22×Q811yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C2×C4×C61H(5,𝔽2)11yescharacteristic
226C2×C4×C612−1+411yescharacteristic
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—22no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248D244—22no—
249D244—22no—
250D244—41no—
251D244—41no—
252C4×D61—48no—
253Dic122—84no—
254C8×C61—41no—
255C8×C61—41no—
256C8×C61—41no—
257C8×C61—41no—
258#26032—611nomaximal, Sylow
259C22×C61C2×C22⋊Q811yescharacteristic
260C22×C61#54611yescharacteristic
261C22×C61#54811yescharacteristic
262C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C61#57511yescharacteristic
264C22×C61#57711yescharacteristic
265C22×C61#57711yescharacteristic
266C2×D61—42no—
267C2×D61—42no—
268C2×D61—42no—
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C2×D61—81no—
273C4×C61—22no—
274C4×C61—22no—
275C4×C61—22no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61#53311yescharacteristic
280C4×C61#54411yescharacteristic
281C4×C61#55511yescharacteristic
282C4×C61#55611yescharacteristic
283Dic61—42no—
284Dic61—42no—
285Dic61—42no—
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289Dic61—81no—
290#2550—611no—
291#2354—611no—
292#2065—611no—
293#2065—611no—
294#2025—611no—
295#2023—611no—
296#1989—611no—
297#1988—611no—
298#1948—611no—
299#1940D6111yescharacteristic, complemented
300#1920—611no—
301#1919—611no—
302#1836—611no—
303#1804—611no—
304#1762—611no—
305C2×C61#243911yescharacteristic
306C2×C61#307711yescharacteristic
307C2×C61#308411yescharacteristic
308C2×C61#330611yescharacteristic
309C2×C61#332111yescharacteristic
310C2×C61#336811yescharacteristic
311C2×C61#337611yescharacteristic
312D61—82no—
313C2×C4⋊Q8—611no—
314C2×#125—611no—
315C2×C4×D4—611no—
316C2×#117—1221no—
317C2×#106—611no—
318C2×#106—611no—
319C2×C4⋊C8C2×D6111yescharacteristic
320C2×C4⋊C8C2×D6111yescharacteristic
321C2×C4⋊C8C2×D6111yescharacteristic
322C2×#102—611no—
323C2×#102—611no—
324C2×#102—611no—
325C2×#102—611no—
326C2×#97C2×D6111yescharacteristic
327#398—1221no—
328#395—1221no—
329#391—1221no—
330#390—611no—
331#390—611no—
332#389—611no—
333#389—611no—
334#389—1221no—
335#388—1221no—
336#388—1221no—
337#384—611no—
338#382—611no—
339#380—1221no—
340C4×C4⋊C4—611no—
341C4×C4⋊C4—611no—
342C4×C4⋊C4—611no—
343C4×C4⋊C4C2×D6111yescharacteristic
344#340—611no—
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#336C2×D6111yescharacteristic
355#336C2×D6111yescharacteristic
356C61#2603211yescharacteristic, complemented, Sylow
357C22×Q8—1221no—
358C22×D4—611no—
359C23×C4—1221no—
360C22×C8C22×D6111yescharacteristic
361C22×C8C22×D6111yescharacteristic
362C22×C8C22×D6111yescharacteristic
363C22×C8C22×D6111yescharacteristic
364C4⋊Q8—1222no—
365C4⋊Q8—2441no—
366#125—1222no—
367#125—2441no—
368C4×D4—614no—
369C4×D4—1222no—
370#117—2444no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4D24411yescharacteristic
386C2×C4⋊C4D24411yescharacteristic
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C42—1221no—
393C2×C42—1221no—
394C2×C42—1221no—
395C2×C42C22×D6111yescharacteristic
396C2×C42C22×D6111yescharacteristic
397C2×C42C22×D6111yescharacteristic
398#106—1222no—
399#106—1222no—
400C4⋊C8—22no—
401C4⋊C8—41no—
402C4⋊C8—41no—
403#102—1222no—
404#102—1222no—
405#102—2441no—
406#102—2441no—
407#97—22no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415#95D24411yescharacteristic
416#95D24411yescharacteristic
417C24—1221no—
418C2×Q8—4881no—
419C2×Q8—2442no—
420C2×Q8—2442no—
421C2×D4—612no—
422C2×D4—1221no—
423C2×D4—1221no—
424C2×D4—1221no—
425C2×D4—1221no—
426C2×D4—1221no—
427C22×C4—1221no—
428C22×C4—1221no—
429C22×C4—1221no—
430C22×C4—1224no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—2442no—
436C22×C4—2442no—
437C22×C4C2×D24411yescharacteristic
438C22×C4C2×D24411yescharacteristic
439C22×C4C2×D24411yescharacteristic
440C22×C4C2×D24411yescharacteristic
441C22×C4C2×D24411yescharacteristic
442C22×C4C2×D24411yescharacteristic
443C22×C4C23×D6111yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C4⋊C4—22no—
457C4⋊C4—41no—
458C4⋊C4—612no—
459C4⋊C4—612no—
460C4⋊C4—612no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—4881no—
473C4⋊C4—4881no—
474C4⋊C4—2442no—
475C4⋊C4—2442no—
476C4⋊C4—2442no—
477C4⋊C4—2442no—
478C4⋊C4—2442no—
479C22⋊C4—1224no—
480C22⋊C4—4881no—
481C22⋊C4—4881no—
482C22⋊C4—2442no—
483C22⋊C4—2442no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—4881no—
489C42—2442no—
490C42—2442no—
491C42#1175822412yes—
492C42Q8×D6112yes—
493C23—1222no—
494C23—2441no—
495C23—2441no—
496C23—2441no—
497C23—2441no—
498C23—2441no—
499C23—2441no—
500C23C22×D24411yescharacteristic
501Q8—4884no—
502D4—1222no—
503D4—1222no—
504D4—2441no—
505D4—2441no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—1222no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—2448no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4#1451975712yes—
544C2×C4#1451975712yes—
545C2×C4#1451980512yes—
546C2×C4C2×Q8×D6111yescharacteristic
547C2×C4#41×D6111yescharacteristic
548C2×C4#41×D6111yescharacteristic
549C2×C4C2×#1175822411yescharacteristic
550C2×C4#1451982211yescharacteristic
551C2×C4#1451982511yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—4881no—
557C22—4881no—
558C22—4881no—
559C22—4881no—
560C22—2442no—
561C22—2442no—
562C22—2442no—
563C22C2×#1451975711yescharacteristic
564C22#1684040711yescharacteristic
565C22#1684042411yescharacteristic
566C22C2×#1451980511yescharacteristic
567C22#1684056211yescharacteristic
568C22#1684057411yescharacteristic
569C22#1684057411yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—4881no—
577C4—4881no—
578C4—4881no—
579C4—4881no—
580C4—2442no—
581C4—2442no—
582C4—2442no—
583C4#1684031811yescharacteristic
584C4#1684038911yescharacteristic
585C4#1684047611yescharacteristic
586C4#1684048311yescharacteristic
587C2—4882no—
588C2#2144950811yescharacteristic
589C2#2145561811yescharacteristic
590C2#2145568311yescharacteristic
591C2#2145778211yescharacteristic
592C2#2145800711yescharacteristic
593C2#2145855011yescharacteristic
594C2#2145864811yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1940C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1940D61
hypocenterC61#26032
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
1. #21450840C2semidirect
7. #21446774C2semidirect
8. #21446770C2semidirect
9. #21446583C2semidirect
10. #21446405C2semidirect
11. #21446398C2semidirect
12. #21445953C2semidirect
15. C61×#1940C2semidirect
67. C4×D244Q8semidirect
299. #1940D61semidirect
356. C61#26032semidirect

Maximal subgroups

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

subgroupindex
#214508402
#214487662
#214471922
#214469662
#214469562
#214467742
#214467702
#214465832
#214464052
#214463982
#214459532
#214458302
#214456452
C61×#19402
#2603261