Subgroups — #44500506

Order 30656.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₈₃₂	C₂	1	1	yes	maximal, characteristic
2	#29506344	C₂	1	2	yes	maximal, complemented
3	#29506302	C₂	1	2	yes	maximal, complemented
4	#29506292	C₂	1	1	yes	maximal, characteristic, complemented
5	#106×C₄₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₉₁₆	C₂²	1	2	yes	—
7	C₂×C₄×D₄₇₉	—	2	2	no	—
8	D₃₈₃₂	C₄	1	4	yes	complemented
9	C₂×C₄₇₉⋊C₈	C₂²	1	1	yes	characteristic
10	(C₂×D₄₇₉)⋊C₄	—	2	2	no	—
11	C₄×Dic₄₇₉	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₄₇₉	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₄₇₉	C₂²	1	2	yes	—
14	C₂²×D₄₇₉	—	2	2	no	—
15	D₁₉₁₆	—	2	2	no	—
16	D₁₉₁₆	C₂×C₄	1	4	yes	complemented
17	C₂×Dic₄₇₉	D₄	1	2	yes	—
18	C₄×D₄₇₉	—	4	4	no	—
19	C₄₇₉⋊C₈	—	2	1	no	—
20	C₂×C₄×C₄₇₉	—	2	2	no	—
21	C₂×C₄×C₄₇₉	C₂³	1	1	yes	characteristic
22	C₈×C₄₇₉	C₂×C₄	1	2	yes	complemented
23	C₂²×C₄₇₉	C₂×D₄	1	1	yes	characteristic
24	C₂×D₄₇₉	—	2	4	no	—
25	C₂×D₄₇₉	—	4	2	no	—
26	C₂×D₄₇₉	—	4	2	no	—
27	C₄×C₄₇₉	—	4	2	no	—
28	C₄×C₄₇₉	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₄₇₉	#41	1	1	yes	characteristic
30	Dic₄₇₉	—	2	2	no	—
31	C₂×C₄₇₉	C₄×D₄	1	1	yes	characteristic
32	C₂×C₄₇₉	AGL(1,ℤ/8)	1	2	yes	—
33	D₄₇₉	—	4	4	no	—
34	C₄₇₉	#442	1	1	yes	characteristic, complemented, Sylow
35	#442	—	479	1	no	maximal, Sylow
36	C₂×D₈	—	479	1	no	—
37	C₄×D₄	—	479	2	no	—
38	#106	D₄₇₉	1	1	yes	characteristic, complemented
39	#102	—	479	2	no	—
40	#97	—	479	1	no	—
41	C₂×D₄	—	479	2	no	—
42	C₂²×C₄	—	958	2	no	—
43	D₈	—	479	4	no	—
44	C₂×C₈	—	479	1	no	—
45	C₂×C₈	C₂×D₄₇₉	1	1	yes	characteristic
46	C₄⋊C₄	C₂×D₄₇₉	1	2	yes	—
47	C₂²⋊C₄	—	958	2	no	—
48	C₄²	—	479	1	no	—
49	C₂³	—	958	2	no	—
50	D₄	—	958	2	no	—
51	D₄	—	479	4	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	1916	4	no	—
54	C₂×C₄	—	479	2	no	—
55	C₂×C₄	C₂²×D₄₇₉	1	1	yes	characteristic
56	C₈	—	958	1	no	—
57	C₈	C₄×D₄₇₉	1	2	yes	complemented
58	C₂²	—	1916	2	no	—
59	C₂²	—	1916	2	no	—
60	C₂²	—	958	4	no	—
61	C₂²	D₄×D₄₇₉	1	1	yes	characteristic
62	C₄	—	4	2	no	—
63	C₄	—	958	2	no	—
64	C₄	C₂×C₄×D₄₇₉	1	1	yes	characteristic
65	C₄	#21440163	1	1	yes	characteristic
66	C₂	—	1916	4	no	—
67	C₂	#29506344	1	1	yes	characteristic
68	C₂	#29506409	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₇₉
commutator	C₄×C₄₇₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇₉
Fitting	#106×C₄₇₉	C₂
socle	C₂²×C₄₇₉	C₂×D₄
prime radical	C₂×D₃₈₃₂	C₂
cosocle	C₂×C₄×C₄₇₉	C₂³
hypercenter	#106	D₄₇₉
hypocenter	C₄₇₉	#442
LCS	G ▷ C₄×C₄₇₉ ▷ C₂×C₄₇₉ ▷ C₄₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
2. #29506344	C₂	semidirect
3. #29506302	C₂	semidirect
4. #29506292	C₂	semidirect
5. #106×C₄₇₉	C₂	semidirect
8. D₃₈₃₂	C₄	semidirect
16. D₁₉₁₆	C₂×C₄	semidirect
22. C₈×C₄₇₉	C₂×C₄	semidirect
34. C₄₇₉	#442	semidirect
38. #106	D₄₇₉	semidirect
57. C₈	C₄×D₄₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₈₃₂	2
#29506344	2
#29506302	2
#29506292	2
#106×C₄₇₉	2
#442	479