Subgroups — #44500591

Order 30656.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₈₃₂	C₂	1	2	yes	maximal, complemented
2	#29506379	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₁₉₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#29506304	C₂	1	2	yes	maximal, complemented
5	C₄⋊C₈×C₄₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₉₁₆	—	2	1	no	—
7	C₂×D₁₉₁₆	—	2	1	no	—
8	C₂×D₁₉₁₆	C₂²	1	2	yes	—
9	C₂×D₁₉₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄₇₉	—	2	1	no	—
11	D₃₈₃₂	—	2	4	no	—
12	C₄⋊Dic₄₇₉	C₂²	1	1	yes	characteristic
13	(C₂×D₄₇₉)⋊C₄	—	2	1	no	—
14	C₂×C₈×C₄₇₉	C₂²	1	2	yes	—
15	C₄²×C₄₇₉	C₂²	1	1	yes	characteristic
16	C₂²×D₄₇₉	—	2	1	no	—
17	C₂²×D₄₇₉	—	2	2	no	—
18	D₁₉₁₆	—	2	2	no	—
19	D₁₉₁₆	—	2	1	no	—
20	D₁₉₁₆	—	2	2	no	—
21	D₁₉₁₆	—	4	2	no	—
22	D₁₉₁₆	—	4	2	no	—
23	D₁₉₁₆	D₄	1	2	yes	complemented
24	C₂×Dic₄₇₉	—	2	1	no	—
25	C₄×D₄₇₉	—	4	2	no	—
26	C₂×C₄×C₄₇₉	D₄	1	1	yes	characteristic
27	C₂×C₄×C₄₇₉	D₄	1	1	yes	characteristic
28	C₂×C₄×C₄₇₉	C₂³	1	1	yes	characteristic
29	C₈×C₄₇₉	—	2	2	no	—
30	C₂²×C₄₇₉	C₂×D₄	1	1	yes	characteristic
31	C₂×D₄₇₉	—	2	2	no	—
32	C₂×D₄₇₉	—	4	1	no	—
33	C₂×D₄₇₉	—	4	1	no	—
34	C₂×D₄₇₉	—	4	2	no	—
35	C₂×D₄₇₉	—	4	2	no	—
36	C₂×D₄₇₉	—	4	2	no	—
37	C₄×C₄₇₉	—	2	1	no	—
38	C₄×C₄₇₉	D₈	1	2	yes	complemented
39	C₄×C₄₇₉	C₂×D₄	1	1	yes	characteristic
40	C₄×C₄₇₉	#41	1	1	yes	characteristic
41	Dic₄₇₉	—	4	1	no	—
42	C₂×C₄₇₉	#121	1	1	yes	characteristic
43	C₂×C₄₇₉	C₂×D₈	1	1	yes	characteristic
44	C₂×C₄₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
45	D₄₇₉	—	4	2	no	—
46	D₄₇₉	—	8	2	no	—
47	C₄₇₉	#459	1	1	yes	characteristic, complemented, Sylow
48	#459	—	479	1	no	maximal, Sylow
49	C₂×D₈	—	479	2	no	—
50	#127	—	479	1	no	—
51	C₄×D₄	—	479	1	no	—
52	C₄⋊C₈	D₄₇₉	1	1	yes	characteristic, complemented
53	#102	—	479	2	no	—
54	C₂×D₄	—	958	1	no	—
55	C₂×D₄	—	958	1	no	—
56	C₂×D₄	—	479	2	no	—
57	C₂×D₄	—	479	1	no	—
58	C₂²×C₄	—	958	1	no	—
59	D₈	—	958	4	no	—
60	C₂×C₈	C₂×D₄₇₉	1	2	yes	—
61	C₄⋊C₄	—	479	1	no	—
62	C₂²⋊C₄	—	958	1	no	—
63	C₄²	C₂×D₄₇₉	1	1	yes	characteristic
64	C₂³	—	958	2	no	—
65	C₂³	—	958	1	no	—
66	D₄	—	1916	2	no	—
67	D₄	—	1916	2	no	—
68	D₄	—	958	2	no	—
69	D₄	—	958	2	no	—
70	D₄	—	958	1	no	—
71	D₄	—	479	2	no	—
72	C₂×C₄	—	1916	2	no	—
73	C₂×C₄	—	958	1	no	—
74	C₂×C₄	D₁₉₁₆	1	1	yes	characteristic
75	C₂×C₄	D₁₉₁₆	1	1	yes	characteristic
76	C₂×C₄	C₂²×D₄₇₉	1	1	yes	characteristic
77	C₈	—	2	2	no	—
78	C₂²	—	1916	1	no	—
79	C₂²	—	1916	1	no	—
80	C₂²	—	1916	2	no	—
81	C₂²	—	1916	2	no	—
82	C₂²	—	1916	2	no	—
83	C₂²	—	958	2	no	—
84	C₂²	C₂×D₁₉₁₆	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	—	1916	1	no	—
87	C₄	D₃₈₃₂	1	2	yes	complemented
88	C₄	D₄×D₄₇₉	1	1	yes	characteristic
89	C₄	#21440163	1	1	yes	characteristic
90	C₂	—	1916	2	no	—
91	C₂	—	3832	2	no	—
92	C₂	#29506357	1	1	yes	characteristic
93	C₂	C₂×D₃₈₃₂	1	1	yes	characteristic
94	C₂	#29506410	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₉₁₆
commutator, cosocle	C₂×C₄×C₄₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₄₇₉
Fitting	C₄⋊C₈×C₄₇₉	C₂
socle	C₂²×C₄₇₉	C₂×D₄
hypercenter	C₄⋊C₈	D₄₇₉
hypocenter	C₄₇₉	#459
LCS	G ▷ C₂×C₄×C₄₇₉ ▷ C₂×C₄₇₉ ▷ C₄₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₃₈₃₂	C₂	semidirect
2. #29506379	C₂	semidirect
3. C₄×D₁₉₁₆	C₂	semidirect
4. #29506304	C₂	semidirect
5. C₄⋊C₈×C₄₇₉	C₂	semidirect
23. D₁₉₁₆	D₄	semidirect
38. C₄×C₄₇₉	D₈	semidirect
47. C₄₇₉	#459	semidirect
52. C₄⋊C₈	D₄₇₉	semidirect
87. C₄	D₃₈₃₂	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
#29506379	2
C₄×D₁₉₁₆	2
#29506304	2
C₄⋊C₈×C₄₇₉	2
#459	479