Subgroups — C₄×#21441251 #44529143

Order 31168.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21441251	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₉₇₄	C₂	1	1	yes	maximal, characteristic
3	#29510148	C₂	1	1	yes	maximal, characteristic
4	#29510139	C₂	1	1	yes	maximal, characteristic
5	#29510138	C₂	1	1	yes	maximal, characteristic
6	C₄×C₄₈₇⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₄×Q₈×C₄₈₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₉₇₄	C₂²	1	1	yes	characteristic
9	#21441251	C₄	1	4	yes	direct product factor
10	C₂×C₄₈₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄₈₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₈₇	C₂²	1	1	yes	characteristic
13	Dic₄₈₇⋊C₄	—	2	1	no	—
14	C₄×Dic₄₈₇	—	2	1	no	—
15	C₂×Q₈×C₄₈₇	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×C₄₈₇	—	2	1	no	—
17	C₄⋊C₄×C₄₈₇	C₂²	1	1	yes	characteristic
18	C₄²×C₄₈₇	—	2	1	no	—
19	C₄²×C₄₈₇	C₂²	1	1	yes	characteristic
20	Dic₉₇₄	—	2	1	no	—
21	Dic₉₇₄	C₂×C₄	1	2	yes	—
22	C₂×Dic₄₈₇	—	2	1	no	—
23	C₂×Dic₄₈₇	—	2	1	no	—
24	C₄₈₇⋊C₈	—	2	1	no	—
25	C₄₈₇⋊C₈	C₂×C₄	1	2	yes	—
26	Q₈×C₄₈₇	—	2	1	no	—
27	Q₈×C₄₈₇	C₂×C₄	1	2	yes	—
28	C₂×C₄×C₄₈₇	—	2	1	no	—
29	C₂×C₄×C₄₈₇	—	2	1	no	—
30	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
33	C₂²×C₄₈₇	C₂×D₄	1	1	yes	characteristic
34	C₄×C₄₈₇	—	2	2	no	—
35	C₄×C₄₈₇	—	2	1	no	—
36	C₄×C₄₈₇	—	4	1	no	—
37	C₄×C₄₈₇	Q₁₆	1	2	yes	complemented
38	C₄×C₄₈₇	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₄₈₇	#41	1	1	yes	characteristic
40	Dic₄₈₇	—	2	2	no	—
41	Dic₄₈₇	—	4	1	no	—
42	C₂×C₄₈₇	C₄×D₄	1	1	yes	characteristic
43	C₂×C₄₈₇	C₂×Q₁₆	1	1	yes	characteristic
44	C₂×C₄₈₇	#135	1	1	yes	characteristic
45	C₄₈₇	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₁₆	—	487	1	no	maximal, Sylow
47	C₂×Q₁₆	—	487	1	no	—
48	C₄×Q₈	—	487	1	no	—
49	C₄×Q₈	D₄₈₇	1	1	yes	characteristic
50	#107	—	487	1	no	—
51	#103	—	487	1	no	—
52	#103	—	487	1	no	—
53	C₄×C₈	—	487	1	no	—
54	C₂×Q₈	—	487	1	no	—
55	C₂×Q₈	C₂×D₄₈₇	1	1	yes	characteristic
56	Q₁₆	—	487	4	no	—
57	C₂×C₈	—	487	1	no	—
58	C₂×C₈	—	487	1	no	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	974	1	no	—
61	C₄⋊C₄	—	487	1	no	—
62	C₄⋊C₄	C₂×D₄₈₇	1	1	yes	characteristic
63	C₄²	—	2	1	no	—
64	C₄²	—	974	1	no	—
65	C₄²	C₂×D₄₈₇	1	1	yes	characteristic
66	Q₈	—	2	1	no	—
67	Q₈	—	974	1	no	—
68	Q₈	—	487	2	no	—
69	Q₈	C₄×D₄₈₇	1	2	yes	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	974	1	no	—
73	C₂×C₄	—	974	1	no	—
74	C₂×C₄	C₂²⋊D₄₈₇	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊D₄₈₇	1	1	yes	characteristic
76	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
77	C₈	—	974	1	no	—
78	C₈	—	487	2	no	—
79	C₂²	C₂×C₂²⋊D₄₈₇	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	2	1	no	—
82	C₄	—	4	1	no	—
83	C₄	—	1948	1	no	—
84	C₄	—	974	2	no	—
85	C₄	#21441251	1	2	yes	direct product factor
86	C₄	C₂×C₄×D₄₈₇	1	1	yes	characteristic
87	C₄	#21441261	1	1	yes	characteristic
88	C₂	C₄×C₂²⋊D₄₈₇	1	1	yes	characteristic
89	C₂	C₂×#21441251	1	1	yes	characteristic
90	C₂	#29510235	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₄₈₇
commutator	C₄×C₄₈₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₈₇
Fitting	C₄×Q₈×C₄₈₇	C₂
socle, prime radical	C₂²×C₄₈₇	C₂×D₄
cosocle	C₂×C₄×C₄₈₇	C₂³
hypercenter	C₄×Q₈	D₄₈₇
hypocenter	C₄₈₇	C₄×Q₁₆
LCS	G ▷ C₄×C₄₈₇ ▷ C₂×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
9. #21441251	C₄	direct (N × H)
37. C₄×C₄₈₇	Q₁₆	semidirect
45. C₄₈₇	C₄×Q₁₆	semidirect
85. C₄	#21441251	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#21441251	2
C₄×Dic₉₇₄	2
#29510148	2
#29510139	2
#29510138	2
C₄×C₄₈₇⋊C₈	2
C₄×Q₈×C₄₈₇	2
C₄×Q₁₆	487

Subgroups — C4×#21441251 #44529143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#21441251 #44529143