Subgroups — C₂×#14520879 #16847503

Order 3968.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758407	C₂	1	2	yes	maximal
2	#14520879	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic
5	C₂×#92474	—	2	2	no	—
6	C₂×C₁₆×C₃₁	C₄	1	2	yes	—
7	C₂×C₁₆×C₃₁	C₄	1	2	yes	—
8	C₂×C₁₆×C₃₁	C₂²	1	2	yes	—
9	#11758407	—	2	2	no	—
10	#11758407	C₂²	1	4	yes	—
11	C₂²×C₄×C₃₁	D₄	1	1	yes	characteristic
12	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
15	C₂×C₈×C₃₁	Q₈	1	1	yes	characteristic
16	C₂×C₈×C₃₁	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
18	#92474	—	2	4	no	—
19	#92474	—	4	2	no	—
20	C₂×C₃₁⋊C₈	—	4	2	no	—
21	C₁₆×C₃₁	C₂×C₄	1	4	yes	—
22	C₂³×C₃₁	Q₁₆	1	1	yes	characteristic
23	C₂×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₃₁	D₈	1	1	yes	characteristic
26	C₂×C₄×C₃₁	D₈	1	1	yes	characteristic
27	C₂×C₄×C₃₁	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
29	C₈×C₃₁	C₄⋊C₄	1	1	yes	characteristic
30	C₈×C₃₁	C₄⋊C₄	1	1	yes	characteristic
31	C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₃₁	C₂×Q₈	1	1	yes	characteristic
33	C₃₁⋊C₈	—	4	4	no	—
34	C₂×#368	—	31	1	no	maximal, Sylow
35	C₂²×C₃₁	—	2	2	no	—
36	C₂²×C₃₁	#107	1	1	yes	characteristic
37	C₂²×C₃₁	#107	1	1	yes	characteristic
38	C₂²×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
39	C₄×C₃₁	#107	1	1	yes	characteristic
40	C₄×C₃₁	#107	1	1	yes	characteristic
41	C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
43	C₂²×C₁₆	D₃₁	1	1	yes	characteristic
44	C₂×#108	—	31	2	no	—
45	#368	—	31	4	no	—
46	C₂×C₃₁	—	2	1	no	—
47	C₂×C₃₁	—	2	1	no	—
48	C₂×C₃₁	#368	1	2	yes	complemented
49	C₂×C₃₁	C₂×#107	1	1	yes	characteristic
50	C₂×M₁₆	—	62	2	no	—
51	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic
52	C₂×C₁₆	Dic₃₁	1	2	yes	—
53	C₂×C₁₆	Dic₃₁	1	2	yes	—
54	C₂×C₁₆	C₂×D₃₁	1	2	yes	—
55	#108	—	31	4	no	—
56	#108	—	62	2	no	—
57	C₃₁	C₂×#368	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	D₁₂₄	1	1	yes	characteristic
59	M₁₆	—	62	4	no	—
60	M₁₆	—	124	2	no	—
61	C₂×C₈	—	124	2	no	—
62	C₂×C₈	Dic₆₂	1	1	yes	characteristic
63	C₂×C₈	Dic₆₂	1	1	yes	characteristic
64	C₂×C₈	D₁₂₄	1	1	yes	characteristic
65	C₂×C₈	C₂×Dic₃₁	1	1	yes	characteristic
66	C₂×C₈	C₂×Dic₃₁	1	1	yes	characteristic
67	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
68	C₁₆	C₂×Dic₃₁	1	4	yes	—
69	C₂³	Dic₁₂₄	1	1	yes	characteristic
70	C₂×C₄	D₂₄₈	1	1	yes	characteristic
71	C₂×C₄	D₂₄₈	1	1	yes	characteristic
72	C₂×C₄	Dic₁₂₄	1	1	yes	characteristic
73	C₂×C₄	C₄⋊Dic₃₁	1	1	yes	characteristic
74	C₂×C₄	C₄⋊Dic₃₁	1	1	yes	characteristic
75	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
76	C₈	—	124	4	no	—
77	C₈	C₄⋊Dic₃₁	1	1	yes	characteristic
78	C₈	C₄⋊Dic₃₁	1	1	yes	characteristic
79	C₈	C₂×Dic₆₂	1	1	yes	characteristic
80	C₈	C₂²×Dic₃₁	1	1	yes	characteristic
81	C₂²	—	2	2	no	—
82	C₂²	#11758406	1	1	yes	characteristic
83	C₂²	#11758406	1	1	yes	characteristic
84	C₂²	C₂×Dic₁₂₄	1	1	yes	characteristic
85	C₄	#11758406	1	1	yes	characteristic
86	C₄	#11758406	1	1	yes	characteristic
87	C₄	C₂×D₂₄₈	1	1	yes	characteristic
88	C₄	C₂×C₄⋊Dic₃₁	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	2	1	no	—
91	C₂	#14520879	1	2	yes	direct product factor
92	C₂	C₂×#11758406	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₂₄₈
commutator	C₈×C₃₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₁
Fitting	C₂²×C₁₆×C₃₁	C₂
socle	C₂²×C₃₁	#107
prime radical	C₂³×C₃₁	Q₁₆
cosocle	C₂×C₈×C₃₁	C₂³
hypercenter	C₂²×C₁₆	D₃₁
hypocenter	C₃₁	C₂×#368
LCS	G ▷ C₈×C₃₁ ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #14520879	C₂	direct (N × H)
48. C₂×C₃₁	#368	semidirect
57. C₃₁	C₂×#368	semidirect
91. C₂	#14520879	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×#11758407	2
#14520879	2
C₂²×C₁₆×C₃₁	2
C₂×#368	31

Subgroups — C2×#14520879 #16847503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14520879 #16847503