Subgroups — C₂×#21444036 #29601062

Order 15616.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₇₆	C₂	1	1	yes	maximal, characteristic
2	#21444036	C₂	1	4	yes	maximal, direct product factor
3	C₂×#16839481	C₂	1	1	yes	maximal, characteristic
4	C₂×C₆₁×Q₆₄	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₄₈₈	—	2	1	no	—
6	Dic₉₇₆	—	2	1	no	—
7	Dic₉₇₆	C₂²	1	2	yes	—
8	#16839481	C₂²	1	2	yes	—
9	C₂×Q₃₂×C₆₁	—	2	1	no	—
10	C₆₁×Q₆₄	—	2	1	no	—
11	C₆₁×Q₆₄	C₂²	1	2	yes	—
12	C₂×C₃₂×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×Dic₂₄₄	—	4	1	no	—
14	Dic₄₈₈	—	2	2	no	—
15	Dic₄₈₈	—	4	1	no	—
16	C₂×Q₁₆×C₆₁	—	4	1	no	—
17	Q₃₂×C₆₁	—	2	2	no	—
18	Q₃₂×C₆₁	—	4	1	no	—
19	C₂×C₁₆×C₆₁	D₄	1	1	yes	characteristic
20	C₃₂×C₆₁	D₄	1	1	yes	characteristic
21	C₃₂×C₆₁	C₂³	1	1	yes	characteristic
22	C₂×Q₈×C₆₁	—	8	1	no	—
23	C₂×Dic₁₂₂	—	8	1	no	—
24	Q₁₆×C₆₁	—	4	2	no	—
25	Q₁₆×C₆₁	—	8	1	no	—
26	C₂×C₈×C₆₁	D₈	1	1	yes	characteristic
27	Dic₂₄₄	—	4	2	no	—
28	Dic₂₄₄	—	8	1	no	—
29	C₁₆×C₆₁	D₈	1	1	yes	characteristic
30	C₁₆×C₆₁	C₂×D₄	1	1	yes	characteristic
31	Q₈×C₆₁	—	8	2	no	—
32	Q₈×C₆₁	—	16	1	no	—
33	C₂×C₄×C₆₁	—	16	1	no	—
34	C₂×C₄×C₆₁	D₁₆	1	1	yes	characteristic
35	C₂×Dic₆₁	—	16	1	no	—
36	Dic₁₂₂	—	8	2	no	—
37	Dic₁₂₂	—	16	1	no	—
38	C₈×C₆₁	D₁₆	1	1	yes	characteristic
39	C₈×C₆₁	C₂×D₈	1	1	yes	characteristic
40	C₂×Q₁₂₈	—	61	1	no	maximal, Sylow
41	C₂²×C₆₁	D₃₂	1	1	yes	characteristic
42	C₄×C₆₁	—	16	2	no	—
43	C₄×C₆₁	D₃₂	1	1	yes	characteristic
44	C₄×C₆₁	C₂×D₁₆	1	1	yes	characteristic
45	Dic₆₁	—	16	2	no	—
46	C₂×Q₆₄	—	61	1	no	—
47	C₂×Q₆₄	D₆₁	1	1	yes	characteristic
48	Q₁₂₈	—	61	4	no	—
49	C₂×C₆₄	—	61	1	no	—
50	C₂×C₆₁	Q₁₂₈	1	2	yes	complemented
51	C₂×C₆₁	C₂×D₃₂	1	1	yes	characteristic
52	C₂×Q₃₂	—	2	1	no	—
53	C₂×Q₃₂	—	122	1	no	—
54	Q₆₄	—	2	1	no	—
55	Q₆₄	—	61	2	no	—
56	Q₆₄	—	122	1	no	—
57	Q₆₄	C₂×D₆₁	1	2	yes	—
58	C₂×C₃₂	C₂×D₆₁	1	1	yes	characteristic
59	C₆₄	—	61	2	no	—
60	C₆₁	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
61	C₂×Q₁₆	—	4	1	no	—
62	C₂×Q₁₆	—	244	1	no	—
63	Q₃₂	—	2	2	no	—
64	Q₃₂	—	4	1	no	—
65	Q₃₂	—	122	2	no	—
66	Q₃₂	—	244	1	no	—
67	C₂×C₁₆	C₂²⋊D₆₁	1	1	yes	characteristic
68	C₃₂	C₂²⋊D₆₁	1	1	yes	characteristic
69	C₃₂	C₂²×D₆₁	1	1	yes	characteristic
70	C₂×Q₈	—	8	1	no	—
71	C₂×Q₈	—	488	1	no	—
72	Q₁₆	—	4	2	no	—
73	Q₁₆	—	8	1	no	—
74	Q₁₆	—	488	1	no	—
75	Q₁₆	—	244	2	no	—
76	C₂×C₈	#11758199	1	1	yes	characteristic
77	C₁₆	#11758199	1	1	yes	characteristic
78	C₁₆	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
79	Q₈	—	8	2	no	—
80	Q₈	—	16	1	no	—
81	Q₈	—	976	1	no	—
82	Q₈	—	488	2	no	—
83	C₂×C₄	—	16	1	no	—
84	C₂×C₄	—	976	1	no	—
85	C₂×C₄	#14519718	1	1	yes	characteristic
86	C₈	#14519718	1	1	yes	characteristic
87	C₈	C₂×#11758199	1	1	yes	characteristic
88	C₂²	#16839597	1	1	yes	characteristic
89	C₄	—	16	2	no	—
90	C₄	—	976	2	no	—
91	C₄	#16839597	1	1	yes	characteristic
92	C₄	C₂×#14519718	1	1	yes	characteristic
93	C₂	#21444036	1	2	yes	direct product factor
94	C₂	C₂×#16839597	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16839597
commutator, cosocle	C₃₂×C₆₁	C₂³
Frattini	C₃₂	C₂²×D₆₁
Fitting	C₂×C₆₁×Q₆₄	C₂
socle, prime radical	C₂²×C₆₁	D₃₂
hypercenter	C₂×Q₆₄	D₆₁
hypocenter	C₆₁	C₂×Q₁₂₈
LCS	G ▷ C₃₂×C₆₁ ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×Q₆₄

Complements

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

N	H ≅ G/N	type
2. #21444036	C₂	direct (N × H)
50. C₂×C₆₁	Q₁₂₈	semidirect
60. C₆₁	C₂×Q₁₂₈	semidirect
93. C₂	#21444036	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×Dic₉₇₆	2
#21444036	2
C₂×#16839481	2
C₂×C₆₁×Q₆₄	2
C₂×Q₁₂₈	61

Subgroups — C2×#21444036 #29601062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21444036 #29601062