Subgroups — C₂×#824 #5136

Order 192.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×#208	C₂	1	1	yes	maximal, characteristic
4	#824	C₂	1	4	yes	maximal, direct product factor
5	C₂×#101	—	3	1	no	maximal, Sylow
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃	C₄	1	2	yes	—
8	C₂×Dic₆	—	2	1	no	—
9	C₂×Dic₆	—	2	1	no	—
10	C₂×Dic₆	—	2	1	no	—
11	C₂×Dic₆	—	2	1	no	—
12	C₂×Dic₆	C₄	1	2	yes	—
13	C₂×Dic₆	C₂²	1	2	yes	—
14	C₃×M₁₆	—	2	1	no	—
15	C₃×M₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₈	—	2	1	no	—
17	#208	—	2	1	no	—
18	#208	C₂²	1	2	yes	—
19	C₂×C₃⋊C₈	—	2	1	no	—
20	C₂²×Q₈	—	3	1	no	—
21	C₂×M₁₆	—	3	1	no	—
22	C₂×M₁₆	D₃	1	1	yes	characteristic
23	#101	—	3	4	no	—
24	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
26	C₂×C₃×C₄	D₄	1	1	yes	characteristic
27	C₂×C₃×C₄	D₄	1	1	yes	characteristic
28	C₂×C₃×C₄	D₄	1	1	yes	characteristic
29	C₂×C₃×C₄	D₄	1	1	yes	characteristic
30	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
31	C₂×Dic₃	—	2	2	no	—
32	C₂×Dic₃	—	2	2	no	—
33	C₂×Dic₃	C₂×C₄	1	4	yes	—
34	Dic₆	—	2	2	no	—
35	Dic₆	—	2	2	no	—
36	Dic₆	—	2	2	no	—
37	Dic₆	—	2	2	no	—
38	C₃×C₈	—	2	2	no	—
39	C₃⋊C₈	—	2	2	no	—
40	C₂×Q₈	—	3	2	no	—
41	C₂×Q₈	—	3	2	no	—
42	C₂×Q₈	—	6	1	no	—
43	C₂×Q₈	—	6	1	no	—
44	C₂×Q₈	—	6	1	no	—
45	C₂×Q₈	—	6	1	no	—
46	C₂²×C₄	—	3	2	no	—
47	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
48	M₁₆	—	2	1	no	—
49	M₁₆	—	3	2	no	—
50	M₁₆	—	6	1	no	—
51	M₁₆	C₂×D₃	1	2	yes	—
52	C₂×C₈	—	2	1	no	—
53	C₂×C₈	—	6	1	no	—
54	C₂²×C₃	—	2	2	no	—
55	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
58	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
59	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
60	C₃×C₄	C₂×D₄	1	1	yes	characteristic
61	C₃×C₄	C₂×D₄	1	1	yes	characteristic
62	Dic₃	—	2	4	no	—
63	C₂³	C₄×D₃	1	1	yes	characteristic
64	Q₈	—	6	2	no	—
65	Q₈	—	6	2	no	—
66	Q₈	—	6	2	no	—
67	Q₈	—	6	2	no	—
68	C₂×C₄	—	3	4	no	—
69	C₂×C₄	—	6	2	no	—
70	C₂×C₄	—	6	2	no	—
71	C₂×C₄	C₄×D₃	1	1	yes	characteristic
72	C₂×C₄	D₁₂	1	1	yes	characteristic
73	C₂×C₄	D₁₂	1	1	yes	characteristic
74	C₂×C₄	#67	1	1	yes	characteristic
75	C₂×C₄	#67	1	1	yes	characteristic
76	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
77	C₈	—	2	2	no	—
78	C₈	—	6	2	no	—
79	C₂×C₃	—	2	1	no	—
80	C₂×C₃	—	2	1	no	—
81	C₂×C₃	#101	1	2	yes	complemented
82	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂²	—	2	2	no	—
84	C₂²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
85	C₂²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
86	C₂²	C₂×C₄×D₃	1	1	yes	characteristic
87	C₄	—	6	4	no	—
88	C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
89	C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
90	C₄	C₂×D₁₂	1	1	yes	characteristic
91	C₄	C₂×#67	1	1	yes	characteristic
92	C₃	C₂×#101	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	2	1	no	—
94	C₂	—	2	1	no	—
95	C₂	#824	1	2	yes	direct product factor
96	C₂	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₂×C₃×M₁₆	C₂
socle	C₂²×C₃	C₂²⋊C₄
prime radical	C₂³×C₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂³
hypercenter	C₂×M₁₆	D₃
hypocenter	C₃	C₂×#101
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #824	C₂	direct (N × H)
81. C₂×C₃	#101	semidirect
92. C₃	C₂×#101	semidirect
95. C₂	#824	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₆	2
C₂×C₃×M₁₆	2
C₂×#208	2
#824	2
C₂×#101	3

Subgroups — C2×#824 #5136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#824 #5136