Subgroups — C₂×#6398 #89908

Order 448.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×#1136	C₂	1	1	yes	maximal, characteristic
4	#6398	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₂²×Dic₇	C₄	1	2	yes	—
7	C₂×Dic₁₄	—	2	1	no	—
8	C₂×Dic₁₄	—	2	1	no	—
9	C₂×Dic₁₄	—	2	1	no	—
10	C₂×Dic₁₄	—	2	1	no	—
11	C₂×Dic₁₄	C₄	1	2	yes	—
12	C₂×Dic₁₄	C₂²	1	2	yes	—
13	C₇×M₁₆	—	2	1	no	—
14	C₇×M₁₆	C₂²	1	2	yes	—
15	C₂×C₇×C₈	—	2	1	no	—
16	#1136	—	2	1	no	—
17	#1136	C₂²	1	2	yes	—
18	C₂×C₇⋊C₈	—	2	1	no	—
19	C₂×#101	—	7	1	no	maximal, Sylow
20	C₂³×C₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₇	D₄	1	1	yes	characteristic
23	C₂×C₄×C₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₇	D₄	1	1	yes	characteristic
25	C₂×C₄×C₇	D₄	1	1	yes	characteristic
26	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
27	C₂×Dic₇	—	2	2	no	—
28	C₂×Dic₇	—	2	2	no	—
29	C₂×Dic₇	C₂×C₄	1	4	yes	—
30	Dic₁₄	—	2	2	no	—
31	Dic₁₄	—	2	2	no	—
32	Dic₁₄	—	2	2	no	—
33	Dic₁₄	—	2	2	no	—
34	C₇×C₈	—	2	2	no	—
35	C₇⋊C₈	—	2	2	no	—
36	C₂²×Q₈	—	7	1	no	—
37	C₂×M₁₆	—	7	1	no	—
38	C₂×M₁₆	D₇	1	1	yes	characteristic
39	#101	—	7	4	no	—
40	C₂²×C₇	—	2	2	no	—
41	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
42	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
44	C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
45	C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
46	C₄×C₇	C₂×D₄	1	1	yes	characteristic
47	C₄×C₇	C₂×D₄	1	1	yes	characteristic
48	Dic₇	—	2	4	no	—
49	C₂×Q₈	—	7	2	no	—
50	C₂×Q₈	—	7	2	no	—
51	C₂×Q₈	—	14	1	no	—
52	C₂×Q₈	—	14	1	no	—
53	C₂×Q₈	—	14	1	no	—
54	C₂×Q₈	—	14	1	no	—
55	C₂²×C₄	—	7	2	no	—
56	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
57	M₁₆	—	2	1	no	—
58	M₁₆	—	7	2	no	—
59	M₁₆	—	14	1	no	—
60	M₁₆	C₂×D₇	1	2	yes	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	14	1	no	—
63	C₂×C₇	—	2	1	no	—
64	C₂×C₇	—	2	1	no	—
65	C₂×C₇	#101	1	2	yes	complemented
66	C₂×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂³	C₄×D₇	1	1	yes	characteristic
68	Q₈	—	14	2	no	—
69	Q₈	—	14	2	no	—
70	Q₈	—	14	2	no	—
71	Q₈	—	14	2	no	—
72	C₂×C₄	—	7	4	no	—
73	C₂×C₄	—	14	2	no	—
74	C₂×C₄	—	14	2	no	—
75	C₂×C₄	C₄×D₇	1	1	yes	characteristic
76	C₂×C₄	D₂₈	1	1	yes	characteristic
77	C₂×C₄	D₂₈	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊D₇	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊D₇	1	1	yes	characteristic
80	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	14	2	no	—
83	C₇	C₂×#101	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	2	2	no	—
85	C₂²	(C₂×D₇)⋊C₄	1	1	yes	characteristic
86	C₂²	(C₂×D₇)⋊C₄	1	1	yes	characteristic
87	C₂²	C₂×C₄×D₇	1	1	yes	characteristic
88	C₄	—	14	4	no	—
89	C₄	(C₂×D₇)⋊C₄	1	1	yes	characteristic
90	C₄	(C₂×D₇)⋊C₄	1	1	yes	characteristic
91	C₄	C₂×D₂₈	1	1	yes	characteristic
92	C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
93	C₂	—	2	1	no	—
94	C₂	—	2	1	no	—
95	C₂	#6398	1	2	yes	direct product factor
96	C₂	C₂×(C₂×D₇)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₇)⋊C₄
commutator	C₂²×C₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₇
Fitting	C₂×C₇×M₁₆	C₂
socle	C₂²×C₇	C₂²⋊C₄
prime radical	C₂³×C₇	C₂×C₄
cosocle	C₂×C₄×C₇	C₂³
hypercenter	C₂×M₁₆	D₇
hypocenter	C₇	C₂×#101
LCS	G ▷ C₂²×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #6398	C₂	direct (N × H)
65. C₂×C₇	#101	semidirect
83. C₇	C₂×#101	semidirect
95. C₂	#6398	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×Dic₁₄	2
C₂×C₇×M₁₆	2
C₂×#1136	2
#6398	2
C₂×#101	7

Subgroups — C2×#6398 #89908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6398 #89908