Subgroups — (C₂×#11764049)⋊C₄ #22578494

Order 8768.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11764049	C₂	1	2	yes	maximal
2	C₂×C₄×#10587739	C₂	1	1	yes	maximal, characteristic
3	C₂×#11764049	—	2	2	no	—
4	C₂×#11764049	—	2	2	no	—
5	C₂×#11764049	C₄	1	4	yes	complemented
6	C₂²×#10587739	C₄	1	1	yes	characteristic
7	C₂²×#10587739	C₂²	1	1	yes	characteristic
8	C₄×#10587739	—	2	2	no	—
9	C₂×C₄×D₁₃₇	C₄	1	1	yes	characteristic
10	#11764049	—	2	4	no	—
11	C₂×#10587739	—	2	1	no	—
12	C₂×#10587739	—	2	1	no	—
13	C₂×#10587739	C₈	1	2	yes	complemented
14	C₂×#10587739	C₂×C₄	1	2	yes	—
15	C₂×#10587739	D₄	1	1	yes	characteristic
16	C₂×#10587739	D₄	1	2	yes	—
17	C₂×#10587739	Q₈	1	1	yes	characteristic
18	C₂²×D₁₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₁₃₇	C₈	1	1	yes	characteristic, complemented
20	C₄×D₁₃₇	—	2	1	no	—
21	C₄×D₁₃₇	—	2	1	no	—
22	C₂×C₄×C₁₃₇	C₈	1	1	yes	characteristic, complemented
23	C₂²×C₁₃₇	C₂×C₈	1	1	yes	characteristic
24	C₂×D₁₃₇	C₄²	1	1	yes	characteristic
25	C₂×D₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×D₁₃₇	C₄⋊C₄	1	1	yes	characteristic
27	C₂×D₁₃₇	C₂×C₈	1	1	yes	characteristic
28	C₂×D₁₃₇	M₁₆	1	1	yes	characteristic
29	C₂×D₁₃₇	M₁₆	1	1	yes	characteristic
30	#10587739	—	2	2	no	—
31	#10587739	C₂²⋊C₄	1	2	yes	—
32	#10587739	C₄⋊C₄	1	2	yes	—
33	C₄×C₁₃₇	—	2	1	no	—
34	Dic₁₃₇	—	2	1	no	—
35	C₂×C₁₃₇	C₄×C₈	1	1	yes	characteristic
36	C₂×C₁₃₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×C₁₃₇	C₄⋊C₈	1	1	yes	characteristic
38	D₁₃₇	#95	1	1	yes	characteristic
39	D₁₃₇	#97	1	1	yes	characteristic
40	D₁₃₇	C₂²⋊C₈	1	1	yes	characteristic
41	D₁₃₇	C₄⋊C₈	1	1	yes	characteristic
42	C₁₃₇	#336	1	1	yes	characteristic, complemented, Sylow
43	#336	—	137	1	no	maximal, Sylow
44	C₂²×C₈	—	137	2	no	—
45	C₂×C₄²	—	137	1	no	—
46	C₂²×C₄	—	137	1	no	—
47	C₂²×C₄	—	137	1	no	—
48	C₂²×C₄	—	137	1	no	—
49	C₂×C₈	—	274	2	no	—
50	C₂×C₈	—	274	2	no	—
51	C₂×C₈	—	137	4	no	—
52	C₄²	—	274	2	no	—
53	C₂³	—	137	1	no	—
54	C₂×C₄	—	274	1	no	—
55	C₂×C₄	—	274	1	no	—
56	C₂×C₄	—	274	1	no	—
57	C₂×C₄	—	274	1	no	—
58	C₂×C₄	—	137	2	no	—
59	C₂×C₄	—	137	1	no	—
60	C₂×C₄	—	137	2	no	—
61	C₂×C₄	—	137	1	no	—
62	C₂×C₄	—	137	2	no	—
63	C₂×C₄	—	137	1	no	—
64	C₂×C₄	#11764049	1	1	yes	characteristic, complemented
65	C₈	—	274	4	no	—
66	C₂²	—	137	1	no	—
67	C₂²	—	137	1	no	—
68	C₂²	—	137	1	no	—
69	C₂²	—	137	1	no	—
70	C₂²	—	137	1	no	—
71	C₂²	—	137	1	no	—
72	C₂²	C₂×#11764049	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	—	274	2	no	—
75	C₄	—	274	1	no	—
76	C₄	—	137	2	no	—
77	C₄	—	137	2	no	—
78	C₂	—	137	1	no	—
79	C₂	—	137	1	no	—
80	C₂	—	137	1	no	—
81	C₂	—	137	1	no	—
82	C₂	C₄×#11764049	1	1	yes	characteristic
83	C₂	C₂²⋊#11764049	1	1	yes	characteristic
84	C₂	C₄⋊#11764049	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#11764049
commutator	C₂×C₁₃₇	C₄×C₈
Fitting	C₂×C₄×C₁₃₇	C₈
socle	C₂²×C₁₃₇	C₂×C₈
hypercenter	C₂×C₄	#11764049
hypocenter	C₁₃₇	#336
LCS	G ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
5. C₂×#11764049	C₄	semidirect
13. C₂×#10587739	C₈	semidirect
19. C₂×Dic₁₃₇	C₈	semidirect
22. C₂×C₄×C₁₃₇	C₈	semidirect
42. C₁₃₇	#336	semidirect
64. C₂×C₄	#11764049	semidirect

Subgroups — (C2×#11764049)⋊C4 #22578494

Conjugacy classes of subgroups

Complements

Subgroups — (C₂×#11764049)⋊C₄ #22578494