Subgroups — C₂×C₄⋊#11764049 #22578515

Order 8768.

138 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	C₄⋊#11764049	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×#10587739	C₂	1	1	yes	maximal, characteristic
4	C₂×#11764049	—	2	4	no	—
5	C₂×#11764049	C₂²	1	4	yes	—
6	C₂²×#10587739	C₄	1	1	yes	characteristic
7	C₂²×#10587739	C₂²	1	1	yes	characteristic
8	C₄×#10587739	C₄	1	2	yes	—
9	C₄×#10587739	C₂²	1	2	yes	—
10	C₂×C₄×D₁₃₇	C₄	1	1	yes	characteristic
11	#11764049	—	2	4	no	—
12	C₂×#10587739	—	2	2	no	—
13	C₂×#10587739	C₂×C₄	1	2	yes	—
14	C₂×#10587739	C₂×C₄	1	1	yes	characteristic
15	C₂×#10587739	D₄	1	2	yes	—
16	C₂×#10587739	Q₈	1	2	yes	—
17	C₂×#10587739	C₂³	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	C₈	1	2	yes	complemented
21	C₄×D₁₃₇	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₁₃₇	C₈	1	1	yes	characteristic, complemented
23	C₂²×C₁₃₇	C₂×C₈	1	1	yes	characteristic
24	C₂×D₁₃₇	C₄⋊C₄	1	2	yes	—
25	C₂×D₁₃₇	C₂×C₈	1	1	yes	characteristic
26	C₂×D₁₃₇	M₁₆	1	2	yes	—
27	C₂×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
28	#10587739	—	2	2	no	—
29	#10587739	C₄⋊C₄	1	2	yes	—
30	#10587739	C₂×D₄	1	1	yes	characteristic
31	#10587739	C₂×Q₈	1	1	yes	characteristic
32	C₄×C₁₃₇	C₂×C₈	1	2	yes	complemented
33	Dic₁₃₇	C₂×C₈	1	2	yes	complemented
34	C₂×C₁₃₇	C₄⋊C₈	1	2	yes	complemented
35	C₂×C₁₃₇	C₂²×C₈	1	1	yes	characteristic
36	D₁₃₇	C₄⋊C₈	1	2	yes	complemented
37	D₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
38	D₁₃₇	C₂×M₁₆	1	1	yes	characteristic
39	C₁₃₇	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₄⋊C₈	—	137	1	no	maximal, Sylow
41	C₂²×C₈	—	137	2	no	—
42	C₂×C₄²	—	137	1	no	—
43	C₄⋊C₈	—	137	4	no	—
44	C₂²×C₄	—	137	1	no	—
45	C₂²×C₄	—	137	1	no	—
46	C₂²×C₄	—	137	1	no	—
47	C₂×C₈	—	274	4	no	—
48	C₂×C₈	—	137	4	no	—
49	C₄²	—	137	2	no	—
50	C₄²	—	137	2	no	—
51	C₂³	—	137	1	no	—
52	C₂×C₄	—	274	2	no	—
53	C₂×C₄	—	137	2	no	—
54	C₂×C₄	—	137	1	no	—
55	C₂×C₄	—	137	1	no	—
56	C₂×C₄	—	137	2	no	—
57	C₂×C₄	—	137	2	no	—
58	C₂×C₄	—	137	1	no	—
59	C₂×C₄	—	137	2	no	—
60	C₂×C₄	—	137	2	no	—
61	C₂×C₄	#11764049	1	1	yes	characteristic, complemented
62	C₈	—	274	4	no	—
63	C₂²	—	137	2	no	—
64	C₂²	—	137	2	no	—
65	C₂²	—	137	1	no	—
66	C₂²	—	137	1	no	—
67	C₂²	C₂×#11764049	1	1	yes	characteristic
68	C₄	—	274	2	no	—
69	C₄	—	137	1	no	—
70	C₄	—	137	2	no	—
71	C₄	—	137	1	no	—
72	C₄	—	137	2	no	—
73	C₄	C₂×#11764049	1	2	yes	complemented
74	C₂	—	137	1	no	—
75	C₂	—	137	1	no	—
76	C₂	—	137	2	no	—
77	C₂	C₄⋊#11764049	1	2	yes	direct product factor
78	C₂	C₂²×#11764049	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#11764049
commutator	C₂×C₁₃₇	C₂²×C₈
Frattini	C₂	C₂²×#11764049
Fitting	C₂×C₄×C₁₃₇	C₈
socle	C₂²×C₁₃₇	C₂×C₈
hypercenter	C₂×C₄	#11764049
hypocenter	C₁₃₇	C₂×C₄⋊C₈
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
2. C₄⋊#11764049	C₂	direct (N × H)
19. C₂×Dic₁₃₇	C₈	semidirect
20. C₄×D₁₃₇	C₈	semidirect
22. C₂×C₄×C₁₃₇	C₈	semidirect
32. C₄×C₁₃₇	C₂×C₈	semidirect
33. Dic₁₃₇	C₂×C₈	semidirect
34. C₂×C₁₃₇	C₄⋊C₈	semidirect
36. D₁₃₇	C₄⋊C₈	semidirect
39. C₁₃₇	C₂×C₄⋊C₈	semidirect
61. C₂×C₄	#11764049	semidirect
73. C₄	C₂×#11764049	semidirect
77. C₂	C₄⋊#11764049	direct (N × H)

Subgroups — C2×C4⋊#11764049 #22578515

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄⋊#11764049 #22578515