Subgroups — C₂×C₂²⋊#11764047 #22578370

Order 8768.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11764047	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#11764047	C₂	1	4	yes	maximal, direct product factor
3	C₂³×Dic₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#11764047	—	2	4	no	—
5	C₂×#11764047	C₂²	1	4	yes	complemented
6	C₂²×Dic₁₃₇	—	2	4	no	—
7	C₂²×Dic₁₃₇	C₄	1	2	yes	—
8	C₂²×Dic₁₃₇	C₄	1	1	yes	characteristic
9	C₂²×Dic₁₃₇	C₂²	1	2	yes	—
10	C₂²×Dic₁₃₇	C₂²	1	1	yes	characteristic
11	C₂⁴×C₁₃₇	C₄	1	1	yes	characteristic
12	#11764047	—	2	4	no	—
13	C₂×Dic₁₃₇	—	2	2	no	—
14	C₂×Dic₁₃₇	—	2	4	no	—
15	C₂×Dic₁₃₇	—	2	4	no	—
16	C₂×Dic₁₃₇	C₂×C₄	1	2	yes	—
17	C₂×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₃₇	D₄	1	4	yes	—
19	C₂×Dic₁₃₇	C₂³	1	1	yes	characteristic
20	C₂³×C₁₃₇	—	2	2	no	—
21	C₂³×C₁₃₇	—	2	2	no	—
22	C₂³×C₁₃₇	C₈	1	4	yes	complemented
23	C₂³×C₁₃₇	C₂×C₄	1	2	yes	—
24	C₂³×C₁₃₇	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₁₃₇	—	2	8	no	—
26	C₂²×C₁₃₇	—	2	2	no	—
27	C₂²×C₁₃₇	—	2	2	no	—
28	C₂²×C₁₃₇	C₂²⋊C₄	1	2	yes	—
29	C₂²×C₁₃₇	C₂×C₈	1	2	yes	—
30	C₂²×C₁₃₇	C₂×C₈	1	4	yes	complemented
31	C₂²×C₁₃₇	M₁₆	1	2	yes	—
32	C₂²×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
33	Dic₁₃₇	—	2	2	no	—
34	Dic₁₃₇	C₂²⋊C₄	1	2	yes	—
35	Dic₁₃₇	C₂×D₄	1	2	yes	—
36	C₂×C₁₃₇	—	2	4	no	—
37	C₂×C₁₃₇	C₂²⋊C₈	1	4	yes	complemented
38	C₂×C₁₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₁₃₇	C₂²×C₈	1	1	yes	characteristic
40	C₂×C₁₃₇	C₂×M₁₆	1	1	yes	characteristic
41	C₁₃₇	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₂²⋊C₈	—	137	1	no	maximal, Sylow
43	C₂³×C₄	—	137	1	no	—
44	C₂²×C₈	—	137	2	no	—
45	C₂²⋊C₈	—	137	4	no	—
46	C₂⁴	#10587739	1	1	yes	characteristic
47	C₂²×C₄	—	274	4	no	—
48	C₂²×C₄	—	137	2	no	—
49	C₂²×C₄	—	137	2	no	—
50	C₂²×C₄	—	137	1	no	—
51	C₂²×C₄	—	137	1	no	—
52	C₂×C₈	—	274	4	no	—
53	C₂×C₈	—	137	4	no	—
54	C₂³	—	2	2	no	—
55	C₂³	—	2	2	no	—
56	C₂³	#11764047	1	4	yes	complemented
57	C₂³	C₂×#10587739	1	2	yes	—
58	C₂³	C₂×#10587739	1	1	yes	characteristic
59	C₂×C₄	—	274	2	no	—
60	C₂×C₄	—	274	4	no	—
61	C₂×C₄	—	274	4	no	—
62	C₂×C₄	—	137	2	no	—
63	C₂×C₄	—	137	4	no	—
64	C₂×C₄	—	137	1	no	—
65	C₂×C₄	—	137	1	no	—
66	C₈	—	274	4	no	—
67	C₂²	—	2	8	no	—
68	C₂²	—	2	2	no	—
69	C₂²	—	2	2	no	—
70	C₂²	C₂²⋊#10587739	1	2	yes	—
71	C₂²	C₂×#11764047	1	2	yes	—
72	C₂²	C₂×#11764047	1	4	yes	complemented
73	C₂²	#14555519	1	2	yes	—
74	C₂²	C₂²×#10587739	1	1	yes	characteristic
75	C₄	—	274	2	no	—
76	C₄	—	137	2	no	—
77	C₄	—	137	2	no	—
78	C₂	—	2	4	no	—
79	C₂	C₂²⋊#11764047	1	4	yes	direct product factor
80	C₂	C₂×C₂²⋊#10587739	1	1	yes	characteristic
81	C₂	C₂²×#11764047	1	1	yes	characteristic
82	C₂	C₂×#14555519	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#10587739
commutator	C₂×C₁₃₇	C₂²×C₈
Frattini	C₂²	C₂²×#10587739
Fitting	C₂⁴×C₁₃₇	C₄
socle	C₂³×C₁₃₇	C₂×C₄
hypercenter	C₂⁴	#10587739
hypocenter	C₁₃₇	C₂×C₂²⋊C₈
LCS	G ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂²×#11764047	C₂	semidirect
2. C₂²⋊#11764047	C₂	direct (N × H)
5. C₂×#11764047	C₂²	semidirect
22. C₂³×C₁₃₇	C₈	semidirect
30. C₂²×C₁₃₇	C₂×C₈	semidirect
37. C₂×C₁₃₇	C₂²⋊C₈	semidirect
41. C₁₃₇	C₂×C₂²⋊C₈	semidirect
56. C₂³	#11764047	semidirect
72. C₂²	C₂×#11764047	semidirect
79. C₂	C₂²⋊#11764047	direct (N × H)

Subgroups — C2×C22⋊#11764047 #22578370

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₂²⋊#11764047 #22578370