Subgroups — D₈×#10587739 #22578439

Order 8768.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#10587739	C₂	1	2	yes	maximal, complemented
2	#17984157	C₂	1	1	yes	maximal, characteristic, complemented
3	#17984150	C₂	1	2	yes	maximal, complemented
4	C₈×#10587739	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×D₁₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10587739	—	2	2	no	—
7	#14555518	C₂²	1	1	yes	characteristic
8	C₄⋊#10587739	C₂²	1	2	yes	—
9	C₂²⋊#10587739	—	2	2	no	—
10	C₄×#10587739	C₂²	1	1	yes	characteristic
11	D₄×D₁₃₇	C₂²	1	2	yes	—
12	D₁₀₉₆	C₄	1	1	yes	characteristic, complemented
13	#14555495	C₄	1	2	yes	complemented
14	C₈×D₁₃₇	C₂²	1	1	yes	characteristic
15	D₈×C₁₃₇	C₄	1	1	yes	characteristic, complemented
16	C₂×#10587739	—	2	2	no	—
17	C₂×#10587739	—	4	4	no	—
18	C₂×#10587739	D₄	1	1	yes	characteristic
19	C₂×#10587739	D₄	1	1	yes	characteristic
20	#11764047	—	2	1	no	—
21	C₂²×D₁₃₇	—	2	2	no	—
22	D₅₄₈	C₂×C₄	1	2	yes	complemented
23	C₂²⋊D₁₃₇	—	2	2	no	—
24	C₄×D₁₃₇	C₂³	1	1	yes	characteristic
25	#11764040	C₂×C₄	1	1	yes	characteristic, complemented
26	D₄×C₁₃₇	C₂×C₄	1	2	yes	complemented
27	C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic, complemented
28	C₂²×C₁₃₇	—	2	2	no	—
29	C₂×D₁₃₇	—	2	2	no	—
30	C₂×D₁₃₇	—	4	2	no	—
31	C₂×D₁₃₇	—	4	2	no	—
32	C₂×D₁₃₇	C₂×D₄	1	1	yes	characteristic
33	#10587739	—	2	1	no	—
34	#10587739	—	4	2	no	—
35	#10587739	D₈	1	2	yes	direct product factor
36	C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
37	Dic₁₃₇	#41	1	1	yes	characteristic
38	C₂×C₁₃₇	—	4	2	no	—
39	C₂×C₁₃₇	C₄×D₄	1	1	yes	characteristic
40	D₁₃₇	—	4	2	no	—
41	D₁₃₇	C₂×D₈	1	1	yes	characteristic
42	D₁₃₇	#135	1	1	yes	characteristic
43	C₁₃₇	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
44	C₄×D₈	—	137	1	no	maximal, Sylow
45	C₂×D₈	—	137	1	no	—
46	C₄×D₄	—	137	2	no	—
47	#107	—	137	1	no	—
48	#102	—	137	2	no	—
49	C₄×C₈	—	137	1	no	—
50	C₂×D₄	—	137	2	no	—
51	C₂²×C₄	—	274	2	no	—
52	D₈	—	137	2	no	—
53	D₈	—	137	1	no	—
54	D₈	#10587739	1	1	yes	characteristic, direct product factor
55	C₂×C₈	—	137	1	no	—
56	C₂×C₈	—	137	1	no	—
57	C₄⋊C₄	—	137	2	no	—
58	C₂²⋊C₄	—	274	2	no	—
59	C₄²	—	137	1	no	—
60	C₂³	—	274	2	no	—
61	D₄	—	274	2	no	—
62	D₄	—	137	2	no	—
63	D₄	C₂×#10587739	1	2	yes	complemented
64	C₂×C₄	—	274	2	no	—
65	C₂×C₄	—	548	4	no	—
66	C₂×C₄	—	137	1	no	—
67	C₂×C₄	—	137	1	no	—
68	C₂×C₄	—	137	1	no	—
69	C₈	—	274	1	no	—
70	C₈	—	137	1	no	—
71	C₈	C₂×#10587739	1	1	yes	characteristic, complemented
72	C₂²	—	2	2	no	—
73	C₂²	—	274	2	no	—
74	C₂²	—	548	2	no	—
75	C₂²	—	548	2	no	—
76	C₂²	—	137	1	no	—
77	C₄	—	274	1	no	—
78	C₄	—	548	2	no	—
79	C₄	—	137	2	no	—
80	C₄	—	137	1	no	—
81	C₄	C₂²×#10587739	1	1	yes	characteristic
82	C₂	—	4	2	no	—
83	C₂	—	548	2	no	—
84	C₂	—	137	1	no	—
85	C₂	—	137	1	no	—
86	C₂	D₄×#10587739	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#10587739
commutator	C₄×C₁₃₇	C₂²×C₄
Frattini	C₄	C₂²×#10587739
Fitting	D₈×C₁₃₇	C₄
socle	C₂×C₁₃₇	C₄×D₄
hypercenter	D₈	#10587739
hypocenter	C₁₃₇	C₄×D₈
LCS	G ▷ C₄×C₁₃₇ ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#10587739	C₂	semidirect
2. #17984157	C₂	semidirect
3. #17984150	C₂	semidirect
4. C₈×#10587739	C₂	semidirect
12. D₁₀₉₆	C₄	semidirect
13. #14555495	C₄	semidirect
15. D₈×C₁₃₇	C₄	semidirect
22. D₅₄₈	C₂×C₄	semidirect
25. #11764040	C₂×C₄	semidirect
26. D₄×C₁₃₇	C₂×C₄	semidirect
27. C₈×C₁₃₇	C₂×C₄	semidirect
35. #10587739	D₈	direct (N × H)
43. C₁₃₇	C₄×D₈	semidirect
54. D₈	#10587739	direct (N × H)
63. D₄	C₂×#10587739	semidirect
71. C₈	C₂×#10587739	semidirect

Subgroups — D8×#10587739 #22578439

Conjugacy classes of subgroups

Complements

Subgroups — D₈×#10587739 #22578439