Subgroups — D₄×#11744762 #20299712

Order 7232.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11744762	C₂	1	2	yes	maximal, complemented
2	C₄⋊#11744762	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#11744762	C₂	1	2	yes	maximal, complemented
4	C₄×#11744762	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×#90673	C₂	1	1	yes	maximal, characteristic
6	C₂×#11744762	—	2	4	no	—
7	C₂×#11744762	C₂²	1	1	yes	characteristic
8	C₂×#11744762	C₂²	1	2	yes	—
9	C₂×#11744762	C₂²	1	1	yes	characteristic
10	C₂²×#90673	C₂²	1	2	yes	—
11	C₄⋊#90673	C₄	1	1	yes	characteristic
12	C₂²⋊#90673	C₄	1	2	yes	—
13	C₄×#90673	C₂²	1	1	yes	characteristic
14	D₄×D₁₁₃	C₄	1	1	yes	characteristic
15	C₂²×D₁₁₃	C₂×C₄	1	2	yes	—
16	C₂×#90673	—	2	2	no	—
17	C₂×#90673	—	2	2	no	—
18	C₂×#90673	C₂×C₄	1	1	yes	characteristic
19	C₂×#90673	C₂×C₄	1	2	yes	—
20	C₂×#90673	C₂³	1	1	yes	characteristic
21	#11744762	—	2	2	no	—
22	#11744762	—	2	1	no	—
23	#11744762	D₄	1	2	yes	direct product factor
24	D₄×C₁₁₃	C₈	1	1	yes	characteristic, complemented
25	C₂²⋊D₁₁₃	C₈	1	2	yes	complemented
26	D₄₅₂	C₈	1	1	yes	characteristic, complemented
27	C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₁₁₃	C₂×C₈	1	2	yes	complemented
29	C₂×D₁₁₃	—	2	2	no	—
30	C₂×D₁₁₃	—	2	2	no	—
31	C₂×D₁₁₃	C₂×C₈	1	2	yes	complemented
32	C₂×D₁₁₃	C₂²×C₄	1	1	yes	characteristic
33	#90673	—	2	2	no	—
34	#90673	—	2	1	no	—
35	#90673	C₂×D₄	1	1	yes	characteristic
36	#90673	#41	1	1	yes	characteristic
37	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic, complemented
38	Dic₁₁₃	C₂×C₈	1	1	yes	characteristic, complemented
39	C₂×C₁₁₃	—	2	2	no	—
40	C₂×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
41	D₁₁₃	—	2	2	no	—
42	D₁₁₃	C₄×D₄	1	1	yes	characteristic
43	D₁₁₃	#131	1	1	yes	characteristic
44	C₁₁₃	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
45	C₈×D₄	—	113	1	no	maximal, Sylow
46	C₂²×C₈	—	113	2	no	—
47	C₄×D₄	—	113	1	no	—
48	C₄⋊C₈	—	113	1	no	—
49	C₂²⋊C₈	—	113	2	no	—
50	C₄×C₈	—	113	1	no	—
51	C₂×D₄	—	113	1	no	—
52	C₂²×C₄	—	113	2	no	—
53	C₂×C₈	—	113	1	no	—
54	C₂×C₈	—	113	1	no	—
55	C₂×C₈	—	113	2	no	—
56	C₂×C₈	—	226	4	no	—
57	C₄⋊C₄	—	113	1	no	—
58	C₂²⋊C₄	—	113	2	no	—
59	C₄²	—	113	1	no	—
60	C₂³	—	113	2	no	—
61	D₄	—	113	2	no	—
62	D₄	—	113	1	no	—
63	D₄	#11744762	1	1	yes	characteristic, direct product factor
64	C₂×C₄	—	113	1	no	—
65	C₂×C₄	—	113	1	no	—
66	C₂×C₄	—	113	1	no	—
67	C₂×C₄	—	113	2	no	—
68	C₂×C₄	—	226	2	no	—
69	C₂×C₄	—	226	2	no	—
70	C₈	—	113	2	no	—
71	C₈	—	226	2	no	—
72	C₈	—	226	1	no	—
73	C₂²	—	113	1	no	—
74	C₂²	—	113	2	no	—
75	C₂²	—	226	2	no	—
76	C₂²	—	226	2	no	—
77	C₂²	C₂×#11744762	1	2	yes	complemented
78	C₄	—	113	1	no	—
79	C₄	—	113	1	no	—
80	C₄	—	113	1	no	—
81	C₄	—	226	2	no	—
82	C₄	—	226	1	no	—
83	C₄	C₂×#11744762	1	1	yes	characteristic, complemented
84	C₂	—	2	2	no	—
85	C₂	—	113	1	no	—
86	C₂	—	113	1	no	—
87	C₂	—	226	2	no	—
88	C₂	C₂²×#11744762	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#11744762
commutator, socle	C₂×C₁₁₃	C₂²×C₈
Fitting	D₄×C₁₁₃	C₈
hypercenter	D₄	#11744762
hypocenter	C₁₁₃	C₈×D₄
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#11744762	C₂	semidirect
2. C₄⋊#11744762	C₂	semidirect
3. C₂²⋊#11744762	C₂	semidirect
4. C₄×#11744762	C₂	semidirect
23. #11744762	D₄	direct (N × H)
24. D₄×C₁₁₃	C₈	semidirect
25. C₂²⋊D₁₁₃	C₈	semidirect
26. D₄₅₂	C₈	semidirect
28. C₂²×C₁₁₃	C₂×C₈	semidirect
31. C₂×D₁₁₃	C₂×C₈	semidirect
37. C₄×C₁₁₃	C₂×C₈	semidirect
38. Dic₁₁₃	C₂×C₈	semidirect
44. C₁₁₃	C₈×D₄	semidirect
63. D₄	#11744762	direct (N × H)
77. C₂²	C₂×#11744762	semidirect
83. C₄	C₂×#11744762	semidirect

Subgroups — D4×#11744762 #20299712

Conjugacy classes of subgroups

Complements

Subgroups — D₄×#11744762 #20299712