Subgroups — Q₈×D₁₄₈ #14558200

Order 2368.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₃₇	C₂	1	2	yes	maximal, complemented
2	#11924536	C₂	1	3	yes	maximal, complemented
3	#11924516	C₂	1	6	yes	maximal, complemented
4	C₄×D₁₄₈	C₂	1	3	yes	maximal
5	C₄×Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
7	Q₈×D₃₇	—	2	8	no	—
8	C₂×D₁₄₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₃₇	C₂²	1	6	yes	—
10	C₂×Dic₇₄	C₂²	1	6	yes	—
11	C₄⋊C₄×C₃₇	C₂²	1	3	yes	—
12	C₄²×C₃₇	C₂²	1	3	yes	—
13	#10596938	C₂²	1	6	yes	—
14	C₄⋊Dic₃₇	C₂²	1	3	yes	—
15	C₄⋊Dic₃₇	C₂²	1	6	yes	—
16	C₂²×D₃₇	C₂³	1	2	yes	—
17	Q₈×C₃₇	D₄	1	4	yes	complemented
18	C₂×C₄×C₃₇	C₂³	1	3	yes	—
19	C₂×C₄×C₃₇	C₂³	1	3	yes	—
20	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
21	C₂×Dic₃₇	C₂³	1	6	yes	—
22	D₁₄₈	Q₈	1	4	yes	direct product factor
23	C₄×D₃₇	—	2	12	no	—
24	Dic₇₄	—	2	12	no	—
25	C₂²×C₃₇	C₂⁴	1	1	yes	characteristic
26	C₂×D₃₇	—	2	2	no	—
27	C₂×D₃₇	—	2	2	no	—
28	C₂×D₃₇	C₂×Q₈	1	4	yes	complemented
29	C₄×C₃₇	—	2	3	no	—
30	C₄×C₃₇	C₂×D₄	1	6	yes	—
31	C₄×C₃₇	C₂×Q₈	1	2	yes	complemented
32	Dic₃₇	—	2	6	no	—
33	C₂×C₃₇	C₂²×D₄	1	1	yes	characteristic
34	C₂×C₃₇	C₂²×Q₈	1	1	yes	characteristic
35	C₂×C₃₇	2₋¹⁺⁴	1	1	yes	characteristic
36	D₃₇	—	2	4	no	—
37	D₄×Q₈	—	37	1	no	maximal, Sylow
38	C₃₇	D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
39	C₂²×Q₈	—	37	2	no	—
40	C₄⋊Q₈	—	37	3	no	—
41	C₂²⋊Q₈	—	37	6	no	—
42	C₄×Q₈	D₃₇	1	1	yes	characteristic, complemented
43	C₄×D₄	—	37	3	no	—
44	C₂×Q₈	—	37	6	no	—
45	C₂×Q₈	—	74	8	no	—
46	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
47	C₂×D₄	—	37	1	no	—
48	C₂²×C₄	—	37	6	no	—
49	C₄⋊C₄	—	37	3	no	—
50	C₄⋊C₄	—	37	6	no	—
51	C₄⋊C₄	C₂×D₃₇	1	3	yes	—
52	C₂²⋊C₄	—	37	6	no	—
53	C₄²	C₂×D₃₇	1	3	yes	—
54	C₂³	—	37	2	no	—
55	Q₈	—	74	12	no	—
56	Q₈	D₁₄₈	1	4	yes	direct product factor
57	D₄	—	37	4	no	—
58	C₂×C₄	—	37	6	no	—
59	C₂×C₄	—	74	12	no	—
60	C₂×C₄	C₂²×D₃₇	1	3	yes	—
61	C₂×C₄	C₂²×D₃₇	1	3	yes	—
62	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
63	C₂²	—	37	4	no	—
64	C₂²	—	74	2	no	—
65	C₂²	—	74	2	no	—
66	C₂²	C₂³×D₃₇	1	1	yes	characteristic
67	C₄	—	2	3	no	—
68	C₄	—	74	6	no	—
69	C₄	C₂×D₁₄₈	1	6	yes	—
70	C₄	Q₈×D₃₇	1	2	yes	complemented
71	C₂	—	74	4	no	—
72	C₂	C₂²×D₁₄₈	1	1	yes	characteristic
73	C₂	C₂×Q₈×D₃₇	1	1	yes	characteristic
74	C₂	#11924583	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃₇
commutator, socle, cosocle	C₂²×C₃₇	C₂⁴
Fitting	C₄×Q₈×C₃₇	C₂
prime radical	C₂×D₁₄₈	C₂²
hypercenter	C₄×Q₈	D₃₇
hypocenter	C₃₇	D₄×Q₈
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×D₃₇	C₂	semidirect
2. #11924536	C₂	semidirect
3. #11924516	C₂	semidirect
5. C₄×Q₈×C₃₇	C₂	semidirect
17. Q₈×C₃₇	D₄	semidirect
22. D₁₄₈	Q₈	direct (N × H)
28. C₂×D₃₇	C₂×Q₈	semidirect
31. C₄×C₃₇	C₂×Q₈	semidirect
38. C₃₇	D₄×Q₈	semidirect
42. C₄×Q₈	D₃₇	semidirect
56. Q₈	D₁₄₈	direct (N × H)
70. C₄	Q₈×D₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×Q₈×D₃₇	2
#11924536	2
#11924516	2
C₄×D₁₄₈	2
C₄×Q₈×C₃₇	2
D₄×Q₈	37

Subgroups — Q8×D148 #14558200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×D₁₄₈ #14558200