Subgroups — C₂×Q₈×#1181 #14272228

Order 1856.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic
2	Q₈×#1181	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊#1181	C₂	1	3	yes	maximal
4	C₂×C₄×#1181	C₂	1	3	yes	maximal
5	C₂²×#1181	C₂²	1	3	yes	—
6	C₂²×#1181	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₂₉	C₄	1	1	yes	characteristic, complemented
8	Q₈×D₂₉	C₄	1	4	yes	complemented
9	Q₈×D₂₉	C₂²	1	4	yes	—
10	C₂×C₄×D₂₉	C₂²	1	3	yes	—
11	C₂×Dic₅₈	C₄	1	3	yes	complemented
12	C₄⋊#1181	C₂²	1	12	yes	—
13	C₄×#1181	C₂²	1	12	yes	—
14	C₂²×D₂₉	C₂³	1	1	yes	characteristic
15	C₂×#1181	—	2	6	no	—
16	C₂×#1181	Q₈	1	4	yes	direct product factor
17	C₂×#1181	C₂³	1	6	yes	—
18	C₂×#1181	C₂³	1	2	yes	—
19	Q₈×C₂₉	C₂×C₄	1	4	yes	complemented
20	C₂×C₄×C₂₉	C₂×C₄	1	3	yes	—
21	C₂×Dic₂₉	C₂×C₄	1	3	yes	—
22	C₄×D₂₉	C₂×C₄	1	6	yes	—
23	C₄×D₂₉	C₂³	1	6	yes	—
24	Dic₅₈	C₂×C₄	1	12	yes	complemented
25	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
26	C₂×D₂₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₂₉	C₂×Q₈	1	2	yes	—
28	C₂×D₂₉	#41	1	2	yes	—
29	C₂×D₂₉	C₂⁴	1	1	yes	characteristic
30	#1181	—	2	6	no	—
31	#1181	C₂×Q₈	1	4	yes	direct product factor
32	C₄×C₂₉	C₂²×C₄	1	6	yes	—
33	Dic₂₉	C₂²×C₄	1	6	yes	—
34	C₂×C₄×Q₈	—	29	1	no	maximal, Sylow
35	C₂×C₂₉	C₄×Q₈	1	2	yes	complemented
36	C₂×C₂₉	C₂³×C₄	1	1	yes	characteristic
37	D₂₉	C₄×Q₈	1	2	yes	complemented
38	D₂₉	C₂²×Q₈	1	1	yes	characteristic
39	D₂₉	C₂×#41	1	1	yes	characteristic
40	C₂²×Q₈	—	29	1	no	—
41	C₄×Q₈	—	29	8	no	—
42	C₂×C₄⋊C₄	—	29	3	no	—
43	C₂×C₄²	—	29	3	no	—
44	C₂₉	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	29	4	no	—
46	C₂×Q₈	—	29	4	no	—
47	C₂×Q₈	—	29	3	no	—
48	C₂×Q₈	#1181	1	1	yes	characteristic, direct product factor
49	C₂²×C₄	—	29	1	no	—
50	C₂²×C₄	—	29	3	no	—
51	C₂²×C₄	—	29	3	no	—
52	C₄⋊C₄	—	29	12	no	—
53	C₄²	—	29	12	no	—
54	C₂³	—	29	1	no	—
55	Q₈	—	29	12	no	—
56	Q₈	C₂×#1181	1	4	yes	direct product factor
57	C₂×C₄	—	29	2	no	—
58	C₂×C₄	—	29	4	no	—
59	C₂×C₄	—	29	3	no	—
60	C₂×C₄	—	29	6	no	—
61	C₂×C₄	—	29	6	no	—
62	C₂×C₄	—	29	6	no	—
63	C₂×C₄	—	58	6	no	—
64	C₂×C₄	C₂×#1181	1	3	yes	—
65	C₂²	—	29	2	no	—
66	C₂²	—	29	2	no	—
67	C₂²	—	29	1	no	—
68	C₂²	—	29	1	no	—
69	C₂²	C₂²×#1181	1	1	yes	characteristic
70	C₄	—	29	4	no	—
71	C₄	—	29	6	no	—
72	C₄	—	58	6	no	—
73	C₄	C₂²×#1181	1	6	yes	—
74	C₂	—	29	1	no	—
75	C₂	—	29	1	no	—
76	C₂	—	29	2	no	—
77	C₂	Q₈×#1181	1	2	yes	direct product factor
78	C₂	C₂³×#1181	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#1181
commutator	C₂×C₂₉	C₂³×C₄
Frattini	C₂	C₂³×#1181
Fitting	C₂×Q₈×C₂₉	C₄
socle	C₂²×C₂₉	C₂²×C₄
prime radical	C₂²×D₂₉	C₂³
cosocle	C₂×D₂₉	C₂⁴
hypercenter	C₂×Q₈	#1181
hypocenter	C₂₉	C₂×C₄×Q₈
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×#1181	C₂	direct (N × H)
7. C₂×Q₈×C₂₉	C₄	semidirect
8. Q₈×D₂₉	C₄	semidirect
11. C₂×Dic₅₈	C₄	semidirect
16. C₂×#1181	Q₈	direct (N × H)
19. Q₈×C₂₉	C₂×C₄	semidirect
24. Dic₅₈	C₂×C₄	semidirect
31. #1181	C₂×Q₈	direct (N × H)
35. C₂×C₂₉	C₄×Q₈	semidirect
37. D₂₉	C₄×Q₈	semidirect
44. C₂₉	C₂×C₄×Q₈	semidirect
48. C₂×Q₈	#1181	direct (N × H)
56. Q₈	C₂×#1181	direct (N × H)
77. C₂	Q₈×#1181	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₂₉	2
Q₈×#1181	2
C₂×C₄⋊#1181	2
C₂×C₄×#1181	2
C₂×C₄×Q₈	29

Subgroups — C2×Q8×#1181 #14272228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×#1181 #14272228