Subgroups — #14271879

Order 1856.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745309	C₂	1	4	yes	maximal, complemented
3	#11745257	C₂	1	4	yes	maximal, complemented
4	#11745254	C₂	1	4	yes	maximal, complemented
5	C₄×D₁₁₆	C₂	1	2	yes	maximal, complemented
6	C₂×Q₈×C₂₉	C₂²	1	2	yes	—
7	C₂×D₁₁₆	C₂²	1	2	yes	—
8	C₂×D₁₁₆	C₂²	1	4	yes	—
9	C₂×C₄×D₂₉	C₂²	1	4	yes	—
10	C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
11	C₄²×C₂₉	C₂²	1	1	yes	characteristic
12	#90781	C₂²	1	4	yes	—
13	#90781	C₂²	1	8	yes	—
14	C₄⋊Dic₂₉	C₂²	1	2	yes	—
15	C₄×Dic₂₉	C₂²	1	4	yes	—
16	C₂²×D₂₉	C₂³	1	4	yes	—
17	Q₈×C₂₉	—	4	2	no	—
18	C₂×C₄×C₂₉	C₂³	1	4	yes	—
19	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₂₉	C₂³	1	2	yes	—
21	C₂×Dic₂₉	C₂³	1	4	yes	—
22	D₁₁₆	—	2	4	no	—
23	D₁₁₆	—	4	4	no	—
24	C₄×D₂₉	—	2	8	no	—
25	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
26	C₂×D₂₉	—	2	4	no	—
27	C₂×D₂₉	—	2	4	no	—
28	C₂×D₂₉	—	2	4	no	—
29	C₄×C₂₉	—	2	4	no	—
30	C₄×C₂₉	—	2	1	no	—
31	C₄×C₂₉	#41	1	4	yes	—
32	Dic₂₉	—	2	4	no	—
33	#555	—	29	1	no	maximal, Sylow
34	C₂×C₂₉	C₂×#41	1	2	yes	—
35	C₂×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
36	D₂₉	—	4	4	no	—
37	C₄⋊Q₈	D₂₉	1	1	yes	characteristic, complemented
38	#124	—	29	4	no	—
39	#121	—	29	4	no	—
40	C₄×D₄	—	29	2	no	—
41	#117	—	29	4	no	—
42	C₂₉	#555	1	1	yes	characteristic, complemented, Sylow
43	C₂×Q₈	C₂×D₂₉	1	2	yes	—
44	C₂×D₄	—	29	2	no	—
45	C₂×D₄	—	29	4	no	—
46	C₂²×C₄	—	29	4	no	—
47	C₄⋊C₄	—	29	2	no	—
48	C₄⋊C₄	C₂×D₂₉	1	4	yes	—
49	C₂²⋊C₄	—	29	8	no	—
50	C₂²⋊C₄	—	29	4	no	—
51	C₄²	—	29	4	no	—
52	C₄²	C₂×D₂₉	1	1	yes	characteristic
53	C₂³	—	29	4	no	—
54	Q₈	—	4	2	no	—
55	D₄	—	58	4	no	—
56	D₄	—	116	4	no	—
57	C₂×C₄	—	29	4	no	—
58	C₂×C₄	—	58	8	no	—
59	C₂×C₄	C₂²×D₂₉	1	4	yes	—
60	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
61	C₂×C₄	C₂²×D₂₉	1	2	yes	—
62	C₂²	—	58	4	no	—
63	C₂²	—	58	4	no	—
64	C₂²	—	58	4	no	—
65	C₂²	C₂³×D₂₉	1	1	yes	characteristic
66	C₄	—	2	4	no	—
67	C₄	—	2	1	no	—
68	C₄	—	58	4	no	—
69	C₄	#90809	1	4	yes	—
70	C₂	—	116	4	no	—
71	C₂	#11745359	1	1	yes	characteristic
72	C₂	C₂×#90809	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂₉×C₄⋊Q₈	C₂
hypercenter	C₄⋊Q₈	D₂₉
hypocenter	C₂₉	#555
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂₉×C₄⋊Q₈	C₂	semidirect
2. #11745309	C₂	semidirect
3. #11745257	C₂	semidirect
4. #11745254	C₂	semidirect
5. C₄×D₁₁₆	C₂	semidirect
37. C₄⋊Q₈	D₂₉	semidirect
42. C₂₉	#555	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×C₄⋊Q₈	2
#11745309	2
#11745257	2
#11745254	2
C₄×D₁₁₆	2
#555	29