Subgroups — #16818157

Order 3712.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271216	C₂	1	2	yes	maximal
2	#14270909	C₂	1	4	yes	maximal, complemented
3	C₂₉×#533	C₂	1	1	yes	maximal, characteristic
4	C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
5	C₂₉×#125	C₄	1	2	yes	—
6	C₂₉×C₂²⋊Q₈	—	2	2	no	—
7	C₄×Q₈×C₂₉	—	2	2	no	—
8	C₂₉×#117	C₄	1	2	yes	—
9	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂²⋊#6597	—	2	2	no	—
11	C₄⋊#6597	C₂²	1	4	yes	—
12	C₄×#6597	—	2	2	no	—
13	C₂×Q₈×C₂₉	—	2	2	no	—
14	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₂₉	D₄	1	2	yes	—
16	C₄⋊C₄×C₂₉	—	2	4	no	—
17	C₄⋊C₄×C₂₉	—	2	2	no	—
18	C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
19	C₂²⋊C₄×C₂₉	—	2	2	no	—
20	C₄²×C₂₉	—	2	2	no	—
21	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₂₉	D₄	1	2	yes	—
23	C₄²×C₂₉	C₂³	1	1	yes	characteristic
24	C₂×#6597	—	2	4	no	—
25	C₂³×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	Q₈×C₂₉	—	4	4	no	—
27	C₂×C₄×C₂₉	—	2	2	no	—
28	C₂×C₄×C₂₉	—	2	4	no	—
29	C₂×C₄×C₂₉	—	2	4	no	—
30	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
34	#6597	—	4	4	no	—
35	#1544	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	—	2	1	no	—
37	C₂²×C₂₉	—	2	2	no	—
38	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₄×C₂₉	—	2	1	no	—
40	C₄×C₂₉	—	2	2	no	—
41	C₄×C₂₉	—	4	4	no	—
42	C₄×C₂₉	#101	1	2	yes	—
43	C₄×C₂₉	#135	1	4	yes	—
44	#533	D₂₉	1	1	yes	characteristic
45	#431	—	29	2	no	—
46	#332	—	29	4	no	—
47	C₂×C₂₉	—	4	1	no	—
48	C₂×C₂₉	C₂×#101	1	1	yes	characteristic
49	C₂×C₂₉	#416	1	2	yes	—
50	C₄⋊Q₈	C₂×D₂₉	1	2	yes	—
51	#125	Dic₂₉	1	2	yes	—
52	C₂²⋊Q₈	—	2	2	no	—
53	C₄×Q₈	—	2	2	no	—
54	#117	Dic₂₉	1	2	yes	—
55	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
56	C₄⋊C₈	—	29	4	no	—
57	C₂²⋊C₈	—	58	2	no	—
58	C₄×C₈	—	58	2	no	—
59	C₂₉	#1544	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	2	2	no	—
61	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
62	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
63	C₂×C₈	—	58	4	no	—
64	C₄⋊C₄	—	2	4	no	—
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	C₂×Dic₂₉	1	4	yes	—
67	C₂²⋊C₄	—	2	2	no	—
68	C₄²	—	2	2	no	—
69	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
70	C₄²	C₂²⋊D₂₉	1	2	yes	—
71	C₄²	C₂²×D₂₉	1	1	yes	characteristic
72	C₂³	C₂²⋊Dic₂₉	1	1	yes	characteristic
73	Q₈	—	4	4	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	—	2	4	no	—
77	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
79	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
80	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
81	C₈	—	116	4	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	2	no	—
84	C₂²	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	—	2	2	no	—
87	C₄	—	4	4	no	—
88	C₄	#11745184	1	2	yes	—
89	C₄	#11745312	1	4	yes	—
90	C₂	—	4	1	no	—
91	C₂	C₂×#11745184	1	1	yes	characteristic
92	C₂	#14271159	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#533	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₂₉	C₂²⋊C₄
cosocle	C₄²×C₂₉	C₂³
hypercenter	#533	D₂₉
hypocenter	C₂₉	#1544
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

Complements

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

N	H ≅ G/N	type
2. #14270909	C₂	semidirect
59. C₂₉	#1544	semidirect

Maximal subgroups

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

subgroup	index
#14271216	2
#14270909	2
C₂₉×#533	2
#1544	29