Subgroups — #16821072

Order 3712.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271212	C₂	1	1	yes	maximal, characteristic
2	#14270933	C₂	1	2	yes	maximal
3	#14270928	C₂	1	2	yes	maximal
4	#14270921	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#424	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	C₂₉×#117	C₂²	1	1	yes	characteristic
9	C₂×#90777	C₂²	1	2	yes	—
10	C₂×#90777	C₂²	1	2	yes	—
11	C₂₉×C₄⋊C₈	—	2	2	no	—
12	#11745167	—	2	2	no	—
13	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
14	M₁₆×C₂₉	—	2	2	no	—
15	C₂×C₈×C₂₉	—	2	1	no	—
16	C₂×C₈×C₂₉	—	2	2	no	—
17	C₂×C₈×C₂₉	D₄	1	2	yes	—
18	C₄⋊C₄×C₂₉	—	2	1	no	—
19	C₂²⋊C₄×C₂₉	Q₈	1	2	yes	—
20	C₄²×C₂₉	—	2	1	no	—
21	#90777	—	2	2	no	—
22	#90777	—	2	2	no	—
23	#90777	—	2	2	no	—
24	#90777	—	2	2	no	—
25	C₂×#6597	—	2	2	no	—
26	C₂×#6597	—	2	2	no	—
27	C₂³×C₂₉	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₂₉	—	2	2	no	—
29	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
31	C₂×C₄×C₂₉	#41	1	2	yes	—
32	C₂×C₄×C₂₉	#41	1	2	yes	—
33	C₈×C₂₉	—	2	2	no	—
34	C₈×C₂₉	—	4	1	no	—
35	#6597	—	4	2	no	—
36	#6597	—	4	2	no	—
37	#2103	—	29	1	no	maximal, Sylow
38	C₂²×C₂₉	—	4	1	no	—
39	C₂²×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂²×C₂₉	#125	1	2	yes	—
41	C₄×C₂₉	—	4	2	no	—
42	C₄×C₂₉	#123	1	1	yes	characteristic
43	C₄×C₂₉	#124	1	1	yes	characteristic
44	C₄×C₂₉	#126	1	2	yes	—
45	#430	—	29	1	no	—
46	#424	D₂₉	1	1	yes	characteristic
47	#344	—	29	2	no	—
48	#341	—	29	2	no	—
49	#338	—	29	1	no	—
50	C₂×C₂₉	—	2	1	no	—
51	C₂×C₂₉	—	2	2	no	—
52	C₂×C₂₉	#400	1	1	yes	characteristic
53	C₂×M₁₆	—	29	2	no	—
54	C₂×M₁₆	—	29	2	no	—
55	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
56	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
57	#117	C₂×D₂₉	1	1	yes	characteristic
58	#108	—	58	2	no	—
59	C₄⋊C₈	—	2	2	no	—
60	C₂₉	#2103	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	M₁₆	—	58	2	no	—
64	M₁₆	—	58	2	no	—
65	M₁₆	—	58	2	no	—
66	M₁₆	—	58	2	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	58	2	no	—
70	C₂×C₈	—	58	2	no	—
71	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
72	C₄⋊C₄	—	2	1	no	—
73	C₂²⋊C₄	Dic₅₈	1	2	yes	—
74	C₄²	—	2	1	no	—
75	C₂³	C₂×Dic₅₈	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	#90805	1	1	yes	characteristic
78	C₂×C₄	#90807	1	2	yes	—
79	C₂×C₄	#90809	1	2	yes	—
80	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	4	1	no	—
83	C₈	—	116	2	no	—
84	C₈	—	116	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#11745252	1	2	yes	—
87	C₂²	#11745286	1	1	yes	characteristic
88	C₄	—	4	2	no	—
89	C₄	#11745260	1	2	yes	—
90	C₄	#11745297	1	1	yes	characteristic
91	C₄	#11745309	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	#14271102	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11745309
commutator, cosocle	C₂²×C₄×C₂₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#424	C₂
socle	C₂×C₂₉	#400
prime radical	C₂³×C₂₉	C₂×Q₈
hypercenter	#424	D₂₉
hypocenter	C₂₉	#2103
LCS	G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #424

Complements

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

N	H ≅ G/N	type
60. C₂₉	#2103	semidirect

Maximal subgroups

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

subgroup	index
#14271212	2
#14270933	2
#14270928	2
#14270921	2
C₂₉×#424	2
#2103	29