Subgroups — #16819632

Order 3712.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271187	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745151	C₂	1	1	yes	maximal, characteristic
3	#14270927	C₂	1	4	yes	maximal
4	C₂₉×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×#90777	C₂²	1	2	yes	—
8	C₂²×#6597	C₂²	1	2	yes	—
9	C₂₉×C₄⋊C₈	—	2	2	no	—
10	C₄⋊#6597	—	2	2	no	—
11	#11745151	C₄	1	4	yes	—
12	C₂²×C₄×C₂₉	Q₈	1	2	yes	—
13	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
14	M₁₆×C₂₉	—	2	4	no	—
15	C₂×C₈×C₂₉	—	2	2	no	—
16	C₄²×C₂₉	C₂×C₄	1	2	yes	—
17	C₄²×C₂₉	D₄	1	2	yes	—
18	#90777	—	2	4	no	—
19	C₂×#6597	—	2	2	no	—
20	C₂×#6597	—	2	2	no	—
21	C₂×#6597	—	2	2	no	—
22	C₂×#6597	C₂×C₄	1	4	yes	—
23	C₂³×C₂₉	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₂₉	—	4	2	no	—
25	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
26	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₂₉	#41	1	2	yes	—
29	C₂×C₄×C₂₉	#41	1	2	yes	—
30	C₈×C₂₉	—	4	2	no	—
31	#6597	—	2	4	no	—
32	#6597	—	4	2	no	—
33	#1838	—	29	1	no	maximal, Sylow
34	C₂²×C₂₉	—	2	2	no	—
35	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₂₉	#125	1	2	yes	—
37	C₄×C₂₉	—	2	4	no	—
38	C₄×C₂₉	#117	1	2	yes	—
39	C₄×C₂₉	#124	1	1	yes	characteristic
40	C₄×C₂₉	#124	1	1	yes	characteristic
41	#423	—	29	1	no	—
42	#423	D₂₉	1	1	yes	characteristic
43	C₂×#97	—	29	1	no	—
44	#341	—	29	4	no	—
45	C₂×C₂₉	—	2	2	no	—
46	C₂×C₂₉	#382	1	1	yes	characteristic
47	C₂×C₂₉	#430	1	2	yes	—
48	C₂×M₁₆	—	29	2	no	—
49	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
50	C₂²×C₈	—	29	2	no	—
51	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
52	C₄⋊C₈	—	2	2	no	—
53	C₄⋊C₈	—	58	2	no	—
54	#97	—	29	4	no	—
55	C₂₉	#1838	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	Dic₅₈	1	2	yes	—
57	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
58	M₁₆	—	2	4	no	—
59	M₁₆	—	58	4	no	—
60	C₂×C₈	—	2	2	no	—
61	C₂×C₈	—	29	4	no	—
62	C₂×C₈	—	58	2	no	—
63	C₂×C₈	—	58	2	no	—
64	C₂×C₈	—	58	2	no	—
65	C₄²	C₄×D₂₉	1	2	yes	—
66	C₄²	C₂²⋊D₂₉	1	2	yes	—
67	C₂³	C₂×Dic₅₈	1	1	yes	characteristic
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	#90779	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
71	C₂×C₄	#90807	1	2	yes	—
72	C₂×C₄	#90809	1	2	yes	—
73	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
74	C₈	—	4	2	no	—
75	C₈	—	58	4	no	—
76	C₈	—	116	2	no	—
77	C₂²	—	2	2	no	—
78	C₂²	#11745252	1	2	yes	—
79	C₂²	C₂×#90779	1	1	yes	characteristic
80	C₄	—	2	4	no	—
81	C₄	#11745254	1	2	yes	—
82	C₄	#11745298	1	1	yes	characteristic
83	C₄	#11745309	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#14271028	1	1	yes	characteristic
86	C₂	#14271211	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#423	C₂
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂³×C₂₉	C₂×Q₈
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#423	D₂₉
hypocenter	C₂₉	#1838
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
55. C₂₉	#1838	semidirect

Maximal subgroups

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

subgroup	index
#14271187	2
C₂×#11745151	2
#14270927	2
C₂₉×#423	2
#1838	29