Subgroups — #16817379

Order 3712.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊#6597	C₂	1	2	yes	maximal
2	C₂₉×#407	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
4	C₂×M₁₆×C₂₉	C₄	1	2	yes	—
5	C₂²×#6597	—	2	2	no	—
6	C₂₉×C₂²⋊C₈	—	2	2	no	—
7	C₂²⋊#6597	—	2	2	no	—
8	C₂²⋊#6597	C₄	1	4	yes	—
9	C₂⁴×C₂₉	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₂₉	—	4	2	no	—
11	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
14	C₂²×C₄×C₂₉	D₄	1	2	yes	—
15	M₁₆×C₂₉	—	4	2	no	—
16	C₂×C₈×C₂₉	—	2	2	no	—
17	C₂×#6597	—	2	4	no	—
18	C₂×#6597	—	4	4	no	—
19	C₂³×C₂₉	—	2	4	no	—
20	C₂³×C₂₉	—	4	1	no	—
21	C₂³×C₂₉	C₄⋊C₄	1	2	yes	—
22	C₂³×C₂₉	C₄⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₉	—	2	4	no	—
24	C₂×C₄×C₂₉	—	2	2	no	—
25	C₂×C₄×C₂₉	—	4	2	no	—
26	C₂×C₄×C₂₉	—	4	1	no	—
27	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
29	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₈×C₂₉	—	4	2	no	—
31	#6597	—	4	4	no	—
32	#1298	—	29	1	no	maximal, Sylow
33	C₂²×C₂₉	—	2	2	no	—
34	C₂²×C₂₉	—	2	2	no	—
35	C₂²×C₂₉	—	2	2	no	—
36	C₂²×C₂₉	—	2	1	no	—
37	C₂²×C₂₉	—	4	4	no	—
38	C₂²×C₂₉	#95	1	1	yes	characteristic
39	C₂²×C₂₉	#108	1	4	yes	—
40	C₄×C₂₉	—	2	2	no	—
41	C₄×C₂₉	—	2	1	no	—
42	C₄×C₂₉	#99	1	2	yes	—
43	#407	D₂₉	1	1	yes	characteristic
44	C₂×C₂²⋊C₈	—	29	2	no	—
45	C₂×C₂₉	—	2	4	no	—
46	C₂×C₂₉	—	4	1	no	—
47	C₂×C₂₉	#341	1	2	yes	—
48	C₂×C₂₉	#342	1	1	yes	characteristic
49	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
50	C₂×M₁₆	Dic₂₉	1	2	yes	—
51	C₂²×C₈	—	58	2	no	—
52	C₂²⋊C₈	—	2	2	no	—
53	C₂²⋊C₈	—	29	4	no	—
54	C₂²⋊C₈	—	58	2	no	—
55	C₂₉	#1298	1	1	yes	characteristic, complemented, Sylow
56	C₂⁴	Dic₅₈	1	1	yes	characteristic
57	C₂²×C₄	—	4	2	no	—
58	C₂²×C₄	C₄×D₂₉	1	2	yes	—
59	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
60	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
61	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
62	M₁₆	—	4	2	no	—
63	C₂×C₈	—	2	2	no	—
64	C₂×C₈	—	58	4	no	—
65	C₂×C₈	—	116	4	no	—
66	C₂³	—	2	4	no	—
67	C₂³	—	4	1	no	—
68	C₂³	#90779	1	2	yes	—
69	C₂³	C₄⋊Dic₂₉	1	1	yes	characteristic
70	C₂×C₄	—	2	4	no	—
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
75	C₂×C₄	#90781	1	2	yes	—
76	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
77	C₈	—	4	2	no	—
78	C₈	—	116	4	no	—
79	C₂²	—	2	2	no	—
80	C₂²	—	2	2	no	—
81	C₂²	—	2	2	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	4	4	no	—
84	C₂²	#11745170	1	4	yes	—
85	C₂²	#11745179	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	#11745182	1	2	yes	—
89	C₂	—	2	4	no	—
90	C₂	—	4	1	no	—
91	C₂	#14270927	1	2	yes	—
92	C₂	#14270930	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₂₉
commutator	C₂×C₄×C₂₉	C₄²
Frattini	C₂³×C₄	C₂×D₂₉
Fitting	C₂₉×#407	C₂
socle	C₂²×C₂₉	#95
prime radical	C₂⁴×C₂₉	Q₈
cosocle	C₂³×C₄×C₂₉	C₂²
hypercenter	#407	D₂₉
hypocenter	C₂₉	#1298
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

Complements

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

N	H ≅ G/N	type
55. C₂₉	#1298	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂²⋊#6597	2
C₂₉×#407	2
#1298	29