Subgroups — #16835829

Order 3712.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745214	C₂	1	1	yes	maximal, characteristic
2	C₂²×#90770	C₂	1	1	yes	maximal, characteristic
3	#14272084	C₂	1	4	yes	maximal, complemented
4	#14271121	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×C₂₉	C₄	1	1	yes	characteristic
6	#11745288	C₄	1	1	yes	characteristic
7	C₂²×#6597	C₂²	1	1	yes	characteristic
8	#11745214	—	2	2	no	—
9	C₂×#90770	—	2	2	no	—
10	C₂×#90770	C₂²	1	2	yes	—
11	C₂×#90770	C₂²	1	2	yes	—
12	#11745163	C₄	1	2	yes	—
13	C₈×Dic₂₉	C₂²	1	2	yes	—
14	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	M₁₆×C₂₉	—	2	2	no	—
16	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
17	C₂²⋊Dic₂₉	C₈	1	2	yes	—
18	C₄⋊Dic₂₉	C₈	1	2	yes	—
19	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
20	C₂×#6597	C₂×C₄	1	1	yes	characteristic
21	C₂×#6597	D₄	1	2	yes	—
22	C₂×#6597	Q₈	1	2	yes	—
23	C₂×#6597	C₂³	1	1	yes	characteristic
24	#90770	—	2	2	no	—
25	#90770	—	2	2	no	—
26	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
30	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₂₉	C₂×C₈	1	4	yes	—
32	C₈×C₂₉	—	2	2	no	—
33	#6597	C₄⋊C₄	1	2	yes	—
34	#6597	C₂×D₄	1	1	yes	characteristic
35	#6597	C₂×Q₈	1	1	yes	characteristic
36	#2151	—	29	1	no	maximal, Sylow
37	C₂²×C₂₉	—	2	2	no	—
38	C₂²×C₂₉	C₄⋊C₈	1	2	yes	—
39	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₂₉	C₄⋊C₈	1	2	yes	—
41	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
43	Dic₂₉	—	2	4	no	—
44	C₂×M₃₂	—	29	1	no	—
45	C₂²×C₁₆	—	29	1	no	—
46	#405	—	29	1	no	—
47	C₄⋊C₁₆	—	29	4	no	—
48	C₂×C₂₉	—	2	2	no	—
49	C₂×C₂₉	C₂×C₄⋊C₈	1	1	yes	characteristic
50	C₂×C₂₉	#504	1	2	yes	—
51	C₂×M₁₆	#1181	1	1	yes	characteristic
52	C₂²×C₈	—	29	1	no	—
53	#117	—	29	1	no	—
54	M₃₂	—	58	2	no	—
55	C₂×C₁₆	—	29	2	no	—
56	C₂×C₁₆	—	29	2	no	—
57	C₂×C₁₆	—	58	2	no	—
58	#97	—	29	2	no	—
59	C₄×C₈	—	29	2	no	—
60	C₂₉	#2151	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	C₂×C₈	—	29	2	no	—
64	C₂×C₈	—	29	2	no	—
65	C₂×C₈	—	29	1	no	—
66	C₂×C₈	—	29	1	no	—
67	C₂×C₈	C₂×#1181	1	2	yes	—
68	C₄⋊C₄	—	29	2	no	—
69	C₂²⋊C₄	—	29	2	no	—
70	C₄²	—	29	2	no	—
71	C₁₆	—	58	2	no	—
72	C₁₆	—	58	2	no	—
73	C₂³	D₂₉⋊C₈	1	1	yes	characteristic
74	C₂×C₄	—	29	4	no	—
75	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
76	C₂×C₄	C₄⋊#1181	1	2	yes	—
77	C₂×C₄	#90800	1	2	yes	—
78	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	29	1	no	—
81	C₈	—	29	2	no	—
82	C₈	—	29	1	no	—
83	C₂²	—	2	2	no	—
84	C₂²	#11745220	1	2	yes	—
85	C₂²	C₂×D₂₉⋊C₈	1	1	yes	characteristic
86	C₄	—	58	4	no	—
87	C₄	#11745220	1	2	yes	—
88	C₄	C₂×C₄⋊#1181	1	1	yes	characteristic
89	C₄	C₂×#90800	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×#11745220	1	1	yes	characteristic
92	C₂	#14272222	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#1181
commutator, socle	C₂²×C₂₉	C₂²×C₈
Fitting	C₂×M₁₆×C₂₉	C₄
prime radical	C₂³×C₂₉	C₂×C₈
cosocle	C₂×#6597	C₂³
hypercenter	C₂×M₁₆	#1181
hypocenter	C₂₉	#2151
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #14272084	C₂	semidirect
60. C₂₉	#2151	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745214	2
C₂²×#90770	2
#14272084	2
#14271121	2
#2151	29