Subgroups — #16817786

Order 3712.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271214	C₂	1	2	yes	maximal
2	C₄×#90772	C₂	1	1	yes	maximal, characteristic
3	#14270885	C₂	1	2	yes	maximal, complemented
4	#14270884	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#90772	C₄	1	2	yes	—
7	C₄²×D₂₉	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₂₉	C₂²	1	2	yes	—
10	#11745168	C₄	1	4	yes	—
11	#11745163	C₄	1	2	yes	—
12	#11745162	C₄	1	4	yes	—
13	C₄×#6597	C₂²	1	1	yes	characteristic
14	C₄×#6597	C₂²	1	2	yes	—
15	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
19	C₄²×C₂₉	C₂³	1	1	yes	characteristic
20	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
21	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂×#6597	C₂×C₄	1	4	yes	—
23	C₂×#6597	C₂×C₄	1	2	yes	—
24	#90772	—	2	4	no	—
25	C₂²×D₂₉	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
28	C₂×Dic₂₉	C₄²	1	1	yes	characteristic
29	C₂×Dic₂₉	C₄²	1	2	yes	—
30	C₄×D₂₉	—	2	2	no	—
31	C₄×D₂₉	—	2	4	no	—
32	C₈×C₂₉	—	2	4	no	—
33	C₈×C₂₉	M₁₆	1	4	yes	—
34	#6597	—	2	2	no	—
35	#6597	—	2	4	no	—
36	#1453	—	29	1	no	maximal, Sylow
37	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
38	C₂×D₂₉	—	2	1	no	—
39	C₂×D₂₉	—	2	2	no	—
40	C₄×C₂₉	C₂×M₁₆	1	2	yes	—
41	C₄×C₂₉	#131	1	4	yes	—
42	Dic₂₉	—	2	1	no	—
43	Dic₂₉	—	2	2	no	—
44	#431	—	29	2	no	—
45	C₄×M₁₆	—	29	1	no	—
46	#322	—	29	1	no	—
47	#322	—	29	2	no	—
48	C₈²	D₂₉	1	1	yes	characteristic, complemented
49	C₂×C₂₉	C₄×M₁₆	1	1	yes	characteristic
50	C₂×C₂₉	#405	1	2	yes	—
51	D₂₉	—	4	1	no	—
52	C₂×M₁₆	—	29	2	no	—
53	C₂×C₄²	—	29	1	no	—
54	C₄⋊C₈	—	29	4	no	—
55	C₂²⋊C₈	—	29	4	no	—
56	#97	—	29	2	no	—
57	C₄×C₈	—	29	1	no	—
58	C₄×C₈	—	29	2	no	—
59	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
60	C₄×C₈	C₂×D₂₉	1	2	yes	—
61	C₂₉	#1453	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₄	—	29	2	no	—
63	C₂²×C₄	—	29	1	no	—
64	M₁₆	—	58	4	no	—
65	C₂×C₈	—	29	2	no	—
66	C₂×C₈	—	29	4	no	—
67	C₂×C₈	C₄×D₂₉	1	4	yes	—
68	C₂×C₈	C₄×D₂₉	1	2	yes	—
69	C₄²	—	29	1	no	—
70	C₄²	—	29	2	no	—
71	C₄²	C₂²×D₂₉	1	1	yes	characteristic
72	C₂³	—	29	1	no	—
73	C₂×C₄	—	29	1	no	—
74	C₂×C₄	—	29	2	no	—
75	C₂×C₄	—	58	2	no	—
76	C₂×C₄	—	58	4	no	—
77	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
78	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
79	C₈	—	2	4	no	—
80	C₈	—	58	2	no	—
81	C₈	—	58	4	no	—
82	C₈	#90772	1	4	yes	—
83	C₂²	—	58	1	no	—
84	C₂²	—	58	2	no	—
85	C₂²	C₄²×D₂₉	1	1	yes	characteristic
86	C₄	—	58	1	no	—
87	C₄	—	58	2	no	—
88	C₄	C₂×#90772	1	2	yes	—
89	C₄	#11745263	1	4	yes	—
90	C₂	—	116	1	no	—
91	C₂	C₄×#90772	1	1	yes	characteristic
92	C₂	#14271117	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂×C₄²
Fitting	C₈²×C₂₉	C₂
prime radical	C₂²×D₂₉	C₄²
cosocle	C₄²×C₂₉	C₂³
hypercenter	C₈²	D₂₉
hypocenter	C₂₉	#1453
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
3. #14270885	C₂	semidirect
4. #14270884	C₂	semidirect
5. C₈²×C₂₉	C₂	semidirect
48. C₈²	D₂₉	semidirect
61. C₂₉	#1453	semidirect

Maximal subgroups

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

subgroup	index
#14271214	2
C₄×#90772	2
#14270885	2
#14270884	2
C₈²×C₂₉	2
#1453	29