Subgroups — #16817796

Order 3712.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#90772	C₂	1	2	yes	maximal
2	C₄×#90772	C₂	1	1	yes	maximal, characteristic
3	#14270885	C₂	1	2	yes	maximal, complemented
4	C₈×#6597	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#90772	C₄	1	2	yes	—
7	C₂×#90772	C₄	1	4	yes	—
8	C₄²×D₂₉	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₂₉	C₂²	1	2	yes	—
11	#11745163	C₄	1	2	yes	—
12	#11745163	C₄	1	4	yes	—
13	C₄×#6597	C₂²	1	2	yes	—
14	C₄×#6597	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
21	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
22	C₂×#6597	C₂×C₄	1	2	yes	—
23	C₂×#6597	C₂×C₄	1	4	yes	—
24	#90772	—	2	4	no	—
25	#90772	—	2	8	no	—
26	C₂²×D₂₉	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
29	C₂×Dic₂₉	C₄²	1	1	yes	characteristic
30	C₂×Dic₂₉	C₄²	1	2	yes	—
31	C₄×D₂₉	—	2	2	no	—
32	C₄×D₂₉	—	2	4	no	—
33	C₈×C₂₉	—	2	4	no	—
34	C₈×C₂₉	M₁₆	1	4	yes	complemented
35	#6597	—	2	2	no	—
36	#6597	M₁₆	1	8	yes	complemented
37	#1455	—	29	1	no	maximal, Sylow
38	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
39	C₂×D₂₉	—	2	1	no	—
40	C₂×D₂₉	—	2	2	no	—
41	C₄×C₂₉	C₂×M₁₆	1	2	yes	—
42	C₄×C₂₉	C₂×M₁₆	1	4	yes	—
43	Dic₂₉	—	2	1	no	—
44	Dic₂₉	—	2	2	no	—
45	C₄×M₁₆	—	29	2	no	—
46	C₄×M₁₆	—	29	1	no	—
47	#322	—	29	2	no	—
48	#322	D₂₉	1	1	yes	characteristic, complemented
49	C₈²	—	29	1	no	—
50	C₂×C₂₉	C₄×M₁₆	1	1	yes	characteristic
51	C₂×C₂₉	C₄×M₁₆	1	2	yes	—
52	D₂₉	—	4	1	no	—
53	C₂×M₁₆	—	29	4	no	—
54	C₂×M₁₆	—	29	2	no	—
55	C₂×C₄²	—	29	1	no	—
56	#97	—	29	4	no	—
57	#97	—	29	2	no	—
58	C₄×C₈	—	29	2	no	—
59	C₄×C₈	—	29	1	no	—
60	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
61	C₄×C₈	C₂×D₂₉	1	2	yes	—
62	C₂₉	#1455	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₄	—	29	1	no	—
64	C₂²×C₄	—	29	2	no	—
65	M₁₆	—	58	8	no	—
66	M₁₆	—	58	4	no	—
67	C₂×C₈	—	29	4	no	—
68	C₂×C₈	—	29	2	no	—
69	C₂×C₈	C₄×D₂₉	1	4	yes	—
70	C₂×C₈	C₄×D₂₉	1	2	yes	—
71	C₄²	—	29	1	no	—
72	C₄²	—	29	2	no	—
73	C₄²	C₂²×D₂₉	1	1	yes	characteristic
74	C₂³	—	29	1	no	—
75	C₂×C₄	—	29	1	no	—
76	C₂×C₄	—	29	2	no	—
77	C₂×C₄	—	58	2	no	—
78	C₂×C₄	—	58	4	no	—
79	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
80	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
81	C₈	—	2	4	no	—
82	C₈	—	29	8	no	—
83	C₈	—	58	2	no	—
84	C₈	#90772	1	4	yes	complemented
85	C₂²	—	58	1	no	—
86	C₂²	—	58	2	no	—
87	C₂²	C₄²×D₂₉	1	1	yes	characteristic
88	C₄	—	58	1	no	—
89	C₄	—	58	2	no	—
90	C₄	C₂×#90772	1	2	yes	—
91	C₄	M₁₆×D₂₉	1	4	yes	—
92	C₂	—	116	1	no	—
93	C₂	C₄×#90772	1	1	yes	characteristic
94	C₂	#14271115	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂×C₄²
Fitting	C₂₉×#322	C₂
prime radical	C₂²×D₂₉	C₄²
cosocle	C₄²×C₂₉	C₂³
hypercenter	#322	D₂₉
hypocenter	C₂₉	#1455
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
3. #14270885	C₂	semidirect
4. C₈×#6597	C₂	semidirect
5. C₂₉×#322	C₂	semidirect
34. C₈×C₂₉	M₁₆	semidirect
36. #6597	M₁₆	semidirect
48. #322	D₂₉	semidirect
62. C₂₉	#1455	semidirect
84. C₈	#90772	semidirect

Maximal subgroups

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

subgroup	index
C₄×#90772	2
#14270885	2
C₈×#6597	2
C₂₉×#322	2
#1455	29