Subgroups — #16822668

Order 3712.

648 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745236	C₂	1	1	yes	maximal, characteristic
2	#14271041	C₂	1	12	yes	maximal, complemented
3	#14271031	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#383	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₁₆	C₂²	1	6	yes	—
6	C₂²×C₄×D₂₉	C₂²	1	4	yes	—
7	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×#90781	C₂²	1	12	yes	—
9	#11745236	C₄	1	8	yes	complemented
10	C₂₉×#95	C₂²	1	6	yes	—
11	#11745179	C₂²	1	6	yes	—
12	C₂³×D₂₉	C₂³	1	4	yes	—
13	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
14	C₂²×C₄×C₂₉	C₂³	1	3	yes	—
15	C₂²×Dic₂₉	C₂³	1	4	yes	—
16	C₂×D₁₁₆	—	4	6	no	—
17	C₂×D₁₁₆	—	4	6	no	—
18	C₂×D₁₁₆	C₂×C₄	1	24	yes	complemented
19	C₂×C₄×D₂₉	—	4	12	no	—
20	C₄²×C₂₉	C₂×C₄	1	4	yes	complemented
21	#90781	—	4	12	no	—
22	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
23	C₂²×D₂₉	—	2	12	no	—
24	C₂²×D₂₉	—	2	12	no	—
25	C₂²×D₂₉	C₂²×C₄	1	8	yes	—
26	C₂×C₄×C₂₉	—	2	6	no	—
27	C₂×C₄×C₂₉	—	2	12	no	—
28	C₂×C₄×C₂₉	C₂²×C₄	1	6	yes	—
29	C₂×Dic₂₉	—	2	12	no	—
30	D₁₁₆	—	4	24	no	—
31	C₄×D₂₉	—	4	16	no	—
32	#2380	—	29	1	no	maximal, Sylow
33	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
34	C₂²×C₂₉	H(5,𝔽₂)	1	6	yes	—
35	C₂×D₂₉	—	2	24	no	—
36	C₂×D₂₉	—	4	4	no	—
37	C₂×D₂₉	—	4	12	no	—
38	C₄×C₂₉	—	2	6	no	—
39	C₄×C₂₉	—	4	4	no	—
40	Dic₂₉	—	4	4	no	—
41	C₂×#127	—	29	1	no	—
42	#386	—	29	12	no	—
43	#383	—	29	1	no	—
44	#383	D₂₉	1	1	yes	characteristic, complemented
45	C₂×C₂₉	#518	1	3	yes	—
46	C₂×C₂₉	#560	1	4	yes	—
47	D₂₉	—	4	8	no	—
48	C₂²×D₄	—	29	6	no	—
49	C₂³×C₄	—	29	4	no	—
50	#127	—	29	8	no	—
51	C₂×C₂²⋊C₄	—	29	12	no	—
52	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
53	#95	—	29	6	no	—
54	#95	C₂×D₂₉	1	6	yes	—
55	C₂₉	#2380	1	1	yes	characteristic, complemented, Sylow
56	C₂⁴	—	29	4	no	—
57	C₂×D₄	—	29	24	no	—
58	C₂×D₄	—	116	6	no	—
59	C₂×D₄	—	116	6	no	—
60	C₂²×C₄	—	29	4	no	—
61	C₂²×C₄	—	116	12	no	—
62	C₂²×C₄	C₂²×D₂₉	1	4	yes	—
63	C₂²×C₄	C₂²×D₂₉	1	3	yes	—
64	C₂²⋊C₄	—	116	12	no	—
65	C₄²	C₄×D₂₉	1	4	yes	complemented
66	C₂³	—	29	8	no	—
67	C₂³	—	58	12	no	—
68	C₂³	—	58	12	no	—
69	C₂³	C₂³×D₂₉	1	1	yes	characteristic
70	D₄	—	116	24	no	—
71	C₂×C₄	—	2	6	no	—
72	C₂×C₄	—	2	12	no	—
73	C₂×C₄	—	58	12	no	—
74	C₂×C₄	—	116	16	no	—
75	C₂×C₄	C₂×C₄×D₂₉	1	6	yes	—
76	C₂²	—	58	24	no	—
77	C₂²	—	116	4	no	—
78	C₂²	—	116	12	no	—
79	C₂²	C₂²×C₄×D₂₉	1	1	yes	characteristic
80	C₂²	#11745364	1	6	yes	—
81	C₄	—	2	6	no	—
82	C₄	—	4	4	no	—
83	C₄	—	116	4	no	—
84	C₂	—	116	8	no	—
85	C₂	#14271637	1	3	yes	—
86	C₂	#14271904	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₉
commutator	C₂²×C₂₉	C₂³×C₄
Fitting	C₂₉×#383	C₂
socle, cosocle	C₂³×C₂₉	C₂⁴
prime radical	C₂×#11745236	C₂
hypercenter	#383	D₂₉
hypocenter	C₂₉	#2380
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ #383

Complements

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

N	H ≅ G/N	type
2. #14271041	C₂	semidirect
3. #14271031	C₂	semidirect
4. C₂₉×#383	C₂	semidirect
9. #11745236	C₄	semidirect
18. C₂×D₁₁₆	C₂×C₄	semidirect
20. C₄²×C₂₉	C₂×C₄	semidirect
44. #383	D₂₉	semidirect
55. C₂₉	#2380	semidirect
65. C₄²	C₄×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745236	2
#14271041	2
#14271031	2
C₂₉×#383	2
#2380	29