Subgroups — #16835421

Order 3712.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272029	C₂	1	6	yes	maximal
2	#14271008	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6599	C₂²	1	4	yes	—
4	C₂×C₄×Dic₂₉	C₂²	1	3	yes	—
5	C₂₉×#95	C₄	1	1	yes	characteristic
6	#11745179	C₄	1	3	yes	—
7	C₂²×C₄×C₂₉	C₂×C₄	1	3	yes	—
8	C₂²×Dic₂₉	C₂×C₄	1	3	yes	—
9	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
10	C₂×#6599	—	2	12	no	—
11	C₄×Dic₂₉	—	2	6	no	—
12	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₉	—	2	3	no	—
14	C₂×C₄×C₂₉	—	2	6	no	—
15	C₂×Dic₂₉	—	2	3	no	—
16	C₂×Dic₂₉	—	2	3	no	—
17	C₂×Dic₂₉	—	2	3	no	—
18	C₂×Dic₂₉	#41	1	6	yes	—
19	#6599	—	4	4	no	—
20	#1840	—	29	1	no	maximal, Sylow
21	C₂²×C₂₉	#117	1	3	yes	—
22	C₂²×C₂₉	#131	1	3	yes	—
23	C₂²×C₂₉	#131	1	1	yes	characteristic
24	C₄×C₂₉	—	4	3	no	—
25	Dic₂₉	—	4	3	no	—
26	Dic₂₉	#126	1	4	yes	—
27	#376	—	29	1	no	—
28	#336	—	29	6	no	—
29	C₂×C₂₉	#383	1	1	yes	characteristic
30	C₂×C₂₉	#433	1	3	yes	—
31	C₂×C₂₉	#433	1	3	yes	—
32	C₂²×C₈	—	29	4	no	—
33	C₂×C₄²	—	29	3	no	—
34	#95	—	29	3	no	—
35	#95	#1181	1	1	yes	characteristic
36	C₂₉	#1840	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₄	—	29	1	no	—
38	C₂²×C₄	—	29	3	no	—
39	C₂²×C₄	C₂×#1181	1	3	yes	—
40	C₂×C₈	—	58	12	no	—
41	C₄²	—	58	6	no	—
42	C₂³	C₂²×#1181	1	1	yes	characteristic
43	C₂×C₄	—	2	3	no	—
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	29	6	no	—
46	C₂×C₄	—	58	3	no	—
47	C₂×C₄	—	58	3	no	—
48	C₂×C₄	—	58	3	no	—
49	C₈	—	116	4	no	—
50	C₂²	#11745345	1	3	yes	—
51	C₂²	#11745346	1	3	yes	—
52	C₂²	#11745348	1	1	yes	characteristic
53	C₄	—	4	3	no	—
54	C₄	—	29	4	no	—
55	C₄	—	116	3	no	—
56	C₂	#14272108	1	1	yes	characteristic
57	C₂	#14272187	1	3	yes	—
58	C₂	#14272188	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#1181
commutator, socle, prime radical	C₂³×C₂₉	C₂²×C₄
Fitting	C₂₉×#95	C₄
cosocle	C₂²×Dic₂₉	C₂³
hypercenter	#95	#1181
hypocenter	C₂₉	#1840
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
36. C₂₉	#1840	semidirect

Maximal subgroups

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

subgroup	index
#14272029	2
#14271008	2
#1840	29