Subgroups — #16819612

Order 3712.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#6597	C₂	1	2	yes	maximal
2	#14270918	C₂	1	4	yes	maximal
3	C₂₉×#376	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
5	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
6	C₂²×#6597	C₂²	1	4	yes	—
7	C₂₉×#95	C₄	1	4	yes	—
8	C₄⋊#6597	—	2	4	no	—
9	C₂²×C₄×C₂₉	C₂×C₄	1	4	yes	—
10	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
11	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
12	C₄²×C₂₉	—	2	4	no	—
13	C₄²×C₂₉	D₄	1	2	yes	—
14	C₄²×C₂₉	Q₈	1	2	yes	—
15	C₂×#6597	—	2	4	no	—
16	C₂×#6597	—	2	8	no	—
17	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	—	2	4	no	—
19	C₂×C₄×C₂₉	—	2	4	no	—
20	C₂×C₄×C₂₉	—	2	8	no	—
21	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
23	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₂₉	#41	1	4	yes	—
25	#6597	—	4	4	no	—
26	#1832	—	29	1	no	maximal, Sylow
27	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₂₉	#117	1	2	yes	—
29	C₂²×C₂₉	#131	1	4	yes	—
30	C₄×C₂₉	—	2	4	no	—
31	C₄×C₂₉	—	4	4	no	—
32	C₄×C₂₉	#124	1	2	yes	—
33	C₄×C₂₉	#125	1	2	yes	—
34	C₂×C₄⋊C₈	—	29	2	no	—
35	#376	D₂₉	1	1	yes	characteristic
36	#336	—	29	4	no	—
37	C₂×C₂₉	#382	1	1	yes	characteristic
38	C₂×C₂₉	#424	1	2	yes	—
39	C₂×C₂₉	#433	1	4	yes	—
40	C₂²×C₈	—	29	4	no	—
41	C₂×C₄²	C₂×D₂₉	1	2	yes	—
42	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
43	C₄⋊C₈	—	58	4	no	—
44	#95	Dic₂₉	1	4	yes	—
45	C₂₉	#1832	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	C₂×Dic₂₉	1	4	yes	—
47	C₂²×C₄	C₂×Dic₂₉	1	2	yes	—
48	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
49	C₂×C₈	—	58	4	no	—
50	C₂×C₈	—	58	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	Dic₅₈	1	2	yes	—
53	C₄²	D₁₁₆	1	2	yes	—
54	C₂³	C₂²×Dic₂₉	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	2	8	no	—
58	C₂×C₄	C₄⋊Dic₂₉	1	4	yes	—
59	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
60	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
61	C₂×C₄	#90805	1	4	yes	—
62	C₈	—	116	4	no	—
63	C₂²	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
64	C₂²	#11745288	1	2	yes	—
65	C₂²	#11745310	1	4	yes	—
66	C₄	—	2	4	no	—
67	C₄	—	4	4	no	—
68	C₄	#11745232	1	2	yes	—
69	C₄	#11745237	1	2	yes	—
70	C₂	#14271029	1	1	yes	characteristic
71	C₂	#14271190	1	2	yes	—
72	C₂	#14271224	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator, socle, prime radical	C₂³×C₂₉	C₂²×C₄
Fitting	C₂₉×#376	C₂
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#376	D₂₉
hypocenter	C₂₉	#1832
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
45. C₂₉	#1832	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊#6597	2
#14270918	2
C₂₉×#376	2
#1832	29