Subgroups — #16819622

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	1	yes	maximal, characteristic
2	#14271029	C₂	1	1	yes	maximal, characteristic
3	#14270925	C₂	1	4	yes	maximal
4	C₂₉×#382	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
8	C₂²×#6597	C₂²	1	2	yes	—
9	C₂₉×#95	—	2	2	no	—
10	#11745179	—	2	2	no	—
11	C₄×#6597	C₄	1	4	yes	complemented
12	C₂²×C₄×C₂₉	—	2	2	no	—
13	C₂²×C₄×C₂₉	D₄	1	2	yes	—
14	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
15	C₂²×Dic₂₉	—	2	2	no	—
16	C₄⋊C₄×C₂₉	—	2	4	no	—
17	C₄²×C₂₉	C₂×C₄	1	2	yes	—
18	C₄²×C₂₉	Q₈	1	2	yes	—
19	C₄⋊Dic₂₉	—	2	4	no	—
20	C₂×#6597	—	2	2	no	—
21	C₂×#6597	—	2	2	no	—
22	C₂×#6597	C₂×C₄	1	4	yes	—
23	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₉	—	2	4	no	—
25	C₂×C₄×C₂₉	—	4	2	no	—
26	C₂×C₄×C₂₉	—	4	4	no	—
27	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
28	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄×C₂₉	#41	1	2	yes	—
31	C₂×C₄×C₂₉	#41	1	2	yes	—
32	C₂×Dic₂₉	—	4	2	no	—
33	C₂×Dic₂₉	—	4	4	no	—
34	#6597	—	2	4	no	—
35	#1835	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂²×C₂₉	#124	1	1	yes	characteristic
38	C₂²×C₂₉	#124	1	1	yes	characteristic
39	C₂²×C₂₉	#135	1	4	yes	—
40	C₄×C₂₉	—	2	4	no	—
41	C₄×C₂₉	—	8	2	no	—
42	C₄×C₂₉	#117	1	2	yes	—
43	C₄×C₂₉	#125	1	2	yes	—
44	Dic₂₉	—	8	2	no	—
45	C₂×C₄×C₈	—	29	1	no	—
46	#382	—	29	1	no	—
47	#382	D₂₉	1	1	yes	characteristic
48	#340	—	29	4	no	—
49	C₂×C₂₉	#382	1	1	yes	characteristic
50	C₂×C₂₉	#427	1	2	yes	—
51	C₂×C₂₉	#488	1	2	yes	—
52	C₂×C₂₉	#488	1	2	yes	—
53	C₂²×C₈	—	29	2	no	—
54	C₂×C₄⋊C₄	—	29	2	no	—
55	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
56	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
57	C₄×C₈	—	29	4	no	—
58	#95	—	2	2	no	—
59	#95	—	58	2	no	—
60	C₂₉	#1835	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	—	2	2	no	—
62	C₂²×C₄	—	58	2	no	—
63	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
64	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
65	C₂×C₈	—	29	4	no	—
66	C₂×C₈	—	58	2	no	—
67	C₂×C₈	—	58	2	no	—
68	C₄⋊C₄	—	2	4	no	—
69	C₄⋊C₄	—	58	4	no	—
70	C₄²	Dic₅₈	1	2	yes	—
71	C₄²	C₄×D₂₉	1	2	yes	—
72	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
73	C₂×C₄	—	2	4	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	4	4	no	—
76	C₂×C₄	—	116	2	no	—
77	C₂×C₄	—	116	4	no	—
78	C₂×C₄	#90779	1	4	yes	—
79	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
80	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
81	C₂×C₄	#90807	1	2	yes	—
82	C₂×C₄	#90809	1	2	yes	—
83	C₈	—	58	4	no	—
84	C₂²	C₂×#90779	1	1	yes	characteristic
85	C₂²	#11745298	1	1	yes	characteristic
86	C₂²	#11745309	1	1	yes	characteristic
87	C₂²	#11745312	1	4	yes	—
88	C₄	—	2	4	no	—
89	C₄	—	8	2	no	—
90	C₄	—	232	2	no	—
91	C₄	#11745252	1	2	yes	—
92	C₄	#11745254	1	2	yes	—
93	C₂	#14271028	1	1	yes	characteristic
94	C₂	#14271199	1	2	yes	—
95	C₂	#14271517	1	2	yes	—
96	C₂	#14271520	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#382	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#382	D₂₉
hypocenter	C₂₉	#1835
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

Complements

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

N	H ≅ G/N	type
11. C₄×#6597	C₄	semidirect
60. C₂₉	#1835	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
#14271029	2
#14270925	2
C₂₉×#382	2
#1835	29