Subgroups — #16818218

Order 3712.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271220	C₂	1	2	yes	maximal
2	#14270912	C₂	1	4	yes	maximal, complemented
3	C₂×C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₂²×Q₈×C₂₉	C₄	1	2	yes	—
5	C₂₉×C₄⋊Q₈	—	2	2	no	—
6	C₂₉×C₄⋊Q₈	C₄	1	2	yes	—
7	C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
9	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂²⋊#6597	—	2	2	no	—
11	C₄⋊#6597	C₂²	1	4	yes	—
12	#11745151	—	2	2	no	—
13	C₂×Q₈×C₂₉	—	2	2	no	—
14	C₂×Q₈×C₂₉	—	4	4	no	—
15	C₂×Q₈×C₂₉	C₂×C₄	1	4	yes	—
16	C₂²×C₄×C₂₉	—	2	2	no	—
17	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₂₉	D₄	1	2	yes	—
19	C₄⋊C₄×C₂₉	—	2	4	no	—
20	C₄⋊C₄×C₂₉	—	2	4	no	—
21	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₂₉	D₄	1	2	yes	—
23	C₄²×C₂₉	C₂³	1	1	yes	characteristic
24	C₂×#6597	—	2	4	no	—
25	C₂³×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	Q₈×C₂₉	—	4	4	no	—
27	Q₈×C₂₉	—	4	4	no	—
28	C₂×C₄×C₂₉	—	2	2	no	—
29	C₂×C₄×C₂₉	—	2	4	no	—
30	C₂×C₄×C₂₉	—	2	4	no	—
31	C₂×C₄×C₂₉	—	4	4	no	—
32	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
33	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
36	#6597	—	4	4	no	—
37	#1558	—	29	1	no	maximal, Sylow
38	C₂²×C₂₉	—	2	2	no	—
39	C₂²×C₂₉	#100	1	2	yes	—
40	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₄×C₂₉	—	2	1	no	—
42	C₄×C₂₉	—	2	1	no	—
43	C₄×C₂₉	—	2	2	no	—
44	C₄×C₂₉	—	4	4	no	—
45	C₄×C₂₉	#137	1	4	yes	—
46	C₂×C₄⋊Q₈	D₂₉	1	1	yes	characteristic
47	#432	—	29	2	no	—
48	#333	—	29	4	no	—
49	C₂×C₂₉	—	2	2	no	—
50	C₂×C₂₉	C₂×#100	1	1	yes	characteristic
51	C₂×C₂₉	#419	1	2	yes	—
52	C₂²×Q₈	Dic₂₉	1	2	yes	—
53	C₄⋊Q₈	—	2	2	no	—
54	C₄⋊Q₈	Dic₂₉	1	2	yes	—
55	C₄⋊Q₈	C₂×D₂₉	1	2	yes	—
56	C₂×C₄⋊C₄	—	2	2	no	—
57	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
58	C₄⋊C₈	—	29	4	no	—
59	C₂²⋊C₈	—	58	2	no	—
60	#97	—	58	2	no	—
61	C₂₉	#1558	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	2	2	no	—
63	C₂×Q₈	—	4	4	no	—
64	C₂×Q₈	C₂×Dic₂₉	1	4	yes	—
65	C₂²×C₄	—	2	2	no	—
66	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
67	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
68	C₂×C₈	—	58	4	no	—
69	C₄⋊C₄	—	2	4	no	—
70	C₄⋊C₄	—	2	4	no	—
71	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
72	C₄²	C₂²⋊D₂₉	1	2	yes	—
73	C₄²	C₂²×D₂₉	1	1	yes	characteristic
74	C₂³	C₂²⋊Dic₂₉	1	1	yes	characteristic
75	Q₈	—	4	4	no	—
76	Q₈	—	4	4	no	—
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	2	4	no	—
79	C₂×C₄	—	2	4	no	—
80	C₂×C₄	—	4	4	no	—
81	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
82	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
83	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
84	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
85	C₈	—	116	4	no	—
86	C₂²	—	2	2	no	—
87	C₂²	#11745181	1	2	yes	—
88	C₂²	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	2	1	no	—
91	C₄	—	2	2	no	—
92	C₄	—	4	4	no	—
93	C₄	#11745304	1	4	yes	—
94	C₂	—	2	2	no	—
95	C₂	C₂×#11745181	1	1	yes	characteristic
96	C₂	#14271172	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂×C₂₉×C₄⋊Q₈	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₂₉	C₂²⋊C₄
cosocle	C₄²×C₂₉	C₂³
hypercenter	C₂×C₄⋊Q₈	D₂₉
hypocenter	C₂₉	#1558
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #14270912	C₂	semidirect
61. C₂₉	#1558	semidirect

Maximal subgroups

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

subgroup	index
#14271220	2
#14270912	2
C₂×C₂₉×C₄⋊Q₈	2
#1558	29