Subgroups — #46825820

Order 34432.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771501	C₂	1	2	yes	maximal, complemented
2	#31770571	C₂	1	1	yes	maximal, characteristic
3	#22575527	—	2	2	no	—
4	C₂×#16864402	C₄	1	1	yes	characteristic
5	C₂×#16864386	C₂²	1	1	yes	characteristic
6	#22575365	—	2	2	no	—
7	C₂²×C₈×C₂₆₉	C₄	1	1	yes	characteristic
8	#16864405	—	4	2	no	—
9	#16864402	—	4	1	no	—
10	#16864402	—	4	1	no	—
11	C₂×Dic₅₃₈	C₈	1	1	yes	characteristic
12	C₂×D₁₀₇₆	C₈	1	1	yes	characteristic
13	C₂×C₂²⋊D₂₆₉	—	2	1	no	—
14	C₂×C₄×D₂₆₉	—	2	1	no	—
15	#16864386	—	4	1	no	—
16	C₂×#14524130	D₄	1	2	yes	—
17	C₂²×C₄×C₂₆₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₂₆₉	—	2	1	no	—
19	C₂×C₈×C₂₆₉	—	4	1	no	—
20	C₂²×D₂₆₉	—	2	1	no	—
21	Dic₅₃₈	—	4	1	no	—
22	D₁₀₇₆	—	4	1	no	—
23	C₂²⋊D₂₆₉	—	4	2	no	—
24	C₂×Dic₂₆₉	—	2	1	no	—
25	C₄×D₂₆₉	—	4	1	no	—
26	C₄×D₂₆₉	—	4	1	no	—
27	#14524130	—	2	2	no	—
28	C₂³×C₂₆₉	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₂₆₉	—	2	1	no	—
30	C₂×C₄×C₂₆₉	—	2	1	no	—
31	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₆₉	C₂×C₈	1	1	yes	characteristic
33	C₈×C₂₆₉	—	4	1	no	—
34	C₂²×C₂₆₉	—	2	1	no	—
35	C₂²×C₂₆₉	—	4	1	no	—
36	C₂²×C₂₆₉	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₂₆₉	—	4	2	no	—
38	C₂×D₂₆₉	—	4	1	no	—
39	C₄×C₂₆₉	—	2	1	no	—
40	C₄×C₂₆₉	#99	1	1	yes	characteristic
41	C₄×C₂₆₉	#100	1	1	yes	characteristic
42	Dic₂₆₉	—	4	1	no	—
43	C₂×C₂₆₉	—	2	1	no	—
44	C₂×C₂₆₉	—	4	1	no	—
45	C₂×C₂₆₉	#323	1	1	yes	characteristic
46	D₂₆₉	—	8	1	no	—
47	C₂₆₉	#1321	1	1	yes	characteristic, complemented, Sylow
48	#1321	—	269	1	no	maximal, Sylow
49	#408	—	269	1	no	—
50	#349	—	269	2	no	—
51	C₂×#41	—	269	1	no	—
52	C₂×M₁₆	—	269	1	no	—
53	C₂²×C₈	#11761640	1	1	yes	characteristic
54	M₃₂	—	538	2	no	—
55	C₂²⋊C₈	—	538	2	no	—
56	#41	—	1076	1	no	—
57	#41	—	1076	1	no	—
58	C₂×Q₈	—	269	1	no	—
59	C₂×D₄	—	269	1	no	—
60	C₂×D₄	—	538	1	no	—
61	C₂²×C₄	—	538	1	no	—
62	C₂²×C₄	C₂×#11761640	1	1	yes	characteristic
63	M₁₆	—	1076	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	4	1	no	—
66	C₂×C₈	—	269	2	no	—
67	C₁₆	—	1076	2	no	—
68	C₂³	—	538	1	no	—
69	C₂³	#16864412	1	1	yes	characteristic
70	Q₈	—	1076	1	no	—
71	D₄	—	1076	1	no	—
72	D₄	—	1076	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	538	1	no	—
76	C₂×C₄	—	1076	1	no	—
77	C₂×C₄	—	1076	1	no	—
78	C₂×C₄	C₂²⋊#11761640	1	1	yes	characteristic
79	C₂×C₄	D₂₆₉⋊C₈	1	1	yes	characteristic
80	C₈	—	4	1	no	—
81	C₈	—	538	2	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	1076	2	no	—
85	C₂²	—	1076	1	no	—
86	C₂²	#22575510	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	1076	1	no	—
89	C₄	#22575512	1	1	yes	characteristic
90	C₄	#22575513	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	4	1	no	—
93	C₂	—	2152	1	no	—
94	C₂	#31771449	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#22575512
commutator	C₂×C₄×C₂₆₉	C₂×C₈
Frattini	C₂²×C₄	C₂×#11761640
Fitting	C₂²×C₈×C₂₆₉	C₄
socle	C₂×C₂₆₉	#323
prime radical	C₂×#16864402	C₄
cosocle	C₂×#16864386	C₂²
hypercenter	C₂²×C₈	#11761640
hypocenter	C₂₆₉	#1321
LCS	G ▷ C₂×C₄×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. #31771501	C₂	semidirect
47. C₂₆₉	#1321	semidirect

Maximal subgroups

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

subgroup	index
#31771501	2
#31770571	2
#1321	269