Subgroups — #46825857

Order 34432.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771502	C₂	1	1	yes	maximal, characteristic
2	#31771473	C₂	1	1	yes	maximal, characteristic
3	#31770860	C₂	1	1	yes	maximal, characteristic
4	#22575532	—	2	1	no	—
5	#22575527	—	2	1	no	—
6	C₂×#16864385	C₂²	1	1	yes	characteristic
7	#22575429	—	2	1	no	—
8	#22575385	C₄	1	1	yes	characteristic, complemented
9	#22575377	—	2	1	no	—
10	C₂×Q₁₆×C₂₆₉	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#11761640	—	4	1	no	—
12	C₂²⋊#11761640	—	4	1	no	—
13	C₄×#11761640	—	2	2	no	—
14	#16864405	—	4	1	no	—
15	C₂×C₄×D₂₆₉	D₄	1	1	yes	characteristic
16	#16864385	—	4	1	no	—
17	C₂×#14524130	D₄	1	1	yes	characteristic
18	C₄⋊Dic₂₆₉	—	2	1	no	—
19	#16864381	—	4	1	no	—
20	#16864379	—	4	1	no	—
21	C₂×Q₈×C₂₆₉	—	2	1	no	—
22	Q₁₆×C₂₆₉	—	4	1	no	—
23	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
24	C₂×#11761640	—	4	2	no	—
25	C₂²×D₂₆₉	D₈	1	1	yes	characteristic
26	C₂×Dic₂₆₉	—	4	1	no	—
27	C₂×Dic₂₆₉	SD₁₆	1	1	yes	characteristic
28	C₄×D₂₆₉	—	2	1	no	—
29	C₄×D₂₆₉	—	2	1	no	—
30	#14524130	—	2	1	no	—
31	Q₈×C₂₆₉	—	4	1	no	—
32	Q₈×C₂₆₉	—	4	1	no	—
33	C₂×C₄×C₂₆₉	—	4	1	no	—
34	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₈×C₂₆₉	—	2	1	no	—
36	C₂²×C₂₆₉	#102	1	1	yes	characteristic
37	C₂×D₂₆₉	—	2	1	no	—
38	C₂×D₂₆₉	—	4	1	no	—
39	#11761640	—	8	2	no	—
40	C₄×C₂₆₉	—	8	1	no	—
41	C₄×C₂₆₉	#99	1	1	yes	characteristic
42	C₄×C₂₆₉	#104	1	1	yes	characteristic
43	Dic₂₆₉	—	2	1	no	—
44	Dic₂₆₉	—	8	1	no	—
45	C₂×C₂₆₉	—	2	1	no	—
46	C₂×C₂₆₉	#327	1	1	yes	characteristic
47	D₂₆₉	—	4	1	no	—
48	C₂₆₉	#1340	1	1	yes	characteristic, complemented, Sylow
49	#1340	—	269	1	no	maximal, Sylow
50	#470	—	269	1	no	—
51	#349	—	269	1	no	—
52	H(3,ℤ/4)	—	269	1	no	—
53	C₂×Q₁₆	#11761640	1	1	yes	characteristic, complemented
54	C₂×M₁₆	—	269	1	no	—
55	C₂²⋊Q₈	—	538	1	no	—
56	#117	—	538	1	no	—
57	M₃₂	—	538	1	no	—
58	#106	—	269	1	no	—
59	#103	—	538	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂²×C₄	—	269	1	no	—
62	Q₁₆	—	4	1	no	—
63	M₁₆	—	1076	1	no	—
64	C₂×C₈	—	269	1	no	—
65	C₂×C₈	C₂×#11761640	1	1	yes	characteristic
66	C₄⋊C₄	—	538	1	no	—
67	C₄⋊C₄	—	1076	1	no	—
68	C₄⋊C₄	—	1076	1	no	—
69	C₂²⋊C₄	—	1076	1	no	—
70	C₂²⋊C₄	—	1076	1	no	—
71	C₄²	—	538	2	no	—
72	C₁₆	—	1076	1	no	—
73	C₂³	—	269	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	4	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	269	1	no	—
78	C₂×C₄	—	538	1	no	—
79	C₂×C₄	—	538	1	no	—
80	C₂×C₄	—	1076	2	no	—
81	C₂×C₄	—	1076	1	no	—
82	C₂×C₄	C₂²⋊#11761640	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	538	1	no	—
85	C₂²	—	538	1	no	—
86	C₂²	—	1076	1	no	—
87	C₂²	#22575515	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	538	1	no	—
90	C₄	—	2152	1	no	—
91	C₄	—	2152	2	no	—
92	C₄	#22575511	1	1	yes	characteristic
93	C₄	#22575517	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	1076	1	no	—
96	C₂	#31771456	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31771456
commutator	C₂×C₈×C₂₆₉	C₂×C₄
Frattini	C₂×C₈	C₂×#11761640
Fitting	C₂×Q₁₆×C₂₆₉	C₄
socle	C₂×C₂₆₉	#327
prime radical	C₂²×D₂₆₉	D₈
cosocle	C₂×#16864385	C₂²
hypercenter	C₂×Q₁₆	#11761640
hypocenter	C₂₆₉	#1340
LCS	G ▷ C₂×C₈×C₂₆₉ ▷ C₂×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
8. #22575385	C₄	semidirect
10. C₂×Q₁₆×C₂₆₉	C₄	semidirect
48. C₂₆₉	#1340	semidirect
53. C₂×Q₁₆	#11761640	semidirect

Maximal subgroups

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

subgroup	index
#31771502	2
#31771473	2
#31770860	2
#1340	269