Subgroups — #46825900

Order 34432.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771526	C₂	1	1	yes	maximal, characteristic
2	#31771469	C₂	1	1	yes	maximal, characteristic
3	#31770983	C₂	1	1	yes	maximal, characteristic
4	C₂×#16864405	—	2	1	no	—
5	C₄⋊#14524137	—	2	1	no	—
6	C₂×Dic₁₀₇₆	C₄	1	1	yes	characteristic
7	C₂×#16864392	—	2	1	no	—
8	#22575451	—	2	1	no	—
9	C₈×Dic₂₆₉	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₂₆₉	C₄	1	1	yes	characteristic
11	C₂×#14524137	—	4	1	no	—
12	#16864405	—	4	1	no	—
13	C₂×Dic₅₃₈	—	2	1	no	—
14	Dic₁₀₇₆	—	4	1	no	—
15	#16864392	—	4	1	no	—
16	#16864392	—	4	1	no	—
17	C₂×#14524130	D₄	1	1	yes	characteristic
18	#16864381	—	4	1	no	—
19	#16864381	—	4	1	no	—
20	C₄×Dic₂₆₉	D₄	1	1	yes	characteristic
21	C₂×Q₈×C₂₆₉	—	2	1	no	—
22	Q₁₆×C₂₆₉	—	4	1	no	—
23	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
24	#14524137	—	8	1	no	—
25	Dic₅₃₈	—	4	1	no	—
26	Dic₅₃₈	—	4	1	no	—
27	C₂×Dic₂₆₉	—	4	1	no	—
28	C₂×Dic₂₆₉	D₈	1	1	yes	characteristic
29	C₂×Dic₂₆₉	SD₁₆	1	1	yes	characteristic
30	#14524130	D₈	1	1	yes	characteristic
31	#14524130	SD₁₆	1	1	yes	characteristic
32	Q₈×C₂₆₉	—	4	1	no	—
33	Q₈×C₂₆₉	—	4	1	no	—
34	C₂×C₄×C₂₆₉	—	4	1	no	—
35	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₈×C₂₆₉	—	2	1	no	—
37	C₂²×C₂₆₉	#102	1	1	yes	characteristic
38	C₄×C₂₆₉	—	8	1	no	—
39	C₄×C₂₆₉	#100	1	1	yes	characteristic
40	C₄×C₂₆₉	#102	1	1	yes	characteristic
41	Dic₂₆₉	—	2	1	no	—
42	Dic₂₆₉	—	8	1	no	—
43	Dic₂₆₉	SD₃₂	1	1	yes	characteristic
44	Dic₂₆₉	Q₃₂	1	1	yes	characteristic
45	C₂×C₂₆₉	#331	1	1	yes	characteristic
46	C₂×C₂₆₉	#358	1	1	yes	characteristic
47	C₂×C₂₆₉	#362	1	1	yes	characteristic
48	C₂₆₉	#1362	1	1	yes	characteristic, complemented, Sylow
49	#1362	—	269	1	no	maximal, Sylow
50	#494	—	269	1	no	—
51	C₄⋊C₁₆	—	269	1	no	—
52	#335	—	269	1	no	—
53	C₂×Q₁₆	—	269	1	no	—
54	C₂×Q₁₆	—	538	1	no	—
55	C₂×Q₁₆	#11761640	1	1	yes	characteristic
56	C₄⋊Q₈	—	538	1	no	—
57	C₂×C₁₆	—	538	1	no	—
58	C₄⋊C₈	—	538	1	no	—
59	C₄×C₈	—	269	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	538	1	no	—
62	Q₁₆	—	4	1	no	—
63	Q₁₆	—	1076	1	no	—
64	Q₁₆	—	1076	1	no	—
65	Q₁₆	—	1076	1	no	—
66	C₂×C₈	—	269	1	no	—
67	C₂×C₈	—	1076	1	no	—
68	C₂×C₈	C₂×#11761640	1	1	yes	characteristic
69	C₄⋊C₄	—	1076	1	no	—
70	C₄⋊C₄	—	1076	1	no	—
71	C₄²	—	269	1	no	—
72	C₁₆	—	1076	1	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	1076	1	no	—
76	Q₈	—	1076	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	269	1	no	—
79	C₂×C₄	—	269	1	no	—
80	C₂×C₄	—	1076	1	no	—
81	C₂×C₄	C₂²⋊#11761640	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	269	1	no	—
84	C₈	—	269	1	no	—
85	C₈	—	2152	1	no	—
86	C₂²	#22575515	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	269	1	no	—
89	C₄	—	269	1	no	—
90	C₄	—	538	1	no	—
91	C₄	—	2152	1	no	—
92	C₄	#22575513	1	1	yes	characteristic
93	C₄	#22575515	1	1	yes	characteristic
94	C₂	#31771463	1	1	yes	characteristic
95	C₂	#31771518	1	1	yes	characteristic
96	C₂	#31771524	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22575515
commutator	C₂×C₈×C₂₆₉	C₂×C₄
Frattini	C₂×C₈	C₂×#11761640
Fitting	C₂×Q₁₆×C₂₆₉	C₄
socle, prime radical	C₂²×C₂₆₉	#102
cosocle	C₈×Dic₂₆₉	C₂²
hypercenter	C₂×Q₁₆	#11761640
hypocenter	C₂₆₉	#1362
LCS	G ▷ C₂×C₈×C₂₆₉ ▷ C₂×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
48. C₂₆₉	#1362	semidirect

Maximal subgroups

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

subgroup	index
#31771526	2
#31771469	2
#31770983	2
#1362	269