Subgroups — #46825903

Order 34432.

86 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	#31771009	C₂	1	1	yes	maximal, characteristic
4	C₂×#16864405	—	2	1	no	—
5	C₄⋊#14524137	—	2	1	no	—
6	#22575452	—	2	1	no	—
7	#22575387	C₄	1	1	yes	characteristic
8	#22575386	—	2	1	no	—
9	C₈×Dic₂₆₉	C₂²	1	1	yes	characteristic
10	#107×C₂₆₉	C₄	1	1	yes	characteristic
11	C₂×#14524137	—	4	1	no	—
12	#16864405	—	4	1	no	—
13	C₂×Dic₅₃₈	—	4	1	no	—
14	C₂×#14524130	D₄	1	1	yes	characteristic
15	C₄⋊Dic₂₆₉	—	2	1	no	—
16	#16864381	—	4	1	no	—
17	C₄×Dic₂₆₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
19	C₄⋊C₄×C₂₆₉	—	2	1	no	—
20	#14524137	—	8	1	no	—
21	Dic₅₃₈	—	8	1	no	—
22	Dic₅₃₈	—	8	1	no	—
23	C₂×Dic₂₆₉	—	4	1	no	—
24	C₂×Dic₂₆₉	D₈	1	1	yes	characteristic
25	C₂×Dic₂₆₉	SD₁₆	1	1	yes	characteristic
26	#14524130	SD₁₆	1	1	yes	characteristic
27	#14524130	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₂₆₉	—	4	1	no	—
29	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₈×C₂₆₉	—	2	1	no	—
31	C₂²×C₂₆₉	#102	1	1	yes	characteristic
32	C₄×C₂₆₉	—	8	1	no	—
33	C₄×C₂₆₉	#101	1	1	yes	characteristic
34	C₄×C₂₆₉	#103	1	1	yes	characteristic
35	Dic₂₆₉	—	2	1	no	—
36	Dic₂₆₉	—	8	1	no	—
37	Dic₂₆₉	D₁₆	1	1	yes	characteristic
38	Dic₂₆₉	SD₃₂	1	1	yes	characteristic
39	C₂×C₂₆₉	#332	1	1	yes	characteristic
40	C₂×C₂₆₉	#357	1	1	yes	characteristic
41	C₂×C₂₆₉	#362	1	1	yes	characteristic
42	C₂₆₉	#1364	1	1	yes	characteristic, complemented, Sylow
43	#1364	—	269	1	no	maximal, Sylow
44	#500	—	269	1	no	—
45	C₄⋊C₁₆	—	269	1	no	—
46	#335	—	269	1	no	—
47	C₄⋊Q₈	—	538	1	no	—
48	C₂×C₁₆	—	538	1	no	—
49	#107	—	269	1	no	—
50	#107	—	538	1	no	—
51	#107	#11761640	1	1	yes	characteristic
52	C₄⋊C₈	—	538	1	no	—
53	C₄×C₈	—	269	1	no	—
54	C₂×Q₈	—	1076	1	no	—
55	C₂×C₈	—	269	1	no	—
56	C₂×C₈	—	1076	1	no	—
57	C₂×C₈	C₂×#11761640	1	1	yes	characteristic
58	C₄⋊C₄	—	2	1	no	—
59	C₄⋊C₄	—	538	1	no	—
60	C₄⋊C₄	—	1076	1	no	—
61	C₄²	—	269	1	no	—
62	C₁₆	—	1076	1	no	—
63	Q₈	—	2152	1	no	—
64	Q₈	—	2152	1	no	—
65	C₂×C₄	—	4	1	no	—
66	C₂×C₄	—	269	1	no	—
67	C₂×C₄	—	269	1	no	—
68	C₂×C₄	—	1076	1	no	—
69	C₂×C₄	C₂²⋊#11761640	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	269	1	no	—
72	C₈	—	269	1	no	—
73	C₈	—	2152	1	no	—
74	C₂²	#22575515	1	1	yes	characteristic
75	C₄	—	8	1	no	—
76	C₄	—	269	1	no	—
77	C₄	—	269	1	no	—
78	C₄	—	538	1	no	—
79	C₄	—	2152	1	no	—
80	C₄	#22575514	1	1	yes	characteristic
81	C₄	#22575516	1	1	yes	characteristic
82	C₂	#31771464	1	1	yes	characteristic
83	C₂	#31771517	1	1	yes	characteristic
84	C₂	#31771524	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22575515
commutator	C₂×C₈×C₂₆₉	C₂×C₄
Frattini	C₂×C₈	C₂×#11761640
Fitting	#107×C₂₆₉	C₄
socle, prime radical	C₂²×C₂₆₉	#102
cosocle	C₈×Dic₂₆₉	C₂²
hypercenter	#107	#11761640
hypocenter	C₂₆₉	#1364
LCS	G ▷ C₂×C₈×C₂₆₉ ▷ C₂×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
42. C₂₆₉	#1364	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
#31771009	2
#1364	269