Subgroups — #46826014

Order 34432.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771514	C₂	1	1	yes	maximal, characteristic
2	#31771512	C₂	1	1	yes	maximal, characteristic
3	#31770997	C₂	1	1	yes	maximal, characteristic
4	#22575514	—	2	1	no	—
5	#22575512	—	2	1	no	—
6	C₂×#16864392	—	2	1	no	—
7	C₂×#16864389	—	2	1	no	—
8	#22575441	C₂²	1	1	yes	characteristic
9	#22575364	C₄	1	1	yes	characteristic, complemented
10	C₄⋊Q₈×C₂₆₉	C₄	1	1	yes	characteristic, complemented
11	#16864411	—	4	1	no	—
12	C₂²⋊#11761640	—	4	1	no	—
13	C₂×Dic₅₃₈	D₄	1	1	yes	characteristic
14	C₂×D₁₀₇₆	D₄	1	1	yes	characteristic
15	#16864392	—	4	2	no	—
16	#16864389	—	4	2	no	—
17	C₂×#14524130	—	2	1	no	—
18	#16864379	—	4	1	no	—
19	C₂×Q₈×C₂₆₉	—	2	1	no	—
20	C₄⋊C₄×C₂₆₉	—	4	1	no	—
21	C₄²×C₂₆₉	C₂×C₄	1	1	yes	characteristic
22	C₂×#11761640	—	8	1	no	—
23	#14524137	—	8	1	no	—
24	C₂²×D₂₆₉	—	2	1	no	—
25	Dic₅₃₈	—	4	1	no	—
26	D₁₀₇₆	—	4	1	no	—
27	C₂×Dic₂₆₉	—	2	1	no	—
28	#14524130	—	2	2	no	—
29	Q₈×C₂₆₉	—	4	1	no	—
30	Q₈×C₂₆₉	—	4	1	no	—
31	C₂×C₄×C₂₆₉	—	2	1	no	—
32	C₂×C₄×C₂₆₉	—	4	1	no	—
33	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂²×C₂₆₉	#99	1	1	yes	characteristic
35	C₂×D₂₆₉	—	4	1	no	—
36	C₂×D₂₆₉	—	8	1	no	—
37	#11761640	—	16	1	no	—
38	C₄×C₂₆₉	—	2	1	no	—
39	C₄×C₂₆₉	—	4	1	no	—
40	C₄×C₂₆₉	—	8	1	no	—
41	Dic₂₆₉	—	4	1	no	—
42	C₂×C₂₆₉	—	2	1	no	—
43	C₂×C₂₆₉	#353	1	1	yes	characteristic
44	D₂₆₉	—	8	1	no	—
45	C₂₆₉	#1407	1	1	yes	characteristic, complemented, Sylow
46	#1407	—	269	1	no	maximal, Sylow
47	#497	—	269	1	no	—
48	#355	—	269	1	no	—
49	#354	—	269	1	no	—
50	C₂×Q₁₆	—	538	1	no	—
51	C₂×SD₁₆	—	538	1	no	—
52	C₄⋊Q₈	#11761640	1	1	yes	characteristic, complemented
53	#124	—	269	1	no	—
54	#101	—	538	1	no	—
55	#99	—	538	1	no	—
56	#97	—	269	1	no	—
57	C₂×Q₈	—	2	1	no	—
58	C₂×Q₈	—	269	1	no	—
59	C₂×D₄	—	269	1	no	—
60	Q₁₆	—	1076	2	no	—
61	SD₁₆	—	1076	2	no	—
62	M₁₆	—	1076	1	no	—
63	C₂×C₈	—	538	1	no	—
64	C₄⋊C₄	—	4	1	no	—
65	C₂²⋊C₄	—	1076	1	no	—
66	C₂²⋊C₄	—	1076	1	no	—
67	C₄²	C₂×#11761640	1	1	yes	characteristic
68	C₂³	—	538	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	4	1	no	—
71	Q₈	—	1076	1	no	—
72	D₄	—	1076	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	538	1	no	—
76	C₂×C₄	—	2152	1	no	—
77	C₂×C₄	C₂²⋊#11761640	1	1	yes	characteristic
78	C₈	—	538	2	no	—
79	C₈	—	2152	1	no	—
80	C₂²	—	1076	1	no	—
81	C₂²	—	2152	1	no	—
82	C₂²	#22575511	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	1076	1	no	—
87	C₄	—	4304	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	2152	1	no	—
90	C₂	#31771509	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31771509
commutator	C₄²×C₂₆₉	C₂×C₄
Frattini	C₄²	C₂×#11761640
Fitting	C₄⋊Q₈×C₂₆₉	C₄
socle	C₂×C₂₆₉	#353
prime radical	C₂×D₁₀₇₆	D₄
cosocle	#22575441	C₂²
hypercenter	C₄⋊Q₈	#11761640
hypocenter	C₂₆₉	#1407
LCS	G ▷ C₄²×C₂₆₉ ▷ C₂×C₄×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
9. #22575364	C₄	semidirect
10. C₄⋊Q₈×C₂₆₉	C₄	semidirect
45. C₂₆₉	#1407	semidirect
52. C₄⋊Q₈	#11761640	semidirect

Maximal subgroups

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

subgroup	index
#31771514	2
#31771512	2
#31770997	2
#1407	269