Subgroups — #46825953

Order 34432.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771615	C₂	1	2	yes	maximal
2	C₂×#22575392	C₂	1	1	yes	maximal, characteristic
3	#22575532	—	2	2	no	—
4	#22575522	—	2	2	no	—
5	#22575521	C₄	1	4	yes	complemented
6	C₂×C₈×D₂₆₉	C₂²	1	1	yes	characteristic
7	#22575392	—	2	2	no	—
8	C₂×#16864377	C₄	1	1	yes	characteristic, complemented
9	C₂×C₁₆×C₂₆₉	C₄	1	1	yes	characteristic, complemented
10	C₄⋊#11761640	—	2	4	no	—
11	C₂²⋊#11761640	—	4	2	no	—
12	C₄×#11761640	—	4	2	no	—
13	C₂×C₄×D₂₆₉	D₄	1	1	yes	characteristic
14	C₂×#14524130	Q₈	1	1	yes	characteristic
15	C₈×D₂₆₉	C₂×C₄	1	2	yes	—
16	C₈×D₂₆₉	D₄	1	2	yes	—
17	#16864377	—	2	1	no	—
18	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₂₆₉	—	2	1	no	—
20	C₂×#11761640	—	4	4	no	—
21	C₂²×D₂₆₉	D₈	1	1	yes	characteristic
22	C₂×Dic₂₆₉	Q₁₆	1	1	yes	characteristic
23	C₄×D₂₆₉	C₂²⋊C₄	1	2	yes	—
24	C₄×D₂₆₉	SD₁₆	1	2	yes	—
25	#14524130	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
27	C₈×C₂₆₉	C₄²	1	1	yes	characteristic
28	C₈×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₂₆₉	#107	1	1	yes	characteristic
30	C₂×D₂₆₉	—	4	1	no	—
31	C₂×D₂₆₉	#102	1	2	yes	—
32	#11761640	—	8	4	no	—
33	C₄×C₂₆₉	#95	1	1	yes	characteristic
34	C₄×C₂₆₉	#106	1	1	yes	characteristic
35	Dic₂₆₉	#103	1	2	yes	—
36	C₂×C₂₆₉	—	2	1	no	—
37	C₂×C₂₆₉	#340	1	1	yes	characteristic
38	D₂₆₉	—	2	2	no	—
39	C₂₆₉	#1384	1	1	yes	characteristic, complemented, Sylow
40	#1384	—	269	1	no	maximal, Sylow
41	C₂×M₃₂	—	269	1	no	—
42	#427	—	269	2	no	—
43	C₂²×C₈	—	269	1	no	—
44	#117	—	538	2	no	—
45	M₃₂	—	538	2	no	—
46	C₂×C₁₆	—	269	1	no	—
47	C₂×C₁₆	#11761640	1	1	yes	characteristic, complemented
48	#107	—	538	2	no	—
49	#106	—	269	4	no	—
50	C₂²×C₄	—	269	1	no	—
51	C₂×C₈	—	269	1	no	—
52	C₂×C₈	—	269	2	no	—
53	C₂×C₈	—	269	2	no	—
54	C₂×C₈	C₂×#11761640	1	1	yes	characteristic
55	C₄⋊C₄	—	538	4	no	—
56	C₂²⋊C₄	—	1076	2	no	—
57	C₄²	—	1076	2	no	—
58	C₁₆	—	2	1	no	—
59	C₁₆	—	538	1	no	—
60	C₂³	—	269	1	no	—
61	C₂×C₄	—	269	1	no	—
62	C₂×C₄	—	269	2	no	—
63	C₂×C₄	—	269	2	no	—
64	C₂×C₄	—	1076	4	no	—
65	C₂×C₄	C₄⋊#11761640	1	1	yes	characteristic
66	C₈	—	269	2	no	—
67	C₈	C₄×#11761640	1	1	yes	characteristic
68	C₈	C₂²⋊#11761640	1	1	yes	characteristic
69	C₂²	—	269	2	no	—
70	C₂²	—	1076	1	no	—
71	C₂²	#22575522	1	1	yes	characteristic
72	C₄	—	269	2	no	—
73	C₄	—	2152	4	no	—
74	C₄	(C₂×#11761640)⋊C₄	1	1	yes	characteristic
75	C₄	#22575521	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	538	2	no	—
78	C₂	#31771479	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#22575521
commutator	C₈×C₂₆₉	C₄²
Frattini	C₂×C₈	C₂×#11761640
Fitting	C₂×C₁₆×C₂₆₉	C₄
socle	C₂×C₂₆₉	#340
prime radical	C₂²×D₂₆₉	D₈
cosocle	C₂×C₈×D₂₆₉	C₂²
hypercenter	C₂×C₁₆	#11761640
hypocenter	C₂₆₉	#1384
LCS	G ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
5. #22575521	C₄	semidirect
8. C₂×#16864377	C₄	semidirect
9. C₂×C₁₆×C₂₆₉	C₄	semidirect
39. C₂₆₉	#1384	semidirect
47. C₂×C₁₆	#11761640	semidirect

Maximal subgroups

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

subgroup	index
#31771615	2
C₂×#22575392	2
#1384	269