Subgroups — #46825943

Order 34432.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22575522	C₂	1	2	yes	maximal
2	C₂×C₁₆×D₂₆₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊#11761640	—	2	2	no	—
4	#22575522	—	2	2	no	—
5	#22575522	C₄	1	4	yes	complemented
6	C₂×C₈×D₂₆₉	C₂²	1	1	yes	characteristic
7	C₂×#16864377	C₄	1	1	yes	characteristic, complemented
8	C₁₆×D₂₆₉	—	2	2	no	—
9	C₂×C₁₆×C₂₆₉	C₄	1	1	yes	characteristic, complemented
10	C₂²×#11761640	—	4	2	no	—
11	C₄⋊#11761640	—	2	4	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	C₂×#11761640	—	8	2	no	—
22	C₂×#11761640	—	8	2	no	—
23	C₂²×D₂₆₉	D₈	1	1	yes	characteristic
24	C₂×Dic₂₆₉	Q₁₆	1	1	yes	characteristic
25	C₄×D₂₆₉	C₂²⋊C₄	1	2	yes	—
26	C₄×D₂₆₉	SD₁₆	1	2	yes	—
27	#14524130	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
29	C₈×C₂₆₉	C₄²	1	1	yes	characteristic
30	C₈×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₂₆₉	#107	1	1	yes	characteristic
32	C₂×D₂₆₉	#102	1	2	yes	—
33	C₂×D₂₆₉	D₁₆	1	1	yes	characteristic
34	C₂×D₂₆₉	SD₃₂	1	2	yes	—
35	C₂×D₂₆₉	Q₃₂	1	1	yes	characteristic
36	#11761640	—	8	4	no	—
37	C₄×C₂₆₉	#95	1	1	yes	characteristic
38	C₄×C₂₆₉	#106	1	1	yes	characteristic
39	Dic₂₆₉	#103	1	2	yes	—
40	C₂×C₂₆₉	#340	1	1	yes	characteristic
41	C₂×C₂₆₉	#366	1	1	yes	characteristic
42	C₂×C₂₆₉	#367	1	1	yes	characteristic
43	D₂₆₉	#357	1	2	yes	—
44	D₂₆₉	#358	1	2	yes	—
45	C₂₆₉	#1380	1	1	yes	characteristic, complemented, Sylow
46	#1380	—	269	1	no	maximal, Sylow
47	C₂²×C₁₆	—	269	1	no	—
48	C₂×#107	—	269	2	no	—
49	C₂²×C₈	—	269	1	no	—
50	C₂×C₄⋊C₄	—	538	2	no	—
51	C₂×C₁₆	—	269	1	no	—
52	C₂×C₁₆	—	538	2	no	—
53	C₂×C₁₆	#11761640	1	1	yes	characteristic, complemented
54	#107	—	269	4	no	—
55	#107	—	538	2	no	—
56	C₂²×C₄	—	269	1	no	—
57	C₂²×C₄	—	1076	2	no	—
58	C₂×C₈	—	269	1	no	—
59	C₂×C₈	—	269	2	no	—
60	C₂×C₈	—	269	2	no	—
61	C₂×C₈	C₂×#11761640	1	1	yes	characteristic
62	C₄⋊C₄	—	538	4	no	—
63	C₄⋊C₄	—	1076	2	no	—
64	C₁₆	—	2	1	no	—
65	C₁₆	—	538	1	no	—
66	C₂³	—	269	1	no	—
67	C₂×C₄	—	269	1	no	—
68	C₂×C₄	—	269	2	no	—
69	C₂×C₄	—	269	2	no	—
70	C₂×C₄	—	1076	4	no	—
71	C₂×C₄	—	2152	2	no	—
72	C₂×C₄	—	2152	2	no	—
73	C₂×C₄	C₄⋊#11761640	1	1	yes	characteristic
74	C₈	—	269	2	no	—
75	C₈	C₄×#11761640	1	1	yes	characteristic
76	C₈	C₂²⋊#11761640	1	1	yes	characteristic
77	C₂²	—	269	2	no	—
78	C₂²	—	269	1	no	—
79	C₂²	—	269	1	no	—
80	C₂²	—	269	2	no	—
81	C₂²	#22575522	1	1	yes	characteristic
82	C₄	—	269	2	no	—
83	C₄	—	2152	4	no	—
84	C₄	(C₂×#11761640)⋊C₄	1	1	yes	characteristic
85	C₄	#22575521	1	1	yes	characteristic
86	C₂	—	269	2	no	—
87	C₂	—	269	2	no	—
88	C₂	#31771479	1	1	yes	characteristic
89	C₂	#31771531	1	1	yes	characteristic
90	C₂	#31771532	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22575522
commutator	C₈×C₂₆₉	C₄²
Frattini	C₂×C₈	C₂×#11761640
Fitting	C₂×C₁₆×C₂₆₉	C₄
socle	C₂²×C₂₆₉	#107
prime radical	C₂²×D₂₆₉	D₈
cosocle	C₂×C₈×D₂₆₉	C₂²
hypercenter	C₂×C₁₆	#11761640
hypocenter	C₂₆₉	#1380
LCS	G ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
5. #22575522	C₄	semidirect
7. C₂×#16864377	C₄	semidirect
9. C₂×C₁₆×C₂₆₉	C₄	semidirect
45. C₂₆₉	#1380	semidirect
53. 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
C₂×#22575522	2
C₂×C₁₆×D₂₆₉	2
#1380	269