Subgroups — #46825955

Order 34432.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₆₉⋊#108	C₂	1	2	yes	maximal
2	C₂×#22575392	C₂	1	1	yes	maximal, characteristic
3	D₂₆₉⋊M₁₆	—	2	2	no	—
4	#22575524	—	2	2	no	—
5	#22575523	C₄	1	4	yes	—
6	C₂×C₈×D₂₆₉	C₂²	1	1	yes	characteristic
7	#22575392	—	2	2	no	—
8	C₂×#16864377	C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₂₆₉	C₄	1	1	yes	characteristic
10	#16864412	—	2	4	no	—
11	#16864411	—	4	2	no	—
12	D₂₆₉⋊C₈	—	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	#14524137	—	4	4	no	—
21	C₂²×D₂₆₉	Q₁₆	1	1	yes	characteristic
22	C₂×Dic₂₆₉	D₈	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	#103	1	2	yes	—
32	C₄×C₂₆₉	#95	1	1	yes	characteristic
33	C₄×C₂₆₉	#106	1	1	yes	characteristic
34	Dic₂₆₉	#102	1	2	yes	—
35	C₂×C₂₆₉	—	2	1	no	—
36	C₂×C₂₆₉	#340	1	1	yes	characteristic
37	D₂₆₉	—	2	2	no	—
38	C₂₆₉	#1385	1	1	yes	characteristic, complemented, Sylow
39	#1385	—	269	1	no	maximal, Sylow
40	C₂×M₃₂	—	269	1	no	—
41	C₂×#108	—	269	2	no	—
42	C₂×M₁₆	—	538	2	no	—
43	C₂²×C₈	—	269	1	no	—
44	M₃₂	—	538	2	no	—
45	C₂×C₁₆	—	269	1	no	—
46	C₂×C₁₆	#11761640	1	1	yes	characteristic
47	#108	—	269	4	no	—
48	#108	—	538	2	no	—
49	C₂²×C₄	—	269	1	no	—
50	M₁₆	—	538	4	no	—
51	M₁₆	—	1076	2	no	—
52	C₂×C₈	—	269	1	no	—
53	C₂×C₈	—	269	2	no	—
54	C₂×C₈	—	269	2	no	—
55	C₂×C₈	—	1076	2	no	—
56	C₂×C₈	C₂×#11761640	1	1	yes	characteristic
57	C₁₆	—	2	1	no	—
58	C₁₆	—	538	1	no	—
59	C₂³	—	269	1	no	—
60	C₂×C₄	—	269	1	no	—
61	C₂×C₄	—	269	2	no	—
62	C₂×C₄	—	269	2	no	—
63	C₂×C₄	C₄⋊#11761640	1	1	yes	characteristic
64	C₈	—	269	2	no	—
65	C₈	—	1076	4	no	—
66	C₈	C₄×#11761640	1	1	yes	characteristic
67	C₈	C₂²⋊#11761640	1	1	yes	characteristic
68	C₂²	—	269	2	no	—
69	C₂²	—	1076	1	no	—
70	C₂²	#22575522	1	1	yes	characteristic
71	C₄	—	269	2	no	—
72	C₄	(C₂×#11761640)⋊C₄	1	1	yes	characteristic
73	C₄	#22575521	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	538	2	no	—
76	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	Q₁₆
cosocle	C₂×C₈×D₂₆₉	C₂²
hypercenter	C₂×C₁₆	#11761640
hypocenter	C₂₆₉	#1385
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
38. C₂₆₉	#1385	semidirect

Maximal subgroups

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

subgroup	index
D₂₆₉⋊#108	2
C₂×#22575392	2
#1385	269