Subgroups — #46808956

Order 34432.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#16864377	C₂	1	1	yes	maximal, characteristic
2	#31770358	C₂	1	1	yes	maximal, characteristic
3	#335×C₂₆₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#16864377	C₄	1	1	yes	characteristic
5	C₂×#16864377	C₄	1	1	yes	characteristic
6	C₄⋊#14524130	—	2	1	no	—
7	C₄⋊C₈×C₂₆₉	—	2	1	no	—
8	C₄×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
9	C₂×#14524130	—	4	1	no	—
10	#16864377	—	2	1	no	—
11	#16864377	C₈	1	2	yes	complemented
12	C₂×C₈×C₂₆₉	—	4	1	no	—
13	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₆₉	Q₈	1	1	yes	characteristic
15	C₄²×C₂₆₉	D₄	1	1	yes	characteristic
16	#14524130	—	8	1	no	—
17	C₂×C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₆₉	D₈	1	1	yes	characteristic
19	C₂×C₄×C₂₆₉	Q₁₆	1	1	yes	characteristic
20	C₈×C₂₆₉	—	2	1	no	—
21	C₈×C₂₆₉	—	8	1	no	—
22	C₈×C₂₆₉	C₂×C₈	1	1	yes	characteristic
23	C₈×C₂₆₉	M₁₆	1	1	yes	characteristic
24	C₂²×C₂₆₉	#107	1	1	yes	characteristic
25	C₄×C₂₆₉	—	2	1	no	—
26	C₄×C₂₆₉	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₂₆₉	#108	1	1	yes	characteristic
28	C₄×C₂₆₉	D₁₆	1	1	yes	characteristic
29	C₄×C₂₆₉	Q₃₂	1	1	yes	characteristic
30	C₂×C₂₆₉	#335	1	1	yes	characteristic
31	C₂×C₂₆₉	#366	1	1	yes	characteristic
32	C₂×C₂₆₉	#368	1	1	yes	characteristic
33	C₂₆₉	#1371	1	1	yes	characteristic, complemented, Sylow
34	#1371	—	269	1	no	maximal, Sylow
35	C₄×C₁₆	—	269	1	no	—
36	#335	—	269	1	no	—
37	#335	D₂₆₉	1	1	yes	characteristic
38	C₂×C₁₆	—	269	1	no	—
39	C₂×C₁₆	—	269	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	538	1	no	—
42	C₄×C₈	C₂×D₂₆₉	1	1	yes	characteristic
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	1076	1	no	—
45	C₂×C₈	C₄×D₂₆₉	1	1	yes	characteristic
46	C₂×C₈	Dic₅₃₈	1	1	yes	characteristic
47	C₄²	C₂²⋊D₂₆₉	1	1	yes	characteristic
48	C₁₆	—	269	2	no	—
49	C₁₆	—	538	1	no	—
50	C₂×C₄	#16864381	1	1	yes	characteristic
51	C₂×C₄	#16864387	1	1	yes	characteristic
52	C₂×C₄	#16864392	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	2152	1	no	—
56	C₈	C₈×D₂₆₉	1	1	yes	characteristic
57	C₈	#16864385	1	1	yes	characteristic
58	C₂²	#22575386	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#22575382	1	1	yes	characteristic
61	C₄	#22575388	1	1	yes	characteristic
62	C₄	#22575394	1	1	yes	characteristic
63	C₄	#22575399	1	1	yes	characteristic
64	C₂	#31770357	1	1	yes	characteristic
65	C₂	#31770430	1	1	yes	characteristic
66	C₂	#31770434	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#16864387
commutator	C₈×C₂₆₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₆₉
Fitting	#335×C₂₆₉	C₂
socle, prime radical	C₂²×C₂₆₉	#107
cosocle	C₄×C₈×C₂₆₉	C₂²
hypercenter	#335	D₂₆₉
hypocenter	C₂₆₉	#1371
LCS	G ▷ C₈×C₂₆₉ ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
11. #16864377	C₈	semidirect
33. C₂₆₉	#1371	semidirect

Maximal subgroups

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

subgroup	index
C₄×#16864377	2
#31770358	2
#335×C₂₆₉	2
#1371	269