Subgroups — #46825803

Order 34432.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771493	C₂	1	1	yes	maximal, characteristic
2	#31771493	C₂	1	1	yes	maximal, characteristic
3	#31770327	C₂	1	1	yes	maximal, characteristic
4	C₂×#16864405	C₄	1	2	yes	—
5	C₂×#16864405	C₄	1	2	yes	—
6	C₄×#14524130	C₄	1	1	yes	characteristic
7	C₄×#14524130	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₂₆₉	C₄	1	1	yes	characteristic
9	#16864405	—	2	2	no	—
10	#16864405	C₈	1	4	yes	complemented
11	C₂×#14524130	—	2	1	no	—
12	C₂×#14524130	C₂×C₄	1	1	yes	characteristic
13	C₂×#14524130	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₆₉	—	2	1	no	—
15	C₄²×C₂₆₉	C₂×C₄	1	1	yes	characteristic
16	#14524130	—	4	1	no	—
17	#14524130	C₂×C₈	1	2	yes	—
18	#14524130	M₁₆	1	2	yes	—
19	C₂×C₄×C₂₆₉	C₄²	1	1	yes	characteristic
20	C₂×C₄×C₂₆₉	M₁₆	1	1	yes	characteristic
21	C₂×C₄×C₂₆₉	M₁₆	1	1	yes	characteristic
22	C₈×C₂₆₉	—	4	1	no	—
23	C₂²×C₂₆₉	#97	1	1	yes	characteristic
24	C₄×C₂₆₉	—	2	1	no	—
25	C₄×C₂₆₉	—	2	1	no	—
26	C₄×C₂₆₉	C₄×C₈	1	1	yes	characteristic
27	C₄×C₂₆₉	#97	1	1	yes	characteristic
28	C₂×C₂₆₉	#322	1	1	yes	characteristic
29	C₂×C₂₆₉	#347	1	1	yes	characteristic
30	C₂×C₂₆₉	#347	1	1	yes	characteristic
31	C₂₆₉	#1313	1	1	yes	characteristic, complemented, Sylow
32	#1313	—	269	1	no	maximal, Sylow
33	#346	—	269	1	no	—
34	#346	—	269	1	no	—
35	#322	—	269	1	no	—
36	C₂×C₁₆	—	269	2	no	—
37	C₂×C₁₆	—	269	2	no	—
38	C₄×C₈	—	269	1	no	—
39	C₄×C₈	—	269	1	no	—
40	C₄×C₈	#11761640	1	1	yes	characteristic
41	C₂×C₈	—	2	1	no	—
42	C₂×C₈	—	269	1	no	—
43	C₂×C₈	—	269	1	no	—
44	C₂×C₈	—	538	1	no	—
45	C₄²	C₂×#11761640	1	1	yes	characteristic
46	C₁₆	—	269	4	no	—
47	C₁₆	—	538	2	no	—
48	C₂×C₄	C₄×#11761640	1	1	yes	characteristic
49	C₂×C₄	#16864411	1	1	yes	characteristic
50	C₂×C₄	#16864412	1	1	yes	characteristic
51	C₈	—	4	1	no	—
52	C₈	—	269	2	no	—
53	C₈	—	269	2	no	—
54	C₈	—	1076	1	no	—
55	C₂²	#22575508	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	2	1	no	—
58	C₄	C₈×#11761640	1	1	yes	characteristic
59	C₄	#22575507	1	1	yes	characteristic
60	C₂	#14524137⋊C₈	1	1	yes	characteristic
61	C₂	#31771497	1	1	yes	characteristic
62	C₂	#31771498	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#11761640
commutator	C₄×C₂₆₉	C₄×C₈
Frattini	C₄²	C₂×#11761640
Fitting	C₄×C₈×C₂₆₉	C₄
socle, prime radical	C₂²×C₂₆₉	#97
cosocle	C₄×#14524130	C₂²
hypercenter	C₄×C₈	#11761640
hypocenter	C₂₆₉	#1313
LCS	G ▷ C₄×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
10. #16864405	C₈	semidirect
31. C₂₆₉	#1313	semidirect

Maximal subgroups

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

subgroup	index
#31771493	2
#31770327	2
#1313	269