Subgroups — #47982916

Order 35456.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22579791	C₂	1	2	yes	maximal
2	#31799757	C₂	1	4	yes	maximal
3	C₄³×C₂₇₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#14555660	C₂²	1	4	yes	—
5	#22579791	C₄	1	8	yes	complemented
6	C₂×C₄²×C₂₇₇	C₄	1	4	yes	—
7	C₂×C₄²×C₂₇₇	C₂²	1	2	yes	—
8	C₂×C₄²×C₂₇₇	C₂²	1	1	yes	characteristic
9	C₂×#14555660	—	2	8	no	—
10	C₂×#14555660	C₂×C₄	1	8	yes	—
11	C₂²×C₄×C₂₇₇	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₂₇₇	C₂×C₄	1	4	yes	—
13	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
14	C₄²×C₂₇₇	—	2	8	no	—
15	C₄²×C₂₇₇	—	2	4	no	—
16	C₄²×C₂₇₇	C₂×C₄	1	4	yes	—
17	#14555660	—	2	8	no	—
18	C₂³×C₂₇₇	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₄×C₂₇₇	—	2	4	no	—
20	C₂×C₄×C₂₇₇	—	2	4	no	—
21	C₂×C₄×C₂₇₇	—	2	4	no	—
22	C₂×C₄×C₂₇₇	C₄²	1	4	yes	—
23	C₂×C₄×C₂₇₇	M₁₆	1	8	yes	—
24	C₂×C₄×C₂₇₇	C₂²×C₄	1	2	yes	—
25	C₂×C₄×C₂₇₇	#41	1	4	yes	—
26	C₂²×C₂₇₇	C₂×C₄²	1	1	yes	characteristic
27	C₂²×C₂₇₇	#117	1	2	yes	—
28	C₂²×C₂₇₇	C₂×M₁₆	1	4	yes	—
29	C₄×C₂₇₇	—	2	4	no	—
30	C₄×C₂₇₇	—	2	8	no	—
31	C₄×C₂₇₇	#117	1	4	yes	—
32	C₂×C₂₇₇	#376	1	1	yes	characteristic
33	C₂×C₂₇₇	C₄×M₁₆	1	2	yes	—
34	C₂×C₂₇₇	#432	1	4	yes	—
35	C₂₇₇	#1745	1	1	yes	characteristic, complemented, Sylow
36	#1745	—	277	1	no	maximal, Sylow
37	C₂×#97	—	277	2	no	—
38	C₄³	D₂₇₇	1	1	yes	characteristic
39	#336	—	277	4	no	—
40	C₂²×C₈	—	277	4	no	—
41	C₂×C₄²	Dic₂₇₇	1	4	yes	—
42	C₂×C₄²	C₂×D₂₇₇	1	2	yes	—
43	C₂×C₄²	C₂×D₂₇₇	1	1	yes	characteristic
44	#97	—	277	8	no	—
45	C₂²×C₄	C₂×Dic₂₇₇	1	2	yes	—
46	C₂²×C₄	C₂×Dic₂₇₇	1	4	yes	—
47	C₂²×C₄	C₂²×D₂₇₇	1	1	yes	characteristic
48	C₂×C₈	—	277	8	no	—
49	C₂×C₈	—	554	8	no	—
50	C₄²	—	2	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	C₄×D₂₇₇	1	4	yes	—
53	C₂³	C₂²×Dic₂₇₇	1	1	yes	characteristic
54	C₂×C₄	—	2	4	no	—
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	C₄×Dic₂₇₇	1	4	yes	—
58	C₂×C₄	#17984547	1	8	yes	—
59	C₂×C₄	C₂×C₄×D₂₇₇	1	2	yes	—
60	C₂×C₄	#17984563	1	4	yes	—
61	C₈	—	554	8	no	—
62	C₂²	C₂×C₄×Dic₂₇₇	1	1	yes	characteristic
63	C₂²	#22579839	1	2	yes	—
64	C₂²	C₂×#17984547	1	4	yes	—
65	C₄	—	2	4	no	—
66	C₄	—	2	8	no	—
67	C₄	#22579837	1	4	yes	—
68	C₂	#31799848	1	1	yes	characteristic
69	C₂	C₄×#17984547	1	2	yes	—
70	C₂	#31800059	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₇₇
commutator	C₂²×C₂₇₇	C₂×C₄²
Fitting	C₄³×C₂₇₇	C₂
socle, prime radical	C₂³×C₂₇₇	C₂²×C₄
cosocle	C₂²×C₄×C₂₇₇	C₂³
hypercenter	C₄³	D₂₇₇
hypocenter	C₂₇₇	#1745
LCS	G ▷ C₂²×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
5. #22579791	C₄	semidirect
35. C₂₇₇	#1745	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22579791	2
#31799757	2
C₄³×C₂₇₇	2
#1745	277