Subgroups — #46834396

Order 34688.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31774262	C₂	1	1	yes	maximal, characteristic
2	#31773675	C₂	1	1	yes	maximal, characteristic, complemented
3	#347×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#22576157	C₄	1	1	yes	characteristic
5	#22576152	C₄	1	1	yes	characteristic
6	#22576100	—	2	1	no	—
7	#22576082	—	2	1	no	—
8	#22576082	—	2	1	no	—
9	M₃₂×C₂₇₁	—	2	1	no	—
10	#97×C₂₇₁	C₂²	1	1	yes	characteristic
11	C₂×D₁₀₈₄	—	2	1	no	—
12	C₂×D₁₀₈₄	—	4	1	no	—
13	C₄⋊Dic₂₇₁	—	2	1	no	—
14	Dic₂₇₁⋊C₄	—	4	1	no	—
15	C₂₇₁⋊C₁₆	—	2	2	no	—
16	C₂×C₈×C₂₇₁	D₄	1	1	yes	characteristic
17	C₂×C₈×C₂₇₁	D₄	1	1	yes	characteristic
18	C₄²×C₂₇₁	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₂₇₁	—	2	2	no	—
20	C₂²×D₂₇₁	—	4	1	no	—
21	D₁₀₈₄	—	4	1	no	—
22	D₁₀₈₄	—	4	1	no	—
23	D₁₀₈₄	—	8	2	no	—
24	C₂×Dic₂₇₁	—	4	1	no	—
25	C₂×C₄×C₂₇₁	—	2	1	no	—
26	C₂×C₄×C₂₇₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₂₇₁	—	2	1	no	—
28	C₈×C₂₇₁	—	2	1	no	—
29	C₂²×C₂₇₁	#100	1	1	yes	characteristic
30	C₂×D₂₇₁	—	8	2	no	—
31	C₂×D₂₇₁	—	8	1	no	—
32	C₄×C₂₇₁	—	4	1	no	—
33	C₄×C₂₇₁	#104	1	1	yes	characteristic
34	C₄×C₂₇₁	#104	1	1	yes	characteristic
35	Dic₂₇₁	—	8	1	no	—
36	C₂×C₂₇₁	—	2	1	no	—
37	C₂×C₂₇₁	#329	1	1	yes	characteristic
38	D₂₇₁	—	16	1	no	—
39	C₂₇₁	#1355	1	1	yes	characteristic, complemented, Sylow
40	#1355	—	271	1	no	maximal, Sylow
41	#490	—	271	1	no	—
42	#347	—	271	1	no	—
43	#347	D₂₇₁	1	1	yes	characteristic, complemented
44	#127	—	271	1	no	—
45	#125	—	271	1	no	—
46	M₃₂	—	2	1	no	—
47	M₃₂	—	542	1	no	—
48	#102	—	542	1	no	—
49	#102	—	542	1	no	—
50	#97	C₂×D₂₇₁	1	1	yes	characteristic
51	C₂×D₄	—	542	1	no	—
52	C₂×D₄	—	1084	1	no	—
53	C₂×C₈	C₂²⋊D₂₇₁	1	1	yes	characteristic
54	C₂×C₈	D₁₀₈₄	1	1	yes	characteristic
55	C₄⋊C₄	—	542	1	no	—
56	C₄⋊C₄	—	1084	1	no	—
57	C₄²	C₄×D₂₇₁	1	1	yes	characteristic
58	C₁₆	—	2	2	no	—
59	C₁₆	—	542	2	no	—
60	C₂³	—	1084	1	no	—
61	D₄	—	1084	1	no	—
62	D₄	—	1084	1	no	—
63	D₄	—	2168	2	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	1084	1	no	—
66	C₂×C₄	(C₂×D₂₇₁)⋊C₄	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	—	2	1	no	—
69	C₂²	—	2168	2	no	—
70	C₂²	—	2168	1	no	—
71	C₂²	#22576076	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	2168	1	no	—
74	C₄	#22576086	1	1	yes	characteristic
75	C₄	#22576088	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4336	1	no	—
78	C₂	#31773636	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31773636
commutator	C₄²×C₂₇₁	C₂×C₄
Frattini	#97	C₂×D₂₇₁
Fitting	#347×C₂₇₁	C₂
socle	C₂×C₂₇₁	#329
prime radical	#22576157	C₄
cosocle	#97×C₂₇₁	C₂²
hypercenter	#347	D₂₇₁
hypocenter	C₂₇₁	#1355
LCS	G ▷ C₄²×C₂₇₁ ▷ C₂×C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

Complements

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

N	H ≅ G/N	type
2. #31773675	C₂	semidirect
3. #347×C₂₇₁	C₂	semidirect
39. C₂₇₁	#1355	semidirect
43. #347	D₂₇₁	semidirect

Maximal subgroups

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

subgroup	index
#31774262	2
#31773675	2
#347×C₂₇₁	2
#1355	271