Subgroups — C₂×#34039231 #49183142

Order 37952.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₃₇₂	C₂	1	1	yes	maximal, characteristic
2	#34039231	C₂	1	4	yes	maximal, direct product factor
3	C₂×#23748708	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₅₉₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₁₈₆	—	2	1	no	—
6	Dic₂₃₇₂	—	2	1	no	—
7	Dic₂₃₇₂	C₂²	1	2	yes	—
8	#23748708	C₂²	1	2	yes	—
9	C₂×Q₈×C₅₉₃	—	2	1	no	—
10	Q₁₆×C₅₉₃	—	2	1	no	—
11	Q₁₆×C₅₉₃	C₂²	1	2	yes	—
12	C₂×C₈×C₅₉₃	C₂²	1	1	yes	characteristic
13	Dic₁₁₈₆	—	2	2	no	—
14	Dic₁₁₈₆	—	4	1	no	—
15	C₂×Dic₅₉₃	—	4	1	no	—
16	Q₈×C₅₉₃	—	2	2	no	—
17	Q₈×C₅₉₃	—	4	1	no	—
18	C₂×C₄×C₅₉₃	—	4	1	no	—
19	C₂×C₄×C₅₉₃	D₄	1	1	yes	characteristic
20	C₈×C₅₉₃	D₄	1	1	yes	characteristic
21	C₈×C₅₉₃	C₂³	1	1	yes	characteristic
22	C₂²×C₅₉₃	D₈	1	1	yes	characteristic
23	C₄×C₅₉₃	—	4	2	no	—
24	C₄×C₅₉₃	D₈	1	1	yes	characteristic
25	C₄×C₅₉₃	C₂×D₄	1	1	yes	characteristic
26	Dic₅₉₃	—	4	2	no	—
27	C₂×C₅₉₃	Q₃₂	1	2	yes	complemented
28	C₂×C₅₉₃	C₂×D₈	1	1	yes	characteristic
29	C₅₉₃	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₃₂	—	593	1	no	maximal, Sylow
31	C₂×Q₁₆	—	593	1	no	—
32	C₂×Q₁₆	D₅₉₃	1	1	yes	characteristic
33	Q₃₂	—	593	4	no	—
34	C₂×C₁₆	—	593	1	no	—
35	C₂×Q₈	—	2	1	no	—
36	C₂×Q₈	—	1186	1	no	—
37	Q₁₆	—	2	1	no	—
38	Q₁₆	—	593	2	no	—
39	Q₁₆	—	1186	1	no	—
40	Q₁₆	C₂×D₅₉₃	1	2	yes	—
41	C₂×C₈	C₂×D₅₉₃	1	1	yes	characteristic
42	C₁₆	—	593	2	no	—
43	Q₈	—	2	2	no	—
44	Q₈	—	4	1	no	—
45	Q₈	—	2372	1	no	—
46	Q₈	—	1186	2	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	2372	1	no	—
49	C₂×C₄	C₂²⋊D₅₉₃	1	1	yes	characteristic
50	C₈	C₂²⋊D₅₉₃	1	1	yes	characteristic
51	C₈	C₂²×D₅₉₃	1	1	yes	characteristic
52	C₂²	#23748718	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	2372	2	no	—
55	C₄	#23748718	1	1	yes	characteristic
56	C₄	C₂×C₂²⋊D₅₉₃	1	1	yes	characteristic
57	C₂	#34039231	1	2	yes	direct product factor
58	C₂	C₂×#23748718	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#23748718
commutator, cosocle	C₈×C₅₉₃	C₂³
Frattini	C₈	C₂²×D₅₉₃
Fitting	C₂×Q₁₆×C₅₉₃	C₂
socle, prime radical	C₂²×C₅₉₃	D₈
hypercenter	C₂×Q₁₆	D₅₉₃
hypocenter	C₅₉₃	C₂×Q₃₂
LCS	G ▷ C₈×C₅₉₃ ▷ C₄×C₅₉₃ ▷ C₂×C₅₉₃ ▷ C₅₉₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #34039231	C₂	direct (N × H)
27. C₂×C₅₉₃	Q₃₂	semidirect
29. C₅₉₃	C₂×Q₃₂	semidirect
57. C₂	#34039231	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₂₃₇₂	2
#34039231	2
C₂×#23748708	2
C₂×Q₁₆×C₅₉₃	2
C₂×Q₃₂	593

Subgroups — C2×#34039231 #49183142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#34039231 #49183142