Subgroups — Q₃₂×D₃₇₉ #37565670

Order 24256.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₃₇₉	C₂	1	2	yes	maximal
2	Dic₃₀₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#27131277	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₃₇₉	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₃₇₉	—	2	2	no	—
7	Dic₁₅₁₆	C₂²	1	2	yes	—
8	#20258596	—	2	2	no	—
9	C₈×D₃₇₉	C₂²	1	1	yes	characteristic
10	C₃₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
11	Q₁₆×C₃₇₉	C₂²	1	2	yes	—
12	C₁₆×C₃₇₉	C₂²	1	1	yes	characteristic
13	Dic₇₅₈	—	2	2	no	—
14	Dic₇₅₈	—	4	2	no	—
15	C₄×D₃₇₉	—	4	2	no	—
16	C₄×D₃₇₉	D₄	1	1	yes	characteristic
17	C₃₇₉⋊C₈	D₄	1	1	yes	characteristic
18	Q₈×C₃₇₉	—	2	2	no	—
19	C₈×C₃₇₉	C₂³	1	1	yes	characteristic
20	C₂×D₃₇₉	D₈	1	1	yes	characteristic
21	C₄×C₃₇₉	—	4	2	no	—
22	C₄×C₃₇₉	C₂×D₄	1	1	yes	characteristic
23	Dic₃₇₉	—	4	2	no	—
24	Dic₃₇₉	D₈	1	1	yes	characteristic
25	C₂×C₃₇₉	C₂×D₈	1	1	yes	characteristic
26	D₃₇₉	Q₃₂	1	2	yes	direct product factor
27	C₃₇₉	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₃₂	—	379	1	no	maximal, Sylow
29	C₂×Q₁₆	—	379	2	no	—
30	Q₃₂	—	379	2	no	—
31	Q₃₂	—	379	1	no	—
32	Q₃₂	D₃₇₉	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	379	1	no	—
34	C₂×Q₈	—	758	2	no	—
35	Q₁₆	—	379	2	no	—
36	Q₁₆	—	758	2	no	—
37	Q₁₆	C₂×D₃₇₉	1	2	yes	—
38	C₂×C₈	—	379	1	no	—
39	C₁₆	—	379	1	no	—
40	C₁₆	C₂×D₃₇₉	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	1516	2	no	—
43	Q₈	—	758	2	no	—
44	C₂×C₄	—	379	1	no	—
45	C₂×C₄	—	1516	2	no	—
46	C₈	—	379	1	no	—
47	C₈	C₂²×D₃₇₉	1	1	yes	characteristic
48	C₂²	—	379	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	379	1	no	—
51	C₄	—	1516	2	no	—
52	C₄	D₄×D₃₇₉	1	1	yes	characteristic
53	C₂	—	379	2	no	—
54	C₂	D₈×D₃₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₃₇₉
commutator, cosocle	C₈×C₃₇₉	C₂³
Frattini	C₈	C₂²×D₃₇₉
Fitting	Q₃₂×C₃₇₉	C₂
socle	C₂×C₃₇₉	C₂×D₈
prime radical	C₂×D₃₇₉	D₈
hypercenter	Q₃₂	D₃₇₉
hypocenter	C₃₇₉	C₂×Q₃₂
LCS	G ▷ C₈×C₃₇₉ ▷ C₄×C₃₇₉ ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₃₀₃₂	C₂	semidirect
3. #27131277	C₂	semidirect
5. Q₃₂×C₃₇₉	C₂	semidirect
26. D₃₇₉	Q₃₂	direct (N × H)
27. C₃₇₉	C₂×Q₃₂	semidirect
32. Q₃₂	D₃₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₁₆×D₃₇₉	2
Dic₃₀₃₂	2
#27131277	2
C₁₆×D₃₇₉	2
Q₃₂×C₃₇₉	2
C₂×Q₃₂	379

Subgroups — Q32×D379 #37565670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₃₂×D₃₇₉ #37565670