Subgroups — #31825221⋊C₂ #49115331

Order 36084.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31825229	C₂	1	1	yes	maximal, characteristic, complemented
2	#31825225	C₂	1	1	yes	maximal, characteristic, complemented
3	#31825221	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₁×D₉₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	#22583233	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₀₀₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃₁×D₉₇	C₂×C₃	1	1	yes	characteristic, complemented
8	D₃₁×C₉₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃₁×C₉₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₉₇⋊C₃	—	31	1	no	maximal, Hall
11	C₂×C₉₇⋊C₃	—	31	1	no	—
12	D₉₇⋊C₃	—	31	1	no	—
13	D₉₇⋊C₃	—	31	1	no	—
14	C₂×D₉₇	—	31	1	no	Hall
15	C₂×D₃₁⋊C₃	—	97	1	no	maximal, Hall
16	C₉₇⋊C₃	—	31	1	no	Hall
17	C₂×C₉₇	—	31	1	no	—
18	D₉₇	—	31	1	no	—
19	D₉₇	D₃₁⋊C₃	1	1	yes	characteristic, complemented
20	C₂×C₃₁⋊C₃	—	97	1	no	—
21	D₃₁⋊C₃	—	97	1	no	—
22	D₃₁⋊C₃	—	97	1	no	—
23	C₂×D₃₁	—	97	1	no	Hall
24	C₉₇	C₂×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃₁⋊C₃	—	97	1	no	Hall
26	C₂×C₃₁	—	97	1	no	—
27	D₃₁	—	97	1	no	—
28	D₃₁	D₉₇⋊C₃	1	1	yes	characteristic, complemented
29	C₃₁	C₂×D₉₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	3007	1	no	Hall
31	C₂×C₃	—	3007	1	no	—
32	C₂×C₃	—	3007	1	no	—
33	C₂×C₃	—	3007	1	no	—
34	C₂²	—	3007	1	no	Sylow
35	C₃	—	3007	1	no	Sylow
36	C₂	—	31	1	no	—
37	C₂	—	97	1	no	—
38	C₂	—	3007	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₁×C₉₇	C₂²×C₃
LCS	G ▷ C₃₁×C₉₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #31825229	C₂	semidirect
2. #31825225	C₂	semidirect
3. #31825221	C₂	semidirect
4. D₃₁×D₉₇	C₃	semidirect
5. #22583233	C₂²	semidirect
6. D₃₀₀₇	C₂×C₃	semidirect
7. C₃₁×D₉₇	C₂×C₃	semidirect
8. D₃₁×C₉₇	C₂×C₃	semidirect
9. C₃₁×C₉₇	C₂²×C₃	semidirect
19. D₉₇	D₃₁⋊C₃	semidirect
24. C₉₇	C₂×D₃₁⋊C₃	semidirect
28. D₃₁	D₉₇⋊C₃	semidirect
29. C₃₁	C₂×D₉₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#31825229	2
#31825225	2
#31825221	2
D₃₁×D₉₇	3
C₂×D₉₇⋊C₃	31
C₂×D₃₁⋊C₃	97

Subgroups — #31825221⋊C2 #49115331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #31825221⋊C₂ #49115331