Subgroups — C₂×#34038920 #49181601

Order 37926.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34038920	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₇²×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
4	C₂×#14582151	—	7	8	no	maximal
5	C₂×C₇²×C₄₃	C₉	1	1	yes	characteristic, complemented, Hall
6	#14582151	—	7	8	no	—
7	C₇²×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₇×C₄₃	ΓL(1,𝔽₈)	1	8	yes	—
9	C₃×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	8	yes	—
10	C₂×#89204	—	43	1	no	maximal, Hall
11	C₂×C₄₃⋊C₉	—	49	1	no	Hall
12	C₂×C₇×C₄₃	C₇⋊C₉	1	8	yes	complemented
13	#89204	—	43	1	no	Hall
14	C₄₃⋊C₉	—	49	1	no	Hall
15	C₇×C₄₃	C₂×C₇⋊C₉	1	8	yes	complemented
16	C₂×C₃×C₇²	C₄₃⋊C₃	1	1	yes	characteristic
17	C₂×C₃×C₄₃	#3861	1	1	yes	characteristic
18	C₃×C₇²	C₂×C₄₃⋊C₃	1	1	yes	characteristic
19	C₃×C₄₃	C₂×#3861	1	1	yes	characteristic
20	C₂×C₇⋊C₉	—	301	8	no	—
21	C₂×C₇²	C₄₃⋊C₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₄₃	#89204	1	1	yes	characteristic, complemented, Hall
23	C₇⋊C₉	—	301	8	no	—
24	C₇²	C₂×C₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
25	C₄₃	C₂×#89204	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×C₇	#11744749	1	8	yes	—
27	C₃×C₇	C₂×#11744749	1	8	yes	—
28	C₂×C₉	—	2107	1	no	Hall
29	C₂×C₇	#14582151	1	8	yes	complemented
30	C₉	—	2107	1	no	Sylow
31	C₇	C₂×#14582151	1	8	yes	complemented
32	C₂×C₃	#20263479	1	1	yes	characteristic
33	C₃	C₂×#20263479	1	1	yes	characteristic
34	C₂	#34038920	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃	#20263479
commutator, hypocenter	C₇²×C₄₃	C₂×C₉
Frattini	C₃	C₂×#20263479
Fitting, socle, prime radical	C₂×C₃×C₇²×C₄₃	C₃
cosocle	C₃×C₇²×C₄₃	C₂×C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. #34038920	C₂	direct (N × H)
5. C₂×C₇²×C₄₃	C₉	semidirect
7. C₇²×C₄₃	C₂×C₉	semidirect
12. C₂×C₇×C₄₃	C₇⋊C₉	semidirect
15. C₇×C₄₃	C₂×C₇⋊C₉	semidirect
21. C₂×C₇²	C₄₃⋊C₉	semidirect
22. C₂×C₄₃	#89204	semidirect
24. C₇²	C₂×C₄₃⋊C₉	semidirect
25. C₄₃	C₂×#89204	semidirect
29. C₂×C₇	#14582151	semidirect
31. C₇	C₂×#14582151	semidirect
34. C₂	#34038920	direct (N × H)

Maximal subgroups

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

subgroup	index
#34038920	2
C₂×C₃×C₇²×C₄₃	3
C₂×#14582151	7
C₂×#89204	43

Subgroups — C2×#34038920 #49181601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#34038920 #49181601