Subgroups — C₂×#30654579 #45657489

Order 32634.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654579	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
4	C₂×#14556422	—	7	8	no	maximal
5	C₂×C₇²×C₃₇	C₉	1	1	yes	characteristic, complemented, Hall
6	#14556422	—	7	8	no	—
7	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇×C₃₇⋊C₃	ΓL(1,𝔽₈)	1	8	yes	—
9	C₂×#89204	—	37	1	no	maximal, Hall
10	C₇×C₃₇⋊C₃	C₂×ΓL(1,𝔽₈)	1	8	yes	—
11	C₂×#66526	—	49	1	no	Hall
12	C₂×C₇×C₃₇	C₇⋊C₉	1	8	yes	complemented
13	#89204	—	37	1	no	Hall
14	#66526	—	49	1	no	Hall
15	C₂×C₃×C₇²	—	37	1	no	—
16	C₇×C₃₇	C₂×C₇⋊C₉	1	8	yes	complemented
17	C₂×C₃₇⋊C₃	#3861	1	1	yes	characteristic
18	C₃×C₇²	—	37	1	no	—
19	C₂×C₇⋊C₉	—	259	8	no	—
20	C₃₇⋊C₃	C₂×#3861	1	1	yes	characteristic
21	C₂×C₇²	#66526	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃₇	#89204	1	1	yes	characteristic, complemented, Hall
23	C₇⋊C₉	—	259	8	no	—
24	C₇²	C₂×#66526	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₇	—	37	8	no	—
26	C₃₇	C₂×#89204	1	1	yes	characteristic, complemented, Sylow
27	C₃×C₇	—	37	8	no	—
28	C₂×C₉	—	1813	1	no	Hall
29	C₂×C₇	#14556422	1	8	yes	complemented
30	C₉	—	1813	1	no	Sylow
31	C₇	C₂×#14556422	1	8	yes	complemented
32	C₂×C₃	—	37	1	no	—
33	C₃	—	37	1	no	—
34	C₂	#30654579	1	1	yes	characteristic, direct product factor, Sylow

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

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