Subgroups — #44525205

Order 30861.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779870	C₃	1	8	yes	maximal, complemented
2	C₃×#16812186	C₃	1	4	yes	maximal, complemented
3	#23779859	C₃	1	1	yes	maximal, characteristic
4	#16812186	C₃²	1	1	yes	characteristic
5	#16812186	C₃²	1	8	yes	—
6	#16812184	C₉	1	8	yes	—
7	C₃×#11765917	C₃²	1	4	yes	—
8	H(3,𝔽₃)×C₁₂₇	C₉	1	1	yes	characteristic
9	C₃²×C₁₂₇	C₃×C₉	1	4	yes	—
10	#11765917	C₃×C₉	1	8	yes	—
11	#11765917	C₃³	1	1	yes	characteristic
12	C₃×C₁₂₇	—	3	4	no	—
13	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
14	#6903	—	127	1	no	maximal, Sylow
15	C₁₂₇	#6903	1	1	yes	characteristic, complemented, Sylow
16	#737	—	127	1	no	—
17	C₂₇⋊C₃	—	127	8	no	—
18	C₃×C₂₇	—	127	4	no	—
19	3₋¹⁺²	—	127	8	no	—
20	H(3,𝔽₃)	#11765919	1	1	yes	characteristic
21	C₃×C₉	—	127	4	no	—
22	C₂₇	—	127	1	no	—
23	C₂₇	—	127	8	no	—
24	C₃²	C₃×#11765919	1	4	yes	—
25	C₉	—	127	1	no	—
26	C₉	—	127	8	no	—
27	C₃	—	3	4	no	—
28	C₃	C₃²×#11765919	1	1	yes	characteristic

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.