Subgroups — #30638875

Order 16256.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22549631	C₂	1	6	yes	maximal
2	#376×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₂₇⋊C₈	C₂²	1	4	yes	—
4	C₂×C₄²×C₁₂₇	C₂²	1	3	yes	—
5	#95×C₁₂₇	C₄	1	4	yes	—
6	C₂×C₁₂₇⋊C₈	—	2	12	no	—
7	C₂²×C₄×C₁₂₇	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
9	C₄²×C₁₂₇	—	2	6	no	—
10	C₁₂₇⋊C₈	—	4	4	no	—
11	C₂³×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₂₇	—	2	6	no	—
13	C₂×C₄×C₁₂₇	—	2	12	no	—
14	C₂×C₄×C₁₂₇	#41	1	6	yes	—
15	C₂²×C₁₂₇	#117	1	3	yes	—
16	C₂²×C₁₂₇	#131	1	4	yes	—
17	C₄×C₁₂₇	—	4	6	no	—
18	C₄×C₁₂₇	#126	1	4	yes	—
19	C₂×C₁₂₇	#383	1	1	yes	characteristic
20	C₂×C₁₂₇	#433	1	6	yes	—
21	#1840	—	127	1	no	maximal, Sylow
22	C₁₂₇	#1840	1	1	yes	characteristic, complemented, Sylow
23	#376	D₁₂₇	1	1	yes	characteristic
24	#336	—	127	6	no	—
25	C₂²×C₈	—	127	4	no	—
26	C₂×C₄²	C₂×D₁₂₇	1	3	yes	—
27	#95	Dic₁₂₇	1	4	yes	—
28	C₂²×C₄	C₂×Dic₁₂₇	1	6	yes	—
29	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
30	C₂×C₈	—	254	12	no	—
31	C₄²	—	2	6	no	—
32	C₂³	C₂²×Dic₁₂₇	1	1	yes	characteristic
33	C₂×C₄	—	2	12	no	—
34	C₂×C₄	—	2	6	no	—
35	C₂×C₄	#14523248	1	6	yes	—
36	C₈	—	508	4	no	—
37	C₂²	#16861168	1	3	yes	—
38	C₂²	#16861216	1	4	yes	—
39	C₄	—	4	6	no	—
40	C₄	#16861203	1	4	yes	—
41	C₂	#22549744	1	1	yes	characteristic
42	C₂	#22549937	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₂₇
commutator, socle, prime radical	C₂³×C₁₂₇	C₂²×C₄
Fitting	#376×C₁₂₇	C₂
cosocle	C₂²×C₄×C₁₂₇	C₂³
hypercenter	#376	D₁₂₇
hypocenter	C₁₂₇	#1840
LCS	G ▷ C₂³×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

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

N	H ≅ G/N	type
22. C₁₂₇	#1840	semidirect

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