Subgroups — C₁₂₇×#1832 #30634784

Order 16256.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈×C₁₂₇	C₂	1	2	yes	maximal
2	#376×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	#336×C₁₂₇	C₂	1	4	yes	maximal
4	C₂²×C₈×C₁₂₇	C₂²	1	4	yes	—
5	C₂×C₄²×C₁₂₇	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic
7	C₄⋊C₈×C₁₂₇	—	2	4	no	—
8	#95×C₁₂₇	C₄	1	4	yes	—
9	C₂²×C₄×C₁₂₇	C₂×C₄	1	4	yes	—
10	C₂²×C₄×C₁₂₇	C₂×C₄	1	2	yes	—
11	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
12	C₂×C₈×C₁₂₇	—	2	4	no	—
13	C₂×C₈×C₁₂₇	—	2	8	no	—
14	C₄²×C₁₂₇	—	2	4	no	—
15	C₄²×C₁₂₇	D₄	1	2	yes	—
16	C₄²×C₁₂₇	Q₈	1	2	yes	—
17	C₂³×C₁₂₇	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₂₇	—	2	4	no	—
19	C₂×C₄×C₁₂₇	—	2	4	no	—
20	C₂×C₄×C₁₂₇	—	2	8	no	—
21	C₂×C₄×C₁₂₇	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₁₂₇	C₂×D₄	1	1	yes	characteristic
23	C₂×C₄×C₁₂₇	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₁₂₇	#41	1	4	yes	—
25	C₈×C₁₂₇	—	4	4	no	—
26	C₂²×C₁₂₇	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₁₂₇	#117	1	2	yes	—
28	C₂²×C₁₂₇	#131	1	4	yes	—
29	C₄×C₁₂₇	—	2	4	no	—
30	C₄×C₁₂₇	—	4	4	no	—
31	C₄×C₁₂₇	#124	1	2	yes	—
32	C₄×C₁₂₇	#125	1	2	yes	—
33	C₂×C₁₂₇	#382	1	1	yes	characteristic
34	C₂×C₁₂₇	#424	1	2	yes	—
35	C₂×C₁₂₇	#433	1	4	yes	—
36	#1832	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₁₂₇	#1832	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₄⋊C₈	C₂×C₁₂₇	1	2	yes	—
39	#376	C₂×C₁₂₇	1	1	yes	characteristic
40	#336	C₂×C₁₂₇	1	4	yes	—
41	C₂²×C₈	C₂²×C₁₂₇	1	4	yes	—
42	C₂×C₄²	C₂²×C₁₂₇	1	2	yes	—
43	C₂×C₄²	C₂²×C₁₂₇	1	1	yes	characteristic
44	C₄⋊C₈	—	2	4	no	—
45	#95	C₄×C₁₂₇	1	4	yes	—
46	C₂²×C₄	C₂×C₄×C₁₂₇	1	4	yes	—
47	C₂²×C₄	C₂×C₄×C₁₂₇	1	2	yes	—
48	C₂²×C₄	C₂³×C₁₂₇	1	1	yes	characteristic
49	C₂×C₈	—	2	4	no	—
50	C₂×C₈	—	2	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	D₄×C₁₂₇	1	2	yes	—
53	C₄²	Q₈×C₁₂₇	1	2	yes	—
54	C₂³	C₂²×C₄×C₁₂₇	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	2	8	no	—
58	C₂×C₄	C₄⋊C₄×C₁₂₇	1	4	yes	—
59	C₂×C₄	C₂×D₄×C₁₂₇	1	1	yes	characteristic
60	C₂×C₄	C₂×Q₈×C₁₂₇	1	1	yes	characteristic
61	C₂×C₄	#41×C₁₂₇	1	4	yes	—
62	C₈	—	4	4	no	—
63	C₂²	C₂×C₄⋊C₄×C₁₂₇	1	1	yes	characteristic
64	C₂²	#117×C₁₂₇	1	2	yes	—
65	C₂²	#131×C₁₂₇	1	4	yes	—
66	C₄	—	2	4	no	—
67	C₄	—	4	4	no	—
68	C₄	#124×C₁₂₇	1	2	yes	—
69	C₄	#125×C₁₂₇	1	2	yes	—
70	C₂	#382×C₁₂₇	1	1	yes	characteristic
71	C₂	#424×C₁₂₇	1	2	yes	—
72	C₂	#433×C₁₂₇	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₂₇	C₂³
commutator	C₂³	C₂²×C₄×C₁₂₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₂₇
socle, prime radical	C₂³×C₁₂₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
36. #1832	C₁₂₇	direct (N × H)
37. C₁₂₇	#1832	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₈×C₁₂₇	2
#376×C₁₂₇	2
#336×C₁₂₇	2
#1832	127

Subgroups — C127×#1832 #30634784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₇×#1832 #30634784