Subgroups — C₂×C₁₀₇×#1273 #41033811

Order 27392.

982 conjugacy classes of subgroups.

The subgroup lattice has 124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈×C₁₀₇	C₂	1	3	yes	maximal
2	C₁₀₇×#1273	C₂	1	4	yes	maximal, direct product factor
3	C₂³×C₈×C₁₀₇	C₄	1	6	yes	—
4	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₈×C₁₀₇	—	2	12	no	—
6	C₂×C₄×C₈×C₁₀₇	C₄	1	6	yes	—
7	C₂×C₄×C₈×C₁₀₇	C₂²	1	6	yes	—
8	C₂³×C₄×C₁₀₇	C₂×C₄	1	3	yes	—
9	C₂²×C₈×C₁₀₇	—	2	12	no	—
10	C₂²×C₈×C₁₀₇	—	2	12	no	—
11	C₂²×C₈×C₁₀₇	C₈	1	24	yes	complemented
12	C₂²×C₈×C₁₀₇	C₂×C₄	1	12	yes	—
13	C₂×C₄²×C₁₀₇	C₂×C₄	1	3	yes	—
14	C₂×C₄²×C₁₀₇	D₄	1	6	yes	—
15	C₂×C₄²×C₁₀₇	Q₈	1	2	yes	—
16	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
17	C₄×C₈×C₁₀₇	—	2	12	no	—
18	C₄×C₈×C₁₀₇	—	2	12	no	—
19	C₂⁴×C₁₀₇	C₄²	1	1	yes	characteristic
20	C₂²×C₄×C₁₀₇	C₄²	1	3	yes	—
21	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	6	yes	—
22	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	6	yes	—
23	C₂²×C₄×C₁₀₇	C₂×C₈	1	12	yes	—
24	C₂²×C₄×C₁₀₇	M₁₆	1	12	yes	—
25	C₂²×C₄×C₁₀₇	C₂²×C₄	1	3	yes	—
26	C₂×C₈×C₁₀₇	—	2	48	no	—
27	C₂×C₈×C₁₀₇	—	2	12	no	—
28	C₂×C₈×C₁₀₇	—	2	12	no	—
29	C₂×C₈×C₁₀₇	C₂×C₈	1	24	yes	complemented
30	C₄²×C₁₀₇	C₂²⋊C₄	1	6	yes	—
31	C₄²×C₁₀₇	C₄⋊C₄	1	6	yes	—
32	C₄²×C₁₀₇	C₂×D₄	1	3	yes	—
33	C₄²×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
34	C₂³×C₁₀₇	#95	1	2	yes	—
35	C₂³×C₁₀₇	C₄×C₈	1	6	yes	—
36	C₂³×C₁₀₇	#97	1	6	yes	—
37	C₂³×C₁₀₇	C₂×C₄²	1	1	yes	characteristic
38	C₂×C₄×C₁₀₇	#95	1	6	yes	—
39	C₂×C₄×C₁₀₇	C₄×C₈	1	6	yes	—
40	C₂×C₄×C₁₀₇	#97	1	6	yes	—
41	C₂×C₄×C₁₀₇	C₂²⋊C₈	1	24	yes	—
42	C₂×C₄×C₁₀₇	C₄⋊C₈	1	24	yes	—
43	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	3	yes	—
44	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	3	yes	—
45	C₂×C₄×C₁₀₇	C₂²×C₈	1	6	yes	—
46	C₂×C₄×C₁₀₇	C₂×M₁₆	1	6	yes	—
47	C₈×C₁₀₇	—	2	24	no	—
48	C₂²×C₁₀₇	C₈²	1	4	yes	—
49	C₂²×C₁₀₇	#322	1	12	yes	—
50	C₂²×C₁₀₇	#336	1	12	yes	—
51	C₂²×C₁₀₇	C₂×#95	1	1	yes	characteristic
52	C₂²×C₁₀₇	C₂×C₄×C₈	1	3	yes	—
53	C₂²×C₁₀₇	C₂×#97	1	3	yes	—
54	C₄×C₁₀₇	#336	1	12	yes	—
55	C₄×C₁₀₇	C₂×C₂²⋊C₈	1	6	yes	—
56	C₄×C₁₀₇	C₂×C₄⋊C₈	1	6	yes	—
57	C₂×#1273	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂×C₁₀₇	#1273	1	8	yes	direct product factor
59	C₂×C₁₀₇	C₂×C₈²	1	1	yes	characteristic
60	C₂×C₁₀₇	C₂×#322	1	3	yes	—
61	C₂×C₁₀₇	C₂×#336	1	3	yes	—
62	C₂²×C₄×C₈	C₂×C₁₀₇	1	3	yes	—
63	#1273	C₂×C₁₀₇	1	4	yes	direct product factor
64	C₁₀₇	C₂×#1273	1	1	yes	characteristic, direct product factor, Sylow
65	C₂³×C₈	C₄×C₁₀₇	1	6	yes	—
66	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
67	C₂×C₄×C₈	—	2	12	no	—
68	C₂×C₄×C₈	C₄×C₁₀₇	1	6	yes	—
69	C₂×C₄×C₈	C₂²×C₁₀₇	1	6	yes	—
70	C₂³×C₄	C₂×C₄×C₁₀₇	1	3	yes	—
71	C₂²×C₈	—	2	12	no	—
72	C₂²×C₈	—	2	12	no	—
73	C₂²×C₈	C₈×C₁₀₇	1	24	yes	complemented
74	C₂²×C₈	C₂×C₄×C₁₀₇	1	12	yes	—
75	C₂×C₄²	C₂×C₄×C₁₀₇	1	3	yes	—
76	C₂×C₄²	D₄×C₁₀₇	1	6	yes	—
77	C₂×C₄²	Q₈×C₁₀₇	1	2	yes	—
78	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
79	C₄×C₈	—	2	12	no	—
80	C₄×C₈	—	2	12	no	—
81	C₂⁴	C₄²×C₁₀₇	1	1	yes	characteristic
82	C₂²×C₄	C₄²×C₁₀₇	1	3	yes	—
83	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	6	yes	—
84	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	6	yes	—
85	C₂²×C₄	C₂×C₈×C₁₀₇	1	12	yes	—
86	C₂²×C₄	M₁₆×C₁₀₇	1	12	yes	—
87	C₂²×C₄	C₂²×C₄×C₁₀₇	1	3	yes	—
88	C₂×C₈	—	2	48	no	—
89	C₂×C₈	—	2	12	no	—
90	C₂×C₈	—	2	12	no	—
91	C₂×C₈	C₂×C₈×C₁₀₇	1	24	yes	complemented
92	C₄²	C₂²⋊C₄×C₁₀₇	1	6	yes	—
93	C₄²	C₄⋊C₄×C₁₀₇	1	6	yes	—
94	C₄²	C₂×D₄×C₁₀₇	1	3	yes	—
95	C₄²	C₂×Q₈×C₁₀₇	1	1	yes	characteristic
96	C₂³	#95×C₁₀₇	1	2	yes	—
97	C₂³	C₄×C₈×C₁₀₇	1	6	yes	—
98	C₂³	#97×C₁₀₇	1	6	yes	—
99	C₂³	C₂×C₄²×C₁₀₇	1	1	yes	characteristic
100	C₂×C₄	#95×C₁₀₇	1	6	yes	—
101	C₂×C₄	C₄×C₈×C₁₀₇	1	6	yes	—
102	C₂×C₄	#97×C₁₀₇	1	6	yes	—
103	C₂×C₄	C₂²⋊C₈×C₁₀₇	1	24	yes	—
104	C₂×C₄	C₄⋊C₈×C₁₀₇	1	24	yes	—
105	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	3	yes	—
106	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	3	yes	—
107	C₂×C₄	C₂²×C₈×C₁₀₇	1	6	yes	—
108	C₂×C₄	C₂×M₁₆×C₁₀₇	1	6	yes	—
109	C₈	—	2	24	no	—
110	C₂²	C₈²×C₁₀₇	1	4	yes	—
111	C₂²	#322×C₁₀₇	1	12	yes	—
112	C₂²	#336×C₁₀₇	1	12	yes	—
113	C₂²	C₂×#95×C₁₀₇	1	1	yes	characteristic
114	C₂²	C₂×C₄×C₈×C₁₀₇	1	3	yes	—
115	C₂²	C₂×#97×C₁₀₇	1	3	yes	—
116	C₄	#336×C₁₀₇	1	12	yes	—
117	C₄	C₂×C₂²⋊C₈×C₁₀₇	1	6	yes	—
118	C₄	C₂×C₄⋊C₈×C₁₀₇	1	6	yes	—
119	C₂	C₁₀₇×#1273	1	8	yes	direct product factor
120	C₂	C₂×C₈²×C₁₀₇	1	1	yes	characteristic
121	C₂	C₂×#322×C₁₀₇	1	3	yes	—
122	C₂	C₂×#336×C₁₀₇	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄²×C₁₀₇	C₂²
commutator	C₂	C₂×C₈²×C₁₀₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₇
socle, prime radical	C₂⁴×C₁₀₇	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄²×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₇×#1273	C₂	direct (N × H)
11. C₂²×C₈×C₁₀₇	C₈	semidirect
29. C₂×C₈×C₁₀₇	C₂×C₈	semidirect
57. C₂×#1273	C₁₀₇	direct (N × H)
58. C₂×C₁₀₇	#1273	direct (N × H)
63. #1273	C₂×C₁₀₇	direct (N × H)
64. C₁₀₇	C₂×#1273	direct (N × H)
73. C₂²×C₈	C₈×C₁₀₇	semidirect
91. C₂×C₈	C₂×C₈×C₁₀₇	semidirect
119. C₂	C₁₀₇×#1273	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₈×C₁₀₇	2
C₁₀₇×#1273	2
C₂×#1273	107

Subgroups — C2×C107×#1273 #41033811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#1273 #41033811