Subgroups — C₁₀₉×#1298 #28358552

Order 13952.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#407×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊C₈×C₁₀₉	C₂	1	2	yes	maximal
3	C₂³×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
4	C₂×M₁₆×C₁₀₉	C₄	1	2	yes	—
5	C₂²×C₈×C₁₀₉	—	2	2	no	—
6	C₂²⋊C₈×C₁₀₉	—	2	2	no	—
7	C₂²⋊C₈×C₁₀₉	—	2	2	no	—
8	C₂²⋊C₈×C₁₀₉	C₄	1	4	yes	—
9	C₂⁴×C₁₀₉	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₁₀₉	—	4	2	no	—
11	C₂²×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₁₀₉	D₄	1	2	yes	—
14	C₂²×C₄×C₁₀₉	D₄	1	1	yes	characteristic
15	M₁₆×C₁₀₉	—	4	2	no	—
16	C₂×C₈×C₁₀₉	—	2	4	no	—
17	C₂×C₈×C₁₀₉	—	2	2	no	—
18	C₂×C₈×C₁₀₉	—	4	4	no	—
19	C₂³×C₁₀₉	—	2	4	no	—
20	C₂³×C₁₀₉	—	4	1	no	—
21	C₂³×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
22	C₂³×C₁₀₉	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₀₉	—	2	4	no	—
24	C₂×C₄×C₁₀₉	—	2	2	no	—
25	C₂×C₄×C₁₀₉	—	4	2	no	—
26	C₂×C₄×C₁₀₉	—	4	1	no	—
27	C₂×C₄×C₁₀₉	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₁₀₉	C₂²⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₈×C₁₀₉	—	4	4	no	—
31	C₈×C₁₀₉	—	4	2	no	—
32	C₂²×C₁₀₉	—	2	2	no	—
33	C₂²×C₁₀₉	—	2	2	no	—
34	C₂²×C₁₀₉	—	2	2	no	—
35	C₂²×C₁₀₉	—	2	1	no	—
36	C₂²×C₁₀₉	—	4	4	no	—
37	C₂²×C₁₀₉	#95	1	1	yes	characteristic
38	C₂²×C₁₀₉	#108	1	4	yes	—
39	C₄×C₁₀₉	—	2	2	no	—
40	C₄×C₁₀₉	—	2	1	no	—
41	C₄×C₁₀₉	#99	1	2	yes	—
42	C₂×C₁₀₉	—	2	4	no	—
43	C₂×C₁₀₉	—	4	1	no	—
44	C₂×C₁₀₉	#341	1	2	yes	—
45	C₂×C₁₀₉	#342	1	1	yes	characteristic
46	#1298	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₁₀₉	#1298	1	1	yes	characteristic, direct product factor, Sylow
48	#407	C₂×C₁₀₉	1	1	yes	characteristic
49	C₂×C₂²⋊C₈	C₂×C₁₀₉	1	2	yes	—
50	C₂³×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
51	C₂×M₁₆	C₄×C₁₀₉	1	2	yes	—
52	C₂²×C₈	—	2	2	no	—
53	C₂²⋊C₈	—	2	2	no	—
54	C₂²⋊C₈	—	2	2	no	—
55	C₂²⋊C₈	C₄×C₁₀₉	1	4	yes	—
56	C₂⁴	Q₈×C₁₀₉	1	1	yes	characteristic
57	C₂²×C₄	—	4	2	no	—
58	C₂²×C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
59	C₂²×C₄	C₂×C₄×C₁₀₉	1	2	yes	—
60	C₂²×C₄	D₄×C₁₀₉	1	2	yes	—
61	C₂²×C₄	D₄×C₁₀₉	1	1	yes	characteristic
62	M₁₆	—	4	2	no	—
63	C₂×C₈	—	2	2	no	—
64	C₂×C₈	—	2	4	no	—
65	C₂×C₈	—	4	4	no	—
66	C₂³	—	2	4	no	—
67	C₂³	—	4	1	no	—
68	C₂³	C₄⋊C₄×C₁₀₉	1	1	yes	characteristic
69	C₂³	C₄⋊C₄×C₁₀₉	1	2	yes	—
70	C₂×C₄	—	2	4	no	—
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	C₄²×C₁₀₉	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊C₄×C₁₀₉	1	2	yes	—
76	C₂×C₄	C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
77	C₈	—	4	4	no	—
78	C₈	—	4	2	no	—
79	C₂²	—	2	2	no	—
80	C₂²	—	2	2	no	—
81	C₂²	—	2	2	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	4	4	no	—
84	C₂²	#95×C₁₀₉	1	1	yes	characteristic
85	C₂²	#108×C₁₀₉	1	4	yes	—
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	#99×C₁₀₉	1	2	yes	—
89	C₂	—	2	4	no	—
90	C₂	—	4	1	no	—
91	C₂	#341×C₁₀₉	1	2	yes	—
92	C₂	#342×C₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₉	C₂²⋊C₄
commutator	C₂×C₄	C₄²×C₁₀₉
Frattini, cosocle	C₂³×C₄	C₂²×C₁₀₉
socle	C₂²×C₁₀₉	#95
prime radical	C₂⁴×C₁₀₉	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₉ ◁ C₂³×C₄×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
46. #1298	C₁₀₉	direct (N × H)
47. C₁₀₉	#1298	direct (N × H)

Maximal subgroups

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

subgroup	index
#407×C₁₀₉	2
C₂×C₂²⋊C₈×C₁₀₉	2
#1298	109

Subgroups — C109×#1298 #28358552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#1298 #28358552