Subgroups — C₂×#20294768 #28361616

Order 13952.

232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812610	C₂	1	2	yes	maximal
2	#20294768	C₂	1	4	yes	maximal, direct product factor
3	C₂×#125×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11724784	—	2	2	no	—
5	#16812610	—	2	2	no	—
6	#16812610	C₂²	1	4	yes	—
7	#125×C₁₀₉	—	2	2	no	—
8	#125×C₁₀₉	C₄	1	2	yes	—
9	#125×C₁₀₉	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄×C₁₀₉	—	2	2	no	—
11	C₂×C₄⋊C₄×C₁₀₉	C₄	1	2	yes	—
12	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
13	C₂×#11724784	—	2	8	no	—
14	C₂×#11724784	—	2	4	no	—
15	C₂²×C₄×C₁₀₉	—	2	2	no	—
16	C₂²×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₀₉	D₄	1	2	yes	—
18	C₄⋊C₄×C₁₀₉	—	2	4	no	—
19	C₄⋊C₄×C₁₀₉	—	2	2	no	—
20	C₄⋊C₄×C₁₀₉	—	2	4	no	—
21	C₄⋊C₄×C₁₀₉	C₂×C₄	1	4	yes	—
22	C₄²×C₁₀₉	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₁₀₉	D₄	1	2	yes	—
24	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
25	C₂³×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₀₉	—	2	2	no	—
27	C₂×C₄×C₁₀₉	—	2	4	no	—
28	C₂×C₄×C₁₀₉	—	2	4	no	—
29	C₂×C₄×C₁₀₉	—	4	4	no	—
30	C₂×C₄×C₁₀₉	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
34	#11724784	—	2	8	no	—
35	C₂²×C₁₀₉	#101	1	2	yes	—
36	C₂²×C₁₀₉	#104	1	4	yes	—
37	C₂²×C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₄×C₁₀₉	—	2	1	no	—
39	C₄×C₁₀₉	—	2	1	no	—
40	C₄×C₁₀₉	—	2	2	no	—
41	C₄×C₁₀₉	—	2	2	no	—
42	C₄×C₁₀₉	—	4	4	no	—
43	C₂×C₁₀₉	#330	1	4	yes	complemented
44	C₂×C₁₀₉	C₂×#101	1	1	yes	characteristic
45	C₂×C₁₀₉	C₂×#104	1	2	yes	—
46	C₂×#330	—	109	1	no	maximal, Sylow
47	C₁₀₉	C₂×#330	1	1	yes	characteristic, complemented, Sylow
48	C₂×#125	D₁₀₉	1	1	yes	characteristic
49	C₂×#97	—	109	2	no	—
50	#330	—	109	4	no	—
51	C₂²×C₈	—	218	2	no	—
52	#125	—	2	2	no	—
53	#125	Dic₁₀₉	1	2	yes	—
54	#125	C₂×D₁₀₉	1	2	yes	—
55	C₂×C₄⋊C₄	—	2	2	no	—
56	C₂×C₄⋊C₄	Dic₁₀₉	1	2	yes	—
57	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic
58	#97	—	109	4	no	—
59	#97	—	218	2	no	—
60	C₂²×C₄	—	2	2	no	—
61	C₂²×C₄	C₂×Dic₁₀₉	1	1	yes	characteristic
62	C₂²×C₄	C₂²⋊D₁₀₉	1	2	yes	—
63	C₂×C₈	—	218	8	no	—
64	C₂×C₈	—	218	4	no	—
65	C₄⋊C₄	—	2	4	no	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	4	no	—
68	C₄⋊C₄	C₂×Dic₁₀₉	1	4	yes	—
69	C₄²	C₂×Dic₁₀₉	1	1	yes	characteristic
70	C₄²	C₂²⋊D₁₀₉	1	2	yes	—
71	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
72	C₂³	C₂²⋊Dic₁₀₉	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	4	4	no	—
77	C₂×C₄	C₂²⋊Dic₁₀₉	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₁₀₉	1	1	yes	characteristic
79	C₂×C₄	C₂²×Dic₁₀₉	1	1	yes	characteristic
80	C₂×C₄	C₂×C₂²⋊D₁₀₉	1	2	yes	—
81	C₈	—	218	8	no	—
82	C₂²	#16812618	1	2	yes	—
83	C₂²	#16812626	1	4	yes	—
84	C₂²	C₂×C₂²⋊Dic₁₀₉	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	—	2	1	no	—
87	C₄	—	2	2	no	—
88	C₄	—	2	2	no	—
89	C₄	—	4	4	no	—
90	C₂	#20294768	1	4	yes	direct product factor
91	C₂	C₂×#16812618	1	1	yes	characteristic
92	C₂	C₂×#16812626	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²⋊Dic₁₀₉
commutator	C₂×C₄×C₁₀₉	C₂²×C₄
Frattini	C₄²	C₂²×D₁₀₉
Fitting	C₂×#125×C₁₀₉	C₂
socle, prime radical	C₂³×C₁₀₉	C₂²⋊C₄
cosocle	C₄²×C₁₀₉	C₂³
hypercenter	C₂×#125	D₁₀₉
hypocenter	C₁₀₉	C₂×#330
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
2. #20294768	C₂	direct (N × H)
43. C₂×C₁₀₉	#330	semidirect
47. C₁₀₉	C₂×#330	semidirect
90. C₂	#20294768	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×#16812610	2
#20294768	2
C₂×#125×C₁₀₉	2
C₂×#330	109

Subgroups — C2×#20294768 #28361616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20294768 #28361616