Subgroups — C₄×#13182039 #20295988

Order 6976.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182039	C₂	1	2	yes	maximal
2	#16812754	C₂	1	2	yes	maximal, complemented
3	C₄×#11724786	C₂	1	2	yes	maximal, complemented
4	C₄²×D₁₀₉	C₂	1	1	yes	maximal, characteristic
5	#13182039	C₄	1	8	yes	direct product factor
6	C₂×#11724786	C₂²	1	4	yes	—
7	C₂×C₄×D₁₀₉	C₄	1	1	yes	characteristic
8	C₂×C₄×D₁₀₉	C₄	1	1	yes	characteristic
9	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
10	C₄×Dic₁₀₉	C₄	1	1	yes	characteristic
11	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
12	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
13	C₄²×C₁₀₉	C₄	1	1	yes	characteristic
14	C₂²×D₁₀₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₀₉	C₂³	1	1	yes	characteristic
21	C₄×D₁₀₉	—	2	2	no	—
22	C₄×D₁₀₉	—	2	2	no	—
23	C₄×D₁₀₉	C₂×C₄	1	4	yes	—
24	#11724786	C₂×C₄	1	8	yes	complemented
25	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
26	C₂×D₁₀₉	—	2	1	no	—
27	C₂×D₁₀₉	—	2	1	no	—
28	C₂×D₁₀₉	C₄²	1	2	yes	—
29	C₄×C₁₀₉	—	2	1	no	—
30	C₄×C₁₀₉	C₄²	1	2	yes	—
31	C₄×C₁₀₉	M₁₆	1	2	yes	complemented
32	Dic₁₀₉	—	2	1	no	—
33	Dic₁₀₉	M₁₆	1	2	yes	complemented
34	Dic₁₀₉	C₂²×C₄	1	2	yes	—
35	C₂×C₁₀₉	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₁₀₉	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₁₀₉	C₂×M₁₆	1	1	yes	characteristic
38	D₁₀₉	—	2	2	no	—
39	C₁₀₉	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₄×M₁₆	—	109	1	no	maximal, Sylow
41	C₂×M₁₆	—	109	2	no	—
42	C₂×C₄²	—	109	1	no	—
43	#97	—	109	2	no	—
44	C₄×C₈	—	109	2	no	—
45	C₂²×C₄	—	109	1	no	—
46	C₂²×C₄	—	109	1	no	—
47	C₂²×C₄	—	109	1	no	—
48	M₁₆	—	109	8	no	—
49	C₂×C₈	—	109	4	no	—
50	C₄²	—	109	1	no	—
51	C₄²	—	109	1	no	—
52	C₄²	—	109	1	no	—
53	C₄²	#89137	1	1	yes	characteristic
54	C₂³	—	109	1	no	—
55	C₂×C₄	—	109	1	no	—
56	C₂×C₄	—	109	1	no	—
57	C₂×C₄	—	109	4	no	—
58	C₂×C₄	—	109	1	no	—
59	C₂×C₄	—	218	2	no	—
60	C₂×C₄	—	218	2	no	—
61	C₂×C₄	C₂×#89137	1	1	yes	characteristic
62	C₂×C₄	C₂×#89137	1	1	yes	characteristic
63	C₂×C₄	C₂×#89137	1	1	yes	characteristic
64	C₈	—	109	8	no	—
65	C₂²	—	109	2	no	—
66	C₂²	—	218	1	no	—
67	C₂²	—	218	1	no	—
68	C₂²	C₂²×#89137	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	109	2	no	—
71	C₄	—	109	2	no	—
72	C₄	—	218	1	no	—
73	C₄	C₄×#89137	1	2	yes	—
74	C₄	#13182039	1	2	yes	direct product factor
75	C₂	—	218	2	no	—
76	C₂	C₂×C₄×#89137	1	1	yes	characteristic
77	C₂	D₁₀₉⋊M₁₆	1	1	yes	characteristic
78	C₂	C₂×#13182039	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#89137
commutator	C₂×C₁₀₉	C₂×C₄²
Frattini	C₂²	C₂²×#89137
Fitting	C₄²×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂²×C₄
hypercenter	C₄²	#89137
hypocenter	C₁₀₉	C₄×M₁₆
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #16812754	C₂	semidirect
3. C₄×#11724786	C₂	semidirect
5. #13182039	C₄	direct (N × H)
24. #11724786	C₂×C₄	semidirect
31. C₄×C₁₀₉	M₁₆	semidirect
33. Dic₁₀₉	M₁₆	semidirect
39. C₁₀₉	C₄×M₁₆	semidirect
74. C₄	#13182039	direct (N × H)

Subgroups — C4×#13182039 #20295988

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13182039 #20295988