Subgroups — C₂×C₈×#11724784 #28361305

Order 13952.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11724784	C₂	1	2	yes	maximal
2	C₈×#11724784	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11724784	C₄	1	4	yes	—
5	C₄×#11724784	C₄	1	4	yes	—
6	C₄×#11724784	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₀₉	C₄	1	2	yes	—
8	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₁₀₉	C₄	1	2	yes	—
10	C₄×C₈×C₁₀₉	C₂²	1	2	yes	—
11	C₂×#11724784	C₈	1	16	yes	direct product factor
12	C₂×#11724784	C₂×C₄	1	8	yes	—
13	C₂²×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₀₉	C₈	1	8	yes	complemented
16	C₂×C₈×C₁₀₉	C₂×C₄	1	4	yes	—
17	C₄²×C₁₀₉	C₂×C₄	1	2	yes	—
18	C₄²×C₁₀₉	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
20	C₂³×C₁₀₉	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₁₀₉	C₄²	1	2	yes	—
22	C₂×C₄×C₁₀₉	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₁₀₉	C₂×C₈	1	8	yes	—
24	C₂×C₄×C₁₀₉	C₂×C₈	1	4	yes	—
25	C₂×C₄×C₁₀₉	C₂²×C₄	1	2	yes	—
26	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
27	C₈×C₁₀₉	C₂×C₈	1	8	yes	complemented
28	#11724784	C₂×C₈	1	16	yes	direct product factor
29	C₂²×C₁₀₉	C₄×C₈	1	4	yes	—
30	C₂²×C₁₀₉	C₄×C₈	1	2	yes	—
31	C₂²×C₁₀₉	C₂×C₄²	1	1	yes	characteristic
32	C₄×C₁₀₉	C₄×C₈	1	4	yes	—
33	C₄×C₁₀₉	C₄×C₈	1	2	yes	—
34	C₄×C₁₀₉	C₂²×C₈	1	4	yes	—
35	C₄×C₁₀₉	C₂²×C₈	1	2	yes	—
36	C₂×C₁₀₉	C₈²	1	4	yes	complemented
37	C₂×C₁₀₉	C₂×C₄×C₈	1	2	yes	—
38	C₂×C₁₀₉	C₂×C₄×C₈	1	1	yes	characteristic
39	C₂×C₈²	—	109	1	no	maximal, Sylow
40	C₁₀₉	C₂×C₈²	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₄×C₈	—	109	2	no	—
42	C₂×C₄×C₈	D₁₀₉	1	1	yes	characteristic
43	C₈²	—	109	4	no	—
44	C₂²×C₈	—	109	4	no	—
45	C₂²×C₈	Dic₁₀₉	1	2	yes	—
46	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic
47	C₄×C₈	—	109	4	no	—
48	C₄×C₈	—	109	4	no	—
49	C₄×C₈	Dic₁₀₉	1	2	yes	—
50	C₄×C₈	C₂×D₁₀₉	1	2	yes	—
51	C₂²×C₄	C₄×D₁₀₉	1	2	yes	—
52	C₂²×C₄	C₂×Dic₁₀₉	1	1	yes	characteristic
53	C₂×C₈	—	109	16	no	—
54	C₂×C₈	—	109	8	no	—
55	C₂×C₈	#11724784	1	8	yes	direct product factor
56	C₂×C₈	C₂×Dic₁₀₉	1	4	yes	—
57	C₄²	C₄×D₁₀₉	1	2	yes	—
58	C₄²	C₂×Dic₁₀₉	1	1	yes	characteristic
59	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
60	C₂³	C₄×Dic₁₀₉	1	1	yes	characteristic
61	C₂×C₄	C₄×Dic₁₀₉	1	2	yes	—
62	C₂×C₄	C₄×Dic₁₀₉	1	1	yes	characteristic
63	C₂×C₄	C₈×D₁₀₉	1	8	yes	—
64	C₂×C₄	C₂×#11724784	1	4	yes	—
65	C₂×C₄	C₂×C₄×D₁₀₉	1	2	yes	—
66	C₂×C₄	C₂²×Dic₁₀₉	1	1	yes	characteristic
67	C₈	—	109	16	no	—
68	C₈	C₂×#11724784	1	8	yes	direct product factor
69	C₂²	C₈×Dic₁₀₉	1	4	yes	—
70	C₂²	C₄×#11724784	1	2	yes	—
71	C₂²	C₂×C₄×Dic₁₀₉	1	1	yes	characteristic
72	C₄	C₈×Dic₁₀₉	1	4	yes	—
73	C₄	C₄×#11724784	1	2	yes	—
74	C₄	C₂×C₈×D₁₀₉	1	4	yes	—
75	C₄	C₂²×#11724784	1	2	yes	—
76	C₂	C₈×#11724784	1	4	yes	direct product factor
77	C₂	C₂×C₈×Dic₁₀₉	1	2	yes	—
78	C₂	C₂×C₄×#11724784	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₈	D₁₀₉
commutator, hypocenter	C₁₀₉	C₂×C₈²
Frattini	C₄²	C₂²×D₁₀₉
Fitting	C₂×C₄×C₈×C₁₀₉	C₂
socle, prime radical	C₂³×C₁₀₉	C₄²
cosocle	C₄²×C₁₀₉	C₂³
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₈×#11724784	C₂	direct (N × H)
11. C₂×#11724784	C₈	direct (N × H)
15. C₂×C₈×C₁₀₉	C₈	semidirect
27. C₈×C₁₀₉	C₂×C₈	semidirect
28. #11724784	C₂×C₈	direct (N × H)
36. C₂×C₁₀₉	C₈²	semidirect
40. C₁₀₉	C₂×C₈²	semidirect
55. C₂×C₈	#11724784	direct (N × H)
68. C₈	C₂×#11724784	direct (N × H)
76. C₂	C₈×#11724784	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×#11724784	2
C₈×#11724784	2
C₂×C₄×C₈×C₁₀₉	2
C₂×C₈²	109

Subgroups — C2×C8×#11724784 #28361305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×#11724784 #28361305