Subgroups — C₂×C₈×#13063436 #36351836

Order 22144.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#13063436	C₂	1	2	yes	maximal
2	C₈×#13063436	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₁₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13063436	C₄	1	4	yes	—
5	C₄×#13063436	C₄	1	4	yes	—
6	C₄×#13063436	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₇₃	C₄	1	2	yes	—
8	C₂×C₄²×C₁₇₃	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₁₇₃	C₄	1	2	yes	—
10	C₄×C₈×C₁₇₃	C₂²	1	2	yes	—
11	C₂×#13063436	C₈	1	16	yes	direct product factor
12	C₂×#13063436	C₂×C₄	1	8	yes	—
13	C₂²×C₄×C₁₇₃	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₇₃	C₈	1	8	yes	complemented
16	C₂×C₈×C₁₇₃	C₂×C₄	1	4	yes	—
17	C₄²×C₁₇₃	C₂×C₄	1	2	yes	—
18	C₄²×C₁₇₃	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₁₇₃	C₂³	1	1	yes	characteristic
20	#13063436	C₂×C₈	1	16	yes	direct product factor
21	C₂³×C₁₇₃	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₁₇₃	C₄²	1	2	yes	—
23	C₂×C₄×C₁₇₃	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₁₇₃	C₂×C₈	1	4	yes	—
25	C₂×C₄×C₁₇₃	C₂×C₈	1	8	yes	—
26	C₂×C₄×C₁₇₃	C₂²×C₄	1	2	yes	—
27	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₁₇₃	C₂×C₈	1	8	yes	complemented
29	C₂²×C₁₇₃	C₄×C₈	1	4	yes	—
30	C₂²×C₁₇₃	C₄×C₈	1	2	yes	—
31	C₂²×C₁₇₃	C₂×C₄²	1	1	yes	characteristic
32	C₄×C₁₇₃	C₄×C₈	1	4	yes	—
33	C₄×C₁₇₃	C₄×C₈	1	2	yes	—
34	C₄×C₁₇₃	C₂²×C₈	1	4	yes	—
35	C₄×C₁₇₃	C₂²×C₈	1	2	yes	—
36	C₂×C₁₇₃	C₈²	1	4	yes	complemented
37	C₂×C₁₇₃	C₂×C₄×C₈	1	2	yes	—
38	C₂×C₁₇₃	C₂×C₄×C₈	1	1	yes	characteristic
39	C₁₇₃	C₂×C₈²	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₈²	—	173	1	no	maximal, Sylow
41	C₂×C₄×C₈	—	173	2	no	—
42	C₂×C₄×C₈	D₁₇₃	1	1	yes	characteristic
43	C₈²	—	173	4	no	—
44	C₂²×C₈	—	173	4	no	—
45	C₂²×C₈	Dic₁₇₃	1	2	yes	—
46	C₂×C₄²	C₂×D₁₇₃	1	1	yes	characteristic
47	C₄×C₈	—	173	4	no	—
48	C₄×C₈	—	173	4	no	—
49	C₄×C₈	Dic₁₇₃	1	2	yes	—
50	C₄×C₈	C₂×D₁₇₃	1	2	yes	—
51	C₂²×C₄	C₄×D₁₇₃	1	2	yes	—
52	C₂²×C₄	C₂×Dic₁₇₃	1	1	yes	characteristic
53	C₂×C₈	—	173	8	no	—
54	C₂×C₈	—	173	16	no	—
55	C₂×C₈	#13063436	1	8	yes	direct product factor
56	C₂×C₈	C₂×Dic₁₇₃	1	4	yes	—
57	C₄²	C₄×D₁₇₃	1	2	yes	—
58	C₄²	C₂×Dic₁₇₃	1	1	yes	characteristic
59	C₄²	C₂²×D₁₇₃	1	1	yes	characteristic
60	C₂³	C₄×Dic₁₇₃	1	1	yes	characteristic
61	C₂×C₄	C₄×Dic₁₇₃	1	2	yes	—
62	C₂×C₄	C₄×Dic₁₇₃	1	1	yes	characteristic
63	C₂×C₄	C₈×D₁₇₃	1	8	yes	—
64	C₂×C₄	C₂×#13063436	1	4	yes	—
65	C₂×C₄	C₂×C₄×D₁₇₃	1	2	yes	—
66	C₂×C₄	C₂²×Dic₁₇₃	1	1	yes	characteristic
67	C₈	—	173	16	no	—
68	C₈	C₂×#13063436	1	8	yes	direct product factor
69	C₂²	C₈×Dic₁₇₃	1	4	yes	—
70	C₂²	C₄×#13063436	1	2	yes	—
71	C₂²	C₂×C₄×Dic₁₇₃	1	1	yes	characteristic
72	C₄	C₈×Dic₁₇₃	1	4	yes	—
73	C₄	C₄×#13063436	1	2	yes	—
74	C₄	C₂×C₈×D₁₇₃	1	4	yes	—
75	C₄	C₂²×#13063436	1	2	yes	—
76	C₂	C₈×#13063436	1	4	yes	direct product factor
77	C₂	C₂×C₈×Dic₁₇₃	1	2	yes	—
78	C₂	C₂×C₄×#13063436	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₈	D₁₇₃
commutator, hypocenter	C₁₇₃	C₂×C₈²
Frattini	C₄²	C₂²×D₁₇₃
Fitting	C₂×C₄×C₈×C₁₇₃	C₂
socle, prime radical	C₂³×C₁₇₃	C₄²
cosocle	C₄²×C₁₇₃	C₂³
LCS	G ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₈×#13063436	C₂	direct (N × H)
11. C₂×#13063436	C₈	direct (N × H)
15. C₂×C₈×C₁₇₃	C₈	semidirect
20. #13063436	C₂×C₈	direct (N × H)
28. C₈×C₁₇₃	C₂×C₈	semidirect
36. C₂×C₁₇₃	C₈²	semidirect
39. C₁₇₃	C₂×C₈²	semidirect
55. C₂×C₈	#13063436	direct (N × H)
68. C₈	C₂×#13063436	direct (N × H)
76. C₂	C₈×#13063436	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×#13063436	2
C₈×#13063436	2
C₂×C₄×C₈×C₁₇₃	2
C₂×C₈²	173

Subgroups — C2×C8×#13063436 #36351836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×#13063436 #36351836