Subgroups — #26038847

Order 11456.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19153112	C₂	1	1	yes	maximal, characteristic
2	#19153104	C₂	1	1	yes	maximal, characteristic
3	#19153046	C₂	1	1	yes	maximal, characteristic
4	#19153045	C₂	1	1	yes	maximal, characteristic
5	#19153044	C₂	1	1	yes	maximal, characteristic
6	#19153023	C₂	1	1	yes	maximal, characteristic
7	#107×C₁₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₅₈	—	2	1	no	—
9	C₂×C₁₇₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₇₉	—	2	1	no	—
11	C₄⋊Dic₁₇₉	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₇₉	C₂²	1	1	yes	characteristic
13	Dic₁₇₉⋊C₄	—	2	1	no	—
14	Dic₁₇₉⋊C₄	—	2	1	no	—
15	C₄×Dic₁₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₁₇₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₇₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₇₉	C₂²	1	1	yes	characteristic
19	Dic₃₅₈	—	4	2	no	—
20	C₂×Dic₁₇₉	—	2	1	no	—
21	C₂×Dic₁₇₉	—	2	1	no	—
22	C₂×Dic₁₇₉	D₄	1	1	yes	characteristic
23	C₂×Dic₁₇₉	D₄	1	1	yes	characteristic
24	C₁₇₉⋊C₈	Q₈	1	2	yes	complemented
25	C₂×C₄×C₁₇₉	—	2	1	no	—
26	C₂×C₄×C₁₇₉	—	2	1	no	—
27	C₂×C₄×C₁₇₉	C₂³	1	1	yes	characteristic
28	C₈×C₁₇₉	Q₈	1	2	yes	complemented
29	C₂²×C₁₇₉	C₂×D₄	1	1	yes	characteristic
30	C₄×C₁₇₉	—	4	1	no	—
31	C₄×C₁₇₉	—	4	1	no	—
32	C₄×C₁₇₉	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₁₇₉	C₂×Q₈	1	1	yes	characteristic
34	Dic₁₇₉	—	2	1	no	—
35	Dic₁₇₉	—	2	1	no	—
36	Dic₁₇₉	—	4	1	no	—
37	Dic₁₇₉	—	4	1	no	—
38	C₂×C₁₇₉	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₁₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₁₇₉	#137	1	1	yes	characteristic
41	C₁₇₉	#501	1	1	yes	characteristic, complemented, Sylow
42	#501	—	179	1	no	maximal, Sylow
43	C₄⋊Q₈	—	179	1	no	—
44	#125	—	179	1	no	—
45	#107	—	179	1	no	—
46	#107	D₁₇₉	1	1	yes	characteristic
47	#106	—	179	1	no	—
48	#106	—	179	1	no	—
49	#97	—	179	1	no	—
50	C₂×Q₈	—	358	1	no	—
51	C₂×C₈	—	179	1	no	—
52	C₂×C₈	C₂×D₁₇₉	1	1	yes	characteristic
53	C₄⋊C₄	—	358	1	no	—
54	C₄⋊C₄	—	358	1	no	—
55	C₄⋊C₄	—	358	1	no	—
56	C₄⋊C₄	—	179	1	no	—
57	C₄⋊C₄	—	179	1	no	—
58	C₄⋊C₄	C₂×D₁₇₉	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₁₇₉	1	1	yes	characteristic
60	C₄²	—	179	1	no	—
61	Q₈	—	716	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	358	1	no	—
65	C₂×C₄	—	358	1	no	—
66	C₂×C₄	—	179	1	no	—
67	C₂×C₄	—	179	1	no	—
68	C₂×C₄	C₂²×D₁₇₉	1	1	yes	characteristic
69	C₈	—	179	2	no	—
70	C₈	Dic₃₅₈	1	2	yes	complemented
71	C₂²	D₄×D₁₇₉	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	358	1	no	—
75	C₄	—	358	1	no	—
76	C₄	—	716	1	no	—
77	C₄	—	716	1	no	—
78	C₄	Q₈×D₁₇₉	1	1	yes	characteristic
79	C₄	C₂×Dic₃₅₈	1	1	yes	characteristic
80	C₂	#19153112	1	1	yes	characteristic
81	C₂	#19153137	1	1	yes	characteristic
82	C₂	#19153145	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₇₉
commutator, cosocle	C₂×C₄×C₁₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₇₉
Fitting	#107×C₁₇₉	C₂
socle, prime radical	C₂²×C₁₇₉	C₂×D₄
hypercenter	#107	D₁₇₉
hypocenter	C₁₇₉	#501
LCS	G ▷ C₂×C₄×C₁₇₉ ▷ C₂×C₁₇₉ ▷ C₁₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
24. C₁₇₉⋊C₈	Q₈	semidirect
28. C₈×C₁₇₉	Q₈	semidirect
41. C₁₇₉	#501	semidirect
70. C₈	Dic₃₅₈	semidirect

Maximal subgroups

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

subgroup	index
#19153112	2
#19153104	2
#19153046	2
#19153045	2
#19153044	2
#19153023	2
#107×C₁₇₉	2
#501	179