Subgroups — #26038672

Order 11456.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#19153084	C₂	1	2	yes	maximal, complemented
3	#19153047	C₂	1	1	yes	maximal, characteristic, complemented
4	#19153034	C₂	1	2	yes	maximal, complemented
5	C₂×D₈×C₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂²⋊D₁₇₉	—	2	2	no	—
7	C₂×C₄×D₁₇₉	C₂²	1	1	yes	characteristic
8	C₂×C₁₇₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₈×D₁₇₉	—	2	2	no	—
10	C₄⋊Dic₁₇₉	C₂²	1	2	yes	—
11	C₂²⋊Dic₁₇₉	—	2	2	no	—
12	C₂×D₄×C₁₇₉	C₂²	1	2	yes	—
13	D₈×C₁₇₉	—	2	2	no	—
14	C₂×C₈×C₁₇₉	C₂²	1	1	yes	characteristic
15	C₂²×D₁₇₉	D₄	1	1	yes	characteristic
16	C₂²⋊D₁₇₉	—	4	4	no	—
17	C₂×Dic₁₇₉	—	2	2	no	—
18	C₂×Dic₁₇₉	D₄	1	1	yes	characteristic
19	C₄×D₁₇₉	—	2	1	no	—
20	C₄×D₁₇₉	—	2	1	no	—
21	C₁₇₉⋊C₈	—	2	1	no	—
22	C₂³×C₁₇₉	—	2	2	no	—
23	D₄×C₁₇₉	—	2	2	no	—
24	D₄×C₁₇₉	—	2	2	no	—
25	C₂×C₄×C₁₇₉	C₂³	1	1	yes	characteristic
26	C₈×C₁₇₉	D₄	1	2	yes	complemented
27	C₂²×C₁₇₉	—	4	2	no	—
28	C₂²×C₁₇₉	—	4	2	no	—
29	C₂²×C₁₇₉	—	4	2	no	—
30	C₂²×C₁₇₉	C₂×D₄	1	1	yes	characteristic
31	C₂×D₁₇₉	—	2	1	no	—
32	C₂×D₁₇₉	—	2	1	no	—
33	C₂×D₁₇₉	D₈	1	2	yes	complemented
34	C₄×C₁₇₉	C₂×D₄	1	1	yes	characteristic
35	C₄×C₁₇₉	#41	1	1	yes	characteristic
36	Dic₁₇₉	—	2	1	no	—
37	Dic₁₇₉	—	4	2	no	—
38	C₂×C₁₇₉	—	8	2	no	—
39	C₂×C₁₇₉	#121	1	1	yes	characteristic
40	C₂×C₁₇₉	C₂×D₈	1	1	yes	characteristic
41	C₂×C₁₇₉	#135	1	1	yes	characteristic
42	D₁₇₉	—	2	2	no	—
43	C₁₇₉	#466	1	1	yes	characteristic, complemented, Sylow
44	#466	—	179	1	no	maximal, Sylow
45	C₂×D₈	D₁₇₉	1	1	yes	characteristic, complemented
46	C₂²×C₈	—	179	1	no	—
47	#121	—	179	2	no	—
48	#107	—	179	1	no	—
49	#102	—	179	2	no	—
50	C₂×D₄	—	358	2	no	—
51	C₂×D₄	C₂×D₁₇₉	1	2	yes	—
52	C₂²×C₄	—	179	1	no	—
53	D₈	—	2	2	no	—
54	C₂×C₈	—	358	2	no	—
55	C₂×C₈	—	179	1	no	—
56	C₂×C₈	C₂×D₁₇₉	1	1	yes	characteristic
57	C₄⋊C₄	—	179	2	no	—
58	C₂²⋊C₄	—	358	2	no	—
59	C₂³	—	2	2	no	—
60	C₂³	—	179	1	no	—
61	D₄	—	2	2	no	—
62	D₄	—	2	2	no	—
63	D₄	—	716	4	no	—
64	C₂×C₄	—	358	1	no	—
65	C₂×C₄	—	358	1	no	—
66	C₂×C₄	—	358	2	no	—
67	C₂×C₄	—	179	1	no	—
68	C₂×C₄	C₂²×D₁₇₉	1	1	yes	characteristic
69	C₈	—	358	1	no	—
70	C₈	C₂²⋊D₁₇₉	1	2	yes	complemented
71	C₂²	—	4	2	no	—
72	C₂²	—	4	2	no	—
73	C₂²	—	4	2	no	—
74	C₂²	—	358	1	no	—
75	C₂²	—	358	1	no	—
76	C₂²	—	179	2	no	—
77	C₂²	D₄×D₁₇₉	1	1	yes	characteristic
78	C₄	—	358	1	no	—
79	C₄	—	716	2	no	—
80	C₄	C₂×C₂²⋊D₁₇₉	1	1	yes	characteristic
81	C₄	#15668258	1	1	yes	characteristic
82	C₂	—	8	2	no	—
83	C₂	—	358	2	no	—
84	C₂	#19153084	1	1	yes	characteristic
85	C₂	D₈×D₁₇₉	1	1	yes	characteristic
86	C₂	#19153132	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₇₉
commutator, cosocle	C₂×C₄×C₁₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₇₉
Fitting	C₂×D₈×C₁₇₉	C₂
socle	C₂²×C₁₇₉	C₂×D₄
hypercenter	C₂×D₈	D₁₇₉
hypocenter	C₁₇₉	#466
LCS	G ▷ C₂×C₄×C₁₇₉ ▷ C₂×C₁₇₉ ▷ C₁₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×D₁₇₉	C₂	semidirect
2. #19153084	C₂	semidirect
3. #19153047	C₂	semidirect
4. #19153034	C₂	semidirect
5. C₂×D₈×C₁₇₉	C₂	semidirect
26. C₈×C₁₇₉	D₄	semidirect
33. C₂×D₁₇₉	D₈	semidirect
43. C₁₇₉	#466	semidirect
45. C₂×D₈	D₁₇₉	semidirect
70. C₈	C₂²⋊D₁₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₁₇₉	2
#19153084	2
#19153047	2
#19153034	2
C₂×D₈×C₁₇₉	2
#466	179