Subgroups — #37507048

Order 22912.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26038819	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₇₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#335×C₁₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₁₆	—	2	1	no	—
5	C₂×Dic₇₁₆	C₄	1	2	yes	—
6	#19153113	—	2	1	no	—
7	C₂×C₁₇₉⋊C₁₆	—	2	1	no	—
8	C₄⋊C₈×C₁₇₉	—	2	1	no	—
9	C₄×C₈×C₁₇₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₃₅₈	—	2	2	no	—
11	Dic₇₁₆	—	4	2	no	—
12	Dic₇₁₆	—	4	1	no	—
13	Dic₇₁₆	—	4	1	no	—
14	C₄⋊Dic₁₇₉	—	4	1	no	—
15	C₄⋊Dic₁₇₉	—	4	1	no	—
16	C₁₇₉⋊C₁₆	—	4	1	no	—
17	C₂×C₈×C₁₇₉	—	4	1	no	—
18	C₂×C₈×C₁₇₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₇₉	D₄	1	1	yes	characteristic
20	C₄²×C₁₇₉	D₄	1	1	yes	characteristic
21	Dic₃₅₈	—	4	2	no	—
22	Dic₃₅₈	—	4	2	no	—
23	C₂×Dic₁₇₉	—	4	2	no	—
24	C₂×C₄×C₁₇₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₇₉	D₈	1	1	yes	characteristic
26	C₂×C₄×C₁₇₉	SD₁₆	1	1	yes	characteristic
27	C₈×C₁₇₉	—	2	1	no	—
28	C₈×C₁₇₉	—	8	1	no	—
29	C₈×C₁₇₉	D₈	1	1	yes	characteristic
30	C₈×C₁₇₉	SD₁₆	1	1	yes	characteristic
31	C₂²×C₁₇₉	#102	1	1	yes	characteristic
32	C₄×C₁₇₉	—	2	1	no	—
33	C₄×C₁₇₉	#100	1	1	yes	characteristic
34	C₄×C₁₇₉	#102	1	1	yes	characteristic
35	C₄×C₁₇₉	SD₃₂	1	1	yes	characteristic
36	C₄×C₁₇₉	Q₃₂	1	1	yes	characteristic
37	Dic₁₇₉	—	8	2	no	—
38	C₂×C₁₇₉	#331	1	1	yes	characteristic
39	C₂×C₁₇₉	#358	1	1	yes	characteristic
40	C₂×C₁₇₉	#362	1	1	yes	characteristic
41	C₁₇₉	#1362	1	1	yes	characteristic, complemented, Sylow
42	#1362	—	179	1	no	maximal, Sylow
43	#494	—	179	1	no	—
44	C₄⋊C₁₆	—	179	1	no	—
45	#335	D₁₇₉	1	1	yes	characteristic
46	C₂×Q₁₆	—	358	1	no	—
47	C₂×Q₁₆	—	179	2	no	—
48	C₄⋊Q₈	—	358	1	no	—
49	C₂×C₁₆	—	358	1	no	—
50	C₄⋊C₈	—	2	1	no	—
51	C₄×C₈	C₂×D₁₇₉	1	1	yes	characteristic
52	C₂×Q₈	—	358	2	no	—
53	Q₁₆	—	716	2	no	—
54	Q₁₆	—	716	1	no	—
55	Q₁₆	—	716	1	no	—
56	C₂×C₈	—	4	1	no	—
57	C₂×C₈	C₄×D₁₇₉	1	1	yes	characteristic
58	C₂×C₈	D₇₁₆	1	1	yes	characteristic
59	C₄⋊C₄	—	716	1	no	—
60	C₄⋊C₄	—	716	1	no	—
61	C₄²	C₂²⋊D₁₇₉	1	1	yes	characteristic
62	C₁₆	—	716	1	no	—
63	Q₈	—	716	2	no	—
64	Q₈	—	716	2	no	—
65	C₂×C₄	—	716	2	no	—
66	C₂×C₄	(C₂×D₁₇₉)⋊C₄	1	1	yes	characteristic
67	C₂×C₄	#15668244	1	1	yes	characteristic
68	C₂×C₄	#15668246	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	8	1	no	—
71	C₈	D₁₄₃₂	1	1	yes	characteristic
72	C₈	#15668248	1	1	yes	characteristic
73	C₂²	#19153033	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	1432	2	no	—
76	C₄	#19153029	1	1	yes	characteristic
77	C₄	#19153035	1	1	yes	characteristic
78	C₄	#19153057	1	1	yes	characteristic
79	C₄	#19153059	1	1	yes	characteristic
80	C₂	#26038182	1	1	yes	characteristic
81	C₂	#26038242	1	1	yes	characteristic
82	C₂	#26038254	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19153033
commutator	C₂×C₈×C₁₇₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₇₉
Fitting	#335×C₁₇₉	C₂
socle, prime radical	C₂²×C₁₇₉	#102
cosocle	C₄×C₈×C₁₇₉	C₂²
hypercenter	#335	D₁₇₉
hypocenter	C₁₇₉	#1362
LCS	G ▷ C₂×C₈×C₁₇₉ ▷ C₂×C₄×C₁₇₉ ▷ C₂×C₁₇₉ ▷ C₁₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
41. C₁₇₉	#1362	semidirect

Maximal subgroups

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

subgroup	index
#26038819	2
C₄⋊(C₁₇₉⋊C₁₆)	2
#335×C₁₇₉	2
#1362	179