Subgroups — #37507205

Order 22912.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26038273	C₂	1	1	yes	maximal, characteristic
2	#26038269	C₂	1	1	yes	maximal, characteristic
3	#367×C₁₇₉	C₂	1	1	yes	maximal, characteristic
4	#19153049	—	2	1	no	—
5	C₁₇₉⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₇₉	C₂²	1	1	yes	characteristic
7	#107×C₁₇₉	—	2	1	no	—
8	#15668243	—	4	1	no	—
9	C₂×C₈×C₁₇₉	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₁₇₉	—	4	1	no	—
11	C₁₆×C₁₇₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₇₉	Q₈	1	1	yes	characteristic
13	C₁₇₉⋊C₈	—	8	1	no	—
14	C₂×C₄×C₁₇₉	—	8	1	no	—
15	C₂×C₄×C₁₇₉	D₈	1	1	yes	characteristic
16	C₈×C₁₇₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₇₉	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₇₉	SD₃₂	1	1	yes	characteristic
19	C₄×C₁₇₉	—	16	1	no	—
20	C₄×C₁₇₉	#107	1	1	yes	characteristic
21	C₄×C₁₇₉	SD₃₂	1	1	yes	characteristic
22	C₂×C₁₇₉	—	2	1	no	—
23	C₂×C₁₇₉	#367	1	1	yes	characteristic
24	C₁₇₉	#1426	1	1	yes	characteristic, complemented, Sylow
25	#1426	—	179	1	no	maximal, Sylow
26	M₆₄	—	179	1	no	—
27	#368	—	179	1	no	—
28	#367	D₁₇₉	1	1	yes	characteristic
29	C₂×C₁₆	C₂×D₁₇₉	1	1	yes	characteristic
30	#108	—	358	1	no	—
31	#107	—	2	1	no	—
32	C₃₂	—	179	2	no	—
33	M₁₆	—	716	1	no	—
34	C₂×C₈	C₂²⋊D₁₇₉	1	1	yes	characteristic
35	C₄⋊C₄	—	4	1	no	—
36	C₁₆	C₄×D₁₇₉	1	1	yes	characteristic
37	C₁₆	Dic₃₅₈	1	1	yes	characteristic
38	C₂×C₄	—	8	1	no	—
39	C₂×C₄	#15668244	1	1	yes	characteristic
40	C₈	—	1432	1	no	—
41	C₈	Dic₁₇₉⋊C₄	1	1	yes	characteristic
42	C₈	#15668249	1	1	yes	characteristic
43	C₂²	#19153057	1	1	yes	characteristic
44	C₄	—	16	1	no	—
45	C₄	#19153046	1	1	yes	characteristic
46	C₄	#19153056	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#26038266	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26038266
commutator	C₁₆×C₁₇₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₇₉
Fitting	#367×C₁₇₉	C₂
socle	C₂×C₁₇₉	#367
prime radical	C₂²×C₁₇₉	SD₃₂
cosocle	C₂×C₁₆×C₁₇₉	C₂²
hypercenter	#367	D₁₇₉
hypocenter	C₁₇₉	#1426
LCS	G ▷ C₁₆×C₁₇₉ ▷ C₈×C₁₇₉ ▷ C₄×C₁₇₉ ▷ C₂×C₁₇₉ ▷ C₁₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #367

Complements

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

N	H ≅ G/N	type
5. C₁₇₉⋊C₃₂	C₄	semidirect
24. C₁₇₉	#1426	semidirect

Maximal subgroups

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

subgroup	index
#26038273	2
#26038269	2
#367×C₁₇₉	2
#1426	179