Subgroups — #41000763

Order 26816.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27211710	C₂	1	2	yes	maximal
2	#27211652	C₂	1	2	yes	maximal
3	#27211650	C₂	1	2	yes	maximal
4	C₄×C₈×C₄₁₉	C₂	1	1	yes	maximal, characteristic
5	C₄⋊Dic₄₁₉	C₂²	1	4	yes	—
6	Dic₄₁₉⋊C₄	—	2	4	no	—
7	C₂×C₈×C₄₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₁₉	C₂²	1	1	yes	characteristic
9	C₄²×C₄₁₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₄₁₉	—	2	4	no	—
11	C₂×C₄×C₄₁₉	D₄	1	2	yes	—
12	C₂×C₄×C₄₁₉	C₂³	1	1	yes	characteristic
13	C₈×C₄₁₉	Q₈	1	2	yes	—
14	C₈×C₄₁₉	Q₈	1	2	yes	—
15	C₂²×C₄₁₉	C₂×D₄	1	1	yes	characteristic
16	C₄×C₄₁₉	—	2	2	no	—
17	C₄×C₄₁₉	C₂×Q₈	1	1	yes	characteristic
18	C₄×C₄₁₉	C₂×Q₈	1	1	yes	characteristic
19	Dic₄₁₉	—	4	4	no	—
20	C₂×C₄₁₉	C₄⋊Q₈	1	1	yes	characteristic
21	C₂×C₄₁₉	#135	1	2	yes	—
22	C₄₁₉	#499	1	1	yes	characteristic, complemented, Sylow
23	#499	—	419	1	no	maximal, Sylow
24	#125	—	419	2	no	—
25	#107	—	419	2	no	—
26	#106	—	419	2	no	—
27	C₄×C₈	D₄₁₉	1	1	yes	characteristic
28	C₂×C₈	C₂×D₄₁₉	1	1	yes	characteristic
29	C₂×C₈	C₂×D₄₁₉	1	1	yes	characteristic
30	C₄⋊C₄	—	838	4	no	—
31	C₄⋊C₄	—	419	4	no	—
32	C₄²	C₂×D₄₁₉	1	1	yes	characteristic
33	C₂×C₄	—	838	4	no	—
34	C₂×C₄	D₁₆₇₆	1	2	yes	—
35	C₂×C₄	C₂²×D₄₁₉	1	1	yes	characteristic
36	C₈	Dic₈₃₈	1	2	yes	—
37	C₈	Dic₈₃₈	1	2	yes	—
38	C₂²	C₂×D₁₆₇₆	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	1676	4	no	—
41	C₄	C₂×Dic₈₃₈	1	1	yes	characteristic
42	C₄	C₂×Dic₈₃₈	1	1	yes	characteristic
43	C₂	#27211718	1	1	yes	characteristic
44	C₂	#27211740	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₆₇₆
commutator, cosocle	C₂×C₄×C₄₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₄₁₉
Fitting	C₄×C₈×C₄₁₉	C₂
socle, prime radical	C₂²×C₄₁₉	C₂×D₄
hypercenter	C₄×C₈	D₄₁₉
hypocenter	C₄₁₉	#499
LCS	G ▷ C₂×C₄×C₄₁₉ ▷ C₂×C₄₁₉ ▷ C₄₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
22. C₄₁₉	#499	semidirect

Maximal subgroups

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

subgroup	index
#27211710	2
#27211652	2
#27211650	2
C₄×C₈×C₄₁₉	2
#499	419