Subgroups — #446×C₄₁₉ #40999939

Order 26816.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₄₁₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×C₄₁₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₄₁₉	C₂	1	2	yes	maximal
4	#97×C₄₁₉	C₂	1	2	yes	maximal
5	C₄×C₈×C₄₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₄₁₉	C₄	1	1	yes	characteristic
7	C₂×C₈×C₄₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₁₉	C₂²	1	2	yes	—
9	C₂×C₈×C₄₁₉	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₁₉	C₄	1	2	yes	—
11	C₄⋊C₄×C₄₁₉	C₄	1	1	yes	characteristic
12	C₄²×C₄₁₉	C₂²	1	1	yes	characteristic
13	C₄²×C₄₁₉	C₂²	1	2	yes	—
14	Q₈×C₄₁₉	—	2	2	no	—
15	C₂×C₄×C₄₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₁₉	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₄₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₄₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₄₁₉	C₂³	1	1	yes	characteristic
20	C₈×C₄₁₉	—	2	1	no	—
21	C₈×C₄₁₉	—	2	2	no	—
22	C₈×C₄₁₉	Q₈	1	2	yes	complemented
23	C₂²×C₄₁₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₄₁₉	—	2	2	no	—
25	C₄×C₄₁₉	—	2	1	no	—
26	C₄×C₄₁₉	—	2	2	no	—
27	C₄×C₄₁₉	M₁₆	1	2	yes	—
28	C₄×C₄₁₉	C₂×Q₈	1	1	yes	characteristic
29	C₄×C₄₁₉	#41	1	1	yes	characteristic
30	C₂×C₄₁₉	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₄₁₉	C₂×M₁₆	1	1	yes	characteristic
32	C₂×C₄₁₉	#131	1	1	yes	characteristic
33	C₄₁₉	#446	1	1	yes	characteristic, direct product factor, Sylow
34	#446	C₄₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₄×Q₈	C₂×C₄₁₉	1	1	yes	characteristic
36	C₄⋊C₈	C₂×C₄₁₉	1	1	yes	characteristic
37	C₄⋊C₈	C₂×C₄₁₉	1	2	yes	—
38	#97	C₂×C₄₁₉	1	2	yes	—
39	C₄×C₈	C₂×C₄₁₉	1	1	yes	characteristic
40	C₂×Q₈	C₄×C₄₁₉	1	1	yes	characteristic
41	C₂×C₈	C₂²×C₄₁₉	1	1	yes	characteristic
42	C₂×C₈	C₂²×C₄₁₉	1	2	yes	—
43	C₂×C₈	C₂²×C₄₁₉	1	1	yes	characteristic
44	C₄⋊C₄	C₄×C₄₁₉	1	2	yes	—
45	C₄⋊C₄	C₄×C₄₁₉	1	1	yes	characteristic
46	C₄²	C₂²×C₄₁₉	1	1	yes	characteristic
47	C₄²	C₂²×C₄₁₉	1	2	yes	—
48	Q₈	—	2	2	no	—
49	C₂×C₄	C₂×C₄×C₄₁₉	1	1	yes	characteristic
50	C₂×C₄	C₂×C₄×C₄₁₉	1	2	yes	—
51	C₂×C₄	C₂×C₄×C₄₁₉	1	2	yes	—
52	C₂×C₄	C₂×C₄×C₄₁₉	1	1	yes	characteristic
53	C₂×C₄	C₂³×C₄₁₉	1	1	yes	characteristic
54	C₈	—	2	1	no	—
55	C₈	—	2	2	no	—
56	C₈	Q₈×C₄₁₉	1	2	yes	complemented
57	C₂²	C₂²×C₄×C₄₁₉	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	2	1	no	—
60	C₄	—	2	2	no	—
61	C₄	M₁₆×C₄₁₉	1	2	yes	—
62	C₄	C₂×Q₈×C₄₁₉	1	1	yes	characteristic
63	C₄	#41×C₄₁₉	1	1	yes	characteristic
64	C₂	C₄×Q₈×C₄₁₉	1	1	yes	characteristic
65	C₂	C₂×M₁₆×C₄₁₉	1	1	yes	characteristic
66	C₂	#131×C₄₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁₉	C₂³
commutator	C₂²	C₂²×C₄×C₄₁₉
Frattini, cosocle	C₂×C₄	C₂³×C₄₁₉
socle, prime radical	C₂²×C₄₁₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
22. C₈×C₄₁₉	Q₈	semidirect
33. C₄₁₉	#446	direct (N × H)
34. #446	C₄₁₉	direct (N × H)
56. C₈	Q₈×C₄₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₈×C₄₁₉	2
C₄⋊C₈×C₄₁₉	2
#97×C₄₁₉	2
C₄×C₈×C₄₁₉	2
#446	419

Subgroups — #446×C419 #40999939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #446×C₄₁₉ #40999939