Subgroups — #44508550

Order 30848.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29508517	C₂	1	3	yes	maximal, complemented
2	#29507685	C₂	1	3	yes	maximal, complemented
3	#338×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16838770	C₂²	1	3	yes	—
5	#21440675	—	2	6	no	—
6	#21440670	—	2	6	no	—
7	#21440664	—	2	6	no	—
8	C₂²×#14515349	C₂²	1	1	yes	characteristic
9	#21440554	—	2	6	no	—
10	C₂×M₁₆×C₂₄₁	C₂²	1	3	yes	—
11	#16838770	—	2	6	no	—
12	#16838770	—	2	6	no	—
13	C₂×Dic₄₈₂	D₄	1	3	yes	—
14	C₂×D₉₆₄	D₄	1	3	yes	—
15	C₂×C₂²⋊D₂₄₁	—	2	3	no	—
16	C₂×C₄×D₂₄₁	—	2	3	no	—
17	Dic₉₆₄	—	2	6	no	—
18	#16838759	—	2	12	no	—
19	D₁₉₂₈	—	2	6	no	—
20	C₂×#14515349	—	2	3	no	—
21	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
22	M₁₆×C₂₄₁	—	2	6	no	—
23	C₂×C₈×C₂₄₁	D₄	1	6	yes	—
24	C₂²×D₂₄₁	—	2	3	no	—
25	Dic₄₈₂	—	2	6	no	—
26	D₉₆₄	—	2	6	no	—
27	C₂²⋊D₂₄₁	—	4	6	no	—
28	C₂×Dic₂₄₁	—	2	3	no	—
29	C₄×D₂₄₁	—	4	3	no	—
30	C₄×D₂₄₁	—	4	3	no	—
31	#14515349	—	4	1	no	—
32	C₂³×C₂₄₁	#41	1	1	yes	characteristic
33	C₂×C₄×C₂₄₁	C₂×D₄	1	3	yes	—
34	C₂×C₄×C₂₄₁	C₂×D₄	1	3	yes	—
35	C₈×C₂₄₁	—	2	6	no	—
36	C₂²×C₂₄₁	—	4	1	no	—
37	C₂²×C₂₄₁	#121	1	3	yes	—
38	C₂×D₂₄₁	—	4	6	no	—
39	C₂×D₂₄₁	—	4	3	no	—
40	C₄×C₂₄₁	#120	1	3	yes	—
41	C₄×C₂₄₁	#127	1	1	yes	characteristic
42	Dic₂₄₁	—	4	3	no	—
43	C₂×C₂₄₁	—	2	3	no	—
44	C₂×C₂₄₁	#392	1	1	yes	characteristic
45	D₂₄₁	—	8	3	no	—
46	C₂₄₁	#2017	1	1	yes	characteristic, complemented, Sylow
47	#2017	—	241	1	no	maximal, Sylow
48	#575	—	241	3	no	—
49	#408	—	241	3	no	—
50	#338	D₂₄₁	1	1	yes	characteristic, complemented
51	C₂×#41	—	241	3	no	—
52	#137	—	482	6	no	—
53	AGL(1,ℤ/8)	—	482	6	no	—
54	#135	—	482	6	no	—
55	C₂×M₁₆	C₂×D₂₄₁	1	3	yes	—
56	C₂²×C₈	—	241	1	no	—
57	C₂²⋊C₈	—	482	6	no	—
58	#41	—	482	6	no	—
59	#41	—	482	6	no	—
60	C₂×Q₈	—	241	3	no	—
61	C₂×D₄	—	482	3	no	—
62	C₂×D₄	—	241	3	no	—
63	C₂²×C₄	—	482	3	no	—
64	C₂²×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
65	Q₁₆	—	482	6	no	—
66	SD₁₆	—	482	12	no	—
67	D₈	—	482	6	no	—
68	M₁₆	—	2	6	no	—
69	C₂×C₈	—	482	3	no	—
70	C₂×C₈	D₉₆₄	1	6	yes	—
71	C₂³	—	482	3	no	—
72	C₂³	#16838771	1	1	yes	characteristic
73	Q₈	—	482	6	no	—
74	D₄	—	964	6	no	—
75	D₄	—	482	6	no	—
76	C₂×C₄	—	964	3	no	—
77	C₂×C₄	—	964	3	no	—
78	C₂×C₄	—	482	3	no	—
79	C₂×C₄	D₄×D₂₄₁	1	3	yes	—
80	C₂×C₄	C₂×D₉₆₄	1	3	yes	—
81	C₈	—	2	6	no	—
82	C₈	—	964	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	964	6	no	—
85	C₂²	—	964	3	no	—
86	C₂²	#21440617	1	3	yes	—
87	C₄	—	964	3	no	—
88	C₄	#21440612	1	3	yes	—
89	C₄	#21440639	1	1	yes	characteristic
90	C₂	—	2	3	no	—
91	C₂	—	1928	3	no	—
92	C₂	#29507627	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#21440639
commutator, cosocle	C₂²×C₄×C₂₄₁	C₂³
Frattini	C₂²×C₄	C₂²×D₂₄₁
Fitting	#338×C₂₄₁	C₂
socle	C₂×C₂₄₁	#392
hypercenter	#338	D₂₄₁
hypocenter	C₂₄₁	#2017
LCS	G ▷ C₂²×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #29508517	C₂	semidirect
2. #29507685	C₂	semidirect
3. #338×C₂₄₁	C₂	semidirect
46. C₂₄₁	#2017	semidirect
50. #338	D₂₄₁	semidirect

Maximal subgroups

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

subgroup	index
#29508517	2
#29507685	2
#338×C₂₄₁	2
#2017	241