Subgroups — #43271874

Order 28736.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₄₄₉	C₂	1	1	yes	maximal, characteristic
2	#28385247	C₂	1	1	yes	maximal, characteristic
3	#28385247	C₂	1	2	yes	maximal
4	#28385247	C₂	1	2	yes	maximal
5	#95×C₄₄₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₄₄₉	C₂²	1	2	yes	—
7	C₂²×Dic₄₄₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₄₄₉	C₂²	1	1	yes	characteristic
9	C₄×Dic₄₄₉	C₄	1	4	yes	complemented
10	C₂²×C₄×C₄₄₉	C₂²	1	2	yes	—
11	C₂²×C₄×C₄₄₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₄₄₉	—	2	1	no	—
13	C₂×Dic₄₄₉	—	2	2	no	—
14	C₂×Dic₄₄₉	—	2	1	no	—
15	C₂×Dic₄₄₉	—	2	2	no	—
16	C₂×Dic₄₄₉	—	2	2	no	—
17	C₂×Dic₄₄₉	—	2	2	no	—
18	C₂×Dic₄₄₉	C₂×C₄	1	2	yes	—
19	C₂×Dic₄₄₉	C₂×C₄	1	2	yes	—
20	C₂³×C₄₄₉	C₂³	1	1	yes	characteristic
21	C₂×C₄×C₄₄₉	—	2	2	no	—
22	C₂×C₄×C₄₄₉	—	2	2	no	—
23	C₂×C₄×C₄₄₉	—	2	2	no	—
24	C₂×C₄×C₄₄₉	—	2	2	no	—
25	C₂×C₄×C₄₄₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄₄₉	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄₄₉	#41	1	2	yes	—
28	C₂²×C₄₄₉	#41	1	1	yes	characteristic
29	C₂²×C₄₄₉	#41	1	2	yes	—
30	C₂²×C₄₄₉	#41	1	1	yes	characteristic
31	C₄×C₄₄₉	—	2	2	no	—
32	C₄×C₄₄₉	—	4	2	no	—
33	Dic₄₄₉	—	2	2	no	—
34	Dic₄₄₉	—	2	2	no	—
35	Dic₄₄₉	—	4	2	no	—
36	C₂×C₄₄₉	#117	1	1	yes	characteristic
37	C₂×C₄₄₉	#117	1	1	yes	characteristic
38	C₂×C₄₄₉	#117	1	1	yes	characteristic
39	C₂×C₄₄₉	#126	1	2	yes	—
40	C₂×C₄₄₉	#126	1	2	yes	—
41	C₄₄₉	#383	1	1	yes	characteristic, complemented, Sylow
42	#383	—	449	1	no	maximal, Sylow
43	C₂×C₄²	—	449	1	no	—
44	#95	—	449	1	no	—
45	#95	—	449	2	no	—
46	#95	—	449	2	no	—
47	#95	D₄₄₉	1	1	yes	characteristic
48	C₂²×C₄	—	449	2	no	—
49	C₂²×C₄	—	449	1	no	—
50	C₂²×C₄	—	449	1	no	—
51	C₂²×C₄	C₂×D₄₄₉	1	2	yes	—
52	C₂²×C₄	C₂×D₄₄₉	1	1	yes	characteristic
53	C₄²	—	449	4	no	—
54	C₂³	C₂²×D₄₄₉	1	1	yes	characteristic
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	898	2	no	—
60	C₂×C₄	—	898	2	no	—
61	C₂×C₄	—	898	2	no	—
62	C₂×C₄	—	898	1	no	—
63	C₂×C₄	—	898	2	no	—
64	C₂×C₄	—	898	1	no	—
65	C₂×C₄	—	449	2	no	—
66	C₂×C₄	—	449	2	no	—
67	C₂×C₄	C₄×D₄₄₉	1	2	yes	—
68	C₂²	C₂×C₄×D₄₄₉	1	1	yes	characteristic
69	C₂²	#20297735	1	2	yes	—
70	C₂²	#20297735	1	1	yes	characteristic
71	C₂²	#20297736	1	2	yes	—
72	C₂²	#20297737	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	4	2	no	—
75	C₄	—	1796	2	no	—
76	C₄	—	898	2	no	—
77	C₄	—	898	2	no	—
78	C₂	#28385296	1	1	yes	characteristic
79	C₂	#28385297	1	1	yes	characteristic
80	C₂	#28385298	1	1	yes	characteristic
81	C₂	#28385333	1	2	yes	—
82	C₂	#28385335	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₄₉
commutator	C₂²×C₄₄₉	C₂²×C₄
Fitting	#95×C₄₄₉	C₂
socle, prime radical, cosocle	C₂³×C₄₄₉	C₂³
hypercenter	#95	D₄₄₉
hypocenter	C₄₄₉	#383
LCS	G ▷ C₂²×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
9. C₄×Dic₄₄₉	C₄	semidirect
41. C₄₄₉	#383	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₄₄₉	2
#28385247	2
#95×C₄₄₉	2
#383	449