Subgroups — #43272859

Order 28736.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28385397	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂×#14267798)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#28385315	C₂	1	1	yes	maximal, characteristic
4	C₂²×#14267798	—	2	1	no	—
5	C₂×#16813318	—	2	1	no	—
6	C₂×D₁₇₉₆	—	2	1	no	—
7	C₂×D₁₇₉₆	C₄	1	1	yes	characteristic, complemented
8	C₂×C₄×D₄₄₉	C₂²	1	1	yes	characteristic
9	#20297713	—	2	1	no	—
10	C₄⋊C₄×C₄₄₉	C₄	1	1	yes	characteristic, complemented
11	C₂×#14267798	—	2	2	no	—
12	C₂×#14267798	—	4	1	no	—
13	C₂×#14267798	—	4	1	no	—
14	#16813318	—	4	1	no	—
15	C₂²×D₄₄₉	—	2	1	no	—
16	C₂²×D₄₄₉	D₄	1	1	yes	characteristic
17	D₁₇₉₆	—	4	1	no	—
18	D₁₇₉₆	—	4	1	no	—
19	D₁₇₉₆	—	4	1	no	—
20	C₂×Dic₄₄₉	D₄	1	1	yes	characteristic
21	C₄×D₄₄₉	—	4	1	no	—
22	C₂×C₄×C₄₄₉	—	2	1	no	—
23	C₂×C₄×C₄₄₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×D₄₄₉	—	2	1	no	—
26	C₂×D₄₄₉	—	2	1	no	—
27	C₂×D₄₄₉	—	4	1	no	—
28	C₂×D₄₄₉	—	4	1	no	—
29	C₂×D₄₄₉	—	4	1	no	—
30	C₂×D₄₄₉	D₈	1	1	yes	characteristic
31	C₂×D₄₄₉	SD₁₆	1	1	yes	characteristic
32	#14267798	—	4	2	no	—
33	C₄×C₄₄₉	—	2	1	no	—
34	C₄×C₄₄₉	—	4	1	no	—
35	Dic₄₄₉	—	2	1	no	—
36	C₂×C₄₄₉	#99	1	1	yes	characteristic
37	C₂×C₄₄₉	#102	1	1	yes	characteristic
38	C₂×C₄₄₉	#104	1	1	yes	characteristic
39	D₄₄₉	—	2	1	no	—
40	D₄₄₉	—	2	1	no	—
41	D₄₄₉	—	8	1	no	—
42	C₄₄₉	#327	1	1	yes	characteristic, complemented, Sylow
43	#327	—	449	1	no	maximal, Sylow
44	#121	—	449	1	no	—
45	C₂²⋊C₈	—	449	1	no	—
46	#95	—	449	1	no	—
47	C₂×D₄	—	898	1	no	—
48	C₂×D₄	—	449	1	no	—
49	C₂²×C₄	—	898	1	no	—
50	C₂²×C₄	—	449	1	no	—
51	C₂×C₈	—	898	1	no	—
52	C₄⋊C₄	#14267798	1	1	yes	characteristic, complemented
53	C₂²⋊C₄	—	898	1	no	—
54	C₂³	—	898	1	no	—
55	C₂³	—	449	1	no	—
56	D₄	—	1796	1	no	—
57	D₄	—	1796	1	no	—
58	D₄	—	1796	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	1796	1	no	—
61	C₂×C₄	—	1796	1	no	—
62	C₂×C₄	—	1796	1	no	—
63	C₂×C₄	—	898	2	no	—
64	C₂×C₄	—	449	1	no	—
65	C₂×C₄	C₂×#14267798	1	1	yes	characteristic
66	C₈	—	1796	1	no	—
67	C₂²	—	1796	1	no	—
68	C₂²	—	1796	1	no	—
69	C₂²	—	1796	1	no	—
70	C₂²	—	898	1	no	—
71	C₂²	—	898	1	no	—
72	C₂²	—	449	1	no	—
73	C₂²	—	449	1	no	—
74	C₂²	C₂²⋊#14267798	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	1796	2	no	—
78	C₄	—	898	1	no	—
79	C₂	—	3592	1	no	—
80	C₂	—	898	1	no	—
81	C₂	—	898	1	no	—
82	C₂	#28385399	1	1	yes	characteristic
83	C₂	#28385402	1	1	yes	characteristic
84	C₂	#28385405	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#14267798
commutator	C₂×C₄×C₄₄₉	C₂×C₄
Frattini	C₂×C₄	C₂×#14267798
Fitting	C₄⋊C₄×C₄₄₉	C₄
socle	C₂²×C₄₄₉	C₂²⋊C₄
prime radical	#28385315	C₂
cosocle	C₂×C₄×D₄₄₉	C₂²
hypercenter	C₄⋊C₄	#14267798
hypocenter	C₄₄₉	#327
LCS	G ▷ C₂×C₄×C₄₄₉ ▷ C₂²×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #28385397	C₂	semidirect
2. (C₂×#14267798)⋊C₄	C₂	semidirect
7. C₂×D₁₇₉₆	C₄	semidirect
10. C₄⋊C₄×C₄₄₉	C₄	semidirect
42. C₄₄₉	#327	semidirect
52. C₄⋊C₄	#14267798	semidirect

Maximal subgroups

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

subgroup	index
#28385397	2
(C₂×#14267798)⋊C₄	2
#28385315	2
#327	449