Subgroups — #44449793

Order 29824.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28416565	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#16836569	C₂	1	1	yes	maximal, characteristic
3	#346×C₂₃₃	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₄₆₆	C₄	1	1	yes	characteristic
5	C₂×#16836569	—	2	1	no	—
6	C₄⋊#14272338	C₄	1	1	yes	characteristic
7	#21418464	—	2	1	no	—
8	#21418445	—	2	1	no	—
9	C₂×C₁₆×C₂₃₃	—	2	1	no	—
10	C₄×C₈×C₂₃₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₆₆	C₈	1	1	yes	characteristic
12	C₂×#14272338	—	2	1	no	—
13	C₄⋊Dic₂₃₃	C₈	1	1	yes	characteristic
14	#16836573	—	2	1	no	—
15	C₄×Dic₂₃₃	—	2	1	no	—
16	#16836569	—	4	1	no	—
17	C₂×C₈×C₂₃₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₃₃	D₄	1	1	yes	characteristic
19	C₄²×C₂₃₃	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₂₃₃	—	2	2	no	—
21	Dic₄₆₆	—	4	1	no	—
22	C₂×Dic₂₃₃	—	2	1	no	—
23	C₂×Dic₂₃₃	—	2	1	no	—
24	#14272338	—	4	1	no	—
25	C₂×C₄×C₂₃₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₃₃	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₂₃₃	M₁₆	1	1	yes	characteristic
28	C₈×C₂₃₃	—	2	1	no	—
29	C₈×C₂₃₃	SD₁₆	1	1	yes	characteristic
30	C₈×C₂₃₃	Q₁₆	1	1	yes	characteristic
31	C₂²×C₂₃₃	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₂₃₃	—	2	1	no	—
33	C₄×C₂₃₃	—	2	1	no	—
34	C₄×C₂₃₃	#103	1	1	yes	characteristic
35	C₄×C₂₃₃	#104	1	1	yes	characteristic
36	Dic₂₃₃	—	4	1	no	—
37	Dic₂₃₃	—	4	1	no	—
38	C₂×C₂₃₃	Q₈⋊C₈	1	1	yes	characteristic
39	C₂×C₂₃₃	#349	1	1	yes	characteristic
40	C₂×C₂₃₃	#350	1	1	yes	characteristic
41	C₂₃₃	#1338	1	1	yes	characteristic, complemented, Sylow
42	#1338	—	233	1	no	maximal, Sylow
43	#446	—	233	1	no	—
44	C₄⋊C₁₆	—	233	1	no	—
45	#346	D₂₃₃	1	1	yes	characteristic
46	C₄×Q₈	—	233	1	no	—
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	466	1	no	—
49	C₄⋊C₈	—	466	1	no	—
50	C₄⋊C₈	—	233	1	no	—
51	#97	—	466	1	no	—
52	C₄×C₈	C₂×D₂₃₃	1	1	yes	characteristic
53	C₂×Q₈	—	233	1	no	—
54	C₂×C₈	—	466	1	no	—
55	C₂×C₈	C₂²⋊D₂₃₃	1	1	yes	characteristic
56	C₂×C₈	D₉₃₂	1	1	yes	characteristic
57	C₄⋊C₄	—	466	1	no	—
58	C₄⋊C₄	—	233	1	no	—
59	C₄²	—	466	1	no	—
60	C₄²	C₄×D₂₃₃	1	1	yes	characteristic
61	C₁₆	—	2	2	no	—
62	C₁₆	—	932	1	no	—
63	Q₈	—	932	1	no	—
64	C₂×C₄	—	466	1	no	—
65	C₂×C₄	—	466	1	no	—
66	C₂×C₄	#16836571	1	1	yes	characteristic
67	C₂×C₄	C₈×D₂₃₃	1	1	yes	characteristic
68	C₂×C₄	#16836577	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	932	1	no	—
71	C₈	#16836583	1	1	yes	characteristic
72	C₈	Dic₉₃₂	1	1	yes	characteristic
73	C₂²	#21418447	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	932	1	no	—
77	C₄	—	932	1	no	—
78	C₄	#21418460	1	1	yes	characteristic
79	C₄	#21418463	1	1	yes	characteristic
80	C₂	#28416167	1	1	yes	characteristic
81	C₂	#28416216	1	1	yes	characteristic
82	C₂	#28416220	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#16836571
commutator	C₂×C₄×C₂₃₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₃₃
Fitting	#346×C₂₃₃	C₂
socle, prime radical	C₂²×C₂₃₃	C₂²⋊C₈
cosocle	C₄×C₈×C₂₃₃	C₂²
hypercenter	#346	D₂₃₃
hypocenter	C₂₃₃	#1338
LCS	G ▷ C₂×C₄×C₂₃₃ ▷ C₂²×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
41. C₂₃₃	#1338	semidirect

Maximal subgroups

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

subgroup	index
#28416565	2
C₄⋊#16836569	2
#346×C₂₃₃	2
#1338	233