Subgroups — #28417481

Order 14912.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21418623	C₂	1	2	yes	maximal, complemented
2	#21418605	C₂	1	1	yes	maximal, characteristic, complemented
3	#21418600	C₂	1	2	yes	maximal, complemented
4	#21418589	C₂	1	1	yes	maximal, characteristic, complemented
5	#21418558	C₂	1	1	yes	maximal, characteristic
6	#16836604	—	2	2	no	—
7	#16836604	C₂²	1	2	yes	—
8	#16836602	—	2	2	no	—
9	#16836602	C₂²	1	1	yes	characteristic
10	C₄×#11745400	C₂²	1	1	yes	characteristic
11	#16836595	C₂²	1	2	yes	—
12	#16836581	C₄	1	2	yes	complemented
13	D₁₈₆₄	C₄	1	1	yes	characteristic, complemented
14	C₈×D₂₃₃	C₂²	1	1	yes	characteristic
15	Q₁₆×C₂₃₃	C₄	1	1	yes	characteristic, complemented
16	C₂×#11745400	—	2	1	no	—
17	#14272345	—	2	2	no	—
18	#14272345	D₄	1	2	yes	—
19	D₉₃₂	—	2	2	no	—
20	D₉₃₂	C₂×C₄	1	2	yes	—
21	C₄×D₂₃₃	—	2	2	no	—
22	C₄×D₂₃₃	C₂³	1	1	yes	characteristic
23	#14272338	C₂×C₄	1	1	yes	characteristic
24	Q₈×C₂₃₃	C₂×C₄	1	2	yes	—
25	C₈×C₂₃₃	C₂×C₄	1	1	yes	characteristic
26	C₂×D₂₃₃	—	2	2	no	—
27	C₂×D₂₃₃	#41	1	1	yes	characteristic
28	#11745400	—	4	1	no	—
29	C₄×C₂₃₃	—	2	2	no	—
30	C₄×C₂₃₃	C₂²×C₄	1	1	yes	characteristic
31	Dic₂₃₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₂₃₃	C₄×D₄	1	1	yes	characteristic
33	D₂₃₃	—	2	1	no	—
34	D₂₃₃	—	4	2	no	—
35	C₂₃₃	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	233	1	no	maximal, Sylow
37	#135	—	233	1	no	—
38	#131	—	233	2	no	—
39	#108	—	233	1	no	—
40	#104	—	233	2	no	—
41	#97	—	233	1	no	—
42	#41	—	233	2	no	—
43	Q₁₆	#11745400	1	1	yes	characteristic, complemented
44	SD₁₆	—	233	2	no	—
45	D₈	—	233	1	no	—
46	M₁₆	—	466	2	no	—
47	M₁₆	—	233	2	no	—
48	C₂×C₈	—	466	2	no	—
49	C₂×C₈	—	233	1	no	—
50	C₂×C₈	—	233	1	no	—
51	C₄²	—	233	1	no	—
52	Q₈	C₂×#11745400	1	2	yes	—
53	D₄	—	466	2	no	—
54	D₄	—	233	2	no	—
55	C₂×C₄	—	466	2	no	—
56	C₂×C₄	—	466	1	no	—
57	C₂×C₄	—	233	1	no	—
58	C₈	—	466	2	no	—
59	C₈	—	233	2	no	—
60	C₈	—	233	1	no	—
61	C₈	C₂×#11745400	1	1	yes	characteristic
62	C₂²	—	466	2	no	—
63	C₂²	—	233	1	no	—
64	C₄	—	2	2	no	—
65	C₄	—	932	1	no	—
66	C₄	—	233	1	no	—
67	C₄	C₂²×#11745400	1	1	yes	characteristic
68	C₂	—	932	2	no	—
69	C₂	—	466	1	no	—
70	C₂	D₄×#11745400	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#11745400
commutator	C₄×C₂₃₃	C₂²×C₄
Frattini	C₄	C₂²×#11745400
Fitting	Q₁₆×C₂₃₃	C₄
socle	C₂×C₂₃₃	C₄×D₄
prime radical	#21418558	C₂
cosocle	C₄×D₂₃₃	C₂³
hypercenter	Q₁₆	#11745400
hypocenter	C₂₃₃	#444
LCS	G ▷ C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #21418623	C₂	semidirect
2. #21418605	C₂	semidirect
3. #21418600	C₂	semidirect
4. #21418589	C₂	semidirect
12. #16836581	C₄	semidirect
13. D₁₈₆₄	C₄	semidirect
15. Q₁₆×C₂₃₃	C₄	semidirect
35. C₂₃₃	#444	semidirect
43. Q₁₆	#11745400	semidirect

Maximal subgroups

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

subgroup	index
#21418623	2
#21418605	2
#21418600	2
#21418589	2
#21418558	2
#444	233