Subgroups — #28417410

Order 14912.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16836604	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16836602	C₂	1	1	yes	maximal, characteristic, complemented
3	#21418592	C₂	1	4	yes	maximal, complemented
4	C₂×#16836595	C₂	1	1	yes	maximal, characteristic
5	#16836604	—	2	2	no	—
6	#16836602	—	2	2	no	—
7	C₂×#14272345	C₂²	1	2	yes	—
8	C₂×#14272345	C₂²	1	2	yes	—
9	#16836595	—	2	2	no	—
10	#16836595	—	2	2	no	—
11	C₂×D₉₃₂	C₄	1	2	yes	—
12	C₂×D₉₃₂	C₄	1	1	yes	characteristic
13	C₂×C₄×D₂₃₃	C₂²	1	2	yes	—
14	C₂×C₄×D₂₃₃	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₂₃₃	C₄	1	1	yes	characteristic
16	#14272345	—	2	2	no	—
17	#14272345	—	2	2	no	—
18	C₂²×D₂₃₃	C₂×C₄	1	2	yes	—
19	C₂²×D₂₃₃	C₂×C₄	1	1	yes	characteristic
20	D₉₃₂	—	2	4	no	—
21	D₉₃₂	—	2	2	no	—
22	C₂×Dic₂₃₃	C₂³	1	1	yes	characteristic
23	C₄×D₂₃₃	—	2	2	no	—
24	C₄×D₂₃₃	—	2	2	no	—
25	C₄×D₂₃₃	D₄	1	2	yes	—
26	C₄×D₂₃₃	D₄	1	2	yes	—
27	Q₈×C₂₃₃	—	2	2	no	—
28	C₂×C₄×C₂₃₃	C₂×C₄	1	2	yes	—
29	C₂×C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₂₃₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×D₂₃₃	—	2	2	no	—
32	C₂×D₂₃₃	—	2	2	no	—
33	C₂×D₂₃₃	—	2	4	no	—
34	C₂×D₂₃₃	C₂²⋊C₄	1	2	yes	—
35	C₄×C₂₃₃	—	2	2	no	—
36	C₄×C₂₃₃	C₂²⋊C₄	1	2	yes	—
37	Dic₂₃₃	C₂×D₄	1	1	yes	characteristic
38	Dic₂₃₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₂₃₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₂₃₃	#131	1	2	yes	—
41	D₂₃₃	—	2	2	no	—
42	D₂₃₃	—	4	2	no	—
43	C₂₃₃	#408	1	1	yes	characteristic, complemented, Sylow
44	#408	—	233	1	no	maximal, Sylow
45	C₂×#41	—	233	1	no	—
46	C₂×M₁₆	—	233	1	no	—
47	C₂²×C₈	—	233	1	no	—
48	C₂²⋊C₈	—	233	4	no	—
49	#41	—	466	2	no	—
50	#41	—	466	2	no	—
51	C₂×Q₈	#11745400	1	1	yes	characteristic
52	C₂×D₄	—	233	2	no	—
53	C₂×D₄	—	233	1	no	—
54	C₂²×C₄	—	233	2	no	—
55	C₂²×C₄	—	233	1	no	—
56	M₁₆	—	466	2	no	—
57	C₂×C₈	—	466	2	no	—
58	C₂×C₈	—	233	2	no	—
59	C₂×C₈	—	233	2	no	—
60	C₂³	—	233	2	no	—
61	C₂³	—	233	1	no	—
62	Q₈	—	2	2	no	—
63	D₄	—	466	4	no	—
64	D₄	—	466	2	no	—
65	C₂×C₄	—	466	2	no	—
66	C₂×C₄	—	466	2	no	—
67	C₂×C₄	—	233	1	no	—
68	C₂×C₄	—	233	2	no	—
69	C₂×C₄	—	233	2	no	—
70	C₂×C₄	C₂×#11745400	1	2	yes	—
71	C₂×C₄	C₂×#11745400	1	1	yes	characteristic
72	C₈	—	466	2	no	—
73	C₈	—	466	2	no	—
74	C₂²	—	466	2	no	—
75	C₂²	—	466	4	no	—
76	C₂²	—	466	2	no	—
77	C₂²	—	233	2	no	—
78	C₂²	C₂²×#11745400	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	233	1	no	—
81	C₄	—	233	1	no	—
82	C₄	C₂²⋊#11745400	1	2	yes	—
83	C₂	—	932	2	no	—
84	C₂	—	466	2	no	—
85	C₂	C₂×C₂²⋊#11745400	1	1	yes	characteristic
86	C₂	#21418623	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#11745400
commutator, socle	C₂²×C₂₃₃	C₂²×C₄
Fitting	C₂×Q₈×C₂₃₃	C₄
prime radical	C₂×#16836595	C₂
cosocle	C₂×Dic₂₃₃	C₂³
hypercenter	C₂×Q₈	#11745400
hypocenter	C₂₃₃	#408
LCS	G ▷ C₂²×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#16836604	C₂	semidirect
2. C₂×#16836602	C₂	semidirect
3. #21418592	C₂	semidirect
43. C₂₃₃	#408	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16836604	2
C₂×#16836602	2
#21418592	2
C₂×#16836595	2
#408	233