Subgroups — D₂₃₃⋊#108 #28417448

Order 14912.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₃₃⋊M₁₆	C₂	1	2	yes	maximal
2	#21418606	C₂	1	2	yes	maximal, complemented
3	#21418605	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₂₃₃	C₂	1	1	yes	maximal, characteristic
5	#16836604	C₂²	1	4	yes	—
6	#16836603	—	2	2	no	—
7	#16836602	—	2	2	no	—
8	C₂×C₄×D₂₃₃	C₂²	1	1	yes	characteristic
9	C₂×#14272338	C₄	1	1	yes	characteristic
10	C₈×D₂₃₃	C₄	1	1	yes	characteristic
11	C₈×D₂₃₃	C₄	1	1	yes	characteristic
12	C₈×D₂₃₃	C₂²	1	1	yes	characteristic
13	C₈×D₂₃₃	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₂₃₃	C₄	1	1	yes	characteristic
15	#14272345	—	2	4	no	—
16	C₂²×D₂₃₃	Q₈	1	1	yes	characteristic
17	C₂×Dic₂₃₃	D₄	1	1	yes	characteristic
18	C₄×D₂₃₃	C₂×C₄	1	1	yes	characteristic
19	C₄×D₂₃₃	D₄	1	1	yes	characteristic
20	C₄×D₂₃₃	Q₈	1	1	yes	characteristic
21	C₄×D₂₃₃	C₂³	1	1	yes	characteristic
22	#14272338	C₂×C₄	1	1	yes	characteristic
23	#14272338	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
25	C₈×C₂₃₃	C₂×C₄	1	1	yes	characteristic
26	C₈×C₂₃₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₂₃₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₂₃₃	—	2	2	no	—
29	C₂×D₂₃₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₂₃₃	C₂×Q₈	1	1	yes	characteristic
31	C₄×C₂₃₃	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₂₃₃	C₂²×C₄	1	1	yes	characteristic
33	Dic₂₃₃	C₄⋊C₄	1	1	yes	characteristic
34	Dic₂₃₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₂₃₃	—	2	1	no	—
36	C₂×C₂₃₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	D₂₃₃	—	2	1	no	—
38	D₂₃₃	#108	1	2	yes	complemented
39	C₂₃₃	C₂×#108	1	1	yes	characteristic, complemented, Sylow
40	C₂×#108	—	233	1	no	maximal, Sylow
41	C₂×M₁₆	—	233	2	no	—
42	C₂²×C₈	—	233	1	no	—
43	#108	—	233	2	no	—
44	#108	—	233	2	no	—
45	C₂²×C₄	—	233	1	no	—
46	M₁₆	—	466	2	no	—
47	M₁₆	—	233	4	no	—
48	C₂×C₈	—	466	2	no	—
49	C₂×C₈	—	233	1	no	—
50	C₂×C₈	—	233	1	no	—
51	C₂×C₈	—	233	1	no	—
52	C₂×C₈	—	233	1	no	—
53	C₂×C₈	—	233	1	no	—
54	C₂×C₈	#11745400	1	1	yes	characteristic
55	C₂³	—	233	1	no	—
56	C₂×C₄	—	233	1	no	—
57	C₂×C₄	—	233	1	no	—
58	C₂×C₄	—	233	1	no	—
59	C₂×C₄	—	233	1	no	—
60	C₂×C₄	—	233	1	no	—
61	C₂×C₄	C₂×#11745400	1	1	yes	characteristic
62	C₈	—	466	4	no	—
63	C₈	—	233	1	no	—
64	C₈	—	233	1	no	—
65	C₈	C₂×#11745400	1	1	yes	characteristic
66	C₈	C₂×#11745400	1	1	yes	characteristic
67	C₂²	—	466	2	no	—
68	C₂²	—	233	1	no	—
69	C₂²	—	233	1	no	—
70	C₂²	C₄⋊#11745400	1	1	yes	characteristic
71	C₄	—	233	1	no	—
72	C₄	—	233	1	no	—
73	C₄	C₄⋊#11745400	1	1	yes	characteristic
74	C₄	C₂²×#11745400	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	466	1	no	—
77	C₂	—	233	2	no	—
78	C₂	C₂×C₄⋊#11745400	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#11745400
commutator	C₄×C₂₃₃	C₂²×C₄
Frattini	C₄	C₂²×#11745400
Fitting	C₂×C₈×C₂₃₃	C₄
socle	C₂×C₂₃₃	C₂×C₄⋊C₄
prime radical	C₂²×D₂₃₃	Q₈
cosocle	C₄×D₂₃₃	C₂³
hypercenter	C₂×C₈	#11745400
hypocenter	C₂₃₃	C₂×#108
LCS	G ▷ C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #21418606	C₂	semidirect
3. #21418605	C₂	semidirect
38. D₂₃₃	#108	semidirect
39. C₂₃₃	C₂×#108	semidirect

Maximal subgroups

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

subgroup	index
D₂₃₃⋊M₁₆	2
#21418606	2
#21418605	2
C₂×C₈×D₂₃₃	2
C₂×#108	233

Subgroups — D233⋊#108 #28417448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃₃⋊#108 #28417448