Subgroups — D₄₃₃⋊#101 #42122796

Order 27712.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₃₃⋊M₁₆	C₂	1	2	yes	maximal
2	#28357281	C₂	1	4	yes	maximal, complemented
3	C₂×Q₈×D₄₃₃	C₂	1	1	yes	maximal, characteristic
4	#20294107	—	2	2	no	—
5	#20294106	C₂²	1	4	yes	—
6	#20294105	—	2	2	no	—
7	C₂×Dic₈₆₆	C₄	1	1	yes	characteristic
8	C₂×Dic₈₆₆	C₂²	1	2	yes	—
9	Q₈×D₄₃₃	—	2	2	no	—
10	Q₈×D₄₃₃	—	2	2	no	—
11	C₂×C₄×D₄₃₃	C₄	1	2	yes	—
12	C₂×C₄×D₄₃₃	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₄₃₃	C₄	1	1	yes	characteristic
14	#16812365	—	2	4	no	—
15	C₂²×D₄₃₃	C₂×C₄	1	1	yes	characteristic
16	Dic₈₆₆	—	2	2	no	—
17	Dic₈₆₆	—	2	4	no	—
18	C₂×Dic₄₃₃	C₂×C₄	1	2	yes	—
19	C₂×Dic₄₃₃	C₂³	1	1	yes	characteristic
20	C₄×D₄₃₃	—	2	2	no	—
21	C₄×D₄₃₃	—	2	2	no	—
22	C₄×D₄₃₃	D₄	1	2	yes	—
23	C₄×D₄₃₃	D₄	1	2	yes	—
24	Q₈×C₄₃₃	—	2	2	no	—
25	C₂×C₄×C₄₃₃	C₂×C₄	1	2	yes	—
26	C₂×C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄₃₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₄₃₃	—	2	2	no	—
29	C₂×D₄₃₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₄₃₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₄₃₃	—	2	2	no	—
32	C₄×C₄₃₃	C₂²⋊C₄	1	2	yes	—
33	Dic₄₃₃	—	2	2	no	—
34	Dic₄₃₃	C₂×D₄	1	2	yes	—
35	C₂×C₄₃₃	—	2	1	no	—
36	C₂×C₄₃₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	D₄₃₃	—	2	1	no	—
38	D₄₃₃	#101	1	2	yes	complemented
39	C₄₃₃	C₂×#101	1	1	yes	characteristic, complemented, Sylow
40	C₂×#101	—	433	1	no	maximal, Sylow
41	C₂²×Q₈	—	433	1	no	—
42	C₂×M₁₆	—	433	2	no	—
43	#101	—	433	4	no	—
44	C₂×Q₈	—	866	2	no	—
45	C₂×Q₈	—	866	2	no	—
46	C₂×Q₈	—	433	2	no	—
47	C₂×Q₈	—	433	1	no	—
48	C₂×Q₈	#13181884	1	1	yes	characteristic
49	C₂²×C₄	—	433	2	no	—
50	C₂²×C₄	—	433	1	no	—
51	M₁₆	—	866	2	no	—
52	M₁₆	—	433	4	no	—
53	C₂×C₈	—	866	2	no	—
54	C₂³	—	433	1	no	—
55	Q₈	—	2	2	no	—
56	Q₈	—	866	4	no	—
57	Q₈	—	866	2	no	—
58	C₂×C₄	—	866	2	no	—
59	C₂×C₄	—	866	2	no	—
60	C₂×C₄	—	433	2	no	—
61	C₂×C₄	—	433	1	no	—
62	C₂×C₄	—	433	2	no	—
63	C₂×C₄	—	433	2	no	—
64	C₂×C₄	C₂×#13181884	1	2	yes	—
65	C₂×C₄	C₂×#13181884	1	1	yes	characteristic
66	C₈	—	866	4	no	—
67	C₂²	—	866	2	no	—
68	C₂²	—	433	1	no	—
69	C₂²	—	433	1	no	—
70	C₂²	C₂²×#13181884	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	866	2	no	—
73	C₄	—	433	2	no	—
74	C₄	C₂²⋊#13181884	1	2	yes	—
75	C₂	—	2	1	no	—
76	C₂	—	866	1	no	—
77	C₂	—	433	2	no	—
78	C₂	C₂×C₂²⋊#13181884	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#13181884
commutator	C₂²×C₄₃₃	C₂²×C₄
Frattini	C₂²	C₂²×#13181884
Fitting	C₂×Q₈×C₄₃₃	C₄
socle	C₂×C₄₃₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₄₃₃	C₂×C₄
cosocle	C₂×Dic₄₃₃	C₂³
hypercenter	C₂×Q₈	#13181884
hypocenter	C₄₃₃	C₂×#101
LCS	G ▷ C₂²×C₄₃₃ ▷ C₂×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #28357281	C₂	semidirect
38. D₄₃₃	#101	semidirect
39. C₄₃₃	C₂×#101	semidirect

Maximal subgroups

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

subgroup	index
D₄₃₃⋊M₁₆	2
#28357281	2
C₂×Q₈×D₄₃₃	2
C₂×#101	433

Subgroups — D433⋊#101 #42122796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃₃⋊#101 #42122796