Subgroups — C₄×#20294106 #42122772

Order 27712.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20294106	C₂	1	2	yes	maximal
2	#28357275	C₂	1	2	yes	maximal, complemented
3	C₄×#16812365	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×Dic₄₃₃	C₂	1	1	yes	maximal, characteristic
5	#20294106	C₄	1	8	yes	direct product factor
6	C₂×#16812365	C₂²	1	4	yes	—
7	C₂²×Dic₄₃₃	C₄	1	1	yes	characteristic
8	C₂²×Dic₄₃₃	C₂²	1	1	yes	characteristic
9	C₄×Dic₄₃₃	C₄	1	1	yes	characteristic
10	C₄×Dic₄₃₃	C₄	1	1	yes	characteristic
11	C₄×Dic₄₃₃	C₂²	1	1	yes	characteristic
12	C₄×Dic₄₃₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₄₃₃	C₄	1	1	yes	characteristic
14	#16812365	C₂×C₄	1	8	yes	complemented
15	C₂×Dic₄₃₃	—	2	2	no	—
16	C₂×Dic₄₃₃	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₄₃₃	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₄₃₃	C₂×C₄	1	4	yes	—
19	C₂×Dic₄₃₃	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₄₃₃	C₂³	1	1	yes	characteristic
21	C₂³×C₄₃₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₄₃₃	—	2	2	no	—
23	C₂×C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄₃₃	—	2	1	no	—
26	C₂²×C₄₃₃	—	2	1	no	—
27	C₂²×C₄₃₃	C₄²	1	2	yes	—
28	C₂²×C₄₃₃	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₄₃₃	—	2	1	no	—
30	C₄×C₄₃₃	M₁₆	1	2	yes	complemented
31	Dic₄₃₃	—	2	1	no	—
32	Dic₄₃₃	C₄²	1	2	yes	—
33	Dic₄₃₃	M₁₆	1	2	yes	complemented
34	Dic₄₃₃	C₂²×C₄	1	2	yes	—
35	C₂×C₄₃₃	—	2	2	no	—
36	C₂×C₄₃₃	C₂×C₄²	1	1	yes	characteristic
37	C₂×C₄₃₃	C₂×M₁₆	1	1	yes	characteristic
38	C₂×C₄₃₃	C₂×M₁₆	1	1	yes	characteristic
39	C₄₃₃	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₄×M₁₆	—	433	1	no	maximal, Sylow
41	C₂×M₁₆	—	433	2	no	—
42	C₂×C₄²	—	433	1	no	—
43	#97	—	433	2	no	—
44	C₄×C₈	—	433	2	no	—
45	C₂²×C₄	—	433	1	no	—
46	C₂²×C₄	—	433	1	no	—
47	C₂²×C₄	#13181884	1	1	yes	characteristic
48	M₁₆	—	433	8	no	—
49	C₂×C₈	—	433	4	no	—
50	C₄²	—	433	1	no	—
51	C₄²	—	433	1	no	—
52	C₄²	—	433	1	no	—
53	C₄²	—	433	1	no	—
54	C₂³	C₂×#13181884	1	1	yes	characteristic
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	866	2	no	—
57	C₂×C₄	—	433	1	no	—
58	C₂×C₄	—	433	4	no	—
59	C₂×C₄	—	433	1	no	—
60	C₂×C₄	—	433	1	no	—
61	C₂×C₄	—	433	1	no	—
62	C₂×C₄	C₂×#13181884	1	1	yes	characteristic
63	C₂×C₄	C₂×#13181884	1	1	yes	characteristic
64	C₈	—	433	8	no	—
65	C₂²	—	2	1	no	—
66	C₂²	—	2	1	no	—
67	C₂²	C₄×#13181884	1	2	yes	—
68	C₂²	C₂²×#13181884	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	866	1	no	—
71	C₄	—	433	2	no	—
72	C₄	—	433	2	no	—
73	C₄	—	433	2	no	—
74	C₄	#20294106	1	2	yes	direct product factor
75	C₂	—	2	2	no	—
76	C₂	C₂×C₄×#13181884	1	1	yes	characteristic
77	C₂	C₂×#20294106	1	1	yes	characteristic
78	C₂	D₄₃₃⋊M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#13181884
commutator	C₂×C₄₃₃	C₂×C₄²
Frattini	C₂²	C₂²×#13181884
Fitting	C₂²×C₄×C₄₃₃	C₄
socle	C₂²×C₄₃₃	C₂²×C₄
prime radical	C₂³×C₄₃₃	C₂×C₄
cosocle	C₂×Dic₄₃₃	C₂³
hypercenter	C₂²×C₄	#13181884
hypocenter	C₄₃₃	C₄×M₁₆
LCS	G ▷ C₂×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. #28357275	C₂	semidirect
3. C₄×#16812365	C₂	semidirect
5. #20294106	C₄	direct (N × H)
14. #16812365	C₂×C₄	semidirect
30. C₄×C₄₃₃	M₁₆	semidirect
33. Dic₄₃₃	M₁₆	semidirect
39. C₄₃₃	C₄×M₁₆	semidirect
74. C₄	#20294106	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#20294106	2
#28357275	2
C₄×#16812365	2
C₂×C₄×Dic₄₃₃	2
C₄×M₁₆	433

Subgroups — C4×#20294106 #42122772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#20294106 #42122772