Subgroups — D₄⋊#16812367 #42122898

Order 27712.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#16812367	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#16812367	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#13181884	C₂	1	1	yes	maximal, characteristic
4	C₂×#16812367	—	2	1	no	—
5	C₂×#16812367	—	2	1	no	—
6	C₂²×#13181884	—	2	1	no	—
7	C₄⋊#13181884	C₄	1	1	yes	characteristic
8	C₂²⋊#13181884	—	2	1	no	—
9	C₄×#13181884	C₂²	1	1	yes	characteristic
10	D₄×D₄₃₃	C₄	1	1	yes	characteristic
11	#16812367	—	2	2	no	—
12	#16812367	—	4	1	no	—
13	C₂×#13181884	—	2	1	no	—
14	C₂×#13181884	—	4	1	no	—
15	C₂×#13181884	—	4	1	no	—
16	C₂×#13181884	D₄	1	1	yes	characteristic
17	C₂×#13181884	D₄	1	1	yes	characteristic
18	C₂²×D₄₃₃	—	2	1	no	—
19	D₁₇₃₂	C₈	1	1	yes	characteristic, complemented
20	C₂²⋊D₄₃₃	—	2	1	no	—
21	C₄×D₄₃₃	C₂×C₄	1	1	yes	characteristic
22	D₄×C₄₃₃	C₈	1	1	yes	characteristic, complemented
23	C₂²×C₄₃₃	—	2	1	no	—
24	C₂×D₄₃₃	—	2	1	no	—
25	C₂×D₄₃₃	—	4	1	no	—
26	C₂×D₄₃₃	—	4	1	no	—
27	C₂×D₄₃₃	C₂²⋊C₄	1	1	yes	characteristic
28	#13181884	—	2	1	no	—
29	#13181884	—	4	1	no	—
30	#13181884	D₈	1	1	yes	characteristic
31	#13181884	SD₁₆	1	1	yes	characteristic
32	C₄×C₄₃₃	C₂×C₈	1	1	yes	characteristic
33	Dic₄₃₃	M₁₆	1	1	yes	characteristic
34	C₂×C₄₃₃	—	4	1	no	—
35	C₂×C₄₃₃	C₂²⋊C₈	1	1	yes	characteristic
36	D₄₃₃	—	4	1	no	—
37	D₄₃₃	#102	1	1	yes	characteristic
38	D₄₃₃	#104	1	1	yes	characteristic
39	C₄₃₃	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
40	D₄⋊C₈	—	433	1	no	maximal, Sylow
41	C₄×D₄	—	433	1	no	—
42	C₄⋊C₈	—	433	1	no	—
43	C₄×C₈	—	433	1	no	—
44	C₂×D₄	—	433	1	no	—
45	C₂²×C₄	—	866	1	no	—
46	C₂×C₈	—	866	1	no	—
47	C₂×C₈	—	866	1	no	—
48	C₄⋊C₄	—	433	1	no	—
49	C₂²⋊C₄	—	866	1	no	—
50	C₄²	—	433	1	no	—
51	C₂³	—	866	1	no	—
52	D₄	—	866	1	no	—
53	D₄	—	433	1	no	—
54	D₄	#16812367	1	1	yes	characteristic, complemented
55	C₂×C₄	—	866	1	no	—
56	C₂×C₄	—	433	1	no	—
57	C₂×C₄	—	433	1	no	—
58	C₂×C₄	—	433	1	no	—
59	C₂×C₄	—	1732	1	no	—
60	C₂×C₄	—	1732	1	no	—
61	C₈	—	866	2	no	—
62	C₈	—	1732	1	no	—
63	C₂²	—	2	1	no	—
64	C₂²	—	866	1	no	—
65	C₂²	—	433	1	no	—
66	C₂²	—	1732	1	no	—
67	C₂²	—	1732	1	no	—
68	C₄	—	866	1	no	—
69	C₄	—	433	1	no	—
70	C₄	—	433	1	no	—
71	C₄	—	433	1	no	—
72	C₄	—	1732	1	no	—
73	C₄	C₂×#16812367	1	1	yes	characteristic
74	C₂	—	4	1	no	—
75	C₂	—	433	1	no	—
76	C₂	—	433	1	no	—
77	C₂	—	1732	1	no	—
78	C₂	C₂²⋊#16812367	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#16812367
commutator	C₄×C₄₃₃	C₂×C₈
Frattini	C₄	C₂×#16812367
Fitting	D₄×C₄₃₃	C₈
socle	C₂×C₄₃₃	C₂²⋊C₈
prime radical	D₄×D₄₃₃	C₄
cosocle	C₄×#13181884	C₂²
hypercenter	D₄	#16812367
hypocenter	C₄₃₃	D₄⋊C₈
LCS	G ▷ C₄×C₄₃₃ ▷ C₂×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊#16812367	C₂	semidirect
2. C₄×#16812367	C₂	semidirect
19. D₁₇₃₂	C₈	semidirect
22. D₄×C₄₃₃	C₈	semidirect
39. C₄₃₃	D₄⋊C₈	semidirect
54. D₄	#16812367	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#16812367	2
C₄×#16812367	2
D₄×#13181884	2
D₄⋊C₈	433

Subgroups — D4⋊#16812367 #42122898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄⋊#16812367 #42122898