Subgroups — D₄×#15692552 #39910361

Order 26176.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15692552	C₂	1	2	yes	maximal, complemented
2	C₄⋊#15692552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#15692552	C₂	1	2	yes	maximal, complemented
4	C₄×#15692552	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×#13109888	C₂	1	1	yes	maximal, characteristic
6	C₂×#15692552	—	2	4	no	—
7	C₂×#15692552	C₂²	1	1	yes	characteristic
8	C₂×#15692552	C₂²	1	2	yes	—
9	C₂×#15692552	C₂²	1	1	yes	characteristic
10	C₂²×#13109888	C₂²	1	2	yes	—
11	C₄⋊#13109888	C₄	1	1	yes	characteristic
12	C₂²⋊#13109888	C₄	1	2	yes	—
13	C₄×#13109888	C₂²	1	1	yes	characteristic
14	D₄×D₄₀₉	C₄	1	1	yes	characteristic
15	#15692552	—	2	2	no	—
16	#15692552	—	2	1	no	—
17	#15692552	D₄	1	2	yes	direct product factor
18	C₂×#13109888	—	2	2	no	—
19	C₂×#13109888	—	2	2	no	—
20	C₂×#13109888	C₂×C₄	1	1	yes	characteristic
21	C₂×#13109888	C₂×C₄	1	2	yes	—
22	C₂×#13109888	C₂³	1	1	yes	characteristic
23	C₂²×D₄₀₉	C₂×C₄	1	2	yes	—
24	D₁₆₃₆	C₈	1	1	yes	characteristic, complemented
25	C₂²⋊D₄₀₉	C₈	1	2	yes	complemented
26	C₄×D₄₀₉	C₂×C₄	1	1	yes	characteristic
27	D₄×C₄₀₉	C₈	1	1	yes	characteristic, complemented
28	C₂²×C₄₀₉	C₂×C₈	1	2	yes	complemented
29	C₂×D₄₀₉	—	2	2	no	—
30	C₂×D₄₀₉	—	2	2	no	—
31	C₂×D₄₀₉	C₂×C₈	1	2	yes	complemented
32	C₂×D₄₀₉	C₂²×C₄	1	1	yes	characteristic
33	#13109888	—	2	2	no	—
34	#13109888	—	2	1	no	—
35	#13109888	C₂×D₄	1	1	yes	characteristic
36	#13109888	#41	1	1	yes	characteristic
37	C₄×C₄₀₉	C₂×C₈	1	1	yes	characteristic, complemented
38	Dic₄₀₉	C₂×C₈	1	1	yes	characteristic, complemented
39	C₂×C₄₀₉	—	2	2	no	—
40	C₂×C₄₀₉	C₂²×C₈	1	1	yes	characteristic
41	D₄₀₉	—	2	2	no	—
42	D₄₀₉	C₄×D₄	1	1	yes	characteristic
43	D₄₀₉	#131	1	1	yes	characteristic
44	C₄₀₉	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
45	C₈×D₄	—	409	1	no	maximal, Sylow
46	C₂²×C₈	—	409	2	no	—
47	C₄×D₄	—	409	1	no	—
48	C₄⋊C₈	—	409	1	no	—
49	C₂²⋊C₈	—	409	2	no	—
50	C₄×C₈	—	409	1	no	—
51	C₂×D₄	—	409	1	no	—
52	C₂²×C₄	—	409	2	no	—
53	C₂×C₈	—	818	4	no	—
54	C₂×C₈	—	409	1	no	—
55	C₂×C₈	—	409	2	no	—
56	C₂×C₈	—	409	1	no	—
57	C₄⋊C₄	—	409	1	no	—
58	C₂²⋊C₄	—	409	2	no	—
59	C₄²	—	409	1	no	—
60	C₂³	—	409	2	no	—
61	D₄	—	409	2	no	—
62	D₄	—	409	1	no	—
63	D₄	#15692552	1	1	yes	characteristic, direct product factor
64	C₂×C₄	—	818	2	no	—
65	C₂×C₄	—	818	2	no	—
66	C₂×C₄	—	409	1	no	—
67	C₂×C₄	—	409	2	no	—
68	C₂×C₄	—	409	1	no	—
69	C₂×C₄	—	409	1	no	—
70	C₈	—	818	2	no	—
71	C₈	—	818	1	no	—
72	C₈	—	409	2	no	—
73	C₂²	—	818	2	no	—
74	C₂²	—	818	2	no	—
75	C₂²	—	409	2	no	—
76	C₂²	—	409	1	no	—
77	C₂²	C₂×#15692552	1	2	yes	complemented
78	C₄	—	818	2	no	—
79	C₄	—	818	1	no	—
80	C₄	—	409	1	no	—
81	C₄	—	409	1	no	—
82	C₄	—	409	1	no	—
83	C₄	C₂×#15692552	1	1	yes	characteristic, complemented
84	C₂	—	2	2	no	—
85	C₂	—	818	2	no	—
86	C₂	—	409	1	no	—
87	C₂	—	409	1	no	—
88	C₂	C₂²×#15692552	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#15692552
commutator, socle	C₂×C₄₀₉	C₂²×C₈
Fitting	D₄×C₄₀₉	C₈
prime radical	D₄×D₄₀₉	C₄
cosocle	C₂×#13109888	C₂³
hypercenter	D₄	#15692552
hypocenter	C₄₀₉	C₈×D₄
LCS	G ▷ C₂×C₄₀₉ ▷ C₄₀₉
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#15692552	C₂	semidirect
2. C₄⋊#15692552	C₂	semidirect
3. C₂²⋊#15692552	C₂	semidirect
4. C₄×#15692552	C₂	semidirect
17. #15692552	D₄	direct (N × H)
24. D₁₆₃₆	C₈	semidirect
25. C₂²⋊D₄₀₉	C₈	semidirect
27. D₄×C₄₀₉	C₈	semidirect
28. C₂²×C₄₀₉	C₂×C₈	semidirect
31. C₂×D₄₀₉	C₂×C₈	semidirect
37. C₄×C₄₀₉	C₂×C₈	semidirect
38. Dic₄₀₉	C₂×C₈	semidirect
44. C₄₀₉	C₈×D₄	semidirect
63. D₄	#15692552	direct (N × H)
77. C₂²	C₂×#15692552	semidirect
83. C₄	C₂×#15692552	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#15692552	2
C₄⋊#15692552	2
C₂²⋊#15692552	2
C₄×#15692552	2
D₄×#13109888	2
C₈×D₄	409

Subgroups — D4×#15692552 #39910361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#15692552 #39910361