Subgroups — C₂×#27189788 #39910261

Order 26176.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20266998	C₂	1	2	yes	maximal
2	#27189788	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×D₄₀₉	C₂	1	1	yes	maximal, characteristic
4	#20266998	—	2	2	no	—
5	#20266998	C₂²	1	4	yes	—
6	C₂×#15692550	—	2	2	no	—
7	C₂×C₄×D₄₀₉	C₂²	1	1	yes	characteristic
8	C₂×#15692543	C₄	1	1	yes	characteristic
9	C₈×D₄₀₉	C₄	1	2	yes	—
10	C₈×D₄₀₉	C₂²	1	2	yes	—
11	C₂×C₈×C₄₀₉	C₄	1	1	yes	characteristic
12	#15692550	—	2	4	no	—
13	C₂²×D₄₀₉	Q₈	1	1	yes	characteristic
14	C₂×Dic₄₀₉	D₄	1	1	yes	characteristic
15	C₄×D₄₀₉	C₂×C₄	1	1	yes	characteristic
16	C₄×D₄₀₉	D₄	1	1	yes	characteristic
17	C₄×D₄₀₉	Q₈	1	1	yes	characteristic
18	C₄×D₄₀₉	C₂³	1	1	yes	characteristic
19	#15692543	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₄₀₉	C₂×C₄	1	1	yes	characteristic
21	C₈×C₄₀₉	C₂×C₄	1	2	yes	—
22	C₂²×C₄₀₉	C₄⋊C₄	1	1	yes	characteristic
23	C₂×D₄₀₉	—	2	2	no	—
24	C₂×D₄₀₉	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₄₀₉	C₂×Q₈	1	1	yes	characteristic
26	C₄×C₄₀₉	C₄⋊C₄	1	1	yes	characteristic
27	C₄×C₄₀₉	C₂²×C₄	1	1	yes	characteristic
28	Dic₄₀₉	C₄⋊C₄	1	1	yes	characteristic
29	Dic₄₀₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄₀₉	#108	1	2	yes	complemented
31	C₂×C₄₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
32	D₄₀₉	—	2	1	no	—
33	D₄₀₉	—	2	1	no	—
34	C₄₀₉	C₂×#108	1	1	yes	characteristic, complemented, Sylow
35	C₂×#108	—	409	1	no	maximal, Sylow
36	C₂×M₁₆	—	409	2	no	—
37	C₂²×C₈	—	409	1	no	—
38	#108	—	409	4	no	—
39	C₂²×C₄	—	409	1	no	—
40	M₁₆	—	818	2	no	—
41	M₁₆	—	409	4	no	—
42	C₂×C₈	—	818	2	no	—
43	C₂×C₈	—	409	1	no	—
44	C₂×C₈	—	409	2	no	—
45	C₂×C₈	—	409	2	no	—
46	C₂×C₈	#13109888	1	1	yes	characteristic
47	C₂³	—	409	1	no	—
48	C₂×C₄	—	409	1	no	—
49	C₂×C₄	—	409	1	no	—
50	C₂×C₄	—	409	1	no	—
51	C₂×C₄	—	409	1	no	—
52	C₂×C₄	—	409	1	no	—
53	C₂×C₄	C₂×#13109888	1	1	yes	characteristic
54	C₈	—	818	4	no	—
55	C₈	—	409	2	no	—
56	C₈	C₂×#13109888	1	2	yes	—
57	C₂²	—	818	2	no	—
58	C₂²	—	409	1	no	—
59	C₂²	—	409	1	no	—
60	C₂²	C₄⋊#13109888	1	1	yes	characteristic
61	C₄	—	409	1	no	—
62	C₄	—	409	1	no	—
63	C₄	C₄⋊#13109888	1	1	yes	characteristic
64	C₄	C₂²×#13109888	1	1	yes	characteristic
65	C₂	—	818	1	no	—
66	C₂	—	818	1	no	—
67	C₂	#27189788	1	2	yes	direct product factor
68	C₂	C₂×C₄⋊#13109888	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#13109888
commutator	C₄×C₄₀₉	C₂²×C₄
Frattini	C₄	C₂²×#13109888
Fitting	C₂×C₈×C₄₀₉	C₄
socle	C₂²×C₄₀₉	C₄⋊C₄
prime radical	C₂²×D₄₀₉	Q₈
cosocle	C₄×D₄₀₉	C₂³
hypercenter	C₂×C₈	#13109888
hypocenter	C₄₀₉	C₂×#108
LCS	G ▷ C₄×C₄₀₉ ▷ C₂×C₄₀₉ ▷ C₄₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #27189788	C₂	direct (N × H)
30. C₂×C₄₀₉	#108	semidirect
34. C₄₀₉	C₂×#108	semidirect
67. C₂	#27189788	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×#20266998	2
#27189788	2
C₂×C₈×D₄₀₉	2
C₂×#108	409

Subgroups — C2×#27189788 #39910261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27189788 #39910261