Subgroups — C₂×#13112910 #15774500

Order 3328.

262 conjugacy classes of subgroups.

The subgroup lattice has 154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718050	C₂	1	2	yes	maximal
2	#13112910	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊#1055	—	2	2	no	—
8	C₄×C₁₃×C₁₆	C₄	1	2	yes	—
9	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
10	#11718050	—	2	2	no	—
11	#11718050	C₂²	1	4	yes	—
12	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
14	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
15	C₂²×#1055	—	4	2	no	—
16	C₂×C₁₃×C₁₆	—	2	2	no	—
17	C₂×C₁₃×C₁₆	C₈	1	4	yes	complemented
18	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
22	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
23	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₄⋊#1055	—	2	4	no	—
25	C₄⋊#1055	—	4	2	no	—
26	C₂×#1372	—	13	1	no	maximal, Sylow
27	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
29	C₂²×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
30	C₂×C₈×C₁₃	—	2	2	no	—
31	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
34	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
35	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
37	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
38	C₄²×C₁₃	D₈	1	1	yes	characteristic
39	C₄²×C₁₃	Q₁₆	1	1	yes	characteristic
40	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂×#1055	—	4	4	no	—
42	C₂×#1055	—	8	4	no	—
43	C₁₃×C₁₆	—	2	2	no	—
44	C₁₃×C₁₆	C₂×C₈	1	4	yes	complemented
45	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic
46	C₂×#335	—	13	2	no	—
47	#1372	—	13	4	no	—
48	C₂³×C₁₃	#107	1	1	yes	characteristic
49	C₂×C₄×C₁₃	—	2	2	no	—
50	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
51	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
52	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
53	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
54	C₂×C₄×C₁₃	#108	1	2	yes	—
55	C₂×C₄×C₁₃	SD₃₂	1	4	yes	—
56	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
59	C₈×C₁₃	—	2	1	no	—
60	C₈×C₁₃	—	2	1	no	—
61	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
62	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
63	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
64	#1055	—	8	4	no	—
65	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
66	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
67	C₂×C₄⋊C₈	—	26	2	no	—
68	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
69	C₄×C₁₆	Dic₁₃	1	2	yes	—
70	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
71	#335	—	13	4	no	—
72	#335	—	26	2	no	—
73	C₂²×C₁₃	#335	1	2	yes	—
74	C₂²×C₁₃	#367	1	2	yes	—
75	C₂²×C₁₃	#368	1	2	yes	—
76	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
77	C₄×C₁₃	—	2	1	no	—
78	C₄×C₁₃	—	2	1	no	—
79	C₄×C₁₃	#335	1	2	yes	—
80	C₄×C₁₃	#367	1	2	yes	—
81	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
82	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
83	C₄×C₁₃	C₂×SD₃₂	1	2	yes	—
84	C₂²×C₈	—	52	2	no	—
85	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
86	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
87	C₂×C₄²	D₅₂	1	1	yes	characteristic
88	C₂×C₁₆	—	2	2	no	—
89	C₂×C₁₆	#1055	1	4	yes	complemented
90	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
91	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
92	C₄⋊C₈	—	26	4	no	—
93	C₄⋊C₈	—	52	2	no	—
94	C₄×C₈	Dic₂₆	1	1	yes	characteristic
95	C₄×C₈	D₅₂	1	1	yes	characteristic
96	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
97	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
98	C₂×C₁₃	#1372	1	4	yes	complemented
99	C₂×C₁₃	C₂×#335	1	1	yes	characteristic
100	C₂×C₁₃	C₂×#367	1	1	yes	characteristic
101	C₂×C₁₃	C₂×#368	1	1	yes	characteristic
102	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
103	C₂²×C₄	Dic₅₂	1	1	yes	characteristic
104	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	—	52	4	no	—
107	C₂×C₈	—	104	4	no	—
108	C₂×C₈	C₂×#1055	1	2	yes	—
109	C₂×C₈	#6099	1	2	yes	—
110	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
111	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
112	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
113	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
114	C₄²	D₁₀₄	1	1	yes	characteristic
115	C₄²	Dic₅₂	1	1	yes	characteristic
116	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
117	C₄²	C₂×D₅₂	1	1	yes	characteristic
118	C₁₆	—	2	2	no	—
119	C₁₆	C₂×#1055	1	4	yes	complemented
120	C₁₃	C₂×#1372	1	1	yes	characteristic, complemented, Sylow
121	C₂³	#88058	1	1	yes	characteristic
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	#88040	1	4	yes	—
124	C₂×C₄	C₄⋊#1055	1	2	yes	—
125	C₂×C₄	#88058	1	1	yes	characteristic
126	C₂×C₄	#88058	1	1	yes	characteristic
127	C₂×C₄	#88058	1	1	yes	characteristic
128	C₂×C₄	#88059	1	2	yes	—
129	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
130	C₂×C₄	C₂×Dic₅₂	1	1	yes	characteristic
131	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
132	C₈	—	2	1	no	—
133	C₈	—	2	1	no	—
134	C₈	—	104	4	no	—
135	C₈	C₄⋊#1055	1	2	yes	—
136	C₈	C₂²×#1055	1	1	yes	characteristic
137	C₈	C₂×#6099	1	1	yes	characteristic
138	C₂²	#11718050	1	2	yes	—
139	C₂²	#11718097	1	2	yes	—
140	C₂²	#11718098	1	2	yes	—
141	C₂²	C₂×#88058	1	1	yes	characteristic
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	#11718050	1	2	yes	—
145	C₄	#11718097	1	2	yes	—
146	C₄	C₂×#88040	1	2	yes	—
147	C₄	C₂×C₄⋊#1055	1	1	yes	characteristic
148	C₄	C₂×#88059	1	1	yes	characteristic
149	C₂	#13112910	1	4	yes	direct product factor
150	C₂	C₂×#11718050	1	1	yes	characteristic
151	C₂	C₂×#11718097	1	1	yes	characteristic
152	C₂	C₂×#11718098	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₁₀₄
commutator	C₈×C₁₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂³×C₁₃	#107
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×C₄×C₁₆	D₁₃
hypocenter	C₁₃	C₂×#1372
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13112910	C₂	direct (N × H)
17. C₂×C₁₃×C₁₆	C₈	semidirect
44. C₁₃×C₁₆	C₂×C₈	semidirect
89. C₂×C₁₆	#1055	semidirect
98. C₂×C₁₃	#1372	semidirect
119. C₁₆	C₂×#1055	semidirect
120. C₁₃	C₂×#1372	semidirect
149. C₂	#13112910	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×#11718050	2
#13112910	2
C₂×C₄×C₁₃×C₁₆	2
C₂×#1372	13

Subgroups — C2×#13112910 #15774500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112910 #15774500