Subgroups — C₂×#13114977 #15863149

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718585	C₂	1	2	yes	maximal
2	#13114977	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718144	C₂	1	4	yes	maximal
4	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6099	C₂²	1	4	yes	—
8	C₂×C₁₃×#97	C₄	1	4	yes	—
9	C₂×C₁₃×#97	C₄	1	4	yes	—
10	C₂×C₁₃×#97	C₂²	1	4	yes	—
11	#11718585	—	2	4	no	—
12	#11718585	C₂²	1	8	yes	—
13	C₂×C₄⋊#1055	—	2	4	no	—
14	#11718144	C₂²	1	16	yes	—
15	C₂³×C₄×C₁₃	Q₈	1	2	yes	—
16	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	—	2	8	no	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
20	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₃	D₄	1	2	yes	—
24	C₂×C₄²×C₁₃	D₄	1	2	yes	—
25	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
26	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
27	C₂×#6099	—	2	4	no	—
28	C₂×#6099	—	2	16	no	—
29	C₂×#6099	C₂³	1	8	yes	—
30	C₂²×#1055	—	2	4	no	—
31	C₁₃×#97	C₂×C₄	1	16	yes	—
32	C₄⋊#1055	—	2	16	no	—
33	C₂×#1838	—	13	1	no	maximal, Sylow
34	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	—	4	4	no	—
36	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
37	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
38	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
43	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	#41	1	8	yes	—
45	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
46	C₂×C₈×C₁₃	—	2	8	no	—
47	C₂×C₈×C₁₃	—	2	8	no	—
48	C₂×C₈×C₁₃	—	2	8	no	—
49	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
50	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
51	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
52	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
53	C₄²×C₁₃	C₂×D₄	1	4	yes	—
54	#6099	—	2	16	no	—
55	#6099	—	4	8	no	—
56	C₂×#1055	—	2	8	no	—
57	C₂×#1055	—	4	8	no	—
58	C₂×#423	—	13	2	no	—
59	C₂²×#97	D₁₃	1	1	yes	characteristic
60	#1838	—	13	8	no	—
61	C₂×#341	—	13	4	no	—
62	C₂³×C₁₃	—	2	4	no	—
63	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂³×C₁₃	#125	1	4	yes	—
66	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
67	C₂×C₄×C₁₃	—	2	8	no	—
68	C₂×C₄×C₁₃	—	4	4	no	—
69	C₂×C₄×C₁₃	—	4	4	no	—
70	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
71	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	#117	1	4	yes	—
74	C₂×C₄×C₁₃	#117	1	4	yes	—
75	C₂×C₄×C₁₃	#124	1	4	yes	—
76	C₂×C₄×C₁₃	#124	1	4	yes	—
77	C₂×C₄×C₁₃	#125	1	4	yes	—
78	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
81	C₈×C₁₃	—	2	8	no	—
82	#1055	—	4	8	no	—
83	C₂²×M₁₆	—	13	4	no	—
84	C₂³×C₈	C₂×D₁₃	1	2	yes	—
85	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
86	#423	—	13	8	no	—
87	#423	—	26	4	no	—
88	C₂×C₄⋊C₈	—	26	4	no	—
89	C₂×#97	Dic₁₃	1	4	yes	—
90	C₂×#97	Dic₁₃	1	4	yes	—
91	C₂×#97	C₂×D₁₃	1	4	yes	—
92	#341	—	13	16	no	—
93	C₂²×C₁₃	—	2	8	no	—
94	C₂²×C₁₃	—	2	2	no	—
95	C₂²×C₁₃	—	2	2	no	—
96	C₂²×C₁₃	#382	1	2	yes	—
97	C₂²×C₁₃	#382	1	2	yes	—
98	C₂²×C₁₃	#430	1	4	yes	—
99	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
100	C₂²×C₁₃	C₂×#125	1	2	yes	—
101	C₄×C₁₃	—	2	8	no	—
102	C₄×C₁₃	#382	1	2	yes	—
103	C₄×C₁₃	#382	1	2	yes	—
104	C₄×C₁₃	C₂×#117	1	2	yes	—
105	C₄×C₁₃	C₂×#124	1	2	yes	—
106	C₂³×C₄	Dic₂₆	1	2	yes	—
107	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
108	C₂×M₁₆	—	13	8	no	—
109	C₂×M₁₆	—	26	4	no	—
110	C₂×M₁₆	—	26	16	no	—
111	C₂²×C₈	—	2	8	no	—
112	C₂²×C₈	—	26	4	no	—
113	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
114	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
115	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
116	C₂×C₄²	Dic₂₆	1	2	yes	—
117	C₂×C₄²	D₅₂	1	2	yes	—
118	C₂×C₄²	D₅₂	1	2	yes	—
119	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
120	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
121	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
122	C₄⋊C₈	—	26	16	no	—
123	#97	C₂×Dic₁₃	1	16	yes	—
124	C₂×C₁₃	—	2	2	no	—
125	C₂×C₁₃	—	2	2	no	—
126	C₂×C₁₃	#1838	1	4	yes	complemented
127	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
128	C₂×C₁₃	C₂×#430	1	2	yes	—
129	C₂⁴	C₂×Dic₂₆	1	1	yes	characteristic
130	C₂²×C₄	—	4	4	no	—
131	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
132	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
133	C₂²×C₄	C₂×Dic₂₆	1	4	yes	—
134	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
135	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
136	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
137	C₂²×C₄	#6127	1	8	yes	—
138	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
139	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
140	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
141	M₁₆	—	26	16	no	—
142	M₁₆	—	52	8	no	—
143	C₂×C₈	—	2	8	no	—
144	C₂×C₈	—	2	8	no	—
145	C₂×C₈	—	2	8	no	—
146	C₂×C₈	—	26	8	no	—
147	C₂×C₈	—	52	8	no	—
148	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
149	C₄²	C₄⋊Dic₁₃	1	4	yes	—
150	C₄²	C₄⋊Dic₁₃	1	4	yes	—
151	C₄²	C₂×D₅₂	1	4	yes	—
152	C₄²	C₂²×Dic₁₃	1	4	yes	—
153	C₁₃	C₂×#1838	1	1	yes	characteristic, complemented, Sylow
154	C₂³	—	2	4	no	—
155	C₂³	#88124	1	4	yes	—
156	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
157	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
158	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
159	C₂×C₄	—	2	8	no	—
160	C₂×C₄	—	4	4	no	—
161	C₂×C₄	—	4	4	no	—
162	C₂×C₄	#88124	1	4	yes	—
163	C₂×C₄	#88129	1	4	yes	—
164	C₂×C₄	#88129	1	4	yes	—
165	C₂×C₄	C₂×C₄⋊Dic₁₃	1	8	yes	—
166	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
167	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
168	C₂×C₄	#88180	1	4	yes	—
169	C₂×C₄	#88180	1	4	yes	—
170	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
171	C₂×C₄	C₂×#6127	1	4	yes	—
172	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
173	C₈	—	2	8	no	—
174	C₈	—	52	8	no	—
175	C₂²	—	2	8	no	—
176	C₂²	—	2	2	no	—
177	C₂²	—	2	2	no	—
178	C₂²	#11718597	1	2	yes	—
179	C₂²	#11718597	1	2	yes	—
180	C₂²	#11718786	1	4	yes	—
181	C₂²	C₂×#88124	1	2	yes	—
182	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
183	C₄	—	2	8	no	—
184	C₄	#11718597	1	2	yes	—
185	C₄	#11718597	1	2	yes	—
186	C₄	C₂×#88129	1	2	yes	—
187	C₄	C₂×#88180	1	2	yes	—
188	C₂	—	2	2	no	—
189	C₂	—	2	2	no	—
190	C₂	#13114977	1	4	yes	direct product factor
191	C₂	C₂×#11718597	1	1	yes	characteristic
192	C₂	C₂×#11718786	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₁₃×#97	C₂
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×#97	D₁₃
hypocenter	C₁₃	C₂×#1838
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
2. #13114977	C₂	direct (N × H)
126. C₂×C₁₃	#1838	semidirect
153. C₁₃	C₂×#1838	semidirect
190. C₂	#13114977	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×#11718585	2
#13114977	2
C₂×#11718144	2
C₂²×C₁₃×#97	2
C₂×#1838	13

Subgroups — C2×#13114977 #15863149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13114977 #15863149