Subgroups — C₂×#13131803 #16809618

Order 3328.

2074 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131803	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11719162	C₂	1	8	yes	maximal, complemented
3	C₂²×#88106	C₂	1	6	yes	maximal, complemented
4	C₂²×#88202	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×#41	C₄	1	1	yes	characteristic
6	C₂×#88202	C₄	1	4	yes	—
7	C₂×#88202	C₄	1	8	yes	—
8	C₂×#88202	C₂²	1	4	yes	—
9	C₂×#88202	C₂²	1	8	yes	—
10	C₂²×#6099	C₄	1	3	yes	—
11	C₂³×#1055	C₂²	1	3	yes	—
12	#11719162	C₂²	1	64	yes	complemented
13	C₂×#88106	C₂²	1	4	yes	—
14	C₂×#88106	C₂²	1	12	yes	complemented
15	C₂×#88106	C₂²	1	48	yes	complemented
16	C₂²×#6092	C₂²	1	12	yes	complemented
17	C₂×C₁₃×#41	C₈	1	4	yes	—
18	C₂×C₁₃×#41	C₈	1	8	yes	—
19	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
20	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
21	C₂²×Q₈×C₁₃	C₈	1	1	yes	characteristic
22	C₂²×D₄×C₁₃	C₈	1	3	yes	—
23	C₂³×C₄×C₁₃	C₂×C₄	1	3	yes	—
24	#88202	C₂×C₄	1	16	yes	—
25	#88202	C₂×C₄	1	32	yes	—
26	#88202	C₂³	1	16	yes	—
27	C₂×#6099	C₂×C₄	1	12	yes	—
28	C₂×#6099	C₂×C₄	1	24	yes	—
29	C₂²×#1055	C₂×C₄	1	3	yes	—
30	C₂²×#1055	C₂×C₄	1	12	yes	—
31	C₂²×#1055	C₂×C₄	1	6	yes	—
32	C₂²×#1055	C₂³	1	1	yes	characteristic
33	C₂²×#1055	C₂³	1	6	yes	—
34	C₂²×#1055	C₂³	1	12	yes	—
35	#88106	C₂³	1	16	yes	—
36	#88106	C₂³	1	48	yes	complemented
37	C₂×#6092	C₂³	1	8	yes	—
38	C₂×#6092	C₂³	1	48	yes	complemented
39	C₂×#3407	—	13	1	no	maximal, Sylow
40	C₂⁴×C₁₃	C₂×C₈	1	3	yes	—
41	C₁₃×#41	C₂×C₈	1	16	yes	—
42	C₁₃×#41	C₂×C₈	1	32	yes	—
43	C₁₃×#41	C₂²×C₄	1	16	yes	—
44	C₂×Q₈×C₁₃	C₂×C₈	1	8	yes	—
45	C₂×Q₈×C₁₃	C₂×C₈	1	4	yes	—
46	C₂×D₄×C₁₃	C₂×C₈	1	12	yes	—
47	C₂×D₄×C₁₃	C₂×C₈	1	24	yes	—
48	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
49	C₂²×C₄×C₁₃	C₂×C₈	1	6	yes	—
50	C₂²×C₄×C₁₃	C₂×C₈	1	12	yes	—
51	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
53	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
54	#6099	C₂²×C₄	1	48	yes	—
55	C₂×#1055	C₂²×C₄	1	2	yes	—
56	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
57	C₂×#1055	C₂²×C₄	1	12	yes	—
58	C₂×#1055	C₂²×C₄	1	6	yes	—
59	C₂×#1055	C₂²×C₄	1	12	yes	—
60	C₂×#1055	C₂²×C₄	1	24	yes	—
61	C₂×#1055	C₂⁴	1	1	yes	characteristic
62	C₂×#1055	C₂⁴	1	12	yes	—
63	C₂×#1055	C₂⁴	1	2	yes	—
64	#6092	C₂⁴	1	16	yes	—
65	C₂²×#131	—	13	1	no	—
66	#3407	—	13	16	no	—
67	C₂×#504	—	13	8	no	—
68	C₂²×M₃₂	—	13	6	no	—
69	C₂³×C₁₃	—	4	6	no	—
70	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
71	C₂³×C₁₃	C₂²×C₈	1	6	yes	—
72	C₂³×C₁₃	C₂²×C₈	1	12	yes	—
73	Q₈×C₁₃	C₂²×C₈	1	16	yes	—
74	D₄×C₁₃	C₂²×C₈	1	48	yes	—
75	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
76	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₂²×C₈	1	12	yes	—
78	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
79	C₂×C₄×C₁₃	C₂²×C₈	1	24	yes	—
80	C₂×C₄×C₁₃	C₂²×C₈	1	12	yes	—
81	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
82	C₂×C₄×C₁₃	C₂³×C₄	1	12	yes	—
83	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
84	#1055	C₂³×C₄	1	1	yes	characteristic
85	#1055	C₂³×C₄	1	2	yes	—
86	#1055	C₂³×C₄	1	12	yes	—
87	#1055	C₂⁵	1	1	yes	characteristic
88	C₂²×#41	#261	1	1	yes	characteristic
89	C₂×#131	—	13	4	no	—
90	C₂×#131	—	13	8	no	—
91	C₂×#131	—	13	8	no	—
92	C₂×#131	—	13	4	no	—
93	C₂²×M₁₆	—	13	3	no	—
94	C₂³×C₈	—	13	3	no	—
95	#504	—	13	64	no	—
96	C₂×M₃₂	—	13	4	no	—
97	C₂×M₃₂	—	13	12	no	—
98	C₂×M₃₂	—	13	48	no	—
99	C₂²×C₁₆	—	13	12	no	—
100	C₂²×C₁₃	—	2	2	no	—
101	C₂²×C₁₃	—	2	12	no	—
102	C₂²×C₁₃	—	4	12	no	—
103	C₂²×C₁₃	C₂³×C₈	1	2	yes	—
104	C₂²×C₁₃	C₂³×C₈	1	12	yes	—
105	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
106	C₄×C₁₃	C₂³×C₈	1	2	yes	—
107	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
108	C₄×C₁₃	C₂³×C₈	1	12	yes	—
109	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
110	C₂×#41	#1057	1	4	yes	—
111	C₂×#41	#1057	1	8	yes	—
112	C₂×#41	C₂×#261	1	8	yes	—
113	C₂×#41	C₂×#261	1	4	yes	—
114	C₂²×Q₈	#1057	1	1	yes	characteristic
115	C₂²×D₄	#1057	1	3	yes	—
116	C₂³×C₄	C₂×#261	1	3	yes	—
117	#131	—	13	16	no	—
118	#131	—	13	32	no	—
119	#131	—	13	16	no	—
120	C₂×M₁₆	—	13	24	no	—
121	C₂×M₁₆	—	13	12	no	—
122	C₂²×C₈	—	13	1	no	—
123	C₂²×C₈	—	13	3	no	—
124	C₂²×C₈	—	13	12	no	—
125	C₂²×C₈	—	13	6	no	—
126	C₂²×C₈	—	13	6	no	—
127	C₂²×C₈	—	13	12	no	—
128	M₃₂	—	13	16	no	—
129	M₃₂	—	13	48	no	—
130	C₂×C₁₆	—	13	8	no	—
131	C₂×C₁₆	—	13	48	no	—
132	C₂×C₁₃	—	2	2	no	—
133	C₂×C₁₃	—	2	12	no	—
134	C₂×C₁₃	#3407	1	2	yes	complemented
135	C₂×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
136	C₂⁴	C₂×#1057	1	3	yes	—
137	#41	C₂×#1057	1	32	yes	—
138	#41	C₂×#1057	1	16	yes	—
139	#41	C₂²×#261	1	16	yes	—
140	C₂×Q₈	C₂×#1057	1	8	yes	—
141	C₂×Q₈	C₂×#1057	1	4	yes	—
142	C₂×D₄	C₂×#1057	1	12	yes	—
143	C₂×D₄	C₂×#1057	1	24	yes	—
144	C₂²×C₄	C₂×#1057	1	3	yes	—
145	C₂²×C₄	C₂×#1057	1	6	yes	—
146	C₂²×C₄	C₂×#1057	1	12	yes	—
147	C₂²×C₄	C₂²×#261	1	12	yes	—
148	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
149	C₂²×C₄	C₂²×#261	1	6	yes	—
150	M₁₆	—	13	48	no	—
151	C₂×C₈	—	13	12	no	—
152	C₂×C₈	—	13	2	no	—
153	C₂×C₈	—	13	2	no	—
154	C₂×C₈	—	13	12	no	—
155	C₂×C₈	—	13	12	no	—
156	C₂×C₈	—	13	24	no	—
157	C₂×C₈	—	13	1	no	—
158	C₂×C₈	—	13	1	no	—
159	C₂×C₈	—	13	6	no	—
160	C₁₆	—	13	16	no	—
161	C₁₃	C₂×#3407	1	1	yes	characteristic, complemented, Sylow
162	C₂³	—	4	6	no	—
163	C₂³	C₂²×#1057	1	1	yes	characteristic
164	C₂³	C₂²×#1057	1	6	yes	—
165	C₂³	C₂²×#1057	1	12	yes	—
166	Q₈	C₂²×#1057	1	16	yes	—
167	D₄	C₂²×#1057	1	48	yes	—
168	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
169	C₂×C₄	C₂²×#1057	1	2	yes	—
170	C₂×C₄	C₂²×#1057	1	12	yes	—
171	C₂×C₄	C₂²×#1057	1	6	yes	—
172	C₂×C₄	C₂²×#1057	1	24	yes	—
173	C₂×C₄	C₂²×#1057	1	12	yes	—
174	C₂×C₄	C₂³×#261	1	2	yes	—
175	C₂×C₄	C₂³×#261	1	12	yes	—
176	C₂×C₄	C₂³×#261	1	1	yes	characteristic
177	C₈	—	13	1	no	—
178	C₈	—	13	2	no	—
179	C₈	—	13	1	no	—
180	C₈	—	13	12	no	—
181	C₂²	—	2	2	no	—
182	C₂²	—	2	12	no	—
183	C₂²	—	4	12	no	—
184	C₂²	C₂³×#1057	1	2	yes	—
185	C₂²	C₂³×#1057	1	12	yes	—
186	C₂²	C₂³×#1057	1	1	yes	characteristic
187	C₄	C₂³×#1057	1	2	yes	—
188	C₄	C₂³×#1057	1	1	yes	characteristic
189	C₄	C₂³×#1057	1	12	yes	—
190	C₄	C₂⁴×#261	1	1	yes	characteristic
191	C₂	—	2	2	no	—
192	C₂	—	2	12	no	—
193	C₂	#13131803	1	2	yes	direct product factor
194	C₂	C₂⁴×#1057	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×#261
commutator	C₂×C₁₃	C₂⁴×C₈
Frattini	C₄	C₂⁴×#261
Fitting, prime radical	C₂²×C₁₃×#41	C₄
socle	C₂²×C₁₃	C₂³×C₈
cosocle	#1055	C₂⁵
hypercenter	C₂²×#41	#261
hypocenter	C₁₃	C₂×#3407
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. #13131803	C₂	direct (N × H)
2. C₂×#11719162	C₂	semidirect
3. C₂²×#88106	C₂	semidirect
12. #11719162	C₂²	semidirect
14. C₂×#88106	C₂²	semidirect
15. C₂×#88106	C₂²	semidirect
16. C₂²×#6092	C₂²	semidirect
36. #88106	C₂³	semidirect
38. C₂×#6092	C₂³	semidirect
134. C₂×C₁₃	#3407	semidirect
161. C₁₃	C₂×#3407	semidirect
193. C₂	#13131803	direct (N × H)

Maximal subgroups

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

subgroup	index
#13131803	2
C₂×#11719162	2
C₂²×#88106	2
C₂²×#88202	2
C₂×#3407	13

Subgroups — C2×#13131803 #16809618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13131803 #16809618