Subgroups — C₂×#13116618 #16015946

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6090	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718767	C₂	1	1	yes	maximal, characteristic
3	#13116618	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718082	C₂	1	2	yes	maximal, complemented
5	C₂×#11718081	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×#117	—	2	1	no	—
9	C₂×#88180	—	2	1	no	—
10	C₁₃×#427	—	2	2	no	—
11	C₁₃×#427	C₂²	1	4	yes	—
12	C₂×C₁₃×#107	C₂²	1	2	yes	—
13	C₂×C₁₃×#106	—	2	1	no	—
14	#11718767	—	2	2	no	—
15	#11718767	C₂²	1	4	yes	—
16	C₂×#88058	C₂²	1	2	yes	—
17	C₂×#88057	—	2	1	no	—
18	C₂²×#6090	C₄	1	8	yes	complemented
19	C₂²×#6090	C₂²	1	1	yes	characteristic
20	C₂²×#6090	C₂²	1	1	yes	characteristic
21	C₂²×#6090	C₂²	1	4	yes	—
22	#11718082	C₂²	1	8	yes	complemented
23	#11718081	C₂²	1	8	yes	complemented
24	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
26	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	D₄	1	2	yes	—
28	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
29	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
31	C₁₃×#117	—	2	4	no	—
32	C₁₃×#117	—	4	2	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
35	C₂×C₄²×C₁₃	—	4	1	no	—
36	C₂×C₂²⋊Dic₁₃	—	4	1	no	—
37	#88180	—	2	4	no	—
38	#88180	—	4	2	no	—
39	C₂×C₄⋊Dic₁₃	—	2	2	no	—
40	C₂×C₄×Dic₁₃	—	4	1	no	—
41	C₁₃×#107	—	2	2	no	—
42	C₁₃×#107	C₂³	1	4	yes	—
43	C₁₃×#106	—	2	4	no	—
44	#88058	—	2	2	no	—
45	#88058	C₂³	1	4	yes	—
46	#88057	—	2	4	no	—
47	C₂×#6090	C₂×C₄	1	4	yes	—
48	C₂×#6090	C₂×C₄	1	4	yes	—
49	C₂×#6090	C₂×C₄	1	16	yes	complemented
50	C₂×#6090	C₂³	1	2	yes	—
51	C₂×#6090	C₂³	1	2	yes	—
52	C₂×#2158	—	13	1	no	maximal, Sylow
53	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	—	4	2	no	—
55	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
56	C₂²×C₄×C₁₃	D₈	1	2	yes	—
57	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
59	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
61	C₂²×Dic₁₃	—	4	2	no	—
62	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
63	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	—
64	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
65	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
66	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
67	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
69	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
70	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
71	C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₁₃×C₄⋊C₄	—	4	2	no	—
73	C₁₃×C₂²⋊C₄	—	4	4	no	—
74	C₄²×C₁₃	—	4	4	no	—
75	C₂²⋊Dic₁₃	—	4	4	no	—
76	C₄⋊Dic₁₃	—	2	4	no	—
77	C₄⋊Dic₁₃	—	4	2	no	—
78	C₄×Dic₁₃	—	4	4	no	—
79	#6090	C₂²×C₄	1	4	yes	—
80	#6090	C₂²×C₄	1	4	yes	—
81	C₂³×C₁₆	—	13	1	no	—
82	C₂×#427	—	13	1	no	—
83	C₂×#427	D₁₃	1	1	yes	characteristic
84	#2158	—	13	8	no	—
85	C₂×#367	—	13	2	no	—
86	C₂×#366	—	13	2	no	—
87	C₂³×C₁₃	—	2	4	no	—
88	C₂³×C₁₃	#107	1	4	yes	—
89	C₂³×C₁₃	C₂×D₈	1	2	yes	—
90	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₁₃	—	4	4	no	—
92	C₂×C₄×C₁₃	—	8	4	no	—
93	C₂×C₄×C₁₃	#107	1	8	yes	—
94	C₂×C₄×C₁₃	#107	1	4	yes	—
95	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
96	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
97	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
98	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
100	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
101	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
102	C₂×Dic₁₃	—	4	4	no	—
103	C₂×Dic₁₃	—	8	4	no	—
104	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
105	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
106	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
107	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
108	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
109	C₂×#117	—	2	1	no	—
110	C₂×#117	—	26	1	no	—
111	C₂²×C₁₆	—	13	8	no	—
112	C₂²×C₁₆	—	13	1	no	—
113	C₂²×C₁₆	—	13	1	no	—
114	C₂²×C₁₆	—	13	4	no	—
115	#427	—	2	2	no	—
116	#427	—	13	4	no	—
117	#427	—	26	2	no	—
118	#427	C₂×D₁₃	1	4	yes	—
119	C₂×#107	—	13	2	no	—
120	C₂×#107	C₂×D₁₃	1	2	yes	—
121	C₂×#106	—	2	1	no	—
122	C₂×#106	—	26	1	no	—
123	#367	—	13	8	no	—
124	#366	—	13	8	no	—
125	C₂²×C₁₃	—	2	4	no	—
126	C₂²×C₁₃	—	2	8	no	—
127	C₂²×C₁₃	C₂×#107	1	4	yes	—
128	C₂²×C₁₃	C₂×#107	1	2	yes	—
129	C₂²×C₁₃	#508	1	4	yes	—
130	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
131	C₄×C₁₃	—	8	4	no	—
132	C₄×C₁₃	C₂×#107	1	4	yes	—
133	C₄×C₁₃	C₂×#107	1	2	yes	—
134	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
135	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
136	Dic₁₃	—	8	4	no	—
137	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
138	C₂²×C₈	Dic₂₆	1	4	yes	—
139	C₂²×C₈	C₄×D₁₃	1	4	yes	—
140	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
141	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
142	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
143	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
144	#117	—	2	4	no	—
145	#117	—	4	2	no	—
146	#117	—	26	4	no	—
147	#117	—	52	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	26	2	no	—
150	C₂×C₂²⋊C₄	—	4	1	no	—
151	C₂×C₂²⋊C₄	—	52	1	no	—
152	C₂×C₄²	—	4	1	no	—
153	C₂×C₄²	—	52	1	no	—
154	C₂×C₁₆	—	13	4	no	—
155	C₂×C₁₆	—	13	4	no	—
156	C₂×C₁₆	—	13	16	no	—
157	C₂×C₁₆	—	13	2	no	—
158	C₂×C₁₆	—	13	2	no	—
159	#107	—	2	2	no	—
160	#107	—	13	4	no	—
161	#107	—	26	2	no	—
162	#107	C₂²×D₁₃	1	4	yes	—
163	#106	—	2	4	no	—
164	#106	—	26	4	no	—
165	C₂×C₁₃	—	2	4	no	—
166	C₂×C₁₃	#2158	1	4	yes	complemented
167	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
168	C₂×C₁₃	C₂×#508	1	2	yes	—
169	C₂⁴	#6104	1	1	yes	characteristic
170	C₂²×C₄	—	4	2	no	—
171	C₂²×C₄	—	52	2	no	—
172	C₂²×C₄	#6101	1	4	yes	—
173	C₂²×C₄	#6104	1	2	yes	—
174	C₂²×C₄	#6104	1	1	yes	characteristic
175	C₂²×C₄	#6107	1	4	yes	—
176	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
178	C₂×C₈	#6101	1	4	yes	—
179	C₂×C₈	#6101	1	8	yes	—
180	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
181	C₂×C₈	C₂×Dic₂₆	1	4	yes	—
182	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
183	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
184	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
185	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
186	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
187	C₄⋊C₄	—	2	4	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	26	4	no	—
190	C₄⋊C₄	—	52	2	no	—
191	C₂²⋊C₄	—	4	4	no	—
192	C₂²⋊C₄	—	52	4	no	—
193	C₄²	—	4	4	no	—
194	C₄²	—	52	4	no	—
195	C₁₆	—	13	4	no	—
196	C₁₆	—	13	4	no	—
197	C₁₃	C₂×#2158	1	1	yes	characteristic, complemented, Sylow
198	C₂³	—	2	4	no	—
199	C₂³	#88047	1	4	yes	—
200	C₂³	C₂×#6104	1	2	yes	—
201	C₂³	C₂×#6104	1	1	yes	characteristic
202	C₂×C₄	—	4	4	no	—
203	C₂×C₄	—	8	4	no	—
204	C₂×C₄	—	52	4	no	—
205	C₂×C₄	—	104	4	no	—
206	C₂×C₄	#88047	1	8	yes	—
207	C₂×C₄	#88047	1	4	yes	—
208	C₂×C₄	C₂×#6101	1	4	yes	—
209	C₂×C₄	C₂×#6101	1	2	yes	—
210	C₂×C₄	C₂×#6104	1	2	yes	—
211	C₂×C₄	C₂×#6104	1	1	yes	characteristic
212	C₂×C₄	C₂×#6107	1	4	yes	—
213	C₂×C₄	C₂×#6107	1	2	yes	—
214	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
215	C₈	C₂×#6101	1	4	yes	—
216	C₈	C₂×#6101	1	2	yes	—
217	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
218	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
219	C₂²	—	2	4	no	—
220	C₂²	—	2	8	no	—
221	C₂²	C₂×#88047	1	4	yes	—
222	C₂²	C₂×#88047	1	2	yes	—
223	C₂²	#11718855	1	4	yes	—
224	C₂²	C₂²×#6104	1	1	yes	characteristic
225	C₄	—	8	4	no	—
226	C₄	—	104	4	no	—
227	C₄	C₂×#88047	1	4	yes	—
228	C₄	C₂×#88047	1	2	yes	—
229	C₄	C₂²×#6101	1	1	yes	characteristic
230	C₄	C₂²×#6107	1	1	yes	characteristic
231	C₂	—	2	4	no	—
232	C₂	#13116618	1	4	yes	direct product factor
233	C₂	C₂²×#88047	1	1	yes	characteristic
234	C₂	C₂×#11718855	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	#6104
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#427	C₂
socle	C₂³×C₁₃	C₂×D₈
prime radical	C₂⁴×C₁₃	D₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#427	D₁₃
hypocenter	C₁₃	C₂×#2158
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
3. #13116618	C₂	direct (N × H)
4. C₂×#11718082	C₂	semidirect
5. C₂×#11718081	C₂	semidirect
18. C₂²×#6090	C₄	semidirect
22. #11718082	C₂²	semidirect
23. #11718081	C₂²	semidirect
49. C₂×#6090	C₂×C₄	semidirect
166. C₂×C₁₃	#2158	semidirect
197. C₁₃	C₂×#2158	semidirect
232. C₂	#13116618	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#6090	2
C₂×#11718767	2
#13116618	2
C₂×#11718082	2
C₂×#11718081	2
C₂×C₁₃×#427	2
C₂×#2158	13

Subgroups — C2×#13116618 #16015946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116618 #16015946