Subgroups — C₂×#13116621 #16015950

Order 3328.

718 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88038	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718541	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₃×#107	C₂	1	1	yes	maximal, characteristic
4	#13116621	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11718097	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11718082	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718081	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88146	—	2	1	no	—
11	C₂×C₄⋊C₄×D₁₃	—	2	1	no	—
12	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
15	C₂×#88058	C₂²	1	1	yes	characteristic
16	C₂×#88058	C₂²	1	1	yes	characteristic
17	C₂²×#6090	C₂²	1	1	yes	characteristic
18	C₂×#88048	—	2	1	no	—
19	C₂×#88047	—	2	1	no	—
20	C₂×#88038	C₄	1	8	yes	complemented
21	C₂×#88038	C₂²	1	4	yes	—
22	#11718541	—	2	2	no	—
23	#11718541	C₂²	1	4	yes	—
24	D₁₃×#107	—	2	2	no	—
25	D₁₃×#107	C₂²	1	4	yes	—
26	C₁₃×#366	C₂²	1	4	yes	complemented
27	#11718097	C₂²	1	4	yes	complemented
28	#11718082	C₂²	1	4	yes	complemented
29	#11718081	C₂²	1	4	yes	complemented
30	C₂²×C₄×D₁₃	—	4	1	no	—
31	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₂×#6103	—	4	1	no	—
36	C₂×C₄⋊Dic₁₃	—	2	1	no	—
37	C₂×C₄⋊Dic₁₃	—	2	1	no	—
38	C₂×#6101	—	4	1	no	—
39	C₂×C₄×Dic₁₃	—	4	1	no	—
40	C₂²×#1055	D₄	1	1	yes	characteristic
41	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
42	C₂×C₈×D₁₃	D₄	1	2	yes	—
43	C₂×C₈×D₁₃	Q₈	1	4	yes	—
44	C₂×C₈×D₁₃	C₂³	1	2	yes	—
45	#88146	—	2	4	no	—
46	#88146	—	4	2	no	—
47	C₄⋊C₄×D₁₃	—	2	4	no	—
48	C₄⋊C₄×D₁₃	—	4	2	no	—
49	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	complemented
50	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
51	C₁₃×#107	—	2	1	no	—
52	C₁₃×#107	—	2	1	no	—
53	C₁₃×#107	C₂³	1	2	yes	—
54	C₁₃×#107	C₂³	1	2	yes	—
55	#88058	—	2	1	no	—
56	#88058	—	2	1	no	—
57	#88058	C₂³	1	2	yes	—
58	#88058	C₂³	1	2	yes	—
59	C₂×#6090	C₂×C₄	1	4	yes	complemented
60	C₂×#6090	C₂³	1	2	yes	—
61	#88048	—	2	4	no	—
62	#88047	—	2	4	no	—
63	#88038	C₂×C₄	1	16	yes	complemented
64	C₂×#2159	—	13	1	no	maximal, Sylow
65	C₂³×D₁₃	D₈	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	—	4	1	no	—
67	C₂²×C₄×C₁₃	—	4	1	no	—
68	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×Dic₁₃	—	4	1	no	—
70	C₂²×Dic₁₃	—	4	1	no	—
71	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
72	C₂×C₄×D₁₃	—	4	4	no	—
73	C₂×C₄×D₁₃	—	8	4	no	—
74	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
75	C₂×C₄×D₁₃	D₈	1	2	yes	—
76	C₂×C₄×D₁₃	Q₁₆	1	4	yes	—
77	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
78	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
79	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
81	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
82	C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₁₃×C₄⋊C₄	—	4	1	no	—
85	C₁₃×C₄⋊C₄	—	4	1	no	—
86	#6103	—	4	4	no	—
87	C₄⋊Dic₁₃	—	2	2	no	—
88	C₄⋊Dic₁₃	—	2	2	no	—
89	C₄⋊Dic₁₃	—	4	1	no	—
90	C₄⋊Dic₁₃	—	4	1	no	—
91	#6101	—	4	4	no	—
92	C₄×Dic₁₃	—	4	4	no	—
93	C₂×#1055	C₄⋊C₄	1	4	yes	—
94	C₂×#1055	C₂×D₄	1	2	yes	—
95	C₈×D₁₃	C₄⋊C₄	1	8	yes	—
96	C₈×D₁₃	C₂²×C₄	1	4	yes	—
97	C₈×D₁₃	C₂×Q₈	1	4	yes	—
98	C₁₃×C₁₆	C₂²×C₄	1	4	yes	complemented
99	#6090	C₂²×C₄	1	4	yes	complemented
100	C₂²×M₃₂	—	13	1	no	—
101	C₂×#427	—	13	1	no	—
102	C₂²×#107	—	13	1	no	—
103	#2159	—	13	8	no	—
104	C₂×#367	—	13	1	no	—
105	C₂×#367	—	13	1	no	—
106	C₂×#366	—	13	1	no	—
107	C₂×#366	D₁₃	1	1	yes	characteristic, complemented
108	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
109	C₂²×D₁₃	—	2	2	no	—
110	C₂²×D₁₃	—	2	2	no	—
111	C₂²×D₁₃	#107	1	4	yes	—
112	C₂²×D₁₃	C₂×D₈	1	2	yes	—
113	C₂×C₄×C₁₃	—	4	2	no	—
114	C₂×C₄×C₁₃	—	4	2	no	—
115	C₂×C₄×C₁₃	—	8	2	no	—
116	C₂×C₄×C₁₃	—	8	2	no	—
117	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
118	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
119	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
120	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
121	C₂×Dic₁₃	—	4	2	no	—
122	C₂×Dic₁₃	—	4	2	no	—
123	C₂×Dic₁₃	—	8	2	no	—
124	C₂×Dic₁₃	—	8	2	no	—
125	C₂×Dic₁₃	#107	1	4	yes	—
126	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
127	C₄×D₁₃	—	8	8	no	—
128	C₄×D₁₃	#107	1	8	yes	—
129	C₄×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
130	C₄×D₁₃	C₂×Q₁₆	1	4	yes	—
131	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
132	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
133	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
134	#1055	C₂×C₄⋊C₄	1	4	yes	—
135	C₂³×C₈	—	13	1	no	—
136	C₂×#117	—	26	1	no	—
137	C₂²×C₄⋊C₄	—	26	1	no	—
138	C₂×M₃₂	—	13	8	no	—
139	C₂×M₃₂	—	13	4	no	—
140	C₂²×C₁₆	—	13	1	no	—
141	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
142	#427	—	13	4	no	—
143	#427	—	26	2	no	—
144	C₂×#107	—	13	1	no	—
145	C₂×#107	—	13	1	no	—
146	C₂×#107	—	13	4	no	—
147	C₂×#107	—	26	2	no	—
148	C₂×#107	—	26	1	no	—
149	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
150	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
151	C₂×#106	—	26	1	no	—
152	#367	—	13	4	no	—
153	#367	—	13	4	no	—
154	#366	—	13	4	no	—
155	#366	C₂×D₁₃	1	4	yes	complemented
156	C₂²×C₁₃	C₂×#107	1	2	yes	—
157	C₂²×C₁₃	#509	1	2	yes	—
158	C₂²×C₁₃	#510	1	2	yes	—
159	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
160	C₂×D₁₃	—	2	2	no	—
161	C₂×D₁₃	—	2	2	no	—
162	C₂×D₁₃	—	2	8	no	—
163	C₂×D₁₃	C₂×#107	1	4	yes	—
164	C₄×C₁₃	—	8	2	no	—
165	C₄×C₁₃	—	8	2	no	—
166	C₄×C₁₃	C₂×#107	1	2	yes	—
167	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
168	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
169	Dic₁₃	—	8	2	no	—
170	Dic₁₃	—	8	2	no	—
171	Dic₁₃	C₂×#107	1	4	yes	—
172	C₂³×C₄	—	13	1	no	—
173	C₂³×C₄	—	52	1	no	—
174	C₂²×C₈	—	13	1	no	—
175	C₂²×C₈	—	13	4	no	—
176	C₂²×C₈	—	13	2	no	—
177	C₂²×C₈	—	13	4	no	—
178	C₂²×C₈	—	13	2	no	—
179	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
180	#117	—	26	4	no	—
181	#117	—	52	2	no	—
182	C₂×C₄⋊C₄	—	2	1	no	—
183	C₂×C₄⋊C₄	—	2	1	no	—
184	C₂×C₄⋊C₄	—	26	4	no	—
185	C₂×C₄⋊C₄	—	26	1	no	—
186	C₂×C₄⋊C₄	—	26	1	no	—
187	C₂×C₄⋊C₄	—	52	2	no	—
188	C₂×C₄⋊C₄	—	52	1	no	—
189	C₂×C₂²⋊C₄	—	52	1	no	—
190	C₂×C₄²	—	52	1	no	—
191	M₃₂	—	13	16	no	—
192	C₂×C₁₆	—	13	4	no	—
193	C₂×C₁₆	—	13	2	no	—
194	C₂×C₁₆	C₄×D₁₃	1	4	yes	complemented
195	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
196	#107	—	2	1	no	—
197	#107	—	2	1	no	—
198	#107	—	13	2	no	—
199	#107	—	13	2	no	—
200	#107	—	26	4	no	—
201	#107	—	26	1	no	—
202	#107	—	26	1	no	—
203	#107	C₂²×D₁₃	1	2	yes	—
204	#107	C₂²×D₁₃	1	2	yes	—
205	#106	—	26	4	no	—
206	C₂×C₁₃	#2159	1	4	yes	complemented
207	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
208	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
209	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
210	D₁₃	—	2	4	no	—
211	C₂⁴	—	13	1	no	—
212	C₂²×C₄	—	4	1	no	—
213	C₂²×C₄	—	4	1	no	—
214	C₂²×C₄	—	13	1	no	—
215	C₂²×C₄	—	13	4	no	—
216	C₂²×C₄	—	13	2	no	—
217	C₂²×C₄	—	13	4	no	—
218	C₂²×C₄	—	13	2	no	—
219	C₂²×C₄	—	52	4	no	—
220	C₂²×C₄	—	52	1	no	—
221	C₂²×C₄	—	52	1	no	—
222	C₂²×C₄	—	104	4	no	—
223	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
224	C₂×C₈	—	13	4	no	—
225	C₂×C₈	—	13	2	no	—
226	C₂×C₈	—	13	8	no	—
227	C₂×C₈	—	13	4	no	—
228	C₂×C₈	—	13	4	no	—
229	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
230	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
231	C₂×C₈	Q₈×D₁₃	1	2	yes	—
232	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
233	C₄⋊C₄	—	2	2	no	—
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	4	1	no	—
236	C₄⋊C₄	—	4	1	no	—
237	C₄⋊C₄	—	26	2	no	—
238	C₄⋊C₄	—	26	2	no	—
239	C₄⋊C₄	—	52	4	no	—
240	C₄⋊C₄	—	52	1	no	—
241	C₄⋊C₄	—	52	1	no	—
242	C₂²⋊C₄	—	52	4	no	—
243	C₄²	—	52	4	no	—
244	C₁₆	—	13	4	no	—
245	C₁₆	C₂×C₄×D₁₃	1	4	yes	complemented
246	C₁₃	C₂×#2159	1	1	yes	characteristic, complemented, Sylow
247	C₂³	—	13	2	no	—
248	C₂³	—	13	4	no	—
249	C₂³	—	26	2	no	—
250	C₂³	—	26	2	no	—
251	C₂³	D₈×D₁₃	1	1	yes	characteristic
252	C₂×C₄	—	4	2	no	—
253	C₂×C₄	—	4	2	no	—
254	C₂×C₄	—	8	2	no	—
255	C₂×C₄	—	8	2	no	—
256	C₂×C₄	—	13	2	no	—
257	C₂×C₄	—	13	4	no	—
258	C₂×C₄	—	13	4	no	—
259	C₂×C₄	—	13	4	no	—
260	C₂×C₄	—	13	8	no	—
261	C₂×C₄	—	52	2	no	—
262	C₂×C₄	—	52	2	no	—
263	C₂×C₄	—	104	8	no	—
264	C₂×C₄	—	104	2	no	—
265	C₂×C₄	—	104	2	no	—
266	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
267	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
268	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
269	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
270	C₈	—	13	4	no	—
271	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
272	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
273	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
274	C₂²	—	13	4	no	—
275	C₂²	—	26	2	no	—
276	C₂²	—	26	2	no	—
277	C₂²	—	26	8	no	—
278	C₂²	D₁₃×#107	1	2	yes	—
279	C₂²	#11718572	1	2	yes	—
280	C₂²	#11718579	1	2	yes	—
281	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
282	C₄	—	8	2	no	—
283	C₄	—	8	2	no	—
284	C₄	—	13	4	no	—
285	C₄	—	104	2	no	—
286	C₄	—	104	2	no	—
287	C₄	D₁₃×#107	1	2	yes	—
288	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
289	C₄	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
290	C₂	—	26	4	no	—
291	C₂	#13116621	1	4	yes	direct product factor
292	C₂	C₂×D₁₃×#107	1	1	yes	characteristic
293	C₂	C₂×#11718572	1	1	yes	characteristic
294	C₂	C₂×#11718579	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈×D₁₃
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#366	C₂
socle	C₂³×C₁₃	C₂×D₈
prime radical	C₂³×D₁₃	D₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#366	D₁₃
hypocenter	C₁₃	C₂×#2159
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

Complements

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

N	H ≅ G/N	type
4. #13116621	C₂	direct (N × H)
5. C₂×#11718097	C₂	semidirect
6. C₂×#11718082	C₂	semidirect
7. C₂×#11718081	C₂	semidirect
8. C₂×C₁₃×#366	C₂	semidirect
20. C₂×#88038	C₄	semidirect
26. C₁₃×#366	C₂²	semidirect
27. #11718097	C₂²	semidirect
28. #11718082	C₂²	semidirect
29. #11718081	C₂²	semidirect
49. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
59. C₂×#6090	C₂×C₄	semidirect
63. #88038	C₂×C₄	semidirect
98. C₁₃×C₁₆	C₂²×C₄	semidirect
99. #6090	C₂²×C₄	semidirect
107. C₂×#366	D₁₃	semidirect
155. #366	C₂×D₁₃	semidirect
194. C₂×C₁₆	C₄×D₁₃	semidirect
206. C₂×C₁₃	#2159	semidirect
245. C₁₆	C₂×C₄×D₁₃	semidirect
246. C₁₃	C₂×#2159	semidirect
291. C₂	#13116621	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88038	2
C₂×#11718541	2
C₂×D₁₃×#107	2
#13116621	2
C₂×#11718097	2
C₂×#11718082	2
C₂×#11718081	2
C₂×C₁₃×#366	2
C₂×#2159	13

Subgroups — C2×#13116621 #16015950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116621 #16015950