Subgroups — C₂×#13116942 #16017369

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88069	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#88052	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718777	C₂	1	1	yes	maximal, characteristic
4	#13116942	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11718082	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11718156	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718084	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
12	C₂×#88178	—	2	1	no	—
13	C₂²×Dic₅₂	C₂²	1	1	yes	characteristic
14	C₁₃×#467	—	2	2	no	—
15	C₁₃×#467	C₂²	1	4	yes	—
16	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#103	—	2	1	no	—
18	C₂×#88069	—	2	4	no	—
19	C₂×#88069	C₂²	1	4	yes	complemented
20	#11718777	—	2	2	no	—
21	#11718777	C₂²	1	4	yes	—
22	C₂×#88058	C₂²	1	1	yes	characteristic
23	C₂×#88056	—	2	1	no	—
24	C₂×#88052	—	2	4	no	—
25	C₂×#88052	C₂²	1	4	yes	—
26	C₂²×#6090	C₂²	1	1	yes	characteristic
27	C₂²×#6090	C₂²	1	1	yes	characteristic
28	#11718156	C₂²	1	4	yes	complemented
29	#11718084	C₂²	1	4	yes	complemented
30	#11718082	C₂²	1	4	yes	complemented
31	C₂²×Q₈×C₁₃	—	2	1	no	—
32	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
33	C₂²×Dic₂₆	—	2	1	no	—
34	C₂×C₁₃×Q₁₆	—	2	2	no	—
35	C₂×C₁₃×Q₁₆	—	2	1	no	—
36	C₂×C₁₃×Q₁₆	—	2	2	no	—
37	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₃	—	2	2	no	—
39	C₂²×C₈×C₁₃	—	2	2	no	—
40	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	D₄	1	2	yes	—
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₁₃×C₂²⋊Q₈	—	2	4	no	—
45	C₁₃×C₂²⋊Q₈	—	4	2	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
47	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
48	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
49	C₂×C₂²⋊Dic₁₃	—	4	1	no	—
50	C₂×C₄⋊Dic₁₃	—	2	1	no	—
51	#88178	—	2	4	no	—
52	#88178	—	4	2	no	—
53	C₂×#6101	—	4	1	no	—
54	C₂×Dic₅₂	—	2	2	no	—
55	C₂×Dic₅₂	—	2	2	no	—
56	C₂×Dic₅₂	—	2	1	no	—
57	C₂×Dic₅₂	C₂³	1	2	yes	—
58	C₁₃×#107	—	2	1	no	—
59	C₁₃×#107	C₂³	1	2	yes	—
60	C₁₃×#103	—	2	4	no	—
61	#88069	—	2	8	no	—
62	#88058	—	2	1	no	—
63	#88058	C₂³	1	2	yes	—
64	#88056	—	2	4	no	—
65	#88052	—	2	8	no	—
66	C₂×#6090	—	2	2	no	—
67	C₂×#6090	D₄	1	4	yes	—
68	C₂×#6090	C₂³	1	2	yes	—
69	C₂×#6090	C₂³	1	2	yes	—
70	C₂×#2219	—	13	1	no	maximal, Sylow
71	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
72	C₂×Q₈×C₁₃	—	2	2	no	—
73	C₂×Q₈×C₁₃	—	4	1	no	—
74	C₂×Q₈×C₁₃	—	4	2	no	—
75	C₂×Q₈×C₁₃	—	4	2	no	—
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	4	1	no	—
79	C₂²×C₄×C₁₃	—	4	1	no	—
80	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	D₈	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×Dic₁₃	—	4	1	no	—
85	C₂²×Dic₁₃	—	4	1	no	—
86	C₂×Dic₂₆	—	2	2	no	—
87	C₂×Dic₂₆	—	4	2	no	—
88	C₂×Dic₂₆	—	4	2	no	—
89	C₂×Dic₂₆	—	4	1	no	—
90	C₁₃×Q₁₆	—	2	2	no	—
91	C₁₃×Q₁₆	—	2	2	no	—
92	C₁₃×Q₁₆	—	4	2	no	—
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	—	2	4	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
98	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₁₃	#41	1	2	yes	—
101	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
102	C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₁₃×C₄⋊C₄	—	4	1	no	—
104	C₁₃×C₄⋊C₄	—	4	4	no	—
105	C₁₃×C₂²⋊C₄	—	4	4	no	—
106	C₂²⋊Dic₁₃	—	4	4	no	—
107	C₄⋊Dic₁₃	—	2	2	no	—
108	C₄⋊Dic₁₃	—	4	1	no	—
109	#6101	—	4	4	no	—
110	Dic₅₂	—	2	2	no	—
111	Dic₅₂	—	2	2	no	—
112	Dic₅₂	—	4	2	no	—
113	#6090	—	2	2	no	—
114	#6090	C₂×D₄	1	4	yes	—
115	C₂²×Q₃₂	—	13	1	no	—
116	C₂²×M₃₂	—	13	1	no	—
117	C₂×#467	—	13	1	no	—
118	C₂×#467	D₁₃	1	1	yes	characteristic
119	#2219	—	13	8	no	—
120	C₂×#367	—	13	1	no	—
121	C₂×#358	—	13	1	no	—
122	C₂×#358	—	13	1	no	—
123	C₂³×C₁₃	—	2	2	no	—
124	C₂³×C₁₃	—	2	2	no	—
125	C₂³×C₁₃	—	2	2	no	—
126	C₂³×C₁₃	C₂×D₈	1	2	yes	—
127	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
128	Q₈×C₁₃	—	4	2	no	—
129	Q₈×C₁₃	—	4	2	no	—
130	Q₈×C₁₃	—	8	2	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	4	no	—
135	C₂×C₄×C₁₃	—	4	2	no	—
136	C₂×C₄×C₁₃	—	4	2	no	—
137	C₂×C₄×C₁₃	—	8	2	no	—
138	C₂×C₄×C₁₃	—	8	2	no	—
139	C₂×C₄×C₁₃	#121	1	2	yes	—
140	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
141	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
142	C₂×C₄×C₁₃	#135	1	2	yes	—
143	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
144	C₂×Dic₁₃	—	4	2	no	—
145	C₂×Dic₁₃	—	4	2	no	—
146	C₂×Dic₁₃	—	8	2	no	—
147	C₂×Dic₁₃	—	8	2	no	—
148	Dic₂₆	—	4	2	no	—
149	Dic₂₆	—	4	2	no	—
150	Dic₂₆	—	8	2	no	—
151	C₈×C₁₃	—	2	2	no	—
152	C₈×C₁₃	#121	1	2	yes	—
153	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
154	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
155	C₂²×Q₁₆	—	13	1	no	—
156	C₂²×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
157	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
158	C₂×C₂²⋊Q₈	—	2	1	no	—
159	C₂×C₂²⋊Q₈	—	26	1	no	—
160	C₂×Q₃₂	—	13	4	no	—
161	C₂×Q₃₂	—	26	4	no	—
162	C₂×M₃₂	—	13	4	no	—
163	C₂×M₃₂	—	26	4	no	—
164	C₂²×C₁₆	—	13	1	no	—
165	C₂²×C₁₆	—	13	1	no	—
166	#467	—	2	2	no	—
167	#467	—	13	4	no	—
168	#467	—	26	2	no	—
169	#467	C₂×D₁₃	1	4	yes	—
170	C₂×#107	—	13	1	no	—
171	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
172	C₂×#103	—	2	1	no	—
173	C₂×#103	—	26	1	no	—
174	#367	—	13	4	no	—
175	#358	—	13	4	no	—
176	#358	—	13	4	no	—
177	C₂²×C₁₃	—	2	2	no	—
178	C₂²×C₁₃	—	2	2	no	—
179	C₂²×C₁₃	—	2	2	no	—
180	C₂²×C₁₃	—	4	4	no	—
181	C₂²×C₁₃	#466	1	2	yes	—
182	C₂²×C₁₃	#510	1	2	yes	—
183	C₂²×C₁₃	#510	1	2	yes	—
184	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
185	C₄×C₁₃	—	2	2	no	—
186	C₄×C₁₃	—	8	2	no	—
187	C₄×C₁₃	—	8	2	no	—
188	C₄×C₁₃	#466	1	2	yes	—
189	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
190	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
191	Dic₁₃	—	8	2	no	—
192	Dic₁₃	—	8	2	no	—
193	C₂²×Q₈	—	2	1	no	—
194	C₂²×Q₈	—	26	1	no	—
195	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
196	C₂×Q₁₆	—	2	2	no	—
197	C₂×Q₁₆	—	2	2	no	—
198	C₂×Q₁₆	—	2	1	no	—
199	C₂×Q₁₆	—	13	2	no	—
200	C₂×Q₁₆	—	26	2	no	—
201	C₂×Q₁₆	—	26	2	no	—
202	C₂×Q₁₆	—	26	1	no	—
203	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	—	2	2	no	—
206	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
207	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
208	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
209	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
210	C₂²⋊Q₈	—	2	4	no	—
211	C₂²⋊Q₈	—	4	2	no	—
212	C₂²⋊Q₈	—	26	4	no	—
213	C₂²⋊Q₈	—	52	2	no	—
214	C₂×C₄⋊C₄	—	2	1	no	—
215	C₂×C₄⋊C₄	—	4	1	no	—
216	C₂×C₄⋊C₄	—	26	1	no	—
217	C₂×C₄⋊C₄	—	52	1	no	—
218	C₂×C₂²⋊C₄	—	4	1	no	—
219	C₂×C₂²⋊C₄	—	52	1	no	—
220	Q₃₂	—	26	8	no	—
221	M₃₂	—	26	8	no	—
222	C₂×C₁₆	—	13	4	no	—
223	C₂×C₁₆	—	13	2	no	—
224	C₂×C₁₆	—	13	2	no	—
225	C₂×C₁₆	—	26	2	no	—
226	#107	—	2	1	no	—
227	#107	—	13	2	no	—
228	#107	—	26	1	no	—
229	#107	C₂²×D₁₃	1	2	yes	—
230	#103	—	2	4	no	—
231	#103	—	26	4	no	—
232	C₂×C₁₃	—	4	2	no	—
233	C₂×C₁₃	#2219	1	4	yes	complemented
234	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
235	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
236	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
237	C₂⁴	#6104	1	1	yes	characteristic
238	C₂×Q₈	—	2	2	no	—
239	C₂×Q₈	—	4	1	no	—
240	C₂×Q₈	—	4	2	no	—
241	C₂×Q₈	—	4	2	no	—
242	C₂×Q₈	—	26	2	no	—
243	C₂×Q₈	—	52	1	no	—
244	C₂×Q₈	—	52	2	no	—
245	C₂×Q₈	—	52	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	4	1	no	—
249	C₂²×C₄	—	4	1	no	—
250	C₂²×C₄	—	52	1	no	—
251	C₂²×C₄	—	52	1	no	—
252	C₂²×C₄	#6104	1	2	yes	—
253	C₂²×C₄	#6104	1	1	yes	characteristic
254	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
255	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
256	Q₁₆	—	2	2	no	—
257	Q₁₆	—	2	2	no	—
258	Q₁₆	—	4	2	no	—
259	Q₁₆	—	26	2	no	—
260	Q₁₆	—	26	2	no	—
261	Q₁₆	—	52	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	D₄×D₁₃	1	2	yes	—
267	C₂×C₈	#6129	1	2	yes	—
268	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
269	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
270	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	4	1	no	—
273	C₄⋊C₄	—	4	4	no	—
274	C₄⋊C₄	—	26	2	no	—
275	C₄⋊C₄	—	52	1	no	—
276	C₄⋊C₄	—	52	4	no	—
277	C₂²⋊C₄	—	4	4	no	—
278	C₂²⋊C₄	—	52	4	no	—
279	C₁₆	—	13	4	no	—
280	C₁₆	—	26	2	no	—
281	C₁₃	C₂×#2219	1	1	yes	characteristic, complemented, Sylow
282	C₂³	—	2	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	C₂×#6104	1	2	yes	—
286	C₂³	C₂×#6104	1	1	yes	characteristic
287	Q₈	—	4	2	no	—
288	Q₈	—	4	2	no	—
289	Q₈	—	8	2	no	—
290	Q₈	—	52	2	no	—
291	Q₈	—	52	2	no	—
292	Q₈	—	104	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	8	2	no	—
300	C₂×C₄	—	8	2	no	—
301	C₂×C₄	—	52	2	no	—
302	C₂×C₄	—	52	2	no	—
303	C₂×C₄	—	104	2	no	—
304	C₂×C₄	—	104	2	no	—
305	C₂×C₄	C₂×#6104	1	2	yes	—
306	C₂×C₄	C₂×#6104	1	1	yes	characteristic
307	C₂×C₄	#88193	1	2	yes	—
308	C₂×C₄	#88204	1	2	yes	—
309	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
310	C₈	—	2	2	no	—
311	C₈	#88193	1	2	yes	—
312	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
313	C₈	C₂×#6129	1	1	yes	characteristic
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	2	no	—
317	C₂²	—	4	4	no	—
318	C₂²	#11718699	1	2	yes	—
319	C₂²	#11718840	1	2	yes	—
320	C₂²	#11718856	1	2	yes	—
321	C₂²	C₂²×#6104	1	1	yes	characteristic
322	C₄	—	2	2	no	—
323	C₄	—	8	2	no	—
324	C₄	—	8	2	no	—
325	C₄	—	104	2	no	—
326	C₄	—	104	2	no	—
327	C₄	#11718699	1	2	yes	—
328	C₄	C₂×#88193	1	1	yes	characteristic
329	C₄	C₂×#88204	1	1	yes	characteristic
330	C₂	—	4	2	no	—
331	C₂	#13116942	1	4	yes	direct product factor
332	C₂	C₂×#11718699	1	1	yes	characteristic
333	C₂	C₂×#11718856	1	1	yes	characteristic
334	C₂	C₂×#11718840	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#467	C₂
socle	C₂³×C₁₃	C₂×D₈
prime radical	C₂⁴×C₁₃	D₈
hypercenter	C₂×#467	D₁₃
hypocenter	C₁₃	C₂×#2219
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×#467

Complements

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

N	H ≅ G/N	type
1. C₂²×#88069	C₂	semidirect
4. #13116942	C₂	direct (N × H)
5. C₂×#11718082	C₂	semidirect
6. C₂×#11718156	C₂	semidirect
7. C₂×#11718084	C₂	semidirect
19. C₂×#88069	C₂²	semidirect
28. #11718156	C₂²	semidirect
29. #11718084	C₂²	semidirect
30. #11718082	C₂²	semidirect
233. C₂×C₁₃	#2219	semidirect
281. C₁₃	C₂×#2219	semidirect
331. C₂	#13116942	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×#88069	2
C₂²×#88052	2
C₂×#11718777	2
#13116942	2
C₂×#11718082	2
C₂×#11718156	2
C₂×#11718084	2
C₂×C₁₃×#467	2
C₂×#2219	13

Subgroups — C2×#13116942 #16017369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116942 #16017369