Subgroups — C₂×#13123688 #16727047

Order 3328.

3086 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719503	C₂	1	2	yes	maximal, complemented
2	#13123688	C₂	1	16	yes	maximal, direct product factor
3	C₂×#11718813	C₂	1	4	yes	maximal, complemented
4	C₂×D₈×Dic₁₃	C₂	1	4	yes	maximal, complemented
5	C₂×#11718767	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11718876	C₂	1	2	yes	maximal, complemented
7	C₂×#11718762	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
9	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
10	C₂²×C₁₃×D₈	C₄	1	16	yes	complemented
11	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
12	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	8	yes	—
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊Dic₁₃	—	2	4	no	—
16	#11719503	—	2	8	no	—
17	#11719503	C₂²	1	16	yes	complemented
18	C₂×D₄×Dic₁₃	—	2	4	no	—
19	C₂×D₄×Dic₁₃	C₂²	1	8	yes	complemented
20	C₂×#88180	C₂²	1	2	yes	—
21	C₂×#88180	C₂²	1	1	yes	characteristic
22	C₂²×#6099	C₂²	1	1	yes	characteristic
23	#11718876	C₂²	1	16	yes	complemented
24	C₂×#88072	C₂²	1	8	yes	complemented
25	#11718813	C₂²	1	32	yes	complemented
26	D₈×Dic₁₃	C₂²	1	32	yes	complemented
27	#11718767	C₂²	1	8	yes	complemented
28	C₂×#88058	C₂²	1	2	yes	complemented
29	C₂×#88057	C₂²	1	2	yes	complemented
30	#11718762	C₂²	1	8	yes	complemented
31	C₂×#88055	C₂²	1	2	yes	complemented
32	C₂×C₈×Dic₁₃	C₂²	1	2	yes	complemented
33	C₂⁵×C₁₃	—	2	2	no	—
34	C₂²×D₄×C₁₃	—	2	2	no	—
35	C₂²×D₄×C₁₃	—	2	4	no	—
36	C₂²×D₄×C₁₃	—	2	8	no	—
37	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
38	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
39	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×Dic₁₃	—	2	8	no	—
42	C₂×C₁₃×D₈	C₂×C₄	1	16	yes	complemented
43	C₂×C₁₃×D₈	C₂×C₄	1	16	yes	complemented
44	C₂×C₁₃×D₈	C₂×C₄	1	64	yes	complemented
45	C₂×C₁₃×D₈	C₂³	1	8	yes	—
46	C₂×C₁₃×D₈	C₂³	1	8	yes	—
47	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
51	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
52	C₂×C₂²⋊Dic₁₃	—	2	8	no	—
53	C₂×C₂²⋊Dic₁₃	—	2	32	no	—
54	C₂×C₂²⋊Dic₁₃	D₄	1	2	yes	—
55	D₄×Dic₁₃	—	2	32	no	—
56	D₄×Dic₁₃	—	2	16	no	—
57	D₄×Dic₁₃	C₂³	1	32	yes	complemented
58	#88180	—	2	4	no	—
59	#88180	D₄	1	4	yes	—
60	#88180	C₂³	1	8	yes	—
61	#88180	C₂³	1	4	yes	—
62	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
63	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
64	C₂×C₄×Dic₁₃	—	2	2	no	—
65	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
66	C₂×#6099	—	2	4	no	—
67	C₂×#6099	C₂³	1	4	yes	—
68	C₂²×#1055	C₂³	1	2	yes	—
69	#88072	C₂³	1	32	yes	complemented
70	#88058	C₂³	1	8	yes	complemented
71	#88057	C₂³	1	8	yes	complemented
72	#88055	C₂³	1	8	yes	complemented
73	C₈×Dic₁₃	C₂³	1	8	yes	complemented
74	C₂×#2948	—	13	1	no	maximal, Sylow
75	C₂⁴×C₁₃	—	2	4	no	—
76	C₂⁴×C₁₃	—	2	16	no	—
77	C₂⁴×C₁₃	—	2	8	no	—
78	C₂⁴×C₁₃	—	8	8	no	—
79	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂×D₄×C₁₃	—	2	32	no	—
81	C₂×D₄×C₁₃	—	2	16	no	—
82	C₂×D₄×C₁₃	—	2	8	no	—
83	C₂×D₄×C₁₃	—	2	4	no	—
84	C₂×D₄×C₁₃	—	2	8	no	—
85	C₂×D₄×C₁₃	—	2	16	no	—
86	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
87	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	complemented
88	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₃	#41	1	4	yes	—
93	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
95	C₂²×Dic₁₃	—	2	4	no	—
96	C₂²×Dic₁₃	—	2	32	no	—
97	C₂²×Dic₁₃	—	8	16	no	—
98	C₂²×Dic₁₃	C₂×D₄	1	4	yes	—
99	C₁₃×D₈	C₂²×C₄	1	32	yes	complemented
100	C₁₃×D₈	C₂²×C₄	1	32	yes	complemented
101	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₁₃	C₂²×C₄	1	16	yes	complemented
104	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
105	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
106	C₂²⋊Dic₁₃	—	2	8	no	—
107	C₂²⋊Dic₁₃	—	2	32	no	—
108	C₂²⋊Dic₁₃	C₂×D₄	1	8	yes	—
109	C₄⋊Dic₁₃	—	2	4	no	—
110	C₄⋊Dic₁₃	C₂×D₄	1	8	yes	—
111	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
112	C₄×Dic₁₃	—	2	8	no	—
113	C₄×Dic₁₃	C₂×D₄	1	4	yes	—
114	C₄×Dic₁₃	C₂⁴	1	4	yes	—
115	#6099	—	2	8	no	—
116	C₂×#1055	—	2	4	no	—
117	C₂×#1055	C₂⁴	1	4	yes	—
118	C₂³×D₈	D₁₃	1	1	yes	characteristic
119	C₂×#518	—	13	2	no	—
120	#2948	—	13	16	no	—
121	C₂×#442	—	13	4	no	—
122	C₂×C₄×D₈	—	13	4	no	—
123	C₂×#427	—	13	1	no	—
124	C₂×#418	—	13	2	no	—
125	C₂×#405	—	13	1	no	—
126	C₂³×C₁₃	—	2	4	no	—
127	C₂³×C₁₃	—	2	16	no	—
128	C₂³×C₁₃	—	2	8	no	—
129	C₂³×C₁₃	—	2	32	no	—
130	C₂³×C₁₃	—	4	16	no	—
131	C₂³×C₁₃	—	8	32	no	—
132	C₂³×C₁₃	—	8	16	no	—
133	C₂³×C₁₃	C₄×D₄	1	4	yes	—
134	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
135	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
136	D₄×C₁₃	—	2	16	no	—
137	D₄×C₁₃	—	2	32	no	—
138	D₄×C₁₃	—	2	8	no	—
139	D₄×C₁₃	C₂³×C₄	1	16	yes	—
140	C₂×C₄×C₁₃	C₄×D₄	1	8	yes	—
141	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
142	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
143	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
144	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
145	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
147	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
148	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
149	C₂×Dic₁₃	—	2	8	no	—
150	C₂×Dic₁₃	—	2	8	no	—
151	C₂×Dic₁₃	—	4	8	no	—
152	C₂×Dic₁₃	—	8	32	no	—
153	C₂×Dic₁₃	C₂²×D₄	1	8	yes	—
154	C₈×C₁₃	C₂³×C₄	1	4	yes	—
155	C₈×C₁₃	C₂³×C₄	1	4	yes	—
156	#1055	—	2	4	no	—
157	C₂³×D₄	C₂×D₁₃	1	2	yes	—
158	C₂²×D₈	Dic₁₃	1	16	yes	complemented
159	C₂²×D₈	C₂×D₁₃	1	2	yes	—
160	C₂²×D₈	C₂×D₁₃	1	2	yes	—
161	C₂²×D₈	C₂×D₁₃	1	8	yes	—
162	C₂²×M₁₆	—	13	1	no	—
163	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
164	#518	—	13	16	no	—
165	#518	—	26	8	no	—
166	C₂×C₄×D₄	—	13	8	no	—
167	C₂×C₄×D₄	—	26	4	no	—
168	C₂×#117	—	13	1	no	—
169	C₂×#117	—	13	2	no	—
170	C₂²×C₂²⋊C₄	—	26	4	no	—
171	#442	—	13	32	no	—
172	C₄×D₈	—	13	32	no	—
173	#427	—	13	8	no	—
174	C₂×#107	—	13	2	no	—
175	C₂×#106	—	13	2	no	—
176	#418	—	13	16	no	—
177	C₂×#102	—	13	8	no	—
178	#405	—	13	8	no	—
179	C₂×#97	—	13	2	no	—
180	C₂×C₄×C₈	—	13	2	no	—
181	C₂²×C₁₃	—	2	8	no	—
182	C₂²×C₁₃	—	2	4	no	—
183	C₂²×C₁₃	—	2	16	no	—
184	C₂²×C₁₃	—	4	32	no	—
185	C₂²×C₁₃	—	4	16	no	—
186	C₂²×C₁₃	—	8	32	no	—
187	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
188	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
189	C₂²×C₁₃	#576	1	4	yes	—
190	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
191	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
192	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
193	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
194	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
195	Dic₁₃	—	2	8	no	—
196	Dic₁₃	—	4	8	no	—
197	C₂⁵	—	2	2	no	—
198	C₂²×D₄	—	2	2	no	—
199	C₂²×D₄	—	2	4	no	—
200	C₂²×D₄	—	2	8	no	—
201	C₂²×D₄	C₂×Dic₁₃	1	16	yes	complemented
202	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
203	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
204	C₂³×C₄	—	26	8	no	—
205	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
206	C₂×D₈	C₂×Dic₁₃	1	16	yes	complemented
207	C₂×D₈	C₂×Dic₁₃	1	16	yes	complemented
208	C₂×D₈	C₂×Dic₁₃	1	64	yes	complemented
209	C₂×D₈	C₂²×D₁₃	1	8	yes	—
210	C₂×D₈	C₂²×D₁₃	1	8	yes	—
211	C₂×M₁₆	—	13	4	no	—
212	C₂×M₁₆	—	26	4	no	—
213	C₂²×C₈	—	13	2	no	—
214	C₂²×C₈	C₂×Dic₁₃	1	8	yes	complemented
215	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
216	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
217	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
218	C₄×D₄	—	13	32	no	—
219	C₄×D₄	—	26	16	no	—
220	C₄×D₄	—	26	32	no	—
221	#117	—	13	4	no	—
222	#117	—	13	4	no	—
223	#117	—	13	8	no	—
224	#117	—	26	4	no	—
225	C₂×C₄⋊C₄	—	13	2	no	—
226	C₂×C₄⋊C₄	—	13	4	no	—
227	C₂×C₂²⋊C₄	—	13	2	no	—
228	C₂×C₂²⋊C₄	—	26	32	no	—
229	C₂×C₂²⋊C₄	—	26	8	no	—
230	C₂×C₂²⋊C₄	—	26	2	no	—
231	C₂×C₄²	—	13	2	no	—
232	C₂×C₄²	—	26	2	no	—
233	#107	—	13	8	no	—
234	#106	—	13	8	no	—
235	#102	—	13	32	no	—
236	#97	—	13	8	no	—
237	C₄×C₈	—	13	8	no	—
238	C₂×C₁₃	—	2	4	no	—
239	C₂×C₁₃	—	4	16	no	—
240	C₂×C₁₃	#2948	1	4	yes	complemented
241	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
242	C₂×C₁₃	C₂×#576	1	2	yes	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	2	16	no	—
245	C₂⁴	—	2	8	no	—
246	C₂⁴	—	8	8	no	—
247	C₂⁴	D₄×D₁₃	1	1	yes	characteristic
248	C₂×D₄	—	2	32	no	—
249	C₂×D₄	—	2	16	no	—
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	16	no	—
254	C₂×D₄	C₂²×Dic₁₃	1	16	yes	—
255	C₂×D₄	C₂²×Dic₁₃	1	32	yes	complemented
256	C₂×D₄	C₂³×D₁₃	1	8	yes	—
257	C₂²×C₄	—	13	4	no	—
258	C₂²×C₄	—	26	32	no	—
259	C₂²×C₄	—	26	4	no	—
260	C₂²×C₄	—	104	16	no	—
261	C₂²×C₄	D₄×D₁₃	1	2	yes	—
262	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
263	C₂²×C₄	#6129	1	4	yes	—
264	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
265	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
266	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
267	D₈	C₂²×Dic₁₃	1	32	yes	complemented
268	D₈	C₂²×Dic₁₃	1	32	yes	complemented
269	M₁₆	—	26	8	no	—
270	C₂×C₈	—	13	4	no	—
271	C₂×C₈	—	26	4	no	—
272	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
273	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
274	C₂×C₈	C₂²×Dic₁₃	1	16	yes	complemented
275	C₂×C₈	C₂³×D₁₃	1	2	yes	—
276	C₂×C₈	C₂³×D₁₃	1	2	yes	—
277	C₄⋊C₄	—	13	8	no	—
278	C₄⋊C₄	—	13	8	no	—
279	C₄⋊C₄	—	26	4	no	—
280	C₂²⋊C₄	—	13	8	no	—
281	C₂²⋊C₄	—	26	32	no	—
282	C₂²⋊C₄	—	26	8	no	—
283	C₄²	—	13	4	no	—
284	C₄²	—	13	4	no	—
285	C₄²	—	26	8	no	—
286	C₁₃	C₂×#2948	1	1	yes	characteristic, complemented, Sylow
287	C₂³	—	2	4	no	—
288	C₂³	—	2	16	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	2	32	no	—
291	C₂³	—	4	16	no	—
292	C₂³	—	8	32	no	—
293	C₂³	—	8	16	no	—
294	C₂³	D₄×Dic₁₃	1	4	yes	—
295	C₂³	C₂×D₄×D₁₃	1	2	yes	—
296	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
297	D₄	—	2	16	no	—
298	D₄	—	2	32	no	—
299	D₄	—	2	8	no	—
300	D₄	C₂³×Dic₁₃	1	16	yes	—
301	C₂×C₄	—	13	8	no	—
302	C₂×C₄	—	26	8	no	—
303	C₂×C₄	—	26	8	no	—
304	C₂×C₄	—	52	8	no	—
305	C₂×C₄	—	104	32	no	—
306	C₂×C₄	D₄×Dic₁₃	1	8	yes	—
307	C₂×C₄	D₄×Dic₁₃	1	4	yes	—
308	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
309	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
310	C₂×C₄	C₂×#6129	1	2	yes	—
311	C₂×C₄	C₂×#6129	1	4	yes	—
312	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
313	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
314	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
315	C₈	—	26	4	no	—
316	C₈	C₂³×Dic₁₃	1	4	yes	—
317	C₈	C₂³×Dic₁₃	1	4	yes	—
318	C₂²	—	2	8	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	16	no	—
321	C₂²	—	4	32	no	—
322	C₂²	—	4	16	no	—
323	C₂²	—	8	32	no	—
324	C₂²	#11719462	1	4	yes	—
325	C₂²	C₂×D₄×Dic₁₃	1	4	yes	—
326	C₂²	C₂×D₄×Dic₁₃	1	2	yes	—
327	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
328	C₄	—	26	8	no	—
329	C₄	—	52	8	no	—
330	C₄	C₂×D₄×Dic₁₃	1	2	yes	—
331	C₄	C₂×D₄×Dic₁₃	1	4	yes	—
332	C₄	C₂²×#6129	1	1	yes	characteristic
333	C₄	C₂⁴×Dic₁₃	1	1	yes	characteristic
334	C₂	—	2	4	no	—
335	C₂	—	4	16	no	—
336	C₂	#13123688	1	4	yes	direct product factor
337	C₂	C₂²×D₄×Dic₁₃	1	1	yes	characteristic
338	C₂	C₂×#11719462	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₁₃
commutator	C₄×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting, prime radical	C₂³×C₁₃×D₈	C₂
socle	C₂³×C₁₃	C₂²×D₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂³×D₈	D₁₃
hypocenter	C₁₃	C₂×#2948
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×#11719503	C₂	semidirect
2. #13123688	C₂	direct (N × H)
3. C₂×#11718813	C₂	semidirect
4. C₂×D₈×Dic₁₃	C₂	semidirect
5. C₂×#11718767	C₂	semidirect
6. C₂×#11718876	C₂	semidirect
7. C₂×#11718762	C₂	semidirect
10. C₂²×C₁₃×D₈	C₄	semidirect
17. #11719503	C₂²	semidirect
19. C₂×D₄×Dic₁₃	C₂²	semidirect
23. #11718876	C₂²	semidirect
24. C₂×#88072	C₂²	semidirect
25. #11718813	C₂²	semidirect
26. D₈×Dic₁₃	C₂²	semidirect
27. #11718767	C₂²	semidirect
28. C₂×#88058	C₂²	semidirect
29. C₂×#88057	C₂²	semidirect
30. #11718762	C₂²	semidirect
31. C₂×#88055	C₂²	semidirect
32. C₂×C₈×Dic₁₃	C₂²	semidirect
37. C₂²×D₄×C₁₃	C₂×C₄	semidirect
42. C₂×C₁₃×D₈	C₂×C₄	semidirect
43. C₂×C₁₃×D₈	C₂×C₄	semidirect
44. C₂×C₁₃×D₈	C₂×C₄	semidirect
47. C₂²×C₈×C₁₃	C₂×C₄	semidirect
57. D₄×Dic₁₃	C₂³	semidirect
69. #88072	C₂³	semidirect
70. #88058	C₂³	semidirect
71. #88057	C₂³	semidirect
72. #88055	C₂³	semidirect
73. C₈×Dic₁₃	C₂³	semidirect
87. C₂×D₄×C₁₃	C₂²×C₄	semidirect
99. C₁₃×D₈	C₂²×C₄	semidirect
100. C₁₃×D₈	C₂²×C₄	semidirect
103. C₂×C₈×C₁₃	C₂²×C₄	semidirect
158. C₂²×D₈	Dic₁₃	semidirect
201. C₂²×D₄	C₂×Dic₁₃	semidirect
206. C₂×D₈	C₂×Dic₁₃	semidirect
207. C₂×D₈	C₂×Dic₁₃	semidirect
208. C₂×D₈	C₂×Dic₁₃	semidirect
214. C₂²×C₈	C₂×Dic₁₃	semidirect
240. C₂×C₁₃	#2948	semidirect
255. C₂×D₄	C₂²×Dic₁₃	semidirect
267. D₈	C₂²×Dic₁₃	semidirect
268. D₈	C₂²×Dic₁₃	semidirect
274. C₂×C₈	C₂²×Dic₁₃	semidirect
286. C₁₃	C₂×#2948	semidirect
336. C₂	#13123688	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×#11719503	2
#13123688	2
C₂×#11718813	2
C₂×D₈×Dic₁₃	2
C₂×#11718767	2
C₂×#11718876	2
C₂×#11718762	2
C₂³×C₁₃×D₈	2
C₂×#2948	13

Subgroups — C2×#13123688 #16727047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123688 #16727047