Subgroups — C₄×D₁₃⋊M₃₂ #16806718

Order 3328.

918 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊M₃₂	C₂	1	2	yes	maximal
2	#13131043	C₂	1	2	yes	maximal, complemented
3	#13131042	C₂	1	2	yes	maximal, complemented
4	C₄×#88098	C₂	1	2	yes	maximal, complemented
5	C₄×#88106	C₂	1	2	yes	maximal, complemented
6	#13131037	C₂	1	2	yes	maximal, complemented
7	C₄×D₁₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
10	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄²×D₁₃	C₄	1	1	yes	characteristic
12	C₂×#88106	C₂²	1	4	yes	—
13	D₁₃⋊M₃₂	C₄	1	16	yes	direct product factor
14	C₂×#88098	C₂²	1	4	yes	—
15	C₂×D₁₃⋊C₁₆	C₂²	1	4	yes	—
16	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
17	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
18	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
20	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
21	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
22	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
23	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
24	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
25	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
28	#11718258	C₂²	1	4	yes	complemented
29	#11718257	C₂²	1	4	yes	complemented
30	#11718231	C₂²	1	4	yes	complemented
31	C₄×#6092	C₂²	1	4	yes	complemented
32	C₂²×C₄×D₁₃	C₈	1	2	yes	—
33	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
38	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
40	C₂²×#1055	C₂³	1	1	yes	characteristic
41	C₂×C₈×D₁₃	C₈	1	8	yes	—
42	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
45	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
51	C₄²×D₁₃	C₈	1	2	yes	—
52	C₄²×D₁₃	C₈	1	2	yes	—
53	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	#88106	C₂×C₄	1	16	yes	complemented
58	C₂×#6092	C₂³	1	8	yes	—
59	#88098	C₂×C₄	1	16	yes	complemented
60	D₁₃⋊C₁₆	C₂×C₄	1	16	yes	complemented
61	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
66	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
67	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
68	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
69	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
70	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
72	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
73	C₄×#1055	C₂×C₄	1	1	yes	characteristic
74	C₄×#1055	C₂×C₄	1	1	yes	characteristic
75	C₄×#1055	C₂³	1	1	yes	characteristic
76	C₄×#1055	C₂³	1	1	yes	characteristic
77	C₂×C₄×M₃₂	—	13	1	no	maximal, Sylow
78	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
82	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
83	C₂×C₄×D₁₃	—	2	8	no	—
84	C₂×C₄×D₁₃	C₄²	1	4	yes	—
85	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
86	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
87	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
88	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂×C₈	1	4	yes	—
91	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
92	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₃	C₄²	1	4	yes	—
95	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
96	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₄²×C₁₃	C₂×C₈	1	2	yes	—
101	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
104	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
105	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
106	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
107	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
108	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×#1055	C₂×C₈	1	4	yes	—
111	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
112	C₂×#1055	C₂²×C₄	1	4	yes	—
113	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
114	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
115	C₂×#1055	C₂⁴	1	1	yes	characteristic
116	C₈×D₁₃	C₄²	1	4	yes	—
117	C₈×D₁₃	C₄²	1	4	yes	—
118	C₈×D₁₃	C₂×C₈	1	4	yes	—
119	C₈×D₁₃	C₂×C₈	1	4	yes	—
120	C₈×D₁₃	C₂×C₈	1	4	yes	—
121	C₈×D₁₃	C₂×C₈	1	4	yes	—
122	C₈×D₁₃	C₂²×C₄	1	4	yes	—
123	C₈×D₁₃	C₂²×C₄	1	4	yes	—
124	#6092	C₂²×C₄	1	16	yes	complemented
125	C₂²×M₃₂	—	13	2	no	—
126	C₂²×C₄×C₈	—	13	1	no	—
127	C₄×M₃₂	—	13	2	no	—
128	C₄×M₃₂	—	13	2	no	—
129	C₄×M₃₂	—	13	2	no	—
130	C₄×M₃₂	—	13	2	no	—
131	C₂×#346	—	13	2	no	—
132	C₂×C₄×C₁₆	—	13	2	no	—
133	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
134	C₂²×D₁₃	—	2	4	no	—
135	C₂²×D₁₃	C₄×C₈	1	4	yes	—
136	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
137	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
140	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
142	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
144	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
145	C₂×Dic₁₃	—	2	4	no	—
146	C₂×Dic₁₃	C₄×C₈	1	4	yes	—
147	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
148	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
149	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
150	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
151	C₄×D₁₃	—	2	4	no	—
152	C₄×D₁₃	—	2	4	no	—
153	C₄×D₁₃	—	2	4	no	—
154	C₄×D₁₃	C₄×C₈	1	4	yes	—
155	C₄×D₁₃	C₄×C₈	1	4	yes	—
156	C₄×D₁₃	M₃₂	1	8	yes	complemented
157	C₄×D₁₃	C₂×C₄²	1	2	yes	—
158	C₄×D₁₃	C₂×C₄²	1	2	yes	—
159	C₄×D₁₃	C₂²×C₈	1	2	yes	—
160	C₄×D₁₃	C₂²×C₈	1	2	yes	—
161	C₈×C₁₃	C₂×C₄²	1	2	yes	—
162	C₈×C₁₃	C₂×C₄²	1	2	yes	—
163	C₈×C₁₃	C₂²×C₈	1	2	yes	—
164	C₈×C₁₃	C₂²×C₈	1	2	yes	—
165	#1055	C₂×C₄²	1	2	yes	—
166	#1055	C₂²×C₈	1	2	yes	—
167	#1055	C₂²×C₈	1	2	yes	—
168	#1055	C₂³×C₄	1	2	yes	—
169	C₂³×C₈	—	13	1	no	—
170	C₂³×C₈	—	13	1	no	—
171	C₂²×C₄²	—	13	1	no	—
172	C₂×M₃₂	—	13	4	no	—
173	C₂×M₃₂	—	13	4	no	—
174	C₂×M₃₂	—	13	16	no	—
175	C₂²×C₁₆	—	13	4	no	—
176	C₂×C₄×C₈	—	13	1	no	—
177	C₂×C₄×C₈	—	13	1	no	—
178	C₂×C₄×C₈	—	13	1	no	—
179	C₂×C₄×C₈	—	13	1	no	—
180	C₂×C₄×C₈	—	13	1	no	—
181	C₂×C₄×C₈	—	13	1	no	—
182	C₂×C₄×C₈	—	13	1	no	—
183	C₂×C₄×C₈	—	13	1	no	—
184	C₂×C₄×C₈	—	13	1	no	—
185	C₂×C₄×C₈	—	13	1	no	—
186	C₂×C₄×C₈	—	13	1	no	—
187	C₂×C₄×C₈	#261	1	1	yes	characteristic
188	#346	—	13	4	no	—
189	#346	—	13	4	no	—
190	C₄×C₁₆	—	13	4	no	—
191	C₄×C₁₆	—	13	4	no	—
192	C₂²×C₁₃	—	2	2	no	—
193	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
194	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
195	C₂×D₁₃	—	2	2	no	—
196	C₂×D₁₃	—	2	8	no	—
197	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
198	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
199	C₂×D₁₃	C₂×M₃₂	1	4	yes	—
200	C₄×C₁₃	—	2	2	no	—
201	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
202	C₄×C₁₃	C₂×M₃₂	1	4	yes	complemented
203	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
204	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
205	Dic₁₃	—	2	2	no	—
206	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
207	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
208	Dic₁₃	C₂×M₃₂	1	4	yes	complemented
209	C₂³×C₄	—	13	1	no	—
210	C₂³×C₄	—	13	2	no	—
211	C₂²×C₈	—	13	1	no	—
212	C₂²×C₈	—	13	1	no	—
213	C₂²×C₈	—	13	8	no	—
214	C₂²×C₈	—	13	8	no	—
215	C₂²×C₈	—	13	1	no	—
216	C₂²×C₈	—	13	1	no	—
217	C₂²×C₈	—	13	1	no	—
218	C₂²×C₈	—	13	1	no	—
219	C₂²×C₈	—	13	1	no	—
220	C₂²×C₈	—	13	1	no	—
221	C₂²×C₈	—	13	1	no	—
222	C₂²×C₈	—	13	1	no	—
223	C₂²×C₈	C₂×#261	1	1	yes	characteristic
224	C₂²×C₈	C₂×#261	1	1	yes	characteristic
225	C₂×C₄²	—	13	2	no	—
226	C₂×C₄²	—	13	1	no	—
227	C₂×C₄²	—	13	2	no	—
228	C₂×C₄²	—	13	2	no	—
229	C₂×C₄²	—	13	1	no	—
230	C₂×C₄²	—	13	1	no	—
231	C₂×C₄²	—	13	1	no	—
232	C₂×C₄²	—	13	1	no	—
233	C₂×C₄²	C₂×#261	1	1	yes	characteristic
234	M₃₂	—	13	16	no	—
235	M₃₂	—	13	16	no	—
236	C₂×C₁₆	—	13	16	no	—
237	C₂×C₁₆	—	13	8	no	—
238	C₄×C₈	—	13	1	no	—
239	C₄×C₈	—	13	1	no	—
240	C₄×C₈	—	13	1	no	—
241	C₄×C₈	—	13	1	no	—
242	C₄×C₈	—	13	1	no	—
243	C₄×C₈	—	13	1	no	—
244	C₄×C₈	—	13	1	no	—
245	C₄×C₈	—	13	1	no	—
246	C₄×C₈	—	13	1	no	—
247	C₄×C₈	—	13	1	no	—
248	C₄×C₈	—	13	1	no	—
249	C₄×C₈	—	13	1	no	—
250	C₄×C₈	C₂×#261	1	1	yes	characteristic
251	C₄×C₈	C₂×#261	1	1	yes	characteristic
252	C₄×C₈	C₂×#261	1	1	yes	characteristic
253	C₄×C₈	C₂×#261	1	1	yes	characteristic
254	C₂×C₁₃	—	2	2	no	—
255	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
256	C₂×C₁₃	C₂²×M₃₂	1	2	yes	—
257	D₁₃	—	2	2	no	—
258	D₁₃	C₄×M₃₂	1	4	yes	complemented
259	C₂⁴	—	13	1	no	—
260	C₂²×C₄	—	13	1	no	—
261	C₂²×C₄	—	13	1	no	—
262	C₂²×C₄	—	13	1	no	—
263	C₂²×C₄	—	13	2	no	—
264	C₂²×C₄	—	13	4	no	—
265	C₂²×C₄	—	13	4	no	—
266	C₂²×C₄	—	13	1	no	—
267	C₂²×C₄	—	13	1	no	—
268	C₂²×C₄	—	13	2	no	—
269	C₂²×C₄	—	13	2	no	—
270	C₂²×C₄	—	13	2	no	—
271	C₂²×C₄	—	13	2	no	—
272	C₂²×C₄	—	26	8	no	—
273	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
274	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
275	C₂×C₈	—	13	4	no	—
276	C₂×C₈	—	13	4	no	—
277	C₂×C₈	—	13	1	no	—
278	C₂×C₈	—	13	1	no	—
279	C₂×C₈	—	13	1	no	—
280	C₂×C₈	—	13	1	no	—
281	C₂×C₈	—	13	4	no	—
282	C₂×C₈	—	13	4	no	—
283	C₂×C₈	—	13	4	no	—
284	C₂×C₈	—	13	4	no	—
285	C₂×C₈	—	13	4	no	—
286	C₂×C₈	—	13	4	no	—
287	C₂×C₈	—	13	4	no	—
288	C₂×C₈	—	13	4	no	—
289	C₂×C₈	D₁₃⋊C₈	1	4	yes	—
290	C₂×C₈	C₄×#261	1	4	yes	—
291	C₂×C₈	C₂²×#261	1	1	yes	characteristic
292	C₂×C₈	C₂²×#261	1	1	yes	characteristic
293	C₂×C₈	C₂²×#261	1	1	yes	characteristic
294	C₂×C₈	C₂²×#261	1	1	yes	characteristic
295	C₄²	—	13	2	no	—
296	C₄²	—	13	2	no	—
297	C₄²	—	13	2	no	—
298	C₄²	—	13	2	no	—
299	C₄²	—	13	2	no	—
300	C₄²	—	13	1	no	—
301	C₄²	—	13	1	no	—
302	C₄²	D₁₃⋊C₈	1	2	yes	—
303	C₄²	C₂²×#261	1	1	yes	characteristic
304	C₄²	C₂²×#261	1	1	yes	characteristic
305	C₁₆	—	13	16	no	—
306	C₁₃	C₂×C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
307	C₂³	—	13	1	no	—
308	C₂³	—	13	4	no	—
309	C₂³	—	13	1	no	—
310	C₂³	—	26	4	no	—
311	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	13	4	no	—
314	C₂×C₄	—	13	2	no	—
315	C₂×C₄	—	13	1	no	—
316	C₂×C₄	—	13	1	no	—
317	C₂×C₄	—	13	4	no	—
318	C₂×C₄	—	13	4	no	—
319	C₂×C₄	—	13	8	no	—
320	C₂×C₄	—	13	2	no	—
321	C₂×C₄	—	13	2	no	—
322	C₂×C₄	—	13	2	no	—
323	C₂×C₄	—	13	2	no	—
324	C₂×C₄	—	13	2	no	—
325	C₂×C₄	—	26	4	no	—
326	C₂×C₄	—	26	4	no	—
327	C₂×C₄	—	26	4	no	—
328	C₂×C₄	—	26	4	no	—
329	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
330	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
331	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
332	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
333	C₂×C₄	C₂×C₄×#261	1	2	yes	—
334	C₂×C₄	C₂³×#261	1	1	yes	characteristic
335	C₈	—	13	2	no	—
336	C₈	—	13	2	no	—
337	C₈	—	13	2	no	—
338	C₈	—	13	2	no	—
339	C₈	C₂×D₁₃⋊C₈	1	2	yes	—
340	C₈	C₂×D₁₃⋊C₈	1	2	yes	—
341	C₈	C₂×C₄×#261	1	2	yes	—
342	C₈	C₂×C₄×#261	1	2	yes	—
343	C₂²	—	2	2	no	—
344	C₂²	—	13	4	no	—
345	C₂²	—	13	2	no	—
346	C₂²	—	13	2	no	—
347	C₂²	—	26	8	no	—
348	C₂²	—	26	2	no	—
349	C₂²	C₄×D₁₃⋊C₈	1	2	yes	—
350	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	13	4	no	—
353	C₄	—	13	2	no	—
354	C₄	—	13	2	no	—
355	C₄	—	26	2	no	—
356	C₄	C₄×D₁₃⋊C₈	1	2	yes	—
357	C₄	D₁₃⋊M₃₂	1	4	yes	direct product factor
358	C₄	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
359	C₄	C₂²×C₄×#261	1	1	yes	characteristic
360	C₂	—	2	2	no	—
361	C₂	—	13	4	no	—
362	C₂	—	26	2	no	—
363	C₂	C₂×C₄×D₁₃⋊C₈	1	1	yes	characteristic
364	C₂	C₂×D₁₃⋊M₃₂	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂³×C₈
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×C₄×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13131043	C₂	semidirect
3. #13131042	C₂	semidirect
4. C₄×#88098	C₂	semidirect
5. C₄×#88106	C₂	semidirect
6. #13131037	C₂	semidirect
7. C₄×D₁₃⋊C₁₆	C₂	semidirect
13. D₁₃⋊M₃₂	C₄	direct (N × H)
28. #11718258	C₂²	semidirect
29. #11718257	C₂²	semidirect
30. #11718231	C₂²	semidirect
31. C₄×#6092	C₂²	semidirect
57. #88106	C₂×C₄	semidirect
59. #88098	C₂×C₄	semidirect
60. D₁₃⋊C₁₆	C₂×C₄	semidirect
124. #6092	C₂²×C₄	semidirect
156. C₄×D₁₃	M₃₂	semidirect
202. C₄×C₁₃	C₂×M₃₂	semidirect
208. Dic₁₃	C₂×M₃₂	semidirect
258. D₁₃	C₄×M₃₂	semidirect
306. C₁₃	C₂×C₄×M₃₂	semidirect
357. C₄	D₁₃⋊M₃₂	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×D₁₃⋊M₃₂	2
#13131043	2
#13131042	2
C₄×#88098	2
C₄×#88106	2
#13131037	2
C₄×D₁₃⋊C₁₆	2
C₂×C₄×C₈×D₁₃	2
C₂×C₄×M₃₂	13

Subgroups — C4×D13⋊M32 #16806718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₁₃⋊M₃₂ #16806718