Subgroups — C₁₃₁×#33872 #45719756

Order 33536.

568 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3341×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3287×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2240×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2234×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2227×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2215×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2206×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2186×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	C₄×SD₃₂×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#2138×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₁₃₁	C₂²	1	2	yes	—
13	#555×C₁₃₁	—	2	1	no	—
14	#550×C₁₃₁	—	2	1	no	—
15	C₂×SD₃₂×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×D₁₆×C₁₃₁	C₂²	1	2	yes	—
17	C₂²×C₁₆×C₁₃₁	C₂²	1	2	yes	—
18	#500×C₁₃₁	C₂²	1	1	yes	characteristic
19	#493×C₁₃₁	C₂²	1	1	yes	characteristic
20	#482×C₁₃₁	—	2	2	no	—
21	#476×C₁₃₁	—	2	1	no	—
22	#466×C₁₃₁	C₂²	1	2	yes	—
23	#466×C₁₃₁	C₂²	1	2	yes	—
24	#460×C₁₃₁	—	2	1	no	—
25	#449×C₁₃₁	—	2	2	no	—
26	C₄×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₄×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
29	#427×C₁₃₁	C₂²	1	2	yes	—
30	#367×C₁₃₁	C₂²	1	1	yes	characteristic
31	#366×C₁₃₁	C₂²	1	2	yes	—
32	C₄⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
33	#358×C₁₃₁	C₂²	1	2	yes	—
34	#358×C₁₃₁	C₂²	1	1	yes	characteristic
35	#357×C₁₃₁	C₂²	1	2	yes	—
36	#357×C₁₃₁	C₂²	1	2	yes	—
37	#357×C₁₃₁	C₂²	1	2	yes	—
38	#357×C₁₃₁	C₂²	1	1	yes	characteristic
39	C₂²⋊C₁₆×C₁₃₁	C₂²	1	2	yes	—
40	C₄×C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂×#41×C₁₃₁	—	2	2	no	—
42	#135×C₁₃₁	—	2	4	no	—
43	#135×C₁₃₁	—	4	2	no	—
44	C₂×Q₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
46	C₂×D₈×C₁₃₁	—	2	1	no	—
47	C₂×D₈×C₁₃₁	C₂³	1	1	yes	characteristic
48	C₂×D₈×C₁₃₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
51	#127×C₁₃₁	—	2	1	no	—
52	#127×C₁₃₁	—	4	1	no	—
53	#124×C₁₃₁	—	4	2	no	—
54	#121×C₁₃₁	—	2	2	no	—
55	#121×C₁₃₁	—	2	2	no	—
56	#121×C₁₃₁	—	4	1	no	—
57	#121×C₁₃₁	—	4	2	no	—
58	C₄×Q₈×C₁₃₁	—	2	1	no	—
59	C₄×D₄×C₁₃₁	—	2	1	no	—
60	C₄×D₄×C₁₃₁	—	4	1	no	—
61	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
62	#117×C₁₃₁	—	2	2	no	—
63	#117×C₁₃₁	—	4	1	no	—
64	SD₃₂×C₁₃₁	—	2	2	no	—
65	D₁₆×C₁₃₁	—	4	2	no	—
66	C₂×C₁₆×C₁₃₁	—	4	2	no	—
67	C₂×C₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
68	C₂×C₁₆×C₁₃₁	C₂³	1	2	yes	—
69	C₂×C₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
70	#107×C₁₃₁	—	2	1	no	—
71	#107×C₁₃₁	C₂³	1	1	yes	characteristic
72	#107×C₁₃₁	C₂³	1	2	yes	—
73	#107×C₁₃₁	C₂³	1	1	yes	characteristic
74	#106×C₁₃₁	—	2	2	no	—
75	C₄⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
76	#103×C₁₃₁	—	2	1	no	—
77	#102×C₁₃₁	—	2	1	no	—
78	#102×C₁₃₁	—	2	2	no	—
79	#102×C₁₃₁	—	2	2	no	—
80	C₂²⋊C₈×C₁₃₁	D₄	1	2	yes	—
81	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
82	#41×C₁₃₁	—	4	4	no	—
83	#41×C₁₃₁	—	8	2	no	—
84	C₂×Q₈×C₁₃₁	—	2	1	no	—
85	C₂×Q₈×C₁₃₁	—	4	1	no	—
86	C₂×D₄×C₁₃₁	—	2	1	no	—
87	C₂×D₄×C₁₃₁	—	2	2	no	—
88	C₂×D₄×C₁₃₁	—	4	2	no	—
89	C₂×D₄×C₁₃₁	—	4	2	no	—
90	C₂×D₄×C₁₃₁	—	4	2	no	—
91	C₂×D₄×C₁₃₁	—	4	1	no	—
92	C₂×D₄×C₁₃₁	—	4	1	no	—
93	C₂×D₄×C₁₃₁	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₁	—	4	1	no	—
95	C₂²×C₄×C₁₃₁	—	4	2	no	—
96	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
97	Q₁₆×C₁₃₁	—	2	1	no	—
98	Q₁₆×C₁₃₁	#41	1	2	yes	—
99	SD₁₆×C₁₃₁	—	4	4	no	—
100	D₈×C₁₃₁	—	2	1	no	—
101	D₈×C₁₃₁	—	2	2	no	—
102	D₈×C₁₃₁	—	2	1	no	—
103	D₈×C₁₃₁	—	2	2	no	—
104	D₈×C₁₃₁	—	8	1	no	—
105	C₂×C₈×C₁₃₁	—	2	2	no	—
106	C₂×C₈×C₁₃₁	—	2	2	no	—
107	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
110	C₄⋊C₄×C₁₃₁	—	2	1	no	—
111	C₄⋊C₄×C₁₃₁	—	2	1	no	—
112	C₄⋊C₄×C₁₃₁	—	2	2	no	—
113	C₄⋊C₄×C₁₃₁	—	4	1	no	—
114	C₄⋊C₄×C₁₃₁	—	4	1	no	—
115	C₄⋊C₄×C₁₃₁	D₈	1	1	yes	characteristic
116	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
117	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
118	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
119	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
120	C₂²⋊C₄×C₁₃₁	D₈	1	2	yes	—
121	C₄²×C₁₃₁	—	4	2	no	—
122	C₄²×C₁₃₁	—	4	1	no	—
123	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
124	C₁₆×C₁₃₁	—	2	1	no	—
125	C₁₆×C₁₃₁	—	2	1	no	—
126	C₁₆×C₁₃₁	—	2	2	no	—
127	C₂³×C₁₃₁	—	4	1	no	—
128	C₂³×C₁₃₁	—	4	2	no	—
129	C₂³×C₁₃₁	C₂×D₈	1	2	yes	—
130	Q₈×C₁₃₁	—	2	2	no	—
131	Q₈×C₁₃₁	—	4	1	no	—
132	Q₈×C₁₃₁	—	16	1	no	—
133	D₄×C₁₃₁	—	2	2	no	—
134	D₄×C₁₃₁	—	4	2	no	—
135	D₄×C₁₃₁	—	4	1	no	—
136	D₄×C₁₃₁	—	4	2	no	—
137	D₄×C₁₃₁	—	4	1	no	—
138	D₄×C₁₃₁	—	8	4	no	—
139	D₄×C₁₃₁	—	8	2	no	—
140	D₄×C₁₃₁	—	16	1	no	—
141	D₄×C₁₃₁	—	16	2	no	—
142	D₄×C₁₃₁	—	16	2	no	—
143	C₂×C₄×C₁₃₁	—	2	2	no	—
144	C₂×C₄×C₁₃₁	—	2	2	no	—
145	C₂×C₄×C₁₃₁	—	4	1	no	—
146	C₂×C₄×C₁₃₁	—	4	1	no	—
147	C₂×C₄×C₁₃₁	—	4	1	no	—
148	C₂×C₄×C₁₃₁	—	4	2	no	—
149	C₂×C₄×C₁₃₁	—	8	4	no	—
150	C₂×C₄×C₁₃₁	—	8	2	no	—
151	C₂×C₄×C₁₃₁	C₂×D₈	1	2	yes	—
152	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
155	C₈×C₁₃₁	—	2	2	no	—
156	C₈×C₁₃₁	—	2	1	no	—
157	C₈×C₁₃₁	C₂×#41	1	1	yes	characteristic
158	C₈×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂²×C₁₃₁	—	2	2	no	—
160	C₂²×C₁₃₁	—	2	2	no	—
161	C₂²×C₁₃₁	—	2	2	no	—
162	C₂²×C₁₃₁	—	8	1	no	—
163	C₂²×C₁₃₁	—	8	2	no	—
164	C₂²×C₁₃₁	—	8	2	no	—
165	C₂²×C₁₃₁	—	8	1	no	—
166	C₂²×C₁₃₁	—	8	2	no	—
167	C₂²×C₁₃₁	—	8	1	no	—
168	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
169	C₄×C₁₃₁	—	2	1	no	—
170	C₄×C₁₃₁	—	2	2	no	—
171	C₄×C₁₃₁	—	4	2	no	—
172	C₄×C₁₃₁	—	8	1	no	—
173	C₄×C₁₃₁	—	8	1	no	—
174	C₄×C₁₃₁	—	8	2	no	—
175	C₄×C₁₃₁	#508	1	2	yes	—
176	C₄×C₁₃₁	#546	1	1	yes	characteristic
177	C₄×C₁₃₁	#577	1	1	yes	characteristic
178	C₂×C₁₃₁	—	4	2	no	—
179	C₂×C₁₃₁	—	16	1	no	—
180	C₂×C₁₃₁	—	16	2	no	—
181	C₂×C₁₃₁	#3294	1	1	yes	characteristic
182	C₂×C₁₃₁	C₂×#508	1	1	yes	characteristic
183	C₂×C₁₃₁	#3415	1	1	yes	characteristic
184	#33872	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₁₃₁	#33872	1	1	yes	characteristic, direct product factor, Sylow
186	#3341	C₂×C₁₃₁	1	1	yes	characteristic, complemented
187	#3287	C₂×C₁₃₁	1	1	yes	characteristic, complemented
188	#2240	C₂×C₁₃₁	1	1	yes	characteristic, complemented
189	#2234	C₂×C₁₃₁	1	2	yes	complemented
190	#2227	C₂×C₁₃₁	1	1	yes	characteristic, complemented
191	#2215	C₂×C₁₃₁	1	2	yes	complemented
192	#2206	C₂×C₁₃₁	1	1	yes	characteristic, complemented
193	#2186	C₂×C₁₃₁	1	2	yes	complemented
194	C₄×SD₃₂	C₂×C₁₃₁	1	1	yes	characteristic, complemented
195	D₄×C₁₆	C₂×C₁₃₁	1	1	yes	characteristic, complemented
196	#2138	C₂×C₁₃₁	1	2	yes	complemented
197	C₂×#135	C₂²×C₁₃₁	1	2	yes	—
198	#555	—	2	1	no	—
199	#550	—	2	1	no	—
200	C₂×SD₃₂	C₂²×C₁₃₁	1	1	yes	characteristic
201	C₂×D₁₆	C₂²×C₁₃₁	1	2	yes	—
202	C₂²×C₁₆	C₂²×C₁₃₁	1	2	yes	—
203	#500	C₂²×C₁₃₁	1	1	yes	characteristic
204	#493	C₂²×C₁₃₁	1	1	yes	characteristic
205	#482	—	2	2	no	—
206	#476	—	2	1	no	—
207	#466	C₂²×C₁₃₁	1	2	yes	—
208	#466	C₂²×C₁₃₁	1	2	yes	—
209	#460	—	2	1	no	—
210	#449	—	2	2	no	—
211	C₄×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
212	C₄×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
213	C₈×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
214	#427	C₂²×C₁₃₁	1	2	yes	—
215	#367	C₂²×C₁₃₁	1	1	yes	characteristic
216	#366	C₂²×C₁₃₁	1	2	yes	—
217	C₄⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
218	#358	C₂²×C₁₃₁	1	1	yes	characteristic
219	#358	C₂²×C₁₃₁	1	2	yes	—
220	#357	C₂²×C₁₃₁	1	2	yes	—
221	#357	C₂²×C₁₃₁	1	2	yes	—
222	#357	C₂²×C₁₃₁	1	1	yes	characteristic
223	#357	C₂²×C₁₃₁	1	2	yes	—
224	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
225	C₄×C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
226	C₂×#41	—	2	2	no	—
227	#135	—	2	4	no	—
228	#135	—	4	2	no	—
229	C₂×Q₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
230	C₂×SD₁₆	—	2	2	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂×D₈	C₂³×C₁₃₁	1	2	yes	—
233	C₂×D₈	C₂³×C₁₃₁	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
235	C₄⋊Q₈	—	2	1	no	—
236	#127	—	2	1	no	—
237	#127	—	4	1	no	—
238	#124	—	4	2	no	—
239	#121	—	2	2	no	—
240	#121	—	2	2	no	—
241	#121	—	4	1	no	—
242	#121	—	4	2	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	4	1	no	—
246	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
247	#117	—	2	2	no	—
248	#117	—	4	1	no	—
249	SD₃₂	—	2	2	no	—
250	D₁₆	—	4	2	no	—
251	C₂×C₁₆	—	4	2	no	—
252	C₂×C₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
253	C₂×C₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
254	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
255	#107	—	2	1	no	—
256	#107	C₂³×C₁₃₁	1	2	yes	—
257	#107	C₂³×C₁₃₁	1	1	yes	characteristic
258	#107	C₂³×C₁₃₁	1	1	yes	characteristic
259	#106	—	2	2	no	—
260	C₄⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
261	#103	—	2	1	no	—
262	#102	—	2	1	no	—
263	#102	—	2	2	no	—
264	#102	—	2	2	no	—
265	C₂²⋊C₈	D₄×C₁₃₁	1	2	yes	—
266	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
267	#41	—	4	4	no	—
268	#41	—	8	2	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×Q₈	—	4	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	D₈×C₁₃₁	1	1	yes	characteristic
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
282	Q₁₆	—	2	1	no	—
283	Q₁₆	#41×C₁₃₁	1	2	yes	—
284	SD₁₆	—	4	4	no	—
285	D₈	—	2	1	no	—
286	D₈	—	2	2	no	—
287	D₈	—	2	1	no	—
288	D₈	—	2	2	no	—
289	D₈	—	8	1	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
294	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	D₈×C₁₃₁	1	1	yes	characteristic
301	C₂²⋊C₄	—	4	2	no	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	—	4	1	no	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₂²⋊C₄	D₈×C₁₃₁	1	2	yes	—
306	C₄²	—	4	2	no	—
307	C₄²	—	4	1	no	—
308	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
309	C₁₆	—	2	1	no	—
310	C₁₆	—	2	1	no	—
311	C₁₆	—	2	2	no	—
312	C₂³	—	4	1	no	—
313	C₂³	—	4	2	no	—
314	C₂³	C₂×D₈×C₁₃₁	1	2	yes	—
315	Q₈	—	2	2	no	—
316	Q₈	—	4	1	no	—
317	Q₈	—	16	1	no	—
318	D₄	—	2	2	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	1	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	1	no	—
323	D₄	—	8	4	no	—
324	D₄	—	8	2	no	—
325	D₄	—	16	1	no	—
326	D₄	—	16	2	no	—
327	D₄	—	16	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	8	4	no	—
335	C₂×C₄	—	8	2	no	—
336	C₂×C₄	C₂×D₈×C₁₃₁	1	2	yes	—
337	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
338	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
340	C₈	—	2	2	no	—
341	C₈	—	2	1	no	—
342	C₈	C₂×#41×C₁₃₁	1	1	yes	characteristic
343	C₈	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	1	no	—
349	C₂²	—	8	1	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	1	no	—
353	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	2	no	—
357	C₄	—	8	1	no	—
358	C₄	—	8	1	no	—
359	C₄	—	8	2	no	—
360	C₄	#508×C₁₃₁	1	2	yes	—
361	C₄	#546×C₁₃₁	1	1	yes	characteristic
362	C₄	#577×C₁₃₁	1	1	yes	characteristic
363	C₂	—	4	2	no	—
364	C₂	—	16	2	no	—
365	C₂	—	16	1	no	—
366	C₂	#3294×C₁₃₁	1	1	yes	characteristic
367	C₂	C₂×#508×C₁₃₁	1	1	yes	characteristic
368	C₂	#3415×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₄×D₄×C₁₃₁ ◁ C₈×D₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3341×C₁₃₁	C₂	semidirect
2. #3287×C₁₃₁	C₂	semidirect
3. #2240×C₁₃₁	C₂	semidirect
4. #2234×C₁₃₁	C₂	semidirect
5. #2227×C₁₃₁	C₂	semidirect
6. #2215×C₁₃₁	C₂	semidirect
7. #2206×C₁₃₁	C₂	semidirect
8. #2186×C₁₃₁	C₂	semidirect
9. C₄×SD₃₂×C₁₃₁	C₂	semidirect
10. D₄×C₁₆×C₁₃₁	C₂	semidirect
11. #2138×C₁₃₁	C₂	semidirect
184. #33872	C₁₃₁	direct (N × H)
185. C₁₃₁	#33872	direct (N × H)
186. #3341	C₂×C₁₃₁	semidirect
187. #3287	C₂×C₁₃₁	semidirect
188. #2240	C₂×C₁₃₁	semidirect
189. #2234	C₂×C₁₃₁	semidirect
190. #2227	C₂×C₁₃₁	semidirect
191. #2215	C₂×C₁₃₁	semidirect
192. #2206	C₂×C₁₃₁	semidirect
193. #2186	C₂×C₁₃₁	semidirect
194. C₄×SD₃₂	C₂×C₁₃₁	semidirect
195. D₄×C₁₆	C₂×C₁₃₁	semidirect
196. #2138	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3341×C₁₃₁	2
#3287×C₁₃₁	2
#2240×C₁₃₁	2
#2234×C₁₃₁	2
#2227×C₁₃₁	2
#2215×C₁₃₁	2
#2206×C₁₃₁	2
#2186×C₁₃₁	2
C₄×SD₃₂×C₁₃₁	2
D₄×C₁₆×C₁₃₁	2
#2138×C₁₃₁	2
#33872	131

Subgroups — C131×#33872 #45719756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33872 #45719756