Subgroups — C₁₃₁×#33865 #45719749

Order 33536.

580 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3334×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	D₄×Q₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2241×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2235×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2225×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2217×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2208×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#2185×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	C₂×#358×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₁₃₁	C₂²	1	2	yes	—
13	D₄×Q₈×C₁₃₁	—	2	1	no	—
14	#547×C₁₃₁	—	2	1	no	—
15	C₂×SD₃₂×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×SD₃₂×C₁₃₁	C₂²	1	2	yes	—
17	C₂²×C₁₆×C₁₃₁	C₂²	1	2	yes	—
18	#500×C₁₃₁	C₂²	1	1	yes	characteristic
19	#494×C₁₃₁	C₂²	1	1	yes	characteristic
20	#480×C₁₃₁	—	2	2	no	—
21	#474×C₁₃₁	—	2	1	no	—
22	#467×C₁₃₁	C₂²	1	2	yes	—
23	#466×C₁₃₁	C₂²	1	2	yes	—
24	#462×C₁₃₁	—	2	1	no	—
25	#451×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	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
30	#367×C₁₃₁	C₂²	1	2	yes	—
31	#367×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₄⋊C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
33	#358×C₁₃₁	C₂²	1	2	yes	—
34	#358×C₁₃₁	C₂²	1	2	yes	—
35	#358×C₁₃₁	C₂²	1	2	yes	—
36	#358×C₁₃₁	C₂²	1	2	yes	—
37	#358×C₁₃₁	C₂²	1	1	yes	characteristic
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	—	4	1	no	—
42	C₂²×Q₈×C₁₃₁	—	2	2	no	—
43	C₂×Q₁₆×C₁₃₁	—	2	4	no	—
44	C₂×Q₁₆×C₁₃₁	—	2	2	no	—
45	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
46	C₂×Q₁₆×C₁₃₁	—	4	2	no	—
47	C₂×Q₁₆×C₁₃₁	C₂³	1	2	yes	—
48	C₂×Q₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
52	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
53	C₄⋊Q₈×C₁₃₁	—	4	1	no	—
54	#123×C₁₃₁	—	4	2	no	—
55	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
56	C₂²⋊Q₈×C₁₃₁	—	4	1	no	—
57	C₂²⋊Q₈×C₁₃₁	—	4	2	no	—
58	#121×C₁₃₁	—	2	2	no	—
59	C₄×Q₈×C₁₃₁	—	2	1	no	—
60	C₄×D₄×C₁₃₁	—	2	1	no	—
61	C₄×D₄×C₁₃₁	—	4	1	no	—
62	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
64	SD₃₂×C₁₃₁	—	2	2	no	—
65	SD₃₂×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	2	no	—
71	#107×C₁₃₁	—	2	1	no	—
72	#107×C₁₃₁	C₂³	1	1	yes	characteristic
73	#107×C₁₃₁	C₂³	1	2	yes	—
74	#107×C₁₃₁	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
76	#103×C₁₃₁	—	2	1	no	—
77	#103×C₁₃₁	—	2	2	no	—
78	#102×C₁₃₁	—	2	1	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	—	8	4	no	—
83	C₂×Q₈×C₁₃₁	—	2	1	no	—
84	C₂×Q₈×C₁₃₁	—	2	2	no	—
85	C₂×Q₈×C₁₃₁	—	4	4	no	—
86	C₂×Q₈×C₁₃₁	—	4	1	no	—
87	C₂×Q₈×C₁₃₁	—	4	2	no	—
88	C₂×Q₈×C₁₃₁	—	8	2	no	—
89	C₂×D₄×C₁₃₁	—	2	1	no	—
90	C₂×D₄×C₁₃₁	—	4	2	no	—
91	C₂×D₄×C₁₃₁	D₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₁	—	4	2	no	—
93	C₂²×C₄×C₁₃₁	—	4	2	no	—
94	C₂²×C₄×C₁₃₁	—	4	1	no	—
95	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
96	Q₁₆×C₁₃₁	—	2	2	no	—
97	Q₁₆×C₁₃₁	—	2	1	no	—
98	Q₁₆×C₁₃₁	—	2	2	no	—
99	Q₁₆×C₁₃₁	—	4	4	no	—
100	Q₁₆×C₁₃₁	—	8	1	no	—
101	Q₁₆×C₁₃₁	#41	1	2	yes	complemented
102	D₈×C₁₃₁	—	2	1	no	—
103	D₈×C₁₃₁	—	2	1	no	—
104	C₂×C₈×C₁₃₁	—	2	2	no	—
105	C₂×C₈×C₁₃₁	—	2	2	no	—
106	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
109	C₄⋊C₄×C₁₃₁	—	2	1	no	—
110	C₄⋊C₄×C₁₃₁	—	2	2	no	—
111	C₄⋊C₄×C₁₃₁	—	2	1	no	—
112	C₄⋊C₄×C₁₃₁	—	4	2	no	—
113	C₄⋊C₄×C₁₃₁	—	4	1	no	—
114	C₄⋊C₄×C₁₃₁	—	4	1	no	—
115	C₄⋊C₄×C₁₃₁	—	4	2	no	—
116	C₄⋊C₄×C₁₃₁	—	4	1	no	—
117	C₄⋊C₄×C₁₃₁	—	4	1	no	—
118	C₄⋊C₄×C₁₃₁	D₈	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
120	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
121	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
122	C₂²⋊C₄×C₁₃₁	D₈	1	2	yes	—
123	C₄²×C₁₃₁	—	4	1	no	—
124	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
125	C₁₆×C₁₃₁	—	2	1	no	—
126	C₁₆×C₁₃₁	—	2	1	no	—
127	C₁₆×C₁₃₁	—	2	2	no	—
128	C₂³×C₁₃₁	—	4	1	no	—
129	C₂³×C₁₃₁	C₂×D₈	1	2	yes	—
130	Q₈×C₁₃₁	—	2	2	no	—
131	Q₈×C₁₃₁	—	4	1	no	—
132	Q₈×C₁₃₁	—	4	2	no	—
133	Q₈×C₁₃₁	—	4	2	no	—
134	Q₈×C₁₃₁	—	8	4	no	—
135	Q₈×C₁₃₁	—	8	2	no	—
136	D₄×C₁₃₁	—	4	1	no	—
137	D₄×C₁₃₁	—	4	1	no	—
138	D₄×C₁₃₁	—	8	4	no	—
139	D₄×C₁₃₁	SD₃₂	1	4	yes	complemented
140	C₂×C₄×C₁₃₁	—	2	2	no	—
141	C₂×C₄×C₁₃₁	—	2	2	no	—
142	C₂×C₄×C₁₃₁	—	4	1	no	—
143	C₂×C₄×C₁₃₁	—	4	1	no	—
144	C₂×C₄×C₁₃₁	—	4	1	no	—
145	C₂×C₄×C₁₃₁	—	4	2	no	—
146	C₂×C₄×C₁₃₁	—	4	2	no	—
147	C₂×C₄×C₁₃₁	—	8	4	no	—
148	C₂×C₄×C₁₃₁	—	8	4	no	—
149	C₂×C₄×C₁₃₁	—	8	2	no	—
150	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃₁	C₂×D₈	1	2	yes	—
152	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
154	C₈×C₁₃₁	—	2	2	no	—
155	C₈×C₁₃₁	—	2	1	no	—
156	C₈×C₁₃₁	C₂×#41	1	1	yes	characteristic
157	C₈×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂²×C₁₃₁	—	2	2	no	—
159	C₂²×C₁₃₁	—	2	2	no	—
160	C₂²×C₁₃₁	—	8	1	no	—
161	C₂²×C₁₃₁	—	8	1	no	—
162	C₂²×C₁₃₁	—	8	1	no	—
163	C₂²×C₁₃₁	C₂×SD₃₂	1	4	yes	—
164	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
165	C₄×C₁₃₁	—	2	1	no	—
166	C₄×C₁₃₁	—	2	2	no	—
167	C₄×C₁₃₁	—	4	2	no	—
168	C₄×C₁₃₁	—	8	1	no	—
169	C₄×C₁₃₁	—	8	2	no	—
170	C₄×C₁₃₁	—	8	1	no	—
171	C₄×C₁₃₁	—	8	2	no	—
172	C₄×C₁₃₁	C₂×SD₃₂	1	2	yes	—
173	C₄×C₁₃₁	#546	1	1	yes	characteristic
174	C₄×C₁₃₁	#577	1	1	yes	characteristic
175	C₂×C₁₃₁	—	2	4	no	—
176	C₂×C₁₃₁	—	16	1	no	—
177	C₂×C₁₃₁	#3294	1	1	yes	characteristic
178	C₂×C₁₃₁	C₂²×SD₃₂	1	1	yes	characteristic
179	C₂×C₁₃₁	#3417	1	1	yes	characteristic
180	#33865	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃₁	#33865	1	1	yes	characteristic, direct product factor, Sylow
182	#3334	C₂×C₁₃₁	1	1	yes	characteristic
183	D₄×Q₁₆	C₂×C₁₃₁	1	1	yes	characteristic, complemented
184	#2241	C₂×C₁₃₁	1	1	yes	characteristic, complemented
185	#2235	C₂×C₁₃₁	1	2	yes	complemented
186	#2225	C₂×C₁₃₁	1	1	yes	characteristic, complemented
187	#2217	C₂×C₁₃₁	1	2	yes	complemented
188	#2208	C₂×C₁₃₁	1	1	yes	characteristic, complemented
189	#2185	C₂×C₁₃₁	1	2	yes	complemented
190	C₄×SD₃₂	C₂×C₁₃₁	1	1	yes	characteristic, complemented
191	D₄×C₁₆	C₂×C₁₃₁	1	1	yes	characteristic, complemented
192	C₂×#358	C₂×C₁₃₁	1	2	yes	complemented
193	C₂²×Q₁₆	C₂²×C₁₃₁	1	2	yes	—
194	D₄×Q₈	—	2	1	no	—
195	#547	—	2	1	no	—
196	C₂×SD₃₂	C₂²×C₁₃₁	1	1	yes	characteristic
197	C₂×SD₃₂	C₂²×C₁₃₁	1	2	yes	—
198	C₂²×C₁₆	C₂²×C₁₃₁	1	2	yes	—
199	#500	C₂²×C₁₃₁	1	1	yes	characteristic
200	#494	C₂²×C₁₃₁	1	1	yes	characteristic
201	#480	—	2	2	no	—
202	#474	—	2	1	no	—
203	#467	C₂²×C₁₃₁	1	2	yes	—
204	#466	C₂²×C₁₃₁	1	2	yes	—
205	#462	—	2	1	no	—
206	#451	—	2	2	no	—
207	C₄×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
208	C₄×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
209	C₈×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
210	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
211	#367	C₂²×C₁₃₁	1	1	yes	characteristic
212	#367	C₂²×C₁₃₁	1	2	yes	—
213	C₄⋊C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
214	#358	C₂²×C₁₃₁	1	1	yes	characteristic
215	#358	C₂²×C₁₃₁	1	2	yes	—
216	#358	C₂²×C₁₃₁	1	2	yes	—
217	#358	C₂²×C₁₃₁	1	2	yes	—
218	#358	C₂²×C₁₃₁	1	2	yes	—
219	#357	C₂²×C₁₃₁	1	1	yes	characteristic
220	C₂²⋊C₁₆	C₂²×C₁₃₁	1	2	yes	—
221	C₄×C₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
222	C₂×#41	—	4	1	no	—
223	C₂²×Q₈	—	2	2	no	—
224	C₂×Q₁₆	—	2	4	no	—
225	C₂×Q₁₆	—	2	2	no	—
226	C₂×Q₁₆	—	2	1	no	—
227	C₂×Q₁₆	—	4	2	no	—
228	C₂×Q₁₆	C₂³×C₁₃₁	1	2	yes	—
229	C₂×Q₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
230	C₂×D₈	C₂³×C₁₃₁	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	4	1	no	—
235	#123	—	4	2	no	—
236	C₂²⋊Q₈	—	2	2	no	—
237	C₂²⋊Q₈	—	4	1	no	—
238	C₂²⋊Q₈	—	4	2	no	—
239	#121	—	2	2	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	4	1	no	—
243	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	2	2	no	—
245	SD₃₂	—	2	2	no	—
246	SD₃₂	—	4	2	no	—
247	C₂×C₁₆	—	4	2	no	—
248	C₂×C₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
249	C₂×C₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
250	C₂×C₁₆	C₂³×C₁₃₁	1	2	yes	—
251	#107	—	2	2	no	—
252	#107	—	2	1	no	—
253	#107	C₂³×C₁₃₁	1	1	yes	characteristic
254	#107	C₂³×C₁₃₁	1	1	yes	characteristic
255	#107	C₂³×C₁₃₁	1	2	yes	—
256	C₄⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
257	#103	—	2	1	no	—
258	#103	—	2	2	no	—
259	#102	—	2	1	no	—
260	#102	—	2	2	no	—
261	C₂²⋊C₈	D₄×C₁₃₁	1	2	yes	—
262	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
263	#41	—	8	4	no	—
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	4	4	no	—
267	C₂×Q₈	—	4	1	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×Q₈	—	8	2	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	D₈×C₁₃₁	1	1	yes	characteristic
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
277	Q₁₆	—	2	2	no	—
278	Q₁₆	—	2	1	no	—
279	Q₁₆	—	2	2	no	—
280	Q₁₆	—	4	4	no	—
281	Q₁₆	—	8	1	no	—
282	Q₁₆	#41×C₁₃₁	1	2	yes	complemented
283	D₈	—	2	1	no	—
284	D₈	—	2	1	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
288	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
289	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	D₈×C₁₃₁	1	1	yes	characteristic
300	C₂²⋊C₄	—	4	2	no	—
301	C₂²⋊C₄	—	4	1	no	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	D₈×C₁₃₁	1	2	yes	—
304	C₄²	—	4	1	no	—
305	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
306	C₁₆	—	2	1	no	—
307	C₁₆	—	2	1	no	—
308	C₁₆	—	2	2	no	—
309	C₂³	—	4	1	no	—
310	C₂³	C₂×D₈×C₁₃₁	1	2	yes	—
311	Q₈	—	2	2	no	—
312	Q₈	—	4	1	no	—
313	Q₈	—	4	2	no	—
314	Q₈	—	4	2	no	—
315	Q₈	—	8	4	no	—
316	Q₈	—	8	2	no	—
317	D₄	—	4	1	no	—
318	D₄	—	4	1	no	—
319	D₄	—	8	4	no	—
320	D₄	SD₃₂×C₁₃₁	1	4	yes	complemented
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	8	4	no	—
329	C₂×C₄	—	8	4	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
332	C₂×C₄	C₂×D₈×C₁₃₁	1	2	yes	—
333	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
335	C₈	—	2	2	no	—
336	C₈	—	2	1	no	—
337	C₈	C₂×#41×C₁₃₁	1	1	yes	characteristic
338	C₈	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	8	1	no	—
342	C₂²	—	8	1	no	—
343	C₂²	—	8	1	no	—
344	C₂²	C₂×SD₃₂×C₁₃₁	1	4	yes	—
345	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
346	C₄	—	2	2	no	—
347	C₄	—	2	1	no	—
348	C₄	—	4	2	no	—
349	C₄	—	8	2	no	—
350	C₄	—	8	1	no	—
351	C₄	—	8	2	no	—
352	C₄	—	8	1	no	—
353	C₄	C₂×SD₃₂×C₁₃₁	1	2	yes	—
354	C₄	#546×C₁₃₁	1	1	yes	characteristic
355	C₄	#577×C₁₃₁	1	1	yes	characteristic
356	C₂	—	2	4	no	—
357	C₂	—	16	1	no	—
358	C₂	#3294×C₁₃₁	1	1	yes	characteristic
359	C₂	C₂²×SD₃₂×C₁₃₁	1	1	yes	characteristic
360	C₂	#3417×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
prime radical	#3334×C₁₃₁	C₂
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
2. D₄×Q₁₆×C₁₃₁	C₂	semidirect
3. #2241×C₁₃₁	C₂	semidirect
4. #2235×C₁₃₁	C₂	semidirect
5. #2225×C₁₃₁	C₂	semidirect
6. #2217×C₁₃₁	C₂	semidirect
7. #2208×C₁₃₁	C₂	semidirect
8. #2185×C₁₃₁	C₂	semidirect
9. C₄×SD₃₂×C₁₃₁	C₂	semidirect
10. D₄×C₁₆×C₁₃₁	C₂	semidirect
11. C₂×#358×C₁₃₁	C₂	semidirect
101. Q₁₆×C₁₃₁	#41	semidirect
139. D₄×C₁₃₁	SD₃₂	semidirect
180. #33865	C₁₃₁	direct (N × H)
181. C₁₃₁	#33865	direct (N × H)
183. D₄×Q₁₆	C₂×C₁₃₁	semidirect
184. #2241	C₂×C₁₃₁	semidirect
185. #2235	C₂×C₁₃₁	semidirect
186. #2225	C₂×C₁₃₁	semidirect
187. #2217	C₂×C₁₃₁	semidirect
188. #2208	C₂×C₁₃₁	semidirect
189. #2185	C₂×C₁₃₁	semidirect
190. C₄×SD₃₂	C₂×C₁₃₁	semidirect
191. D₄×C₁₆	C₂×C₁₃₁	semidirect
192. C₂×#358	C₂×C₁₃₁	semidirect
282. Q₁₆	#41×C₁₃₁	semidirect
320. D₄	SD₃₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3334×C₁₃₁	2
D₄×Q₁₆×C₁₃₁	2
#2241×C₁₃₁	2
#2235×C₁₃₁	2
#2225×C₁₃₁	2
#2217×C₁₃₁	2
#2208×C₁₃₁	2
#2185×C₁₃₁	2
C₄×SD₃₂×C₁₃₁	2
D₄×C₁₆×C₁₃₁	2
C₂×#358×C₁₃₁	2
#33865	131

Subgroups — C131×#33865 #45719749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33865 #45719749