Subgroups — C₁₃₁×#21296 #45707180

Order 33536.

730 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	#2943×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2922×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#1975×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1974×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#1946×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1945×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1938×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1937×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1778×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1759×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1726×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₄×#41×C₁₃₁	C₂²	1	2	yes	—
14	#442×C₁₃₁	C₄	1	2	yes	complemented
15	#441×C₁₃₁	C₄	1	2	yes	complemented
16	#440×C₁₃₁	C₄	1	4	yes	complemented
17	#433×C₁₃₁	—	2	4	no	—
18	#431×C₁₃₁	—	2	4	no	—
19	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
21	#427×C₁₃₁	C₂²	1	1	yes	characteristic
22	#424×C₁₃₁	C₂²	1	2	yes	—
23	#424×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#104×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#104×C₁₃₁	C₂²	1	2	yes	—
26	#416×C₁₃₁	C₂²	1	2	yes	—
27	#408×C₁₃₁	C₂²	1	2	yes	—
28	#408×C₁₃₁	C₂²	1	2	yes	—
29	C₄×M₁₆×C₁₃₁	C₂²	1	2	yes	—
30	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
36	#376×C₁₃₁	C₂²	1	1	yes	characteristic
37	#341×C₁₃₁	C₂²	1	2	yes	—
38	#339×C₁₃₁	C₂²	1	2	yes	—
39	#339×C₁₃₁	C₂²	1	2	yes	—
40	C₂×#41×C₁₃₁	C₂³	1	2	yes	—
41	#135×C₁₃₁	—	2	2	no	—
42	#135×C₁₃₁	—	2	2	no	—
43	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂×SD₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
45	C₂×D₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
47	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₁₃₁	C₂×C₄	1	4	yes	—
53	C₄×D₄×C₁₃₁	—	2	4	no	—
54	C₄×D₄×C₁₃₁	C₂×C₄	1	4	yes	—
55	#117×C₁₃₁	—	2	2	no	—
56	#117×C₁₃₁	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₃₁	—	2	2	no	—
58	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
61	#108×C₁₃₁	—	2	2	no	—
62	#108×C₁₃₁	—	2	2	no	—
63	#107×C₁₃₁	C₂×C₄	1	2	yes	—
64	#106×C₁₃₁	C₂×C₄	1	2	yes	—
65	C₄⋊C₈×C₁₃₁	—	2	4	no	—
66	C₄⋊C₈×C₁₃₁	—	2	4	no	—
67	#104×C₁₃₁	—	2	4	no	—
68	#104×C₁₃₁	—	2	4	no	—
69	#103×C₁₃₁	C₂×C₄	1	4	yes	—
70	#102×C₁₃₁	C₂×C₄	1	4	yes	—
71	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
72	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
73	#97×C₁₃₁	—	2	2	no	—
74	#97×C₁₃₁	—	2	2	no	—
75	#97×C₁₃₁	—	2	2	no	—
76	#97×C₁₃₁	C₂×C₄	1	2	yes	—
77	#97×C₁₃₁	C₂×C₄	1	2	yes	—
78	C₄×C₈×C₁₃₁	—	2	2	no	—
79	C₄×C₈×C₁₃₁	—	2	2	no	—
80	C₄×C₈×C₁₃₁	—	2	2	no	—
81	C₄×C₈×C₁₃₁	D₄	1	4	yes	—
82	#95×C₁₃₁	—	2	2	no	—
83	#41×C₁₃₁	—	2	2	no	—
84	#41×C₁₃₁	—	2	2	no	—
85	#41×C₁₃₁	—	2	2	no	—
86	#41×C₁₃₁	—	2	2	no	—
87	C₂×Q₈×C₁₃₁	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₁₃₁	—	2	2	no	—
89	C₂×D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃₁	—	2	1	no	—
91	C₂²×C₄×C₁₃₁	—	2	1	no	—
92	C₂²×C₄×C₁₃₁	—	2	4	no	—
93	C₂²×C₄×C₁₃₁	—	2	2	no	—
94	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
95	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
96	Q₁₆×C₁₃₁	—	2	2	no	—
97	SD₁₆×C₁₃₁	—	2	4	no	—
98	D₈×C₁₃₁	—	2	2	no	—
99	M₁₆×C₁₃₁	—	2	2	no	—
100	M₁₆×C₁₃₁	—	2	2	no	—
101	M₁₆×C₁₃₁	—	2	2	no	—
102	M₁₆×C₁₃₁	—	2	2	no	—
103	C₂×C₈×C₁₃₁	—	2	1	no	—
104	C₂×C₈×C₁₃₁	—	2	1	no	—
105	C₂×C₈×C₁₃₁	—	2	1	no	—
106	C₂×C₈×C₁₃₁	—	2	1	no	—
107	C₂×C₈×C₁₃₁	—	2	1	no	—
108	C₂×C₈×C₁₃₁	—	2	1	no	—
109	C₂×C₈×C₁₃₁	—	2	2	no	—
110	C₂×C₈×C₁₃₁	—	2	2	no	—
111	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃₁	#41	1	2	yes	—
117	C₂×C₈×C₁₃₁	#41	1	2	yes	—
118	C₄⋊C₄×C₁₃₁	—	2	4	no	—
119	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
120	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
121	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
122	C₄²×C₁₃₁	—	2	4	no	—
123	C₄²×C₁₃₁	—	2	2	no	—
124	C₄²×C₁₃₁	—	2	1	no	—
125	C₄²×C₁₃₁	—	2	1	no	—
126	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
127	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
128	C₄²×C₁₃₁	#41	1	2	yes	—
129	C₄²×C₁₃₁	#41	1	2	yes	—
130	C₂³×C₁₃₁	—	2	2	no	—
131	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
132	Q₈×C₁₃₁	—	2	2	no	—
133	Q₈×C₁₃₁	—	2	2	no	—
134	D₄×C₁₃₁	—	2	2	no	—
135	D₄×C₁₃₁	—	2	2	no	—
136	D₄×C₁₃₁	—	4	2	no	—
137	D₄×C₁₃₁	—	4	2	no	—
138	C₂×C₄×C₁₃₁	—	2	4	no	—
139	C₂×C₄×C₁₃₁	—	2	2	no	—
140	C₂×C₄×C₁₃₁	—	2	2	no	—
141	C₂×C₄×C₁₃₁	—	2	2	no	—
142	C₂×C₄×C₁₃₁	—	4	2	no	—
143	C₂×C₄×C₁₃₁	—	4	8	no	—
144	C₂×C₄×C₁₃₁	—	4	2	no	—
145	C₂×C₄×C₁₃₁	—	4	2	no	—
146	C₂×C₄×C₁₃₁	—	4	2	no	—
147	C₂×C₄×C₁₃₁	—	4	2	no	—
148	C₂×C₄×C₁₃₁	C₄×D₄	1	4	yes	—
149	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
155	C₈×C₁₃₁	—	2	2	no	—
156	C₈×C₁₃₁	—	2	2	no	—
157	C₈×C₁₃₁	—	2	2	no	—
158	C₈×C₁₃₁	—	4	2	no	—
159	C₈×C₁₃₁	—	4	2	no	—
160	C₈×C₁₃₁	#117	1	2	yes	—
161	C₈×C₁₃₁	#117	1	2	yes	—
162	C₂²×C₁₃₁	—	2	2	no	—
163	C₂²×C₁₃₁	—	4	4	no	—
164	C₂²×C₁₃₁	—	4	2	no	—
165	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂²×C₁₃₁	#529	1	1	yes	characteristic
167	C₂²×C₁₃₁	#529	1	1	yes	characteristic
168	C₄×C₁₃₁	—	2	4	no	—
169	C₄×C₁₃₁	—	4	2	no	—
170	C₄×C₁₃₁	—	4	2	no	—
171	C₄×C₁₃₁	—	4	4	no	—
172	C₄×C₁₃₁	—	4	2	no	—
173	C₄×C₁₃₁	C₂×#117	1	1	yes	characteristic
174	C₄×C₁₃₁	C₄×#41	1	1	yes	characteristic
175	C₄×C₁₃₁	#532	1	1	yes	characteristic
176	C₄×C₁₃₁	#532	1	1	yes	characteristic
177	C₂×C₁₃₁	—	2	1	no	—
178	C₂×C₁₃₁	—	2	1	no	—
179	C₂×C₁₃₁	—	8	2	no	—
180	C₂×C₁₃₁	#2293	1	1	yes	characteristic
181	C₂×C₁₃₁	#2955	1	2	yes	—
182	#21296	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₁₃₁	#21296	1	1	yes	characteristic, direct product factor, Sylow
184	#2943	C₂×C₁₃₁	1	1	yes	characteristic
185	#2922	C₂×C₁₃₁	1	2	yes	complemented
186	#1975	C₂×C₁₃₁	1	1	yes	characteristic
187	#1974	C₂×C₁₃₁	1	1	yes	characteristic
188	#1946	C₂×C₁₃₁	1	1	yes	characteristic, complemented
189	#1945	C₂×C₁₃₁	1	1	yes	characteristic, complemented
190	#1938	C₂×C₁₃₁	1	2	yes	complemented
191	#1937	C₂×C₁₃₁	1	2	yes	complemented
192	#1778	C₂×C₁₃₁	1	1	yes	characteristic, complemented
193	#1759	C₂×C₁₃₁	1	2	yes	complemented
194	#1726	C₂×C₁₃₁	1	1	yes	characteristic, complemented
195	C₂×#135	C₂²×C₁₃₁	1	1	yes	characteristic
196	C₄×#41	C₂²×C₁₃₁	1	2	yes	—
197	#442	C₄×C₁₃₁	1	2	yes	complemented
198	#441	C₄×C₁₃₁	1	2	yes	complemented
199	#440	C₄×C₁₃₁	1	4	yes	complemented
200	#433	—	2	4	no	—
201	#431	—	2	4	no	—
202	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
203	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
204	#427	C₂²×C₁₃₁	1	1	yes	characteristic
205	#424	C₂²×C₁₃₁	1	2	yes	—
206	#424	C₂²×C₁₃₁	1	2	yes	—
207	C₂×#104	C₂²×C₁₃₁	1	2	yes	—
208	C₂×#104	C₂²×C₁₃₁	1	2	yes	—
209	#416	C₂²×C₁₃₁	1	2	yes	—
210	#408	C₂²×C₁₃₁	1	2	yes	—
211	#408	C₂²×C₁₃₁	1	2	yes	—
212	C₄×M₁₆	C₂²×C₁₃₁	1	2	yes	—
213	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
214	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
215	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
217	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
219	#376	C₂²×C₁₃₁	1	1	yes	characteristic
220	#341	C₂²×C₁₃₁	1	2	yes	—
221	#339	C₂²×C₁₃₁	1	2	yes	—
222	#339	C₂²×C₁₃₁	1	2	yes	—
223	C₂×#41	C₂³×C₁₃₁	1	2	yes	—
224	#135	—	2	2	no	—
225	#135	—	2	2	no	—
226	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
227	C₂×SD₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
228	C₂×D₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
229	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
230	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
231	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
235	C₄×Q₈	C₂×C₄×C₁₃₁	1	4	yes	—
236	C₄×D₄	—	2	4	no	—
237	C₄×D₄	C₂×C₄×C₁₃₁	1	4	yes	—
238	#117	—	2	2	no	—
239	#117	C₂³×C₁₃₁	1	2	yes	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
244	#108	—	2	2	no	—
245	#108	—	2	2	no	—
246	#107	C₂×C₄×C₁₃₁	1	2	yes	—
247	#106	C₂×C₄×C₁₃₁	1	2	yes	—
248	C₄⋊C₈	—	2	4	no	—
249	C₄⋊C₈	—	2	4	no	—
250	#104	—	2	4	no	—
251	#104	—	2	4	no	—
252	#103	C₂×C₄×C₁₃₁	1	4	yes	—
253	#102	C₂×C₄×C₁₃₁	1	4	yes	—
254	C₂²⋊C₈	—	2	4	no	—
255	C₂²⋊C₈	—	2	4	no	—
256	#97	—	2	2	no	—
257	#97	—	2	2	no	—
258	#97	—	2	2	no	—
259	#97	C₂×C₄×C₁₃₁	1	2	yes	—
260	#97	C₂×C₄×C₁₃₁	1	2	yes	—
261	C₄×C₈	—	2	2	no	—
262	C₄×C₈	—	2	2	no	—
263	C₄×C₈	—	2	2	no	—
264	C₄×C₈	D₄×C₁₃₁	1	4	yes	—
265	#95	—	2	2	no	—
266	#41	—	2	2	no	—
267	#41	—	2	2	no	—
268	#41	—	2	2	no	—
269	#41	—	2	2	no	—
270	C₂×Q₈	C₂²×C₄×C₁₃₁	1	2	yes	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	C₂²×C₄×C₁₃₁	1	2	yes	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
278	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
279	Q₁₆	—	2	2	no	—
280	SD₁₆	—	2	4	no	—
281	D₈	—	2	2	no	—
282	M₁₆	—	2	2	no	—
283	M₁₆	—	2	2	no	—
284	M₁₆	—	2	2	no	—
285	M₁₆	—	2	2	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
295	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
296	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
297	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
298	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
299	C₂×C₈	#41×C₁₃₁	1	2	yes	—
300	C₂×C₈	#41×C₁₃₁	1	2	yes	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₄²	—	2	4	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	1	no	—
309	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
310	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
311	C₄²	#41×C₁₃₁	1	2	yes	—
312	C₄²	#41×C₁₃₁	1	2	yes	—
313	C₂³	—	2	2	no	—
314	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
315	Q₈	—	2	2	no	—
316	Q₈	—	2	2	no	—
317	D₄	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	2	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	8	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	C₄×D₄×C₁₃₁	1	4	yes	—
332	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
335	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
336	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
337	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
338	C₈	—	2	2	no	—
339	C₈	—	2	2	no	—
340	C₈	—	2	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	4	2	no	—
343	C₈	#117×C₁₃₁	1	2	yes	—
344	C₈	#117×C₁₃₁	1	2	yes	—
345	C₂²	—	2	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	4	4	no	—
348	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
349	C₂²	#529×C₁₃₁	1	1	yes	characteristic
350	C₂²	#529×C₁₃₁	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	4	2	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	4	4	no	—
356	C₄	C₂×#117×C₁₃₁	1	1	yes	characteristic
357	C₄	C₄×#41×C₁₃₁	1	1	yes	characteristic
358	C₄	#532×C₁₃₁	1	1	yes	characteristic
359	C₄	#532×C₁₃₁	1	1	yes	characteristic
360	C₂	—	2	1	no	—
361	C₂	—	2	1	no	—
362	C₂	—	8	2	no	—
363	C₂	#2293×C₁₃₁	1	1	yes	characteristic
364	C₂	#2955×C₁₃₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂×C₄×D₄
prime radical	C₂×#135×C₁₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₂×C₄×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2922×C₁₃₁	C₂	semidirect
5. #1946×C₁₃₁	C₂	semidirect
6. #1945×C₁₃₁	C₂	semidirect
7. #1938×C₁₃₁	C₂	semidirect
8. #1937×C₁₃₁	C₂	semidirect
9. #1778×C₁₃₁	C₂	semidirect
10. #1759×C₁₃₁	C₂	semidirect
11. #1726×C₁₃₁	C₂	semidirect
14. #442×C₁₃₁	C₄	semidirect
15. #441×C₁₃₁	C₄	semidirect
16. #440×C₁₃₁	C₄	semidirect
182. #21296	C₁₃₁	direct (N × H)
183. C₁₃₁	#21296	direct (N × H)
185. #2922	C₂×C₁₃₁	semidirect
188. #1946	C₂×C₁₃₁	semidirect
189. #1945	C₂×C₁₃₁	semidirect
190. #1938	C₂×C₁₃₁	semidirect
191. #1937	C₂×C₁₃₁	semidirect
192. #1778	C₂×C₁₃₁	semidirect
193. #1759	C₂×C₁₃₁	semidirect
194. #1726	C₂×C₁₃₁	semidirect
197. #442	C₄×C₁₃₁	semidirect
198. #441	C₄×C₁₃₁	semidirect
199. #440	C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2943×C₁₃₁	2
#2922×C₁₃₁	2
#1975×C₁₃₁	2
#1974×C₁₃₁	2
#1946×C₁₃₁	2
#1945×C₁₃₁	2
#1938×C₁₃₁	2
#1937×C₁₃₁	2
#1778×C₁₃₁	2
#1759×C₁₃₁	2
#1726×C₁₃₁	2
#21296	131

Subgroups — C131×#21296 #45707180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#21296 #45707180