Subgroups — C₂×#1969×C₁₃₁ #45707106

Order 33536.

1614 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#107×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#103×C₁₃₁	C₂	1	2	yes	maximal
4	C₂²×C₄×C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#391×C₁₃₁	C₂	1	2	yes	maximal
6	#1969×C₁₃₁	C₂	1	8	yes	maximal, direct product factor
7	C₂³×Q₈×C₁₃₁	C₂²	1	2	yes	—
8	C₂²×Q₁₆×C₁₃₁	—	2	4	no	—
9	C₂²×Q₁₆×C₁₃₁	—	2	4	no	—
10	C₂²×Q₁₆×C₁₃₁	C₄	1	8	yes	complemented
11	C₂²×Q₁₆×C₁₃₁	C₂²	1	4	yes	—
12	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×#107×C₁₃₁	—	2	4	no	—
17	C₂×#107×C₁₃₁	C₂²	1	4	yes	—
18	C₂×#103×C₁₃₁	—	2	8	no	—
19	C₂×#103×C₁₃₁	C₂²	1	8	yes	—
20	C₂×C₄×C₈×C₁₃₁	—	2	4	no	—
21	C₂×C₄×C₈×C₁₃₁	C₂²	1	4	yes	—
22	#391×C₁₃₁	—	2	4	no	—
23	#391×C₁₃₁	C₂²	1	8	yes	—
24	C₂×#95×C₁₃₁	—	2	4	no	—
25	C₂²×Q₈×C₁₃₁	—	2	2	no	—
26	C₂²×Q₈×C₁₃₁	—	2	4	no	—
27	C₂²×Q₈×C₁₃₁	—	2	4	no	—
28	C₂²×Q₈×C₁₃₁	—	2	4	no	—
29	C₂²×Q₈×C₁₃₁	—	2	4	no	—
30	C₂²×Q₈×C₁₃₁	—	2	4	no	—
31	C₂²×Q₈×C₁₃₁	C₂×C₄	1	8	yes	—
32	C₂²×Q₈×C₁₃₁	C₂³	1	4	yes	—
33	C₂³×C₄×C₁₃₁	—	2	2	no	—
34	C₂³×C₄×C₁₃₁	—	2	2	no	—
35	C₂³×C₄×C₁₃₁	D₄	1	2	yes	—
36	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
37	C₂×Q₁₆×C₁₃₁	—	2	32	no	—
38	C₂×Q₁₆×C₁₃₁	—	2	8	no	—
39	C₂×Q₁₆×C₁₃₁	—	2	8	no	—
40	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	16	yes	complemented
41	C₂²×C₈×C₁₃₁	—	2	2	no	—
42	C₂²×C₈×C₁₃₁	—	2	2	no	—
43	C₂²×C₈×C₁₃₁	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₁₃₁	D₄	1	4	yes	—
45	C₂²×C₈×C₁₃₁	D₄	1	4	yes	—
46	C₂²×C₈×C₁₃₁	D₄	1	4	yes	—
47	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
53	C₂×C₄²×C₁₃₁	—	2	2	no	—
54	C₂×C₄²×C₁₃₁	—	2	2	no	—
55	C₂×C₄²×C₁₃₁	D₄	1	2	yes	—
56	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
57	#107×C₁₃₁	—	2	8	no	—
58	#103×C₁₃₁	—	2	16	no	—
59	C₄×C₈×C₁₃₁	—	2	8	no	—
60	#95×C₁₃₁	—	2	16	no	—
61	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
62	C₂×Q₈×C₁₃₁	—	2	8	no	—
63	C₂×Q₈×C₁₃₁	—	2	4	no	—
64	C₂×Q₈×C₁₃₁	—	2	16	no	—
65	C₂×Q₈×C₁₃₁	—	2	16	no	—
66	C₂×Q₈×C₁₃₁	—	2	4	no	—
67	C₂×Q₈×C₁₃₁	—	2	4	no	—
68	C₂×Q₈×C₁₃₁	—	2	4	no	—
69	C₂×Q₈×C₁₃₁	—	2	4	no	—
70	C₂×Q₈×C₁₃₁	—	4	4	no	—
71	C₂×Q₈×C₁₃₁	—	4	8	no	—
72	C₂×Q₈×C₁₃₁	—	4	8	no	—
73	C₂×Q₈×C₁₃₁	—	4	4	no	—
74	C₂×Q₈×C₁₃₁	C₂²×C₄	1	8	yes	—
75	C₂²×C₄×C₁₃₁	—	2	4	no	—
76	C₂²×C₄×C₁₃₁	—	2	4	no	—
77	C₂²×C₄×C₁₃₁	—	2	8	no	—
78	C₂²×C₄×C₁₃₁	—	2	4	no	—
79	C₂²×C₄×C₁₃₁	—	2	4	no	—
80	C₂²×C₄×C₁₃₁	—	4	4	no	—
81	C₂²×C₄×C₁₃₁	—	4	4	no	—
82	C₂²×C₄×C₁₃₁	—	4	4	no	—
83	C₂²×C₄×C₁₃₁	—	4	8	no	—
84	C₂²×C₄×C₁₃₁	Q₁₆	1	8	yes	complemented
85	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
92	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
93	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
94	Q₁₆×C₁₃₁	—	2	32	no	—
95	C₂×C₈×C₁₃₁	—	2	8	no	—
96	C₂×C₈×C₁₃₁	—	2	2	no	—
97	C₂×C₈×C₁₃₁	—	2	2	no	—
98	C₂×C₈×C₁₃₁	C₂²⋊C₄	1	16	yes	—
99	C₂×C₈×C₁₃₁	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
101	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
102	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
103	C₄⋊C₄×C₁₃₁	—	2	4	no	—
104	C₄⋊C₄×C₁₃₁	—	2	4	no	—
105	C₄⋊C₄×C₁₃₁	—	4	4	no	—
106	C₄²×C₁₃₁	—	2	4	no	—
107	C₄²×C₁₃₁	—	2	2	no	—
108	C₄²×C₁₃₁	—	2	2	no	—
109	C₂³×C₁₃₁	C₄×D₄	1	2	yes	—
110	C₂³×C₁₃₁	#121	1	2	yes	—
111	C₂³×C₁₃₁	#127	1	2	yes	—
112	C₂³×C₁₃₁	C₂×Q₁₆	1	4	yes	—
113	C₂³×C₁₃₁	#135	1	4	yes	—
114	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
115	Q₈×C₁₃₁	—	2	8	no	—
116	Q₈×C₁₃₁	—	2	8	no	—
117	Q₈×C₁₃₁	—	4	4	no	—
118	Q₈×C₁₃₁	—	4	4	no	—
119	Q₈×C₁₃₁	—	4	16	no	—
120	C₂×C₄×C₁₃₁	—	2	4	no	—
121	C₂×C₄×C₁₃₁	—	2	4	no	—
122	C₂×C₄×C₁₃₁	—	2	16	no	—
123	C₂×C₄×C₁₃₁	—	2	8	no	—
124	C₂×C₄×C₁₃₁	—	4	4	no	—
125	C₂×C₄×C₁₃₁	—	4	4	no	—
126	C₂×C₄×C₁₃₁	—	4	16	no	—
127	C₂×C₄×C₁₃₁	—	4	4	no	—
128	C₂×C₄×C₁₃₁	—	4	8	no	—
129	C₂×C₄×C₁₃₁	—	8	8	no	—
130	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	4	yes	—
131	C₂×C₄×C₁₃₁	C₄×D₄	1	4	yes	—
132	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
133	C₂×C₄×C₁₃₁	#121	1	4	yes	—
134	C₂×C₄×C₁₃₁	#121	1	2	yes	—
135	C₂×C₄×C₁₃₁	#124	1	4	yes	—
136	C₂×C₄×C₁₃₁	#127	1	2	yes	—
137	C₂×C₄×C₁₃₁	C₂×Q₁₆	1	8	yes	complemented
138	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
143	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
144	C₈×C₁₃₁	—	2	4	no	—
145	C₈×C₁₃₁	C₂×C₂²⋊C₄	1	8	yes	—
146	C₂²×C₁₃₁	#390	1	4	yes	—
147	C₂²×C₁₃₁	C₄×Q₁₆	1	8	yes	—
148	C₂²×C₁₃₁	#467	1	8	yes	—
149	C₂²×C₁₃₁	#494	1	4	yes	—
150	C₂²×C₁₃₁	#495	1	4	yes	—
151	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
152	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
153	C₂²×C₁₃₁	C₂×#127	1	1	yes	characteristic
154	C₂²×C₁₃₁	C₂²×Q₁₆	1	2	yes	—
155	C₂²×C₁₃₁	C₂×#135	1	2	yes	—
156	C₄×C₁₃₁	—	2	8	no	—
157	C₄×C₁₃₁	—	4	8	no	—
158	C₄×C₁₃₁	—	8	4	no	—
159	C₄×C₁₃₁	#390	1	4	yes	—
160	C₄×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
161	C₄×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
162	C₄×C₁₃₁	C₂×#121	1	1	yes	characteristic
163	C₄×C₁₃₁	C₂×#124	1	1	yes	characteristic
164	C₂×C₁₃₁	#1969	1	8	yes	direct product factor
165	C₂×C₁₃₁	C₂×#390	1	1	yes	characteristic
166	C₂×C₁₃₁	C₂×C₄×Q₁₆	1	2	yes	—
167	C₂×C₁₃₁	C₂×#467	1	2	yes	—
168	C₂×C₁₃₁	C₂×#494	1	1	yes	characteristic
169	C₂×C₁₃₁	C₂×#495	1	1	yes	characteristic
170	C₂×#1969	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₁₃₁	C₂×#1969	1	1	yes	characteristic, direct product factor, Sylow
172	C₂³×Q₁₆	C₂×C₁₃₁	1	1	yes	characteristic
173	C₂²×#107	C₂×C₁₃₁	1	1	yes	characteristic
174	C₂²×#103	C₂×C₁₃₁	1	2	yes	—
175	C₂²×C₄×C₈	C₂×C₁₃₁	1	1	yes	characteristic
176	C₂×#391	C₂×C₁₃₁	1	2	yes	—
177	#1969	C₂×C₁₃₁	1	8	yes	direct product factor
178	C₂³×Q₈	C₂²×C₁₃₁	1	2	yes	—
179	C₂²×Q₁₆	—	2	4	no	—
180	C₂²×Q₁₆	—	2	4	no	—
181	C₂²×Q₁₆	C₄×C₁₃₁	1	8	yes	complemented
182	C₂²×Q₁₆	C₂²×C₁₃₁	1	4	yes	—
183	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
184	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
185	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
186	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
187	C₂×#107	—	2	4	no	—
188	C₂×#107	C₂²×C₁₃₁	1	4	yes	—
189	C₂×#103	—	2	8	no	—
190	C₂×#103	C₂²×C₁₃₁	1	8	yes	—
191	C₂×C₄×C₈	—	2	4	no	—
192	C₂×C₄×C₈	C₂²×C₁₃₁	1	4	yes	—
193	#391	—	2	4	no	—
194	#391	C₂²×C₁₃₁	1	8	yes	—
195	C₂×#95	—	2	4	no	—
196	C₂²×Q₈	—	2	2	no	—
197	C₂²×Q₈	—	2	4	no	—
198	C₂²×Q₈	—	2	4	no	—
199	C₂²×Q₈	—	2	4	no	—
200	C₂²×Q₈	—	2	4	no	—
201	C₂²×Q₈	—	2	4	no	—
202	C₂²×Q₈	C₂×C₄×C₁₃₁	1	8	yes	—
203	C₂²×Q₈	C₂³×C₁₃₁	1	4	yes	—
204	C₂³×C₄	—	2	2	no	—
205	C₂³×C₄	—	2	2	no	—
206	C₂³×C₄	D₄×C₁₃₁	1	2	yes	—
207	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
208	C₂×Q₁₆	—	2	32	no	—
209	C₂×Q₁₆	—	2	8	no	—
210	C₂×Q₁₆	—	2	8	no	—
211	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	16	yes	complemented
212	C₂²×C₈	—	2	2	no	—
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	C₂×C₄×C₁₃₁	1	4	yes	—
215	C₂²×C₈	D₄×C₁₃₁	1	4	yes	—
216	C₂²×C₈	D₄×C₁₃₁	1	4	yes	—
217	C₂²×C₈	D₄×C₁₃₁	1	4	yes	—
218	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
219	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
224	C₂×C₄²	—	2	2	no	—
225	C₂×C₄²	—	2	2	no	—
226	C₂×C₄²	D₄×C₁₃₁	1	2	yes	—
227	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
228	#107	—	2	8	no	—
229	#103	—	2	16	no	—
230	C₄×C₈	—	2	8	no	—
231	#95	—	2	16	no	—
232	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
233	C₂×Q₈	—	2	8	no	—
234	C₂×Q₈	—	2	4	no	—
235	C₂×Q₈	—	2	16	no	—
236	C₂×Q₈	—	2	16	no	—
237	C₂×Q₈	—	2	4	no	—
238	C₂×Q₈	—	2	4	no	—
239	C₂×Q₈	—	2	4	no	—
240	C₂×Q₈	—	2	4	no	—
241	C₂×Q₈	—	4	8	no	—
242	C₂×Q₈	—	4	4	no	—
243	C₂×Q₈	—	4	8	no	—
244	C₂×Q₈	—	4	4	no	—
245	C₂×Q₈	C₂²×C₄×C₁₃₁	1	8	yes	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	4	4	no	—
252	C₂²×C₄	—	4	4	no	—
253	C₂²×C₄	—	4	4	no	—
254	C₂²×C₄	—	4	8	no	—
255	C₂²×C₄	Q₁₆×C₁₃₁	1	8	yes	complemented
256	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
257	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
258	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
259	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
260	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
261	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
262	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
263	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
264	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
265	Q₁₆	—	2	32	no	—
266	C₂×C₈	—	2	8	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	C₂²⋊C₄×C₁₃₁	1	16	yes	—
270	C₂×C₈	C₂²×C₄×C₁₃₁	1	4	yes	—
271	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
272	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
273	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄²	—	2	4	no	—
278	C₄²	—	2	2	no	—
279	C₄²	—	2	2	no	—
280	C₂³	C₄×D₄×C₁₃₁	1	2	yes	—
281	C₂³	#121×C₁₃₁	1	2	yes	—
282	C₂³	#127×C₁₃₁	1	2	yes	—
283	C₂³	C₂×Q₁₆×C₁₃₁	1	4	yes	—
284	C₂³	#135×C₁₃₁	1	4	yes	—
285	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
286	Q₈	—	2	8	no	—
287	Q₈	—	2	8	no	—
288	Q₈	—	4	16	no	—
289	Q₈	—	4	4	no	—
290	Q₈	—	4	4	no	—
291	C₂×C₄	—	2	16	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	4	16	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	—	4	8	no	—
300	C₂×C₄	—	8	8	no	—
301	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	4	yes	—
302	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
303	C₂×C₄	C₄×D₄×C₁₃₁	1	4	yes	—
304	C₂×C₄	#121×C₁₃₁	1	2	yes	—
305	C₂×C₄	#121×C₁₃₁	1	4	yes	—
306	C₂×C₄	#124×C₁₃₁	1	4	yes	—
307	C₂×C₄	#127×C₁₃₁	1	2	yes	—
308	C₂×C₄	C₂×Q₁₆×C₁₃₁	1	8	yes	complemented
309	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
310	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
311	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
312	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
313	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
314	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
315	C₈	—	2	4	no	—
316	C₈	C₂×C₂²⋊C₄×C₁₃₁	1	8	yes	—
317	C₂²	#390×C₁₃₁	1	4	yes	—
318	C₂²	C₄×Q₁₆×C₁₃₁	1	8	yes	—
319	C₂²	#467×C₁₃₁	1	8	yes	—
320	C₂²	#494×C₁₃₁	1	4	yes	—
321	C₂²	#495×C₁₃₁	1	4	yes	—
322	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
323	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
324	C₂²	C₂×#127×C₁₃₁	1	1	yes	characteristic
325	C₂²	C₂²×Q₁₆×C₁₃₁	1	2	yes	—
326	C₂²	C₂×#135×C₁₃₁	1	2	yes	—
327	C₄	—	2	8	no	—
328	C₄	—	4	8	no	—
329	C₄	—	8	4	no	—
330	C₄	#390×C₁₃₁	1	4	yes	—
331	C₄	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
332	C₄	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
333	C₄	C₂×#121×C₁₃₁	1	1	yes	characteristic
334	C₄	C₂×#124×C₁₃₁	1	1	yes	characteristic
335	C₂	#1969×C₁₃₁	1	8	yes	direct product factor
336	C₂	C₂×#390×C₁₃₁	1	1	yes	characteristic
337	C₂	C₂×C₄×Q₁₆×C₁₃₁	1	2	yes	—
338	C₂	C₂×#467×C₁₃₁	1	2	yes	—
339	C₂	C₂×#494×C₁₃₁	1	1	yes	characteristic
340	C₂	C₂×#495×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₁ ◁ C₂²×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. #1969×C₁₃₁	C₂	direct (N × H)
10. C₂²×Q₁₆×C₁₃₁	C₄	semidirect
40. C₂×Q₁₆×C₁₃₁	C₂×C₄	semidirect
84. C₂²×C₄×C₁₃₁	Q₁₆	semidirect
137. C₂×C₄×C₁₃₁	C₂×Q₁₆	semidirect
164. C₂×C₁₃₁	#1969	direct (N × H)
170. C₂×#1969	C₁₃₁	direct (N × H)
171. C₁₃₁	C₂×#1969	direct (N × H)
177. #1969	C₂×C₁₃₁	direct (N × H)
181. C₂²×Q₁₆	C₄×C₁₃₁	semidirect
211. C₂×Q₁₆	C₂×C₄×C₁₃₁	semidirect
255. C₂²×C₄	Q₁₆×C₁₃₁	semidirect
308. C₂×C₄	C₂×Q₁₆×C₁₃₁	semidirect
335. C₂	#1969×C₁₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₁₃₁	2
C₂²×#107×C₁₃₁	2
C₂²×#103×C₁₃₁	2
C₂²×C₄×C₈×C₁₃₁	2
C₂×#391×C₁₃₁	2
#1969×C₁₃₁	2
C₂×#1969	131

Subgroups — C2×#1969×C131 #45707106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1969×C₁₃₁ #45707106