Subgroups — C₁₅₁×#23362 #50328287

Order 38656.

706 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3153×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	#1905×C₁₅₁	C₂	1	2	yes	maximal, complemented
3	#1904×C₁₅₁	C₂	1	2	yes	maximal, complemented
4	#1903×C₁₅₁	C₂	1	2	yes	maximal, complemented
5	#1902×C₁₅₁	C₂	1	2	yes	maximal, complemented
6	#1888×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1885×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1884×C₁₅₁	C₂	1	2	yes	maximal, complemented
9	#1841×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	C₂×#137×C₁₅₁	C₂²	1	2	yes	—
11	C₂×AGL(1,ℤ/8)×C₁₅₁	C₂²	1	2	yes	—
12	#568×C₁₅₁	C₂²	1	2	yes	—
13	#532×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₂×#124×C₁₅₁	C₂²	1	1	yes	characteristic
15	#519×C₁₅₁	C₂²	1	1	yes	characteristic
16	#518×C₁₅₁	C₂²	1	1	yes	characteristic
17	#497×C₁₅₁	C₄	1	2	yes	complemented
18	#496×C₁₅₁	C₄	1	2	yes	complemented
19	#495×C₁₅₁	C₄	1	4	yes	complemented
20	#421×C₁₅₁	C₂²	1	2	yes	—
21	#421×C₁₅₁	C₂²	1	2	yes	—
22	#419×C₁₅₁	C₂²	1	2	yes	—
23	#418×C₁₅₁	C₂²	1	2	yes	—
24	C₂×#101×C₁₅₁	C₂²	1	1	yes	characteristic
25	C₂×#100×C₁₅₁	C₂²	1	1	yes	characteristic
26	#410×C₁₅₁	C₂²	1	2	yes	—
27	C₄×M₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
28	#344×C₁₅₁	C₂²	1	2	yes	—
29	#344×C₁₅₁	C₂²	1	2	yes	—
30	#339×C₁₅₁	C₂²	1	2	yes	—
31	#339×C₁₅₁	C₂²	1	2	yes	—
32	#338×C₁₅₁	C₂²	1	2	yes	—
33	H(3,ℤ/4)×C₁₅₁	C₂²	1	2	yes	—
34	C₂×#41×C₁₅₁	C₂³	1	2	yes	—
35	C₂²×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
37	#137×C₁₅₁	—	4	2	no	—
38	#137×C₁₅₁	—	4	2	no	—
39	AGL(1,ℤ/8)×C₁₅₁	—	4	2	no	—
40	AGL(1,ℤ/8)×C₁₅₁	—	4	2	no	—
41	C₂×Q₁₆×C₁₅₁	C₂×C₄	1	4	yes	complemented
42	C₂×SD₁₆×C₁₅₁	C₂×C₄	1	4	yes	—
43	C₂×SD₁₆×C₁₅₁	C₂×C₄	1	4	yes	complemented
44	C₂×D₈×C₁₅₁	C₂×C₄	1	4	yes	—
45	#131×C₁₅₁	—	4	2	no	—
46	#131×C₁₅₁	—	4	2	no	—
47	C₂×M₁₆×C₁₅₁	—	4	2	no	—
48	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
50	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic, complemented
52	#127×C₁₅₁	C₂×C₄	1	1	yes	characteristic, complemented
53	#124×C₁₅₁	—	4	1	no	—
54	#124×C₁₅₁	C₂×C₄	1	2	yes	—
55	#124×C₁₅₁	C₂×C₄	1	2	yes	—
56	#124×C₁₅₁	C₂×C₄	1	2	yes	complemented
57	#121×C₁₅₁	—	4	1	no	—
58	C₄×Q₈×C₁₅₁	—	4	2	no	—
59	C₄×D₄×C₁₅₁	—	4	2	no	—
60	C₄×D₄×C₁₅₁	—	4	1	no	—
61	#117×C₁₅₁	—	4	1	no	—
62	#117×C₁₅₁	C₂³	1	2	yes	—
63	#117×C₁₅₁	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₅₁	—	4	1	no	—
65	C₂×C₂²⋊C₄×C₁₅₁	—	4	1	no	—
66	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
67	#104×C₁₅₁	—	4	2	no	—
68	#104×C₁₅₁	—	4	2	no	—
69	#103×C₁₅₁	—	4	2	no	—
70	#102×C₁₅₁	—	4	2	no	—
71	#101×C₁₅₁	—	4	1	no	—
72	#100×C₁₅₁	—	4	1	no	—
73	#99×C₁₅₁	—	4	2	no	—
74	#97×C₁₅₁	C₂×C₄	1	2	yes	complemented
75	C₄×C₈×C₁₅₁	C₂×C₄	1	2	yes	complemented
76	C₂⁴×C₁₅₁	—	2	1	no	—
77	#41×C₁₅₁	—	2	2	no	—
78	#41×C₁₅₁	—	2	2	no	—
79	#41×C₁₅₁	—	2	2	no	—
80	#41×C₁₅₁	—	2	2	no	—
81	C₂×Q₈×C₁₅₁	—	2	1	no	—
82	C₂×Q₈×C₁₅₁	—	2	2	no	—
83	C₂×Q₈×C₁₅₁	—	2	2	no	—
84	C₂×Q₈×C₁₅₁	C₂²×C₄	1	2	yes	—
85	C₂×Q₈×C₁₅₁	C₂²×C₄	1	2	yes	—
86	C₂×D₄×C₁₅₁	—	2	2	no	—
87	C₂×D₄×C₁₅₁	—	2	2	no	—
88	C₂×D₄×C₁₅₁	—	2	2	no	—
89	C₂×D₄×C₁₅₁	—	2	1	no	—
90	C₂×D₄×C₁₅₁	—	4	1	no	—
91	C₂×D₄×C₁₅₁	C₂²×C₄	1	2	yes	—
92	C₂×D₄×C₁₅₁	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₅₁	—	2	1	no	—
94	C₂²×C₄×C₁₅₁	—	2	1	no	—
95	C₂²×C₄×C₁₅₁	—	2	2	no	—
96	C₂²×C₄×C₁₅₁	—	4	2	no	—
97	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
98	Q₁₆×C₁₅₁	—	4	4	no	—
99	SD₁₆×C₁₅₁	—	4	4	no	—
100	SD₁₆×C₁₅₁	—	4	4	no	—
101	D₈×C₁₅₁	—	4	4	no	—
102	M₁₆×C₁₅₁	—	2	2	no	—
103	M₁₆×C₁₅₁	—	2	2	no	—
104	M₁₆×C₁₅₁	—	2	2	no	—
105	M₁₆×C₁₅₁	—	2	2	no	—
106	M₁₆×C₁₅₁	—	2	2	no	—
107	M₁₆×C₁₅₁	—	2	2	no	—
108	M₁₆×C₁₅₁	—	4	4	no	—
109	C₂×C₈×C₁₅₁	—	2	2	no	—
110	C₂×C₈×C₁₅₁	—	2	2	no	—
111	C₂×C₈×C₁₅₁	—	4	4	no	—
112	C₂×C₈×C₁₅₁	C₂²×C₄	1	4	yes	—
113	C₄⋊C₄×C₁₅₁	—	2	2	no	—
114	C₄⋊C₄×C₁₅₁	—	2	2	no	—
115	C₄⋊C₄×C₁₅₁	—	4	1	no	—
116	C₄⋊C₄×C₁₅₁	—	4	2	no	—
117	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
118	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
119	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
120	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
121	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
122	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
123	C₄²×C₁₅₁	—	2	1	no	—
124	C₄²×C₁₅₁	—	2	2	no	—
125	C₄²×C₁₅₁	—	2	2	no	—
126	C₄²×C₁₅₁	—	4	2	no	—
127	C₄²×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
129	C₂³×C₁₅₁	—	2	2	no	—
130	C₂³×C₁₅₁	—	2	2	no	—
131	C₂³×C₁₅₁	—	4	1	no	—
132	C₂³×C₁₅₁	—	4	1	no	—
133	C₂³×C₁₅₁	—	8	2	no	—
134	C₂³×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
135	Q₈×C₁₅₁	—	2	4	no	—
136	Q₈×C₁₅₁	—	2	2	no	—
137	Q₈×C₁₅₁	—	2	2	no	—
138	Q₈×C₁₅₁	—	4	2	no	—
139	D₄×C₁₅₁	—	2	2	no	—
140	D₄×C₁₅₁	—	2	2	no	—
141	D₄×C₁₅₁	—	2	4	no	—
142	D₄×C₁₅₁	—	4	2	no	—
143	D₄×C₁₅₁	—	4	2	no	—
144	D₄×C₁₅₁	—	4	2	no	—
145	D₄×C₁₅₁	—	8	2	no	—
146	C₂×C₄×C₁₅₁	—	2	2	no	—
147	C₂×C₄×C₁₅₁	—	2	2	no	—
148	C₂×C₄×C₁₅₁	—	2	1	no	—
149	C₂×C₄×C₁₅₁	—	2	1	no	—
150	C₂×C₄×C₁₅₁	—	4	1	no	—
151	C₂×C₄×C₁₅₁	—	4	1	no	—
152	C₂×C₄×C₁₅₁	—	4	2	no	—
153	C₂×C₄×C₁₅₁	—	4	2	no	—
154	C₂×C₄×C₁₅₁	—	4	2	no	—
155	C₂×C₄×C₁₅₁	—	4	2	no	—
156	C₂×C₄×C₁₅₁	—	8	1	no	—
157	C₂×C₄×C₁₅₁	—	16	2	no	—
158	C₂×C₄×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	2	yes	—
160	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	2	yes	—
161	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
162	C₈×C₁₅₁	—	2	4	no	—
163	C₈×C₁₅₁	—	4	2	no	—
164	C₈×C₁₅₁	—	4	2	no	—
165	C₂²×C₁₅₁	—	4	1	no	—
166	C₂²×C₁₅₁	—	4	2	no	—
167	C₂²×C₁₅₁	—	4	2	no	—
168	C₂²×C₁₅₁	—	8	2	no	—
169	C₂²×C₁₅₁	—	8	2	no	—
170	C₂²×C₁₅₁	—	8	2	no	—
171	C₂²×C₁₅₁	—	16	1	no	—
172	C₂²×C₁₅₁	#518	1	1	yes	characteristic
173	C₂²×C₁₅₁	#560	1	1	yes	characteristic
174	C₂²×C₁₅₁	#560	1	1	yes	characteristic
175	C₄×C₁₅₁	—	4	1	no	—
176	C₄×C₁₅₁	—	4	1	no	—
177	C₄×C₁₅₁	—	4	2	no	—
178	C₄×C₁₅₁	—	4	2	no	—
179	C₄×C₁₅₁	—	8	2	no	—
180	C₄×C₁₅₁	—	8	2	no	—
181	C₄×C₁₅₁	#518	1	2	yes	—
182	C₄×C₁₅₁	#560	1	2	yes	—
183	C₂×C₁₅₁	—	2	1	no	—
184	C₂×C₁₅₁	—	2	1	no	—
185	C₂×C₁₅₁	—	2	1	no	—
186	C₂×C₁₅₁	—	8	2	no	—
187	C₂×C₁₅₁	—	8	2	no	—
188	C₂×C₁₅₁	#2380	1	1	yes	characteristic
189	#23362	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₁₅₁	#23362	1	1	yes	characteristic, direct product factor, Sylow
191	#3153	C₂×C₁₅₁	1	1	yes	characteristic
192	#1905	C₂×C₁₅₁	1	2	yes	complemented
193	#1904	C₂×C₁₅₁	1	2	yes	complemented
194	#1903	C₂×C₁₅₁	1	2	yes	complemented
195	#1902	C₂×C₁₅₁	1	2	yes	complemented
196	#1888	C₂×C₁₅₁	1	1	yes	characteristic, complemented
197	#1885	C₂×C₁₅₁	1	1	yes	characteristic, complemented
198	#1884	C₂×C₁₅₁	1	2	yes	complemented
199	#1841	C₂×C₁₅₁	1	2	yes	complemented
200	C₂×#137	C₂²×C₁₅₁	1	2	yes	—
201	C₂×AGL(1,ℤ/8)	C₂²×C₁₅₁	1	2	yes	—
202	#568	C₂²×C₁₅₁	1	2	yes	—
203	#532	C₂²×C₁₅₁	1	1	yes	characteristic
204	C₂×#124	C₂²×C₁₅₁	1	1	yes	characteristic
205	#519	C₂²×C₁₅₁	1	1	yes	characteristic
206	#518	C₂²×C₁₅₁	1	1	yes	characteristic
207	#497	C₄×C₁₅₁	1	2	yes	complemented
208	#496	C₄×C₁₅₁	1	2	yes	complemented
209	#495	C₄×C₁₅₁	1	4	yes	complemented
210	#421	C₂²×C₁₅₁	1	2	yes	—
211	#421	C₂²×C₁₅₁	1	2	yes	—
212	#419	C₂²×C₁₅₁	1	2	yes	—
213	#418	C₂²×C₁₅₁	1	2	yes	—
214	C₂×#101	C₂²×C₁₅₁	1	1	yes	characteristic
215	C₂×#100	C₂²×C₁₅₁	1	1	yes	characteristic
216	#410	C₂²×C₁₅₁	1	2	yes	—
217	C₄×M₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
218	#344	C₂²×C₁₅₁	1	2	yes	—
219	#344	C₂²×C₁₅₁	1	2	yes	—
220	#339	C₂²×C₁₅₁	1	2	yes	—
221	#339	C₂²×C₁₅₁	1	2	yes	—
222	#338	C₂²×C₁₅₁	1	2	yes	—
223	H(3,ℤ/4)	C₂²×C₁₅₁	1	2	yes	—
224	C₂×#41	C₂³×C₁₅₁	1	2	yes	—
225	C₂²×Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
226	C₂²×D₄	C₂³×C₁₅₁	1	1	yes	characteristic
227	#137	—	4	2	no	—
228	#137	—	4	2	no	—
229	AGL(1,ℤ/8)	—	4	2	no	—
230	AGL(1,ℤ/8)	—	4	2	no	—
231	C₂×Q₁₆	C₂×C₄×C₁₅₁	1	4	yes	complemented
232	C₂×SD₁₆	C₂×C₄×C₁₅₁	1	4	yes	—
233	C₂×SD₁₆	C₂×C₄×C₁₅₁	1	4	yes	complemented
234	C₂×D₈	C₂×C₄×C₁₅₁	1	4	yes	—
235	#131	—	4	2	no	—
236	#131	—	4	2	no	—
237	C₂×M₁₆	—	4	2	no	—
238	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
239	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
240	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
241	C₄⋊Q₈	C₂×C₄×C₁₅₁	1	1	yes	characteristic, complemented
242	#127	C₂×C₄×C₁₅₁	1	1	yes	characteristic, complemented
243	#124	—	4	1	no	—
244	#124	C₂×C₄×C₁₅₁	1	2	yes	—
245	#124	C₂×C₄×C₁₅₁	1	2	yes	—
246	#124	C₂×C₄×C₁₅₁	1	2	yes	complemented
247	#121	—	4	1	no	—
248	C₄×Q₈	—	4	2	no	—
249	C₄×D₄	—	4	2	no	—
250	C₄×D₄	—	4	1	no	—
251	#117	—	4	1	no	—
252	#117	C₂³×C₁₅₁	1	2	yes	—
253	#117	C₂³×C₁₅₁	1	2	yes	—
254	C₂×C₂²⋊C₄	—	4	1	no	—
255	C₂×C₂²⋊C₄	—	4	1	no	—
256	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
257	#104	—	4	2	no	—
258	#104	—	4	2	no	—
259	#103	—	4	2	no	—
260	#102	—	4	2	no	—
261	#101	—	4	1	no	—
262	#100	—	4	1	no	—
263	#99	—	4	2	no	—
264	#97	C₂×C₄×C₁₅₁	1	2	yes	complemented
265	C₄×C₈	C₂×C₄×C₁₅₁	1	2	yes	complemented
266	C₂⁴	—	2	1	no	—
267	#41	—	2	2	no	—
268	#41	—	2	2	no	—
269	#41	—	2	2	no	—
270	#41	—	2	2	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	C₂²×C₄×C₁₅₁	1	2	yes	—
275	C₂×Q₈	C₂²×C₄×C₁₅₁	1	2	yes	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	C₂²×C₄×C₁₅₁	1	2	yes	—
282	C₂×D₄	C₂²×C₄×C₁₅₁	1	2	yes	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
288	Q₁₆	—	4	4	no	—
289	SD₁₆	—	4	4	no	—
290	SD₁₆	—	4	4	no	—
291	D₈	—	4	4	no	—
292	M₁₆	—	2	2	no	—
293	M₁₆	—	2	2	no	—
294	M₁₆	—	2	2	no	—
295	M₁₆	—	2	2	no	—
296	M₁₆	—	2	2	no	—
297	M₁₆	—	2	2	no	—
298	M₁₆	—	4	4	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	4	no	—
302	C₂×C₈	C₂²×C₄×C₁₅₁	1	4	yes	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	4	2	no	—
317	C₄²	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
318	C₄²	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	4	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	8	2	no	—
324	C₂³	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
325	Q₈	—	2	2	no	—
326	Q₈	—	2	4	no	—
327	Q₈	—	2	2	no	—
328	Q₈	—	4	2	no	—
329	D₄	—	2	2	no	—
330	D₄	—	2	4	no	—
331	D₄	—	2	2	no	—
332	D₄	—	4	2	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	2	no	—
335	D₄	—	8	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	8	1	no	—
347	C₂×C₄	—	16	2	no	—
348	C₂×C₄	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
349	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	2	yes	—
350	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	2	yes	—
351	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
352	C₈	—	2	4	no	—
353	C₈	—	4	2	no	—
354	C₈	—	4	2	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	16	1	no	—
362	C₂²	#518×C₁₅₁	1	1	yes	characteristic
363	C₂²	#560×C₁₅₁	1	1	yes	characteristic
364	C₂²	#560×C₁₅₁	1	1	yes	characteristic
365	C₄	—	4	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	8	2	no	—
370	C₄	—	8	2	no	—
371	C₄	#518×C₁₅₁	1	2	yes	—
372	C₄	#560×C₁₅₁	1	2	yes	—
373	C₂	—	2	1	no	—
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	—	8	2	no	—
377	C₂	—	8	2	no	—
378	C₂	#2380×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₅₁	#2380
commutator	C₂×C₄	C₂³×C₄×C₁₅₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
prime radical	#3153×C₁₅₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₅₁ ◁ C₂²×C₄×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #1905×C₁₅₁	C₂	semidirect
3. #1904×C₁₅₁	C₂	semidirect
4. #1903×C₁₅₁	C₂	semidirect
5. #1902×C₁₅₁	C₂	semidirect
6. #1888×C₁₅₁	C₂	semidirect
7. #1885×C₁₅₁	C₂	semidirect
8. #1884×C₁₅₁	C₂	semidirect
9. #1841×C₁₅₁	C₂	semidirect
17. #497×C₁₅₁	C₄	semidirect
18. #496×C₁₅₁	C₄	semidirect
19. #495×C₁₅₁	C₄	semidirect
41. C₂×Q₁₆×C₁₅₁	C₂×C₄	semidirect
43. C₂×SD₁₆×C₁₅₁	C₂×C₄	semidirect
51. C₄⋊Q₈×C₁₅₁	C₂×C₄	semidirect
52. #127×C₁₅₁	C₂×C₄	semidirect
56. #124×C₁₅₁	C₂×C₄	semidirect
74. #97×C₁₅₁	C₂×C₄	semidirect
75. C₄×C₈×C₁₅₁	C₂×C₄	semidirect
189. #23362	C₁₅₁	direct (N × H)
190. C₁₅₁	#23362	direct (N × H)
192. #1905	C₂×C₁₅₁	semidirect
193. #1904	C₂×C₁₅₁	semidirect
194. #1903	C₂×C₁₅₁	semidirect
195. #1902	C₂×C₁₅₁	semidirect
196. #1888	C₂×C₁₅₁	semidirect
197. #1885	C₂×C₁₅₁	semidirect
198. #1884	C₂×C₁₅₁	semidirect
199. #1841	C₂×C₁₅₁	semidirect
207. #497	C₄×C₁₅₁	semidirect
208. #496	C₄×C₁₅₁	semidirect
209. #495	C₄×C₁₅₁	semidirect
231. C₂×Q₁₆	C₂×C₄×C₁₅₁	semidirect
233. C₂×SD₁₆	C₂×C₄×C₁₅₁	semidirect
241. C₄⋊Q₈	C₂×C₄×C₁₅₁	semidirect
242. #127	C₂×C₄×C₁₅₁	semidirect
246. #124	C₂×C₄×C₁₅₁	semidirect
264. #97	C₂×C₄×C₁₅₁	semidirect
265. C₄×C₈	C₂×C₄×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#3153×C₁₅₁	2
#1905×C₁₅₁	2
#1904×C₁₅₁	2
#1903×C₁₅₁	2
#1902×C₁₅₁	2
#1888×C₁₅₁	2
#1885×C₁₅₁	2
#1884×C₁₅₁	2
#1841×C₁₅₁	2
#23362	151

Subgroups — C151×#23362 #50328287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#23362 #50328287