Subgroups — C₁₅₁×#19206 #50324131

Order 38656.

678 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	#3246×C₁₅₁	C₂	1	2	yes	maximal, complemented
2	#3147×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	#2960×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#1686×C₁₅₁	C₂	1	4	yes	maximal, complemented
5	#1670×C₁₅₁	C₂	1	2	yes	maximal, complemented
6	#1668×C₁₅₁	C₂	1	2	yes	maximal, complemented
7	C₂×#335×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1547×C₁₅₁	C₂	1	2	yes	maximal, complemented
9	C₂×#135×C₁₅₁	—	2	1	no	—
10	C₂×#135×C₁₅₁	—	2	1	no	—
11	#533×C₁₅₁	C₂²	1	1	yes	characteristic
12	#532×C₁₅₁	C₂²	1	2	yes	—
13	#495×C₁₅₁	—	2	1	no	—
14	#495×C₁₅₁	—	2	1	no	—
15	#494×C₁₅₁	C₂²	1	1	yes	characteristic
16	#493×C₁₅₁	C₂²	1	1	yes	characteristic
17	#492×C₁₅₁	C₂²	1	2	yes	—
18	#476×C₁₅₁	—	2	2	no	—
19	#475×C₁₅₁	C₂²	1	4	yes	—
20	#465×C₁₅₁	—	2	4	no	—
21	#461×C₁₅₁	—	2	2	no	—
22	#460×C₁₅₁	C₂²	1	4	yes	—
23	#446×C₁₅₁	—	2	1	no	—
24	#446×C₁₅₁	C₂²	1	2	yes	—
25	C₈×Q₈×C₁₅₁	—	2	1	no	—
26	C₈×Q₈×C₁₅₁	C₂²	1	2	yes	—
27	#424×C₁₅₁	—	2	1	no	—
28	#423×C₁₅₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	2	yes	—
30	#405×C₁₅₁	—	2	1	no	—
31	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
32	#335×C₁₅₁	C₂²	1	2	yes	—
33	#335×C₁₅₁	C₂²	1	2	yes	—
34	#332×C₁₅₁	C₂²	1	4	yes	—
35	#331×C₁₅₁	C₂²	1	4	yes	—
36	C₂×#41×C₁₅₁	—	2	2	no	—
37	#135×C₁₅₁	—	4	4	no	—
38	#135×C₁₅₁	—	4	4	no	—
39	C₂×Q₁₆×C₁₅₁	—	2	1	no	—
40	C₂×Q₁₆×C₁₅₁	—	2	1	no	—
41	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
42	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
43	C₂×SD₁₆×C₁₅₁	—	2	4	no	—
44	C₂×D₈×C₁₅₁	—	2	1	no	—
45	C₂×D₈×C₁₅₁	—	2	1	no	—
46	C₂×M₁₆×C₁₅₁	—	2	1	no	—
47	C₂²×C₈×C₁₅₁	—	2	2	no	—
48	C₂²×C₈×C₁₅₁	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₅₁	D₄	1	1	yes	characteristic
50	C₄⋊Q₈×C₁₅₁	D₄	1	1	yes	characteristic
51	C₄⋊Q₈×C₁₅₁	D₄	1	1	yes	characteristic
52	C₄⋊Q₈×C₁₅₁	C₂³	1	2	yes	—
53	#127×C₁₅₁	C₂³	1	2	yes	—
54	#125×C₁₅₁	—	2	1	no	—
55	#124×C₁₅₁	—	2	2	no	—
56	C₂²⋊Q₈×C₁₅₁	—	2	1	no	—
57	C₂²⋊Q₈×C₁₅₁	D₄	1	2	yes	—
58	#121×C₁₅₁	—	2	2	no	—
59	#121×C₁₅₁	—	2	2	no	—
60	C₄×Q₈×C₁₅₁	—	2	1	no	—
61	C₄×Q₈×C₁₅₁	C₂³	1	2	yes	—
62	C₄×D₄×C₁₅₁	—	2	2	no	—
63	C₄×D₄×C₁₅₁	—	2	2	no	—
64	#117×C₁₅₁	—	2	1	no	—
65	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
66	#106×C₁₅₁	—	2	4	no	—
67	C₄⋊C₈×C₁₅₁	—	2	2	no	—
68	C₄⋊C₈×C₁₅₁	—	2	2	no	—
69	C₄⋊C₈×C₁₅₁	—	2	2	no	—
70	C₄⋊C₈×C₁₅₁	—	2	1	no	—
71	C₄⋊C₈×C₁₅₁	C₂³	1	4	yes	—
72	C₄⋊C₈×C₁₅₁	C₂³	1	2	yes	—
73	#103×C₁₅₁	—	2	4	no	—
74	#102×C₁₅₁	—	2	4	no	—
75	#97×C₁₅₁	—	2	2	no	—
76	C₄×C₈×C₁₅₁	—	2	2	no	—
77	C₄×C₈×C₁₅₁	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₅₁	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
81	#41×C₁₅₁	—	4	4	no	—
82	#41×C₁₅₁	—	4	4	no	—
83	C₂×Q₈×C₁₅₁	—	2	1	no	—
84	C₂×Q₈×C₁₅₁	—	2	2	no	—
85	C₂×Q₈×C₁₅₁	C₂×D₄	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	—	4	2	no	—
90	C₂²×C₄×C₁₅₁	—	4	2	no	—
91	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
94	Q₁₆×C₁₅₁	—	4	2	no	—
95	Q₁₆×C₁₅₁	—	4	2	no	—
96	SD₁₆×C₁₅₁	—	4	4	no	—
97	SD₁₆×C₁₅₁	—	4	4	no	—
98	SD₁₆×C₁₅₁	—	8	4	no	—
99	D₈×C₁₅₁	—	4	2	no	—
100	D₈×C₁₅₁	—	4	2	no	—
101	M₁₆×C₁₅₁	—	4	2	no	—
102	C₂×C₈×C₁₅₁	—	2	2	no	—
103	C₂×C₈×C₁₅₁	—	2	2	no	—
104	C₂×C₈×C₁₅₁	—	2	4	no	—
105	C₂×C₈×C₁₅₁	—	8	2	no	—
106	C₂×C₈×C₁₅₁	SD₁₆	1	4	yes	complemented
107	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
111	C₄⋊C₄×C₁₅₁	—	2	1	no	—
112	C₄⋊C₄×C₁₅₁	—	2	1	no	—
113	C₄⋊C₄×C₁₅₁	—	2	1	no	—
114	C₄⋊C₄×C₁₅₁	—	2	2	no	—
115	C₄⋊C₄×C₁₅₁	—	2	2	no	—
116	C₄⋊C₄×C₁₅₁	—	2	2	no	—
117	C₄⋊C₄×C₁₅₁	—	2	2	no	—
118	C₄⋊C₄×C₁₅₁	C₂×D₄	1	2	yes	—
119	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
120	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
121	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
122	C₄²×C₁₅₁	—	2	2	no	—
123	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₅₁	#41	1	1	yes	characteristic
126	C₄²×C₁₅₁	C₂⁴	1	1	yes	characteristic
127	C₂³×C₁₅₁	—	4	2	no	—
128	C₂³×C₁₅₁	#121	1	1	yes	characteristic
129	Q₈×C₁₅₁	—	2	2	no	—
130	Q₈×C₁₅₁	—	2	2	no	—
131	Q₈×C₁₅₁	—	4	2	no	—
132	Q₈×C₁₅₁	—	4	2	no	—
133	Q₈×C₁₅₁	—	4	2	no	—
134	D₄×C₁₅₁	—	4	2	no	—
135	D₄×C₁₅₁	—	4	2	no	—
136	D₄×C₁₅₁	—	4	2	no	—
137	D₄×C₁₅₁	—	4	2	no	—
138	D₄×C₁₅₁	—	8	2	no	—
139	D₄×C₁₅₁	—	8	4	no	—
140	C₂×C₄×C₁₅₁	—	2	1	no	—
141	C₂×C₄×C₁₅₁	—	2	1	no	—
142	C₂×C₄×C₁₅₁	—	2	2	no	—
143	C₂×C₄×C₁₅₁	—	2	2	no	—
144	C₂×C₄×C₁₅₁	—	4	1	no	—
145	C₂×C₄×C₁₅₁	—	4	2	no	—
146	C₂×C₄×C₁₅₁	—	8	4	no	—
147	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₅₁	C₂×SD₁₆	1	2	yes	—
151	C₂×C₄×C₁₅₁	AGL(1,ℤ/8)	1	2	yes	—
152	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
155	C₈×C₁₅₁	—	2	1	no	—
156	C₈×C₁₅₁	—	2	1	no	—
157	C₈×C₁₅₁	—	4	2	no	—
158	C₈×C₁₅₁	—	4	4	no	—
159	C₈×C₁₅₁	C₂×SD₁₆	1	2	yes	—
160	C₈×C₁₅₁	C₂×SD₁₆	1	2	yes	—
161	C₂²×C₁₅₁	—	2	1	no	—
162	C₂²×C₁₅₁	—	2	1	no	—
163	C₂²×C₁₅₁	—	8	2	no	—
164	C₂²×C₁₅₁	—	8	2	no	—
165	C₂²×C₁₅₁	—	8	2	no	—
166	C₂²×C₁₅₁	#460	1	2	yes	—
167	C₂²×C₁₅₁	C₂×#121	1	1	yes	characteristic
168	C₄×C₁₅₁	—	2	1	no	—
169	C₄×C₁₅₁	—	2	1	no	—
170	C₄×C₁₅₁	—	2	1	no	—
171	C₄×C₁₅₁	—	4	2	no	—
172	C₄×C₁₅₁	—	4	2	no	—
173	C₄×C₁₅₁	—	8	2	no	—
174	C₄×C₁₅₁	#460	1	2	yes	—
175	C₄×C₁₅₁	C₂²×SD₁₆	1	1	yes	characteristic
176	C₄×C₁₅₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₄×C₁₅₁	#576	1	1	yes	characteristic
178	C₄×C₁₅₁	#578	1	1	yes	characteristic
179	C₂×C₁₅₁	—	2	2	no	—
180	C₂×C₁₅₁	—	16	2	no	—
181	C₂×C₁₅₁	C₂×#460	1	1	yes	characteristic
182	C₂×C₁₅₁	#3061	1	1	yes	characteristic
183	C₂×C₁₅₁	#3067	1	1	yes	characteristic
184	#19206	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₁₅₁	#19206	1	1	yes	characteristic, direct product factor, Sylow
186	#3246	C₂×C₁₅₁	1	2	yes	complemented
187	#3147	C₂×C₁₅₁	1	1	yes	characteristic
188	#2960	C₂×C₁₅₁	1	1	yes	characteristic, complemented
189	#1686	C₂×C₁₅₁	1	4	yes	complemented
190	#1670	C₂×C₁₅₁	1	2	yes	complemented
191	#1668	C₂×C₁₅₁	1	2	yes	complemented
192	C₂×#335	C₂×C₁₅₁	1	1	yes	characteristic, complemented
193	#1547	C₂×C₁₅₁	1	2	yes	complemented
194	C₂×#135	—	2	1	no	—
195	C₂×#135	—	2	1	no	—
196	#533	C₂²×C₁₅₁	1	1	yes	characteristic
197	#532	C₂²×C₁₅₁	1	2	yes	—
198	#495	—	2	1	no	—
199	#495	—	2	1	no	—
200	#494	C₂²×C₁₅₁	1	1	yes	characteristic
201	#493	C₂²×C₁₅₁	1	1	yes	characteristic
202	#492	C₂²×C₁₅₁	1	2	yes	—
203	#476	—	2	2	no	—
204	#475	C₂²×C₁₅₁	1	4	yes	—
205	#465	—	2	4	no	—
206	#461	—	2	2	no	—
207	#460	C₂²×C₁₅₁	1	4	yes	—
208	#446	—	2	1	no	—
209	#446	C₂²×C₁₅₁	1	2	yes	—
210	C₈×Q₈	—	2	1	no	—
211	C₈×Q₈	C₂²×C₁₅₁	1	2	yes	—
212	#424	—	2	1	no	—
213	#423	C₂²×C₁₅₁	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	2	yes	—
215	#405	—	2	1	no	—
216	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
217	#335	C₂²×C₁₅₁	1	2	yes	—
218	#335	C₂²×C₁₅₁	1	2	yes	—
219	#332	C₂²×C₁₅₁	1	4	yes	—
220	#331	C₂²×C₁₅₁	1	4	yes	—
221	C₂×#41	—	2	2	no	—
222	#135	—	4	4	no	—
223	#135	—	4	4	no	—
224	C₂×Q₁₆	—	2	1	no	—
225	C₂×Q₁₆	—	2	1	no	—
226	C₂×SD₁₆	—	2	4	no	—
227	C₂×SD₁₆	—	2	2	no	—
228	C₂×SD₁₆	—	2	2	no	—
229	C₂×D₈	—	2	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×M₁₆	—	2	1	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	D₄×C₁₅₁	1	1	yes	characteristic
234	C₂²×C₈	D₄×C₁₅₁	1	1	yes	characteristic
235	C₄⋊Q₈	D₄×C₁₅₁	1	1	yes	characteristic
236	C₄⋊Q₈	D₄×C₁₅₁	1	1	yes	characteristic
237	C₄⋊Q₈	C₂³×C₁₅₁	1	2	yes	—
238	#127	C₂³×C₁₅₁	1	2	yes	—
239	#125	—	2	1	no	—
240	#124	—	2	2	no	—
241	C₂²⋊Q₈	—	2	1	no	—
242	C₂²⋊Q₈	D₄×C₁₅₁	1	2	yes	—
243	#121	—	2	2	no	—
244	#121	—	2	2	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	C₂³×C₁₅₁	1	2	yes	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	2	no	—
249	#117	—	2	1	no	—
250	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
251	#106	—	2	4	no	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	2	2	no	—
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	C₂³×C₁₅₁	1	2	yes	—
257	C₄⋊C₈	C₂³×C₁₅₁	1	4	yes	—
258	#103	—	2	4	no	—
259	#102	—	2	4	no	—
260	#97	—	2	2	no	—
261	C₄×C₈	—	2	2	no	—
262	C₄×C₈	D₄×C₁₅₁	1	1	yes	characteristic
263	C₄×C₈	D₄×C₁₅₁	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
265	C₄×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
266	#41	—	4	4	no	—
267	#41	—	4	4	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	C₂×D₄×C₁₅₁	1	2	yes	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
278	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
279	Q₁₆	—	4	2	no	—
280	Q₁₆	—	4	2	no	—
281	SD₁₆	—	4	4	no	—
282	SD₁₆	—	4	4	no	—
283	SD₁₆	—	8	4	no	—
284	D₈	—	4	2	no	—
285	D₈	—	4	2	no	—
286	M₁₆	—	4	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	8	2	no	—
291	C₂×C₈	SD₁₆×C₁₅₁	1	4	yes	complemented
292	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
295	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	C₂×D₄×C₁₅₁	1	2	yes	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
310	C₄²	#41×C₁₅₁	1	1	yes	characteristic
311	C₄²	C₂⁴×C₁₅₁	1	1	yes	characteristic
312	C₂³	—	4	2	no	—
313	C₂³	#121×C₁₅₁	1	1	yes	characteristic
314	Q₈	—	2	2	no	—
315	Q₈	—	2	2	no	—
316	Q₈	—	4	2	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	4	2	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	2	no	—
323	D₄	—	8	2	no	—
324	D₄	—	8	4	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	8	4	no	—
332	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
333	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
334	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
335	C₂×C₄	C₂×SD₁₆×C₁₅₁	1	2	yes	—
336	C₂×C₄	AGL(1,ℤ/8)×C₁₅₁	1	2	yes	—
337	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
340	C₈	—	2	1	no	—
341	C₈	—	2	1	no	—
342	C₈	—	4	2	no	—
343	C₈	—	4	4	no	—
344	C₈	C₂×SD₁₆×C₁₅₁	1	2	yes	—
345	C₈	C₂×SD₁₆×C₁₅₁	1	2	yes	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	#460×C₁₅₁	1	2	yes	—
352	C₂²	C₂×#121×C₁₅₁	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	2	no	—
358	C₄	—	8	2	no	—
359	C₄	#460×C₁₅₁	1	2	yes	—
360	C₄	C₂²×SD₁₆×C₁₅₁	1	1	yes	characteristic
361	C₄	C₂×AGL(1,ℤ/8)×C₁₅₁	1	1	yes	characteristic
362	C₄	#576×C₁₅₁	1	1	yes	characteristic
363	C₄	#578×C₁₅₁	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	16	2	no	—
366	C₂	C₂×#460×C₁₅₁	1	1	yes	characteristic
367	C₂	#3061×C₁₅₁	1	1	yes	characteristic
368	C₂	#3067×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₅₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₅₁
prime radical	#3147×C₁₅₁	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₅₁ ◁ C₂×C₄²×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3246×C₁₅₁	C₂	semidirect
3. #2960×C₁₅₁	C₂	semidirect
4. #1686×C₁₅₁	C₂	semidirect
5. #1670×C₁₅₁	C₂	semidirect
6. #1668×C₁₅₁	C₂	semidirect
7. C₂×#335×C₁₅₁	C₂	semidirect
8. #1547×C₁₅₁	C₂	semidirect
106. C₂×C₈×C₁₅₁	SD₁₆	semidirect
184. #19206	C₁₅₁	direct (N × H)
185. C₁₅₁	#19206	direct (N × H)
186. #3246	C₂×C₁₅₁	semidirect
188. #2960	C₂×C₁₅₁	semidirect
189. #1686	C₂×C₁₅₁	semidirect
190. #1670	C₂×C₁₅₁	semidirect
191. #1668	C₂×C₁₅₁	semidirect
192. C₂×#335	C₂×C₁₅₁	semidirect
193. #1547	C₂×C₁₅₁	semidirect
291. C₂×C₈	SD₁₆×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#3246×C₁₅₁	2
#3147×C₁₅₁	2
#2960×C₁₅₁	2
#1686×C₁₅₁	2
#1670×C₁₅₁	2
#1668×C₁₅₁	2
C₂×#335×C₁₅₁	2
#1547×C₁₅₁	2
#19206	151

Subgroups — C151×#19206 #50324131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#19206 #50324131