Subgroups — C₁₅₁×#19396 #50324321

Order 38656.

686 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3208×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	#3078×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#460×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#2982×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1678×C₁₅₁	C₂	1	4	yes	maximal, complemented
6	#1666×C₁₅₁	C₂	1	4	yes	maximal, complemented
7	#1570×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1545×C₁₅₁	C₂	1	1	yes	maximal, characteristic
9	#1542×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₁₅₁	—	2	1	no	—
11	#533×C₁₅₁	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₅₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
14	#492×C₁₅₁	C₂²	1	2	yes	—
15	#486×C₁₅₁	C₂²	1	2	yes	—
16	#479×C₁₅₁	—	2	2	no	—
17	#477×C₁₅₁	C₂²	1	2	yes	complemented
18	#475×C₁₅₁	C₂²	1	2	yes	complemented
19	#460×C₁₅₁	—	2	2	no	—
20	#460×C₁₅₁	—	2	2	no	—
21	#460×C₁₅₁	C₂²	1	4	yes	—
22	#450×C₁₅₁	—	2	2	no	—
23	C₈×Q₈×C₁₅₁	—	2	2	no	—
24	C₈×Q₈×C₁₅₁	C₂²	1	4	yes	complemented
25	#431×C₁₅₁	—	2	2	no	—
26	#431×C₁₅₁	C₂²	1	1	yes	characteristic
27	#431×C₁₅₁	C₂²	1	1	yes	characteristic
28	#428×C₁₅₁	—	2	1	no	—
29	#423×C₁₅₁	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic
31	#419×C₁₅₁	—	2	1	no	—
32	C₂×#102×C₁₅₁	—	2	1	no	—
33	#334×C₁₅₁	C₂²	1	4	yes	complemented
34	#333×C₁₅₁	C₂²	1	2	yes	complemented
35	#332×C₁₅₁	C₂²	1	2	yes	complemented
36	#331×C₁₅₁	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₅₁	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₅₁	—	2	1	no	—
39	C₂²×D₄×C₁₅₁	—	2	1	no	—
40	C₂²×D₄×C₁₅₁	—	2	1	no	—
41	C₂×SD₁₆×C₁₅₁	—	2	4	no	—
42	C₂×SD₁₆×C₁₅₁	—	2	4	no	—
43	C₂×SD₁₆×C₁₅₁	—	4	4	no	—
44	C₂×M₁₆×C₁₅₁	—	2	1	no	—
45	C₂²×C₈×C₁₅₁	—	2	1	no	—
46	C₄⋊Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
47	C₄⋊Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
48	#127×C₁₅₁	—	2	1	no	—
49	#127×C₁₅₁	—	2	1	no	—
50	#127×C₁₅₁	—	2	1	no	—
51	#127×C₁₅₁	C₂³	1	2	yes	—
52	#125×C₁₅₁	—	2	1	no	—
53	C₂²⋊Q₈×C₁₅₁	—	2	1	no	—
54	C₂²⋊Q₈×C₁₅₁	—	2	1	no	—
55	C₄×Q₈×C₁₅₁	—	2	1	no	—
56	C₄×Q₈×C₁₅₁	—	2	1	no	—
57	C₄×Q₈×C₁₅₁	—	2	1	no	—
58	C₄×Q₈×C₁₅₁	—	2	1	no	—
59	C₄×Q₈×C₁₅₁	D₄	1	2	yes	—
60	C₄×Q₈×C₁₅₁	C₂³	1	2	yes	—
61	#117×C₁₅₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₅₁	—	2	1	no	—
65	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
66	#107×C₁₅₁	—	2	2	no	—
67	#106×C₁₅₁	—	2	2	no	—
68	C₄⋊C₈×C₁₅₁	—	2	4	no	—
69	C₄⋊C₈×C₁₅₁	—	2	1	no	—
70	C₄⋊C₈×C₁₅₁	—	2	1	no	—
71	C₄⋊C₈×C₁₅₁	D₄	1	2	yes	—
72	C₄⋊C₈×C₁₅₁	C₂³	1	2	yes	—
73	C₄⋊C₈×C₁₅₁	C₂³	1	2	yes	—
74	C₄⋊C₈×C₁₅₁	C₂³	1	2	yes	—
75	#103×C₁₅₁	—	2	2	no	—
76	#103×C₁₅₁	—	2	2	no	—
77	#102×C₁₅₁	—	2	4	no	—
78	#102×C₁₅₁	—	2	4	no	—
79	C₂²⋊C₈×C₁₅₁	—	2	1	no	—
80	C₂²⋊C₈×C₁₅₁	D₄	1	2	yes	—
81	C₄×C₈×C₁₅₁	—	2	4	no	—
82	C₄×C₈×C₁₅₁	—	2	1	no	—
83	C₄×C₈×C₁₅₁	C₂³	1	2	yes	—
84	C₂⁴×C₁₅₁	—	4	1	no	—
85	C₂×Q₈×C₁₅₁	—	2	1	no	—
86	C₂×Q₈×C₁₅₁	—	2	2	no	—
87	C₂×Q₈×C₁₅₁	—	2	1	no	—
88	C₂×Q₈×C₁₅₁	—	2	1	no	—
89	C₂×Q₈×C₁₅₁	SD₁₆	1	4	yes	complemented
90	C₂×Q₈×C₁₅₁	C₂×D₄	1	2	yes	—
91	C₂×D₄×C₁₅₁	—	2	2	no	—
92	C₂×D₄×C₁₅₁	—	2	2	no	—
93	C₂×D₄×C₁₅₁	—	2	2	no	—
94	C₂×D₄×C₁₅₁	—	4	1	no	—
95	C₂×D₄×C₁₅₁	—	4	1	no	—
96	C₂×D₄×C₁₅₁	—	4	1	no	—
97	C₂×D₄×C₁₅₁	—	4	2	no	—
98	C₂×D₄×C₁₅₁	—	4	2	no	—
99	C₂×D₄×C₁₅₁	—	8	2	no	—
100	C₂×D₄×C₁₅₁	—	8	2	no	—
101	C₂²×C₄×C₁₅₁	—	2	1	no	—
102	C₂²×C₄×C₁₅₁	—	2	1	no	—
103	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
106	SD₁₆×C₁₅₁	—	4	8	no	—
107	SD₁₆×C₁₅₁	—	8	4	no	—
108	M₁₆×C₁₅₁	—	4	2	no	—
109	C₂×C₈×C₁₅₁	—	2	2	no	—
110	C₂×C₈×C₁₅₁	—	2	2	no	—
111	C₂×C₈×C₁₅₁	—	2	2	no	—
112	C₂×C₈×C₁₅₁	—	4	2	no	—
113	C₂×C₈×C₁₅₁	C₂×D₄	1	4	yes	—
114	C₄⋊C₄×C₁₅₁	—	2	2	no	—
115	C₄⋊C₄×C₁₅₁	—	2	1	no	—
116	C₄⋊C₄×C₁₅₁	—	2	2	no	—
117	C₄⋊C₄×C₁₅₁	—	2	1	no	—
118	C₄⋊C₄×C₁₅₁	—	2	1	no	—
119	C₄⋊C₄×C₁₅₁	—	2	1	no	—
120	C₄⋊C₄×C₁₅₁	—	2	1	no	—
121	C₄⋊C₄×C₁₅₁	—	4	1	no	—
122	C₄⋊C₄×C₁₅₁	—	4	1	no	—
123	C₄⋊C₄×C₁₅₁	C₂×D₄	1	2	yes	—
124	C₂²⋊C₄×C₁₅₁	—	4	1	no	—
125	C₄²×C₁₅₁	—	2	2	no	—
126	C₄²×C₁₅₁	—	2	2	no	—
127	C₄²×C₁₅₁	—	4	1	no	—
128	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₅₁	#41	1	1	yes	characteristic
131	C₄²×C₁₅₁	C₂⁴	1	1	yes	characteristic
132	C₂³×C₁₅₁	—	4	2	no	—
133	C₂³×C₁₅₁	—	8	2	no	—
134	C₂³×C₁₅₁	—	8	2	no	—
135	C₂³×C₁₅₁	—	8	2	no	—
136	C₂³×C₁₅₁	#121	1	1	yes	characteristic
137	Q₈×C₁₅₁	—	2	2	no	—
138	Q₈×C₁₅₁	—	2	4	no	—
139	Q₈×C₁₅₁	—	4	2	no	—
140	Q₈×C₁₅₁	—	8	1	no	—
141	Q₈×C₁₅₁	C₂×SD₁₆	1	4	yes	—
142	D₄×C₁₅₁	—	4	2	no	—
143	D₄×C₁₅₁	—	4	2	no	—
144	D₄×C₁₅₁	—	4	4	no	—
145	D₄×C₁₅₁	—	8	2	no	—
146	D₄×C₁₅₁	—	8	2	no	—
147	D₄×C₁₅₁	—	8	2	no	—
148	D₄×C₁₅₁	—	8	2	no	—
149	C₂×C₄×C₁₅₁	—	2	2	no	—
150	C₂×C₄×C₁₅₁	—	2	4	no	—
151	C₂×C₄×C₁₅₁	—	2	2	no	—
152	C₂×C₄×C₁₅₁	—	2	2	no	—
153	C₂×C₄×C₁₅₁	—	4	1	no	—
154	C₂×C₄×C₁₅₁	—	4	1	no	—
155	C₂×C₄×C₁₅₁	—	4	1	no	—
156	C₂×C₄×C₁₅₁	—	8	1	no	—
157	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
159	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
160	C₂×C₄×C₁₅₁	C₂×SD₁₆	1	2	yes	—
161	C₂×C₄×C₁₅₁	#135	1	2	yes	—
162	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
165	C₈×C₁₅₁	—	2	4	no	—
166	C₈×C₁₅₁	—	4	2	no	—
167	C₈×C₁₅₁	—	4	2	no	—
168	C₈×C₁₅₁	—	4	2	no	—
169	C₂²×C₁₅₁	—	2	1	no	—
170	C₂²×C₁₅₁	—	2	1	no	—
171	C₂²×C₁₅₁	—	8	2	no	—
172	C₂²×C₁₅₁	—	8	2	no	—
173	C₂²×C₁₅₁	—	8	2	no	—
174	C₂²×C₁₅₁	—	16	4	no	—
175	C₂²×C₁₅₁	#465	1	2	yes	—
176	C₂²×C₁₅₁	C₂×#121	1	1	yes	characteristic
177	C₄×C₁₅₁	—	2	1	no	—
178	C₄×C₁₅₁	—	2	4	no	—
179	C₄×C₁₅₁	—	2	1	no	—
180	C₄×C₁₅₁	—	2	1	no	—
181	C₄×C₁₅₁	—	4	2	no	—
182	C₄×C₁₅₁	—	8	1	no	—
183	C₄×C₁₅₁	—	8	1	no	—
184	C₄×C₁₅₁	#465	1	2	yes	—
185	C₄×C₁₅₁	C₂²×SD₁₆	1	1	yes	characteristic
186	C₄×C₁₅₁	C₂×#135	1	1	yes	characteristic
187	C₄×C₁₅₁	#577	1	2	yes	—
188	C₂×C₁₅₁	—	2	2	no	—
189	C₂×C₁₅₁	—	16	2	no	—
190	C₂×C₁₅₁	#3043	1	1	yes	characteristic
191	C₂×C₁₅₁	C₂×#465	1	1	yes	characteristic
192	C₂×C₁₅₁	#3068	1	1	yes	characteristic
193	#19396	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₁₅₁	#19396	1	1	yes	characteristic, direct product factor, Sylow
195	#3208	C₂×C₁₅₁	1	1	yes	characteristic
196	#3078	C₂×C₁₅₁	1	1	yes	characteristic, complemented
197	C₂×#460	C₂×C₁₅₁	1	1	yes	characteristic
198	#2982	C₂×C₁₅₁	1	1	yes	characteristic, complemented
199	#1678	C₂×C₁₅₁	1	4	yes	complemented
200	#1666	C₂×C₁₅₁	1	4	yes	complemented
201	#1570	C₂×C₁₅₁	1	1	yes	characteristic, complemented
202	#1545	C₂×C₁₅₁	1	1	yes	characteristic
203	#1542	C₂×C₁₅₁	1	1	yes	characteristic, complemented
204	C₂²×SD₁₆	—	2	1	no	—
205	#533	C₂²×C₁₅₁	1	1	yes	characteristic
206	C₂×#127	C₂²×C₁₅₁	1	1	yes	characteristic
207	C₂×C₄×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
208	#492	C₂²×C₁₅₁	1	2	yes	—
209	#486	C₂²×C₁₅₁	1	2	yes	—
210	#479	—	2	2	no	—
211	#477	C₂²×C₁₅₁	1	2	yes	complemented
212	#475	C₂²×C₁₅₁	1	2	yes	complemented
213	#460	—	2	2	no	—
214	#460	—	2	2	no	—
215	#460	C₂²×C₁₅₁	1	4	yes	—
216	#450	—	2	2	no	—
217	C₈×Q₈	—	2	2	no	—
218	C₈×Q₈	C₂²×C₁₅₁	1	4	yes	complemented
219	#431	—	2	2	no	—
220	#431	C₂²×C₁₅₁	1	1	yes	characteristic
221	#431	C₂²×C₁₅₁	1	1	yes	characteristic
222	#428	—	2	1	no	—
223	#423	C₂²×C₁₅₁	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
225	#419	—	2	1	no	—
226	C₂×#102	—	2	1	no	—
227	#334	C₂²×C₁₅₁	1	4	yes	complemented
228	#333	C₂²×C₁₅₁	1	2	yes	complemented
229	#332	C₂²×C₁₅₁	1	2	yes	complemented
230	#331	C₂²×C₁₅₁	1	4	yes	—
231	C₂²×Q₈	D₄×C₁₅₁	1	1	yes	characteristic
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂×SD₁₆	—	2	4	no	—
236	C₂×SD₁₆	—	2	4	no	—
237	C₂×SD₁₆	—	4	4	no	—
238	C₂×M₁₆	—	2	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₄⋊Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
241	C₄⋊Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
242	#127	—	2	1	no	—
243	#127	—	2	1	no	—
244	#127	—	2	1	no	—
245	#127	C₂³×C₁₅₁	1	2	yes	—
246	#125	—	2	1	no	—
247	C₂²⋊Q₈	—	2	1	no	—
248	C₂²⋊Q₈	—	2	1	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	—	2	1	no	—
253	C₄×Q₈	D₄×C₁₅₁	1	2	yes	—
254	C₄×Q₈	C₂³×C₁₅₁	1	2	yes	—
255	#117	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
260	#107	—	2	2	no	—
261	#106	—	2	2	no	—
262	C₄⋊C₈	—	2	4	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	D₄×C₁₅₁	1	2	yes	—
266	C₄⋊C₈	C₂³×C₁₅₁	1	2	yes	—
267	C₄⋊C₈	C₂³×C₁₅₁	1	2	yes	—
268	C₄⋊C₈	C₂³×C₁₅₁	1	2	yes	—
269	#103	—	2	2	no	—
270	#103	—	2	2	no	—
271	#102	—	2	4	no	—
272	#102	—	2	4	no	—
273	C₂²⋊C₈	—	2	1	no	—
274	C₂²⋊C₈	D₄×C₁₅₁	1	2	yes	—
275	C₄×C₈	—	2	4	no	—
276	C₄×C₈	—	2	1	no	—
277	C₄×C₈	C₂³×C₁₅₁	1	2	yes	—
278	C₂⁴	—	4	1	no	—
279	C₂×Q₈	—	2	1	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	SD₁₆×C₁₅₁	1	4	yes	complemented
284	C₂×Q₈	C₂×D₄×C₁₅₁	1	2	yes	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂×D₄	—	8	2	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
299	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
300	SD₁₆	—	4	8	no	—
301	SD₁₆	—	8	4	no	—
302	M₁₆	—	4	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	C₂×D₄×C₁₅₁	1	4	yes	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	C₂×D₄×C₁₅₁	1	2	yes	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	4	1	no	—
322	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
323	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
324	C₄²	#41×C₁₅₁	1	1	yes	characteristic
325	C₄²	C₂⁴×C₁₅₁	1	1	yes	characteristic
326	C₂³	—	4	2	no	—
327	C₂³	—	8	2	no	—
328	C₂³	—	8	2	no	—
329	C₂³	—	8	2	no	—
330	C₂³	#121×C₁₅₁	1	1	yes	characteristic
331	Q₈	—	2	4	no	—
332	Q₈	—	2	2	no	—
333	Q₈	—	4	2	no	—
334	Q₈	—	8	1	no	—
335	Q₈	C₂×SD₁₆×C₁₅₁	1	4	yes	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	4	no	—
339	D₄	—	8	2	no	—
340	D₄	—	8	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
352	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
353	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
354	C₂×C₄	C₂×SD₁₆×C₁₅₁	1	2	yes	—
355	C₂×C₄	#135×C₁₅₁	1	2	yes	—
356	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
357	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
359	C₈	—	2	4	no	—
360	C₈	—	4	2	no	—
361	C₈	—	4	2	no	—
362	C₈	—	4	2	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	16	4	no	—
369	C₂²	#465×C₁₅₁	1	2	yes	—
370	C₂²	C₂×#121×C₁₅₁	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	4	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	8	1	no	—
377	C₄	—	8	1	no	—
378	C₄	#465×C₁₅₁	1	2	yes	—
379	C₄	C₂²×SD₁₆×C₁₅₁	1	1	yes	characteristic
380	C₄	C₂×#135×C₁₅₁	1	1	yes	characteristic
381	C₄	#577×C₁₅₁	1	2	yes	—
382	C₂	—	2	2	no	—
383	C₂	—	16	2	no	—
384	C₂	#3043×C₁₅₁	1	1	yes	characteristic
385	C₂	C₂×#465×C₁₅₁	1	1	yes	characteristic
386	C₂	#3068×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₅₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₅₁
prime radical	C₂×#127×C₁₅₁	C₂²
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
2. #3078×C₁₅₁	C₂	semidirect
4. #2982×C₁₅₁	C₂	semidirect
5. #1678×C₁₅₁	C₂	semidirect
6. #1666×C₁₅₁	C₂	semidirect
7. #1570×C₁₅₁	C₂	semidirect
9. #1542×C₁₅₁	C₂	semidirect
17. #477×C₁₅₁	C₂²	semidirect
18. #475×C₁₅₁	C₂²	semidirect
24. C₈×Q₈×C₁₅₁	C₂²	semidirect
33. #334×C₁₅₁	C₂²	semidirect
34. #333×C₁₅₁	C₂²	semidirect
35. #332×C₁₅₁	C₂²	semidirect
89. C₂×Q₈×C₁₅₁	SD₁₆	semidirect
193. #19396	C₁₅₁	direct (N × H)
194. C₁₅₁	#19396	direct (N × H)
196. #3078	C₂×C₁₅₁	semidirect
198. #2982	C₂×C₁₅₁	semidirect
199. #1678	C₂×C₁₅₁	semidirect
200. #1666	C₂×C₁₅₁	semidirect
201. #1570	C₂×C₁₅₁	semidirect
203. #1542	C₂×C₁₅₁	semidirect
211. #477	C₂²×C₁₅₁	semidirect
212. #475	C₂²×C₁₅₁	semidirect
218. C₈×Q₈	C₂²×C₁₅₁	semidirect
227. #334	C₂²×C₁₅₁	semidirect
228. #333	C₂²×C₁₅₁	semidirect
229. #332	C₂²×C₁₅₁	semidirect
283. C₂×Q₈	SD₁₆×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#3208×C₁₅₁	2
#3078×C₁₅₁	2
C₂×#460×C₁₅₁	2
#2982×C₁₅₁	2
#1678×C₁₅₁	2
#1666×C₁₅₁	2
#1570×C₁₅₁	2
#1545×C₁₅₁	2
#1542×C₁₅₁	2
#19396	151

Subgroups — C151×#19396 #50324321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#19396 #50324321