Subgroups — C₁₅₁×#22807 #50327732

Order 38656.

934 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	#2354×C₁₅₁	C₂	1	2	yes	maximal, complemented
3	#1970×C₁₅₁	C₂	1	2	yes	maximal
4	#1925×C₁₅₁	C₂	1	4	yes	maximal, complemented
5	#1845×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1802×C₁₅₁	C₂	1	2	yes	maximal, complemented
7	C₄×#107×C₁₅₁	C₂	1	2	yes	maximal, complemented
8	C₈×C₄⋊C₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₁₅₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₅₁	C₂²	1	2	yes	—
11	C₂×#117×C₁₅₁	—	2	2	no	—
12	C₄×D₈×C₁₅₁	C₄	1	8	yes	complemented
13	C₂×#107×C₁₅₁	C₂²	1	2	yes	—
14	C₂×#107×C₁₅₁	C₂²	1	2	yes	—
15	C₂×#107×C₁₅₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic
17	C₂×#102×C₁₅₁	C₂²	1	4	yes	—
18	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₅₁	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
21	#390×C₁₅₁	C₂²	1	4	yes	—
22	#388×C₁₅₁	—	2	4	no	—
23	#384×C₁₅₁	C₂²	1	2	yes	—
24	#380×C₁₅₁	—	2	2	no	—
25	C₄×C₄⋊C₄×C₁₅₁	C₂²	1	4	yes	—
26	C₄×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
27	#340×C₁₅₁	C₂²	1	4	yes	—
28	#336×C₁₅₁	C₂²	1	2	yes	—
29	C₂²×D₄×C₁₅₁	C₂³	1	2	yes	—
30	C₂³×C₄×C₁₅₁	—	2	2	no	—
31	C₂×D₈×C₁₅₁	—	2	2	no	—
32	C₂×D₈×C₁₅₁	—	2	2	no	—
33	C₂×D₈×C₁₅₁	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₁₅₁	C₂³	1	2	yes	—
35	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
37	C₄×D₄×C₁₅₁	—	2	4	no	—
38	C₄×D₄×C₁₅₁	C₂×C₄	1	8	yes	—
39	#117×C₁₅₁	—	4	8	no	—
40	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	4	yes	—
45	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
46	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₁₅₁	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₁₅₁	—	2	4	no	—
49	C₂×C₄²×C₁₅₁	—	2	4	no	—
50	C₂×C₄²×C₁₅₁	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
52	#107×C₁₅₁	—	2	4	no	—
53	#107×C₁₅₁	—	4	2	no	—
54	#107×C₁₅₁	C₂×C₄	1	4	yes	—
55	C₄⋊C₈×C₁₅₁	—	2	2	no	—
56	#102×C₁₅₁	—	4	4	no	—
57	#102×C₁₅₁	C₂×C₄	1	8	yes	—
58	C₄×C₈×C₁₅₁	—	2	4	no	—
59	C₄×C₈×C₁₅₁	C₂×C₄	1	4	yes	—
60	#95×C₁₅₁	—	2	4	no	—
61	#95×C₁₅₁	D₄	1	2	yes	—
62	C₂⁴×C₁₅₁	—	2	2	no	—
63	C₂×D₄×C₁₅₁	—	2	2	no	—
64	C₂×D₄×C₁₅₁	—	2	2	no	—
65	C₂×D₄×C₁₅₁	—	2	2	no	—
66	C₂×D₄×C₁₅₁	—	2	2	no	—
67	C₂×D₄×C₁₅₁	—	2	2	no	—
68	C₂×D₄×C₁₅₁	C₂²×C₄	1	4	yes	—
69	C₂²×C₄×C₁₅₁	—	2	2	no	—
70	C₂²×C₄×C₁₅₁	—	2	8	no	—
71	C₂²×C₄×C₁₅₁	—	2	4	no	—
72	C₂²×C₄×C₁₅₁	—	4	4	no	—
73	C₂²×C₄×C₁₅₁	—	4	4	no	—
74	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
75	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
79	D₈×C₁₅₁	—	2	8	no	—
80	C₂×C₈×C₁₅₁	—	2	1	no	—
81	C₂×C₈×C₁₅₁	—	2	1	no	—
82	C₂×C₈×C₁₅₁	—	2	2	no	—
83	C₂×C₈×C₁₅₁	—	2	2	no	—
84	C₂×C₈×C₁₅₁	—	2	2	no	—
85	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
86	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
87	C₂×C₈×C₁₅₁	#41	1	2	yes	—
88	C₂×C₈×C₁₅₁	#41	1	2	yes	—
89	C₄⋊C₄×C₁₅₁	—	2	2	no	—
90	C₄⋊C₄×C₁₅₁	—	2	2	no	—
91	C₄⋊C₄×C₁₅₁	—	2	4	no	—
92	C₄⋊C₄×C₁₅₁	—	2	4	no	—
93	C₄⋊C₄×C₁₅₁	—	4	4	no	—
94	C₄⋊C₄×C₁₅₁	—	8	2	no	—
95	C₄⋊C₄×C₁₅₁	D₈	1	4	yes	complemented
96	C₄⋊C₄×C₁₅₁	C₂²×C₄	1	4	yes	—
97	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
98	C₂²⋊C₄×C₁₅₁	—	4	8	no	—
99	C₂²⋊C₄×C₁₅₁	—	8	4	no	—
100	C₄²×C₁₅₁	—	2	2	no	—
101	C₄²×C₁₅₁	—	2	2	no	—
102	C₄²×C₁₅₁	—	4	8	no	—
103	C₄²×C₁₅₁	C₂²×C₄	1	2	yes	—
104	C₄²×C₁₅₁	#41	1	2	yes	—
105	C₂³×C₁₅₁	—	2	4	no	—
106	C₂³×C₁₅₁	—	4	2	no	—
107	C₂³×C₁₅₁	—	4	2	no	—
108	C₂³×C₁₅₁	—	4	2	no	—
109	C₂³×C₁₅₁	—	4	2	no	—
110	C₂³×C₁₅₁	—	4	2	no	—
111	C₂³×C₁₅₁	—	4	2	no	—
112	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
113	D₄×C₁₅₁	—	2	4	no	—
114	D₄×C₁₅₁	—	2	4	no	—
115	D₄×C₁₅₁	—	4	2	no	—
116	D₄×C₁₅₁	—	4	2	no	—
117	C₂×C₄×C₁₅₁	—	2	2	no	—
118	C₂×C₄×C₁₅₁	—	2	1	no	—
119	C₂×C₄×C₁₅₁	—	2	2	no	—
120	C₂×C₄×C₁₅₁	—	2	1	no	—
121	C₂×C₄×C₁₅₁	—	2	4	no	—
122	C₂×C₄×C₁₅₁	—	2	2	no	—
123	C₂×C₄×C₁₅₁	—	2	2	no	—
124	C₂×C₄×C₁₅₁	—	2	2	no	—
125	C₂×C₄×C₁₅₁	—	4	2	no	—
126	C₂×C₄×C₁₅₁	—	4	2	no	—
127	C₂×C₄×C₁₅₁	—	4	16	no	—
128	C₂×C₄×C₁₅₁	—	4	4	no	—
129	C₂×C₄×C₁₅₁	—	4	4	no	—
130	C₂×C₄×C₁₅₁	—	4	4	no	—
131	C₂×C₄×C₁₅₁	C₄×D₄	1	2	yes	—
132	C₂×C₄×C₁₅₁	C₄×D₄	1	2	yes	—
133	C₂×C₄×C₁₅₁	C₂×D₈	1	4	yes	—
134	C₂×C₄×C₁₅₁	C₂×D₈	1	2	yes	—
135	C₂×C₄×C₁₅₁	#135	1	2	yes	—
136	C₂×C₄×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
138	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
139	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
140	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
141	C₂×C₄×C₁₅₁	2₋¹⁺⁴	1	1	yes	characteristic
142	C₈×C₁₅₁	—	2	2	no	—
143	C₈×C₁₅₁	—	4	2	no	—
144	C₈×C₁₅₁	#117	1	4	yes	complemented
145	C₂²×C₁₅₁	—	4	4	no	—
146	C₂²×C₁₅₁	—	4	4	no	—
147	C₂²×C₁₅₁	—	4	4	no	—
148	C₂²×C₁₅₁	—	8	2	no	—
149	C₂²×C₁₅₁	—	8	2	no	—
150	C₂²×C₁₅₁	—	8	2	no	—
151	C₂²×C₁₅₁	—	8	2	no	—
152	C₂²×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
153	C₂²×C₁₅₁	#547	1	1	yes	characteristic
154	C₂²×C₁₅₁	#550	1	1	yes	characteristic
155	C₂²×C₁₅₁	C₂²×D₈	1	1	yes	characteristic
156	C₂²×C₁₅₁	C₂×#135	1	1	yes	characteristic
157	C₂²×C₁₅₁	#576	1	1	yes	characteristic
158	C₂²×C₁₅₁	#578	1	1	yes	characteristic
159	C₄×C₁₅₁	—	2	4	no	—
160	C₄×C₁₅₁	—	2	2	no	—
161	C₄×C₁₅₁	—	4	2	no	—
162	C₄×C₁₅₁	—	4	4	no	—
163	C₄×C₁₅₁	—	8	4	no	—
164	C₄×C₁₅₁	C₄×D₈	1	4	yes	—
165	C₄×C₁₅₁	C₂×#117	1	1	yes	characteristic
166	C₄×C₁₅₁	#520	1	1	yes	characteristic
167	C₄×C₁₅₁	#555	1	1	yes	characteristic
168	C₄×C₁₅₁	#556	1	1	yes	characteristic
169	C₂×C₁₅₁	—	8	4	no	—
170	C₂×C₁₅₁	#2354	1	1	yes	characteristic
171	C₂×C₁₅₁	C₂×C₄×D₈	1	1	yes	characteristic
172	C₂×C₁₅₁	#2951	1	1	yes	characteristic
173	C₂×C₁₅₁	#3334	1	1	yes	characteristic
174	C₂×C₁₅₁	#3341	1	1	yes	characteristic
175	C₂×C₁₅₁	#3391	1	1	yes	characteristic
176	C₂×C₁₅₁	#3393	1	1	yes	characteristic
177	#22807	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₁₅₁	#22807	1	1	yes	characteristic, direct product factor, Sylow
179	C₂×C₄×D₈	C₂×C₁₅₁	1	1	yes	characteristic
180	#2354	C₂×C₁₅₁	1	2	yes	complemented
181	#1970	C₂×C₁₅₁	1	2	yes	—
182	#1925	C₂×C₁₅₁	1	4	yes	complemented
183	#1845	C₂×C₁₅₁	1	1	yes	characteristic, complemented
184	#1802	C₂×C₁₅₁	1	2	yes	complemented
185	C₄×#107	C₂×C₁₅₁	1	2	yes	complemented
186	C₈×C₄⋊C₄	C₂×C₁₅₁	1	1	yes	characteristic, complemented
187	C₂²×D₈	C₂²×C₁₅₁	1	1	yes	characteristic
188	C₂×C₄×D₄	C₂²×C₁₅₁	1	2	yes	—
189	C₂×#117	—	2	2	no	—
190	C₄×D₈	C₄×C₁₅₁	1	8	yes	complemented
191	C₂×#107	C₂²×C₁₅₁	1	2	yes	—
192	C₂×#107	C₂²×C₁₅₁	1	2	yes	—
193	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
195	C₂×#102	C₂²×C₁₅₁	1	4	yes	—
196	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₁₅₁	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
199	#390	C₂²×C₁₅₁	1	4	yes	—
200	#388	—	2	4	no	—
201	#384	C₂²×C₁₅₁	1	2	yes	—
202	#380	—	2	2	no	—
203	C₄×C₄⋊C₄	C₂²×C₁₅₁	1	4	yes	—
204	C₄×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
205	#340	C₂²×C₁₅₁	1	4	yes	—
206	#336	C₂²×C₁₅₁	1	2	yes	—
207	C₂²×D₄	C₂³×C₁₅₁	1	2	yes	—
208	C₂³×C₄	—	2	2	no	—
209	C₂×D₈	—	2	2	no	—
210	C₂×D₈	—	2	2	no	—
211	C₂×D₈	C₂×C₄×C₁₅₁	1	4	yes	—
212	C₂²×C₈	C₂³×C₁₅₁	1	2	yes	—
213	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
215	C₄×D₄	—	2	4	no	—
216	C₄×D₄	C₂×C₄×C₁₅₁	1	8	yes	—
217	#117	—	4	8	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
221	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
222	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	4	yes	—
223	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
224	C₂×C₂²⋊C₄	—	2	2	no	—
225	C₂×C₂²⋊C₄	—	2	4	no	—
226	C₂×C₂²⋊C₄	—	2	4	no	—
227	C₂×C₄²	—	2	4	no	—
228	C₂×C₄²	C₂³×C₁₅₁	1	2	yes	—
229	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
230	#107	—	2	4	no	—
231	#107	—	4	2	no	—
232	#107	C₂×C₄×C₁₅₁	1	4	yes	—
233	C₄⋊C₈	—	2	2	no	—
234	#102	—	4	4	no	—
235	#102	C₂×C₄×C₁₅₁	1	8	yes	—
236	C₄×C₈	—	2	4	no	—
237	C₄×C₈	C₂×C₄×C₁₅₁	1	4	yes	—
238	#95	—	2	4	no	—
239	#95	D₄×C₁₅₁	1	2	yes	—
240	C₂⁴	—	2	2	no	—
241	C₂×D₄	—	2	2	no	—
242	C₂×D₄	—	2	2	no	—
243	C₂×D₄	—	2	2	no	—
244	C₂×D₄	—	2	2	no	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	C₂²×C₄×C₁₅₁	1	4	yes	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	4	4	no	—
251	C₂²×C₄	—	4	4	no	—
252	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
253	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
254	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
255	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
256	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
257	D₈	—	2	8	no	—
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	—	2	1	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
264	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
265	C₂×C₈	#41×C₁₅₁	1	2	yes	—
266	C₂×C₈	#41×C₁₅₁	1	2	yes	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	4	4	no	—
272	C₄⋊C₄	—	8	2	no	—
273	C₄⋊C₄	D₈×C₁₅₁	1	4	yes	complemented
274	C₄⋊C₄	C₂²×C₄×C₁₅₁	1	4	yes	—
275	C₂²⋊C₄	—	2	8	no	—
276	C₂²⋊C₄	—	4	8	no	—
277	C₂²⋊C₄	—	8	4	no	—
278	C₄²	—	2	2	no	—
279	C₄²	—	2	2	no	—
280	C₄²	—	4	8	no	—
281	C₄²	C₂²×C₄×C₁₅₁	1	2	yes	—
282	C₄²	#41×C₁₅₁	1	2	yes	—
283	C₂³	—	2	4	no	—
284	C₂³	—	4	2	no	—
285	C₂³	—	4	2	no	—
286	C₂³	—	4	2	no	—
287	C₂³	—	4	2	no	—
288	C₂³	—	4	2	no	—
289	C₂³	—	4	2	no	—
290	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
291	D₄	—	2	4	no	—
292	D₄	—	2	4	no	—
293	D₄	—	4	2	no	—
294	D₄	—	4	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	16	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	C₄×D₄×C₁₅₁	1	2	yes	—
310	C₂×C₄	C₄×D₄×C₁₅₁	1	2	yes	—
311	C₂×C₄	C₂×D₈×C₁₅₁	1	4	yes	—
312	C₂×C₄	C₂×D₈×C₁₅₁	1	2	yes	—
313	C₂×C₄	#135×C₁₅₁	1	2	yes	—
314	C₂×C₄	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
315	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
316	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
317	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
318	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
319	C₂×C₄	2₋¹⁺⁴×C₁₅₁	1	1	yes	characteristic
320	C₈	—	2	2	no	—
321	C₈	—	4	2	no	—
322	C₈	#117×C₁₅₁	1	4	yes	complemented
323	C₂²	—	4	4	no	—
324	C₂²	—	4	4	no	—
325	C₂²	—	4	4	no	—
326	C₂²	—	8	2	no	—
327	C₂²	—	8	2	no	—
328	C₂²	—	8	2	no	—
329	C₂²	—	8	2	no	—
330	C₂²	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
331	C₂²	#547×C₁₅₁	1	1	yes	characteristic
332	C₂²	#550×C₁₅₁	1	1	yes	characteristic
333	C₂²	C₂²×D₈×C₁₅₁	1	1	yes	characteristic
334	C₂²	C₂×#135×C₁₅₁	1	1	yes	characteristic
335	C₂²	#576×C₁₅₁	1	1	yes	characteristic
336	C₂²	#578×C₁₅₁	1	1	yes	characteristic
337	C₄	—	2	2	no	—
338	C₄	—	2	4	no	—
339	C₄	—	4	4	no	—
340	C₄	—	4	2	no	—
341	C₄	—	8	4	no	—
342	C₄	C₄×D₈×C₁₅₁	1	4	yes	—
343	C₄	C₂×#117×C₁₅₁	1	1	yes	characteristic
344	C₄	#520×C₁₅₁	1	1	yes	characteristic
345	C₄	#555×C₁₅₁	1	1	yes	characteristic
346	C₄	#556×C₁₅₁	1	1	yes	characteristic
347	C₂	—	8	4	no	—
348	C₂	#2354×C₁₅₁	1	1	yes	characteristic
349	C₂	C₂×C₄×D₈×C₁₅₁	1	1	yes	characteristic
350	C₂	#2951×C₁₅₁	1	1	yes	characteristic
351	C₂	#3334×C₁₅₁	1	1	yes	characteristic
352	C₂	#3341×C₁₅₁	1	1	yes	characteristic
353	C₂	#3391×C₁₅₁	1	1	yes	characteristic
354	C₂	#3393×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₅₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₅₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
prime radical	C₂²×D₈×C₁₅₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ C₄×C₄⋊C₄×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2354×C₁₅₁	C₂	semidirect
4. #1925×C₁₅₁	C₂	semidirect
5. #1845×C₁₅₁	C₂	semidirect
6. #1802×C₁₅₁	C₂	semidirect
7. C₄×#107×C₁₅₁	C₂	semidirect
8. C₈×C₄⋊C₄×C₁₅₁	C₂	semidirect
12. C₄×D₈×C₁₅₁	C₄	semidirect
95. C₄⋊C₄×C₁₅₁	D₈	semidirect
144. C₈×C₁₅₁	#117	semidirect
177. #22807	C₁₅₁	direct (N × H)
178. C₁₅₁	#22807	direct (N × H)
180. #2354	C₂×C₁₅₁	semidirect
182. #1925	C₂×C₁₅₁	semidirect
183. #1845	C₂×C₁₅₁	semidirect
184. #1802	C₂×C₁₅₁	semidirect
185. C₄×#107	C₂×C₁₅₁	semidirect
186. C₈×C₄⋊C₄	C₂×C₁₅₁	semidirect
190. C₄×D₈	C₄×C₁₅₁	semidirect
273. C₄⋊C₄	D₈×C₁₅₁	semidirect
322. C₈	#117×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₈×C₁₅₁	2
#2354×C₁₅₁	2
#1970×C₁₅₁	2
#1925×C₁₅₁	2
#1845×C₁₅₁	2
#1802×C₁₅₁	2
C₄×#107×C₁₅₁	2
C₈×C₄⋊C₄×C₁₅₁	2
#22807	151

Subgroups — C151×#22807 #50327732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#22807 #50327732