Subgroups — #34078572

Order 19328.

548 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18012766	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#18012763	C₂	1	1	yes	maximal, characteristic, complemented
3	#23752761	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₄×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#23752428	C₂	1	1	yes	maximal, characteristic, complemented
6	#23752427	C₂	1	1	yes	maximal, characteristic, complemented
7	#23752424	C₂	1	1	yes	maximal, characteristic, complemented
8	#23752416	C₂	1	1	yes	maximal, characteristic, complemented
9	#23752415	C₂	1	1	yes	maximal, characteristic, complemented
10	#23752406	C₂	1	1	yes	maximal, characteristic, complemented
11	#23752405	C₂	1	1	yes	maximal, characteristic, complemented
12	#23752234	C₂	1	1	yes	maximal, characteristic, complemented
13	#23752212	C₂	1	1	yes	maximal, characteristic, complemented
14	#23752210	C₂	1	1	yes	maximal, characteristic, complemented
15	#463×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14559005	C₂²	1	1	yes	characteristic
17	C₂×#14559003	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₁₅₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₅₁	—	2	1	no	—
20	#18012766	—	2	4	no	—
21	#18012763	—	2	4	no	—
22	C₂×#14558993	C₂²	1	1	yes	characteristic
23	C₂×#14558992	C₂²	1	1	yes	characteristic
24	C₂×#14558991	C₂²	1	1	yes	characteristic
25	C₂×D₁₂₀₈	C₂²	1	1	yes	characteristic
26	C₂×#14558989	C₂²	1	1	yes	characteristic
27	C₂×#14558989	C₂²	1	1	yes	characteristic
28	C₂×#14558987	C₂²	1	1	yes	characteristic
29	C₂×#14558987	C₂²	1	1	yes	characteristic
30	#18012737	C₂²	1	1	yes	characteristic, complemented
31	#18012735	C₂²	1	1	yes	characteristic, complemented
32	#18012727	C₂²	1	1	yes	characteristic, complemented
33	#18012712	—	2	1	no	—
34	#18012712	—	2	1	no	—
35	C₄×D₆₀₄	C₂²	1	1	yes	characteristic
36	D₄×Dic₁₅₁	C₂²	1	1	yes	characteristic
37	#18012701	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊D₁₅₁	—	2	1	no	—
39	(C₂²⋊D₁₅₁)⋊C₄	—	2	1	no	—
40	(C₂²⋊D₁₅₁)⋊C₄	—	2	1	no	—
41	(C₂²⋊D₁₅₁)⋊C₄	—	2	1	no	—
42	C₄⋊C₄×D₁₅₁	C₂²	1	1	yes	characteristic
43	C₂²⋊C₄×D₁₅₁	—	2	1	no	—
44	C₄²×D₁₅₁	C₂²	1	1	yes	characteristic
45	C₄⋊(C₁₅₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
46	Dic₁₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	Dic₁₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	#18012664	C₂²	1	1	yes	characteristic, complemented
49	#18012663	C₂²	1	1	yes	characteristic, complemented
50	#18012662	C₂²	1	1	yes	characteristic, complemented
51	#18012661	C₂²	1	1	yes	characteristic, complemented
52	#18012660	C₂²	1	1	yes	characteristic, complemented
53	#18012659	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
55	C₂×D₈×C₁₅₁	C₂²	1	1	yes	characteristic
56	#124×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
58	C₄⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
59	#103×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
60	#102×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₅₁	—	2	1	no	—
62	#14559005	—	2	2	no	—
63	#14559005	—	2	2	no	—
64	#14559003	—	2	2	no	—
65	#14559003	—	2	2	no	—
66	C₂×Dic₃₀₂	C₂³	1	1	yes	characteristic
67	C₂×D₆₀₄	—	2	1	no	—
68	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
69	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₅₁	—	2	1	no	—
71	C₂×C₂²⋊D₁₅₁	—	2	1	no	—
72	C₂×C₂²⋊D₁₅₁	—	2	1	no	—
73	C₂×C₂²⋊D₁₅₁	—	2	1	no	—
74	D₄×D₁₅₁	—	2	2	no	—
75	D₄×D₁₅₁	D₄	1	4	yes	complemented
76	C₂²×Dic₁₅₁	—	2	1	no	—
77	C₂²×Dic₁₅₁	—	2	1	no	—
78	C₂×C₄×D₁₅₁	—	2	1	no	—
79	C₂×C₄×D₁₅₁	—	2	1	no	—
80	C₂×C₄×D₁₅₁	—	2	1	no	—
81	C₂×C₄×D₁₅₁	—	2	1	no	—
82	C₂×C₄×D₁₅₁	—	4	4	no	—
83	C₂×C₄×D₁₅₁	D₄	1	1	yes	characteristic
84	C₂×C₄×D₁₅₁	D₄	1	1	yes	characteristic
85	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
86	#14558993	—	2	2	no	—
87	#14558992	—	2	2	no	—
88	#14558991	—	2	2	no	—
89	D₁₂₀₈	—	2	2	no	—
90	#14558989	—	2	2	no	—
91	#14558989	—	2	2	no	—
92	#14558987	—	2	2	no	—
93	#14558987	—	2	2	no	—
94	C₂×C₁₅₁⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×C₁₅₁⋊C₈	C₂³	1	1	yes	characteristic
96	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
97	Dic₁₅₁⋊C₄	—	2	1	no	—
98	Dic₁₅₁⋊C₄	—	2	1	no	—
99	Dic₁₅₁⋊C₄	—	2	1	no	—
100	C₂²⋊Dic₁₅₁	—	2	1	no	—
101	(C₂×D₁₅₁)⋊C₄	—	2	1	no	—
102	(C₂×D₁₅₁)⋊C₄	—	2	1	no	—
103	(C₂×D₁₅₁)⋊C₄	—	2	1	no	—
104	(C₂×D₁₅₁)⋊C₄	—	2	1	no	—
105	C₄×Dic₁₅₁	D₄	1	1	yes	characteristic
106	C₄×Dic₁₅₁	D₄	1	1	yes	characteristic
107	C₄×Dic₁₅₁	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₁₅₁	—	2	1	no	—
112	SD₁₆×C₁₅₁	—	2	2	no	—
113	D₈×C₁₅₁	—	2	2	no	—
114	C₂×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
118	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
119	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
120	C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
121	C₂²×D₁₅₁	—	2	1	no	—
122	C₂²×D₁₅₁	—	2	4	no	—
123	C₂²×D₁₅₁	—	2	1	no	—
124	C₂²×D₁₅₁	—	4	2	no	—
125	C₂²×D₁₅₁	—	4	2	no	—
126	C₂²×D₁₅₁	C₂×D₄	1	1	yes	characteristic
127	Dic₃₀₂	—	2	1	no	—
128	Dic₃₀₂	—	2	1	no	—
129	D₆₀₄	—	2	1	no	—
130	D₆₀₄	—	2	1	no	—
131	D₆₀₄	—	2	1	no	—
132	D₆₀₄	—	4	2	no	—
133	D₆₀₄	C₂×D₄	1	2	yes	—
134	C₂²⋊D₁₅₁	—	2	4	no	—
135	C₂²⋊D₁₅₁	—	4	2	no	—
136	C₂²⋊D₁₅₁	—	4	2	no	—
137	C₂²⋊D₁₅₁	—	4	2	no	—
138	C₂×Dic₁₅₁	—	2	1	no	—
139	C₂×Dic₁₅₁	—	2	1	no	—
140	C₂×Dic₁₅₁	—	4	2	no	—
141	C₂×Dic₁₅₁	—	4	2	no	—
142	C₂×Dic₁₅₁	C₂×D₄	1	1	yes	characteristic
143	C₂×Dic₁₅₁	C₂×D₄	1	1	yes	characteristic
144	C₂×Dic₁₅₁	C₂×D₄	1	1	yes	characteristic
145	C₄×D₁₅₁	—	2	2	no	—
146	C₄×D₁₅₁	—	4	1	no	—
147	C₄×D₁₅₁	—	4	2	no	—
148	C₄×D₁₅₁	—	4	2	no	—
149	C₄×D₁₅₁	—	4	2	no	—
150	C₄×D₁₅₁	—	4	2	no	—
151	C₄×D₁₅₁	C₂×D₄	1	2	yes	—
152	C₄×D₁₅₁	#41	1	2	yes	—
153	C₁₅₁⋊C₈	—	2	1	no	—
154	C₁₅₁⋊C₈	—	2	1	no	—
155	C₂³×C₁₅₁	—	2	1	no	—
156	C₂³×C₁₅₁	—	2	1	no	—
157	Q₈×C₁₅₁	—	2	1	no	—
158	Q₈×C₁₅₁	—	2	1	no	—
159	D₄×C₁₅₁	—	2	1	no	—
160	D₄×C₁₅₁	—	2	1	no	—
161	D₄×C₁₅₁	—	2	1	no	—
162	D₄×C₁₅₁	C₂×D₄	1	2	yes	—
163	C₂×C₄×C₁₅₁	—	2	1	no	—
164	C₂×C₄×C₁₅₁	—	2	1	no	—
165	C₂×C₄×C₁₅₁	—	4	2	no	—
166	C₂×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
169	C₈×C₁₅₁	—	2	1	no	—
170	C₈×C₁₅₁	—	2	1	no	—
171	C₂²×C₁₅₁	—	2	2	no	—
172	C₂²×C₁₅₁	—	4	1	no	—
173	C₂²×C₁₅₁	—	4	1	no	—
174	C₂²×C₁₅₁	—	4	1	no	—
175	C₂²×C₁₅₁	—	4	1	no	—
176	C₂²×C₁₅₁	—	4	1	no	—
177	C₂²×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×D₁₅₁	—	2	1	no	—
179	C₂×D₁₅₁	—	2	1	no	—
180	C₂×D₁₅₁	—	2	2	no	—
181	C₂×D₁₅₁	—	4	8	no	—
182	C₂×D₁₅₁	—	4	1	no	—
183	C₂×D₁₅₁	—	4	1	no	—
184	C₂×D₁₅₁	—	4	1	no	—
185	C₂×D₁₅₁	—	4	1	no	—
186	C₂×D₁₅₁	—	4	1	no	—
187	C₂×D₁₅₁	#121	1	2	yes	—
188	C₄×C₁₅₁	—	2	1	no	—
189	C₄×C₁₅₁	—	2	1	no	—
190	C₄×C₁₅₁	—	4	1	no	—
191	C₄×C₁₅₁	—	4	1	no	—
192	C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
193	C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
194	Dic₁₅₁	—	2	1	no	—
195	Dic₁₅₁	—	4	1	no	—
196	Dic₁₅₁	—	4	1	no	—
197	Dic₁₅₁	#121	1	2	yes	—
198	Dic₁₅₁	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₂×C₁₅₁	—	4	2	no	—
200	C₂×C₁₅₁	—	8	1	no	—
201	C₂×C₁₅₁	C₂×#121	1	1	yes	characteristic
202	C₂×C₁₅₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂×C₁₅₁	#575	1	1	yes	characteristic
204	D₁₅₁	—	2	2	no	—
205	D₁₅₁	—	4	2	no	—
206	D₁₅₁	—	8	1	no	—
207	C₁₅₁	#3036	1	1	yes	characteristic, complemented, Sylow
208	#3036	—	151	1	no	maximal, Sylow
209	C₂×AGL(1,ℤ/8)	—	151	1	no	—
210	C₂×AGL(1,ℤ/8)	—	151	1	no	—
211	#532	—	151	1	no	—
212	C₂×C₄×D₄	—	151	1	no	—
213	#463	—	151	1	no	—
214	#463	—	151	1	no	—
215	#463	—	151	1	no	—
216	#463	D₁₅₁	1	1	yes	characteristic, complemented
217	#461	—	151	1	no	—
218	#461	—	151	1	no	—
219	#459	—	151	1	no	—
220	#459	—	151	1	no	—
221	#423	—	151	1	no	—
222	#417	—	151	1	no	—
223	#417	—	151	1	no	—
224	C₂×#41	—	151	1	no	—
225	C₂×#41	—	151	1	no	—
226	C₂²×D₄	—	151	1	no	—
227	C₂³×C₄	—	302	1	no	—
228	AGL(1,ℤ/8)	—	302	4	no	—
229	AGL(1,ℤ/8)	—	302	4	no	—
230	C₂×SD₁₆	—	151	1	no	—
231	C₂×SD₁₆	—	151	1	no	—
232	C₂×SD₁₆	—	151	1	no	—
233	C₂×SD₁₆	C₂×D₁₅₁	1	1	yes	characteristic
234	C₂×D₈	—	151	1	no	—
235	C₂×D₈	—	151	1	no	—
236	C₂×D₈	—	151	1	no	—
237	C₂×D₈	C₂×D₁₅₁	1	1	yes	characteristic
238	C₂×M₁₆	—	151	1	no	—
239	C₂×M₁₆	—	151	1	no	—
240	C₄⋊Q₈	—	151	1	no	—
241	#127	—	151	1	no	—
242	#124	—	151	1	no	—
243	#124	C₂×D₁₅₁	1	1	yes	characteristic, complemented
244	#121	—	302	1	no	—
245	#121	—	302	1	no	—
246	C₄×D₄	—	302	1	no	—
247	C₄×D₄	—	302	1	no	—
248	C₄×D₄	—	302	1	no	—
249	C₄×D₄	—	302	1	no	—
250	C₄×D₄	—	151	1	no	—
251	C₄×D₄	—	151	1	no	—
252	C₄×D₄	—	151	1	no	—
253	C₄×D₄	C₂×D₁₅₁	1	1	yes	characteristic
254	C₂×C₄⋊C₄	—	151	1	no	—
255	C₂×C₂²⋊C₄	—	302	1	no	—
256	C₂×C₄²	—	151	1	no	—
257	C₄⋊C₈	—	151	1	no	—
258	C₄⋊C₈	—	151	1	no	—
259	C₄⋊C₈	—	151	1	no	—
260	C₄⋊C₈	C₂×D₁₅₁	1	1	yes	characteristic, complemented
261	#103	—	151	1	no	—
262	#103	—	151	1	no	—
263	#103	—	151	1	no	—
264	#103	C₂×D₁₅₁	1	1	yes	characteristic, complemented
265	#102	—	151	1	no	—
266	#102	—	151	1	no	—
267	#102	—	151	1	no	—
268	#102	C₂×D₁₅₁	1	1	yes	characteristic, complemented
269	C₂⁴	—	302	1	no	—
270	#41	—	302	2	no	—
271	#41	—	302	2	no	—
272	#41	—	302	2	no	—
273	#41	—	302	2	no	—
274	C₂×Q₈	—	151	1	no	—
275	C₂×Q₈	C₂²×D₁₅₁	1	1	yes	characteristic
276	C₂×D₄	—	302	1	no	—
277	C₂×D₄	—	302	1	no	—
278	C₂×D₄	—	302	2	no	—
279	C₂×D₄	—	302	1	no	—
280	C₂×D₄	—	302	1	no	—
281	C₂×D₄	—	302	1	no	—
282	C₂×D₄	—	151	4	no	—
283	C₂×D₄	—	151	1	no	—
284	C₂×D₄	—	151	1	no	—
285	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
286	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	302	1	no	—
289	C₂²×C₄	—	302	1	no	—
290	C₂²×C₄	—	302	1	no	—
291	C₂²×C₄	—	302	1	no	—
292	C₂²×C₄	—	302	1	no	—
293	C₂²×C₄	—	302	1	no	—
294	C₂²×C₄	—	604	4	no	—
295	C₂²×C₄	—	151	1	no	—
296	C₂²×C₄	—	151	1	no	—
297	C₂²×C₄	—	151	1	no	—
298	SD₁₆	—	2	2	no	—
299	SD₁₆	—	302	2	no	—
300	SD₁₆	—	302	2	no	—
301	SD₁₆	—	302	2	no	—
302	D₈	—	2	2	no	—
303	D₈	—	302	2	no	—
304	D₈	—	302	2	no	—
305	D₈	—	302	2	no	—
306	M₁₆	—	302	2	no	—
307	M₁₆	—	302	2	no	—
308	C₂×C₈	—	151	1	no	—
309	C₂×C₈	—	151	1	no	—
310	C₂×C₈	C₂²×D₁₅₁	1	1	yes	characteristic
311	C₂×C₈	C₂²×D₁₅₁	1	1	yes	characteristic
312	C₄⋊C₄	—	302	1	no	—
313	C₄⋊C₄	—	302	1	no	—
314	C₄⋊C₄	—	302	1	no	—
315	C₄⋊C₄	—	151	1	no	—
316	C₄⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	302	1	no	—
321	C₂²⋊C₄	—	302	1	no	—
322	C₂²⋊C₄	—	302	1	no	—
323	C₂²⋊C₄	—	302	1	no	—
324	C₂²⋊C₄	—	302	1	no	—
325	C₄²	—	151	1	no	—
326	C₄²	—	151	1	no	—
327	C₄²	—	151	1	no	—
328	C₄²	C₂²×D₁₅₁	1	1	yes	characteristic
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	302	4	no	—
332	C₂³	—	302	1	no	—
333	C₂³	—	302	1	no	—
334	C₂³	—	604	2	no	—
335	C₂³	—	604	2	no	—
336	C₂³	—	151	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	2	1	no	—
339	Q₈	—	302	1	no	—
340	Q₈	—	302	1	no	—
341	D₄	—	2	1	no	—
342	D₄	—	2	1	no	—
343	D₄	—	2	1	no	—
344	D₄	—	302	4	no	—
345	D₄	—	302	1	no	—
346	D₄	—	302	1	no	—
347	D₄	—	302	1	no	—
348	D₄	—	604	2	no	—
349	D₄	—	604	2	no	—
350	D₄	—	604	2	no	—
351	D₄	—	604	2	no	—
352	D₄	—	151	2	no	—
353	D₄	D₄×D₁₅₁	1	2	yes	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	302	2	no	—
358	C₂×C₄	—	302	1	no	—
359	C₂×C₄	—	302	1	no	—
360	C₂×C₄	—	604	1	no	—
361	C₂×C₄	—	604	2	no	—
362	C₂×C₄	—	604	2	no	—
363	C₂×C₄	—	604	2	no	—
364	C₂×C₄	—	604	2	no	—
365	C₂×C₄	—	604	2	no	—
366	C₂×C₄	—	604	2	no	—
367	C₂×C₄	—	151	1	no	—
368	C₂×C₄	—	151	1	no	—
369	C₂×C₄	—	151	1	no	—
370	C₂×C₄	—	151	2	no	—
371	C₂×C₄	—	151	2	no	—
372	C₂×C₄	D₄×D₁₅₁	1	1	yes	characteristic
373	C₂×C₄	D₄×D₁₅₁	1	1	yes	characteristic
374	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	302	1	no	—
378	C₈	—	302	1	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	302	1	no	—
386	C₂²	—	302	1	no	—
387	C₂²	—	302	2	no	—
388	C₂²	—	604	8	no	—
389	C₂²	—	604	1	no	—
390	C₂²	—	604	1	no	—
391	C₂²	—	604	1	no	—
392	C₂²	—	604	1	no	—
393	C₂²	—	604	1	no	—
394	C₂²	—	151	2	no	—
395	C₂²	C₂×D₄×D₁₅₁	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	302	1	no	—
401	C₄	—	604	1	no	—
402	C₄	—	604	1	no	—
403	C₄	—	151	2	no	—
404	C₄	—	151	2	no	—
405	C₄	C₂×D₄×D₁₅₁	1	1	yes	characteristic
406	C₄	#41×D₁₅₁	1	1	yes	characteristic
407	C₂	—	4	2	no	—
408	C₂	—	8	1	no	—
409	C₂	—	302	2	no	—
410	C₂	—	604	2	no	—
411	C₂	—	1208	1	no	—
412	C₂	#121×D₁₅₁	1	1	yes	characteristic
413	C₂	AGL(1,ℤ/8)×D₁₅₁	1	1	yes	characteristic
414	C₂	#23753009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₅₁
commutator, cosocle	C₂×C₄×C₁₅₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅₁
Fitting	#463×C₁₅₁	C₂
socle	C₂²×C₁₅₁	C₂²×D₄
hypercenter	#463	D₁₅₁
hypocenter	C₁₅₁	#3036
LCS	G ▷ C₂×C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #463

Complements

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

N	H ≅ G/N	type
1. C₂×#18012766	C₂	semidirect
2. C₂×#18012763	C₂	semidirect
3. #23752761	C₂	semidirect
4. C₄×D₄×D₁₅₁	C₂	semidirect
5. #23752428	C₂	semidirect
6. #23752427	C₂	semidirect
7. #23752424	C₂	semidirect
8. #23752416	C₂	semidirect
9. #23752415	C₂	semidirect
10. #23752406	C₂	semidirect
11. #23752405	C₂	semidirect
12. #23752234	C₂	semidirect
13. #23752212	C₂	semidirect
14. #23752210	C₂	semidirect
15. #463×C₁₅₁	C₂	semidirect
30. #18012737	C₂²	semidirect
31. #18012735	C₂²	semidirect
32. #18012727	C₂²	semidirect
45. C₄⋊(C₁₅₁⋊C₈)	C₂²	semidirect
46. Dic₁₅₁⋊C₈	C₂²	semidirect
47. Dic₁₅₁⋊C₈	C₂²	semidirect
48. #18012664	C₂²	semidirect
49. #18012663	C₂²	semidirect
50. #18012662	C₂²	semidirect
51. #18012661	C₂²	semidirect
52. #18012660	C₂²	semidirect
53. #18012659	C₂²	semidirect
56. #124×C₁₅₁	C₂²	semidirect
58. C₄⋊C₈×C₁₅₁	C₂²	semidirect
59. #103×C₁₅₁	C₂²	semidirect
60. #102×C₁₅₁	C₂²	semidirect
75. D₄×D₁₅₁	D₄	semidirect
198. Dic₁₅₁	AGL(1,ℤ/8)	semidirect
207. C₁₅₁	#3036	semidirect
216. #463	D₁₅₁	semidirect
243. #124	C₂×D₁₅₁	semidirect
260. C₄⋊C₈	C₂×D₁₅₁	semidirect
264. #103	C₂×D₁₅₁	semidirect
268. #102	C₂×D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#18012766	2
C₂×#18012763	2
#23752761	2
C₄×D₄×D₁₅₁	2
#23752428	2
#23752427	2
#23752424	2
#23752416	2
#23752415	2
#23752406	2
#23752405	2
#23752234	2
#23752212	2
#23752210	2
#463×C₁₅₁	2
#3036	151