Subgroups — #46845097

Order 34688.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16864637	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₂₇₁	C₂	1	1	yes	maximal, characteristic
4	#31773973	C₂	1	1	yes	maximal, characteristic, complemented
5	#31773972	C₂	1	1	yes	maximal, characteristic, complemented
6	#31773970	C₂	1	1	yes	maximal, characteristic, complemented
7	#31773969	C₂	1	1	yes	maximal, characteristic, complemented
8	#31773967	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
10	(C₂²⋊D₂₇₁)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#31773919	C₂	1	1	yes	maximal, characteristic, complemented
12	#31773859	C₂	1	1	yes	maximal, characteristic, complemented
13	#31773859	C₂	1	1	yes	maximal, characteristic, complemented
14	#31773849	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₂₇₁	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₂₇₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₂₇₁	C₂²	1	1	yes	characteristic
19	C₂×#16864638	C₂²	1	1	yes	characteristic, complemented
20	C₂×#16864637	—	2	4	no	—
21	C₂×#16864637	C₂²	1	1	yes	characteristic
22	C₂×#16864637	C₂²	1	1	yes	characteristic
23	C₂×#16864637	C₂²	1	1	yes	characteristic
24	C₂×#16864637	C₂²	1	1	yes	characteristic
25	C₂×#16864637	C₂²	1	1	yes	characteristic, complemented
26	C₂×#16864637	C₂²	1	1	yes	characteristic, complemented
27	M₁₆×D₂₇₁	—	2	4	no	—
28	C₂²×C₂₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₈×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
31	C₄×D₁₀₈₄	C₂²	1	1	yes	characteristic
32	D₄×Dic₂₇₁	C₄	1	1	yes	characteristic
33	#22576122	C₄	1	1	yes	characteristic
34	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
36	(C₂²⋊D₂₇₁)⋊C₄	C₄	1	1	yes	characteristic
37	(C₂²⋊D₂₇₁)⋊C₄	C₄	1	1	yes	characteristic
38	C₄⋊C₄×D₂₇₁	C₄	1	1	yes	characteristic
39	C₂²⋊C₄×D₂₇₁	C₄	1	1	yes	characteristic
40	C₂²⋊C₄×D₂₇₁	C₄	1	1	yes	characteristic
41	C₄²×D₂₇₁	C₂²	1	1	yes	characteristic
42	C₄⋊(C₂₇₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
43	Dic₂₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	Dic₂₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊(C₂₇₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊(C₂₇₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₂₇₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	(C₂×D₂₇₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	(C₂×D₂₇₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₂₇₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	#22576071	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₁₆×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₂₇₁	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊C₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
60	#97×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₂₇₁	C₂×C₄	1	1	yes	characteristic
62	C₂³×D₂₇₁	C₂×C₄	1	1	yes	characteristic
63	C₂×D₁₀₈₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊D₂₇₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₂₇₁	C₂×C₄	1	1	yes	characteristic
66	D₄×D₂₇₁	—	2	4	no	—
67	C₂²×Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
68	C₂²×Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×D₂₇₁	—	2	2	no	—
70	C₂×C₄×D₂₇₁	—	2	2	no	—
71	C₂×C₄×D₂₇₁	—	2	2	no	—
72	C₂×C₄×D₂₇₁	—	2	2	no	—
73	C₂×C₄×D₂₇₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₂₇₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₂₇₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₂₇₁	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₂₇₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₂₇₁	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
82	#16864638	—	2	2	no	—
83	#16864637	—	2	2	no	—
84	#16864637	—	2	2	no	—
85	#16864637	—	2	2	no	—
86	#16864637	—	2	2	no	—
87	#16864637	—	2	2	no	—
88	#16864637	D₄	1	4	yes	complemented
89	C₂×C₂₇₁⋊C₈	—	2	2	no	—
90	C₂×C₂₇₁⋊C₈	C₂³	1	1	yes	characteristic
91	C₂×C₂₇₁⋊C₈	C₂³	1	1	yes	characteristic
92	C₂×C₂₇₁⋊C₈	C₂³	1	1	yes	characteristic
93	C₂×C₂₇₁⋊C₈	C₂³	1	1	yes	characteristic
94	C₈×D₂₇₁	—	2	2	no	—
95	C₈×D₂₇₁	—	2	2	no	—
96	C₄⋊Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
97	Dic₂₇₁⋊C₄	C₂×C₄	1	1	yes	characteristic
98	Dic₂₇₁⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
101	(C₂×D₂₇₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
102	(C₂×D₂₇₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
103	(C₂×D₂₇₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
104	(C₂×D₂₇₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
107	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₂₇₁	C₂×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
111	M₁₆×C₂₇₁	—	2	2	no	—
112	C₂×C₈×C₂₇₁	—	2	2	no	—
113	C₂×C₈×C₂₇₁	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₂₇₁	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₂₇₁	C₂³	1	1	yes	characteristic
116	C₂×C₈×C₂₇₁	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₂₇₁	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₂₇₁	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊C₄×C₂₇₁	C₂×C₄	1	1	yes	characteristic
120	C₄²×C₂₇₁	C₂³	1	1	yes	characteristic
121	C₂²×D₂₇₁	—	2	2	no	—
122	C₂²×D₂₇₁	—	2	2	no	—
123	C₂²×D₂₇₁	—	2	2	no	—
124	C₂²×D₂₇₁	—	2	2	no	—
125	C₂²×D₂₇₁	—	4	1	no	—
126	C₂²×D₂₇₁	—	4	1	no	—
127	C₂²×D₂₇₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×D₂₇₁	C₂²×C₄	1	1	yes	characteristic
129	C₂²×D₂₇₁	C₂²×C₄	1	1	yes	characteristic
130	D₁₀₈₄	—	2	2	no	—
131	C₂²⋊D₂₇₁	—	2	2	no	—
132	C₂²⋊D₂₇₁	M₁₆	1	4	yes	complemented
133	C₂×Dic₂₇₁	—	2	2	no	—
134	C₂×Dic₂₇₁	—	2	2	no	—
135	C₂×Dic₂₇₁	C₂²×C₄	1	1	yes	characteristic
136	C₂×Dic₂₇₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×Dic₂₇₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₂₇₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×Dic₂₇₁	C₂²×C₄	1	1	yes	characteristic
140	C₄×D₂₇₁	—	2	2	no	—
141	C₄×D₂₇₁	—	2	2	no	—
142	C₄×D₂₇₁	—	2	1	no	—
143	C₄×D₂₇₁	—	2	1	no	—
144	C₄×D₂₇₁	—	2	1	no	—
145	C₄×D₂₇₁	—	2	1	no	—
146	C₄×D₂₇₁	—	2	2	no	—
147	C₄×D₂₇₁	—	2	2	no	—
148	C₄×D₂₇₁	—	2	2	no	—
149	C₄×D₂₇₁	—	4	1	no	—
150	C₄×D₂₇₁	C₂×D₄	1	2	yes	—
151	C₄×D₂₇₁	#41	1	2	yes	—
152	C₂₇₁⋊C₈	—	2	1	no	—
153	C₂₇₁⋊C₈	—	2	1	no	—
154	C₂₇₁⋊C₈	—	2	1	no	—
155	C₂₇₁⋊C₈	C₂×D₄	1	2	yes	complemented
156	C₂³×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
157	C₂³×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
158	D₄×C₂₇₁	—	2	2	no	—
159	C₂×C₄×C₂₇₁	—	2	1	no	—
160	C₂×C₄×C₂₇₁	—	2	1	no	—
161	C₂×C₄×C₂₇₁	—	2	1	no	—
162	C₂×C₄×C₂₇₁	—	2	1	no	—
163	C₂×C₄×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
168	C₈×C₂₇₁	—	2	1	no	—
169	C₈×C₂₇₁	—	2	1	no	—
170	C₈×C₂₇₁	—	2	1	no	—
171	C₈×C₂₇₁	C₂×D₄	1	2	yes	complemented
172	C₂²×C₂₇₁	—	2	1	no	—
173	C₂²×C₂₇₁	—	2	1	no	—
174	C₂²×C₂₇₁	—	2	1	no	—
175	C₂²×C₂₇₁	—	2	1	no	—
176	C₂²×C₂₇₁	—	2	1	no	—
177	C₂²×C₂₇₁	C₂×M₁₆	1	2	yes	complemented
178	C₂²×C₂₇₁	C₂³×C₄	1	1	yes	characteristic
179	C₂×D₂₇₁	—	2	1	no	—
180	C₂×D₂₇₁	—	2	1	no	—
181	C₂×D₂₇₁	—	2	1	no	—
182	C₂×D₂₇₁	—	2	1	no	—
183	C₂×D₂₇₁	—	2	1	no	—
184	C₂×D₂₇₁	—	2	1	no	—
185	C₂×D₂₇₁	—	2	1	no	—
186	C₂×D₂₇₁	—	4	4	no	—
187	C₂×D₂₇₁	—	4	4	no	—
188	C₂×D₂₇₁	C₄×D₄	1	2	yes	—
189	C₂×D₂₇₁	C₂×M₁₆	1	2	yes	complemented
190	C₄×C₂₇₁	—	2	1	no	—
191	C₄×C₂₇₁	—	2	1	no	—
192	C₄×C₂₇₁	—	2	1	no	—
193	C₄×C₂₇₁	—	2	1	no	—
194	C₄×C₂₇₁	C₂²×D₄	1	1	yes	characteristic
195	C₄×C₂₇₁	C₂×#41	1	1	yes	characteristic
196	Dic₂₇₁	—	2	1	no	—
197	Dic₂₇₁	—	2	1	no	—
198	Dic₂₇₁	—	2	1	no	—
199	Dic₂₇₁	C₄×D₄	1	2	yes	—
200	Dic₂₇₁	C₂×M₁₆	1	2	yes	complemented
201	C₂×C₂₇₁	—	2	2	no	—
202	C₂×C₂₇₁	—	4	1	no	—
203	C₂×C₂₇₁	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂×C₂₇₁	C₂²×M₁₆	1	1	yes	characteristic
205	C₂×C₂₇₁	#568	1	1	yes	characteristic
206	D₂₇₁	—	2	2	no	—
207	D₂₇₁	—	2	2	no	—
208	D₂₇₁	—	4	1	no	—
209	C₂₇₁	D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
210	D₄×M₁₆	—	271	1	no	maximal, Sylow
211	C₂²×M₁₆	—	271	1	no	—
212	C₂²×M₁₆	—	271	1	no	—
213	C₂×C₄×D₄	—	271	1	no	—
214	#436	—	271	1	no	—
215	#436	—	271	1	no	—
216	#435	—	271	1	no	—
217	#435	—	271	1	no	—
218	#435	—	271	1	no	—
219	#435	D₂₇₁	1	1	yes	characteristic, complemented
220	C₈×D₄	—	271	1	no	—
221	C₈×D₄	—	271	1	no	—
222	#423	—	271	1	no	—
223	#407	—	271	1	no	—
224	#407	—	271	1	no	—
225	C₄×M₁₆	—	271	1	no	—
226	C₂²×D₄	—	271	1	no	—
227	C₂³×C₄	—	271	1	no	—
228	C₂³×C₄	—	271	1	no	—
229	C₂×M₁₆	—	271	1	no	—
230	C₂×M₁₆	—	271	1	no	—
231	C₂×M₁₆	—	271	1	no	—
232	C₂×M₁₆	—	271	1	no	—
233	C₂×M₁₆	—	271	1	no	—
234	C₂×M₁₆	—	271	1	no	—
235	C₂×M₁₆	—	271	1	no	—
236	C₂×M₁₆	—	542	4	no	—
237	C₂×M₁₆	—	542	4	no	—
238	C₂×M₁₆	C₂×D₂₇₁	1	1	yes	characteristic, complemented
239	C₂²×C₈	—	271	1	no	—
240	C₂²×C₈	—	271	1	no	—
241	C₂²×C₈	—	271	1	no	—
242	C₂²×C₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
243	C₄×D₄	—	271	1	no	—
244	C₄×D₄	—	271	1	no	—
245	C₄×D₄	—	271	1	no	—
246	C₄×D₄	—	271	1	no	—
247	C₄×D₄	—	271	1	no	—
248	C₄×D₄	—	271	1	no	—
249	C₄×D₄	—	271	1	no	—
250	C₄×D₄	C₂×D₂₇₁	1	1	yes	characteristic
251	C₂×C₄⋊C₄	—	271	1	no	—
252	C₂×C₂²⋊C₄	—	271	1	no	—
253	C₂×C₂²⋊C₄	—	271	1	no	—
254	C₂×C₄²	—	271	1	no	—
255	C₄⋊C₈	—	271	1	no	—
256	C₄⋊C₈	—	271	1	no	—
257	C₄⋊C₈	—	271	1	no	—
258	C₄⋊C₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
259	C₂²⋊C₈	—	271	1	no	—
260	C₂²⋊C₈	—	271	1	no	—
261	C₂²⋊C₈	—	271	1	no	—
262	C₂²⋊C₈	—	271	1	no	—
263	C₂²⋊C₈	—	271	1	no	—
264	C₂²⋊C₈	—	271	1	no	—
265	C₂²⋊C₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
266	C₂²⋊C₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
267	#97	—	271	1	no	—
268	#97	C₂×D₂₇₁	1	1	yes	characteristic, complemented
269	C₄×C₈	—	271	1	no	—
270	C₄×C₈	—	271	1	no	—
271	C₂⁴	—	271	1	no	—
272	C₂⁴	—	271	1	no	—
273	C₂×D₄	—	271	1	no	—
274	C₂×D₄	—	271	1	no	—
275	C₂×D₄	—	271	1	no	—
276	C₂×D₄	—	542	4	no	—
277	C₂×D₄	C₄×D₂₇₁	1	1	yes	characteristic
278	C₂²×C₄	—	271	1	no	—
279	C₂²×C₄	—	271	1	no	—
280	C₂²×C₄	—	271	1	no	—
281	C₂²×C₄	—	271	1	no	—
282	C₂²×C₄	—	271	1	no	—
283	C₂²×C₄	—	271	1	no	—
284	C₂²×C₄	—	271	1	no	—
285	C₂²×C₄	—	271	1	no	—
286	C₂²×C₄	—	271	1	no	—
287	C₂²×C₄	—	271	1	no	—
288	C₂²×C₄	—	271	1	no	—
289	C₂²×C₄	—	542	2	no	—
290	C₂²×C₄	—	542	2	no	—
291	C₂²×C₄	—	542	2	no	—
292	C₂²×C₄	—	542	2	no	—
293	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
294	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
295	M₁₆	—	2	2	no	—
296	M₁₆	—	271	4	no	—
297	M₁₆	—	542	2	no	—
298	M₁₆	—	542	2	no	—
299	M₁₆	—	542	2	no	—
300	M₁₆	—	542	2	no	—
301	M₁₆	—	542	2	no	—
302	M₁₆	—	542	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	271	1	no	—
305	C₂×C₈	—	271	1	no	—
306	C₂×C₈	—	271	1	no	—
307	C₂×C₈	—	271	1	no	—
308	C₂×C₈	—	542	2	no	—
309	C₂×C₈	—	542	2	no	—
310	C₂×C₈	—	542	2	no	—
311	C₂×C₈	C₂²×D₂₇₁	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₂₇₁	1	1	yes	characteristic
313	C₂×C₈	C₂²×D₂₇₁	1	1	yes	characteristic
314	C₂×C₈	C₂²×D₂₇₁	1	1	yes	characteristic
315	C₄⋊C₄	—	271	1	no	—
316	C₄⋊C₄	—	271	1	no	—
317	C₄⋊C₄	—	271	1	no	—
318	C₄⋊C₄	C₄×D₂₇₁	1	1	yes	characteristic
319	C₂²⋊C₄	—	271	1	no	—
320	C₂²⋊C₄	—	271	1	no	—
321	C₂²⋊C₄	—	271	1	no	—
322	C₂²⋊C₄	—	271	1	no	—
323	C₂²⋊C₄	—	271	1	no	—
324	C₂²⋊C₄	—	271	1	no	—
325	C₂²⋊C₄	C₄×D₂₇₁	1	1	yes	characteristic
326	C₂²⋊C₄	C₄×D₂₇₁	1	1	yes	characteristic
327	C₄²	—	271	1	no	—
328	C₄²	—	271	1	no	—
329	C₄²	—	271	1	no	—
330	C₄²	C₂²×D₂₇₁	1	1	yes	characteristic
331	C₂³	—	271	1	no	—
332	C₂³	—	271	1	no	—
333	C₂³	—	271	1	no	—
334	C₂³	—	542	2	no	—
335	C₂³	—	542	2	no	—
336	C₂³	—	542	2	no	—
337	C₂³	—	542	2	no	—
338	C₂³	—	1084	1	no	—
339	C₂³	—	1084	1	no	—
340	C₂³	C₂×C₄×D₂₇₁	1	1	yes	characteristic
341	C₂³	C₂×C₄×D₂₇₁	1	1	yes	characteristic
342	D₄	—	2	2	no	—
343	D₄	—	271	4	no	—
344	D₄	—	542	2	no	—
345	D₄	—	542	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	271	1	no	—
351	C₂×C₄	—	271	1	no	—
352	C₂×C₄	—	271	2	no	—
353	C₂×C₄	—	271	2	no	—
354	C₂×C₄	—	271	1	no	—
355	C₂×C₄	—	271	1	no	—
356	C₂×C₄	—	271	1	no	—
357	C₂×C₄	—	542	2	no	—
358	C₂×C₄	—	542	2	no	—
359	C₂×C₄	—	542	2	no	—
360	C₂×C₄	—	542	2	no	—
361	C₂×C₄	—	542	2	no	—
362	C₂×C₄	—	542	2	no	—
363	C₂×C₄	—	542	2	no	—
364	C₂×C₄	—	542	1	no	—
365	C₂×C₄	—	542	1	no	—
366	C₂×C₄	—	542	1	no	—
367	C₂×C₄	—	542	1	no	—
368	C₂×C₄	—	1084	1	no	—
369	C₂×C₄	C₂×C₄×D₂₇₁	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄×D₂₇₁	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×D₂₇₁	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×D₂₇₁	1	1	yes	characteristic
373	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	271	2	no	—
378	C₈	—	542	1	no	—
379	C₈	—	542	1	no	—
380	C₈	—	542	1	no	—
381	C₈	D₄×D₂₇₁	1	2	yes	complemented
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	271	2	no	—
388	C₂²	—	271	2	no	—
389	C₂²	—	542	1	no	—
390	C₂²	—	542	1	no	—
391	C₂²	—	542	1	no	—
392	C₂²	—	542	1	no	—
393	C₂²	—	542	1	no	—
394	C₂²	—	542	1	no	—
395	C₂²	—	542	1	no	—
396	C₂²	—	1084	4	no	—
397	C₂²	—	1084	4	no	—
398	C₂²	M₁₆×D₂₇₁	1	2	yes	complemented
399	C₂²	C₂²×C₄×D₂₇₁	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	271	2	no	—
405	C₄	—	271	2	no	—
406	C₄	—	542	1	no	—
407	C₄	—	542	1	no	—
408	C₄	—	542	1	no	—
409	C₄	C₂×D₄×D₂₇₁	1	1	yes	characteristic
410	C₄	#41×D₂₇₁	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	4	1	no	—
413	C₂	—	542	2	no	—
414	C₂	—	542	2	no	—
415	C₂	—	1084	1	no	—
416	C₂	C₄×D₄×D₂₇₁	1	1	yes	characteristic
417	C₂	C₂×M₁₆×D₂₇₁	1	1	yes	characteristic
418	C₂	#31774662	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₇₁
commutator, socle	C₂²×C₂₇₁	C₂³×C₄
Fitting	#435×C₂₇₁	C₂
prime radical	C₂×D₄×D₂₇₁	C₄
cosocle	C₂×C₄×C₂₇₁	C₂⁴
hypercenter	#435	D₂₇₁
hypocenter	C₂₇₁	D₄×M₁₆
LCS	G ▷ C₂²×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂²×#16864637	C₂	semidirect
2. C₂×M₁₆×D₂₇₁	C₂	semidirect
4. #31773973	C₂	semidirect
5. #31773972	C₂	semidirect
6. #31773970	C₂	semidirect
7. #31773969	C₂	semidirect
8. #31773967	C₂	semidirect
9. C₈×C₂²⋊D₂₇₁	C₂	semidirect
10. (C₂²⋊D₂₇₁)⋊C₈	C₂	semidirect
11. #31773919	C₂	semidirect
12. #31773859	C₂	semidirect
13. #31773859	C₂	semidirect
14. #31773849	C₂	semidirect
15. #435×C₂₇₁	C₂	semidirect
19. C₂×#16864638	C₂²	semidirect
25. C₂×#16864637	C₂²	semidirect
26. C₂×#16864637	C₂²	semidirect
28. C₂²×C₂₇₁⋊C₈	C₂²	semidirect
29. C₂×C₈×D₂₇₁	C₂²	semidirect
30. C₂×C₈×D₂₇₁	C₂²	semidirect
42. C₄⋊(C₂₇₁⋊C₈)	C₂²	semidirect
43. Dic₂₇₁⋊C₈	C₂²	semidirect
44. Dic₂₇₁⋊C₈	C₂²	semidirect
45. C₂²⋊(C₂₇₁⋊C₈)	C₂²	semidirect
46. C₂²⋊(C₂₇₁⋊C₈)	C₂²	semidirect
47. (C₂×D₂₇₁)⋊C₈	C₂²	semidirect
48. (C₂×D₂₇₁)⋊C₈	C₂²	semidirect
49. (C₂×D₂₇₁)⋊C₈	C₂²	semidirect
50. (C₂×D₂₇₁)⋊C₈	C₂²	semidirect
51. #22576071	C₂²	semidirect
52. C₈×Dic₂₇₁	C₂²	semidirect
53. C₈×Dic₂₇₁	C₂²	semidirect
54. C₂×M₁₆×C₂₇₁	C₂²	semidirect
55. C₂²×C₈×C₂₇₁	C₂²	semidirect
57. C₄⋊C₈×C₂₇₁	C₂²	semidirect
58. C₂²⋊C₈×C₂₇₁	C₂²	semidirect
59. C₂²⋊C₈×C₂₇₁	C₂²	semidirect
60. #97×C₂₇₁	C₂²	semidirect
88. #16864637	D₄	semidirect
132. C₂²⋊D₂₇₁	M₁₆	semidirect
155. C₂₇₁⋊C₈	C₂×D₄	semidirect
171. C₈×C₂₇₁	C₂×D₄	semidirect
177. C₂²×C₂₇₁	C₂×M₁₆	semidirect
189. C₂×D₂₇₁	C₂×M₁₆	semidirect
200. Dic₂₇₁	C₂×M₁₆	semidirect
209. C₂₇₁	D₄×M₁₆	semidirect
219. #435	D₂₇₁	semidirect
238. C₂×M₁₆	C₂×D₂₇₁	semidirect
242. C₂²×C₈	C₂×D₂₇₁	semidirect
258. C₄⋊C₈	C₂×D₂₇₁	semidirect
265. C₂²⋊C₈	C₂×D₂₇₁	semidirect
266. C₂²⋊C₈	C₂×D₂₇₁	semidirect
268. #97	C₂×D₂₇₁	semidirect
381. C₈	D₄×D₂₇₁	semidirect
398. C₂²	M₁₆×D₂₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#16864637	2
C₂×M₁₆×D₂₇₁	2
C₄×D₄×D₂₇₁	2
#31773973	2
#31773972	2
#31773970	2
#31773969	2
#31773967	2
C₈×C₂²⋊D₂₇₁	2
(C₂²⋊D₂₇₁)⋊C₈	2
#31773919	2
#31773859	2
#31773849	2
#435×C₂₇₁	2
D₄×M₁₆	271