Subgroups — #552×D₂₇₁ #46849867

Order 34688.

1124 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31774589	C₂	1	1	yes	maximal, characteristic, complemented
2	#31774588	C₂	1	1	yes	maximal, characteristic, complemented
3	#31774587	C₂	1	1	yes	maximal, characteristic, complemented
4	#31774586	C₂	1	1	yes	maximal, characteristic, complemented
5	#31774585	C₂	1	1	yes	maximal, characteristic, complemented
6	#31774584	C₂	1	2	yes	maximal, complemented
7	#31774583	C₂	1	2	yes	maximal, complemented
8	#31774582	C₂	1	1	yes	maximal, characteristic, complemented
9	#31774581	C₂	1	1	yes	maximal, characteristic, complemented
10	#31774580	C₂	1	2	yes	maximal, complemented
11	#31774579	C₂	1	2	yes	maximal, complemented
12	#126×D₂₇₁	C₂	1	2	yes	maximal, complemented
13	#125×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#125×D₂₇₁	C₂	1	2	yes	maximal, complemented
15	#123×D₂₇₁	C₂	1	2	yes	maximal
16	C₂²⋊Q₈×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²⋊Q₈×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×Q₈×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₄×D₂₇₁	C₂	1	1	yes	maximal, characteristic
20	#117×D₂₇₁	C₂	1	2	yes	maximal, complemented
21	#117×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄⋊C₄×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₂₇₁	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₂₇₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₂₇₁	C₂²	1	2	yes	—
27	C₂²×C₄×D₂₇₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₂₇₁	C₂²	1	1	yes	characteristic
29	#22576155	C₂²	1	2	yes	complemented
30	#22576155	C₂²	1	2	yes	complemented
31	#22576155	C₂²	1	2	yes	complemented
32	#22576154	C₂²	1	2	yes	complemented
33	#22576153	C₂²	1	2	yes	complemented
34	#22576153	C₂²	1	2	yes	complemented
35	#22576153	C₂²	1	2	yes	complemented
36	#22576152	C₂²	1	2	yes	complemented
37	#22576152	C₂²	1	1	yes	characteristic, complemented
38	#22576151	C₂²	1	1	yes	characteristic, complemented
39	#22576151	C₂²	1	2	yes	complemented
40	#22576151	C₂²	1	2	yes	complemented
41	#22576151	C₂²	1	1	yes	characteristic, complemented
42	#22576150	C₂²	1	2	yes	complemented
43	#22576150	C₂²	1	2	yes	complemented
44	#22576150	C₂²	1	2	yes	complemented
45	#22576150	C₂²	1	2	yes	complemented
46	#22576150	C₂²	1	2	yes	complemented
47	#22576150	C₂²	1	2	yes	complemented
48	#22576145	C₂²	1	2	yes	—
49	#22576145	C₂²	1	2	yes	—
50	#22576144	C₂²	1	2	yes	—
51	#22576143	C₂²	1	2	yes	—
52	#22576142	C₂²	1	2	yes	—
53	#22576142	C₂²	1	2	yes	—
54	#22576141	C₂²	1	2	yes	—
55	#22576140	C₂²	1	1	yes	characteristic, complemented
56	#22576140	C₂²	1	1	yes	characteristic, complemented
57	#22576139	C₂²	1	1	yes	characteristic, complemented
58	#22576139	C₂²	1	1	yes	characteristic, complemented
59	#22576138	C₂²	1	2	yes	complemented
60	#22576138	C₂²	1	2	yes	complemented
61	#22576137	C₂²	1	2	yes	complemented
62	#22576137	C₂²	1	2	yes	complemented
63	#22576136	C₂²	1	1	yes	characteristic, complemented
64	#22576136	C₂²	1	1	yes	characteristic, complemented
65	Q₈×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
66	C₄×Dic₅₄₂	C₂²	1	2	yes	complemented
67	C₄×Dic₅₄₂	C₂²	1	1	yes	characteristic, complemented
68	#22576125	C₂²	1	2	yes	complemented
69	#22576125	C₂²	1	1	yes	characteristic, complemented
70	C₄×D₁₀₈₄	C₂²	1	1	yes	characteristic
71	D₄×Dic₂₇₁	C₂²	1	1	yes	characteristic
72	#22576122	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
75	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
76	(C₂²⋊D₂₇₁)⋊C₄	C₂²	1	1	yes	characteristic
77	#22576119	C₂²	1	1	yes	characteristic, complemented
78	#22576119	C₂²	1	2	yes	complemented
79	#22576118	C₂²	1	2	yes	complemented
80	#22576118	C₂²	1	1	yes	characteristic, complemented
81	#22576118	C₂²	1	2	yes	complemented
82	#22576118	C₂²	1	1	yes	characteristic, complemented
83	#22576117	C₂²	1	2	yes	complemented
84	#22576117	C₂²	1	2	yes	complemented
85	#22576117	C₂²	1	2	yes	complemented
86	#22576116	C₂²	1	2	yes	complemented
87	#22576116	C₂²	1	2	yes	complemented
88	#22576116	C₂²	1	2	yes	complemented
89	C₂×C₄⋊Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
90	C₂×Dic₂₇₁⋊C₄	C₂²	1	2	yes	complemented
91	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
92	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
93	C₄⋊C₄×D₂₇₁	C₂²	1	2	yes	—
94	C₄⋊C₄×D₂₇₁	C₂²	1	2	yes	—
95	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
96	C₄⋊C₄×D₂₇₁	C₂²	1	2	yes	—
97	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
98	C₄⋊C₄×D₂₇₁	C₂²	1	2	yes	—
99	C₄⋊C₄×D₂₇₁	C₂²	1	2	yes	—
100	C₄⋊C₄×D₂₇₁	C₂²	1	2	yes	—
101	C₄⋊C₄×D₂₇₁	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic, complemented
104	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
105	C₂²⋊C₄×D₂₇₁	C₂²	1	2	yes	—
106	C₂²⋊C₄×D₂₇₁	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₂₇₁	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₂₇₁	C₂²	1	2	yes	—
109	C₄²×D₂₇₁	C₂²	1	2	yes	—
110	C₄²×D₂₇₁	C₂²	1	2	yes	—
111	C₄²×D₂₇₁	C₂²	1	1	yes	characteristic
112	#126×C₂₇₁	C₂²	1	2	yes	complemented
113	#125×C₂₇₁	C₂²	1	2	yes	complemented
114	#125×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
115	#123×C₂₇₁	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₂₇₁	C₂²	1	1	yes	characteristic
120	#117×C₂₇₁	C₂²	1	2	yes	complemented
121	#117×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₂₇₁	C₂³	1	1	yes	characteristic
124	C₂³×D₂₇₁	C₂³	1	1	yes	characteristic
125	C₂×Dic₅₄₂	C₂³	1	2	yes	—
126	C₂×Dic₅₄₂	C₂³	1	1	yes	characteristic
127	Q₈×D₂₇₁	—	2	4	no	—
128	C₂×D₁₀₈₄	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₂₇₁	C₂³	1	1	yes	characteristic
131	D₄×D₂₇₁	—	2	4	no	—
132	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
133	C₂²×Dic₂₇₁	C₂³	1	1	yes	characteristic
134	C₂²×Dic₂₇₁	C₂³	1	2	yes	—
135	C₂×C₄×D₂₇₁	—	2	8	no	—
136	C₂×C₄×D₂₇₁	—	2	4	no	—
137	C₂×C₄×D₂₇₁	—	2	4	no	—
138	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₂₇₁	C₂³	1	2	yes	—
143	C₂×C₄×D₂₇₁	C₂³	1	2	yes	—
144	C₂×C₄×D₂₇₁	C₂³	1	2	yes	—
145	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₂₇₁	C₂³	1	2	yes	—
147	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₂₇₁	C₂³	1	2	yes	—
150	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₂₇₁	C₂³	1	2	yes	—
152	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₂₇₁	C₂³	1	2	yes	—
156	C₄⋊Dic₂₇₁	C₂³	1	2	yes	—
157	C₄⋊Dic₂₇₁	C₂³	1	2	yes	—
158	C₄⋊Dic₂₇₁	C₂³	1	2	yes	—
159	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₂₇₁	C₂³	1	2	yes	—
161	C₄⋊Dic₂₇₁	C₂³	1	2	yes	—
162	C₄⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
163	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
164	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
165	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
166	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
167	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
168	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
169	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
170	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
171	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
172	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
173	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₂₇₁⋊C₄	C₂³	1	1	yes	characteristic
175	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
176	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
177	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
178	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
179	Dic₂₇₁⋊C₄	C₂³	1	2	yes	—
180	C₂²⋊Dic₂₇₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₂₇₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₂₇₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₂₇₁	C₂³	1	1	yes	characteristic
185	(C₂×D₂₇₁)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₂₇₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₂₇₁)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₂₇₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₂₇₁)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₂₇₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₂₇₁)⋊C₄	C₂³	1	1	yes	characteristic
195	C₄×Dic₂₇₁	C₂³	1	2	yes	—
196	C₄×Dic₂₇₁	C₂³	1	2	yes	—
197	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
198	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
199	C₄×Dic₂₇₁	C₂³	1	2	yes	—
200	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
201	C₄×Dic₂₇₁	C₂³	1	2	yes	—
202	C₄×Dic₂₇₁	C₂³	1	2	yes	—
203	C₄×Dic₂₇₁	C₂³	1	2	yes	—
204	C₂×Q₈×C₂₇₁	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₂₇₁	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₂₇₁	C₂³	1	2	yes	—
209	C₄⋊C₄×C₂₇₁	C₂³	1	2	yes	—
210	C₄⋊C₄×C₂₇₁	C₂³	1	2	yes	—
211	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₂₇₁	C₂³	1	2	yes	—
214	C₄⋊C₄×C₂₇₁	C₂³	1	2	yes	—
215	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₂₇₁	C₂³	1	2	yes	—
217	C₄⋊C₄×C₂₇₁	C₂³	1	2	yes	—
218	C₄⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₂₇₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₂₇₁	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₂₇₁	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₂₇₁	C₂³	1	1	yes	characteristic
224	C₄²×C₂₇₁	C₂³	1	2	yes	—
225	C₄²×C₂₇₁	C₂³	1	1	yes	characteristic
226	C₄²×C₂₇₁	C₂³	1	2	yes	—
227	C₂²×D₂₇₁	—	2	2	no	—
228	C₂²×D₂₇₁	—	2	2	no	—
229	C₂²×D₂₇₁	—	2	2	no	—
230	C₂²×D₂₇₁	—	2	2	no	—
231	C₂²×D₂₇₁	—	2	2	no	—
232	C₂²×D₂₇₁	#41	1	4	yes	—
233	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
234	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
235	C₂²×D₂₇₁	C₂⁴	1	1	yes	characteristic
236	Dic₅₄₂	—	2	2	no	—
237	Dic₅₄₂	—	2	4	no	—
238	D₁₀₈₄	—	2	2	no	—
239	C₂²⋊D₂₇₁	—	2	2	no	—
240	C₂²⋊D₂₇₁	—	2	2	no	—
241	C₂×Dic₂₇₁	—	2	4	no	—
242	C₂×Dic₂₇₁	—	2	2	no	—
243	C₂×Dic₂₇₁	—	2	2	no	—
244	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₂₇₁	C₂⁴	1	2	yes	—
247	C₂×Dic₂₇₁	C₂⁴	1	2	yes	—
248	C₂×Dic₂₇₁	C₂⁴	1	2	yes	—
249	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₂₇₁	C₂⁴	1	2	yes	—
251	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₂₇₁	C₂⁴	1	1	yes	characteristic
253	C₄×D₂₇₁	—	2	4	no	—
254	C₄×D₂₇₁	—	2	4	no	—
255	C₄×D₂₇₁	—	2	4	no	—
256	C₄×D₂₇₁	—	2	4	no	—
257	C₄×D₂₇₁	—	2	2	no	—
258	C₄×D₂₇₁	—	2	2	no	—
259	C₄×D₂₇₁	—	2	2	no	—
260	C₄×D₂₇₁	—	2	4	no	—
261	C₄×D₂₇₁	—	2	2	no	—
262	C₄×D₂₇₁	—	2	4	no	—
263	C₄×D₂₇₁	—	2	2	no	—
264	C₄×D₂₇₁	—	2	2	no	—
265	C₄×D₂₇₁	—	2	2	no	—
266	C₄×D₂₇₁	—	2	2	no	—
267	C₄×D₂₇₁	#41	1	4	yes	—
268	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
269	C₂³×C₂₇₁	C₂⁴	1	1	yes	characteristic
270	Q₈×C₂₇₁	—	2	2	no	—
271	D₄×C₂₇₁	—	2	2	no	—
272	C₂×C₄×C₂₇₁	—	2	4	no	—
273	C₂×C₄×C₂₇₁	—	2	2	no	—
274	C₂×C₄×C₂₇₁	—	2	2	no	—
275	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₂₇₁	C₂⁴	1	2	yes	—
278	C₂×C₄×C₂₇₁	C₂⁴	1	2	yes	—
279	C₂×C₄×C₂₇₁	C₂⁴	1	2	yes	—
280	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₂₇₁	C₂⁴	1	2	yes	—
282	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
284	C₂²×C₂₇₁	—	2	1	no	—
285	C₂²×C₂₇₁	—	2	1	no	—
286	C₂²×C₂₇₁	—	2	1	no	—
287	C₂²×C₂₇₁	—	2	1	no	—
288	C₂²×C₂₇₁	—	2	1	no	—
289	C₂²×C₂₇₁	C₂×#41	1	2	yes	—
290	C₂²×C₂₇₁	C₂⁵	1	1	yes	characteristic
291	C₂×D₂₇₁	—	2	1	no	—
292	C₂×D₂₇₁	—	2	1	no	—
293	C₂×D₂₇₁	—	2	8	no	—
294	C₂×D₂₇₁	—	2	1	no	—
295	C₂×D₂₇₁	—	2	1	no	—
296	C₂×D₂₇₁	—	2	1	no	—
297	C₂×D₂₇₁	—	4	4	no	—
298	C₂×D₂₇₁	C₂×#41	1	2	yes	—
299	C₂×D₂₇₁	C₂×#41	1	2	yes	—
300	C₂×D₂₇₁	C₂×#41	1	2	yes	—
301	C₂×D₂₇₁	2₋¹⁺⁴	1	2	yes	—
302	C₄×C₂₇₁	—	2	2	no	—
303	C₄×C₂₇₁	—	2	2	no	—
304	C₄×C₂₇₁	—	2	1	no	—
305	C₄×C₂₇₁	—	2	1	no	—
306	C₄×C₂₇₁	—	2	1	no	—
307	C₄×C₂₇₁	—	2	2	no	—
308	C₄×C₂₇₁	—	2	1	no	—
309	C₄×C₂₇₁	—	2	2	no	—
310	C₄×C₂₇₁	C₂×#41	1	2	yes	—
311	Dic₂₇₁	—	2	2	no	—
312	Dic₂₇₁	—	2	2	no	—
313	Dic₂₇₁	—	2	1	no	—
314	Dic₂₇₁	—	2	1	no	—
315	Dic₂₇₁	—	2	1	no	—
316	Dic₂₇₁	—	2	2	no	—
317	Dic₂₇₁	—	2	1	no	—
318	Dic₂₇₁	—	2	2	no	—
319	Dic₂₇₁	C₂×#41	1	2	yes	—
320	C₂×C₂₇₁	—	2	2	no	—
321	C₂×C₂₇₁	—	4	1	no	—
322	C₂×C₂₇₁	C₂²×#41	1	1	yes	characteristic
323	C₂×C₂₇₁	C₂²×#41	1	1	yes	characteristic
324	C₂×C₂₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
325	D₂₇₁	—	2	2	no	—
326	D₂₇₁	—	4	1	no	—
327	D₂₇₁	#552	1	4	yes	direct product factor
328	C₂₇₁	C₂×#552	1	1	yes	characteristic, complemented, Sylow
329	C₂×#552	—	271	1	no	maximal, Sylow
330	#552	—	271	2	no	—
331	#552	—	271	2	no	—
332	#552	—	271	1	no	—
333	#552	—	271	2	no	—
334	#552	—	271	1	no	—
335	#552	—	271	1	no	—
336	#552	—	271	1	no	—
337	#552	—	271	1	no	—
338	#552	—	271	2	no	—
339	#552	—	271	1	no	—
340	#552	—	271	1	no	—
341	#552	D₂₇₁	1	1	yes	characteristic, direct product factor
342	C₂×#126	—	271	2	no	—
343	C₂×#125	—	271	2	no	—
344	C₂×#125	—	271	1	no	—
345	C₂×#123	—	271	2	no	—
346	C₂×C₂²⋊Q₈	—	271	1	no	—
347	C₂×C₂²⋊Q₈	—	271	1	no	—
348	C₂×C₄×Q₈	—	271	1	no	—
349	C₂×C₄×D₄	—	271	1	no	—
350	C₂×#117	—	271	1	no	—
351	C₂×#117	—	271	2	no	—
352	C₂²×C₄⋊C₄	—	271	1	no	—
353	C₂²×Q₈	—	271	1	no	—
354	C₂²×D₄	—	271	1	no	—
355	C₂³×C₄	—	271	2	no	—
356	C₂³×C₄	—	271	1	no	—
357	C₂³×C₄	—	271	1	no	—
358	#126	—	271	2	no	—
359	#126	—	271	2	no	—
360	#126	—	271	2	no	—
361	#126	—	271	2	no	—
362	#126	—	271	2	no	—
363	#126	—	271	2	no	—
364	#126	—	271	2	no	—
365	#126	C₂×D₂₇₁	1	2	yes	complemented
366	#125	—	271	2	no	—
367	#125	—	271	2	no	—
368	#125	—	271	2	no	—
369	#125	—	271	2	no	—
370	#125	—	271	2	no	—
371	#125	—	271	2	no	—
372	#125	—	271	2	no	—
373	#125	—	271	2	no	—
374	#125	—	271	1	no	—
375	#125	—	271	1	no	—
376	#125	—	271	2	no	—
377	#125	—	271	1	no	—
378	#125	C₂×D₂₇₁	1	2	yes	complemented
379	#125	C₂×D₂₇₁	1	1	yes	characteristic, complemented
380	#123	—	271	2	no	—
381	#123	—	271	2	no	—
382	#123	—	271	2	no	—
383	#123	—	271	2	no	—
384	#123	—	271	2	no	—
385	#123	—	271	2	no	—
386	#123	—	271	2	no	—
387	#123	C₂×D₂₇₁	1	2	yes	—
388	C₂²⋊Q₈	—	271	1	no	—
389	C₂²⋊Q₈	—	271	1	no	—
390	C₂²⋊Q₈	—	271	1	no	—
391	C₂²⋊Q₈	—	271	1	no	—
392	C₂²⋊Q₈	—	271	2	no	—
393	C₂²⋊Q₈	—	271	2	no	—
394	C₂²⋊Q₈	—	271	1	no	—
395	C₂²⋊Q₈	—	271	1	no	—
396	C₂²⋊Q₈	—	271	2	no	—
397	C₂²⋊Q₈	—	271	2	no	—
398	C₂²⋊Q₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
399	C₂²⋊Q₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
400	C₄×Q₈	—	271	1	no	—
401	C₄×Q₈	—	271	2	no	—
402	C₄×Q₈	—	271	1	no	—
403	C₄×Q₈	—	271	1	no	—
404	C₄×Q₈	—	271	2	no	—
405	C₄×Q₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
406	C₄×D₄	—	271	1	no	—
407	C₄×D₄	—	271	1	no	—
408	C₄×D₄	—	271	1	no	—
409	C₄×D₄	—	271	1	no	—
410	C₄×D₄	—	271	1	no	—
411	C₄×D₄	—	271	1	no	—
412	C₄×D₄	—	271	1	no	—
413	C₄×D₄	C₂×D₂₇₁	1	1	yes	characteristic
414	#117	—	271	1	no	—
415	#117	—	271	2	no	—
416	#117	—	271	1	no	—
417	#117	—	271	1	no	—
418	#117	—	271	2	no	—
419	#117	—	271	2	no	—
420	#117	—	271	2	no	—
421	#117	—	271	2	no	—
422	#117	—	271	2	no	—
423	#117	—	271	2	no	—
424	#117	—	271	2	no	—
425	#117	—	271	2	no	—
426	#117	C₂×D₂₇₁	1	1	yes	characteristic, complemented
427	#117	C₂×D₂₇₁	1	2	yes	complemented
428	C₂×C₄⋊C₄	—	271	2	no	—
429	C₂×C₄⋊C₄	—	271	1	no	—
430	C₂×C₄⋊C₄	—	271	1	no	—
431	C₂×C₄⋊C₄	—	271	1	no	—
432	C₂×C₄⋊C₄	—	271	2	no	—
433	C₂×C₄⋊C₄	—	271	2	no	—
434	C₂×C₄⋊C₄	—	271	1	no	—
435	C₂×C₄⋊C₄	—	271	1	no	—
436	C₂×C₄⋊C₄	—	271	1	no	—
437	C₂×C₄⋊C₄	—	271	2	no	—
438	C₂×C₄⋊C₄	—	271	2	no	—
439	C₂×C₄⋊C₄	—	271	1	no	—
440	C₂×C₄⋊C₄	—	271	2	no	—
441	C₂×C₄⋊C₄	—	271	2	no	—
442	C₂×C₄⋊C₄	—	271	2	no	—
443	C₂×C₄⋊C₄	C₂×D₂₇₁	1	1	yes	characteristic, complemented
444	C₂×C₂²⋊C₄	—	271	1	no	—
445	C₂×C₂²⋊C₄	—	271	2	no	—
446	C₂×C₂²⋊C₄	—	271	2	no	—
447	C₂×C₂²⋊C₄	—	271	1	no	—
448	C₂×C₂²⋊C₄	—	271	2	no	—
449	C₂×C₄²	—	271	2	no	—
450	C₂×C₄²	—	271	2	no	—
451	C₂×C₄²	—	271	1	no	—
452	C₂⁴	—	271	1	no	—
453	C₂⁴	—	271	1	no	—
454	C₂×Q₈	—	271	2	no	—
455	C₂×Q₈	—	271	1	no	—
456	C₂×Q₈	—	542	4	no	—
457	C₂×Q₈	C₂²×D₂₇₁	1	1	yes	characteristic
458	C₂×D₄	—	271	1	no	—
459	C₂×D₄	—	271	1	no	—
460	C₂×D₄	—	271	1	no	—
461	C₂×D₄	—	542	4	no	—
462	C₂×D₄	C₂²×D₂₇₁	1	1	yes	characteristic
463	C₂²×C₄	—	271	1	no	—
464	C₂²×C₄	—	271	2	no	—
465	C₂²×C₄	—	271	1	no	—
466	C₂²×C₄	—	271	1	no	—
467	C₂²×C₄	—	271	1	no	—
468	C₂²×C₄	—	271	1	no	—
469	C₂²×C₄	—	271	2	no	—
470	C₂²×C₄	—	271	2	no	—
471	C₂²×C₄	—	271	2	no	—
472	C₂²×C₄	—	271	1	no	—
473	C₂²×C₄	—	271	1	no	—
474	C₂²×C₄	—	271	2	no	—
475	C₂²×C₄	—	271	2	no	—
476	C₂²×C₄	—	271	2	no	—
477	C₂²×C₄	—	271	1	no	—
478	C₂²×C₄	—	271	1	no	—
479	C₂²×C₄	—	271	1	no	—
480	C₂²×C₄	—	271	1	no	—
481	C₂²×C₄	—	542	4	no	—
482	C₂²×C₄	—	542	4	no	—
483	C₂²×C₄	—	542	8	no	—
484	C₂²×C₄	C₂²×D₂₇₁	1	2	yes	—
485	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
487	C₄⋊C₄	—	271	2	no	—
488	C₄⋊C₄	—	271	1	no	—
489	C₄⋊C₄	—	271	2	no	—
490	C₄⋊C₄	—	271	2	no	—
491	C₄⋊C₄	—	271	2	no	—
492	C₄⋊C₄	—	271	1	no	—
493	C₄⋊C₄	—	271	2	no	—
494	C₄⋊C₄	—	271	2	no	—
495	C₄⋊C₄	—	271	2	no	—
496	C₄⋊C₄	—	271	2	no	—
497	C₄⋊C₄	—	271	2	no	—
498	C₄⋊C₄	—	271	2	no	—
499	C₄⋊C₄	—	271	2	no	—
500	C₄⋊C₄	—	271	1	no	—
501	C₄⋊C₄	—	271	2	no	—
502	C₄⋊C₄	—	271	1	no	—
503	C₄⋊C₄	—	271	1	no	—
504	C₄⋊C₄	—	271	1	no	—
505	C₄⋊C₄	—	271	2	no	—
506	C₄⋊C₄	—	271	2	no	—
507	C₄⋊C₄	—	271	2	no	—
508	C₄⋊C₄	—	271	2	no	—
509	C₄⋊C₄	—	271	2	no	—
510	C₄⋊C₄	—	271	2	no	—
511	C₄⋊C₄	—	271	2	no	—
512	C₄⋊C₄	—	271	2	no	—
513	C₄⋊C₄	—	271	2	no	—
514	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₂₇₁	1	2	yes	—
517	C₄⋊C₄	C₂²×D₂₇₁	1	2	yes	—
518	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₂₇₁	1	2	yes	—
520	C₄⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₂₇₁	1	2	yes	—
522	C₄⋊C₄	C₂²×D₂₇₁	1	2	yes	—
523	C₄⋊C₄	C₂²×D₂₇₁	1	2	yes	—
524	C₂²⋊C₄	—	271	1	no	—
525	C₂²⋊C₄	—	271	2	no	—
526	C₂²⋊C₄	—	271	2	no	—
527	C₂²⋊C₄	—	271	1	no	—
528	C₂²⋊C₄	—	271	2	no	—
529	C₂²⋊C₄	—	271	1	no	—
530	C₂²⋊C₄	—	271	1	no	—
531	C₂²⋊C₄	—	271	2	no	—
532	C₂²⋊C₄	—	271	2	no	—
533	C₂²⋊C₄	—	271	2	no	—
534	C₂²⋊C₄	—	271	2	no	—
535	C₂²⋊C₄	—	271	1	no	—
536	C₂²⋊C₄	—	271	1	no	—
537	C₂²⋊C₄	—	271	2	no	—
538	C₂²⋊C₄	—	271	2	no	—
539	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
540	C₂²⋊C₄	C₂²×D₂₇₁	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₂₇₁	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₂₇₁	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₂₇₁	1	2	yes	—
544	C₄²	—	271	2	no	—
545	C₄²	—	271	2	no	—
546	C₄²	—	271	2	no	—
547	C₄²	—	271	2	no	—
548	C₄²	—	271	2	no	—
549	C₄²	—	271	2	no	—
550	C₄²	—	271	1	no	—
551	C₄²	—	271	1	no	—
552	C₄²	—	271	1	no	—
553	C₄²	C₂²×D₂₇₁	1	2	yes	—
554	C₄²	C₂²×D₂₇₁	1	2	yes	—
555	C₄²	C₂²×D₂₇₁	1	1	yes	characteristic
556	C₂³	—	271	1	no	—
557	C₂³	—	271	4	no	—
558	C₂³	—	271	1	no	—
559	C₂³	—	271	1	no	—
560	C₂³	—	542	2	no	—
561	C₂³	—	542	2	no	—
562	C₂³	—	542	2	no	—
563	C₂³	—	542	2	no	—
564	C₂³	—	542	2	no	—
565	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
566	C₂³	C₂³×D₂₇₁	1	1	yes	characteristic
567	Q₈	—	2	2	no	—
568	Q₈	—	542	4	no	—
569	Q₈	—	542	2	no	—
570	D₄	—	2	2	no	—
571	D₄	—	542	2	no	—
572	D₄	—	542	2	no	—
573	D₄	—	542	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	271	1	no	—
578	C₂×C₄	—	271	4	no	—
579	C₂×C₄	—	271	1	no	—
580	C₂×C₄	—	271	1	no	—
581	C₂×C₄	—	271	2	no	—
582	C₂×C₄	—	271	2	no	—
583	C₂×C₄	—	271	2	no	—
584	C₂×C₄	—	271	1	no	—
585	C₂×C₄	—	271	1	no	—
586	C₂×C₄	—	271	2	no	—
587	C₂×C₄	—	542	2	no	—
588	C₂×C₄	—	542	2	no	—
589	C₂×C₄	—	542	2	no	—
590	C₂×C₄	—	542	2	no	—
591	C₂×C₄	—	542	4	no	—
592	C₂×C₄	—	542	4	no	—
593	C₂×C₄	—	542	4	no	—
594	C₂×C₄	—	542	4	no	—
595	C₂×C₄	—	542	2	no	—
596	C₂×C₄	—	542	4	no	—
597	C₂×C₄	—	542	2	no	—
598	C₂×C₄	—	542	4	no	—
599	C₂×C₄	—	542	2	no	—
600	C₂×C₄	—	542	2	no	—
601	C₂×C₄	—	542	4	no	—
602	C₂×C₄	—	542	2	no	—
603	C₂×C₄	—	542	2	no	—
604	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₂₇₁	1	2	yes	—
607	C₂×C₄	C₂³×D₂₇₁	1	2	yes	—
608	C₂×C₄	C₂³×D₂₇₁	1	2	yes	—
609	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₂₇₁	1	2	yes	—
612	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	271	2	no	—
619	C₂²	—	271	2	no	—
620	C₂²	—	271	2	no	—
621	C₂²	—	271	2	no	—
622	C₂²	—	542	8	no	—
623	C₂²	—	542	1	no	—
624	C₂²	—	542	1	no	—
625	C₂²	—	542	1	no	—
626	C₂²	—	542	1	no	—
627	C₂²	—	542	1	no	—
628	C₂²	—	1084	4	no	—
629	C₂²	#41×D₂₇₁	1	2	yes	—
630	C₂²	C₂⁴×D₂₇₁	1	1	yes	characteristic
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	271	2	no	—
640	C₄	—	542	2	no	—
641	C₄	—	542	2	no	—
642	C₄	—	542	1	no	—
643	C₄	—	542	1	no	—
644	C₄	—	542	1	no	—
645	C₄	—	542	2	no	—
646	C₄	—	542	1	no	—
647	C₄	—	542	2	no	—
648	C₄	#41×D₂₇₁	1	2	yes	—
649	C₂	—	2	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	271	4	no	—
652	C₂	—	542	2	no	—
653	C₂	—	1084	1	no	—
654	C₂	C₂×#41×D₂₇₁	1	1	yes	characteristic
655	C₂	C₂×#41×D₂₇₁	1	1	yes	characteristic
656	C₂	2₋¹⁺⁴×D₂₇₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₇₁
commutator, socle, cosocle	C₂²×C₂₇₁	C₂⁵
Fitting	#552×C₂₇₁	C₂
prime radical	C₂×D₄×D₂₇₁	C₂²
hypercenter	#552	D₂₇₁
hypocenter	C₂₇₁	C₂×#552
LCS	G ▷ C₂²×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #31774589	C₂	semidirect
2. #31774588	C₂	semidirect
3. #31774587	C₂	semidirect
4. #31774586	C₂	semidirect
5. #31774585	C₂	semidirect
6. #31774584	C₂	semidirect
7. #31774583	C₂	semidirect
8. #31774582	C₂	semidirect
9. #31774581	C₂	semidirect
10. #31774580	C₂	semidirect
11. #31774579	C₂	semidirect
12. #126×D₂₇₁	C₂	semidirect
13. #125×D₂₇₁	C₂	semidirect
14. #125×D₂₇₁	C₂	semidirect
16. C₂²⋊Q₈×D₂₇₁	C₂	semidirect
17. C₂²⋊Q₈×D₂₇₁	C₂	semidirect
18. C₄×Q₈×D₂₇₁	C₂	semidirect
20. #117×D₂₇₁	C₂	semidirect
21. #117×D₂₇₁	C₂	semidirect
22. C₂×C₄⋊C₄×D₂₇₁	C₂	semidirect
23. #552×C₂₇₁	C₂	semidirect
29. #22576155	C₂²	semidirect
30. #22576155	C₂²	semidirect
31. #22576155	C₂²	semidirect
32. #22576154	C₂²	semidirect
33. #22576153	C₂²	semidirect
34. #22576153	C₂²	semidirect
35. #22576153	C₂²	semidirect
36. #22576152	C₂²	semidirect
37. #22576152	C₂²	semidirect
38. #22576151	C₂²	semidirect
39. #22576151	C₂²	semidirect
40. #22576151	C₂²	semidirect
41. #22576151	C₂²	semidirect
42. #22576150	C₂²	semidirect
43. #22576150	C₂²	semidirect
44. #22576150	C₂²	semidirect
45. #22576150	C₂²	semidirect
46. #22576150	C₂²	semidirect
47. #22576150	C₂²	semidirect
55. #22576140	C₂²	semidirect
56. #22576140	C₂²	semidirect
57. #22576139	C₂²	semidirect
58. #22576139	C₂²	semidirect
59. #22576138	C₂²	semidirect
60. #22576138	C₂²	semidirect
61. #22576137	C₂²	semidirect
62. #22576137	C₂²	semidirect
63. #22576136	C₂²	semidirect
64. #22576136	C₂²	semidirect
65. Q₈×Dic₂₇₁	C₂²	semidirect
66. C₄×Dic₅₄₂	C₂²	semidirect
67. C₄×Dic₅₄₂	C₂²	semidirect
68. #22576125	C₂²	semidirect
69. #22576125	C₂²	semidirect
77. #22576119	C₂²	semidirect
78. #22576119	C₂²	semidirect
79. #22576118	C₂²	semidirect
80. #22576118	C₂²	semidirect
81. #22576118	C₂²	semidirect
82. #22576118	C₂²	semidirect
83. #22576117	C₂²	semidirect
84. #22576117	C₂²	semidirect
85. #22576117	C₂²	semidirect
86. #22576116	C₂²	semidirect
87. #22576116	C₂²	semidirect
88. #22576116	C₂²	semidirect
89. C₂×C₄⋊Dic₂₇₁	C₂²	semidirect
90. C₂×Dic₂₇₁⋊C₄	C₂²	semidirect
101. C₄⋊C₄×D₂₇₁	C₂²	semidirect
102. C₄⋊C₄×D₂₇₁	C₂²	semidirect
103. C₄⋊C₄×D₂₇₁	C₂²	semidirect
112. #126×C₂₇₁	C₂²	semidirect
113. #125×C₂₇₁	C₂²	semidirect
114. #125×C₂₇₁	C₂²	semidirect
116. C₂²⋊Q₈×C₂₇₁	C₂²	semidirect
117. C₂²⋊Q₈×C₂₇₁	C₂²	semidirect
118. C₄×Q₈×C₂₇₁	C₂²	semidirect
120. #117×C₂₇₁	C₂²	semidirect
121. #117×C₂₇₁	C₂²	semidirect
122. C₂×C₄⋊C₄×C₂₇₁	C₂²	semidirect
327. D₂₇₁	#552	direct (N × H)
328. C₂₇₁	C₂×#552	semidirect
341. #552	D₂₇₁	direct (N × H)
365. #126	C₂×D₂₇₁	semidirect
378. #125	C₂×D₂₇₁	semidirect
379. #125	C₂×D₂₇₁	semidirect
398. C₂²⋊Q₈	C₂×D₂₇₁	semidirect
399. C₂²⋊Q₈	C₂×D₂₇₁	semidirect
405. C₄×Q₈	C₂×D₂₇₁	semidirect
426. #117	C₂×D₂₇₁	semidirect
427. #117	C₂×D₂₇₁	semidirect
443. C₂×C₄⋊C₄	C₂×D₂₇₁	semidirect

Maximal subgroups

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

subgroup	index
#31774589	2
#31774588	2
#31774587	2
#31774586	2
#31774585	2
#31774584	2
#31774583	2
#31774582	2
#31774581	2
#31774580	2
#31774579	2
#126×D₂₇₁	2
#125×D₂₇₁	2
#123×D₂₇₁	2
C₂²⋊Q₈×D₂₇₁	2
C₄×Q₈×D₂₇₁	2
C₄×D₄×D₂₇₁	2
#117×D₂₇₁	2
C₂×C₄⋊C₄×D₂₇₁	2
#552×C₂₇₁	2
C₂×#552	271

Subgroups — #552×D271 #46849867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #552×D₂₇₁ #46849867