Subgroups — #16859267

Order 3968.

1132 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	#14521768	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521763	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521755	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521744	C₂	1	2	yes	maximal, complemented
5	#14521737	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521735	C₂	1	2	yes	maximal, complemented
7	#14521733	C₂	1	1	yes	maximal, characteristic, complemented
8	#14521727	C₂	1	2	yes	maximal, complemented
9	#14521724	C₂	1	2	yes	maximal, complemented
10	#14521701	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521696	C₂	1	1	yes	maximal, characteristic, complemented
12	#14521692	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521603	C₂	1	1	yes	maximal, characteristic, complemented
14	#14521581	C₂	1	2	yes	maximal, complemented
15	#14521581	C₂	1	1	yes	maximal, characteristic, complemented
16	#14521577	C₂	1	2	yes	maximal, complemented
17	#14521558	C₂	1	2	yes	maximal, complemented
18	C₄×#92499	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#92495	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#92495	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₃₁	C₂	1	2	yes	maximal, complemented
23	C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#92499	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
26	C₂×#92495	C₂²	1	1	yes	characteristic
27	C₂×#92495	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₃₁	C₂²	1	2	yes	—
29	C₃₁×#126	C₂²	1	2	yes	complemented
30	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#124	C₂²	1	1	yes	characteristic
32	C₃₁×#123	C₂²	1	2	yes	complemented
33	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#121	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
38	C₃₁×#117	C₂²	1	2	yes	complemented
39	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	#11758523	C₂²	1	1	yes	characteristic
41	Q₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
42	#11758521	C₂²	1	1	yes	characteristic, complemented
43	#11758516	C₂²	1	2	yes	complemented
44	#11758515	C₂²	1	1	yes	characteristic
45	#11758515	C₂²	1	2	yes	—
46	#11758514	C₂²	1	2	yes	—
47	#11758513	C₂²	1	1	yes	characteristic
48	#11758513	C₂²	1	2	yes	complemented
49	D₄×Dic₃₁	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
54	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
56	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
58	#11758503	C₂²	1	1	yes	characteristic, complemented
59	#11758503	C₂²	1	2	yes	complemented
60	#11758503	C₂²	1	1	yes	characteristic, complemented
61	#11758475	C₂²	1	2	yes	complemented
62	#11758474	C₂²	1	1	yes	characteristic
63	#11758474	C₂²	1	1	yes	characteristic, complemented
64	#11758474	C₂²	1	2	yes	complemented
65	#11758473	C₂²	1	2	yes	—
66	#11758473	C₂²	1	2	yes	complemented
67	#11758473	C₂²	1	2	yes	complemented
68	#11758471	C₂²	1	2	yes	—
69	#11758471	C₂²	1	2	yes	complemented
70	#11758470	C₂²	1	1	yes	characteristic
71	#11758470	C₂²	1	1	yes	characteristic
72	#11758470	C₂²	1	2	yes	complemented
73	#11758469	C₂²	1	2	yes	—
74	#11758469	C₂²	1	2	yes	—
75	#11758469	C₂²	1	2	yes	complemented
76	#11758469	C₂²	1	1	yes	characteristic, complemented
77	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₃₁	C₂²	1	2	yes	complemented
79	C₄⋊C₄×D₃₁	C₂²	1	2	yes	complemented
80	#11758467	C₂²	1	1	yes	characteristic, complemented
81	#11758467	C₂²	1	2	yes	complemented
82	#11758466	C₂²	1	2	yes	complemented
83	#11758466	C₂²	1	2	yes	complemented
84	#11758465	C₂²	1	1	yes	characteristic, complemented
85	#11758462	C₂²	1	2	yes	complemented
86	#11758461	C₂²	1	2	yes	—
87	#11758461	C₂²	1	2	yes	complemented
88	#11758460	C₂²	1	2	yes	—
89	#11758460	C₂²	1	2	yes	—
90	#11758460	C₂²	1	2	yes	—
91	#11758460	C₂²	1	2	yes	complemented
92	#11758460	C₂²	1	2	yes	complemented
93	#11758459	C₂²	1	2	yes	—
94	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	—
98	#11758456	C₂²	1	2	yes	complemented
99	#11758456	C₂²	1	2	yes	complemented
100	#11758456	C₂²	1	2	yes	complemented
101	#11758456	C₂²	1	2	yes	complemented
102	#11758455	C₂²	1	2	yes	complemented
103	#11758454	C₂²	1	2	yes	complemented
104	#11758454	C₂²	1	2	yes	complemented
105	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
106	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
107	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
108	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
109	C₄×D₁₂₄	C₂²	1	2	yes	complemented
110	#11758449	C₂²	1	2	yes	—
111	#11758449	C₂²	1	1	yes	characteristic
112	#11758449	C₂²	1	2	yes	complemented
113	#11758449	C₂²	1	1	yes	characteristic, complemented
114	C₄²×D₃₁	C₂²	1	1	yes	characteristic
115	C₄²×D₃₁	C₂²	1	2	yes	complemented
116	C₄²×D₃₁	C₂²	1	2	yes	complemented
117	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
119	C₄×Dic₆₂	C₂²	1	2	yes	complemented
120	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₃₁	C₂³	1	2	yes	—
124	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
129	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
136	C₂²×Dic₃₁	C₂³	1	2	yes	—
137	#92499	—	2	4	no	—
138	D₄×D₃₁	—	2	4	no	—
139	#92495	—	2	4	no	—
140	#92495	—	2	4	no	—
141	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
142	C₂×D₁₂₄	C₂³	1	2	yes	—
143	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₃₁	—	2	8	no	—
145	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₃₁	C₂³	1	2	yes	—
147	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₃₁	C₂³	1	2	yes	—
149	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₃₁	C₂³	1	2	yes	—
151	C₂×C₄×D₃₁	C₂³	1	2	yes	—
152	C₂×C₄×D₃₁	C₂³	1	2	yes	—
153	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₃₁	C₂³	1	2	yes	—
155	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₃₁	C₂³	1	2	yes	—
157	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
158	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
159	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
160	C₂×Dic₆₂	C₂³	1	2	yes	—
161	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₄²×C₃₁	C₂³	1	1	yes	characteristic
173	C₄²×C₃₁	C₂³	1	1	yes	characteristic
174	C₄²×C₃₁	C₂³	1	2	yes	—
175	C₄²×C₃₁	C₂³	1	1	yes	characteristic
176	C₄²×C₃₁	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
184	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
196	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₃₁	C₂³	1	2	yes	—
201	C₄⋊Dic₃₁	C₂³	1	2	yes	—
202	C₄⋊Dic₃₁	C₂³	1	2	yes	—
203	C₄⋊Dic₃₁	C₂³	1	2	yes	—
204	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
205	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₃₁⋊C₄	C₂³	1	2	yes	—
207	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₃₁⋊C₄	C₂³	1	2	yes	—
209	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₃₁⋊C₄	C₂³	1	2	yes	—
211	Dic₃₁⋊C₄	C₂³	1	2	yes	—
212	Dic₃₁⋊C₄	C₂³	1	2	yes	—
213	Dic₃₁⋊C₄	C₂³	1	2	yes	—
214	Dic₃₁⋊C₄	C₂³	1	2	yes	—
215	Dic₃₁⋊C₄	C₂³	1	2	yes	—
216	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
217	C₄×Dic₃₁	C₂³	1	2	yes	—
218	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
219	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
220	C₄×Dic₃₁	C₂³	1	2	yes	—
221	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
222	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₃₁	C₂³	1	2	yes	—
225	C₄×Dic₃₁	C₂³	1	2	yes	—
226	C₄×Dic₃₁	C₂³	1	2	yes	—
227	C₂³×C₃₁	C₂⁴	1	2	yes	—
228	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
229	C₂²×D₃₁	—	2	4	no	—
230	C₂²×D₃₁	—	2	4	no	—
231	C₂²×D₃₁	—	4	2	no	—
232	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
233	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
234	C₂²×D₃₁	C₂⁴	1	2	yes	—
235	Q₈×C₃₁	—	2	2	no	—
236	D₄×C₃₁	—	2	2	no	—
237	D₄×C₃₁	—	4	2	no	—
238	C₂×C₄×C₃₁	—	2	4	no	—
239	C₂×C₄×C₃₁	—	2	2	no	—
240	C₂×C₄×C₃₁	—	2	2	no	—
241	C₂×C₄×C₃₁	—	4	1	no	—
242	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
246	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₃₁	—	2	2	no	—
252	C₂²⋊D₃₁	—	2	4	no	—
253	C₂²⋊D₃₁	—	2	4	no	—
254	C₂²⋊D₃₁	—	2	2	no	—
255	C₂²⋊D₃₁	—	4	2	no	—
256	C₂×Dic₃₁	—	2	4	no	—
257	C₂×Dic₃₁	C₂⁴	1	2	yes	—
258	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₃₁	C₂⁴	1	2	yes	—
262	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₃₁	C₂⁴	1	2	yes	—
264	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
266	D₁₂₄	—	2	2	no	—
267	D₁₂₄	—	2	4	no	—
268	D₁₂₄	#41	1	4	yes	complemented
269	C₄×D₃₁	—	2	4	no	—
270	C₄×D₃₁	—	2	4	no	—
271	C₄×D₃₁	—	2	4	no	—
272	C₄×D₃₁	—	2	4	no	—
273	C₄×D₃₁	—	2	2	no	—
274	C₄×D₃₁	—	2	2	no	—
275	C₄×D₃₁	—	2	2	no	—
276	C₄×D₃₁	—	2	4	no	—
277	C₄×D₃₁	—	4	1	no	—
278	C₄×D₃₁	—	4	2	no	—
279	C₄×D₃₁	—	4	2	no	—
280	C₄×D₃₁	—	4	1	no	—
281	C₄×D₃₁	#41	1	4	yes	complemented
282	Dic₆₂	—	2	2	no	—
283	Dic₆₂	—	2	2	no	—
284	Dic₆₂	—	4	2	no	—
285	#3475	—	31	1	no	maximal, Sylow
286	C₂²×C₃₁	—	2	2	no	—
287	C₂²×C₃₁	—	2	1	no	—
288	C₂²×C₃₁	—	2	1	no	—
289	C₂²×C₃₁	—	2	2	no	—
290	C₂²×C₃₁	—	2	2	no	—
291	C₂²×C₃₁	—	2	1	no	—
292	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
293	C₂×D₃₁	—	2	2	no	—
294	C₂×D₃₁	—	2	1	no	—
295	C₂×D₃₁	—	2	2	no	—
296	C₂×D₃₁	—	2	1	no	—
297	C₂×D₃₁	—	2	1	no	—
298	C₂×D₃₁	—	2	1	no	—
299	C₂×D₃₁	—	2	1	no	—
300	C₂×D₃₁	—	4	8	no	—
301	C₂×D₃₁	C₂×#41	1	2	yes	—
302	C₂×D₃₁	C₂×#41	1	4	yes	—
303	C₄×C₃₁	—	2	1	no	—
304	C₄×C₃₁	—	2	1	no	—
305	C₄×C₃₁	—	2	2	no	—
306	C₄×C₃₁	—	2	2	no	—
307	C₄×C₃₁	—	2	2	no	—
308	C₄×C₃₁	—	2	1	no	—
309	C₄×C₃₁	—	2	1	no	—
310	C₄×C₃₁	C₂×#41	1	2	yes	—
311	C₄×C₃₁	C₂×#41	1	2	yes	—
312	Dic₃₁	—	2	2	no	—
313	Dic₃₁	—	2	1	no	—
314	Dic₃₁	—	2	1	no	—
315	Dic₃₁	—	2	2	no	—
316	Dic₃₁	—	2	1	no	—
317	Dic₃₁	—	2	1	no	—
318	Dic₃₁	—	2	2	no	—
319	Dic₃₁	—	2	1	no	—
320	Dic₃₁	C₂×#41	1	2	yes	—
321	#556	—	31	1	no	—
322	#555	—	31	1	no	—
323	#554	—	31	1	no	—
324	#553	—	31	2	no	—
325	#552	—	31	2	no	—
326	#552	—	31	1	no	—
327	#552	—	31	1	no	—
328	#551	—	31	2	no	—
329	#551	—	31	2	no	—
330	#547	—	31	1	no	—
331	#546	—	31	1	no	—
332	#546	—	31	1	no	—
333	#533	—	31	1	no	—
334	#529	—	31	1	no	—
335	#529	—	31	2	no	—
336	#529	—	31	2	no	—
337	#529	D₃₁	1	1	yes	characteristic, complemented
338	#525	—	31	2	no	—
339	C₄×#41	—	31	1	no	—
340	C₄×#41	—	31	1	no	—
341	C₄×#41	—	31	1	no	—
342	C₂×C₄×D₄	—	31	1	no	—
343	C₂×#117	—	31	2	no	—
344	C₂×C₃₁	—	4	2	no	—
345	C₂×C₃₁	—	4	1	no	—
346	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
347	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
348	C₂×C₃₁	#585	1	1	yes	characteristic
349	D₃₁	—	2	2	no	—
350	D₃₁	—	2	4	no	—
351	D₃₁	—	4	1	no	—
352	C₂×#41	—	31	1	no	—
353	C₂×#41	—	31	1	no	—
354	C₂×#41	—	31	1	no	—
355	C₂²×D₄	—	31	1	no	—
356	C₂³×C₄	—	31	2	no	—
357	C₄⋊Q₈	—	31	1	no	—
358	C₄⋊Q₈	—	31	1	no	—
359	#126	—	31	2	no	—
360	#126	—	31	2	no	—
361	#126	—	31	2	no	—
362	#126	—	31	2	no	—
363	#126	—	31	2	no	—
364	#126	C₂×D₃₁	1	2	yes	complemented
365	#125	—	31	2	no	—
366	#125	—	31	2	no	—
367	#125	—	31	1	no	—
368	#125	—	31	2	no	—
369	#125	C₂×D₃₁	1	1	yes	characteristic, complemented
370	#124	—	31	1	no	—
371	#124	—	31	2	no	—
372	#124	—	31	2	no	—
373	#124	C₂×D₃₁	1	1	yes	characteristic
374	#123	—	31	2	no	—
375	#123	—	31	2	no	—
376	#123	—	31	2	no	—
377	#123	—	31	2	no	—
378	#123	—	31	2	no	—
379	#123	—	31	2	no	—
380	#123	—	31	2	no	—
381	#123	C₂×D₃₁	1	2	yes	complemented
382	C₂²⋊Q₈	—	31	1	no	—
383	C₂²⋊Q₈	—	31	2	no	—
384	C₂²⋊Q₈	—	31	1	no	—
385	C₂²⋊Q₈	—	31	2	no	—
386	C₂²⋊Q₈	—	31	2	no	—
387	C₂²⋊Q₈	—	31	1	no	—
388	C₂²⋊Q₈	—	31	2	no	—
389	C₂²⋊Q₈	—	31	2	no	—
390	C₂²⋊Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
391	#121	—	31	2	no	—
392	#121	—	31	2	no	—
393	#121	—	31	1	no	—
394	#121	—	31	2	no	—
395	#121	—	31	2	no	—
396	#121	C₂×D₃₁	1	1	yes	characteristic
397	#120	—	31	2	no	—
398	#120	—	31	2	no	—
399	C₄×Q₈	—	31	1	no	—
400	C₄×Q₈	—	31	1	no	—
401	C₄×Q₈	—	31	1	no	—
402	C₄×Q₈	—	31	1	no	—
403	C₄×Q₈	—	31	1	no	—
404	C₄×Q₈	—	31	2	no	—
405	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
406	C₄×D₄	—	31	1	no	—
407	C₄×D₄	—	31	2	no	—
408	C₄×D₄	—	31	2	no	—
409	C₄×D₄	—	31	1	no	—
410	C₄×D₄	—	31	1	no	—
411	C₄×D₄	—	31	1	no	—
412	C₄×D₄	—	31	2	no	—
413	C₄×D₄	—	31	1	no	—
414	C₄×D₄	—	31	2	no	—
415	C₄×D₄	—	31	1	no	—
416	C₄×D₄	—	31	1	no	—
417	C₄×D₄	—	31	2	no	—
418	C₄×D₄	—	31	2	no	—
419	C₄×D₄	—	31	1	no	—
420	C₄×D₄	—	31	2	no	—
421	C₄×D₄	—	31	1	no	—
422	C₄×D₄	—	31	1	no	—
423	C₄×D₄	—	31	1	no	—
424	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
425	C₄×D₄	C₂×D₃₁	1	2	yes	complemented
426	#117	—	31	2	no	—
427	#117	—	31	1	no	—
428	#117	—	31	1	no	—
429	#117	—	31	2	no	—
430	#117	—	31	2	no	—
431	#117	—	31	2	no	—
432	#117	—	31	1	no	—
433	#117	—	31	2	no	—
434	#117	—	31	2	no	—
435	#117	—	31	1	no	—
436	#117	—	31	2	no	—
437	#117	—	31	1	no	—
438	#117	—	31	2	no	—
439	#117	C₂×D₃₁	1	2	yes	complemented
440	C₂×C₄⋊C₄	—	31	2	no	—
441	C₂×C₄⋊C₄	—	31	2	no	—
442	C₂×C₄⋊C₄	—	31	1	no	—
443	C₂×C₂²⋊C₄	—	31	2	no	—
444	C₂×C₂²⋊C₄	—	31	2	no	—
445	C₂×C₂²⋊C₄	—	31	2	no	—
446	C₂×C₄²	—	31	2	no	—
447	C₂×C₄²	—	31	2	no	—
448	C₂×C₄²	—	31	1	no	—
449	C₂×C₄²	—	31	1	no	—
450	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic, complemented
451	C₃₁	#3475	1	1	yes	characteristic, complemented, Sylow
452	C₂⁴	—	31	2	no	—
453	#41	—	62	4	no	—
454	#41	—	62	4	no	—
455	#41	—	62	4	no	—
456	C₂×Q₈	—	31	1	no	—
457	C₂×Q₈	—	31	1	no	—
458	C₂×Q₈	—	31	2	no	—
459	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic
460	C₂×D₄	—	31	1	no	—
461	C₂×D₄	—	31	2	no	—
462	C₂×D₄	—	31	1	no	—
463	C₂×D₄	—	31	2	no	—
464	C₂×D₄	—	31	2	no	—
465	C₂×D₄	—	31	1	no	—
466	C₂×D₄	—	31	1	no	—
467	C₂×D₄	—	31	2	no	—
468	C₂×D₄	—	62	4	no	—
469	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
470	C₂×D₄	C₂²×D₃₁	1	2	yes	—
471	C₂²×C₄	—	31	1	no	—
472	C₂²×C₄	—	31	2	no	—
473	C₂²×C₄	—	31	2	no	—
474	C₂²×C₄	—	31	2	no	—
475	C₂²×C₄	—	31	1	no	—
476	C₂²×C₄	—	31	1	no	—
477	C₂²×C₄	—	31	2	no	—
478	C₂²×C₄	—	31	2	no	—
479	C₂²×C₄	—	31	2	no	—
480	C₂²×C₄	—	31	1	no	—
481	C₂²×C₄	—	31	1	no	—
482	C₂²×C₄	—	31	2	no	—
483	C₂²×C₄	—	31	2	no	—
484	C₂²×C₄	—	31	1	no	—
485	C₂²×C₄	—	62	8	no	—
486	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
489	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
490	C₄⋊C₄	—	31	1	no	—
491	C₄⋊C₄	—	31	1	no	—
492	C₄⋊C₄	—	31	2	no	—
493	C₄⋊C₄	—	31	2	no	—
494	C₄⋊C₄	—	31	2	no	—
495	C₄⋊C₄	—	31	1	no	—
496	C₄⋊C₄	—	31	2	no	—
497	C₄⋊C₄	—	31	2	no	—
498	C₄⋊C₄	—	31	1	no	—
499	C₄⋊C₄	—	31	2	no	—
500	C₄⋊C₄	—	31	2	no	—
501	C₄⋊C₄	—	31	2	no	—
502	C₄⋊C₄	—	31	1	no	—
503	C₄⋊C₄	—	31	2	no	—
504	C₄⋊C₄	—	31	2	no	—
505	C₄⋊C₄	—	31	1	no	—
506	C₄⋊C₄	—	31	1	no	—
507	C₄⋊C₄	—	31	2	no	—
508	C₄⋊C₄	—	31	1	no	—
509	C₄⋊C₄	—	31	2	no	—
510	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
511	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
512	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
515	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
516	C₂²⋊C₄	—	31	2	no	—
517	C₂²⋊C₄	—	31	2	no	—
518	C₂²⋊C₄	—	31	2	no	—
519	C₂²⋊C₄	—	31	1	no	—
520	C₂²⋊C₄	—	31	2	no	—
521	C₂²⋊C₄	—	31	1	no	—
522	C₂²⋊C₄	—	31	2	no	—
523	C₂²⋊C₄	—	31	1	no	—
524	C₂²⋊C₄	—	31	1	no	—
525	C₂²⋊C₄	—	31	2	no	—
526	C₂²⋊C₄	—	31	2	no	—
527	C₂²⋊C₄	—	31	2	no	—
528	C₂²⋊C₄	—	31	2	no	—
529	C₂²⋊C₄	—	31	2	no	—
530	C₂²⋊C₄	—	31	2	no	—
531	C₂²⋊C₄	—	31	1	no	—
532	C₂²⋊C₄	—	31	2	no	—
533	C₂²⋊C₄	—	31	1	no	—
534	C₂²⋊C₄	—	31	2	no	—
535	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
537	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
538	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
540	C₄²	—	31	2	no	—
541	C₄²	—	31	2	no	—
542	C₄²	—	31	2	no	—
543	C₄²	—	31	2	no	—
544	C₄²	—	31	1	no	—
545	C₄²	—	31	1	no	—
546	C₄²	—	31	1	no	—
547	C₄²	—	31	1	no	—
548	C₄²	—	31	1	no	—
549	C₄²	—	31	1	no	—
550	C₄²	—	31	2	no	—
551	C₄²	C₂²×D₃₁	1	1	yes	characteristic
552	C₄²	C₂²×D₃₁	1	1	yes	characteristic
553	C₄²	C₂²×D₃₁	1	1	yes	characteristic
554	C₄²	C₂²×D₃₁	1	1	yes	characteristic
555	C₄²	C₂²×D₃₁	1	2	yes	—
556	C₂³	—	31	1	no	—
557	C₂³	—	31	2	no	—
558	C₂³	—	31	1	no	—
559	C₂³	—	62	4	no	—
560	C₂³	—	62	4	no	—
561	C₂³	—	124	2	no	—
562	C₂³	C₂³×D₃₁	1	2	yes	—
563	C₂³	C₂³×D₃₁	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	62	2	no	—
566	Q₈	—	62	2	no	—
567	Q₈	—	124	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	31	4	no	—
571	D₄	—	62	2	no	—
572	D₄	—	62	4	no	—
573	D₄	—	62	2	no	—
574	D₄	—	62	4	no	—
575	D₄	—	62	2	no	—
576	D₄	—	62	4	no	—
577	D₄	—	124	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	31	1	no	—
583	C₂×C₄	—	31	4	no	—
584	C₂×C₄	—	31	2	no	—
585	C₂×C₄	—	31	1	no	—
586	C₂×C₄	—	31	1	no	—
587	C₂×C₄	—	31	1	no	—
588	C₂×C₄	—	31	1	no	—
589	C₂×C₄	—	31	2	no	—
590	C₂×C₄	—	31	2	no	—
591	C₂×C₄	—	31	1	no	—
592	C₂×C₄	—	62	4	no	—
593	C₂×C₄	—	62	4	no	—
594	C₂×C₄	—	62	4	no	—
595	C₂×C₄	—	62	4	no	—
596	C₂×C₄	—	62	4	no	—
597	C₂×C₄	—	62	4	no	—
598	C₂×C₄	—	62	2	no	—
599	C₂×C₄	—	62	2	no	—
600	C₂×C₄	—	62	2	no	—
601	C₂×C₄	—	124	1	no	—
602	C₂×C₄	—	124	2	no	—
603	C₂×C₄	—	124	1	no	—
604	C₂×C₄	—	124	2	no	—
605	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₃₁	1	2	yes	—
609	C₂×C₄	C₂³×D₃₁	1	2	yes	—
610	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₃₁	1	2	yes	—
612	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	31	2	no	—
621	C₂²	—	31	4	no	—
622	C₂²	—	62	2	no	—
623	C₂²	—	62	1	no	—
624	C₂²	—	62	2	no	—
625	C₂²	—	62	1	no	—
626	C₂²	—	62	1	no	—
627	C₂²	—	62	1	no	—
628	C₂²	—	62	1	no	—
629	C₂²	—	124	8	no	—
630	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
631	C₄	—	2	2	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	31	2	no	—
639	C₄	—	62	2	no	—
640	C₄	—	62	1	no	—
641	C₄	—	62	1	no	—
642	C₄	—	62	1	no	—
643	C₄	—	62	2	no	—
644	C₄	—	62	1	no	—
645	C₄	—	62	2	no	—
646	C₄	—	62	1	no	—
647	C₄	#41×D₃₁	1	2	yes	—
648	C₄	#41×D₃₁	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	62	2	no	—
652	C₂	—	62	4	no	—
653	C₂	—	124	1	no	—
654	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
655	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
656	C₂	#14521885	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁵
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₃₁×#529	C₂
hypercenter	#529	D₃₁
hypocenter	C₃₁	#3475
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #14521768	C₂	semidirect
2. #14521763	C₂	semidirect
3. #14521755	C₂	semidirect
4. #14521744	C₂	semidirect
5. #14521737	C₂	semidirect
6. #14521735	C₂	semidirect
7. #14521733	C₂	semidirect
8. #14521727	C₂	semidirect
9. #14521724	C₂	semidirect
10. #14521701	C₂	semidirect
11. #14521696	C₂	semidirect
12. #14521692	C₂	semidirect
13. #14521603	C₂	semidirect
14. #14521581	C₂	semidirect
15. #14521581	C₂	semidirect
16. #14521577	C₂	semidirect
17. #14521558	C₂	semidirect
18. C₄×#92499	C₂	semidirect
19. C₄×#92495	C₂	semidirect
20. C₄×#92495	C₂	semidirect
21. C₄×D₄×D₃₁	C₂	semidirect
22. #117×D₃₁	C₂	semidirect
23. C₃₁×#529	C₂	semidirect
29. C₃₁×#126	C₂²	semidirect
30. C₃₁×#125	C₂²	semidirect
32. C₃₁×#123	C₂²	semidirect
33. C₃₁×C₂²⋊Q₈	C₂²	semidirect
35. C₄×Q₈×C₃₁	C₂²	semidirect
37. C₄×D₄×C₃₁	C₂²	semidirect
38. C₃₁×#117	C₂²	semidirect
39. C₂×C₄²×C₃₁	C₂²	semidirect
41. Q₈×Dic₃₁	C₂²	semidirect
42. #11758521	C₂²	semidirect
43. #11758516	C₂²	semidirect
48. #11758513	C₂²	semidirect
53. C₄×C₂²⋊D₃₁	C₂²	semidirect
54. C₄×C₂²⋊D₃₁	C₂²	semidirect
55. C₄×C₂²⋊D₃₁	C₂²	semidirect
56. C₄×C₂²⋊D₃₁	C₂²	semidirect
57. C₄×C₂²⋊D₃₁	C₂²	semidirect
58. #11758503	C₂²	semidirect
59. #11758503	C₂²	semidirect
60. #11758503	C₂²	semidirect
61. #11758475	C₂²	semidirect
63. #11758474	C₂²	semidirect
64. #11758474	C₂²	semidirect
66. #11758473	C₂²	semidirect
67. #11758473	C₂²	semidirect
69. #11758471	C₂²	semidirect
72. #11758470	C₂²	semidirect
75. #11758469	C₂²	semidirect
76. #11758469	C₂²	semidirect
78. C₄⋊C₄×D₃₁	C₂²	semidirect
79. C₄⋊C₄×D₃₁	C₂²	semidirect
80. #11758467	C₂²	semidirect
81. #11758467	C₂²	semidirect
82. #11758466	C₂²	semidirect
83. #11758466	C₂²	semidirect
84. #11758465	C₂²	semidirect
85. #11758462	C₂²	semidirect
87. #11758461	C₂²	semidirect
91. #11758460	C₂²	semidirect
92. #11758460	C₂²	semidirect
98. #11758456	C₂²	semidirect
99. #11758456	C₂²	semidirect
100. #11758456	C₂²	semidirect
101. #11758456	C₂²	semidirect
102. #11758455	C₂²	semidirect
103. #11758454	C₂²	semidirect
104. #11758454	C₂²	semidirect
109. C₄×D₁₂₄	C₂²	semidirect
112. #11758449	C₂²	semidirect
113. #11758449	C₂²	semidirect
115. C₄²×D₃₁	C₂²	semidirect
116. C₄²×D₃₁	C₂²	semidirect
117. C₄²×D₃₁	C₂²	semidirect
118. C₄×Dic₆₂	C₂²	semidirect
119. C₄×Dic₆₂	C₂²	semidirect
120. C₄×Dic₆₂	C₂²	semidirect
121. C₄×Dic₆₂	C₂²	semidirect
122. C₄×Dic₆₂	C₂²	semidirect
268. D₁₂₄	#41	semidirect
281. C₄×D₃₁	#41	semidirect
337. #529	D₃₁	semidirect
364. #126	C₂×D₃₁	semidirect
369. #125	C₂×D₃₁	semidirect
381. #123	C₂×D₃₁	semidirect
390. C₂²⋊Q₈	C₂×D₃₁	semidirect
405. C₄×Q₈	C₂×D₃₁	semidirect
425. C₄×D₄	C₂×D₃₁	semidirect
439. #117	C₂×D₃₁	semidirect
450. C₂×C₄²	C₂×D₃₁	semidirect
451. C₃₁	#3475	semidirect

Maximal subgroups

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

subgroup	index
#14521768	2
#14521763	2
#14521755	2
#14521744	2
#14521737	2
#14521735	2
#14521733	2
#14521727	2
#14521724	2
#14521701	2
#14521696	2
#14521692	2
#14521603	2
#14521581	2
#14521577	2
#14521558	2
C₄×#92499	2
C₄×#92495	2
C₄×D₄×D₃₁	2
#117×D₃₁	2
C₃₁×#529	2
#3475	31