Subgroups — #16859317

Order 3968.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521781	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521757	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521755	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521752	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521751	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521750	C₂	1	2	yes	maximal, complemented
7	#14521724	C₂	1	2	yes	maximal, complemented
8	#14521722	C₂	1	2	yes	maximal, complemented
9	#14521692	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521691	C₂	1	2	yes	maximal, complemented
11	#14521690	C₂	1	1	yes	maximal, characteristic, complemented
12	#14521683	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521596	C₂	1	1	yes	maximal, characteristic, complemented
14	#14521586	C₂	1	1	yes	maximal, characteristic, complemented
15	#14521577	C₂	1	2	yes	maximal, complemented
16	#14521561	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	C₂×C₄×D₁₂₄	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×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	2	yes	—
26	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
27	C₂×#92495	C₂²	1	1	yes	characteristic
28	C₂×#92495	C₂²	1	2	yes	complemented
29	C₂²×D₁₂₄	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₃₁	C₂²	1	2	yes	complemented
31	C₂²×C₄×D₃₁	C₂²	1	2	yes	complemented
32	C₃₁×#126	C₂²	1	2	yes	complemented
33	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#123	C₂²	1	2	yes	complemented
36	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#121	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
40	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#117	C₂²	1	2	yes	complemented
42	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
43	#11758524	C₂²	1	1	yes	characteristic, complemented
44	#11758523	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
46	#11758517	C₂²	1	1	yes	characteristic
47	#11758516	C₂²	1	2	yes	complemented
48	#11758515	C₂²	1	1	yes	characteristic, complemented
49	#11758514	C₂²	1	2	yes	—
50	D₄×Dic₃₁	C₂²	1	2	yes	complemented
51	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	2	yes	complemented
59	#11758503	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic, complemented
61	#11758475	C₂²	1	2	yes	complemented
62	#11758475	C₂²	1	2	yes	complemented
63	#11758474	C₂²	1	2	yes	complemented
64	#11758474	C₂²	1	2	yes	complemented
65	#11758473	C₂²	1	2	yes	complemented
66	#11758473	C₂²	1	2	yes	complemented
67	#11758472	C₂²	1	1	yes	characteristic
68	#11758472	C₂²	1	2	yes	complemented
69	#11758472	C₂²	1	1	yes	characteristic, complemented
70	#11758472	C₂²	1	2	yes	complemented
71	#11758471	C₂²	1	2	yes	complemented
72	#11758471	C₂²	1	2	yes	complemented
73	#11758471	C₂²	1	2	yes	complemented
74	#11758470	C₂²	1	1	yes	characteristic
75	#11758470	C₂²	1	1	yes	characteristic
76	#11758470	C₂²	1	2	yes	complemented
77	#11758470	C₂²	1	2	yes	complemented
78	#11758469	C₂²	1	2	yes	complemented
79	#11758469	C₂²	1	1	yes	characteristic, complemented
80	C₄⋊C₄×D₃₁	C₂²	1	2	yes	complemented
81	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
82	#11758467	C₂²	1	1	yes	characteristic, complemented
83	#11758466	C₂²	1	2	yes	complemented
84	#11758465	C₂²	1	1	yes	characteristic, complemented
85	#11758463	C₂²	1	2	yes	complemented
86	#11758463	C₂²	1	2	yes	complemented
87	#11758462	C₂²	1	2	yes	complemented
88	#11758462	C₂²	1	2	yes	complemented
89	#11758461	C₂²	1	2	yes	—
90	#11758461	C₂²	1	2	yes	complemented
91	#11758461	C₂²	1	2	yes	complemented
92	#11758460	C₂²	1	2	yes	complemented
93	#11758460	C₂²	1	2	yes	complemented
94	#11758459	C₂²	1	2	yes	—
95	#11758459	C₂²	1	2	yes	complemented
96	#11758459	C₂²	1	2	yes	complemented
97	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	—
98	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
100	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
101	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
102	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
103	#11758456	C₂²	1	2	yes	complemented
104	#11758455	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, complemented
108	C₄×D₁₂₄	C₂²	1	2	yes	complemented
109	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
110	C₄×D₁₂₄	C₂²	1	2	yes	complemented
111	C₄×D₁₂₄	C₂²	1	2	yes	complemented
112	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₁₂₄	C₂²	1	2	yes	complemented
115	#11758449	C₂²	1	1	yes	characteristic, complemented
116	#11758449	C₂²	1	1	yes	characteristic, complemented
117	#11758449	C₂²	1	2	yes	complemented
118	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₃₁	C₂²	1	2	yes	complemented
120	C₄²×D₃₁	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	C₂³×D₃₁	C₂³	1	2	yes	—
125	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
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	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Dic₃₁	C₂³	1	2	yes	—
139	C₂²×Dic₃₁	C₂³	1	2	yes	—
140	#92499	—	2	4	no	—
141	D₄×D₃₁	—	2	8	no	—
142	D₄×D₃₁	—	2	4	no	—
143	#92495	—	2	4	no	—
144	#92495	—	4	4	no	—
145	C₂×D₁₂₄	—	2	4	no	—
146	C₂×D₁₂₄	C₂³	1	2	yes	—
147	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
148	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
149	C₂×D₁₂₄	C₂³	1	2	yes	—
150	C₂×D₁₂₄	C₂³	1	2	yes	—
151	C₂×D₁₂₄	C₂³	1	2	yes	—
152	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₃₁	—	4	4	no	—
154	C₂×C₄×D₃₁	—	4	4	no	—
155	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₃₁	C₂³	1	2	yes	—
158	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₃₁	C₂³	1	2	yes	—
163	C₂×C₄×D₃₁	C₂³	1	2	yes	—
164	C₂×C₄×D₃₁	C₂³	1	2	yes	—
165	C₂×C₄×D₃₁	C₂³	1	2	yes	—
166	C₂×C₄×D₃₁	C₂³	1	2	yes	—
167	C₂×C₄×D₃₁	C₂³	1	2	yes	—
168	C₂×C₄×D₃₁	C₂³	1	2	yes	—
169	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
170	C₂×Dic₆₂	C₂³	1	2	yes	—
171	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₄²×C₃₁	C₂³	1	1	yes	characteristic
184	C₄²×C₃₁	C₂³	1	1	yes	characteristic
185	C₄²×C₃₁	C₂³	1	2	yes	—
186	C₄²×C₃₁	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
189	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
190	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
191	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
207	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₃₁	C₂³	1	2	yes	—
212	C₄⋊Dic₃₁	C₂³	1	2	yes	—
213	C₄⋊Dic₃₁	C₂³	1	2	yes	—
214	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₃₁⋊C₄	C₂³	1	2	yes	—
219	Dic₃₁⋊C₄	C₂³	1	2	yes	—
220	Dic₃₁⋊C₄	C₂³	1	2	yes	—
221	Dic₃₁⋊C₄	C₂³	1	2	yes	—
222	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
225	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
226	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
227	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
228	C₄×Dic₃₁	C₂³	1	2	yes	—
229	C₄×Dic₃₁	C₂³	1	2	yes	—
230	C₂³×C₃₁	C₂⁴	1	2	yes	—
231	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₃₁	—	2	4	no	—
233	C₂²×D₃₁	—	2	4	no	—
234	C₂²×D₃₁	—	2	4	no	—
235	C₂²×D₃₁	—	2	4	no	—
236	C₂²×D₃₁	—	4	2	no	—
237	C₂²×D₃₁	—	4	2	no	—
238	C₂²×D₃₁	C₂⁴	1	2	yes	—
239	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
240	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
241	C₂²×D₃₁	C₂⁴	1	2	yes	—
242	Q₈×C₃₁	—	2	2	no	—
243	D₄×C₃₁	—	2	4	no	—
244	D₄×C₃₁	—	2	2	no	—
245	C₂×C₄×C₃₁	—	2	2	no	—
246	C₂×C₄×C₃₁	—	2	2	no	—
247	C₂×C₄×C₃₁	—	2	2	no	—
248	C₂×C₄×C₃₁	—	2	4	no	—
249	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
251	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
255	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₃₁	—	2	2	no	—
259	C₂²⋊D₃₁	—	2	4	no	—
260	C₂²⋊D₃₁	—	2	4	no	—
261	C₂²⋊D₃₁	—	4	2	no	—
262	C₂²⋊D₃₁	—	4	2	no	—
263	C₂²⋊D₃₁	#41	1	4	yes	complemented
264	C₂×Dic₃₁	—	4	2	no	—
265	C₂×Dic₃₁	—	4	2	no	—
266	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₃₁	C₂⁴	1	2	yes	—
272	C₂×Dic₃₁	C₂⁴	1	2	yes	—
273	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
274	D₁₂₄	—	2	4	no	—
275	D₁₂₄	—	2	2	no	—
276	D₁₂₄	—	2	4	no	—
277	D₁₂₄	—	2	4	no	—
278	D₁₂₄	—	2	2	no	—
279	D₁₂₄	—	4	2	no	—
280	D₁₂₄	#41	1	4	yes	complemented
281	C₄×D₃₁	—	2	2	no	—
282	C₄×D₃₁	—	2	4	no	—
283	C₄×D₃₁	—	2	2	no	—
284	C₄×D₃₁	—	2	2	no	—
285	C₄×D₃₁	—	2	4	no	—
286	C₄×D₃₁	—	2	2	no	—
287	C₄×D₃₁	—	2	4	no	—
288	C₄×D₃₁	—	2	2	no	—
289	C₄×D₃₁	—	2	2	no	—
290	C₄×D₃₁	—	2	4	no	—
291	C₄×D₃₁	—	4	2	no	—
292	C₄×D₃₁	—	4	2	no	—
293	C₄×D₃₁	—	4	2	no	—
294	C₄×D₃₁	—	4	2	no	—
295	Dic₆₂	—	2	2	no	—
296	Dic₆₂	—	4	2	no	—
297	#3481	—	31	1	no	maximal, Sylow
298	C₂²×C₃₁	—	2	1	no	—
299	C₂²×C₃₁	—	2	1	no	—
300	C₂²×C₃₁	—	2	2	no	—
301	C₂²×C₃₁	—	2	2	no	—
302	C₂²×C₃₁	—	2	2	no	—
303	C₂²×C₃₁	C₂×#41	1	2	yes	—
304	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
305	C₂×D₃₁	—	2	1	no	—
306	C₂×D₃₁	—	2	2	no	—
307	C₂×D₃₁	—	2	1	no	—
308	C₂×D₃₁	—	2	2	no	—
309	C₂×D₃₁	—	2	1	no	—
310	C₂×D₃₁	—	2	1	no	—
311	C₂×D₃₁	—	2	2	no	—
312	C₂×D₃₁	—	2	2	no	—
313	C₂×D₃₁	—	2	2	no	—
314	C₂×D₃₁	—	2	1	no	—
315	C₂×D₃₁	—	4	8	no	—
316	C₂×D₃₁	—	4	8	no	—
317	C₂×D₃₁	C₂×#41	1	2	yes	—
318	C₂×D₃₁	C₂×#41	1	4	yes	—
319	C₄×C₃₁	—	2	1	no	—
320	C₄×C₃₁	—	2	1	no	—
321	C₄×C₃₁	—	2	2	no	—
322	C₄×C₃₁	—	2	2	no	—
323	C₄×C₃₁	—	2	1	no	—
324	C₄×C₃₁	—	2	2	no	—
325	C₄×C₃₁	—	2	1	no	—
326	C₄×C₃₁	C₂×#41	1	2	yes	—
327	C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
328	Dic₃₁	—	2	1	no	—
329	Dic₃₁	—	2	1	no	—
330	Dic₃₁	—	2	1	no	—
331	Dic₃₁	—	2	1	no	—
332	Dic₃₁	—	2	2	no	—
333	Dic₃₁	—	2	2	no	—
334	Dic₃₁	—	2	1	no	—
335	Dic₃₁	C₂×#41	1	2	yes	—
336	#559	—	31	1	no	—
337	#554	—	31	1	no	—
338	#554	—	31	1	no	—
339	#553	—	31	2	no	—
340	#553	—	31	1	no	—
341	#553	—	31	1	no	—
342	#551	—	31	2	no	—
343	#551	—	31	2	no	—
344	#546	—	31	1	no	—
345	#546	—	31	2	no	—
346	#546	—	31	1	no	—
347	D₄²	—	31	1	no	—
348	#532	—	31	1	no	—
349	#529	—	31	1	no	—
350	#529	—	31	2	no	—
351	#529	D₃₁	1	1	yes	characteristic, complemented
352	#525	—	31	2	no	—
353	#525	—	31	2	no	—
354	C₄×#41	—	31	1	no	—
355	C₄×#41	—	31	1	no	—
356	C₂×C₄×D₄	—	31	2	no	—
357	C₂×C₄×D₄	—	31	1	no	—
358	C₂×C₄×D₄	—	31	1	no	—
359	C₂×C₃₁	—	2	2	no	—
360	C₂×C₃₁	—	4	2	no	—
361	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
362	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
363	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	D₃₁	—	2	2	no	—
365	D₃₁	—	2	4	no	—
366	D₃₁	—	4	1	no	—
367	D₃₁	—	4	2	no	—
368	C₂×#41	—	31	1	no	—
369	C₂×#41	—	31	1	no	—
370	C₂×#41	—	31	2	no	—
371	C₂²×D₄	—	31	2	no	—
372	C₂²×D₄	—	31	1	no	—
373	C₂²×D₄	—	31	1	no	—
374	C₂³×C₄	—	31	2	no	—
375	C₂³×C₄	—	31	2	no	—
376	C₄⋊Q₈	—	31	1	no	—
377	#127	—	31	1	no	—
378	#126	—	31	2	no	—
379	#126	—	31	2	no	—
380	#126	—	31	2	no	—
381	#126	C₂×D₃₁	1	2	yes	complemented
382	#125	—	31	2	no	—
383	#125	—	31	1	no	—
384	#125	C₂×D₃₁	1	1	yes	characteristic, complemented
385	#124	—	31	1	no	—
386	#124	—	31	2	no	—
387	#124	—	31	2	no	—
388	#124	C₂×D₃₁	1	1	yes	characteristic, complemented
389	#123	—	31	2	no	—
390	#123	—	31	2	no	—
391	#123	—	31	2	no	—
392	#123	—	31	2	no	—
393	#123	—	31	2	no	—
394	#123	—	31	2	no	—
395	#123	—	31	2	no	—
396	#123	C₂×D₃₁	1	2	yes	complemented
397	C₂²⋊Q₈	—	31	1	no	—
398	C₂²⋊Q₈	—	31	2	no	—
399	C₂²⋊Q₈	—	31	2	no	—
400	C₂²⋊Q₈	—	31	2	no	—
401	C₂²⋊Q₈	—	31	2	no	—
402	C₂²⋊Q₈	—	31	2	no	—
403	C₂²⋊Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
404	#121	—	31	2	no	—
405	#121	—	31	1	no	—
406	#121	—	31	2	no	—
407	#121	—	31	2	no	—
408	#121	—	31	1	no	—
409	#121	—	31	1	no	—
410	#121	—	31	2	no	—
411	#121	—	31	2	no	—
412	#121	—	31	2	no	—
413	#121	C₂×D₃₁	1	1	yes	characteristic
414	#120	—	31	2	no	—
415	#120	—	31	2	no	—
416	#120	—	31	2	no	—
417	#120	—	31	2	no	—
418	C₄×Q₈	—	31	1	no	—
419	C₄×Q₈	—	31	1	no	—
420	C₄×Q₈	—	31	1	no	—
421	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
422	C₄×D₄	—	31	2	no	—
423	C₄×D₄	—	31	1	no	—
424	C₄×D₄	—	31	1	no	—
425	C₄×D₄	—	31	2	no	—
426	C₄×D₄	—	31	2	no	—
427	C₄×D₄	—	31	1	no	—
428	C₄×D₄	—	31	1	no	—
429	C₄×D₄	—	31	1	no	—
430	C₄×D₄	—	31	1	no	—
431	C₄×D₄	—	31	2	no	—
432	C₄×D₄	—	31	1	no	—
433	C₄×D₄	—	31	2	no	—
434	C₄×D₄	—	31	2	no	—
435	C₄×D₄	—	31	2	no	—
436	C₄×D₄	—	31	2	no	—
437	C₄×D₄	—	31	1	no	—
438	C₄×D₄	—	31	2	no	—
439	C₄×D₄	—	31	2	no	—
440	C₄×D₄	—	31	1	no	—
441	C₄×D₄	—	31	1	no	—
442	C₄×D₄	—	31	2	no	—
443	C₄×D₄	—	31	1	no	—
444	C₄×D₄	—	31	2	no	—
445	C₄×D₄	—	31	1	no	—
446	C₄×D₄	—	31	1	no	—
447	C₄×D₄	C₂×D₃₁	1	2	yes	complemented
448	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
449	#117	—	31	1	no	—
450	#117	—	31	2	no	—
451	#117	—	31	1	no	—
452	#117	—	31	1	no	—
453	#117	—	31	1	no	—
454	#117	—	31	2	no	—
455	#117	C₂×D₃₁	1	2	yes	complemented
456	C₂×C₄⋊C₄	—	31	1	no	—
457	C₂×C₄⋊C₄	—	31	2	no	—
458	C₂×C₄⋊C₄	—	31	1	no	—
459	C₂×C₂²⋊C₄	—	31	2	no	—
460	C₂×C₂²⋊C₄	—	31	2	no	—
461	C₂×C₂²⋊C₄	—	31	2	no	—
462	C₂×C₂²⋊C₄	—	31	2	no	—
463	C₂×C₄²	—	31	2	no	—
464	C₂×C₄²	—	31	1	no	—
465	C₂×C₄²	—	31	1	no	—
466	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic, complemented
467	C₃₁	#3481	1	1	yes	characteristic, complemented, Sylow
468	C₂⁴	—	31	2	no	—
469	C₂⁴	—	31	2	no	—
470	#41	—	62	4	no	—
471	#41	—	62	4	no	—
472	#41	—	124	4	no	—
473	C₂×Q₈	—	31	1	no	—
474	C₂×Q₈	—	31	2	no	—
475	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic
476	C₂×D₄	—	31	1	no	—
477	C₂×D₄	—	31	1	no	—
478	C₂×D₄	—	31	2	no	—
479	C₂×D₄	—	31	2	no	—
480	C₂×D₄	—	31	2	no	—
481	C₂×D₄	—	31	2	no	—
482	C₂×D₄	—	31	1	no	—
483	C₂×D₄	—	31	2	no	—
484	C₂×D₄	—	31	1	no	—
485	C₂×D₄	—	31	2	no	—
486	C₂×D₄	—	31	2	no	—
487	C₂×D₄	—	31	1	no	—
488	C₂×D₄	—	31	2	no	—
489	C₂×D₄	—	62	4	no	—
490	C₂×D₄	—	62	8	no	—
491	C₂×D₄	—	62	4	no	—
492	C₂×D₄	C₂²×D₃₁	1	2	yes	—
493	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
494	C₂²×C₄	—	31	2	no	—
495	C₂²×C₄	—	31	2	no	—
496	C₂²×C₄	—	31	2	no	—
497	C₂²×C₄	—	31	1	no	—
498	C₂²×C₄	—	31	2	no	—
499	C₂²×C₄	—	31	1	no	—
500	C₂²×C₄	—	31	1	no	—
501	C₂²×C₄	—	31	1	no	—
502	C₂²×C₄	—	31	2	no	—
503	C₂²×C₄	—	31	1	no	—
504	C₂²×C₄	—	31	1	no	—
505	C₂²×C₄	—	31	2	no	—
506	C₂²×C₄	—	31	2	no	—
507	C₂²×C₄	—	31	2	no	—
508	C₂²×C₄	—	31	2	no	—
509	C₂²×C₄	—	31	2	no	—
510	C₂²×C₄	—	124	4	no	—
511	C₂²×C₄	—	124	4	no	—
512	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
515	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
516	C₄⋊C₄	—	31	1	no	—
517	C₄⋊C₄	—	31	2	no	—
518	C₄⋊C₄	—	31	2	no	—
519	C₄⋊C₄	—	31	1	no	—
520	C₄⋊C₄	—	31	1	no	—
521	C₄⋊C₄	—	31	1	no	—
522	C₄⋊C₄	—	31	2	no	—
523	C₄⋊C₄	—	31	2	no	—
524	C₄⋊C₄	—	31	1	no	—
525	C₄⋊C₄	—	31	1	no	—
526	C₄⋊C₄	—	31	2	no	—
527	C₄⋊C₄	—	31	2	no	—
528	C₄⋊C₄	—	31	2	no	—
529	C₄⋊C₄	—	31	1	no	—
530	C₄⋊C₄	—	31	1	no	—
531	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
533	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
534	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
535	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
536	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
537	C₂²⋊C₄	—	31	1	no	—
538	C₂²⋊C₄	—	31	2	no	—
539	C₂²⋊C₄	—	31	2	no	—
540	C₂²⋊C₄	—	31	1	no	—
541	C₂²⋊C₄	—	31	1	no	—
542	C₂²⋊C₄	—	31	2	no	—
543	C₂²⋊C₄	—	31	2	no	—
544	C₂²⋊C₄	—	31	2	no	—
545	C₂²⋊C₄	—	31	2	no	—
546	C₂²⋊C₄	—	31	2	no	—
547	C₂²⋊C₄	—	31	2	no	—
548	C₂²⋊C₄	—	31	2	no	—
549	C₂²⋊C₄	—	31	2	no	—
550	C₂²⋊C₄	—	31	2	no	—
551	C₂²⋊C₄	—	31	1	no	—
552	C₂²⋊C₄	—	31	1	no	—
553	C₂²⋊C₄	—	31	2	no	—
554	C₂²⋊C₄	—	31	1	no	—
555	C₂²⋊C₄	—	31	2	no	—
556	C₂²⋊C₄	—	31	2	no	—
557	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
562	C₄²	—	31	1	no	—
563	C₄²	—	31	2	no	—
564	C₄²	—	31	1	no	—
565	C₄²	—	31	2	no	—
566	C₄²	—	31	1	no	—
567	C₄²	—	31	1	no	—
568	C₄²	—	31	1	no	—
569	C₄²	—	31	1	no	—
570	C₄²	C₂²×D₃₁	1	1	yes	characteristic
571	C₄²	C₂²×D₃₁	1	1	yes	characteristic
572	C₄²	C₂²×D₃₁	1	1	yes	characteristic
573	C₄²	C₂²×D₃₁	1	2	yes	—
574	C₄²	C₂²×D₃₁	1	1	yes	characteristic
575	C₂³	—	31	1	no	—
576	C₂³	—	31	2	no	—
577	C₂³	—	31	2	no	—
578	C₂³	—	31	1	no	—
579	C₂³	—	62	4	no	—
580	C₂³	—	62	4	no	—
581	C₂³	—	62	4	no	—
582	C₂³	—	62	4	no	—
583	C₂³	—	124	2	no	—
584	C₂³	—	124	2	no	—
585	C₂³	C₂³×D₃₁	1	2	yes	—
586	C₂³	C₂³×D₃₁	1	1	yes	characteristic
587	Q₈	—	2	2	no	—
588	Q₈	—	62	2	no	—
589	Q₈	—	124	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	31	4	no	—
593	D₄	—	31	4	no	—
594	D₄	—	62	4	no	—
595	D₄	—	62	4	no	—
596	D₄	—	62	2	no	—
597	D₄	—	62	4	no	—
598	D₄	—	62	4	no	—
599	D₄	—	62	4	no	—
600	D₄	—	62	2	no	—
601	D₄	—	62	2	no	—
602	D₄	—	124	2	no	—
603	D₄	—	124	2	no	—
604	D₄	—	124	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	31	1	no	—
610	C₂×C₄	—	31	1	no	—
611	C₂×C₄	—	31	1	no	—
612	C₂×C₄	—	31	1	no	—
613	C₂×C₄	—	31	1	no	—
614	C₂×C₄	—	31	2	no	—
615	C₂×C₄	—	31	1	no	—
616	C₂×C₄	—	31	2	no	—
617	C₂×C₄	—	62	4	no	—
618	C₂×C₄	—	62	2	no	—
619	C₂×C₄	—	62	2	no	—
620	C₂×C₄	—	62	4	no	—
621	C₂×C₄	—	62	2	no	—
622	C₂×C₄	—	62	2	no	—
623	C₂×C₄	—	62	4	no	—
624	C₂×C₄	—	62	2	no	—
625	C₂×C₄	—	62	4	no	—
626	C₂×C₄	—	62	2	no	—
627	C₂×C₄	—	124	2	no	—
628	C₂×C₄	—	124	2	no	—
629	C₂×C₄	—	124	2	no	—
630	C₂×C₄	—	124	2	no	—
631	C₂×C₄	—	124	2	no	—
632	C₂×C₄	—	124	2	no	—
633	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₃₁	1	2	yes	—
635	C₂×C₄	C₂³×D₃₁	1	2	yes	—
636	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₃₁	1	2	yes	—
640	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
641	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	31	2	no	—
648	C₂²	—	31	4	no	—
649	C₂²	—	62	2	no	—
650	C₂²	—	62	1	no	—
651	C₂²	—	62	2	no	—
652	C₂²	—	62	1	no	—
653	C₂²	—	62	1	no	—
654	C₂²	—	62	1	no	—
655	C₂²	—	62	2	no	—
656	C₂²	—	62	2	no	—
657	C₂²	—	62	2	no	—
658	C₂²	—	62	1	no	—
659	C₂²	—	124	8	no	—
660	C₂²	—	124	8	no	—
661	C₂²	#41×D₃₁	1	2	yes	—
662	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	31	2	no	—
671	C₄	—	62	1	no	—
672	C₄	—	62	1	no	—
673	C₄	—	62	1	no	—
674	C₄	—	62	1	no	—
675	C₄	—	62	2	no	—
676	C₄	—	62	2	no	—
677	C₄	—	62	1	no	—
678	C₄	#41×D₃₁	1	2	yes	—
679	C₄	#11758566	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	4	2	no	—
682	C₂	—	62	4	no	—
683	C₂	—	62	2	no	—
684	C₂	—	124	2	no	—
685	C₂	—	124	1	no	—
686	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
687	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
688	C₂	C₂×#11758566	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	#3481
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. #14521781	C₂	semidirect
2. #14521757	C₂	semidirect
3. #14521755	C₂	semidirect
4. #14521752	C₂	semidirect
5. #14521751	C₂	semidirect
6. #14521750	C₂	semidirect
7. #14521724	C₂	semidirect
8. #14521722	C₂	semidirect
9. #14521692	C₂	semidirect
10. #14521691	C₂	semidirect
11. #14521690	C₂	semidirect
12. #14521683	C₂	semidirect
13. #14521596	C₂	semidirect
14. #14521586	C₂	semidirect
15. #14521577	C₂	semidirect
16. #14521561	C₂	semidirect
17. #14521558	C₂	semidirect
18. C₄×#92499	C₂	semidirect
19. C₄×#92495	C₂	semidirect
20. C₂×C₄×D₁₂₄	C₂	semidirect
21. C₄×D₄×D₃₁	C₂	semidirect
22. C₄×D₄×D₃₁	C₂	semidirect
23. C₃₁×#529	C₂	semidirect
28. C₂×#92495	C₂²	semidirect
30. C₂²×C₄×D₃₁	C₂²	semidirect
31. C₂²×C₄×D₃₁	C₂²	semidirect
32. C₃₁×#126	C₂²	semidirect
33. C₃₁×#125	C₂²	semidirect
34. C₃₁×#124	C₂²	semidirect
35. C₃₁×#123	C₂²	semidirect
36. C₃₁×C₂²⋊Q₈	C₂²	semidirect
38. C₄×Q₈×C₃₁	C₂²	semidirect
39. C₄×D₄×C₃₁	C₂²	semidirect
40. C₄×D₄×C₃₁	C₂²	semidirect
41. C₃₁×#117	C₂²	semidirect
42. C₂×C₄²×C₃₁	C₂²	semidirect
43. #11758524	C₂²	semidirect
44. #11758523	C₂²	semidirect
45. Q₈×Dic₃₁	C₂²	semidirect
47. #11758516	C₂²	semidirect
48. #11758515	C₂²	semidirect
50. D₄×Dic₃₁	C₂²	semidirect
51. D₄×Dic₃₁	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. C₂×(C₂×D₃₁)⋊C₄	C₂²	semidirect
59. #11758503	C₂²	semidirect
60. C₂×C₄⋊Dic₃₁	C₂²	semidirect
61. #11758475	C₂²	semidirect
62. #11758475	C₂²	semidirect
63. #11758474	C₂²	semidirect
64. #11758474	C₂²	semidirect
65. #11758473	C₂²	semidirect
66. #11758473	C₂²	semidirect
68. #11758472	C₂²	semidirect
69. #11758472	C₂²	semidirect
70. #11758472	C₂²	semidirect
71. #11758471	C₂²	semidirect
72. #11758471	C₂²	semidirect
73. #11758471	C₂²	semidirect
76. #11758470	C₂²	semidirect
77. #11758470	C₂²	semidirect
78. #11758469	C₂²	semidirect
79. #11758469	C₂²	semidirect
80. C₄⋊C₄×D₃₁	C₂²	semidirect
81. C₄⋊C₄×D₃₁	C₂²	semidirect
82. #11758467	C₂²	semidirect
83. #11758466	C₂²	semidirect
84. #11758465	C₂²	semidirect
85. #11758463	C₂²	semidirect
86. #11758463	C₂²	semidirect
87. #11758462	C₂²	semidirect
88. #11758462	C₂²	semidirect
90. #11758461	C₂²	semidirect
91. #11758461	C₂²	semidirect
92. #11758460	C₂²	semidirect
93. #11758460	C₂²	semidirect
95. #11758459	C₂²	semidirect
96. #11758459	C₂²	semidirect
98. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
100. C₂²⋊C₄×D₃₁	C₂²	semidirect
101. C₂²⋊C₄×D₃₁	C₂²	semidirect
102. C₂²⋊C₄×D₃₁	C₂²	semidirect
103. #11758456	C₂²	semidirect
104. #11758455	C₂²	semidirect
107. C₄×D₁₂₄	C₂²	semidirect
108. C₄×D₁₂₄	C₂²	semidirect
109. C₄×D₁₂₄	C₂²	semidirect
110. C₄×D₁₂₄	C₂²	semidirect
111. C₄×D₁₂₄	C₂²	semidirect
112. C₄×D₁₂₄	C₂²	semidirect
113. C₄×D₁₂₄	C₂²	semidirect
114. C₄×D₁₂₄	C₂²	semidirect
115. #11758449	C₂²	semidirect
116. #11758449	C₂²	semidirect
117. #11758449	C₂²	semidirect
118. C₄²×D₃₁	C₂²	semidirect
119. C₄²×D₃₁	C₂²	semidirect
120. C₄²×D₃₁	C₂²	semidirect
121. C₄×Dic₆₂	C₂²	semidirect
122. C₄×Dic₆₂	C₂²	semidirect
263. C₂²⋊D₃₁	#41	semidirect
280. D₁₂₄	#41	semidirect
351. #529	D₃₁	semidirect
381. #126	C₂×D₃₁	semidirect
384. #125	C₂×D₃₁	semidirect
388. #124	C₂×D₃₁	semidirect
396. #123	C₂×D₃₁	semidirect
403. C₂²⋊Q₈	C₂×D₃₁	semidirect
421. C₄×Q₈	C₂×D₃₁	semidirect
447. C₄×D₄	C₂×D₃₁	semidirect
448. C₄×D₄	C₂×D₃₁	semidirect
455. #117	C₂×D₃₁	semidirect
466. C₂×C₄²	C₂×D₃₁	semidirect
467. C₃₁	#3481	semidirect

Maximal subgroups

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

subgroup	index
#14521781	2
#14521757	2
#14521755	2
#14521752	2
#14521751	2
#14521750	2
#14521724	2
#14521722	2
#14521692	2
#14521691	2
#14521690	2
#14521683	2
#14521596	2
#14521586	2
#14521577	2
#14521561	2
#14521558	2
C₄×#92499	2
C₄×#92495	2
C₂×C₄×D₁₂₄	2
C₄×D₄×D₃₁	2
C₃₁×#529	2
#3481	31