Subgroups — #16859315

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	#14521782	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521758	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521754	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521749	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521748	C₂	1	2	yes	maximal, complemented
6	#14521747	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521728	C₂	1	2	yes	maximal, complemented
8	#14521725	C₂	1	2	yes	maximal, complemented
9	#14521694	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521693	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521689	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521596	C₂	1	1	yes	maximal, characteristic, complemented
14	#14521583	C₂	1	1	yes	maximal, characteristic, complemented
15	#14521581	C₂	1	1	yes	maximal, characteristic, complemented
16	#14521579	C₂	1	2	yes	maximal, complemented
17	#14521560	C₂	1	2	yes	maximal, complemented
18	#14521558	C₂	1	2	yes	maximal, complemented
19	C₄×#92495	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#92497	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×C₂²⋊D₃₁	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₃₁	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₃₁	C₂²	1	2	yes	—
27	C₂×#92497	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
29	C₂×#92495	C₂²	1	1	yes	characteristic
30	C₂×#92495	C₂²	1	2	yes	complemented
31	C₂²×C₄×D₃₁	C₂²	1	2	yes	complemented
32	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
35	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
37	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
40	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
41	#11758530	C₂²	1	2	yes	—
42	#11758530	C₂²	1	2	yes	complemented
43	C₂×C₂²⋊Dic₃₁	C₂²	1	2	yes	complemented
44	#11758517	C₂²	1	1	yes	characteristic
45	#11758516	C₂²	1	2	yes	—
46	#11758516	C₂²	1	2	yes	complemented
47	#11758515	C₂²	1	1	yes	characteristic
48	#11758515	C₂²	1	1	yes	characteristic, complemented
49	#11758514	C₂²	1	2	yes	—
50	#11758513	C₂²	1	1	yes	characteristic, complemented
51	#11758512	C₂²	1	2	yes	complemented
52	D₄×Dic₃₁	C₂²	1	1	yes	characteristic
53	D₄×Dic₃₁	C₂²	1	1	yes	characteristic
54	#11758507	C₂²	1	1	yes	characteristic
55	#11758507	C₂²	1	2	yes	complemented
56	#11758507	C₂²	1	2	yes	complemented
57	#11758506	C₂²	1	2	yes	complemented
58	#11758506	C₂²	1	2	yes	complemented
59	#11758506	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
73	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	2	yes	complemented
74	#11758503	C₂²	1	1	yes	characteristic, complemented
75	#11758503	C₂²	1	2	yes	complemented
76	#11758501	C₂²	1	1	yes	characteristic, complemented
77	#11758501	C₂²	1	2	yes	complemented
78	#11758501	C₂²	1	2	yes	complemented
79	C₂×Dic₃₁⋊C₄	C₂²	1	2	yes	complemented
80	C₂×C₄×Dic₃₁	C₂²	1	2	yes	complemented
81	#11758475	C₂²	1	2	yes	complemented
82	#11758474	C₂²	1	1	yes	characteristic, complemented
83	#11758473	C₂²	1	2	yes	complemented
84	#11758472	C₂²	1	1	yes	characteristic, complemented
85	#11758471	C₂²	1	2	yes	complemented
86	#11758470	C₂²	1	1	yes	characteristic, complemented
87	#11758469	C₂²	1	1	yes	characteristic, complemented
88	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
89	#11758467	C₂²	1	1	yes	characteristic, complemented
90	#11758466	C₂²	1	2	yes	complemented
91	#11758465	C₂²	1	1	yes	characteristic, complemented
92	#11758464	C₂²	1	1	yes	characteristic, complemented
93	#11758463	C₂²	1	2	yes	complemented
94	#11758462	C₂²	1	2	yes	complemented
95	#11758462	C₂²	1	2	yes	complemented
96	#11758461	C₂²	1	2	yes	complemented
97	#11758461	C₂²	1	2	yes	complemented
98	#11758460	C₂²	1	2	yes	complemented
99	#11758460	C₂²	1	2	yes	complemented
100	#11758459	C₂²	1	2	yes	complemented
101	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
102	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
103	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	complemented
104	#11758456	C₂²	1	2	yes	complemented
105	#11758456	C₂²	1	2	yes	complemented
106	#11758455	C₂²	1	2	yes	complemented
107	#11758455	C₂²	1	2	yes	complemented
108	#11758454	C₂²	1	2	yes	complemented
109	#11758453	C₂²	1	2	yes	complemented
110	#11758452	C₂²	1	1	yes	characteristic, complemented
111	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
114	#11758449	C₂²	1	1	yes	characteristic, complemented
115	#11758449	C₂²	1	1	yes	characteristic, complemented
116	#11758449	C₂²	1	2	yes	complemented
117	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
119	#11758447	C₂²	1	1	yes	characteristic, 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	C₂⁴×C₃₁	C₂³	1	2	yes	—
124	C₂³×D₃₁	C₂³	1	2	yes	—
125	C₂×D₄×C₃₁	—	2	4	no	—
126	C₂×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₃₁	—	4	4	no	—
130	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
131	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
133	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
136	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
137	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₃₁	—	2	8	no	—
139	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
148	C₂²×Dic₃₁	C₂³	1	2	yes	—
149	C₂²×Dic₃₁	C₂³	1	2	yes	—
150	C₂²×Dic₃₁	C₂³	1	2	yes	—
151	#92497	—	2	4	no	—
152	D₄×D₃₁	—	2	4	no	—
153	#92495	—	2	4	no	—
154	#92495	—	4	4	no	—
155	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
156	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
157	C₂×D₁₂₄	C₂³	1	2	yes	—
158	C₂×C₄×D₃₁	—	4	4	no	—
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	1	yes	characteristic
163	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
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×Dic₆₂	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
173	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₄²×C₃₁	C₂³	1	1	yes	characteristic
180	C₄²×C₃₁	C₂³	1	1	yes	characteristic
181	C₄²×C₃₁	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
188	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₃₁	C₂³	1	2	yes	—
208	C₄⋊Dic₃₁	C₂³	1	2	yes	—
209	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₃₁⋊C₄	C₂³	1	2	yes	—
214	Dic₃₁⋊C₄	C₂³	1	2	yes	—
215	Dic₃₁⋊C₄	C₂³	1	2	yes	—
216	Dic₃₁⋊C₄	C₂³	1	2	yes	—
217	Dic₃₁⋊C₄	C₂³	1	2	yes	—
218	Dic₃₁⋊C₄	C₂³	1	2	yes	—
219	Dic₃₁⋊C₄	C₂³	1	2	yes	—
220	Dic₃₁⋊C₄	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	1	yes	characteristic
225	C₄×Dic₃₁	C₂³	1	2	yes	—
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	—	2	4	no	—
231	C₂³×C₃₁	—	2	4	no	—
232	C₂³×C₃₁	—	4	2	no	—
233	C₂³×C₃₁	C₂⁴	1	2	yes	—
234	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂³×C₃₁	C₂⁴	1	2	yes	—
236	C₂²×D₃₁	—	2	4	no	—
237	C₂²×D₃₁	—	2	4	no	—
238	C₂²×D₃₁	—	4	2	no	—
239	C₂²×D₃₁	C₂⁴	1	2	yes	—
240	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
241	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
242	D₄×C₃₁	—	2	4	no	—
243	D₄×C₃₁	—	2	2	no	—
244	D₄×C₃₁	#41	1	4	yes	complemented
245	C₂×C₄×C₃₁	—	2	2	no	—
246	C₂×C₄×C₃₁	—	2	2	no	—
247	C₂×C₄×C₃₁	—	2	4	no	—
248	C₂×C₄×C₃₁	—	2	4	no	—
249	C₂×C₄×C₃₁	—	2	2	no	—
250	C₂×C₄×C₃₁	—	4	2	no	—
251	C₂×C₄×C₃₁	—	4	2	no	—
252	C₂×C₄×C₃₁	—	4	2	no	—
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	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₃₁	—	2	2	no	—
262	C₂²⋊D₃₁	—	2	4	no	—
263	C₂²⋊D₃₁	—	2	4	no	—
264	C₂²⋊D₃₁	—	2	4	no	—
265	C₂²⋊D₃₁	—	2	4	no	—
266	C₂²⋊D₃₁	—	2	4	no	—
267	C₂²⋊D₃₁	—	4	2	no	—
268	C₂²⋊D₃₁	—	4	2	no	—
269	C₂²⋊D₃₁	#41	1	4	yes	complemented
270	C₂×Dic₃₁	—	2	4	no	—
271	C₂×Dic₃₁	—	2	4	no	—
272	C₂×Dic₃₁	—	4	2	no	—
273	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₃₁	C₂⁴	1	2	yes	—
275	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₃₁	C₂⁴	1	2	yes	—
277	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₃₁	C₂⁴	1	2	yes	—
281	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
282	D₁₂₄	—	2	2	no	—
283	D₁₂₄	—	2	2	no	—
284	D₁₂₄	—	4	2	no	—
285	C₄×D₃₁	—	2	2	no	—
286	C₄×D₃₁	—	2	2	no	—
287	C₄×D₃₁	—	2	2	no	—
288	C₄×D₃₁	—	2	2	no	—
289	C₄×D₃₁	—	2	4	no	—
290	C₄×D₃₁	—	2	2	no	—
291	C₄×D₃₁	—	2	2	no	—
292	C₄×D₃₁	—	4	2	no	—
293	C₄×D₃₁	—	4	2	no	—
294	Dic₆₂	—	2	2	no	—
295	Dic₆₂	—	2	2	no	—
296	Dic₆₂	—	4	2	no	—
297	#3481	—	31	1	no	maximal, Sylow
298	C₂²×C₃₁	—	2	2	no	—
299	C₂²×C₃₁	—	2	1	no	—
300	C₂²×C₃₁	—	2	2	no	—
301	C₂²×C₃₁	—	2	1	no	—
302	C₂²×C₃₁	—	2	2	no	—
303	C₂²×C₃₁	—	2	2	no	—
304	C₂²×C₃₁	—	2	2	no	—
305	C₂²×C₃₁	—	4	8	no	—
306	C₂²×C₃₁	C₂×#41	1	4	yes	—
307	C₂²×C₃₁	C₂×#41	1	2	yes	—
308	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
309	C₂×D₃₁	—	2	1	no	—
310	C₂×D₃₁	—	2	1	no	—
311	C₂×D₃₁	—	2	1	no	—
312	C₂×D₃₁	—	2	1	no	—
313	C₂×D₃₁	—	2	2	no	—
314	C₂×D₃₁	—	2	2	no	—
315	C₂×D₃₁	—	2	2	no	—
316	C₂×D₃₁	—	2	1	no	—
317	C₂×D₃₁	—	4	8	no	—
318	C₂×D₃₁	C₂×#41	1	2	yes	—
319	C₄×C₃₁	—	2	1	no	—
320	C₄×C₃₁	—	2	1	no	—
321	C₄×C₃₁	—	2	1	no	—
322	C₄×C₃₁	—	2	2	no	—
323	C₄×C₃₁	—	2	2	no	—
324	C₄×C₃₁	—	2	1	no	—
325	C₄×C₃₁	C₂×#41	1	2	yes	—
326	C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
327	Dic₃₁	—	2	1	no	—
328	Dic₃₁	—	2	2	no	—
329	Dic₃₁	—	2	1	no	—
330	Dic₃₁	—	2	1	no	—
331	Dic₃₁	—	2	2	no	—
332	Dic₃₁	—	2	1	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	1	no	—
346	#546	—	31	2	no	—
347	D₄²	—	31	1	no	—
348	#532	—	31	1	no	—
349	#529	—	31	2	no	—
350	#529	—	31	1	no	—
351	#529	—	31	1	no	—
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	D₃₁	1	1	yes	characteristic, complemented
359	C₂×C₃₁	—	2	4	no	—
360	C₂×C₃₁	—	2	2	no	—
361	C₂×C₃₁	—	4	2	no	—
362	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
363	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
364	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
365	D₃₁	—	2	2	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	C₂×D₃₁	1	1	yes	characteristic
374	C₂³×C₄	—	31	2	no	—
375	C₂³×C₄	C₂×D₃₁	1	2	yes	complemented
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	—	31	2	no	—
382	#125	—	31	2	no	—
383	#125	—	31	1	no	—
384	#125	—	31	1	no	—
385	#124	—	31	1	no	—
386	#124	—	31	2	no	—
387	#124	—	31	2	no	—
388	#124	—	31	1	no	—
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	—	31	2	no	—
397	C₂²⋊Q₈	—	31	2	no	—
398	C₂²⋊Q₈	—	31	2	no	—
399	C₂²⋊Q₈	—	31	1	no	—
400	C₂²⋊Q₈	—	31	2	no	—
401	C₂²⋊Q₈	—	31	1	no	—
402	C₂²⋊Q₈	—	31	2	no	—
403	C₂²⋊Q₈	—	31	2	no	—
404	#121	—	31	2	no	—
405	#121	—	31	1	no	—
406	#121	—	31	2	no	—
407	#121	—	31	1	no	—
408	#121	—	31	2	no	—
409	#121	—	31	2	no	—
410	#121	—	31	1	no	—
411	#121	—	31	1	no	—
412	#121	—	31	2	no	—
413	#121	—	31	2	no	—
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	—	31	1	no	—
422	C₄×D₄	—	31	1	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	2	no	—
428	C₄×D₄	—	31	2	no	—
429	C₄×D₄	—	31	2	no	—
430	C₄×D₄	—	31	2	no	—
431	C₄×D₄	—	31	2	no	—
432	C₄×D₄	—	31	2	no	—
433	C₄×D₄	—	31	2	no	—
434	C₄×D₄	—	31	1	no	—
435	C₄×D₄	—	31	1	no	—
436	C₄×D₄	—	31	1	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	1	no	—
443	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
444	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
445	C₄×D₄	C₂×D₃₁	1	2	yes	complemented
446	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
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	2	no	—
453	#117	—	31	1	no	—
454	#117	—	31	1	no	—
455	#117	—	31	2	no	—
456	C₂×C₄⋊C₄	—	31	2	no	—
457	C₂×C₄⋊C₄	—	31	1	no	—
458	C₂×C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic, complemented
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	C₂×D₃₁	1	2	yes	complemented
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	C₂²×D₃₁	1	2	yes	—
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	1	no	—
475	C₂×Q₈	—	31	2	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	31	1	no	—
478	C₂×D₄	—	31	2	no	—
479	C₂×D₄	—	31	1	no	—
480	C₂×D₄	—	31	2	no	—
481	C₂×D₄	—	31	2	no	—
482	C₂×D₄	—	31	2	no	—
483	C₂×D₄	—	31	2	no	—
484	C₂×D₄	—	31	2	no	—
485	C₂×D₄	—	31	2	no	—
486	C₂×D₄	—	31	1	no	—
487	C₂×D₄	—	31	1	no	—
488	C₂×D₄	—	31	2	no	—
489	C₂×D₄	—	62	8	no	—
490	C₂×D₄	—	62	4	no	—
491	C₂×D₄	C₂²×D₃₁	1	2	yes	—
492	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
493	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
494	C₂²×C₄	—	4	4	no	—
495	C₂²×C₄	—	31	2	no	—
496	C₂²×C₄	—	31	2	no	—
497	C₂²×C₄	—	31	2	no	—
498	C₂²×C₄	—	31	1	no	—
499	C₂²×C₄	—	31	1	no	—
500	C₂²×C₄	—	31	1	no	—
501	C₂²×C₄	—	31	1	no	—
502	C₂²×C₄	—	31	1	no	—
503	C₂²×C₄	—	31	1	no	—
504	C₂²×C₄	—	31	2	no	—
505	C₂²×C₄	—	31	2	no	—
506	C₂²×C₄	—	31	2	no	—
507	C₂²×C₄	—	124	4	no	—
508	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
509	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
511	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
513	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
514	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
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	2	no	—
520	C₄⋊C₄	—	31	2	no	—
521	C₄⋊C₄	—	31	1	no	—
522	C₄⋊C₄	—	31	2	no	—
523	C₄⋊C₄	—	31	1	no	—
524	C₄⋊C₄	—	31	1	no	—
525	C₄⋊C₄	—	31	2	no	—
526	C₄⋊C₄	—	31	2	no	—
527	C₄⋊C₄	—	31	2	no	—
528	C₄⋊C₄	—	31	1	no	—
529	C₄⋊C₄	—	31	1	no	—
530	C₄⋊C₄	—	31	1	no	—
531	C₄⋊C₄	—	31	1	no	—
532	C₄⋊C₄	—	31	2	no	—
533	C₄⋊C₄	—	31	2	no	—
534	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
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	2	no	—
541	C₂²⋊C₄	—	31	2	no	—
542	C₂²⋊C₄	—	31	2	no	—
543	C₂²⋊C₄	—	31	1	no	—
544	C₂²⋊C₄	—	31	2	no	—
545	C₂²⋊C₄	—	31	2	no	—
546	C₂²⋊C₄	—	31	1	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	2	no	—
552	C₂²⋊C₄	—	31	1	no	—
553	C₂²⋊C₄	—	31	2	no	—
554	C₂²⋊C₄	—	31	1	no	—
555	C₂²⋊C₄	—	31	1	no	—
556	C₂²⋊C₄	—	31	2	no	—
557	C₂²⋊C₄	—	31	2	no	—
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	—	31	2	no	—
571	C₄²	C₂²×D₃₁	1	1	yes	characteristic
572	C₄²	C₂²×D₃₁	1	1	yes	characteristic
573	C₄²	C₂²×D₃₁	1	1	yes	characteristic
574	C₄²	C₂²×D₃₁	1	1	yes	characteristic
575	C₂³	—	2	4	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	31	1	no	—
579	C₂³	—	31	2	no	—
580	C₂³	—	31	1	no	—
581	C₂³	—	62	4	no	—
582	C₂³	—	62	4	no	—
583	C₂³	—	124	2	no	—
584	C₂³	C₂³×D₃₁	1	2	yes	—
585	C₂³	C₂³×D₃₁	1	2	yes	—
586	C₂³	C₂³×D₃₁	1	1	yes	characteristic
587	Q₈	—	62	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	—	62	2	no	—
594	D₄	—	62	4	no	—
595	D₄	—	62	4	no	—
596	D₄	—	62	4	no	—
597	D₄	—	62	4	no	—
598	D₄	—	62	4	no	—
599	D₄	—	62	2	no	—
600	D₄	—	62	2	no	—
601	D₄	—	124	2	no	—
602	D₄	—	124	2	no	—
603	D₄	—	124	2	no	—
604	D₄	#92495	1	4	yes	complemented
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	—	2	4	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	31	1	no	—
614	C₂×C₄	—	31	1	no	—
615	C₂×C₄	—	31	1	no	—
616	C₂×C₄	—	31	2	no	—
617	C₂×C₄	—	31	2	no	—
618	C₂×C₄	—	31	1	no	—
619	C₂×C₄	—	31	1	no	—
620	C₂×C₄	—	31	1	no	—
621	C₂×C₄	—	31	2	no	—
622	C₂×C₄	—	62	2	no	—
623	C₂×C₄	—	62	2	no	—
624	C₂×C₄	—	62	4	no	—
625	C₂×C₄	—	62	4	no	—
626	C₂×C₄	—	62	2	no	—
627	C₂×C₄	—	62	2	no	—
628	C₂×C₄	—	62	2	no	—
629	C₂×C₄	—	62	4	no	—
630	C₂×C₄	—	62	2	no	—
631	C₂×C₄	—	124	2	no	—
632	C₂×C₄	—	124	2	no	—
633	C₂×C₄	—	124	2	no	—
634	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
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	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	4	8	no	—
650	C₂²	—	31	2	no	—
651	C₂²	—	62	1	no	—
652	C₂²	—	62	1	no	—
653	C₂²	—	62	1	no	—
654	C₂²	—	62	2	no	—
655	C₂²	—	62	1	no	—
656	C₂²	—	62	2	no	—
657	C₂²	—	62	2	no	—
658	C₂²	—	62	1	no	—
659	C₂²	—	124	8	no	—
660	C₂²	C₂×#92495	1	4	yes	—
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	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	31	2	no	—
670	C₄	—	62	2	no	—
671	C₄	—	62	1	no	—
672	C₄	—	62	1	no	—
673	C₄	—	62	1	no	—
674	C₄	—	62	2	no	—
675	C₄	—	62	1	no	—
676	C₄	—	62	2	no	—
677	C₄	—	62	1	no	—
678	C₄	C₂×#92495	1	2	yes	—
679	C₄	#11758561	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	2	4	no	—
682	C₂	—	4	2	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	C₂²×#92495	1	1	yes	characteristic
688	C₂	C₂×#11758561	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁵
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₂×C₄×D₄×C₃₁	C₂
hypercenter	C₂×C₄×D₄	D₃₁
hypocenter	C₃₁	#3481
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #14521782	C₂	semidirect
2. #14521758	C₂	semidirect
3. #14521754	C₂	semidirect
4. #14521749	C₂	semidirect
5. #14521748	C₂	semidirect
6. #14521747	C₂	semidirect
7. #14521728	C₂	semidirect
8. #14521725	C₂	semidirect
9. #14521694	C₂	semidirect
10. #14521693	C₂	semidirect
11. #14521689	C₂	semidirect
12. D₄×C₂²⋊D₃₁	C₂	semidirect
13. #14521596	C₂	semidirect
14. #14521583	C₂	semidirect
15. #14521581	C₂	semidirect
16. #14521579	C₂	semidirect
17. #14521560	C₂	semidirect
18. #14521558	C₂	semidirect
19. C₄×#92495	C₂	semidirect
20. C₄×#92497	C₂	semidirect
21. C₂×C₄×C₂²⋊D₃₁	C₂	semidirect
22. C₄×D₄×D₃₁	C₂	semidirect
23. C₂×C₄×D₄×C₃₁	C₂	semidirect
25. C₂³×C₄×C₃₁	C₂²	semidirect
30. C₂×#92495	C₂²	semidirect
31. C₂²×C₄×D₃₁	C₂²	semidirect
34. C₄×D₄×C₃₁	C₂²	semidirect
35. C₄×D₄×C₃₁	C₂²	semidirect
36. C₄×D₄×C₃₁	C₂²	semidirect
37. C₄×D₄×C₃₁	C₂²	semidirect
38. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
39. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
40. C₂×C₄²×C₃₁	C₂²	semidirect
42. #11758530	C₂²	semidirect
43. C₂×C₂²⋊Dic₃₁	C₂²	semidirect
46. #11758516	C₂²	semidirect
48. #11758515	C₂²	semidirect
50. #11758513	C₂²	semidirect
51. #11758512	C₂²	semidirect
55. #11758507	C₂²	semidirect
56. #11758507	C₂²	semidirect
57. #11758506	C₂²	semidirect
58. #11758506	C₂²	semidirect
59. #11758506	C₂²	semidirect
63. C₄×C₂²⋊D₃₁	C₂²	semidirect
64. C₄×C₂²⋊D₃₁	C₂²	semidirect
65. C₄×C₂²⋊D₃₁	C₂²	semidirect
66. C₄×C₂²⋊D₃₁	C₂²	semidirect
67. C₄×C₂²⋊D₃₁	C₂²	semidirect
68. C₄×C₂²⋊D₃₁	C₂²	semidirect
69. C₄×C₂²⋊D₃₁	C₂²	semidirect
70. C₄×C₂²⋊D₃₁	C₂²	semidirect
71. C₄×C₂²⋊D₃₁	C₂²	semidirect
72. C₄×C₂²⋊D₃₁	C₂²	semidirect
73. C₂×(C₂×D₃₁)⋊C₄	C₂²	semidirect
74. #11758503	C₂²	semidirect
75. #11758503	C₂²	semidirect
76. #11758501	C₂²	semidirect
77. #11758501	C₂²	semidirect
78. #11758501	C₂²	semidirect
79. C₂×Dic₃₁⋊C₄	C₂²	semidirect
80. C₂×C₄×Dic₃₁	C₂²	semidirect
81. #11758475	C₂²	semidirect
82. #11758474	C₂²	semidirect
83. #11758473	C₂²	semidirect
84. #11758472	C₂²	semidirect
85. #11758471	C₂²	semidirect
86. #11758470	C₂²	semidirect
87. #11758469	C₂²	semidirect
88. C₄⋊C₄×D₃₁	C₂²	semidirect
89. #11758467	C₂²	semidirect
90. #11758466	C₂²	semidirect
91. #11758465	C₂²	semidirect
92. #11758464	C₂²	semidirect
93. #11758463	C₂²	semidirect
94. #11758462	C₂²	semidirect
95. #11758462	C₂²	semidirect
96. #11758461	C₂²	semidirect
97. #11758461	C₂²	semidirect
98. #11758460	C₂²	semidirect
99. #11758460	C₂²	semidirect
100. #11758459	C₂²	semidirect
101. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
102. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
103. C₂²⋊C₄×D₃₁	C₂²	semidirect
104. #11758456	C₂²	semidirect
105. #11758456	C₂²	semidirect
106. #11758455	C₂²	semidirect
107. #11758455	C₂²	semidirect
108. #11758454	C₂²	semidirect
109. #11758453	C₂²	semidirect
110. #11758452	C₂²	semidirect
111. C₄×D₁₂₄	C₂²	semidirect
112. C₄×D₁₂₄	C₂²	semidirect
113. C₄×D₁₂₄	C₂²	semidirect
114. #11758449	C₂²	semidirect
115. #11758449	C₂²	semidirect
116. #11758449	C₂²	semidirect
117. C₄²×D₃₁	C₂²	semidirect
118. C₄²×D₃₁	C₂²	semidirect
119. #11758447	C₂²	semidirect
120. C₄×Dic₆₂	C₂²	semidirect
121. C₄×Dic₆₂	C₂²	semidirect
122. C₄×Dic₆₂	C₂²	semidirect
244. D₄×C₃₁	#41	semidirect
269. C₂²⋊D₃₁	#41	semidirect
358. C₂×C₄×D₄	D₃₁	semidirect
375. C₂³×C₄	C₂×D₃₁	semidirect
445. C₄×D₄	C₂×D₃₁	semidirect
446. C₄×D₄	C₂×D₃₁	semidirect
447. C₄×D₄	C₂×D₃₁	semidirect
448. C₄×D₄	C₂×D₃₁	semidirect
458. C₂×C₄⋊C₄	C₂×D₃₁	semidirect
462. C₂×C₂²⋊C₄	C₂×D₃₁	semidirect
466. C₂×C₄²	C₂×D₃₁	semidirect
467. C₃₁	#3481	semidirect
604. D₄	#92495	semidirect

Maximal subgroups

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

subgroup	index
#14521782	2
#14521758	2
#14521754	2
#14521749	2
#14521748	2
#14521747	2
#14521728	2
#14521725	2
#14521694	2
#14521693	2
#14521689	2
D₄×C₂²⋊D₃₁	2
#14521596	2
#14521583	2
#14521581	2
#14521579	2
#14521560	2
#14521558	2
C₄×#92495	2
C₄×#92497	2
C₂×C₄×C₂²⋊D₃₁	2
C₄×D₄×D₃₁	2
C₂×C₄×D₄×C₃₁	2
#3481	31