Subgroups — D₄×C₃₁×SD₃₂ #21490606

Order 7936.

738 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×SD₃₂	C₂	1	2	yes	maximal, complemented
2	D₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2217	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2208	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2207	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2187	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2185	C₂	1	2	yes	maximal, complemented
10	C₄×C₃₁×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
13	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
14	D₄×Q₈×C₃₁	—	2	1	no	—
15	D₄²×C₃₁	—	2	1	no	—
16	C₂×C₃₁×SD₃₂	—	2	8	no	—
17	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
18	C₂×C₃₁×SD₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	complemented
20	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	complemented
21	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	complemented
22	C₂²×C₁₆×C₃₁	C₂²	1	2	yes	complemented
23	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#493	C₂²	1	1	yes	characteristic
25	C₃₁×#467	C₂²	1	2	yes	complemented
26	C₃₁×#466	C₂²	1	2	yes	—
27	C₃₁×#462	—	2	1	no	—
28	C₃₁×#459	—	2	1	no	—
29	C₃₁×#451	—	2	2	no	—
30	C₃₁×#447	—	2	2	no	—
31	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#367	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#358	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#358	C₂²	1	2	yes	complemented
38	C₃₁×#357	C₂²	1	1	yes	characteristic
39	C₃₁×#357	C₂²	1	2	yes	complemented
40	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
42	C₂²×Q₈×C₃₁	—	2	2	no	—
43	C₂²×D₄×C₃₁	—	2	2	no	—
44	C₂²×D₄×C₃₁	—	4	1	no	—
45	C₂×Q₁₆×C₃₁	—	2	4	no	—
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂×Q₁₆×C₃₁	—	2	1	no	—
48	C₂×Q₁₆×C₃₁	—	4	2	no	—
49	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
50	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
51	C₂×D₈×C₃₁	—	2	4	no	—
52	C₂×D₈×C₃₁	—	2	2	no	—
53	C₂×D₈×C₃₁	—	2	1	no	—
54	C₂×D₈×C₃₁	—	4	2	no	—
55	C₂×D₈×C₃₁	C₂³	1	2	yes	—
56	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
58	C₃₁×C₄⋊Q₈	—	2	1	no	—
59	C₃₁×C₄⋊Q₈	—	4	1	no	—
60	C₃₁×#127	—	2	1	no	—
61	C₃₁×C₂²⋊Q₈	—	2	2	no	—
62	C₃₁×C₂²⋊Q₈	—	4	2	no	—
63	C₃₁×#121	—	2	2	no	—
64	C₃₁×#121	—	4	1	no	—
65	C₃₁×#120	—	4	2	no	—
66	C₄×Q₈×C₃₁	—	2	1	no	—
67	C₄×D₄×C₃₁	—	2	1	no	—
68	C₄×D₄×C₃₁	—	4	1	no	—
69	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
70	C₃₁×SD₃₂	—	2	4	no	—
71	C₃₁×SD₃₂	—	2	4	no	—
72	C₃₁×SD₃₂	—	2	4	no	—
73	C₃₁×SD₃₂	—	4	2	no	—
74	C₃₁×SD₃₂	D₄	1	4	yes	direct product factor
75	C₂×C₁₆×C₃₁	—	2	4	no	—
76	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
77	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
79	C₃₁×#107	C₂³	1	1	yes	characteristic
80	C₃₁×#107	C₂³	1	1	yes	characteristic
81	C₃₁×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₃₁×#103	—	2	1	no	—
83	C₃₁×#103	—	2	2	no	—
84	C₃₁×#102	—	2	1	no	—
85	C₃₁×#102	—	2	2	no	—
86	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₂⁴×C₃₁	—	4	2	no	—
89	C₂×Q₈×C₃₁	—	2	1	no	—
90	C₂×Q₈×C₃₁	—	2	2	no	—
91	C₂×Q₈×C₃₁	—	4	4	no	—
92	C₂×Q₈×C₃₁	—	4	2	no	—
93	C₂×Q₈×C₃₁	—	8	2	no	—
94	C₂×D₄×C₃₁	—	2	1	no	—
95	C₂×D₄×C₃₁	—	2	2	no	—
96	C₂×D₄×C₃₁	—	4	4	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂×D₄×C₃₁	—	4	1	no	—
100	C₂×D₄×C₃₁	—	4	1	no	—
101	C₂×D₄×C₃₁	—	8	2	no	—
102	C₂×D₄×C₃₁	—	8	4	no	—
103	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	—	4	2	no	—
105	C₂²×C₄×C₃₁	—	4	1	no	—
106	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
107	Q₁₆×C₃₁	—	2	2	no	—
108	Q₁₆×C₃₁	—	2	1	no	—
109	Q₁₆×C₃₁	—	2	2	no	—
110	Q₁₆×C₃₁	—	4	4	no	—
111	Q₁₆×C₃₁	—	8	1	no	—
112	Q₁₆×C₃₁	C₂×D₄	1	2	yes	complemented
113	D₈×C₃₁	—	2	2	no	—
114	D₈×C₃₁	—	2	1	no	—
115	D₈×C₃₁	—	2	2	no	—
116	D₈×C₃₁	—	4	4	no	—
117	D₈×C₃₁	—	8	1	no	—
118	D₈×C₃₁	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	—	2	2	no	—
121	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₃₁	—	2	1	no	—
125	C₄⋊C₄×C₃₁	—	2	1	no	—
126	C₄⋊C₄×C₃₁	—	4	1	no	—
127	C₄⋊C₄×C₃₁	—	4	1	no	—
128	C₄⋊C₄×C₃₁	—	4	2	no	—
129	C₄⋊C₄×C₃₁	—	4	1	no	—
130	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₃₁	—	4	1	no	—
133	C₂²⋊C₄×C₃₁	—	4	2	no	—
134	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
135	C₄²×C₃₁	—	4	1	no	—
136	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₃₁	—	2	2	no	—
138	C₁₆×C₃₁	—	2	1	no	—
139	C₁₆×C₃₁	C₂×D₄	1	2	yes	complemented
140	D₄×SD₃₂	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₃₁	—	4	1	no	—
142	C₂³×C₃₁	—	4	2	no	—
143	C₂³×C₃₁	—	8	4	no	—
144	C₂³×C₃₁	—	8	4	no	—
145	C₂³×C₃₁	—	16	2	no	—
146	C₂³×C₃₁	C₂×D₈	1	2	yes	—
147	Q₈×C₃₁	—	2	2	no	—
148	Q₈×C₃₁	—	4	1	no	—
149	Q₈×C₃₁	—	4	2	no	—
150	Q₈×C₃₁	—	4	2	no	—
151	Q₈×C₃₁	—	8	4	no	—
152	D₄×C₃₁	—	2	2	no	—
153	D₄×C₃₁	—	4	2	no	—
154	D₄×C₃₁	—	4	1	no	—
155	D₄×C₃₁	—	4	2	no	—
156	D₄×C₃₁	—	8	4	no	—
157	D₄×C₃₁	—	8	4	no	—
158	D₄×C₃₁	—	8	2	no	—
159	D₄×C₃₁	—	16	1	no	—
160	D₄×C₃₁	SD₃₂	1	4	yes	direct product factor
161	C₂×C₄×C₃₁	—	2	2	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	4	1	no	—
164	C₂×C₄×C₃₁	—	4	1	no	—
165	C₂×C₄×C₃₁	—	4	1	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	—	8	4	no	—
168	C₂×C₄×C₃₁	—	8	2	no	—
169	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
171	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
173	C₈×C₃₁	—	2	2	no	—
174	C₈×C₃₁	—	2	1	no	—
175	C₈×C₃₁	C₂²×D₄	1	1	yes	characteristic
176	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²×SD₃₂	C₂×C₃₁	1	2	yes	complemented
178	D₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
179	D₄×D₈	C₂×C₃₁	1	1	yes	characteristic
180	#2248	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#2217	C₂×C₃₁	1	2	yes	complemented
182	#2208	C₂×C₃₁	1	1	yes	characteristic, complemented
183	#2207	C₂×C₃₁	1	1	yes	characteristic, complemented
184	#2187	C₂×C₃₁	1	2	yes	complemented
185	#2185	C₂×C₃₁	1	2	yes	complemented
186	C₄×SD₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
187	D₄×C₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
188	C₂²×C₃₁	—	2	2	no	—
189	C₂²×C₃₁	—	2	2	no	—
190	C₂²×C₃₁	—	4	2	no	—
191	C₂²×C₃₁	—	8	1	no	—
192	C₂²×C₃₁	—	8	1	no	—
193	C₂²×C₃₁	—	8	2	no	—
194	C₂²×C₃₁	—	8	2	no	—
195	C₂²×C₃₁	—	8	2	no	—
196	C₂²×C₃₁	—	16	8	no	—
197	C₂²×C₃₁	C₂×SD₃₂	1	4	yes	complemented
198	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
199	C₄×C₃₁	—	2	1	no	—
200	C₄×C₃₁	—	2	2	no	—
201	C₄×C₃₁	—	4	2	no	—
202	C₄×C₃₁	—	8	1	no	—
203	C₄×C₃₁	—	8	1	no	—
204	C₄×C₃₁	—	8	2	no	—
205	C₄×C₃₁	C₂×SD₃₂	1	2	yes	complemented
206	C₄×C₃₁	D₄²	1	1	yes	characteristic
207	C₄×C₃₁	#576	1	1	yes	characteristic
208	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
209	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
210	D₄×Q₈	—	2	1	no	—
211	D₄²	—	2	1	no	—
212	C₂×SD₃₂	—	2	8	no	—
213	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
214	C₂×SD₃₂	C₂²×C₃₁	1	1	yes	characteristic
215	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	complemented
216	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	complemented
217	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	complemented
218	C₂²×C₁₆	C₂²×C₃₁	1	2	yes	complemented
219	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
220	#493	C₂²×C₃₁	1	1	yes	characteristic
221	#467	C₂²×C₃₁	1	2	yes	complemented
222	#466	C₂²×C₃₁	1	2	yes	—
223	#462	—	2	1	no	—
224	#459	—	2	1	no	—
225	#451	—	2	2	no	—
226	#447	—	2	2	no	—
227	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
228	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
229	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
230	#367	C₂²×C₃₁	1	1	yes	characteristic, complemented
231	C₄⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
232	#358	C₂²×C₃₁	1	1	yes	characteristic, complemented
233	#358	C₂²×C₃₁	1	2	yes	complemented
234	#357	C₂²×C₃₁	1	1	yes	characteristic
235	#357	C₂²×C₃₁	1	2	yes	complemented
236	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	complemented
237	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
238	C₂×C₃₁	—	2	4	no	—
239	C₂×C₃₁	—	8	2	no	—
240	C₂×C₃₁	—	16	2	no	—
241	C₂×C₃₁	D₄×D₈	1	1	yes	characteristic
242	C₂×C₃₁	C₂²×SD₃₂	1	1	yes	characteristic
243	C₂×C₃₁	#3416	1	1	yes	characteristic
244	C₂²×Q₈	—	2	2	no	—
245	C₂²×D₄	—	2	2	no	—
246	C₂²×D₄	—	4	1	no	—
247	C₂×Q₁₆	—	2	4	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	—	4	2	no	—
251	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
252	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
253	C₂×D₈	—	2	4	no	—
254	C₂×D₈	—	2	2	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	4	2	no	—
257	C₂×D₈	C₂³×C₃₁	1	2	yes	—
258	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	—	4	1	no	—
262	#127	—	2	1	no	—
263	C₂²⋊Q₈	—	2	2	no	—
264	C₂²⋊Q₈	—	4	2	no	—
265	#121	—	2	2	no	—
266	#121	—	4	1	no	—
267	#120	—	4	2	no	—
268	C₄×Q₈	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	—	4	1	no	—
271	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
272	SD₃₂	—	2	4	no	—
273	SD₃₂	—	2	4	no	—
274	SD₃₂	—	2	4	no	—
275	SD₃₂	—	4	2	no	—
276	SD₃₂	D₄×C₃₁	1	4	yes	direct product factor
277	C₂×C₁₆	—	2	4	no	—
278	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
279	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
280	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
281	#107	C₂³×C₃₁	1	1	yes	characteristic
282	#107	C₂³×C₃₁	1	1	yes	characteristic
283	C₄⋊C₈	D₄×C₃₁	1	1	yes	characteristic
284	#103	—	2	1	no	—
285	#103	—	2	2	no	—
286	#102	—	2	1	no	—
287	#102	—	2	2	no	—
288	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
289	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
290	C₃₁	D₄×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	4	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	4	4	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	8	2	no	—
305	C₂×D₄	—	8	4	no	—
306	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
310	Q₁₆	—	2	2	no	—
311	Q₁₆	—	2	1	no	—
312	Q₁₆	—	2	2	no	—
313	Q₁₆	—	4	4	no	—
314	Q₁₆	—	8	1	no	—
315	Q₁₆	C₂×D₄×C₃₁	1	2	yes	complemented
316	D₈	—	2	2	no	—
317	D₈	—	2	1	no	—
318	D₈	—	2	2	no	—
319	D₈	—	4	4	no	—
320	D₈	—	8	1	no	—
321	D₈	C₂×D₄×C₃₁	1	2	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
325	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
326	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
338	C₄²	—	4	1	no	—
339	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
340	C₁₆	—	2	2	no	—
341	C₁₆	—	2	1	no	—
342	C₁₆	C₂×D₄×C₃₁	1	2	yes	complemented
343	C₂³	—	4	1	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	4	no	—
346	C₂³	—	8	4	no	—
347	C₂³	—	16	2	no	—
348	C₂³	C₂×D₈×C₃₁	1	2	yes	—
349	Q₈	—	2	2	no	—
350	Q₈	—	4	1	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	8	4	no	—
354	D₄	—	2	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	2	no	—
358	D₄	—	8	4	no	—
359	D₄	—	8	4	no	—
360	D₄	—	8	2	no	—
361	D₄	—	16	1	no	—
362	D₄	C₃₁×SD₃₂	1	4	yes	direct product factor
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	4	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
372	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
373	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	1	no	—
377	C₈	C₂²×D₄×C₃₁	1	1	yes	characteristic
378	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	16	8	no	—
388	C₂²	C₂×C₃₁×SD₃₂	1	4	yes	complemented
389	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	8	1	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	2	no	—
396	C₄	C₂×C₃₁×SD₃₂	1	2	yes	complemented
397	C₄	D₄²×C₃₁	1	1	yes	characteristic
398	C₄	C₃₁×#576	1	1	yes	characteristic
399	C₂	—	2	4	no	—
400	C₂	—	8	2	no	—
401	C₂	—	16	2	no	—
402	C₂	D₄×D₈×C₃₁	1	1	yes	characteristic
403	C₂	C₂²×C₃₁×SD₃₂	1	1	yes	characteristic
404	C₂	C₃₁×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	D₄×D₈×C₃₁	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×D₄×C₃₁ ◁ C₈×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×SD₃₂	C₂	semidirect
2. D₄×Q₁₆×C₃₁	C₂	semidirect
4. C₃₁×#2248	C₂	semidirect
5. C₃₁×#2217	C₂	semidirect
6. C₃₁×#2208	C₂	semidirect
7. C₃₁×#2207	C₂	semidirect
8. C₃₁×#2187	C₂	semidirect
9. C₃₁×#2185	C₂	semidirect
10. C₄×C₃₁×SD₃₂	C₂	semidirect
11. D₄×C₁₆×C₃₁	C₂	semidirect
12. C₂²×Q₁₆×C₃₁	C₂²	semidirect
19. C₂×C₃₁×SD₃₂	C₂²	semidirect
20. C₂×C₃₁×SD₃₂	C₂²	semidirect
21. C₂×C₃₁×SD₃₂	C₂²	semidirect
22. C₂²×C₁₆×C₃₁	C₂²	semidirect
23. C₃₁×#494	C₂²	semidirect
25. C₃₁×#467	C₂²	semidirect
31. C₄×Q₁₆×C₃₁	C₂²	semidirect
34. C₃₁×#367	C₂²	semidirect
35. C₃₁×C₄⋊C₁₆	C₂²	semidirect
36. C₃₁×#358	C₂²	semidirect
37. C₃₁×#358	C₂²	semidirect
39. C₃₁×#357	C₂²	semidirect
40. C₃₁×C₂²⋊C₁₆	C₂²	semidirect
41. C₄×C₁₆×C₃₁	C₂²	semidirect
74. C₃₁×SD₃₂	D₄	direct (N × H)
112. Q₁₆×C₃₁	C₂×D₄	semidirect
139. C₁₆×C₃₁	C₂×D₄	semidirect
140. D₄×SD₃₂	C₃₁	direct (N × H)
160. D₄×C₃₁	SD₃₂	direct (N × H)
177. C₂²×SD₃₂	C₂×C₃₁	semidirect
178. D₄×Q₁₆	C₂×C₃₁	semidirect
180. #2248	C₂×C₃₁	semidirect
181. #2217	C₂×C₃₁	semidirect
182. #2208	C₂×C₃₁	semidirect
183. #2207	C₂×C₃₁	semidirect
184. #2187	C₂×C₃₁	semidirect
185. #2185	C₂×C₃₁	semidirect
186. C₄×SD₃₂	C₂×C₃₁	semidirect
187. D₄×C₁₆	C₂×C₃₁	semidirect
197. C₂²×C₃₁	C₂×SD₃₂	semidirect
205. C₄×C₃₁	C₂×SD₃₂	semidirect
208. C₂²×Q₁₆	C₂²×C₃₁	semidirect
215. C₂×SD₃₂	C₂²×C₃₁	semidirect
216. C₂×SD₃₂	C₂²×C₃₁	semidirect
217. C₂×SD₃₂	C₂²×C₃₁	semidirect
218. C₂²×C₁₆	C₂²×C₃₁	semidirect
219. #494	C₂²×C₃₁	semidirect
221. #467	C₂²×C₃₁	semidirect
227. C₄×Q₁₆	C₂²×C₃₁	semidirect
230. #367	C₂²×C₃₁	semidirect
231. C₄⋊C₁₆	C₂²×C₃₁	semidirect
232. #358	C₂²×C₃₁	semidirect
233. #358	C₂²×C₃₁	semidirect
235. #357	C₂²×C₃₁	semidirect
236. C₂²⋊C₁₆	C₂²×C₃₁	semidirect
237. C₄×C₁₆	C₂²×C₃₁	semidirect
276. SD₃₂	D₄×C₃₁	direct (N × H)
290. C₃₁	D₄×SD₃₂	direct (N × H)
315. Q₁₆	C₂×D₄×C₃₁	semidirect
342. C₁₆	C₂×D₄×C₃₁	semidirect
362. D₄	C₃₁×SD₃₂	direct (N × H)
388. C₂²	C₂×C₃₁×SD₃₂	semidirect
396. C₄	C₂×C₃₁×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×SD₃₂	2
D₄×Q₁₆×C₃₁	2
D₄×D₈×C₃₁	2
C₃₁×#2248	2
C₃₁×#2217	2
C₃₁×#2208	2
C₃₁×#2207	2
C₃₁×#2187	2
C₃₁×#2185	2
C₄×C₃₁×SD₃₂	2
D₄×C₁₆×C₃₁	2
D₄×SD₃₂	31

Subgroups — D4×C31×SD32 #21490606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₃₁×SD₃₂ #21490606