Subgroups — C₄×SD₁₆×D₃₁ #16854464

Order 3968.

552 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₃₁	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic
4	#14521140	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#92470	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#92481	C₂	1	1	yes	maximal, characteristic, complemented
8	#14521136	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#92480	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521134	C₂	1	1	yes	maximal, characteristic, complemented
11	#106×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#103×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₃₁	C₂	1	1	yes	maximal, characteristic
14	C₄×C₈×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₃₁	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₃₁	—	2	1	no	—
19	C₂×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	Q₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×#92481	C₂²	1	1	yes	characteristic
24	D₄×Dic₃₁	C₂²	1	1	yes	characteristic
25	C₂×#92480	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊D₃₁	—	2	1	no	—
27	SD₁₆×D₃₁	C₄	1	8	yes	direct product factor
28	C₂×#92470	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic
31	#11758470	C₂²	1	1	yes	characteristic
32	C₄⋊C₄×D₃₁	—	2	1	no	—
33	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
34	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
35	#11758464	—	2	1	no	—
36	#11758464	C₂²	1	1	yes	characteristic, complemented
37	(C₂²⋊D₃₁)⋊C₄	—	2	1	no	—
38	C₂²⋊C₄×D₃₁	—	2	1	no	—
39	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
40	C₄²×D₃₁	—	2	1	no	—
41	C₄²×D₃₁	C₂²	1	1	yes	characteristic
42	C₄×Dic₆₂	—	2	1	no	—
43	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#102	C₂²	1	1	yes	characteristic
47	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
48	#11758423	C₂²	1	1	yes	characteristic, complemented
49	#11758420	C₂²	1	1	yes	characteristic
50	#11758409	C₂²	1	1	yes	characteristic
51	#11758405	C₂²	1	1	yes	characteristic, complemented
52	#11758404	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
54	C₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
55	#11758398	C₂²	1	1	yes	characteristic, complemented
56	#11758397	C₂²	1	1	yes	characteristic
57	#11758396	C₂²	1	1	yes	characteristic, complemented
58	#11758396	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₃₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₃₁	—	2	1	no	—
61	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₃₁	—	2	1	no	—
64	C₂×C₂²⋊D₃₁	—	2	1	no	—
65	C₂²×Dic₃₁	—	2	1	no	—
66	Q₈×D₃₁	—	2	2	no	—
67	Q₈×D₃₁	C₂×C₄	1	4	yes	complemented
68	D₄×D₃₁	—	2	2	no	—
69	D₄×D₃₁	C₂×C₄	1	4	yes	—
70	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
71	C₂×C₄×D₃₁	—	2	1	no	—
72	C₂×C₄×D₃₁	—	2	1	no	—
73	C₂×C₄×D₃₁	—	2	1	no	—
74	C₂×C₄×D₃₁	—	2	1	no	—
75	C₂×C₄×D₃₁	—	2	1	no	—
76	C₂×C₄×D₃₁	—	4	4	no	—
77	C₂×C₄×D₃₁	D₄	1	1	yes	characteristic
78	C₂×C₄×D₃₁	D₄	1	1	yes	characteristic
79	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
80	C₂×Dic₆₂	—	2	1	no	—
81	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
82	SD₁₆×C₃₁	C₂×C₄	1	4	yes	complemented
83	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₄⋊C₄×C₃₁	—	2	1	no	—
86	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²⋊C₄×C₃₁	—	2	1	no	—
89	C₄²×C₃₁	—	2	1	no	—
90	C₄²×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²⋊Dic₃₁	—	2	1	no	—
92	#92481	C₂×C₄	1	4	yes	complemented
93	#92480	C₂×C₄	1	4	yes	complemented
94	(C₂×D₃₁)⋊C₄	—	2	1	no	—
95	(C₂×D₃₁)⋊C₄	—	2	1	no	—
96	C₄⋊Dic₃₁	—	2	1	no	—
97	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
99	Dic₃₁⋊C₄	—	2	1	no	—
100	Dic₃₁⋊C₄	—	2	1	no	—
101	Dic₃₁⋊C₄	—	2	1	no	—
102	Dic₃₁⋊C₄	—	2	1	no	—
103	C₄×Dic₃₁	—	2	1	no	—
104	C₄×Dic₃₁	—	2	1	no	—
105	C₄×Dic₃₁	—	2	1	no	—
106	C₄×Dic₃₁	D₄	1	1	yes	characteristic
107	C₄×Dic₃₁	D₄	1	1	yes	characteristic
108	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
109	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
111	#92470	C₂×C₄	1	4	yes	complemented
112	C₈×D₃₁	—	2	2	no	—
113	C₈×D₃₁	C₂×C₄	1	4	yes	complemented
114	C₂³×C₃₁	—	2	1	no	—
115	C₂²×D₃₁	—	2	1	no	—
116	C₂²×D₃₁	—	2	4	no	—
117	C₂²×D₃₁	—	4	2	no	—
118	C₂²×D₃₁	—	4	2	no	—
119	C₂²×D₃₁	C₂×D₄	1	1	yes	characteristic
120	Q₈×C₃₁	—	2	1	no	—
121	Q₈×C₃₁	C₂²×C₄	1	2	yes	complemented
122	D₄×C₃₁	—	2	1	no	—
123	D₄×C₃₁	C₂²×C₄	1	2	yes	—
124	C₂×C₄×C₃₁	—	2	1	no	—
125	C₂×C₄×C₃₁	—	2	1	no	—
126	C₂×C₄×C₃₁	—	2	1	no	—
127	C₂×C₄×C₃₁	—	4	2	no	—
128	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
131	C₂²⋊D₃₁	—	2	4	no	—
132	C₂×Dic₃₁	—	2	1	no	—
133	C₂×Dic₃₁	—	2	1	no	—
134	C₂×Dic₃₁	—	2	1	no	—
135	C₂×Dic₃₁	—	4	2	no	—
136	C₂×Dic₃₁	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₃₁	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₃₁	C₂×D₄	1	1	yes	characteristic
139	D₁₂₄	—	2	1	no	—
140	D₁₂₄	C₂²×C₄	1	2	yes	—
141	C₄×D₃₁	—	2	4	no	—
142	C₄×D₃₁	—	2	2	no	—
143	C₄×D₃₁	—	4	2	no	—
144	C₄×D₃₁	—	4	2	no	—
145	C₄×D₃₁	—	4	2	no	—
146	C₄×D₃₁	—	4	2	no	—
147	C₄×D₃₁	SD₁₆	1	4	yes	direct product factor
148	C₄×D₃₁	C₂²×C₄	1	2	yes	—
149	C₄×D₃₁	#41	1	2	yes	—
150	Dic₆₂	—	2	1	no	—
151	Dic₆₂	—	2	4	no	—
152	Dic₆₂	C₂²×C₄	1	2	yes	complemented
153	C₈×C₃₁	—	2	1	no	—
154	C₈×C₃₁	C₂²×C₄	1	2	yes	complemented
155	C₃₁⋊C₈	—	2	1	no	—
156	C₃₁⋊C₈	C₂²×C₄	1	2	yes	complemented
157	C₂×C₄×SD₁₆	—	31	1	no	maximal, Sylow
158	C₂²×C₃₁	—	2	2	no	—
159	C₂²×C₃₁	—	4	1	no	—
160	C₂²×C₃₁	—	4	1	no	—
161	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×D₃₁	—	2	2	no	—
163	C₂×D₃₁	—	4	1	no	—
164	C₂×D₃₁	—	4	1	no	—
165	C₂×D₃₁	—	4	8	no	—
166	C₂×D₃₁	C₄×D₄	1	2	yes	—
167	C₂×D₃₁	C₂×SD₁₆	1	2	yes	—
168	C₂×D₃₁	#135	1	2	yes	—
169	C₄×C₃₁	—	2	2	no	—
170	C₄×C₃₁	—	2	1	no	—
171	C₄×C₃₁	—	4	1	no	—
172	C₄×C₃₁	—	4	1	no	—
173	C₄×C₃₁	C₂×SD₁₆	1	2	yes	complemented
174	C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
175	C₄×C₃₁	C₂×#41	1	1	yes	characteristic
176	Dic₃₁	—	2	2	no	—
177	Dic₃₁	—	2	1	no	—
178	Dic₃₁	—	4	1	no	—
179	Dic₃₁	—	4	1	no	—
180	Dic₃₁	C₄×D₄	1	2	yes	—
181	Dic₃₁	C₂×SD₁₆	1	2	yes	complemented
182	C₂²×SD₁₆	—	31	1	no	—
183	C₂×C₄×Q₈	—	31	1	no	—
184	C₂×C₄×D₄	—	31	1	no	—
185	C₄×SD₁₆	—	31	1	no	—
186	C₄×SD₁₆	—	31	1	no	—
187	C₄×SD₁₆	—	31	1	no	—
188	C₄×SD₁₆	—	31	1	no	—
189	C₄×SD₁₆	—	31	1	no	—
190	C₄×SD₁₆	—	31	1	no	—
191	C₄×SD₁₆	—	31	1	no	—
192	C₄×SD₁₆	D₃₁	1	1	yes	characteristic, direct product factor
193	C₂×#106	—	31	1	no	—
194	C₂×#103	—	31	1	no	—
195	C₂×#102	—	31	1	no	—
196	C₂×C₄×C₈	—	31	1	no	—
197	C₂×C₃₁	—	4	2	no	—
198	C₂×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
200	C₂×C₃₁	C₂×#135	1	1	yes	characteristic
201	D₃₁	—	4	2	no	—
202	D₃₁	C₄×SD₁₆	1	4	yes	direct product factor
203	C₂²×Q₈	—	31	1	no	—
204	C₂²×D₄	—	31	1	no	—
205	C₂³×C₄	—	62	1	no	—
206	C₂×SD₁₆	—	31	1	no	—
207	C₂×SD₁₆	—	31	1	no	—
208	C₂×SD₁₆	—	31	8	no	—
209	C₂×SD₁₆	—	31	1	no	—
210	C₂×SD₁₆	C₂×D₃₁	1	1	yes	characteristic
211	C₂²×C₈	—	31	1	no	—
212	C₂²×C₈	—	31	1	no	—
213	C₄×Q₈	—	31	1	no	—
214	C₄×Q₈	—	31	1	no	—
215	C₄×Q₈	—	31	1	no	—
216	C₄×Q₈	—	62	1	no	—
217	C₄×Q₈	—	62	1	no	—
218	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
219	C₄×D₄	—	31	1	no	—
220	C₄×D₄	—	31	1	no	—
221	C₄×D₄	—	31	1	no	—
222	C₄×D₄	—	62	1	no	—
223	C₄×D₄	—	62	1	no	—
224	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
225	C₂×C₄⋊C₄	—	31	1	no	—
226	C₂×C₄⋊C₄	—	31	1	no	—
227	C₂×C₄⋊C₄	—	62	1	no	—
228	C₂×C₂²⋊C₄	—	62	1	no	—
229	C₂×C₄²	—	31	1	no	—
230	C₂×C₄²	—	62	1	no	—
231	#106	—	31	1	no	—
232	#106	—	31	1	no	—
233	#106	—	31	1	no	—
234	#106	C₂×D₃₁	1	1	yes	characteristic, complemented
235	#103	—	31	1	no	—
236	#103	—	31	1	no	—
237	#103	—	31	1	no	—
238	#103	C₂×D₃₁	1	1	yes	characteristic, complemented
239	#102	—	31	1	no	—
240	#102	—	31	1	no	—
241	#102	—	31	1	no	—
242	#102	C₂×D₃₁	1	1	yes	characteristic
243	C₄×C₈	—	31	1	no	—
244	C₄×C₈	—	31	1	no	—
245	C₄×C₈	—	31	1	no	—
246	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
247	C₃₁	C₂×C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
248	C₂⁴	—	62	1	no	—
249	C₂×Q₈	—	31	4	no	—
250	C₂×Q₈	—	31	1	no	—
251	C₂×Q₈	—	62	1	no	—
252	C₂×Q₈	—	62	2	no	—
253	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic
254	C₂×D₄	—	31	4	no	—
255	C₂×D₄	—	31	1	no	—
256	C₂×D₄	—	62	2	no	—
257	C₂×D₄	—	62	1	no	—
258	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	31	1	no	—
261	C₂²×C₄	—	31	1	no	—
262	C₂²×C₄	—	31	1	no	—
263	C₂²×C₄	—	62	1	no	—
264	C₂²×C₄	—	62	1	no	—
265	C₂²×C₄	—	62	1	no	—
266	C₂²×C₄	—	62	1	no	—
267	C₂²×C₄	—	62	1	no	—
268	C₂²×C₄	—	62	1	no	—
269	C₂²×C₄	—	124	4	no	—
270	SD₁₆	—	31	4	no	—
271	SD₁₆	—	31	4	no	—
272	SD₁₆	—	31	4	no	—
273	SD₁₆	C₄×D₃₁	1	4	yes	direct product factor
274	C₂×C₈	—	31	1	no	—
275	C₂×C₈	—	31	4	no	—
276	C₂×C₈	—	31	1	no	—
277	C₂×C₈	—	62	2	no	—
278	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
279	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	31	1	no	—
282	C₄⋊C₄	—	31	1	no	—
283	C₄⋊C₄	—	62	1	no	—
284	C₄⋊C₄	—	62	1	no	—
285	C₄⋊C₄	—	62	1	no	—
286	C₄⋊C₄	—	62	1	no	—
287	C₄⋊C₄	—	62	1	no	—
288	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
289	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	62	1	no	—
292	C₂²⋊C₄	—	62	1	no	—
293	C₂²⋊C₄	—	62	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	31	1	no	—
296	C₄²	—	31	1	no	—
297	C₄²	—	31	1	no	—
298	C₄²	—	62	1	no	—
299	C₄²	—	62	1	no	—
300	C₄²	—	62	1	no	—
301	C₄²	C₂²×D₃₁	1	1	yes	characteristic
302	C₂³	—	2	1	no	—
303	C₂³	—	31	1	no	—
304	C₂³	—	62	4	no	—
305	C₂³	—	62	1	no	—
306	C₂³	—	124	2	no	—
307	C₂³	—	124	2	no	—
308	Q₈	—	2	1	no	—
309	Q₈	—	31	2	no	—
310	Q₈	—	62	4	no	—
311	Q₈	—	62	1	no	—
312	Q₈	C₂×C₄×D₃₁	1	2	yes	complemented
313	D₄	—	2	1	no	—
314	D₄	—	31	2	no	—
315	D₄	—	62	4	no	—
316	D₄	—	62	1	no	—
317	D₄	C₂×C₄×D₃₁	1	2	yes	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	31	1	no	—
323	C₂×C₄	—	31	1	no	—
324	C₂×C₄	—	31	4	no	—
325	C₂×C₄	—	31	2	no	—
326	C₂×C₄	—	31	2	no	—
327	C₂×C₄	—	31	1	no	—
328	C₂×C₄	—	62	2	no	—
329	C₂×C₄	—	62	4	no	—
330	C₂×C₄	—	62	1	no	—
331	C₂×C₄	—	62	1	no	—
332	C₂×C₄	—	62	1	no	—
333	C₂×C₄	—	124	2	no	—
334	C₂×C₄	—	124	2	no	—
335	C₂×C₄	—	124	2	no	—
336	C₂×C₄	—	124	2	no	—
337	C₂×C₄	—	124	2	no	—
338	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
339	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
340	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
341	C₈	—	2	1	no	—
342	C₈	—	31	2	no	—
343	C₈	—	62	1	no	—
344	C₈	C₂×C₄×D₃₁	1	2	yes	complemented
345	C₂²	—	2	2	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	31	2	no	—
349	C₂²	—	31	2	no	—
350	C₂²	—	31	2	no	—
351	C₂²	—	62	2	no	—
352	C₂²	—	124	8	no	—
353	C₂²	—	124	1	no	—
354	C₂²	—	124	1	no	—
355	C₂²	C₂×D₄×D₃₁	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	31	2	no	—
361	C₄	—	31	2	no	—
362	C₄	—	62	2	no	—
363	C₄	—	62	1	no	—
364	C₄	—	124	1	no	—
365	C₄	—	124	1	no	—
366	C₄	SD₁₆×D₃₁	1	2	yes	direct product factor
367	C₄	C₂²×C₄×D₃₁	1	1	yes	characteristic
368	C₄	#41×D₃₁	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	—	31	4	no	—
371	C₂	—	124	2	no	—
372	C₂	C₄×D₄×D₃₁	1	1	yes	characteristic
373	C₂	C₂×SD₁₆×D₃₁	1	1	yes	characteristic
374	C₂	#135×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₃₁
commutator	C₄×C₃₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃₁
Fitting	C₄×SD₁₆×C₃₁	C₂
socle	C₂²×C₃₁	C₂²×D₄
prime radical	C₂×D₄×D₃₁	C₂²
cosocle	C₂×C₄×C₃₁	C₂⁴
hypercenter	C₄×SD₁₆	D₃₁
hypocenter	C₃₁	C₂×C₄×SD₁₆
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×D₃₁	C₂	semidirect
4. #14521140	C₂	semidirect
5. C₄×#92470	C₂	semidirect
6. SD₁₆×Dic₃₁	C₂	semidirect
7. C₄×#92481	C₂	semidirect
8. #14521136	C₂	semidirect
9. C₄×#92480	C₂	semidirect
10. #14521134	C₂	semidirect
11. #106×D₃₁	C₂	semidirect
12. #103×D₃₁	C₂	semidirect
14. C₄×C₈×D₃₁	C₂	semidirect
15. C₄×SD₁₆×C₃₁	C₂	semidirect
20. C₄×Q₈×C₃₁	C₂²	semidirect
22. Q₈×Dic₃₁	C₂²	semidirect
27. SD₁₆×D₃₁	C₄	direct (N × H)
36. #11758464	C₂²	semidirect
43. C₄×Dic₆₂	C₂²	semidirect
44. C₃₁×#106	C₂²	semidirect
45. C₃₁×#103	C₂²	semidirect
47. C₄×C₈×C₃₁	C₂²	semidirect
48. #11758423	C₂²	semidirect
51. #11758405	C₂²	semidirect
52. #11758404	C₂²	semidirect
53. C₈×Dic₃₁	C₂²	semidirect
54. C₈×Dic₃₁	C₂²	semidirect
55. #11758398	C₂²	semidirect
57. #11758396	C₂²	semidirect
58. #11758396	C₂²	semidirect
59. C₄×C₃₁⋊C₈	C₂²	semidirect
67. Q₈×D₃₁	C₂×C₄	semidirect
82. SD₁₆×C₃₁	C₂×C₄	semidirect
92. #92481	C₂×C₄	semidirect
93. #92480	C₂×C₄	semidirect
111. #92470	C₂×C₄	semidirect
113. C₈×D₃₁	C₂×C₄	semidirect
121. Q₈×C₃₁	C₂²×C₄	semidirect
147. C₄×D₃₁	SD₁₆	direct (N × H)
152. Dic₆₂	C₂²×C₄	semidirect
154. C₈×C₃₁	C₂²×C₄	semidirect
156. C₃₁⋊C₈	C₂²×C₄	semidirect
173. C₄×C₃₁	C₂×SD₁₆	semidirect
181. Dic₃₁	C₂×SD₁₆	semidirect
192. C₄×SD₁₆	D₃₁	direct (N × H)
202. D₃₁	C₄×SD₁₆	direct (N × H)
218. C₄×Q₈	C₂×D₃₁	semidirect
234. #106	C₂×D₃₁	semidirect
238. #103	C₂×D₃₁	semidirect
246. C₄×C₈	C₂×D₃₁	semidirect
247. C₃₁	C₂×C₄×SD₁₆	semidirect
273. SD₁₆	C₄×D₃₁	direct (N × H)
312. Q₈	C₂×C₄×D₃₁	semidirect
344. C₈	C₂×C₄×D₃₁	semidirect
366. C₄	SD₁₆×D₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₃₁	2
C₄×Q₈×D₃₁	2
C₄×D₄×D₃₁	2
#14521140	2
C₄×#92470	2
SD₁₆×Dic₃₁	2
C₄×#92481	2
#14521136	2
C₄×#92480	2
#14521134	2
#106×D₃₁	2
#103×D₃₁	2
#102×D₃₁	2
C₄×C₈×D₃₁	2
C₄×SD₁₆×C₃₁	2
C₂×C₄×SD₁₆	31

Subgroups — C4×SD16×D31 #16854464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×SD₁₆×D₃₁ #16854464