Subgroups — C₂×C₈×C₄⋊C₄×C₃₁ #21477191

Order 7936.

1438 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈×C₃₁	C₂	1	2	yes	maximal
3	C₂²×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₈×C₄⋊C₄×C₃₁	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×#336	C₂	1	2	yes	maximal
7	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
11	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
12	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×C₄⋊C₈	C₄	1	8	yes	complemented
14	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
15	C₂×C₄×C₈×C₃₁	—	2	8	no	—
16	C₂×C₄×C₈×C₃₁	C₄	1	8	yes	complemented
17	C₂×C₄×C₈×C₃₁	C₂²	1	8	yes	—
18	C₂×C₄×C₈×C₃₁	C₂²	1	4	yes	—
19	C₄×C₄⋊C₄×C₃₁	C₄	1	4	yes	—
20	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
21	C₂×C₃₁×#95	C₄	1	2	yes	—
22	C₃₁×#336	C₂²	1	8	yes	—
23	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₃₁	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₃₁	—	2	4	no	—
28	C₂²×C₈×C₃₁	—	2	2	no	—
29	C₂²×C₈×C₃₁	—	2	2	no	—
30	C₂²×C₈×C₃₁	—	2	4	no	—
31	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₃₁	C₂×C₄	1	8	yes	—
33	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₃₁	D₄	1	4	yes	—
35	C₂²×C₈×C₃₁	Q₈	1	4	yes	—
36	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
37	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
38	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
39	C₂×C₄⋊C₄×C₃₁	C₈	1	16	yes	direct product factor
40	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	—
41	C₂×C₄²×C₃₁	—	2	4	no	—
42	C₂×C₄²×C₃₁	—	2	4	no	—
43	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
48	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
49	C₃₁×C₄⋊C₈	C₂×C₄	1	16	yes	complemented
50	C₄×C₈×C₃₁	—	2	16	no	—
51	C₄×C₈×C₃₁	C₂×C₄	1	16	yes	complemented
52	C₃₁×#95	C₂×C₄	1	8	yes	—
53	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₃₁	—	2	8	no	—
55	C₂²×C₄×C₃₁	—	2	4	no	—
56	C₂²×C₄×C₃₁	—	2	8	no	—
57	C₂²×C₄×C₃₁	C₄²	1	4	yes	—
58	C₂²×C₄×C₃₁	C₄²	1	4	yes	—
59	C₂²×C₄×C₃₁	C₂×C₈	1	16	yes	—
60	C₂²×C₄×C₃₁	C₂×C₈	1	8	yes	—
61	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
62	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
63	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
65	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
66	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
68	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
69	C₂²×C₄×C₃₁	#41	1	2	yes	—
70	C₂²×C₄×C₃₁	#41	1	2	yes	—
71	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
72	C₂×C₈×C₃₁	—	2	8	no	—
73	C₂×C₈×C₃₁	—	2	16	no	—
74	C₂×C₈×C₃₁	—	2	4	no	—
75	C₂×C₈×C₃₁	—	2	2	no	—
76	C₂×C₈×C₃₁	—	2	2	no	—
77	C₂×C₈×C₃₁	—	2	4	no	—
78	C₂×C₈×C₃₁	C₄⋊C₄	1	16	yes	direct product factor
79	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
80	C₂×C₈×C₃₁	C₂²×C₄	1	8	yes	—
81	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
82	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
83	C₂×C₈×C₃₁	C₂×Q₈	1	4	yes	—
84	C₄⋊C₄×C₃₁	C₂×C₈	1	32	yes	direct product factor
85	C₄²×C₃₁	—	2	8	no	—
86	C₄²×C₃₁	—	2	4	no	—
87	C₄²×C₃₁	—	2	4	no	—
88	C₄²×C₃₁	C₄²	1	8	yes	—
89	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
90	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
91	C₂×C₈×C₄⋊C₄	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂³×C₃₁	C₂×C₄²	1	2	yes	—
93	C₂³×C₃₁	C₄×D₄	1	2	yes	—
94	C₂³×C₃₁	C₄×Q₈	1	2	yes	—
95	C₂³×C₃₁	C₂²×C₈	1	4	yes	—
96	C₂³×C₃₁	#131	1	4	yes	—
97	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
98	C₂×C₄×C₃₁	—	2	8	no	—
99	C₂×C₄×C₃₁	—	2	4	no	—
100	C₂×C₄×C₃₁	—	2	8	no	—
101	C₂×C₄×C₃₁	—	2	8	no	—
102	C₂×C₄×C₃₁	—	2	32	no	—
103	C₂×C₄×C₃₁	C₄×C₈	1	16	yes	complemented
104	C₂×C₄×C₃₁	C₂×C₄²	1	4	yes	—
105	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
106	C₂×C₄×C₃₁	C₂×C₄²	1	4	yes	—
107	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
108	C₂×C₄×C₃₁	#117	1	4	yes	—
109	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
110	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
111	C₂×C₄×C₃₁	C₄×Q₈	1	4	yes	—
112	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
113	C₂×C₄×C₃₁	C₂²×C₈	1	16	yes	—
114	C₂×C₄×C₃₁	C₂²×C₈	1	8	yes	—
115	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
116	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
117	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
118	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
119	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
120	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
121	C₈×C₃₁	—	2	4	no	—
122	C₈×C₃₁	—	2	8	no	—
123	C₈×C₃₁	C₂×C₄⋊C₄	1	8	yes	direct product factor
124	C₂²×C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic
125	C₂²×C₄×C₈	C₂×C₃₁	1	2	yes	—
126	C₂²×C₄×C₈	C₂×C₃₁	1	1	yes	characteristic
127	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
128	C₈×C₄⋊C₄	C₂×C₃₁	1	8	yes	direct product factor
129	C₂×#336	C₂×C₃₁	1	2	yes	—
130	C₂²×C₃₁	C₄×C₄⋊C₄	1	4	yes	—
131	C₂²×C₃₁	C₂×C₄×C₈	1	4	yes	—
132	C₂²×C₃₁	#405	1	4	yes	—
133	C₂²×C₃₁	C₈×D₄	1	8	yes	—
134	C₂²×C₃₁	C₈×Q₈	1	8	yes	—
135	C₂²×C₃₁	C₂²×C₄²	1	1	yes	characteristic
136	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
137	C₂²×C₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
138	C₂²×C₃₁	C₂³×C₈	1	2	yes	—
139	C₂²×C₃₁	C₂×#131	1	2	yes	—
140	C₄×C₃₁	—	2	4	no	—
141	C₄×C₃₁	—	2	16	no	—
142	C₄×C₃₁	C₄×C₄⋊C₄	1	4	yes	—
143	C₄×C₃₁	C₂×C₄×C₈	1	8	yes	complemented
144	C₄×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
145	C₄×C₃₁	C₂×#117	1	1	yes	characteristic
146	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
147	C₄×C₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
148	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
149	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
150	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
151	C₂²×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
152	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
153	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
154	C₂×C₄⋊C₈	C₄×C₃₁	1	8	yes	complemented
155	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
156	C₂×C₄×C₈	—	2	8	no	—
157	C₂×C₄×C₈	C₄×C₃₁	1	8	yes	complemented
158	C₂×C₄×C₈	C₂²×C₃₁	1	8	yes	—
159	C₂×C₄×C₈	C₂²×C₃₁	1	4	yes	—
160	C₄×C₄⋊C₄	C₄×C₃₁	1	4	yes	—
161	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
162	C₂×#95	C₄×C₃₁	1	2	yes	—
163	#336	C₂²×C₃₁	1	8	yes	—
164	C₂×C₃₁	C₈×C₄⋊C₄	1	8	yes	direct product factor
165	C₂×C₃₁	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₃₁	C₂²×C₄×C₈	1	1	yes	characteristic
167	C₂×C₃₁	C₂×#405	1	1	yes	characteristic
168	C₂×C₃₁	C₂×C₈×D₄	1	2	yes	—
169	C₂×C₃₁	C₂×C₈×Q₈	1	2	yes	—
170	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
171	C₂³×C₄	C₂×C₄×C₃₁	1	4	yes	—
172	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
173	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
174	C₂²×C₈	—	2	4	no	—
175	C₂²×C₈	—	2	2	no	—
176	C₂²×C₈	—	2	2	no	—
177	C₂²×C₈	—	2	4	no	—
178	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
179	C₂²×C₈	C₂×C₄×C₃₁	1	8	yes	—
180	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
181	C₂²×C₈	D₄×C₃₁	1	4	yes	—
182	C₂²×C₈	Q₈×C₃₁	1	4	yes	—
183	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
184	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
185	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
186	C₂×C₄⋊C₄	C₈×C₃₁	1	16	yes	direct product factor
187	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	—
188	C₂×C₄²	—	2	4	no	—
189	C₂×C₄²	—	2	4	no	—
190	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
191	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
192	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
193	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
194	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
195	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
196	C₄⋊C₈	C₂×C₄×C₃₁	1	16	yes	complemented
197	C₄×C₈	—	2	16	no	—
198	C₄×C₈	C₂×C₄×C₃₁	1	16	yes	complemented
199	#95	C₂×C₄×C₃₁	1	8	yes	—
200	C₃₁	C₂×C₈×C₄⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
201	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
202	C₂²×C₄	—	2	8	no	—
203	C₂²×C₄	—	2	4	no	—
204	C₂²×C₄	—	2	8	no	—
205	C₂²×C₄	C₄²×C₃₁	1	4	yes	—
206	C₂²×C₄	C₄²×C₃₁	1	4	yes	—
207	C₂²×C₄	C₂×C₈×C₃₁	1	16	yes	—
208	C₂²×C₄	C₂×C₈×C₃₁	1	8	yes	—
209	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
210	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
211	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
212	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
213	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
214	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
215	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
216	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
217	C₂²×C₄	#41×C₃₁	1	2	yes	—
218	C₂²×C₄	#41×C₃₁	1	2	yes	—
219	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
220	C₂×C₈	—	2	8	no	—
221	C₂×C₈	—	2	16	no	—
222	C₂×C₈	—	2	4	no	—
223	C₂×C₈	—	2	2	no	—
224	C₂×C₈	—	2	2	no	—
225	C₂×C₈	—	2	4	no	—
226	C₂×C₈	C₄⋊C₄×C₃₁	1	16	yes	direct product factor
227	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
228	C₂×C₈	C₂²×C₄×C₃₁	1	8	yes	—
229	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
230	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
231	C₂×C₈	C₂×Q₈×C₃₁	1	4	yes	—
232	C₄⋊C₄	C₂×C₈×C₃₁	1	32	yes	direct product factor
233	C₄²	—	2	8	no	—
234	C₄²	—	2	4	no	—
235	C₄²	—	2	4	no	—
236	C₄²	C₄²×C₃₁	1	8	yes	—
237	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
238	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
239	C₂³	C₂×C₄²×C₃₁	1	2	yes	—
240	C₂³	C₄×D₄×C₃₁	1	2	yes	—
241	C₂³	C₄×Q₈×C₃₁	1	2	yes	—
242	C₂³	C₂²×C₈×C₃₁	1	4	yes	—
243	C₂³	C₃₁×#131	1	4	yes	—
244	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
245	C₂×C₄	—	2	8	no	—
246	C₂×C₄	—	2	32	no	—
247	C₂×C₄	—	2	8	no	—
248	C₂×C₄	—	2	4	no	—
249	C₂×C₄	—	2	8	no	—
250	C₂×C₄	C₄×C₈×C₃₁	1	16	yes	complemented
251	C₂×C₄	C₂×C₄²×C₃₁	1	4	yes	—
252	C₂×C₄	C₂×C₄²×C₃₁	1	4	yes	—
253	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
254	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
255	C₂×C₄	C₃₁×#117	1	4	yes	—
256	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
257	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
258	C₂×C₄	C₄×Q₈×C₃₁	1	4	yes	—
259	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
260	C₂×C₄	C₂²×C₈×C₃₁	1	16	yes	—
261	C₂×C₄	C₂²×C₈×C₃₁	1	8	yes	—
262	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
263	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
264	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
265	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
266	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
267	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
268	C₈	—	2	4	no	—
269	C₈	—	2	8	no	—
270	C₈	C₂×C₄⋊C₄×C₃₁	1	8	yes	direct product factor
271	C₂²	C₄×C₄⋊C₄×C₃₁	1	4	yes	—
272	C₂²	C₂×C₄×C₈×C₃₁	1	4	yes	—
273	C₂²	C₃₁×#405	1	4	yes	—
274	C₂²	C₈×D₄×C₃₁	1	8	yes	—
275	C₂²	C₈×Q₈×C₃₁	1	8	yes	—
276	C₂²	C₂²×C₄²×C₃₁	1	1	yes	characteristic
277	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
278	C₂²	C₂×C₄×Q₈×C₃₁	1	1	yes	characteristic
279	C₂²	C₂³×C₈×C₃₁	1	2	yes	—
280	C₂²	C₂×C₃₁×#131	1	2	yes	—
281	C₄	—	2	4	no	—
282	C₄	—	2	16	no	—
283	C₄	C₄×C₄⋊C₄×C₃₁	1	4	yes	—
284	C₄	C₂×C₄×C₈×C₃₁	1	8	yes	complemented
285	C₄	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
286	C₄	C₂×C₃₁×#117	1	1	yes	characteristic
287	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
288	C₄	C₂×C₄×Q₈×C₃₁	1	1	yes	characteristic
289	C₂	C₈×C₄⋊C₄×C₃₁	1	8	yes	direct product factor
290	C₂	C₂×C₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic
291	C₂	C₂²×C₄×C₈×C₃₁	1	1	yes	characteristic
292	C₂	C₂×C₃₁×#405	1	1	yes	characteristic
293	C₂	C₂×C₈×D₄×C₃₁	1	2	yes	—
294	C₂	C₂×C₈×Q₈×C₃₁	1	2	yes	—

	subgroup	G/H
center	C₂³×C₈×C₃₁	C₂²
commutator	C₂	C₂²×C₄×C₈×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle, prime radical	C₂⁴×C₃₁	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₈×C₄⋊C₄×C₃₁	C₂	direct (N × H)
13. C₂×C₃₁×C₄⋊C₈	C₄	semidirect
16. C₂×C₄×C₈×C₃₁	C₄	semidirect
39. C₂×C₄⋊C₄×C₃₁	C₈	direct (N × H)
49. C₃₁×C₄⋊C₈	C₂×C₄	semidirect
51. C₄×C₈×C₃₁	C₂×C₄	semidirect
78. C₂×C₈×C₃₁	C₄⋊C₄	direct (N × H)
84. C₄⋊C₄×C₃₁	C₂×C₈	direct (N × H)
91. C₂×C₈×C₄⋊C₄	C₃₁	direct (N × H)
103. C₂×C₄×C₃₁	C₄×C₈	semidirect
123. C₈×C₃₁	C₂×C₄⋊C₄	direct (N × H)
128. C₈×C₄⋊C₄	C₂×C₃₁	direct (N × H)
143. C₄×C₃₁	C₂×C₄×C₈	semidirect
154. C₂×C₄⋊C₈	C₄×C₃₁	semidirect
157. C₂×C₄×C₈	C₄×C₃₁	semidirect
164. C₂×C₃₁	C₈×C₄⋊C₄	direct (N × H)
186. C₂×C₄⋊C₄	C₈×C₃₁	direct (N × H)
196. C₄⋊C₈	C₂×C₄×C₃₁	semidirect
198. C₄×C₈	C₂×C₄×C₃₁	semidirect
200. C₃₁	C₂×C₈×C₄⋊C₄	direct (N × H)
226. C₂×C₈	C₄⋊C₄×C₃₁	direct (N × H)
232. C₄⋊C₄	C₂×C₈×C₃₁	direct (N × H)
250. C₂×C₄	C₄×C₈×C₃₁	semidirect
270. C₈	C₂×C₄⋊C₄×C₃₁	direct (N × H)
284. C₄	C₂×C₄×C₈×C₃₁	semidirect
289. C₂	C₈×C₄⋊C₄×C₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×C₄⋊C₈	2
C₂²×C₄×C₈×C₃₁	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₈×C₄⋊C₄×C₃₁	2
C₂×C₃₁×#336	2
C₂×C₈×C₄⋊C₄	31

Subgroups — C2×C8×C4⋊C4×C31 #21477191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₄⋊C₄×C₃₁ #21477191