Subgroups — C₂×C₃₁×#3489 #21519560

Order 7936.

11438 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3489	C₂	1	32	yes	maximal, direct product factor
4	C₂×D₄×Q₈×C₃₁	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#548	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#547	C₂	1	6	yes	maximal, complemented
7	C₂×C₃₁×#546	C₂	1	6	yes	maximal, complemented
8	C₂×C₃₁×#537	C₂	1	3	yes	maximal, complemented
9	C₂×C₃₁×#536	C₂	1	3	yes	maximal, complemented
10	C₂×C₃₁×#525	C₂	1	3	yes	maximal, complemented
11	C₂²×C₃₁×C₂²⋊Q₈	C₂	1	3	yes	maximal, complemented
12	C₂×C₃₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×2₋¹⁺⁴	—	2	16	no	—
14	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	16	yes	complemented
15	C₂²×#41×C₃₁	—	2	16	no	—
16	C₂²×#41×C₃₁	C₂²	1	3	yes	—
17	C₂²×#41×C₃₁	C₂²	1	3	yes	—
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₃₁	C₂²	1	16	yes	complemented
21	C₂²×#41×C₃₁	C₂²	1	3	yes	complemented
22	C₂²×#41×C₃₁	C₂²	1	6	yes	complemented
23	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₂³×Q₈×C₃₁	C₂²	1	3	yes	complemented
25	C₂³×Q₈×C₃₁	C₂²	1	2	yes	complemented
26	C₂³×D₄×C₃₁	C₂²	1	3	yes	—
27	C₂⁴×C₄×C₃₁	C₂²	1	3	yes	—
28	D₄×Q₈×C₃₁	C₂²	1	32	yes	complemented
29	C₃₁×#548	C₂²	1	32	yes	complemented
30	C₃₁×#547	C₂²	1	96	yes	complemented
31	C₃₁×#546	C₂²	1	96	yes	complemented
32	C₃₁×#537	C₂²	1	48	yes	complemented
33	C₃₁×#536	C₂²	1	48	yes	complemented
34	C₂×C₃₁×C₄⋊Q₈	C₂²	1	6	yes	complemented
35	C₂×C₃₁×#124	C₂²	1	6	yes	complemented
36	C₃₁×#525	C₂²	1	48	yes	complemented
37	C₂×C₃₁×#123	C₂²	1	6	yes	complemented
38	C₂×C₃₁×#123	C₂²	1	12	yes	complemented
39	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	3	yes	—
40	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	6	yes	—
41	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	6	yes	complemented
42	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	6	yes	complemented
43	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	3	yes	complemented
44	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	6	yes	complemented
45	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	48	yes	complemented
46	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#121	C₂²	1	3	yes	complemented
48	C₂×C₃₁×#121	C₂²	1	12	yes	complemented
49	C₂×C₃₁×#121	C₂²	1	6	yes	complemented
50	C₂×C₃₁×#120	C₂²	1	6	yes	—
51	C₃₁×#520	C₂²	1	16	yes	complemented
52	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
53	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	—
54	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	complemented
55	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	complemented
56	C₂×C₃₁×#117	C₂²	1	3	yes	complemented
57	C₂²×C₄⋊C₄×C₃₁	C₂²	1	3	yes	complemented
58	C₂²×C₄⋊C₄×C₃₁	C₂²	1	6	yes	complemented
59	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	6	yes	—
60	C₂⁵×C₃₁	C₂³	1	3	yes	—
61	C₃₁×2₋¹⁺⁴	—	2	128	no	—
62	C₂×#41×C₃₁	—	2	128	no	—
63	C₂×#41×C₃₁	—	2	8	no	—
64	C₂×#41×C₃₁	—	2	24	no	—
65	C₂×#41×C₃₁	—	2	48	no	—
66	C₂×#41×C₃₁	—	2	24	no	—
67	C₂×#41×C₃₁	—	2	24	no	—
68	C₂×#41×C₃₁	D₄	1	16	yes	complemented
69	C₂×#41×C₃₁	C₂³	1	24	yes	—
70	C₂×#41×C₃₁	C₂³	1	24	yes	—
71	C₂×#41×C₃₁	C₂³	1	8	yes	—
72	C₂×#41×C₃₁	C₂³	1	8	yes	—
73	C₂×#41×C₃₁	C₂³	1	24	yes	complemented
74	C₂×#41×C₃₁	C₂³	1	48	yes	complemented
75	C₂²×Q₈×C₃₁	—	2	8	no	—
76	C₂²×Q₈×C₃₁	—	2	16	no	—
77	C₂²×Q₈×C₃₁	—	2	24	no	—
78	C₂²×Q₈×C₃₁	C₂³	1	3	yes	—
79	C₂²×Q₈×C₃₁	C₂³	1	6	yes	—
80	C₂²×Q₈×C₃₁	C₂³	1	3	yes	—
81	C₂²×Q₈×C₃₁	C₂³	1	8	yes	—
82	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₃₁	C₂³	1	24	yes	complemented
84	C₂²×Q₈×C₃₁	C₂³	1	16	yes	complemented
85	C₂²×D₄×C₃₁	—	2	24	no	—
86	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
87	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
88	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
91	C₂²×D₄×C₃₁	C₂³	1	24	yes	—
92	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
93	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
94	C₂³×C₄×C₃₁	—	2	24	no	—
95	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
96	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
97	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
98	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
99	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
100	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
102	C₂³×C₄×C₃₁	C₂³	1	24	yes	—
103	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
104	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
105	C₃₁×C₄⋊Q₈	C₂³	1	48	yes	complemented
106	C₃₁×#124	C₂³	1	48	yes	complemented
107	C₃₁×#123	C₂³	1	48	yes	complemented
108	C₃₁×#123	C₂³	1	96	yes	complemented
109	C₃₁×C₂²⋊Q₈	C₂³	1	24	yes	—
110	C₃₁×C₂²⋊Q₈	C₂³	1	48	yes	—
111	C₃₁×C₂²⋊Q₈	C₂³	1	48	yes	complemented
112	C₃₁×C₂²⋊Q₈	C₂³	1	48	yes	complemented
113	C₃₁×C₂²⋊Q₈	C₂³	1	24	yes	complemented
114	C₃₁×C₂²⋊Q₈	C₂³	1	48	yes	complemented
115	C₃₁×#121	C₂³	1	8	yes	—
116	C₃₁×#121	C₂³	1	24	yes	complemented
117	C₃₁×#121	C₂³	1	96	yes	complemented
118	C₃₁×#121	C₂³	1	48	yes	complemented
119	C₃₁×#120	C₂³	1	48	yes	—
120	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
121	C₄×D₄×C₃₁	C₂³	1	48	yes	—
122	C₄×D₄×C₃₁	C₂³	1	48	yes	complemented
123	C₄×D₄×C₃₁	C₂³	1	48	yes	complemented
124	C₃₁×#117	C₂³	1	24	yes	complemented
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	12	yes	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	24	yes	complemented
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	48	yes	complemented
133	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	48	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
140	C₂×C₄²×C₃₁	C₂³	1	6	yes	—
141	C₂⁴×C₃₁	—	2	12	no	—
142	C₂⁴×C₃₁	—	2	12	no	—
143	C₂⁴×C₃₁	—	4	6	no	—
144	C₂⁴×C₃₁	C₂⁴	1	3	yes	—
145	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
146	C₂⁴×C₃₁	C₂⁴	1	12	yes	—
147	C₂⁴×C₃₁	C₂⁴	1	3	yes	—
148	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
149	#41×C₃₁	—	2	32	no	—
150	#41×C₃₁	—	2	96	no	—
151	#41×C₃₁	—	2	192	no	—
152	#41×C₃₁	—	2	96	no	—
153	#41×C₃₁	—	2	96	no	—
154	#41×C₃₁	C₂×D₄	1	64	yes	complemented
155	C₂×Q₈×C₃₁	—	2	32	no	—
156	C₂×Q₈×C₃₁	—	2	64	no	—
157	C₂×Q₈×C₃₁	—	2	12	no	—
158	C₂×Q₈×C₃₁	—	2	24	no	—
159	C₂×Q₈×C₃₁	—	2	12	no	—
160	C₂×Q₈×C₃₁	—	2	96	no	—
161	C₂×Q₈×C₃₁	C₂×D₄	1	8	yes	—
162	C₂×Q₈×C₃₁	C₂⁴	1	12	yes	—
163	C₂×Q₈×C₃₁	C₂⁴	1	24	yes	—
164	C₂×Q₈×C₃₁	C₂⁴	1	12	yes	—
165	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
166	C₂×D₄×C₃₁	—	2	24	no	—
167	C₂×D₄×C₃₁	—	2	24	no	—
168	C₂×D₄×C₃₁	—	2	8	no	—
169	C₂×D₄×C₃₁	—	2	96	no	—
170	C₂×D₄×C₃₁	—	2	12	no	—
171	C₂×D₄×C₃₁	—	2	4	no	—
172	C₂×D₄×C₃₁	—	4	12	no	—
173	C₂×D₄×C₃₁	C₂×D₄	1	24	yes	—
174	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
175	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
176	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
177	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
178	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
179	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
180	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
181	C₂²×C₄×C₃₁	—	2	12	no	—
182	C₂²×C₄×C₃₁	—	2	24	no	—
183	C₂²×C₄×C₃₁	—	2	4	no	—
184	C₂²×C₄×C₃₁	—	2	12	no	—
185	C₂²×C₄×C₃₁	—	2	12	no	—
186	C₂²×C₄×C₃₁	—	2	12	no	—
187	C₂²×C₄×C₃₁	—	2	96	no	—
188	C₂²×C₄×C₃₁	—	2	24	no	—
189	C₂²×C₄×C₃₁	—	4	12	no	—
190	C₂²×C₄×C₃₁	C₂×D₄	1	24	yes	—
191	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
192	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
193	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
194	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
195	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
196	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
198	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
200	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
201	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
203	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
204	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
205	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
206	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
207	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
208	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
209	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
210	C₄⋊C₄×C₃₁	C₂⁴	1	48	yes	—
211	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
212	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
213	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
214	C₂²⋊C₄×C₃₁	C₂⁴	1	48	yes	—
215	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
216	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
217	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
218	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
219	C₄²×C₃₁	C₂⁴	1	24	yes	—
220	C₂×#3489	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂³×C₃₁	—	2	2	no	—
222	C₂³×C₃₁	—	2	6	no	—
223	C₂³×C₃₁	—	2	6	no	—
224	C₂³×C₃₁	—	2	2	no	—
225	C₂³×C₃₁	—	2	4	no	—
226	C₂³×C₃₁	—	2	24	no	—
227	C₂³×C₃₁	—	2	6	no	—
228	C₂³×C₃₁	—	2	4	no	—
229	C₂³×C₃₁	—	2	6	no	—
230	C₂³×C₃₁	—	2	24	no	—
231	C₂³×C₃₁	—	2	4	no	—
232	C₂³×C₃₁	—	2	6	no	—
233	C₂³×C₃₁	—	4	12	no	—
234	C₂³×C₃₁	—	4	48	no	—
235	C₂³×C₃₁	C₂²×D₄	1	12	yes	—
236	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	complemented
237	C₂³×C₃₁	C₂⁵	1	6	yes	—
238	C₂³×C₃₁	C₂⁵	1	4	yes	—
239	C₂³×C₃₁	C₂⁵	1	6	yes	—
240	C₂³×C₃₁	C₂⁵	1	2	yes	—
241	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
242	Q₈×C₃₁	—	2	24	no	—
243	Q₈×C₃₁	—	2	48	no	—
244	Q₈×C₃₁	—	2	24	no	—
245	Q₈×C₃₁	C₂²×D₄	1	16	yes	—
246	D₄×C₃₁	—	2	48	no	—
247	D₄×C₃₁	—	2	48	no	—
248	D₄×C₃₁	—	2	16	no	—
249	D₄×C₃₁	—	2	24	no	—
250	D₄×C₃₁	—	2	8	no	—
251	D₄×C₃₁	—	4	24	no	—
252	D₄×C₃₁	C₂²×D₄	1	48	yes	—
253	C₂×C₄×C₃₁	—	2	2	no	—
254	C₂×C₄×C₃₁	—	2	6	no	—
255	C₂×C₄×C₃₁	—	2	12	no	—
256	C₂×C₄×C₃₁	—	2	24	no	—
257	C₂×C₄×C₃₁	—	2	48	no	—
258	C₂×C₄×C₃₁	—	2	4	no	—
259	C₂×C₄×C₃₁	—	2	12	no	—
260	C₂×C₄×C₃₁	—	2	8	no	—
261	C₂×C₄×C₃₁	—	2	24	no	—
262	C₂×C₄×C₃₁	—	2	24	no	—
263	C₂×C₄×C₃₁	—	2	24	no	—
264	C₂×C₄×C₃₁	—	2	48	no	—
265	C₂×C₄×C₃₁	—	4	24	no	—
266	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
267	C₂×C₄×C₃₁	C₂²×D₄	1	12	yes	—
268	C₂×C₄×C₃₁	C₂²×D₄	1	48	yes	—
269	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
270	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
271	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
272	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
273	C₂×C₄×C₃₁	C₂⁵	1	6	yes	—
274	C₂×C₄×C₃₁	C₂⁵	1	6	yes	—
275	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
276	C₂²×2₋¹⁺⁴	C₂×C₃₁	1	1	yes	characteristic, complemented
277	C₂³×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
278	#3489	C₂×C₃₁	1	32	yes	direct product factor
279	C₂×D₄×Q₈	C₂×C₃₁	1	2	yes	complemented
280	C₂×#548	C₂×C₃₁	1	2	yes	complemented
281	C₂×#547	C₂×C₃₁	1	6	yes	complemented
282	C₂×#546	C₂×C₃₁	1	6	yes	complemented
283	C₂×#537	C₂×C₃₁	1	3	yes	complemented
284	C₂×#536	C₂×C₃₁	1	3	yes	complemented
285	C₂×#525	C₂×C₃₁	1	3	yes	complemented
286	C₂²×C₂²⋊Q₈	C₂×C₃₁	1	3	yes	complemented
287	C₂×#520	C₂×C₃₁	1	1	yes	characteristic, complemented
288	C₂²×C₃₁	—	2	2	no	—
289	C₂²×C₃₁	—	2	6	no	—
290	C₂²×C₃₁	—	2	6	no	—
291	C₂²×C₃₁	—	2	2	no	—
292	C₂²×C₃₁	—	2	8	no	—
293	C₂²×C₃₁	—	2	24	no	—
294	C₂²×C₃₁	—	2	4	no	—
295	C₂²×C₃₁	—	2	6	no	—
296	C₂²×C₃₁	—	2	4	no	—
297	C₂²×C₃₁	—	2	6	no	—
298	C₂²×C₃₁	—	2	4	no	—
299	C₂²×C₃₁	—	2	6	no	—
300	C₂²×C₃₁	—	4	48	no	—
301	C₂²×C₃₁	—	4	8	no	—
302	C₂²×C₃₁	—	4	12	no	—
303	C₂²×C₃₁	C₂³×D₄	1	12	yes	—
304	C₂²×C₃₁	C₂³×D₄	1	2	yes	—
305	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
306	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	4	yes	complemented
307	C₂²×C₃₁	#585	1	2	yes	—
308	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
309	C₄×C₃₁	—	2	2	no	—
310	C₄×C₃₁	—	2	6	no	—
311	C₄×C₃₁	—	2	12	no	—
312	C₄×C₃₁	—	2	4	no	—
313	C₄×C₃₁	—	2	12	no	—
314	C₄×C₃₁	C₂³×D₄	1	4	yes	—
315	C₄×C₃₁	C₂³×D₄	1	12	yes	—
316	C₂×2₋¹⁺⁴	—	2	16	no	—
317	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	16	yes	complemented
318	C₂²×#41	—	2	16	no	—
319	C₂²×#41	C₂²×C₃₁	1	3	yes	—
320	C₂²×#41	C₂²×C₃₁	1	3	yes	—
321	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
322	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
323	C₂²×#41	C₂²×C₃₁	1	16	yes	complemented
324	C₂²×#41	C₂²×C₃₁	1	3	yes	complemented
325	C₂²×#41	C₂²×C₃₁	1	6	yes	complemented
326	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
327	C₂³×Q₈	C₂²×C₃₁	1	3	yes	complemented
328	C₂³×Q₈	C₂²×C₃₁	1	2	yes	complemented
329	C₂³×D₄	C₂²×C₃₁	1	3	yes	—
330	C₂⁴×C₄	C₂²×C₃₁	1	3	yes	—
331	D₄×Q₈	C₂²×C₃₁	1	32	yes	complemented
332	#548	C₂²×C₃₁	1	32	yes	complemented
333	#547	C₂²×C₃₁	1	96	yes	complemented
334	#546	C₂²×C₃₁	1	96	yes	complemented
335	#537	C₂²×C₃₁	1	48	yes	complemented
336	#536	C₂²×C₃₁	1	48	yes	complemented
337	C₂×C₄⋊Q₈	C₂²×C₃₁	1	6	yes	complemented
338	C₂×#124	C₂²×C₃₁	1	6	yes	complemented
339	#525	C₂²×C₃₁	1	48	yes	complemented
340	C₂×#123	C₂²×C₃₁	1	6	yes	complemented
341	C₂×#123	C₂²×C₃₁	1	12	yes	complemented
342	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	3	yes	—
343	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	6	yes	—
344	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	6	yes	complemented
345	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	6	yes	complemented
346	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	3	yes	complemented
347	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	6	yes	complemented
348	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	48	yes	complemented
349	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
350	C₂×#121	C₂²×C₃₁	1	3	yes	complemented
351	C₂×#121	C₂²×C₃₁	1	12	yes	complemented
352	C₂×#121	C₂²×C₃₁	1	6	yes	complemented
353	C₂×#120	C₂²×C₃₁	1	6	yes	—
354	#520	C₂²×C₃₁	1	16	yes	complemented
355	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
356	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	—
357	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	complemented
358	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	complemented
359	C₂×#117	C₂²×C₃₁	1	3	yes	complemented
360	C₂²×C₄⋊C₄	C₂²×C₃₁	1	3	yes	complemented
361	C₂²×C₄⋊C₄	C₂²×C₃₁	1	6	yes	complemented
362	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	6	yes	—
363	C₂×C₃₁	—	2	4	no	—
364	C₂×C₃₁	—	2	12	no	—
365	C₂×C₃₁	—	4	4	no	—
366	C₂×C₃₁	—	4	6	no	—
367	C₂×C₃₁	#3489	1	4	yes	direct product factor
368	C₂×C₃₁	C₂⁴×D₄	1	1	yes	characteristic
369	C₂×C₃₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
370	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
371	C₂⁵	C₂³×C₃₁	1	3	yes	—
372	2₋¹⁺⁴	—	2	128	no	—
373	C₂×#41	—	2	128	no	—
374	C₂×#41	—	2	8	no	—
375	C₂×#41	—	2	24	no	—
376	C₂×#41	—	2	48	no	—
377	C₂×#41	—	2	24	no	—
378	C₂×#41	—	2	24	no	—
379	C₂×#41	D₄×C₃₁	1	16	yes	complemented
380	C₂×#41	C₂³×C₃₁	1	24	yes	—
381	C₂×#41	C₂³×C₃₁	1	24	yes	—
382	C₂×#41	C₂³×C₃₁	1	8	yes	—
383	C₂×#41	C₂³×C₃₁	1	8	yes	—
384	C₂×#41	C₂³×C₃₁	1	24	yes	complemented
385	C₂×#41	C₂³×C₃₁	1	48	yes	complemented
386	C₂²×Q₈	—	2	8	no	—
387	C₂²×Q₈	—	2	16	no	—
388	C₂²×Q₈	—	2	24	no	—
389	C₂²×Q₈	C₂³×C₃₁	1	3	yes	—
390	C₂²×Q₈	C₂³×C₃₁	1	6	yes	—
391	C₂²×Q₈	C₂³×C₃₁	1	3	yes	—
392	C₂²×Q₈	C₂³×C₃₁	1	8	yes	—
393	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
394	C₂²×Q₈	C₂³×C₃₁	1	24	yes	complemented
395	C₂²×Q₈	C₂³×C₃₁	1	16	yes	complemented
396	C₂²×D₄	—	2	24	no	—
397	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
398	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
399	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
400	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
401	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
402	C₂²×D₄	C₂³×C₃₁	1	24	yes	—
403	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
404	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
405	C₂³×C₄	—	2	24	no	—
406	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
407	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
408	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
409	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
410	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
411	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
412	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
413	C₂³×C₄	C₂³×C₃₁	1	24	yes	—
414	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
415	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
416	C₄⋊Q₈	C₂³×C₃₁	1	48	yes	complemented
417	#124	C₂³×C₃₁	1	48	yes	complemented
418	#123	C₂³×C₃₁	1	48	yes	complemented
419	#123	C₂³×C₃₁	1	96	yes	complemented
420	C₂²⋊Q₈	C₂³×C₃₁	1	24	yes	—
421	C₂²⋊Q₈	C₂³×C₃₁	1	48	yes	—
422	C₂²⋊Q₈	C₂³×C₃₁	1	48	yes	complemented
423	C₂²⋊Q₈	C₂³×C₃₁	1	48	yes	complemented
424	C₂²⋊Q₈	C₂³×C₃₁	1	24	yes	complemented
425	C₂²⋊Q₈	C₂³×C₃₁	1	48	yes	complemented
426	#121	C₂³×C₃₁	1	8	yes	—
427	#121	C₂³×C₃₁	1	24	yes	complemented
428	#121	C₂³×C₃₁	1	96	yes	complemented
429	#121	C₂³×C₃₁	1	48	yes	complemented
430	#120	C₂³×C₃₁	1	48	yes	—
431	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
432	C₄×D₄	C₂³×C₃₁	1	48	yes	—
433	C₄×D₄	C₂³×C₃₁	1	48	yes	complemented
434	C₄×D₄	C₂³×C₃₁	1	48	yes	complemented
435	#117	C₂³×C₃₁	1	24	yes	complemented
436	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
437	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
438	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
439	C₂×C₄⋊C₄	C₂³×C₃₁	1	12	yes	—
440	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
442	C₂×C₄⋊C₄	C₂³×C₃₁	1	24	yes	complemented
443	C₂×C₄⋊C₄	C₂³×C₃₁	1	48	yes	complemented
444	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₃₁	1	48	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
451	C₂×C₄²	C₂³×C₃₁	1	6	yes	—
452	C₃₁	C₂×#3489	1	1	yes	characteristic, direct product factor, Sylow
453	C₂⁴	—	2	12	no	—
454	C₂⁴	—	2	12	no	—
455	C₂⁴	—	4	6	no	—
456	C₂⁴	C₂⁴×C₃₁	1	3	yes	—
457	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
458	C₂⁴	C₂⁴×C₃₁	1	12	yes	—
459	C₂⁴	C₂⁴×C₃₁	1	3	yes	—
460	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
461	#41	—	2	32	no	—
462	#41	—	2	96	no	—
463	#41	—	2	192	no	—
464	#41	—	2	96	no	—
465	#41	—	2	96	no	—
466	#41	C₂×D₄×C₃₁	1	64	yes	complemented
467	C₂×Q₈	—	2	32	no	—
468	C₂×Q₈	—	2	64	no	—
469	C₂×Q₈	—	2	12	no	—
470	C₂×Q₈	—	2	24	no	—
471	C₂×Q₈	—	2	12	no	—
472	C₂×Q₈	—	2	96	no	—
473	C₂×Q₈	C₂×D₄×C₃₁	1	8	yes	—
474	C₂×Q₈	C₂⁴×C₃₁	1	12	yes	—
475	C₂×Q₈	C₂⁴×C₃₁	1	24	yes	—
476	C₂×Q₈	C₂⁴×C₃₁	1	12	yes	—
477	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
478	C₂×D₄	—	2	24	no	—
479	C₂×D₄	—	2	24	no	—
480	C₂×D₄	—	2	8	no	—
481	C₂×D₄	—	2	96	no	—
482	C₂×D₄	—	2	12	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	4	12	no	—
485	C₂×D₄	C₂×D₄×C₃₁	1	24	yes	—
486	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
487	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
488	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
489	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
490	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
491	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
492	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
493	C₂²×C₄	—	2	12	no	—
494	C₂²×C₄	—	2	24	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	12	no	—
497	C₂²×C₄	—	2	12	no	—
498	C₂²×C₄	—	2	12	no	—
499	C₂²×C₄	—	2	96	no	—
500	C₂²×C₄	—	2	24	no	—
501	C₂²×C₄	—	4	12	no	—
502	C₂²×C₄	C₂×D₄×C₃₁	1	24	yes	—
503	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
505	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
506	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
507	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
508	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
509	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
510	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
511	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
512	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
513	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
515	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
516	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
517	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
519	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
520	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
521	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
522	C₄⋊C₄	C₂⁴×C₃₁	1	48	yes	—
523	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
524	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
525	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
526	C₂²⋊C₄	C₂⁴×C₃₁	1	48	yes	—
527	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
528	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
529	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
530	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
531	C₄²	C₂⁴×C₃₁	1	24	yes	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	6	no	—
534	C₂³	—	2	6	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	24	no	—
538	C₂³	—	2	6	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	6	no	—
541	C₂³	—	2	24	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	6	no	—
544	C₂³	—	4	12	no	—
545	C₂³	—	4	48	no	—
546	C₂³	C₂²×D₄×C₃₁	1	12	yes	—
547	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	complemented
548	C₂³	C₂⁵×C₃₁	1	6	yes	—
549	C₂³	C₂⁵×C₃₁	1	4	yes	—
550	C₂³	C₂⁵×C₃₁	1	6	yes	—
551	C₂³	C₂⁵×C₃₁	1	2	yes	—
552	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
553	Q₈	—	2	24	no	—
554	Q₈	—	2	48	no	—
555	Q₈	—	2	24	no	—
556	Q₈	C₂²×D₄×C₃₁	1	16	yes	—
557	D₄	—	2	48	no	—
558	D₄	—	2	48	no	—
559	D₄	—	2	16	no	—
560	D₄	—	2	24	no	—
561	D₄	—	2	8	no	—
562	D₄	—	4	24	no	—
563	D₄	C₂²×D₄×C₃₁	1	48	yes	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	6	no	—
566	C₂×C₄	—	2	12	no	—
567	C₂×C₄	—	2	24	no	—
568	C₂×C₄	—	2	48	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	12	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	24	no	—
573	C₂×C₄	—	2	24	no	—
574	C₂×C₄	—	2	24	no	—
575	C₂×C₄	—	2	48	no	—
576	C₂×C₄	—	4	24	no	—
577	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
578	C₂×C₄	C₂²×D₄×C₃₁	1	12	yes	—
579	C₂×C₄	C₂²×D₄×C₃₁	1	48	yes	—
580	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
581	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
582	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
583	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
584	C₂×C₄	C₂⁵×C₃₁	1	6	yes	—
585	C₂×C₄	C₂⁵×C₃₁	1	6	yes	—
586	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	6	no	—
589	C₂²	—	2	6	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	8	no	—
592	C₂²	—	2	24	no	—
593	C₂²	—	2	4	no	—
594	C₂²	—	2	6	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	6	no	—
597	C₂²	—	2	4	no	—
598	C₂²	—	2	6	no	—
599	C₂²	—	4	48	no	—
600	C₂²	—	4	12	no	—
601	C₂²	—	4	8	no	—
602	C₂²	C₂³×D₄×C₃₁	1	12	yes	—
603	C₂²	C₂³×D₄×C₃₁	1	2	yes	—
604	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
605	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	4	yes	complemented
606	C₂²	C₃₁×#585	1	2	yes	—
607	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
608	C₄	—	2	2	no	—
609	C₄	—	2	6	no	—
610	C₄	—	2	12	no	—
611	C₄	—	2	4	no	—
612	C₄	—	2	12	no	—
613	C₄	C₂³×D₄×C₃₁	1	4	yes	—
614	C₄	C₂³×D₄×C₃₁	1	12	yes	—
615	C₂	—	2	4	no	—
616	C₂	—	2	12	no	—
617	C₂	—	4	6	no	—
618	C₂	—	4	4	no	—
619	C₂	C₃₁×#3489	1	4	yes	direct product factor
620	C₂	C₂⁴×D₄×C₃₁	1	1	yes	characteristic
621	C₂	C₂²×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
622	C₂	C₂×C₃₁×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×2₋¹⁺⁴	C₂	semidirect
2. C₂³×#41×C₃₁	C₂	semidirect
3. C₃₁×#3489	C₂	direct (N × H)
4. C₂×D₄×Q₈×C₃₁	C₂	semidirect
5. C₂×C₃₁×#548	C₂	semidirect
6. C₂×C₃₁×#547	C₂	semidirect
7. C₂×C₃₁×#546	C₂	semidirect
8. C₂×C₃₁×#537	C₂	semidirect
9. C₂×C₃₁×#536	C₂	semidirect
10. C₂×C₃₁×#525	C₂	semidirect
11. C₂²×C₃₁×C₂²⋊Q₈	C₂	semidirect
12. C₂×C₃₁×#520	C₂	semidirect
14. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
20. C₂²×#41×C₃₁	C₂²	semidirect
21. C₂²×#41×C₃₁	C₂²	semidirect
22. C₂²×#41×C₃₁	C₂²	semidirect
24. C₂³×Q₈×C₃₁	C₂²	semidirect
25. C₂³×Q₈×C₃₁	C₂²	semidirect
28. D₄×Q₈×C₃₁	C₂²	semidirect
29. C₃₁×#548	C₂²	semidirect
30. C₃₁×#547	C₂²	semidirect
31. C₃₁×#546	C₂²	semidirect
32. C₃₁×#537	C₂²	semidirect
33. C₃₁×#536	C₂²	semidirect
34. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
35. C₂×C₃₁×#124	C₂²	semidirect
36. C₃₁×#525	C₂²	semidirect
37. C₂×C₃₁×#123	C₂²	semidirect
38. C₂×C₃₁×#123	C₂²	semidirect
41. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
42. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
43. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
45. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
47. C₂×C₃₁×#121	C₂²	semidirect
48. C₂×C₃₁×#121	C₂²	semidirect
49. C₂×C₃₁×#121	C₂²	semidirect
51. C₃₁×#520	C₂²	semidirect
52. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
54. C₂×C₄×D₄×C₃₁	C₂²	semidirect
55. C₂×C₄×D₄×C₃₁	C₂²	semidirect
56. C₂×C₃₁×#117	C₂²	semidirect
57. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
58. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
68. C₂×#41×C₃₁	D₄	semidirect
73. C₂×#41×C₃₁	C₂³	semidirect
74. C₂×#41×C₃₁	C₂³	semidirect
83. C₂²×Q₈×C₃₁	C₂³	semidirect
84. C₂²×Q₈×C₃₁	C₂³	semidirect
105. C₃₁×C₄⋊Q₈	C₂³	semidirect
106. C₃₁×#124	C₂³	semidirect
107. C₃₁×#123	C₂³	semidirect
108. C₃₁×#123	C₂³	semidirect
111. C₃₁×C₂²⋊Q₈	C₂³	semidirect
112. C₃₁×C₂²⋊Q₈	C₂³	semidirect
113. C₃₁×C₂²⋊Q₈	C₂³	semidirect
114. C₃₁×C₂²⋊Q₈	C₂³	semidirect
116. C₃₁×#121	C₂³	semidirect
117. C₃₁×#121	C₂³	semidirect
118. C₃₁×#121	C₂³	semidirect
120. C₄×Q₈×C₃₁	C₂³	semidirect
122. C₄×D₄×C₃₁	C₂³	semidirect
123. C₄×D₄×C₃₁	C₂³	semidirect
124. C₃₁×#117	C₂³	semidirect
131. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
132. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
154. #41×C₃₁	C₂×D₄	semidirect
220. C₂×#3489	C₃₁	direct (N × H)
236. C₂³×C₃₁	2₋¹⁺⁴	semidirect
276. C₂²×2₋¹⁺⁴	C₂×C₃₁	semidirect
277. C₂³×#41	C₂×C₃₁	semidirect
278. #3489	C₂×C₃₁	direct (N × H)
279. C₂×D₄×Q₈	C₂×C₃₁	semidirect
280. C₂×#548	C₂×C₃₁	semidirect
281. C₂×#547	C₂×C₃₁	semidirect
282. C₂×#546	C₂×C₃₁	semidirect
283. C₂×#537	C₂×C₃₁	semidirect
284. C₂×#536	C₂×C₃₁	semidirect
285. C₂×#525	C₂×C₃₁	semidirect
286. C₂²×C₂²⋊Q₈	C₂×C₃₁	semidirect
287. C₂×#520	C₂×C₃₁	semidirect
306. C₂²×C₃₁	C₂×2₋¹⁺⁴	semidirect
317. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
323. C₂²×#41	C₂²×C₃₁	semidirect
324. C₂²×#41	C₂²×C₃₁	semidirect
325. C₂²×#41	C₂²×C₃₁	semidirect
327. C₂³×Q₈	C₂²×C₃₁	semidirect
328. C₂³×Q₈	C₂²×C₃₁	semidirect
331. D₄×Q₈	C₂²×C₃₁	semidirect
332. #548	C₂²×C₃₁	semidirect
333. #547	C₂²×C₃₁	semidirect
334. #546	C₂²×C₃₁	semidirect
335. #537	C₂²×C₃₁	semidirect
336. #536	C₂²×C₃₁	semidirect
337. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
338. C₂×#124	C₂²×C₃₁	semidirect
339. #525	C₂²×C₃₁	semidirect
340. C₂×#123	C₂²×C₃₁	semidirect
341. C₂×#123	C₂²×C₃₁	semidirect
344. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
345. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
346. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
347. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
348. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
350. C₂×#121	C₂²×C₃₁	semidirect
351. C₂×#121	C₂²×C₃₁	semidirect
352. C₂×#121	C₂²×C₃₁	semidirect
354. #520	C₂²×C₃₁	semidirect
355. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
357. C₂×C₄×D₄	C₂²×C₃₁	semidirect
358. C₂×C₄×D₄	C₂²×C₃₁	semidirect
359. C₂×#117	C₂²×C₃₁	semidirect
360. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
361. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
367. C₂×C₃₁	#3489	direct (N × H)
379. C₂×#41	D₄×C₃₁	semidirect
384. C₂×#41	C₂³×C₃₁	semidirect
385. C₂×#41	C₂³×C₃₁	semidirect
394. C₂²×Q₈	C₂³×C₃₁	semidirect
395. C₂²×Q₈	C₂³×C₃₁	semidirect
416. C₄⋊Q₈	C₂³×C₃₁	semidirect
417. #124	C₂³×C₃₁	semidirect
418. #123	C₂³×C₃₁	semidirect
419. #123	C₂³×C₃₁	semidirect
422. C₂²⋊Q₈	C₂³×C₃₁	semidirect
423. C₂²⋊Q₈	C₂³×C₃₁	semidirect
424. C₂²⋊Q₈	C₂³×C₃₁	semidirect
425. C₂²⋊Q₈	C₂³×C₃₁	semidirect
427. #121	C₂³×C₃₁	semidirect
428. #121	C₂³×C₃₁	semidirect
429. #121	C₂³×C₃₁	semidirect
431. C₄×Q₈	C₂³×C₃₁	semidirect
433. C₄×D₄	C₂³×C₃₁	semidirect
434. C₄×D₄	C₂³×C₃₁	semidirect
435. #117	C₂³×C₃₁	semidirect
442. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
443. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
452. C₃₁	C₂×#3489	direct (N × H)
466. #41	C₂×D₄×C₃₁	semidirect
547. C₂³	C₃₁×2₋¹⁺⁴	semidirect
605. C₂²	C₂×C₃₁×2₋¹⁺⁴	semidirect
619. C₂	C₃₁×#3489	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×C₃₁×2₋¹⁺⁴	2
C₂³×#41×C₃₁	2
C₃₁×#3489	2
C₂×D₄×Q₈×C₃₁	2
C₂×C₃₁×#548	2
C₂×C₃₁×#547	2
C₂×C₃₁×#546	2
C₂×C₃₁×#537	2
C₂×C₃₁×#536	2
C₂×C₃₁×#525	2
C₂²×C₃₁×C₂²⋊Q₈	2
C₂×C₃₁×#520	2
C₂×#3489	31

Subgroups — C2×C31×#3489 #21519560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3489 #21519560