Subgroups — C₂²×C₃₁×#548 #21519457

Order 7936.

12142 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#548	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₃₁×#124	C₂	1	3	yes	maximal, complemented
5	C₂²×C₃₁×C₂²⋊Q₈	C₂	1	3	yes	maximal, complemented
6	C₂²×C₃₁×#121	C₂	1	3	yes	maximal, complemented
7	C₂²×C₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₃₁	C₂	1	3	yes	maximal, complemented
9	C₂²×#41×C₃₁	—	2	16	no	—
10	C₂²×#41×C₃₁	C₂²	1	24	yes	complemented
11	C₂³×Q₈×C₃₁	—	2	16	no	—
12	C₂³×Q₈×C₃₁	C₂²	1	3	yes	—
13	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₃₁	C₂²	1	24	yes	complemented
15	C₂³×D₄×C₃₁	C₂²	1	3	yes	—
16	C₂³×D₄×C₃₁	C₂²	1	3	yes	—
17	C₂⁴×C₄×C₃₁	C₂²	1	3	yes	—
18	C₂⁴×C₄×C₃₁	C₂²	1	3	yes	—
19	C₃₁×#548	C₂²	1	256	yes	direct product factor
20	C₂×C₃₁×#124	C₂²	1	72	yes	complemented
21	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	72	yes	complemented
22	C₂×C₃₁×#121	C₂²	1	72	yes	complemented
23	C₂×C₄×Q₈×C₃₁	C₂²	1	24	yes	complemented
24	C₂×C₄×D₄×C₃₁	C₂²	1	72	yes	complemented
25	C₂²×C₄⋊C₄×C₃₁	C₂²	1	3	yes	—
26	C₂²×C₄⋊C₄×C₃₁	C₂²	1	3	yes	—
27	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	3	yes	—
29	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	6	yes	—
30	C₂²×C₄²×C₃₁	C₂²	1	3	yes	—
31	C₂⁵×C₃₁	C₂³	1	3	yes	—
32	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
33	C₂×#41×C₃₁	—	2	192	no	—
34	C₂×#41×C₃₁	C₂³	1	64	yes	complemented
35	C₂²×Q₈×C₃₁	—	2	192	no	—
36	C₂²×Q₈×C₃₁	—	2	24	no	—
37	C₂²×Q₈×C₃₁	D₄	1	16	yes	complemented
38	C₂²×Q₈×C₃₁	C₂³	1	36	yes	—
39	C₂²×Q₈×C₃₁	C₂³	1	12	yes	—
40	C₂²×Q₈×C₃₁	C₂³	1	64	yes	complemented
41	C₂²×D₄×C₃₁	—	2	24	no	—
42	C₂²×D₄×C₃₁	—	2	24	no	—
43	C₂²×D₄×C₃₁	C₂³	1	36	yes	—
44	C₂²×D₄×C₃₁	C₂³	1	36	yes	—
45	C₂³×C₄×C₃₁	—	2	24	no	—
46	C₂³×C₄×C₃₁	—	2	24	no	—
47	C₂³×C₄×C₃₁	C₂³	1	36	yes	—
48	C₂³×C₄×C₃₁	C₂³	1	36	yes	—
49	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
51	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
52	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
54	C₃₁×#124	C₂³	1	192	yes	complemented
55	C₃₁×C₂²⋊Q₈	C₂³	1	192	yes	complemented
56	C₃₁×#121	C₂³	1	192	yes	complemented
57	C₄×Q₈×C₃₁	C₂³	1	64	yes	complemented
58	C₄×D₄×C₃₁	C₂³	1	192	yes	complemented
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	36	yes	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	36	yes	—
61	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
62	C₂×C₂²⋊C₄×C₃₁	C₂³	1	36	yes	—
63	C₂×C₂²⋊C₄×C₃₁	C₂³	1	72	yes	—
64	C₂×C₄²×C₃₁	C₂³	1	36	yes	—
65	C₂⁴×C₃₁	—	2	4	no	—
66	C₂⁴×C₃₁	—	2	4	no	—
67	C₂⁴×C₃₁	—	2	12	no	—
68	C₂⁴×C₃₁	—	2	12	no	—
69	C₂⁴×C₃₁	—	2	12	no	—
70	C₂⁴×C₃₁	#41	1	8	yes	complemented
71	C₂⁴×C₃₁	C₂⁴	1	18	yes	—
72	C₂⁴×C₃₁	C₂⁴	1	6	yes	—
73	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
74	#41×C₃₁	—	2	256	no	—
75	C₂×Q₈×C₃₁	—	2	256	no	—
76	C₂×Q₈×C₃₁	—	2	144	no	—
77	C₂×Q₈×C₃₁	C₂×D₄	1	96	yes	complemented
78	C₂×Q₈×C₃₁	C₂⁴	1	48	yes	—
79	C₂×Q₈×C₃₁	C₂⁴	1	16	yes	—
80	C₂×D₄×C₃₁	—	2	144	no	—
81	C₂×D₄×C₃₁	—	2	144	no	—
82	C₂×D₄×C₃₁	C₂⁴	1	48	yes	—
83	C₂×D₄×C₃₁	C₂⁴	1	48	yes	—
84	C₂²×C₄×C₃₁	—	2	4	no	—
85	C₂²×C₄×C₃₁	—	2	12	no	—
86	C₂²×C₄×C₃₁	—	2	12	no	—
87	C₂²×C₄×C₃₁	—	2	4	no	—
88	C₂²×C₄×C₃₁	—	2	144	no	—
89	C₂²×C₄×C₃₁	—	2	144	no	—
90	C₂²×C₄×C₃₁	C₂×D₄	1	24	yes	—
91	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
92	C₂²×C₄×C₃₁	C₂⁴	1	18	yes	—
93	C₂²×C₄×C₃₁	C₂⁴	1	18	yes	—
94	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	48	yes	—
96	C₂²×C₄×C₃₁	C₂⁴	1	48	yes	—
97	C₂²×C₄×C₃₁	C₂⁴	1	18	yes	—
98	C₄⋊C₄×C₃₁	C₂⁴	1	48	yes	—
99	C₄⋊C₄×C₃₁	C₂⁴	1	48	yes	—
100	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
101	C₂²⋊C₄×C₃₁	C₂⁴	1	48	yes	—
102	C₂²⋊C₄×C₃₁	C₂⁴	1	96	yes	—
103	C₄²×C₃₁	C₂⁴	1	48	yes	—
104	C₂²×#548	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂³×C₃₁	—	2	32	no	—
106	C₂³×C₃₁	—	2	12	no	—
107	C₂³×C₃₁	—	2	12	no	—
108	C₂³×C₃₁	—	2	36	no	—
109	C₂³×C₃₁	—	2	36	no	—
110	C₂³×C₃₁	—	2	36	no	—
111	C₂³×C₃₁	—	4	48	no	—
112	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
113	C₂³×C₃₁	C₂×#41	1	4	yes	—
114	C₂³×C₃₁	C₂×#41	1	24	yes	complemented
115	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	—
116	C₂³×C₃₁	C₂⁵	1	12	yes	—
117	C₂³×C₃₁	C₂⁵	1	4	yes	—
118	C₂³×C₃₁	C₂⁵	1	3	yes	—
119	Q₈×C₃₁	—	2	96	no	—
120	Q₈×C₃₁	C₂²×D₄	1	64	yes	complemented
121	D₄×C₃₁	—	2	96	no	—
122	D₄×C₃₁	—	2	96	no	—
123	C₂×C₄×C₃₁	—	2	12	no	—
124	C₂×C₄×C₃₁	—	2	36	no	—
125	C₂×C₄×C₃₁	—	2	36	no	—
126	C₂×C₄×C₃₁	—	2	12	no	—
127	C₂×C₄×C₃₁	—	2	96	no	—
128	C₂×C₄×C₃₁	—	2	96	no	—
129	C₂×C₄×C₃₁	C₂²×D₄	1	72	yes	—
130	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
131	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
132	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
133	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
134	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
135	C₂³×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
136	C₂⁴×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
137	C₂×#548	C₂×C₃₁	1	48	yes	direct product factor
138	C₂²×#124	C₂×C₃₁	1	3	yes	complemented
139	C₂²×C₂²⋊Q₈	C₂×C₃₁	1	3	yes	complemented
140	C₂²×#121	C₂×C₃₁	1	3	yes	complemented
141	C₂²×C₄×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
142	C₂²×C₄×D₄	C₂×C₃₁	1	3	yes	complemented
143	C₂²×C₃₁	—	2	4	no	—
144	C₂²×C₃₁	—	2	4	no	—
145	C₂²×C₃₁	—	2	48	no	—
146	C₂²×C₃₁	—	2	12	no	—
147	C₂²×C₃₁	—	2	12	no	—
148	C₂²×C₃₁	—	2	12	no	—
149	C₂²×C₃₁	—	4	72	no	—
150	C₂²×C₃₁	#548	1	16	yes	direct product factor
151	C₂²×C₃₁	C₂³×D₄	1	6	yes	—
152	C₂²×C₃₁	C₂²×#41	1	6	yes	—
153	C₂²×C₃₁	C₂²×#41	1	8	yes	complemented
154	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	6	yes	—
155	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
156	C₄×C₃₁	—	2	4	no	—
157	C₄×C₃₁	—	2	12	no	—
158	C₄×C₃₁	—	2	12	no	—
159	C₄×C₃₁	—	2	4	no	—
160	C₄×C₃₁	C₂³×D₄	1	24	yes	—
161	C₂²×#41	—	2	16	no	—
162	C₂²×#41	C₂²×C₃₁	1	24	yes	complemented
163	C₂³×Q₈	—	2	16	no	—
164	C₂³×Q₈	C₂²×C₃₁	1	3	yes	—
165	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
166	C₂³×Q₈	C₂²×C₃₁	1	24	yes	complemented
167	C₂³×D₄	C₂²×C₃₁	1	3	yes	—
168	C₂³×D₄	C₂²×C₃₁	1	3	yes	—
169	C₂⁴×C₄	C₂²×C₃₁	1	3	yes	—
170	C₂⁴×C₄	C₂²×C₃₁	1	3	yes	—
171	#548	C₂²×C₃₁	1	256	yes	direct product factor
172	C₂×#124	C₂²×C₃₁	1	72	yes	complemented
173	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	72	yes	complemented
174	C₂×#121	C₂²×C₃₁	1	72	yes	complemented
175	C₂×C₄×Q₈	C₂²×C₃₁	1	24	yes	complemented
176	C₂×C₄×D₄	C₂²×C₃₁	1	72	yes	complemented
177	C₂²×C₄⋊C₄	C₂²×C₃₁	1	3	yes	—
178	C₂²×C₄⋊C₄	C₂²×C₃₁	1	3	yes	—
179	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
180	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	3	yes	—
181	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	6	yes	—
182	C₂²×C₄²	C₂²×C₃₁	1	3	yes	—
183	C₂×C₃₁	—	2	8	no	—
184	C₂×C₃₁	—	4	12	no	—
185	C₂×C₃₁	C₂×#548	1	12	yes	direct product factor
186	C₂×C₃₁	C₂⁴×D₄	1	1	yes	characteristic
187	C₂×C₃₁	C₂³×#41	1	1	yes	characteristic
188	C₂×C₃₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
189	C₂⁵	C₂³×C₃₁	1	3	yes	—
190	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
191	C₂×#41	—	2	192	no	—
192	C₂×#41	C₂³×C₃₁	1	64	yes	complemented
193	C₂²×Q₈	—	2	192	no	—
194	C₂²×Q₈	—	2	24	no	—
195	C₂²×Q₈	D₄×C₃₁	1	16	yes	complemented
196	C₂²×Q₈	C₂³×C₃₁	1	36	yes	—
197	C₂²×Q₈	C₂³×C₃₁	1	12	yes	—
198	C₂²×Q₈	C₂³×C₃₁	1	64	yes	complemented
199	C₂²×D₄	—	2	24	no	—
200	C₂²×D₄	—	2	24	no	—
201	C₂²×D₄	C₂³×C₃₁	1	36	yes	—
202	C₂²×D₄	C₂³×C₃₁	1	36	yes	—
203	C₂³×C₄	—	2	24	no	—
204	C₂³×C₄	—	2	24	no	—
205	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
206	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
207	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
208	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
209	C₂³×C₄	C₂³×C₃₁	1	36	yes	—
210	C₂³×C₄	C₂³×C₃₁	1	36	yes	—
211	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
212	#124	C₂³×C₃₁	1	192	yes	complemented
213	C₂²⋊Q₈	C₂³×C₃₁	1	192	yes	complemented
214	#121	C₂³×C₃₁	1	192	yes	complemented
215	C₄×Q₈	C₂³×C₃₁	1	64	yes	complemented
216	C₄×D₄	C₂³×C₃₁	1	192	yes	complemented
217	C₂×C₄⋊C₄	C₂³×C₃₁	1	36	yes	—
218	C₂×C₄⋊C₄	C₂³×C₃₁	1	36	yes	—
219	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
220	C₂×C₂²⋊C₄	C₂³×C₃₁	1	36	yes	—
221	C₂×C₂²⋊C₄	C₂³×C₃₁	1	72	yes	—
222	C₂×C₄²	C₂³×C₃₁	1	36	yes	—
223	C₃₁	C₂²×#548	1	1	yes	characteristic, direct product factor, Sylow
224	C₂⁴	—	2	4	no	—
225	C₂⁴	—	2	4	no	—
226	C₂⁴	—	2	12	no	—
227	C₂⁴	—	2	12	no	—
228	C₂⁴	—	2	12	no	—
229	C₂⁴	#41×C₃₁	1	8	yes	complemented
230	C₂⁴	C₂⁴×C₃₁	1	18	yes	—
231	C₂⁴	C₂⁴×C₃₁	1	6	yes	—
232	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
233	#41	—	2	256	no	—
234	C₂×Q₈	—	2	256	no	—
235	C₂×Q₈	—	2	144	no	—
236	C₂×Q₈	C₂×D₄×C₃₁	1	96	yes	complemented
237	C₂×Q₈	C₂⁴×C₃₁	1	48	yes	—
238	C₂×Q₈	C₂⁴×C₃₁	1	16	yes	—
239	C₂×D₄	—	2	144	no	—
240	C₂×D₄	—	2	144	no	—
241	C₂×D₄	C₂⁴×C₃₁	1	48	yes	—
242	C₂×D₄	C₂⁴×C₃₁	1	48	yes	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	12	no	—
245	C₂²×C₄	—	2	12	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	144	no	—
248	C₂²×C₄	—	2	144	no	—
249	C₂²×C₄	C₂×D₄×C₃₁	1	24	yes	—
250	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
251	C₂²×C₄	C₂⁴×C₃₁	1	18	yes	—
252	C₂²×C₄	C₂⁴×C₃₁	1	18	yes	—
253	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
254	C₂²×C₄	C₂⁴×C₃₁	1	48	yes	—
255	C₂²×C₄	C₂⁴×C₃₁	1	48	yes	—
256	C₂²×C₄	C₂⁴×C₃₁	1	18	yes	—
257	C₄⋊C₄	C₂⁴×C₃₁	1	48	yes	—
258	C₄⋊C₄	C₂⁴×C₃₁	1	48	yes	—
259	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
260	C₂²⋊C₄	C₂⁴×C₃₁	1	48	yes	—
261	C₂²⋊C₄	C₂⁴×C₃₁	1	96	yes	—
262	C₄²	C₂⁴×C₃₁	1	48	yes	—
263	C₂³	—	2	32	no	—
264	C₂³	—	2	12	no	—
265	C₂³	—	2	12	no	—
266	C₂³	—	2	36	no	—
267	C₂³	—	2	36	no	—
268	C₂³	—	2	36	no	—
269	C₂³	—	4	48	no	—
270	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
271	C₂³	C₂×#41×C₃₁	1	4	yes	—
272	C₂³	C₂×#41×C₃₁	1	24	yes	complemented
273	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	—
274	C₂³	C₂⁵×C₃₁	1	12	yes	—
275	C₂³	C₂⁵×C₃₁	1	4	yes	—
276	C₂³	C₂⁵×C₃₁	1	3	yes	—
277	Q₈	—	2	96	no	—
278	Q₈	C₂²×D₄×C₃₁	1	64	yes	complemented
279	D₄	—	2	96	no	—
280	D₄	—	2	96	no	—
281	C₂×C₄	—	2	12	no	—
282	C₂×C₄	—	2	36	no	—
283	C₂×C₄	—	2	36	no	—
284	C₂×C₄	—	2	12	no	—
285	C₂×C₄	—	2	96	no	—
286	C₂×C₄	—	2	96	no	—
287	C₂×C₄	C₂²×D₄×C₃₁	1	72	yes	—
288	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
289	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
290	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
291	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
292	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
293	C₂²	—	2	4	no	—
294	C₂²	—	2	4	no	—
295	C₂²	—	2	48	no	—
296	C₂²	—	2	12	no	—
297	C₂²	—	2	12	no	—
298	C₂²	—	2	12	no	—
299	C₂²	—	4	72	no	—
300	C₂²	C₃₁×#548	1	16	yes	direct product factor
301	C₂²	C₂³×D₄×C₃₁	1	6	yes	—
302	C₂²	C₂²×#41×C₃₁	1	6	yes	—
303	C₂²	C₂²×#41×C₃₁	1	8	yes	complemented
304	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	6	yes	—
305	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
306	C₄	—	2	4	no	—
307	C₄	—	2	12	no	—
308	C₄	—	2	12	no	—
309	C₄	—	2	4	no	—
310	C₄	C₂³×D₄×C₃₁	1	24	yes	—
311	C₂	—	2	8	no	—
312	C₂	—	4	12	no	—
313	C₂	C₂×C₃₁×#548	1	12	yes	direct product factor
314	C₂	C₂⁴×D₄×C₃₁	1	1	yes	characteristic
315	C₂	C₂³×#41×C₃₁	1	1	yes	characteristic
316	C₂	C₂²×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₃₁	C₂	semidirect
2. C₂⁴×Q₈×C₃₁	C₂	semidirect
3. C₂×C₃₁×#548	C₂	direct (N × H)
4. C₂²×C₃₁×#124	C₂	semidirect
5. C₂²×C₃₁×C₂²⋊Q₈	C₂	semidirect
6. C₂²×C₃₁×#121	C₂	semidirect
7. C₂²×C₄×Q₈×C₃₁	C₂	semidirect
8. C₂²×C₄×D₄×C₃₁	C₂	semidirect
10. C₂²×#41×C₃₁	C₂²	semidirect
14. C₂³×Q₈×C₃₁	C₂²	semidirect
19. C₃₁×#548	C₂²	direct (N × H)
20. C₂×C₃₁×#124	C₂²	semidirect
21. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
22. C₂×C₃₁×#121	C₂²	semidirect
23. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
24. C₂×C₄×D₄×C₃₁	C₂²	semidirect
34. C₂×#41×C₃₁	C₂³	semidirect
37. C₂²×Q₈×C₃₁	D₄	semidirect
40. C₂²×Q₈×C₃₁	C₂³	semidirect
54. C₃₁×#124	C₂³	semidirect
55. C₃₁×C₂²⋊Q₈	C₂³	semidirect
56. C₃₁×#121	C₂³	semidirect
57. C₄×Q₈×C₃₁	C₂³	semidirect
58. C₄×D₄×C₃₁	C₂³	semidirect
70. C₂⁴×C₃₁	#41	semidirect
77. C₂×Q₈×C₃₁	C₂×D₄	semidirect
104. C₂²×#548	C₃₁	direct (N × H)
114. C₂³×C₃₁	C₂×#41	semidirect
120. Q₈×C₃₁	C₂²×D₄	semidirect
135. C₂³×#41	C₂×C₃₁	semidirect
136. C₂⁴×Q₈	C₂×C₃₁	semidirect
137. C₂×#548	C₂×C₃₁	direct (N × H)
138. C₂²×#124	C₂×C₃₁	semidirect
139. C₂²×C₂²⋊Q₈	C₂×C₃₁	semidirect
140. C₂²×#121	C₂×C₃₁	semidirect
141. C₂²×C₄×Q₈	C₂×C₃₁	semidirect
142. C₂²×C₄×D₄	C₂×C₃₁	semidirect
150. C₂²×C₃₁	#548	direct (N × H)
153. C₂²×C₃₁	C₂²×#41	semidirect
162. C₂²×#41	C₂²×C₃₁	semidirect
166. C₂³×Q₈	C₂²×C₃₁	semidirect
171. #548	C₂²×C₃₁	direct (N × H)
172. C₂×#124	C₂²×C₃₁	semidirect
173. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
174. C₂×#121	C₂²×C₃₁	semidirect
175. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
176. C₂×C₄×D₄	C₂²×C₃₁	semidirect
185. C₂×C₃₁	C₂×#548	direct (N × H)
192. C₂×#41	C₂³×C₃₁	semidirect
195. C₂²×Q₈	D₄×C₃₁	semidirect
198. C₂²×Q₈	C₂³×C₃₁	semidirect
212. #124	C₂³×C₃₁	semidirect
213. C₂²⋊Q₈	C₂³×C₃₁	semidirect
214. #121	C₂³×C₃₁	semidirect
215. C₄×Q₈	C₂³×C₃₁	semidirect
216. C₄×D₄	C₂³×C₃₁	semidirect
223. C₃₁	C₂²×#548	direct (N × H)
229. C₂⁴	#41×C₃₁	semidirect
236. C₂×Q₈	C₂×D₄×C₃₁	semidirect
272. C₂³	C₂×#41×C₃₁	semidirect
278. Q₈	C₂²×D₄×C₃₁	semidirect
300. C₂²	C₃₁×#548	direct (N × H)
303. C₂²	C₂²×#41×C₃₁	semidirect
313. C₂	C₂×C₃₁×#548	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₃₁	2
C₂⁴×Q₈×C₃₁	2
C₂×C₃₁×#548	2
C₂²×C₃₁×#124	2
C₂²×C₃₁×C₂²⋊Q₈	2
C₂²×C₃₁×#121	2
C₂²×C₄×Q₈×C₃₁	2
C₂²×C₄×D₄×C₃₁	2
C₂²×#548	31

Subgroups — C22×C31×#548 #21519457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃₁×#548 #21519457