Subgroups — C₂×C₄×C₃₁×C₄⋊Q₈ #21490796

Order 7936.

3358 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₃₁	C₂	1	2	yes	maximal
3	C₄×C₃₁×C₄⋊Q₈	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#391	C₂	1	2	yes	maximal
5	C₂×C₃₁×#389	C₂	1	4	yes	maximal
6	C₂×C₃₁×#384	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	4	yes	maximal
8	C₂×C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₃₁	C₂²	1	2	yes	—
10	C₂×C₃₁×C₄⋊Q₈	C₄	1	16	yes	direct product factor
11	C₂×C₃₁×C₄⋊Q₈	C₂²	1	8	yes	—
12	C₂×C₄×Q₈×C₃₁	—	2	16	no	—
13	C₂×C₄×Q₈×C₃₁	C₂²	1	16	yes	—
14	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
18	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₃₁	C₂²	1	4	yes	—
21	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
24	C₃₁×#391	C₂²	1	16	yes	—
25	C₃₁×#389	C₂²	1	32	yes	—
26	C₃₁×#384	C₂²	1	8	yes	—
27	C₄×C₄⋊C₄×C₃₁	C₂²	1	32	yes	—
28	C₂×C₃₁×#95	C₂²	1	8	yes	—
29	C₄³×C₃₁	C₂²	1	8	yes	—
30	C₂²×Q₈×C₃₁	—	2	8	no	—
31	C₂²×Q₈×C₃₁	—	2	8	no	—
32	C₂²×Q₈×C₃₁	C₂×C₄	1	16	yes	—
33	C₂²×Q₈×C₃₁	C₂³	1	8	yes	—
34	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
35	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
36	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
41	C₃₁×C₄⋊Q₈	C₂×C₄	1	64	yes	direct product factor
42	C₄×Q₈×C₃₁	—	2	64	no	—
43	C₂×C₄⋊C₄×C₃₁	—	2	16	no	—
44	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
45	C₂×C₄⋊C₄×C₃₁	—	2	16	no	—
46	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	32	yes	—
47	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
48	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
49	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
50	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
51	C₂×C₄²×C₃₁	—	2	16	no	—
52	C₂×C₄²×C₃₁	—	2	4	no	—
53	C₂×C₄²×C₃₁	—	2	8	no	—
54	C₂×C₄²×C₃₁	C₂×C₄	1	8	yes	—
55	C₂×C₄²×C₃₁	D₄	1	8	yes	—
56	C₂×C₄²×C₃₁	Q₈	1	16	yes	complemented
57	C₂×C₄²×C₃₁	C₂³	1	16	yes	—
58	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
59	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
60	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
61	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
62	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
63	C₃₁×#95	C₂³	1	32	yes	—
64	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
65	C₂×Q₈×C₃₁	—	2	64	no	—
66	C₂×Q₈×C₃₁	—	2	16	no	—
67	C₂×Q₈×C₃₁	—	2	16	no	—
68	C₂×Q₈×C₃₁	C₂²×C₄	1	32	yes	—
69	C₂²×C₄×C₃₁	—	2	8	no	—
70	C₂²×C₄×C₃₁	—	2	4	no	—
71	C₂²×C₄×C₃₁	—	2	4	no	—
72	C₂²×C₄×C₃₁	—	2	4	no	—
73	C₂²×C₄×C₃₁	—	2	8	no	—
74	C₂²×C₄×C₃₁	—	2	8	no	—
75	C₂²×C₄×C₃₁	—	2	16	no	—
76	C₂²×C₄×C₃₁	C₂²×C₄	1	16	yes	—
77	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
78	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
79	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
80	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
81	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
82	C₂²×C₄×C₃₁	C₂×Q₈	1	8	yes	—
83	C₂²×C₄×C₃₁	C₂×Q₈	1	8	yes	—
84	C₂²×C₄×C₃₁	C₂×Q₈	1	8	yes	—
85	C₂²×C₄×C₃₁	#41	1	4	yes	—
86	C₂²×C₄×C₃₁	#41	1	8	yes	—
87	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
88	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
89	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
90	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
91	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
92	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
93	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
94	C₄⋊C₄×C₃₁	—	2	32	no	—
95	C₄⋊C₄×C₃₁	—	2	16	no	—
96	C₄⋊C₄×C₃₁	—	2	32	no	—
97	C₄⋊C₄×C₃₁	C₂²×C₄	1	64	yes	—
98	C₄²×C₃₁	—	2	32	no	—
99	C₄²×C₃₁	—	2	8	no	—
100	C₄²×C₃₁	—	2	16	no	—
101	C₄²×C₃₁	C₂²×C₄	1	16	yes	—
102	C₄²×C₃₁	C₂×D₄	1	16	yes	—
103	C₄²×C₃₁	C₂×Q₈	1	32	yes	complemented
104	C₂×C₄×C₄⋊Q₈	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
106	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
107	C₂³×C₃₁	C₂²×Q₈	1	4	yes	—
108	C₂³×C₃₁	C₂×#41	1	2	yes	—
109	C₂³×C₃₁	C₂×#41	1	4	yes	—
110	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
111	Q₈×C₃₁	—	2	64	no	—
112	C₂×C₄×C₃₁	—	2	32	no	—
113	C₂×C₄×C₃₁	—	2	8	no	—
114	C₂×C₄×C₃₁	—	2	16	no	—
115	C₂×C₄×C₃₁	—	2	8	no	—
116	C₂×C₄×C₃₁	—	2	4	no	—
117	C₂×C₄×C₃₁	—	2	4	no	—
118	C₂×C₄×C₃₁	—	2	4	no	—
119	C₂×C₄×C₃₁	—	2	8	no	—
120	C₂×C₄×C₃₁	—	2	8	no	—
121	C₂×C₄×C₃₁	—	2	16	no	—
122	C₂×C₄×C₃₁	—	4	16	no	—
123	C₂×C₄×C₃₁	C₄×D₄	1	16	yes	—
124	C₂×C₄×C₃₁	C₄×Q₈	1	32	yes	complemented
125	C₂×C₄×C₃₁	C₄⋊Q₈	1	16	yes	direct product factor
126	C₂×C₄×C₃₁	C₂³×C₄	1	16	yes	—
127	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
128	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
129	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
130	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
131	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
132	C₂×C₄×C₃₁	C₂²×Q₈	1	8	yes	—
133	C₂×C₄×C₃₁	C₂²×Q₈	1	8	yes	—
134	C₂×C₄×C₃₁	C₂²×Q₈	1	8	yes	—
135	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
136	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
137	C₂²×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
138	C₂²×C₄×Q₈	C₂×C₃₁	1	2	yes	—
139	C₄×C₄⋊Q₈	C₂×C₃₁	1	16	yes	direct product factor
140	C₂×#391	C₂×C₃₁	1	2	yes	—
141	C₂×#389	C₂×C₃₁	1	4	yes	—
142	C₂×#384	C₂×C₃₁	1	1	yes	characteristic
143	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	4	yes	—
144	C₂×C₄³	C₂×C₃₁	1	1	yes	characteristic
145	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
146	C₂²×C₃₁	C₂×C₄×Q₈	1	8	yes	—
147	C₂²×C₃₁	C₂×C₄⋊Q₈	1	4	yes	—
148	C₂²×C₃₁	#532	1	4	yes	—
149	C₂²×C₃₁	#533	1	8	yes	—
150	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
151	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
152	C₂²×C₃₁	C₂³×Q₈	1	2	yes	—
153	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
154	C₂²×C₃₁	C₂²×#41	1	2	yes	—
155	C₄×C₃₁	—	2	16	no	—
156	C₄×C₃₁	—	2	4	no	—
157	C₄×C₃₁	—	2	8	no	—
158	C₄×C₃₁	—	4	8	no	—
159	C₄×C₃₁	C₂×C₄×D₄	1	8	yes	—
160	C₄×C₃₁	C₂×C₄×Q₈	1	16	yes	complemented
161	C₄×C₃₁	C₂×C₄⋊Q₈	1	8	yes	direct product factor
162	C₂³×Q₈	C₂²×C₃₁	1	2	yes	—
163	C₂×C₄⋊Q₈	C₄×C₃₁	1	16	yes	direct product factor
164	C₂×C₄⋊Q₈	C₂²×C₃₁	1	8	yes	—
165	C₂×C₄×Q₈	—	2	16	no	—
166	C₂×C₄×Q₈	C₂²×C₃₁	1	16	yes	—
167	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
168	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
169	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
170	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
171	C₂²×C₄²	C₂²×C₃₁	1	4	yes	—
172	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
173	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
174	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
175	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
176	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
177	#391	C₂²×C₃₁	1	16	yes	—
178	#389	C₂²×C₃₁	1	32	yes	—
179	#384	C₂²×C₃₁	1	8	yes	—
180	C₄×C₄⋊C₄	C₂²×C₃₁	1	32	yes	—
181	C₂×#95	C₂²×C₃₁	1	8	yes	—
182	C₄³	C₂²×C₃₁	1	8	yes	—
183	C₂×C₃₁	C₄×C₄⋊Q₈	1	8	yes	direct product factor
184	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
185	C₂×C₃₁	C₂²×C₄×Q₈	1	2	yes	—
186	C₂×C₃₁	C₂²×C₄⋊Q₈	1	1	yes	characteristic
187	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
188	C₂×C₃₁	C₂×#533	1	2	yes	—
189	C₂²×Q₈	—	2	8	no	—
190	C₂²×Q₈	—	2	8	no	—
191	C₂²×Q₈	C₂×C₄×C₃₁	1	16	yes	—
192	C₂²×Q₈	C₂³×C₃₁	1	8	yes	—
193	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
194	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
195	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
196	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
197	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
198	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
199	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
200	C₄⋊Q₈	C₂×C₄×C₃₁	1	64	yes	direct product factor
201	C₄×Q₈	—	2	64	no	—
202	C₂×C₄⋊C₄	—	2	16	no	—
203	C₂×C₄⋊C₄	—	2	8	no	—
204	C₂×C₄⋊C₄	—	2	16	no	—
205	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	32	yes	—
206	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
207	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
208	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
209	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
210	C₂×C₄²	—	2	16	no	—
211	C₂×C₄²	—	2	4	no	—
212	C₂×C₄²	—	2	8	no	—
213	C₂×C₄²	C₂×C₄×C₃₁	1	8	yes	—
214	C₂×C₄²	D₄×C₃₁	1	8	yes	—
215	C₂×C₄²	Q₈×C₃₁	1	16	yes	complemented
216	C₂×C₄²	C₂³×C₃₁	1	16	yes	—
217	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
218	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
219	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
220	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
221	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
222	#95	C₂³×C₃₁	1	32	yes	—
223	C₃₁	C₂×C₄×C₄⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
224	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
225	C₂×Q₈	—	2	64	no	—
226	C₂×Q₈	—	2	16	no	—
227	C₂×Q₈	—	2	16	no	—
228	C₂×Q₈	C₂²×C₄×C₃₁	1	32	yes	—
229	C₂²×C₄	—	2	8	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	2	8	no	—
234	C₂²×C₄	—	2	8	no	—
235	C₂²×C₄	—	2	16	no	—
236	C₂²×C₄	C₂²×C₄×C₃₁	1	16	yes	—
237	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
238	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
239	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
240	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
241	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
242	C₂²×C₄	C₂×Q₈×C₃₁	1	8	yes	—
243	C₂²×C₄	C₂×Q₈×C₃₁	1	8	yes	—
244	C₂²×C₄	C₂×Q₈×C₃₁	1	8	yes	—
245	C₂²×C₄	#41×C₃₁	1	4	yes	—
246	C₂²×C₄	#41×C₃₁	1	8	yes	—
247	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
248	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
249	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
250	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
251	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
252	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
253	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
254	C₄⋊C₄	—	2	32	no	—
255	C₄⋊C₄	—	2	16	no	—
256	C₄⋊C₄	—	2	32	no	—
257	C₄⋊C₄	C₂²×C₄×C₃₁	1	64	yes	—
258	C₄²	—	2	32	no	—
259	C₄²	—	2	8	no	—
260	C₄²	—	2	16	no	—
261	C₄²	C₂²×C₄×C₃₁	1	16	yes	—
262	C₄²	C₂×D₄×C₃₁	1	16	yes	—
263	C₄²	C₂×Q₈×C₃₁	1	32	yes	complemented
264	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
265	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
266	C₂³	C₂²×Q₈×C₃₁	1	4	yes	—
267	C₂³	C₂×#41×C₃₁	1	2	yes	—
268	C₂³	C₂×#41×C₃₁	1	4	yes	—
269	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
270	Q₈	—	2	64	no	—
271	C₂×C₄	—	2	32	no	—
272	C₂×C₄	—	2	8	no	—
273	C₂×C₄	—	2	16	no	—
274	C₂×C₄	—	2	8	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	8	no	—
279	C₂×C₄	—	2	8	no	—
280	C₂×C₄	—	2	16	no	—
281	C₂×C₄	—	4	16	no	—
282	C₂×C₄	C₄×D₄×C₃₁	1	16	yes	—
283	C₂×C₄	C₄×Q₈×C₃₁	1	32	yes	complemented
284	C₂×C₄	C₃₁×C₄⋊Q₈	1	16	yes	direct product factor
285	C₂×C₄	C₂³×C₄×C₃₁	1	16	yes	—
286	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
287	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
288	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
289	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
290	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
291	C₂×C₄	C₂²×Q₈×C₃₁	1	8	yes	—
292	C₂×C₄	C₂²×Q₈×C₃₁	1	8	yes	—
293	C₂×C₄	C₂²×Q₈×C₃₁	1	8	yes	—
294	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
295	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
296	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
297	C₂²	C₂×C₄×Q₈×C₃₁	1	8	yes	—
298	C₂²	C₂×C₃₁×C₄⋊Q₈	1	4	yes	—
299	C₂²	C₃₁×#532	1	4	yes	—
300	C₂²	C₃₁×#533	1	8	yes	—
301	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
302	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
303	C₂²	C₂³×Q₈×C₃₁	1	2	yes	—
304	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
305	C₂²	C₂²×#41×C₃₁	1	2	yes	—
306	C₄	—	2	16	no	—
307	C₄	—	2	4	no	—
308	C₄	—	2	8	no	—
309	C₄	—	4	8	no	—
310	C₄	C₂×C₄×D₄×C₃₁	1	8	yes	—
311	C₄	C₂×C₄×Q₈×C₃₁	1	16	yes	complemented
312	C₄	C₂×C₃₁×C₄⋊Q₈	1	8	yes	direct product factor
313	C₂	C₄×C₃₁×C₄⋊Q₈	1	8	yes	direct product factor
314	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
315	C₂	C₂²×C₄×Q₈×C₃₁	1	2	yes	—
316	C₂	C₂²×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
317	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
318	C₂	C₂×C₃₁×#533	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₃₁	C₂³
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle, prime radical	C₂⁴×C₃₁	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₃₁×C₄⋊Q₈	C₂	direct (N × H)
10. C₂×C₃₁×C₄⋊Q₈	C₄	direct (N × H)
41. C₃₁×C₄⋊Q₈	C₂×C₄	direct (N × H)
56. C₂×C₄²×C₃₁	Q₈	semidirect
103. C₄²×C₃₁	C₂×Q₈	semidirect
104. C₂×C₄×C₄⋊Q₈	C₃₁	direct (N × H)
124. C₂×C₄×C₃₁	C₄×Q₈	semidirect
125. C₂×C₄×C₃₁	C₄⋊Q₈	direct (N × H)
139. C₄×C₄⋊Q₈	C₂×C₃₁	direct (N × H)
160. C₄×C₃₁	C₂×C₄×Q₈	semidirect
161. C₄×C₃₁	C₂×C₄⋊Q₈	direct (N × H)
163. C₂×C₄⋊Q₈	C₄×C₃₁	direct (N × H)
183. C₂×C₃₁	C₄×C₄⋊Q₈	direct (N × H)
200. C₄⋊Q₈	C₂×C₄×C₃₁	direct (N × H)
215. C₂×C₄²	Q₈×C₃₁	semidirect
223. C₃₁	C₂×C₄×C₄⋊Q₈	direct (N × H)
263. C₄²	C₂×Q₈×C₃₁	semidirect
283. C₂×C₄	C₄×Q₈×C₃₁	semidirect
284. C₂×C₄	C₃₁×C₄⋊Q₈	direct (N × H)
311. C₄	C₂×C₄×Q₈×C₃₁	semidirect
312. C₄	C₂×C₃₁×C₄⋊Q₈	direct (N × H)
313. C₂	C₄×C₃₁×C₄⋊Q₈	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⋊Q₈	2
C₂²×C₄×Q₈×C₃₁	2
C₄×C₃₁×C₄⋊Q₈	2
C₂×C₃₁×#391	2
C₂×C₃₁×#389	2
C₂×C₃₁×#384	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₂×C₄³×C₃₁	2
C₂×C₄×C₄⋊Q₈	31

Subgroups — C2×C4×C31×C4⋊Q8 #21490796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₃₁×C₄⋊Q₈ #21490796