Subgroups — Q₈×#13063284 #25256026

Order 11008.

2434 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137552	C₂	1	6	yes	maximal, complemented
2	Q₈×C₄⋊Dic₄₃	C₂	1	2	yes	maximal, complemented
3	#19137472	C₂	1	6	yes	maximal
4	Q₈×C₂²⋊Dic₄₃	C₂	1	2	yes	maximal
5	#19137073	C₂	1	6	yes	maximal, complemented
6	#19137002	C₂	1	3	yes	maximal
7	C₄×Q₈×Dic₄₃	C₂	1	2	yes	maximal, complemented
8	C₄×#13063284	C₂	1	3	yes	maximal
9	C₂²×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂×Q₈×Dic₄₃	C₂²	1	4	yes	—
11	C₂×#13063284	C₂²	1	3	yes	—
12	C₂×#13063284	C₂²	1	1	yes	characteristic
13	#14582806	C₂²	1	12	yes	—
14	#14582798	C₂²	1	12	yes	—
15	#14582785	C₂²	1	24	yes	—
16	#14582769	C₂²	1	6	yes	—
17	#14582765	C₂²	1	6	yes	—
18	#14582759	C₂²	1	6	yes	—
19	#14582759	C₂²	1	6	yes	—
20	C₄⋊C₄×Dic₄₃	C₂²	1	12	yes	—
21	C₄×C₄⋊Dic₄₃	C₂²	1	6	yes	—
22	C₄×C₄⋊Dic₄₃	C₂²	1	6	yes	—
23	C₄×C₄⋊Dic₄₃	C₂²	1	6	yes	—
24	C₄×C₄⋊Dic₄₃	C₂²	1	6	yes	—
25	C₄×C₂²⋊Dic₄₃	C₂²	1	6	yes	—
26	C₄×C₂²⋊Dic₄₃	C₂²	1	6	yes	—
27	#14582745	C₂²	1	6	yes	—
28	C₄²×Dic₄₃	C₂²	1	6	yes	—
29	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₄₃	C₄	1	16	yes	complemented
31	C₂×C₄×Q₈×C₄₃	C₂²	1	3	yes	—
32	C₂×C₄×Q₈×C₄₃	C₂²	1	3	yes	—
33	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
36	C₂²×C₄²×C₄₃	C₂²	1	3	yes	—
37	Q₈×Dic₄₃	—	2	16	no	—
38	#13063284	—	2	12	no	—
39	#13063284	Q₈	1	8	yes	direct product factor
40	C₂×C₄⋊Dic₄₃	C₂³	1	12	yes	—
41	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
42	C₂×C₄⋊Dic₄₃	C₂³	1	12	yes	—
43	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
44	C₂×C₂²⋊Dic₄₃	C₂³	1	6	yes	—
45	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
46	C₂×C₄×Dic₄₃	C₂³	1	12	yes	—
47	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
48	C₂×C₄×Dic₄₃	C₂³	1	12	yes	—
49	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
50	C₄₃⋊#95	C₂³	1	12	yes	—
51	C₄₃⋊#95	C₂³	1	12	yes	—
52	C₄₃⋊#95	C₂³	1	12	yes	—
53	C₄₃⋊#95	C₂³	1	12	yes	—
54	C₂²×Q₈×C₄₃	—	2	8	no	—
55	C₂²×Q₈×C₄₃	C₂×C₄	1	8	yes	—
56	C₂²×Q₈×C₄₃	C₂³	1	3	yes	—
57	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
59	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
60	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₄×Q₈×C₄₃	C₂×C₄	1	24	yes	—
62	C₄×Q₈×C₄₃	C₂×C₄	1	24	yes	—
63	C₄×Q₈×C₄₃	C₂×C₄	1	8	yes	—
64	C₄×Q₈×C₄₃	C₂×C₄	1	8	yes	—
65	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	24	yes	—
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	6	yes	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
69	C₂×C₄²×C₄₃	C₂×C₄	1	24	yes	—
70	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
71	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
72	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
73	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
74	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
75	C₂×Q₈×C₄₃	—	2	32	no	—
76	C₂×Q₈×C₄₃	—	2	12	no	—
77	C₂×Q₈×C₄₃	C₂²×C₄	1	12	yes	—
78	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
79	C₂×Q₈×C₄₃	#41	1	8	yes	—
80	C₂²×C₄×C₄₃	—	2	12	no	—
81	C₂²×C₄×C₄₃	—	4	6	no	—
82	C₂²×C₄×C₄₃	C₂²×C₄	1	12	yes	—
83	C₂²×C₄×C₄₃	C₂²×C₄	1	12	yes	—
84	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
86	C₂²×C₄×C₄₃	#41	1	4	yes	—
87	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
88	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
89	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
90	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
92	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
93	C₂²×Dic₄₃	C₂⁴	1	12	yes	—
94	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
95	C₄⋊C₄×C₄₃	C₂²×C₄	1	24	yes	—
96	C₄⋊C₄×C₄₃	C₂²×C₄	1	12	yes	—
97	C₄⋊C₄×C₄₃	C₂²×C₄	1	12	yes	—
98	C₄²×C₄₃	C₂²×C₄	1	12	yes	—
99	C₄²×C₄₃	C₂²×C₄	1	12	yes	—
100	C₄²×C₄₃	C₂²×C₄	1	12	yes	—
101	C₄²×C₄₃	C₂²×C₄	1	12	yes	—
102	C₂²⋊Dic₄₃	—	2	12	no	—
103	C₂²⋊Dic₄₃	C₂×Q₈	1	8	yes	—
104	C₄⋊Dic₄₃	—	2	12	no	—
105	C₄⋊Dic₄₃	—	2	24	no	—
106	C₄⋊Dic₄₃	—	4	12	no	—
107	C₄⋊Dic₄₃	C₂×Q₈	1	8	yes	complemented
108	C₄×Dic₄₃	—	2	12	no	—
109	C₄×Dic₄₃	—	2	24	no	—
110	C₄×Dic₄₃	—	4	12	no	—
111	C₄×Dic₄₃	C₂×Q₈	1	8	yes	complemented
112	C₂³×C₄₃	—	2	2	no	—
113	C₂³×C₄₃	—	2	2	no	—
114	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
115	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
116	C₂³×C₄₃	C₂×#41	1	2	yes	—
117	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
118	Q₈×C₄₃	—	2	24	no	—
119	Q₈×C₄₃	#117	1	16	yes	complemented
120	C₂×C₄×C₄₃	—	2	6	no	—
121	C₂×C₄×C₄₃	—	2	6	no	—
122	C₂×C₄×C₄₃	—	2	6	no	—
123	C₂×C₄×C₄₃	—	2	24	no	—
124	C₂×C₄×C₄₃	—	4	12	no	—
125	C₂×C₄×C₄₃	C₄×Q₈	1	16	yes	complemented
126	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
127	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
128	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
129	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
130	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
131	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
132	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
133	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
134	C₂×C₄×C₄₃	C₂×#41	1	12	yes	—
135	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
136	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
137	C₂×Dic₄₃	—	2	4	no	—
138	C₂×Dic₄₃	—	2	4	no	—
139	C₂×Dic₄₃	—	2	12	no	—
140	C₂×Dic₄₃	—	2	12	no	—
141	C₂×Dic₄₃	—	2	12	no	—
142	C₂×Dic₄₃	C₂²×Q₈	1	8	yes	—
143	Q₈×#117	—	43	1	no	maximal, Sylow
144	C₂²×C₄₃	—	2	2	no	—
145	C₂²×C₄₃	—	2	2	no	—
146	C₂²×C₄₃	—	2	4	no	—
147	C₂²×C₄₃	—	2	4	no	—
148	C₂²×C₄₃	C₂×C₄×Q₈	1	4	yes	—
149	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
150	C₂²×C₄₃	C₂³×Q₈	1	1	yes	characteristic
151	C₂²×C₄₃	C₂²×#41	1	2	yes	—
152	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
153	C₂²×C₄₃	#585	1	2	yes	—
154	C₄×C₄₃	—	2	6	no	—
155	C₄×C₄₃	—	2	6	no	—
156	C₄×C₄₃	—	2	6	no	—
157	C₄×C₄₃	C₂×#117	1	12	yes	—
158	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	—
159	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	—
160	Dic₄₃	—	2	8	no	—
161	Dic₄₃	—	4	12	no	—
162	C₂²×C₄×Q₈	D₄₃	1	1	yes	characteristic
163	#2355	—	43	6	no	—
164	Q₈×C₄⋊C₄	—	43	2	no	—
165	#2345	—	43	6	no	—
166	Q₈×C₂²⋊C₄	—	43	2	no	—
167	#2295	—	43	6	no	—
168	#2285	—	43	3	no	—
169	C₄²×Q₈	—	43	2	no	—
170	C₄×#117	—	43	3	no	—
171	C₂×C₄₃	—	2	4	no	—
172	C₂×C₄₃	C₂²×#117	1	1	yes	characteristic
173	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
174	C₂×C₄₃	#3428	1	1	yes	characteristic
175	C₂×C₄₃	Q₈×#41	1	2	yes	—
176	C₂×C₄₃	#3480	1	2	yes	—
177	C₂³×Q₈	C₂×D₄₃	1	1	yes	characteristic
178	C₂×C₄×Q₈	—	43	4	no	—
179	C₂×C₄×Q₈	Dic₄₃	1	16	yes	complemented
180	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
181	C₂×C₄×Q₈	C₂×D₄₃	1	3	yes	—
182	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
183	C₂×C₄×Q₈	C₂×D₄₃	1	3	yes	—
184	C₂×#117	—	43	1	no	—
185	C₂×#117	—	43	3	no	—
186	C₂²×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
187	C₂²×C₄²	C₂×D₄₃	1	3	yes	—
188	#391	—	43	12	no	—
189	#389	—	43	12	no	—
190	#387	—	43	24	no	—
191	#384	—	43	6	no	—
192	#382	—	43	6	no	—
193	#380	—	43	6	no	—
194	#380	—	43	6	no	—
195	C₄×C₄⋊C₄	—	43	12	no	—
196	C₄×C₄⋊C₄	—	43	6	no	—
197	C₄×C₄⋊C₄	—	43	6	no	—
198	C₄×C₄⋊C₄	—	43	6	no	—
199	C₄×C₄⋊C₄	—	43	6	no	—
200	C₄×C₂²⋊C₄	—	43	6	no	—
201	C₄×C₂²⋊C₄	—	43	6	no	—
202	#376	—	43	6	no	—
203	C₄³	—	43	6	no	—
204	C₄₃	Q₈×#117	1	1	yes	characteristic, complemented, Sylow
205	C₂²×Q₈	—	2	8	no	—
206	C₂²×Q₈	C₂×Dic₄₃	1	8	yes	—
207	C₂²×Q₈	C₂²×D₄₃	1	3	yes	—
208	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
209	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
210	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
211	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
212	C₄×Q₈	—	86	16	no	—
213	C₄×Q₈	C₂×Dic₄₃	1	24	yes	—
214	C₄×Q₈	C₂×Dic₄₃	1	24	yes	—
215	C₄×Q₈	C₂×Dic₄₃	1	8	yes	—
216	C₄×Q₈	C₂×Dic₄₃	1	8	yes	—
217	#117	—	43	8	no	—
218	#117	—	86	12	no	—
219	C₂×C₄⋊C₄	—	43	2	no	—
220	C₂×C₄⋊C₄	—	43	6	no	—
221	C₂×C₄⋊C₄	—	43	12	no	—
222	C₂×C₄⋊C₄	—	43	12	no	—
223	C₂×C₄⋊C₄	C₂×Dic₄₃	1	24	yes	—
224	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
225	C₂×C₄⋊C₄	C₂²×D₄₃	1	6	yes	—
226	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
227	C₂×C₂²⋊C₄	—	43	2	no	—
228	C₂×C₂²⋊C₄	—	43	6	no	—
229	C₂×C₄²	—	43	2	no	—
230	C₂×C₄²	—	43	12	no	—
231	C₂×C₄²	—	43	6	no	—
232	C₂×C₄²	—	43	12	no	—
233	C₂×C₄²	C₂×Dic₄₃	1	24	yes	—
234	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
235	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
236	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
237	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
238	#95	—	43	12	no	—
239	#95	—	43	12	no	—
240	#95	—	43	12	no	—
241	#95	—	43	12	no	—
242	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
243	C₂×Q₈	—	2	32	no	—
244	C₂×Q₈	—	2	12	no	—
245	C₂×Q₈	#10621898	1	8	yes	—
246	C₂×Q₈	C₂²×Dic₄₃	1	12	yes	—
247	C₂×Q₈	C₂²×Dic₄₃	1	4	yes	—
248	C₂²×C₄	—	2	12	no	—
249	C₂²×C₄	—	4	6	no	—
250	C₂²×C₄	—	43	4	no	—
251	C₂²×C₄	—	43	12	no	—
252	C₂²×C₄	Q₈×D₄₃	1	4	yes	—
253	C₂²×C₄	#10621902	1	4	yes	—
254	C₂²×C₄	C₂²×Dic₄₃	1	12	yes	—
255	C₂²×C₄	C₂²×Dic₄₃	1	12	yes	—
256	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
257	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
258	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
259	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
260	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
261	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
262	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
263	C₄⋊C₄	—	43	8	no	—
264	C₄⋊C₄	—	86	24	no	—
265	C₄⋊C₄	—	86	12	no	—
266	C₄⋊C₄	—	172	12	no	—
267	C₄⋊C₄	C₂²×Dic₄₃	1	24	yes	—
268	C₄⋊C₄	C₂²×Dic₄₃	1	12	yes	—
269	C₄⋊C₄	C₂²×Dic₄₃	1	12	yes	—
270	C₂²⋊C₄	—	43	8	no	—
271	C₂²⋊C₄	—	86	12	no	—
272	C₄²	—	43	8	no	—
273	C₄²	—	86	24	no	—
274	C₄²	—	86	12	no	—
275	C₄²	—	172	12	no	—
276	C₄²	C₂²×Dic₄₃	1	12	yes	—
277	C₄²	C₂²×Dic₄₃	1	12	yes	—
278	C₄²	C₂²×Dic₄₃	1	12	yes	—
279	C₄²	C₂²×Dic₄₃	1	12	yes	—
280	C₂³	—	2	2	no	—
281	C₂³	—	2	2	no	—
282	C₂³	C₂³×Dic₄₃	1	2	yes	—
283	C₂³	C₂×Q₈×D₄₃	1	2	yes	—
284	C₂³	C₂×#10621902	1	2	yes	—
285	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
286	Q₈	—	2	24	no	—
287	Q₈	#13063284	1	16	yes	direct product factor
288	C₂×C₄	—	2	6	no	—
289	C₂×C₄	—	2	6	no	—
290	C₂×C₄	—	2	6	no	—
291	C₂×C₄	—	2	24	no	—
292	C₂×C₄	—	4	12	no	—
293	C₂×C₄	—	43	8	no	—
294	C₂×C₄	—	86	4	no	—
295	C₂×C₄	—	86	4	no	—
296	C₂×C₄	—	86	12	no	—
297	C₂×C₄	—	86	12	no	—
298	C₂×C₄	—	86	12	no	—
299	C₂×C₄	Q₈×Dic₄₃	1	16	yes	complemented
300	C₂×C₄	C₂³×Dic₄₃	1	6	yes	—
301	C₂×C₄	C₂³×Dic₄₃	1	6	yes	—
302	C₂×C₄	C₂³×Dic₄₃	1	6	yes	—
303	C₂×C₄	C₂³×Dic₄₃	1	6	yes	—
304	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
305	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
306	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
307	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
308	C₂×C₄	C₂×#10621898	1	12	yes	—
309	C₂×C₄	C₂×#10621902	1	2	yes	—
310	C₂×C₄	C₂×#10621902	1	2	yes	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	4	no	—
313	C₂²	—	2	4	no	—
314	C₂²	—	2	2	no	—
315	C₂²	C₂×Q₈×Dic₄₃	1	4	yes	—
316	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
317	C₂²	C₂²×Q₈×D₄₃	1	1	yes	characteristic
318	C₂²	C₂²×#10621898	1	2	yes	—
319	C₂²	C₂²×#10621902	1	1	yes	characteristic
320	C₂²	#14583735	1	2	yes	—
321	C₄	—	2	6	no	—
322	C₄	—	2	6	no	—
323	C₄	—	2	6	no	—
324	C₄	—	86	8	no	—
325	C₄	—	172	12	no	—
326	C₄	C₂×#13063284	1	12	yes	—
327	C₄	C₂×Q₈×Dic₄₃	1	4	yes	—
328	C₄	C₂×Q₈×Dic₄₃	1	4	yes	—
329	C₂	—	2	4	no	—
330	C₂	C₂²×#13063284	1	1	yes	characteristic
331	C₂	C₂²×Q₈×Dic₄₃	1	1	yes	characteristic
332	C₂	#19147798	1	1	yes	characteristic
333	C₂	Q₈×#10621898	1	2	yes	—
334	C₂	#19148190	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₃
Fitting	C₂²×C₄×Q₈×C₄₃	C₂
socle, cosocle	C₂³×C₄₃	C₂⁵
prime radical	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂²×C₄×Q₈	D₄₃
hypocenter	C₄₃	Q₈×#117
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #19137552	C₂	semidirect
2. Q₈×C₄⋊Dic₄₃	C₂	semidirect
5. #19137073	C₂	semidirect
7. C₄×Q₈×Dic₄₃	C₂	semidirect
30. C₂×C₄×Q₈×C₄₃	C₄	semidirect
39. #13063284	Q₈	direct (N × H)
107. C₄⋊Dic₄₃	C₂×Q₈	semidirect
111. C₄×Dic₄₃	C₂×Q₈	semidirect
119. Q₈×C₄₃	#117	semidirect
125. C₂×C₄×C₄₃	C₄×Q₈	semidirect
179. C₂×C₄×Q₈	Dic₄₃	semidirect
204. C₄₃	Q₈×#117	semidirect
287. Q₈	#13063284	direct (N × H)
299. C₂×C₄	Q₈×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19137552	2
Q₈×C₄⋊Dic₄₃	2
#19137472	2
Q₈×C₂²⋊Dic₄₃	2
#19137073	2
#19137002	2
C₄×Q₈×Dic₄₃	2
C₄×#13063284	2
C₂²×C₄×Q₈×C₄₃	2
Q₈×#117	43

Subgroups — Q8×#13063284 #25256026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#13063284 #25256026