Subgroups — C₂²×#15689830 #27123250

Order 12032.

8454 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689830	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#13094024	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13094015	C₂	1	2	yes	maximal, complemented
4	C₂²×#13094003	C₂	1	2	yes	maximal, complemented
5	C₂²×#13094001	C₂	1	4	yes	maximal, complemented
6	C₂²×C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₄×Dic₄₇	C₂	1	2	yes	maximal
8	C₂³×C₄⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂³×Dic₉₄	C₂²	1	1	yes	characteristic
11	C₂³×Dic₉₄	C₂²	1	2	yes	—
12	C₂⁴×Dic₄₇	C₂²	1	4	yes	—
13	#15689830	C₂²	1	256	yes	direct product factor
14	C₂×#13094024	C₂²	1	24	yes	complemented
15	C₂×#13094015	C₂²	1	48	yes	complemented
16	C₂×#13094003	C₂²	1	48	yes	complemented
17	C₂×#13094001	C₂²	1	96	yes	complemented
18	C₂×C₄×Dic₉₄	C₂²	1	24	yes	complemented
19	C₂×D₄×Dic₄₇	C₂²	1	48	yes	—
20	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	—
22	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
23	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
24	C₂²×C₄⋊Dic₄₇	C₂²	1	48	yes	complemented
25	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	—
26	C₂²×Dic₄₇⋊C₄	C₂²	1	4	yes	—
27	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
28	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
29	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₄₇	C₂²	1	24	yes	—
32	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
34	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×Dic₉₄	—	2	8	no	—
36	C₂²×Dic₉₄	—	4	8	no	—
37	C₂²×Dic₉₄	C₂³	1	12	yes	—
38	C₂²×Dic₉₄	C₂³	1	24	yes	—
39	C₂³×Dic₄₇	—	4	16	no	—
40	C₂³×Dic₄₇	C₂³	1	2	yes	—
41	C₂³×Dic₄₇	C₂³	1	2	yes	—
42	C₂³×Dic₄₇	C₂³	1	4	yes	—
43	C₂³×Dic₄₇	C₂³	1	48	yes	—
44	#13094024	C₂³	1	64	yes	complemented
45	#13094015	C₂³	1	128	yes	complemented
46	#13094003	C₂³	1	128	yes	complemented
47	#13094001	C₂³	1	256	yes	complemented
48	C₄×Dic₉₄	C₂³	1	64	yes	complemented
49	D₄×Dic₄₇	C₂³	1	128	yes	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	48	yes	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	24	yes	—
53	C₂×C₄⋊Dic₄₇	C₂³	1	24	yes	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	128	yes	complemented
55	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	—
56	C₂×Dic₄₇⋊C₄	C₂³	1	48	yes	—
57	C₂×C₂²⋊Dic₄₇	C₂³	1	48	yes	—
58	C₂×C₄×Dic₄₇	C₂³	1	24	yes	—
59	C₂⁵×C₄₇	C₂³	1	2	yes	—
60	C₂²×D₄×C₄₇	Q₈	1	16	yes	complemented
61	C₂²×D₄×C₄₇	C₂³	1	12	yes	—
62	C₂³×C₄×C₄₇	—	2	16	no	—
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
65	C₂³×C₄×C₄₇	C₂³	1	24	yes	—
66	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₄₇	C₂³	1	64	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
70	C₂×C₂²⋊C₄×C₄₇	C₂³	1	24	yes	—
71	C₂×C₄²×C₄₇	C₂³	1	12	yes	—
72	C₂⁴×C₄₇	—	2	8	no	—
73	C₂⁴×C₄₇	—	2	8	no	—
74	C₂⁴×C₄₇	C₂×Q₈	1	16	yes	—
75	C₂⁴×C₄₇	C₂⁴	1	12	yes	—
76	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
77	C₂×D₄×C₄₇	C₂×Q₈	1	96	yes	complemented
78	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
79	C₂²×C₄×C₄₇	—	2	8	no	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	96	no	—
82	C₂²×C₄×C₄₇	C₂×Q₈	1	8	yes	—
83	C₂²×C₄×C₄₇	#41	1	8	yes	—
84	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
85	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
86	C₂²×C₄×C₄₇	C₂⁴	1	32	yes	—
87	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
88	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
89	C₂²×Dic₄₇	—	2	8	no	—
90	C₂²×Dic₄₇	—	2	8	no	—
91	C₂²×Dic₄₇	—	2	16	no	—
92	C₂²×Dic₄₇	—	4	96	no	—
93	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
94	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
95	C₂²×Dic₄₇	C₂⁴	1	24	yes	—
96	C₂²×Dic₄₇	C₂⁴	1	64	yes	—
97	C₂×Dic₉₄	—	2	48	no	—
98	C₂×Dic₉₄	—	4	48	no	—
99	C₂×Dic₉₄	C₂⁴	1	16	yes	—
100	C₂×Dic₉₄	C₂⁴	1	32	yes	—
101	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
102	C₂²⋊C₄×C₄₇	C₂⁴	1	32	yes	—
103	C₄²×C₄₇	C₂⁴	1	16	yes	—
104	C₂²⋊Dic₄₇	C₂⁴	1	64	yes	—
105	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
106	C₄⋊Dic₄₇	C₂⁴	1	64	yes	—
107	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
108	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
109	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
110	Dic₄₇⋊C₄	C₂⁴	1	64	yes	—
111	C₄×Dic₄₇	C₂⁴	1	32	yes	—
112	C₂³×C₄₇	—	2	64	no	—
113	C₂³×C₄₇	—	2	24	no	—
114	C₂³×C₄₇	—	2	24	no	—
115	C₂³×C₄₇	C₂²×Q₈	1	48	yes	—
116	C₂³×C₄₇	C₂²×Q₈	1	4	yes	—
117	C₂³×C₄₇	C₂×#41	1	4	yes	—
118	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
119	C₂³×C₄₇	C₂⁵	1	8	yes	—
120	C₂³×C₄₇	C₂⁵	1	3	yes	—
121	D₄×C₄₇	C₂²×Q₈	1	64	yes	complemented
122	C₂×C₄×C₄₇	—	2	24	no	—
123	C₂×C₄×C₄₇	—	2	12	no	—
124	C₂×C₄×C₄₇	—	2	64	no	—
125	C₂×C₄×C₄₇	C₂²×Q₈	1	24	yes	—
126	C₂×C₄×C₄₇	C₂×#41	1	24	yes	—
127	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
128	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
129	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
130	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
131	C₂×Dic₄₇	—	2	24	no	—
132	C₂×Dic₄₇	—	2	48	no	—
133	C₂×Dic₄₇	—	2	24	no	—
134	C₂×Dic₄₇	—	4	64	no	—
135	C₂×Dic₄₇	C₂⁵	1	8	yes	—
136	C₂×Dic₄₇	C₂⁵	1	8	yes	—
137	C₂×Dic₄₇	C₂⁵	1	16	yes	—
138	Dic₉₄	—	2	32	no	—
139	Dic₉₄	—	4	32	no	—
140	C₂²×#554	—	47	1	no	maximal, Sylow
141	C₂²×C₄₇	—	2	8	no	—
142	C₂²×C₄₇	—	2	8	no	—
143	C₂²×C₄₇	—	2	96	no	—
144	C₂²×C₄₇	#554	1	16	yes	complemented
145	C₂²×C₄₇	C₂³×Q₈	1	16	yes	—
146	C₂²×C₄₇	C₂³×Q₈	1	6	yes	—
147	C₂²×C₄₇	C₂²×#41	1	6	yes	—
148	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	6	yes	—
149	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
150	C₄×C₄₇	—	2	8	no	—
151	C₄×C₄₇	—	2	4	no	—
152	C₄×C₄₇	C₂³×Q₈	1	8	yes	—
153	C₄×C₄₇	C₂²×#41	1	8	yes	—
154	Dic₄₇	—	2	8	no	—
155	Dic₄₇	—	2	16	no	—
156	Dic₄₇	—	2	8	no	—
157	C₂×#554	—	47	48	no	—
158	C₂²×C₄⋊Q₈	—	47	1	no	—
159	C₂²×#125	—	47	2	no	—
160	C₂²×C₂²⋊Q₈	—	47	2	no	—
161	C₂²×C₂²⋊Q₈	—	47	4	no	—
162	C₂²×C₄×Q₈	—	47	1	no	—
163	C₂²×C₄×D₄	—	47	2	no	—
164	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
165	C₂³×C₄⋊C₄	—	47	2	no	—
166	C₂×C₄₇	—	2	16	no	—
167	C₂×C₄₇	C₂×#554	1	12	yes	complemented
168	C₂×C₄₇	C₂⁴×Q₈	1	1	yes	characteristic
169	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
170	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
171	C₂³×Q₈	—	47	1	no	—
172	C₂³×Q₈	—	47	2	no	—
173	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
174	C₂⁴×C₄	—	47	4	no	—
175	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
176	#554	—	47	256	no	—
177	C₂×C₄⋊Q₈	—	47	24	no	—
178	C₂×#125	—	47	48	no	—
179	C₂×C₂²⋊Q₈	—	47	48	no	—
180	C₂×C₂²⋊Q₈	—	47	96	no	—
181	C₂×C₄×Q₈	—	47	24	no	—
182	C₂×C₄×D₄	—	47	48	no	—
183	C₂×C₄×D₄	C₂×D₄₇	1	24	yes	—
184	C₂²×C₄⋊C₄	—	47	1	no	—
185	C₂²×C₄⋊C₄	—	47	4	no	—
186	C₂²×C₄⋊C₄	—	47	2	no	—
187	C₂²×C₄⋊C₄	—	47	48	no	—
188	C₂²×C₄⋊C₄	—	47	2	no	—
189	C₂²×C₄⋊C₄	—	47	2	no	—
190	C₂²×C₄⋊C₄	—	47	4	no	—
191	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
192	C₂²×C₂²⋊C₄	—	47	4	no	—
193	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
194	C₂²×C₄²	—	47	2	no	—
195	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
196	C₄₇	C₂²×#554	1	1	yes	characteristic, complemented, Sylow
197	C₂⁵	C₂²×D₄₇	1	2	yes	—
198	C₂²×Q₈	—	47	12	no	—
199	C₂²×Q₈	—	47	24	no	—
200	C₂²×Q₈	—	94	8	no	—
201	C₂²×Q₈	—	188	8	no	—
202	C₂²×D₄	Dic₉₄	1	16	yes	complemented
203	C₂²×D₄	C₂²×D₄₇	1	12	yes	—
204	C₂³×C₄	—	2	16	no	—
205	C₂³×C₄	—	47	2	no	—
206	C₂³×C₄	—	47	4	no	—
207	C₂³×C₄	—	47	2	no	—
208	C₂³×C₄	—	47	48	no	—
209	C₂³×C₄	—	188	16	no	—
210	C₂³×C₄	C₂²×D₄₇	1	24	yes	—
211	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
212	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
213	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
214	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
215	C₄⋊Q₈	—	47	64	no	—
216	#125	—	47	128	no	—
217	C₂²⋊Q₈	—	47	128	no	—
218	C₂²⋊Q₈	—	47	256	no	—
219	C₄×Q₈	—	47	64	no	—
220	C₄×D₄	—	47	128	no	—
221	C₄×D₄	C₂²×D₄₇	1	64	yes	—
222	C₂×C₄⋊C₄	—	47	12	no	—
223	C₂×C₄⋊C₄	—	47	48	no	—
224	C₂×C₄⋊C₄	—	47	24	no	—
225	C₂×C₄⋊C₄	—	47	128	no	—
226	C₂×C₄⋊C₄	—	47	24	no	—
227	C₂×C₄⋊C₄	—	47	24	no	—
228	C₂×C₄⋊C₄	—	47	48	no	—
229	C₂×C₄⋊C₄	C₂²×D₄₇	1	12	yes	—
230	C₂×C₂²⋊C₄	—	47	48	no	—
231	C₂×C₂²⋊C₄	C₂²×D₄₇	1	24	yes	—
232	C₂×C₄²	—	47	24	no	—
233	C₂×C₄²	C₂²×D₄₇	1	12	yes	—
234	C₂⁴	—	2	8	no	—
235	C₂⁴	—	2	8	no	—
236	C₂⁴	C₂×Dic₉₄	1	16	yes	—
237	C₂⁴	C₂³×D₄₇	1	12	yes	—
238	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
239	C₂×Q₈	—	47	16	no	—
240	C₂×Q₈	—	47	32	no	—
241	C₂×Q₈	—	94	48	no	—
242	C₂×Q₈	—	188	48	no	—
243	C₂×D₄	C₂×Dic₉₄	1	96	yes	complemented
244	C₂×D₄	C₂³×D₄₇	1	16	yes	—
245	C₂²×C₄	—	2	8	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	96	no	—
248	C₂²×C₄	—	47	12	no	—
249	C₂²×C₄	—	47	12	no	—
250	C₂²×C₄	—	47	24	no	—
251	C₂²×C₄	—	47	64	no	—
252	C₂²×C₄	—	94	8	no	—
253	C₂²×C₄	—	94	8	no	—
254	C₂²×C₄	—	94	16	no	—
255	C₂²×C₄	—	188	96	no	—
256	C₂²×C₄	C₂×Dic₉₄	1	8	yes	—
257	C₂²×C₄	#10625352	1	8	yes	—
258	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
259	C₂²×C₄	C₂³×D₄₇	1	12	yes	—
260	C₂²×C₄	C₂³×D₄₇	1	32	yes	—
261	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
262	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
263	C₄⋊C₄	—	47	32	no	—
264	C₄⋊C₄	—	47	64	no	—
265	C₄⋊C₄	—	47	16	no	—
266	C₄⋊C₄	—	47	64	no	—
267	C₄⋊C₄	—	47	32	no	—
268	C₄⋊C₄	—	47	32	no	—
269	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
270	C₂²⋊C₄	—	47	64	no	—
271	C₂²⋊C₄	C₂³×D₄₇	1	32	yes	—
272	C₄²	—	47	32	no	—
273	C₄²	C₂³×D₄₇	1	16	yes	—
274	C₂³	—	2	64	no	—
275	C₂³	—	2	24	no	—
276	C₂³	—	2	24	no	—
277	C₂³	C₂²×Dic₉₄	1	48	yes	—
278	C₂³	C₂²×Dic₉₄	1	4	yes	—
279	C₂³	C₂×#10625352	1	4	yes	—
280	C₂³	#13094070	1	4	yes	—
281	C₂³	C₂⁴×D₄₇	1	8	yes	—
282	C₂³	C₂⁴×D₄₇	1	3	yes	—
283	Q₈	—	94	32	no	—
284	Q₈	—	188	32	no	—
285	D₄	C₂²×Dic₉₄	1	64	yes	complemented
286	C₂×C₄	—	2	24	no	—
287	C₂×C₄	—	2	12	no	—
288	C₂×C₄	—	2	64	no	—
289	C₂×C₄	—	47	8	no	—
290	C₂×C₄	—	47	8	no	—
291	C₂×C₄	—	47	16	no	—
292	C₂×C₄	—	94	24	no	—
293	C₂×C₄	—	94	24	no	—
294	C₂×C₄	—	94	48	no	—
295	C₂×C₄	—	188	64	no	—
296	C₂×C₄	C₂²×Dic₉₄	1	24	yes	—
297	C₂×C₄	C₂×#10625352	1	24	yes	—
298	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
299	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
300	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
301	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
302	C₂²	—	2	8	no	—
303	C₂²	—	2	8	no	—
304	C₂²	—	2	96	no	—
305	C₂²	#15689830	1	16	yes	direct product factor
306	C₂²	C₂³×Dic₉₄	1	16	yes	—
307	C₂²	C₂³×Dic₉₄	1	6	yes	—
308	C₂²	C₂²×#10625352	1	6	yes	—
309	C₂²	C₂×#13094070	1	6	yes	—
310	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
311	C₄	—	2	8	no	—
312	C₄	—	2	4	no	—
313	C₄	—	94	8	no	—
314	C₄	—	94	8	no	—
315	C₄	—	94	16	no	—
316	C₄	C₂³×Dic₉₄	1	8	yes	—
317	C₄	C₂²×#10625352	1	8	yes	—
318	C₂	—	2	16	no	—
319	C₂	C₂×#15689830	1	12	yes	direct product factor
320	C₂	C₂⁴×Dic₉₄	1	1	yes	characteristic
321	C₂	C₂³×#10625352	1	1	yes	characteristic
322	C₂	C₂²×#13094070	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂³×D₄×C₄₇	C₂²
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂²×#554
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#15689830	C₂	direct (N × H)
2. C₂²×#13094024	C₂	semidirect
3. C₂²×#13094015	C₂	semidirect
4. C₂²×#13094003	C₂	semidirect
5. C₂²×#13094001	C₂	semidirect
6. C₂²×C₄×Dic₉₄	C₂	semidirect
8. C₂³×C₄⋊Dic₄₇	C₂	semidirect
13. #15689830	C₂²	direct (N × H)
14. C₂×#13094024	C₂²	semidirect
15. C₂×#13094015	C₂²	semidirect
16. C₂×#13094003	C₂²	semidirect
17. C₂×#13094001	C₂²	semidirect
18. C₂×C₄×Dic₉₄	C₂²	semidirect
24. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
44. #13094024	C₂³	semidirect
45. #13094015	C₂³	semidirect
46. #13094003	C₂³	semidirect
47. #13094001	C₂³	semidirect
48. C₄×Dic₉₄	C₂³	semidirect
54. C₂×C₄⋊Dic₄₇	C₂³	semidirect
60. C₂²×D₄×C₄₇	Q₈	semidirect
77. C₂×D₄×C₄₇	C₂×Q₈	semidirect
121. D₄×C₄₇	C₂²×Q₈	semidirect
144. C₂²×C₄₇	#554	semidirect
167. C₂×C₄₇	C₂×#554	semidirect
196. C₄₇	C₂²×#554	semidirect
202. C₂²×D₄	Dic₉₄	semidirect
243. C₂×D₄	C₂×Dic₉₄	semidirect
285. D₄	C₂²×Dic₉₄	semidirect
305. C₂²	#15689830	direct (N × H)
319. C₂	C₂×#15689830	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689830	2
C₂²×#13094024	2
C₂²×#13094015	2
C₂²×#13094003	2
C₂²×#13094001	2
C₂²×C₄×Dic₉₄	2
C₂²×D₄×Dic₄₇	2
C₂³×C₄⋊Dic₄₇	2
C₂²×C₄×D₄×C₄₇	2
C₂²×#554	47

Subgroups — C22×#15689830 #27123250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689830 #27123250