Subgroups — C₄×#15689473 #26224252

Order 12032.

878 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689473	C₂	1	1	yes	maximal, characteristic
2	C₄×#13094024	C₂	1	1	yes	maximal, characteristic
3	#20244348	C₂	1	1	yes	maximal, characteristic
4	#20244191	C₂	1	1	yes	maximal, characteristic
5	#20244067	C₂	1	4	yes	maximal
6	#20243515	C₂	1	1	yes	maximal, characteristic
7	C₄×#13093948	C₂	1	4	yes	maximal
8	C₄²×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂×#13094024	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₉₄	—	2	1	no	—
12	#15689473	C₄	1	8	yes	direct product factor
13	C₂×#13093948	C₂²	1	4	yes	—
14	C₂×#13093948	C₂²	1	4	yes	—
15	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	#15689029	—	2	1	no	—
20	#15689021	—	2	1	no	—
21	#15689021	C₂²	1	2	yes	—
22	#15688993	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊Dic₄₇	—	2	1	no	—
24	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
25	#15688885	C₂²	1	4	yes	—
26	#15688885	C₂²	1	4	yes	—
27	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
29	C₄₇×#391	C₂²	1	2	yes	—
30	C₄₇×#389	—	2	1	no	—
31	C₄₇×#389	—	2	1	no	—
32	C₄₇×#384	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
34	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
35	C₄³×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²×Dic₉₄	—	2	1	no	—
37	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
38	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
39	#13094024	—	2	2	no	—
40	#13094024	C₂×C₄	1	4	yes	—
41	C₄×Dic₉₄	—	4	4	no	—
42	C₂×C₄⋊Dic₄₇	—	2	1	no	—
43	C₂×C₄⋊Dic₄₇	—	2	1	no	—
44	C₂×C₄⋊Dic₄₇	—	2	1	no	—
45	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
47	C₂×Dic₄₇⋊C₄	—	2	2	no	—
48	C₂×C₄×Dic₄₇	—	2	2	no	—
49	#13093948	—	2	8	no	—
50	#13093948	C₂×C₄	1	16	yes	—
51	C₄×C₄₇⋊C₈	—	2	2	no	—
52	C₄×C₄₇⋊C₈	—	2	4	no	—
53	C₄×C₄₇⋊C₈	—	2	4	no	—
54	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
55	C₄₇⋊#95	—	2	2	no	—
56	C₄₇⋊#95	—	2	2	no	—
57	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₄₇	—	2	2	no	—
59	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
60	C₄×Q₈×C₄₇	—	2	8	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
67	C₂×C₄²×C₄₇	—	2	2	no	—
68	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	#95×C₄₇	—	2	2	no	—
76	#95×C₄₇	—	2	2	no	—
77	C₂×Q₈×C₄₇	—	2	2	no	—
78	C₂×Q₈×C₄₇	—	2	4	no	—
79	C₂×Q₈×C₄₇	—	2	4	no	—
80	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₂²×Dic₄₇	—	2	2	no	—
91	C₂²×Dic₄₇	—	2	2	no	—
92	C₂×Dic₉₄	—	2	4	no	—
93	C₂×Dic₉₄	—	4	2	no	—
94	C₂×Dic₉₄	—	4	2	no	—
95	C₄⋊C₄×C₄₇	—	2	4	no	—
96	C₄⋊C₄×C₄₇	—	2	4	no	—
97	C₄⋊C₄×C₄₇	—	2	4	no	—
98	C₄⋊C₄×C₄₇	—	4	4	no	—
99	C₄⋊C₄×C₄₇	—	4	2	no	—
100	C₄⋊C₄×C₄₇	—	4	2	no	—
101	C₄²×C₄₇	—	2	2	no	—
102	C₄²×C₄₇	—	2	2	no	—
103	C₄²×C₄₇	—	2	2	no	—
104	C₄²×C₄₇	—	4	4	no	—
105	C₄²×C₄₇	SD₁₆	1	4	yes	—
106	C₄²×C₄₇	Q₁₆	1	4	yes	—
107	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
108	C₄²×C₄₇	#41	1	2	yes	—
109	C₄²×C₄₇	#41	1	4	yes	—
110	C₄⋊Dic₄₇	—	2	4	no	—
111	C₄⋊Dic₄₇	—	2	2	no	—
112	C₄⋊Dic₄₇	—	2	4	no	—
113	C₄⋊Dic₄₇	—	4	2	no	—
114	C₄⋊Dic₄₇	—	4	2	no	—
115	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
116	Dic₄₇⋊C₄	—	4	4	no	—
117	C₄×Dic₄₇	—	4	4	no	—
118	C₂×C₄₇⋊C₈	—	2	2	no	—
119	C₂×C₄₇⋊C₈	—	2	2	no	—
120	C₂×C₄₇⋊C₈	—	2	2	no	—
121	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
123	C₂×C₄₇⋊C₈	#41	1	4	yes	—
124	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₄₇	—	2	8	no	—
126	Q₈×C₄₇	—	4	4	no	—
127	C₂×C₄×C₄₇	—	2	1	no	—
128	C₂×C₄×C₄₇	—	2	1	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	2	1	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	4	2	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	4	2	no	—
137	C₂×C₄×C₄₇	—	4	2	no	—
138	C₂×C₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
140	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₄₇	#124	1	2	yes	—
142	C₂×C₄×C₄₇	#124	1	2	yes	—
143	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
144	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
145	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
146	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
147	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
148	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
149	C₂×C₄×C₄₇	#135	1	2	yes	—
150	C₂×C₄×C₄₇	#135	1	2	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×Dic₄₇	—	2	4	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	Dic₉₄	—	4	8	no	—
162	C₄₇⋊C₈	—	2	4	no	—
163	C₄₇⋊C₈	—	2	4	no	—
164	C₄×#487	—	47	1	no	maximal, Sylow
165	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
167	C₂²×C₄₇	#532	1	1	yes	characteristic
168	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
169	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
170	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
171	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
172	C₄×C₄₇	—	2	2	no	—
173	C₄×C₄₇	—	2	2	no	—
174	C₄×C₄₇	—	2	2	no	—
175	C₄×C₄₇	—	4	4	no	—
176	C₄×C₄₇	—	8	2	no	—
177	C₄×C₄₇	C₄×SD₁₆	1	4	yes	—
178	C₄×C₄₇	C₄×Q₁₆	1	4	yes	—
179	C₄×C₄₇	#487	1	4	yes	complemented
180	C₄×C₄₇	C₄×#41	1	2	yes	—
181	C₄×C₄₇	#529	1	2	yes	—
182	Dic₄₇	—	4	4	no	—
183	Dic₄₇	—	8	2	no	—
184	C₂×#487	—	47	1	no	—
185	C₄×C₄⋊Q₈	—	47	1	no	—
186	C₄×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
187	#1990	—	47	1	no	—
188	#1956	—	47	1	no	—
189	#1933	—	47	4	no	—
190	#1834	—	47	1	no	—
191	C₄×#103	—	47	4	no	—
192	C₄²×C₈	—	47	1	no	—
193	C₂×C₄₇	C₄×#124	1	1	yes	characteristic
194	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
195	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
196	C₂×C₄₇	C₂×#487	1	1	yes	characteristic
197	C₂×C₄₇	#3131	1	1	yes	characteristic
198	C₂×C₄₇	#3167	1	1	yes	characteristic
199	C₂×C₄₇	#3170	1	1	yes	characteristic
200	C₂×C₄⋊Q₈	—	47	1	no	—
201	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
202	C₂×C₄×Q₈	—	94	1	no	—
203	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
204	#487	—	47	8	no	—
205	C₂×#103	—	47	4	no	—
206	C₂×#103	—	47	4	no	—
207	C₂×C₄×C₈	—	47	1	no	—
208	C₂×C₄×C₈	—	47	2	no	—
209	C₂×C₄×C₈	—	47	1	no	—
210	C₂×C₄×C₈	—	47	2	no	—
211	#391	—	94	1	no	—
212	#391	C₂×D₄₇	1	2	yes	—
213	#389	—	2	1	no	—
214	#389	—	2	1	no	—
215	#389	—	47	2	no	—
216	#389	—	94	1	no	—
217	#384	—	47	1	no	—
218	#384	C₂×D₄₇	1	1	yes	characteristic
219	C₄×C₄⋊C₄	—	2	1	no	—
220	C₄×C₄⋊C₄	—	2	1	no	—
221	C₄×C₄⋊C₄	—	47	2	no	—
222	C₄×C₄⋊C₄	—	94	1	no	—
223	C₄³	C₂×D₄₇	1	1	yes	characteristic
224	#340	—	47	4	no	—
225	#340	—	47	4	no	—
226	C₄₇	C₄×#487	1	1	yes	characteristic, complemented, Sylow
227	C₂²×Q₈	—	94	1	no	—
228	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
229	C₂²×C₈	—	47	2	no	—
230	C₂²×C₈	—	47	2	no	—
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	—	47	4	no	—
233	C₄⋊Q₈	—	94	2	no	—
234	C₄⋊Q₈	C₄×D₄₇	1	4	yes	—
235	C₄×Q₈	—	2	8	no	—
236	C₄×Q₈	—	188	4	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	47	2	no	—
243	C₂×C₄⋊C₄	—	47	2	no	—
244	C₂×C₄⋊C₄	—	94	1	no	—
245	C₂×C₄⋊C₄	—	94	2	no	—
246	C₂×C₄⋊C₄	—	94	1	no	—
247	C₂×C₄⋊C₄	—	94	1	no	—
248	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	—	94	2	no	—
251	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
254	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
256	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
257	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
258	#103	—	47	16	no	—
259	#103	—	94	8	no	—
260	C₄×C₈	—	47	4	no	—
261	C₄×C₈	—	94	4	no	—
262	C₄×C₈	—	94	2	no	—
263	C₄×C₈	—	94	4	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	94	2	no	—
267	#95	—	94	2	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	94	4	no	—
272	C₂×Q₈	—	188	2	no	—
273	C₂×Q₈	—	188	2	no	—
274	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	94	2	no	—
278	C₂²×C₄	—	94	2	no	—
279	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
286	C₂×C₈	—	47	4	no	—
287	C₂×C₈	—	47	4	no	—
288	C₂×C₈	—	94	2	no	—
289	C₂×C₈	—	94	2	no	—
290	C₂×C₈	—	94	2	no	—
291	C₂×C₈	—	94	2	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	4	4	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	—	47	4	no	—
299	C₄⋊C₄	—	94	4	no	—
300	C₄⋊C₄	—	94	2	no	—
301	C₄⋊C₄	—	94	4	no	—
302	C₄⋊C₄	—	188	4	no	—
303	C₄⋊C₄	—	188	2	no	—
304	C₄⋊C₄	—	188	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	4	4	no	—
309	C₄²	—	188	4	no	—
310	C₄²	#10625336	1	4	yes	—
311	C₄²	#10625337	1	4	yes	—
312	C₄²	C₂×C₄×D₄₇	1	2	yes	—
313	C₄²	#10625350	1	2	yes	—
314	C₄²	#10625352	1	4	yes	—
315	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
316	Q₈	—	2	8	no	—
317	Q₈	—	4	4	no	—
318	Q₈	—	188	8	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	94	4	no	—
332	C₂×C₄	—	188	2	no	—
333	C₂×C₄	—	188	2	no	—
334	C₂×C₄	—	188	2	no	—
335	C₂×C₄	—	188	2	no	—
336	C₂×C₄	—	188	2	no	—
337	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
338	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
339	C₂×C₄	#13094011	1	2	yes	—
340	C₂×C₄	#13094011	1	2	yes	—
341	C₂×C₄	C₂×#10625336	1	2	yes	—
342	C₂×C₄	C₂×#10625336	1	2	yes	—
343	C₂×C₄	C₂×#10625336	1	2	yes	—
344	C₂×C₄	C₂×#10625337	1	2	yes	—
345	C₂×C₄	C₂×#10625337	1	2	yes	—
346	C₂×C₄	C₂×#10625337	1	2	yes	—
347	C₂×C₄	#13094044	1	2	yes	—
348	C₂×C₄	#13094044	1	2	yes	—
349	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
350	C₂×C₄	#41×D₄₇	1	2	yes	—
351	C₂×C₄	C₂×#10625352	1	2	yes	—
352	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
353	C₈	—	94	4	no	—
354	C₈	—	94	4	no	—
355	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
356	C₂²	C₂×#13094011	1	1	yes	characteristic
357	C₂²	#15689669	1	1	yes	characteristic
358	C₂²	C₂²×#10625336	1	1	yes	characteristic
359	C₂²	C₂²×#10625337	1	1	yes	characteristic
360	C₂²	C₂×#13094044	1	1	yes	characteristic
361	C₂²	C₂×#13094044	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	4	4	no	—
366	C₄	—	8	2	no	—
367	C₄	—	376	2	no	—
368	C₄	—	188	4	no	—
369	C₄	C₄×#10625336	1	4	yes	—
370	C₄	C₄×#10625337	1	4	yes	—
371	C₄	#15689473	1	4	yes	direct product factor
372	C₄	C₄×#10625352	1	2	yes	—
373	C₄	#15689655	1	2	yes	—
374	C₂	C₄×#13094011	1	1	yes	characteristic
375	C₂	C₂×C₄×#10625336	1	1	yes	characteristic
376	C₂	C₂×C₄×#10625337	1	1	yes	characteristic
377	C₂	C₂×#15689473	1	1	yes	characteristic
378	C₂	#20253710	1	1	yes	characteristic
379	C₂	#20253948	1	1	yes	characteristic
380	C₂	#20253970	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×C₄⋊Q₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	C₄×#487
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
12. #15689473	C₄	direct (N × H)
179. C₄×C₄₇	#487	semidirect
226. C₄₇	C₄×#487	semidirect
371. C₄	#15689473	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×#15689473	2
C₄×#13094024	2
#20244348	2
#20244191	2
#20244067	2
#20243515	2
C₄×#13093948	2
C₄²×C₄₇⋊C₈	2
C₄×C₄⋊Q₈×C₄₇	2
C₄×#487	47

Subgroups — C4×#15689473 #26224252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689473 #26224252