Subgroups — D₄×#10625352 #20256870

Order 6016.

1648 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10625352	C₂	1	2	yes	maximal, complemented
2	#15689793	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689779	C₂	1	2	yes	maximal, complemented
5	#15689777	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689773	C₂	1	2	yes	maximal, complemented
7	#15689767	C₂	1	2	yes	maximal, complemented
8	#15689760	C₂	1	4	yes	maximal, complemented
9	D₄×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
10	#15689671	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689668	C₂	1	2	yes	maximal, complemented
12	#15689633	C₂	1	2	yes	maximal, complemented
13	#15689629	C₂	1	4	yes	maximal, complemented
14	C₄×#10625352	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×D₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625352	—	2	16	no	—
19	C₂×#10625352	C₂²	1	1	yes	characteristic
20	C₂×#10625352	C₂²	1	4	yes	complemented
21	C₂×#10625352	C₂²	1	2	yes	complemented
22	C₂×#10625352	C₂²	1	2	yes	complemented
23	C₂×#10625352	C₂²	1	4	yes	complemented
24	C₂×#10625352	C₂²	1	2	yes	complemented
25	C₂²×Dic₉₄	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
27	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
28	C₂³×Dic₄₇	C₂²	1	4	yes	complemented
29	C₂²×C₄×D₄₇	C₂²	1	2	yes	complemented
30	#13094024	C₂²	1	1	yes	characteristic, complemented
31	#13094023	C₂²	1	2	yes	complemented
32	#13094020	C₂²	1	2	yes	complemented
33	#13094011	C₂²	1	2	yes	complemented
34	#13094010	C₂²	1	4	yes	complemented
35	#13094008	C₂²	1	4	yes	complemented
36	#13094006	C₂²	1	4	yes	complemented
37	#13094005	C₂²	1	4	yes	complemented
38	#13094004	C₂²	1	2	yes	complemented
39	#13094003	C₂²	1	2	yes	complemented
40	#13094001	C₂²	1	4	yes	complemented
41	#13094001	C₂²	1	4	yes	complemented
42	#13093998	C₂²	1	2	yes	complemented
43	#13093996	C₂²	1	4	yes	complemented
44	#13093996	C₂²	1	4	yes	complemented
45	#13093996	C₂²	1	4	yes	complemented
46	#13093995	C₂²	1	2	yes	complemented
47	#13093995	C₂²	1	2	yes	complemented
48	#13093995	C₂²	1	2	yes	complemented
49	#13093993	C₂²	1	4	yes	complemented
50	#13093992	C₂²	1	4	yes	complemented
51	C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
52	#13093989	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
54	D₄×Dic₄₇	C₂²	1	2	yes	—
55	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
56	D₄×Dic₄₇	C₂²	1	4	yes	complemented
57	D₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₄₇	C₂²	1	2	yes	complemented
59	D₄×Dic₄₇	C₂²	1	4	yes	complemented
60	D₄×Dic₄₇	C₂²	1	2	yes	complemented
61	D₄×Dic₄₇	C₂²	1	2	yes	complemented
62	#13093986	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
65	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
66	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
67	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
68	#13093982	C₂²	1	1	yes	characteristic, complemented
69	#13093980	C₂²	1	2	yes	complemented
70	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
74	C₂×C₄×Dic₄₇	C₂²	1	2	yes	complemented
75	C₄²×D₄₇	C₂²	1	1	yes	characteristic, complemented
76	C₂²×D₄×C₄₇	C₂²	1	2	yes	—
77	C₂²×D₄×C₄₇	C₂²	1	2	yes	complemented
78	#127×C₄₇	C₂²	1	1	yes	characteristic, complemented
79	#121×C₄₇	C₂²	1	2	yes	complemented
80	#121×C₄₇	C₂²	1	2	yes	complemented
81	#120×C₄₇	C₂²	1	4	yes	complemented
82	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
83	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
84	C₂⁴×C₄₇	C₂³	1	4	yes	—
85	C₂³×D₄₇	C₂³	1	2	yes	—
86	C₂×D₄×C₄₇	—	2	8	no	—
87	C₂×D₄×C₄₇	—	2	8	no	—
88	C₂×D₄×C₄₇	C₂³	1	4	yes	—
89	C₂×D₄×C₄₇	C₂³	1	4	yes	—
90	C₂×D₄×C₄₇	C₂³	1	2	yes	—
91	C₂×D₄×C₄₇	C₂³	1	2	yes	—
92	C₂×D₄×C₄₇	C₂³	1	2	yes	—
93	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₄₇	—	2	16	no	—
98	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
99	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
104	C₂²×Dic₄₇	—	2	16	no	—
105	C₂²×Dic₄₇	C₂³	1	4	yes	—
106	C₂²×Dic₄₇	C₂³	1	2	yes	—
107	C₂²×Dic₄₇	C₂³	1	4	yes	—
108	C₂²×Dic₄₇	C₂³	1	4	yes	—
109	C₂²×Dic₄₇	C₂³	1	4	yes	—
110	C₂²×Dic₄₇	C₂³	1	2	yes	—
111	C₂²×Dic₄₇	C₂³	1	2	yes	—
112	#10625352	—	2	8	no	—
113	#10625352	—	2	16	no	—
114	#10625352	—	2	16	no	—
115	#10625352	—	2	8	no	—
116	#10625352	—	2	8	no	—
117	#10625352	D₄	1	8	yes	direct product factor
118	D₄×D₄₇	—	2	4	no	—
119	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
120	C₂×C₄×D₄₇	—	2	8	no	—
121	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
122	C₂×C₄×D₄₇	C₂³	1	2	yes	—
123	C₂×C₄×D₄₇	C₂³	1	2	yes	—
124	C₂×C₄×D₄₇	C₂³	1	2	yes	—
125	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
127	C₂×Dic₉₄	—	2	8	no	—
128	C₂×Dic₉₄	C₂³	1	4	yes	—
129	C₂×Dic₉₄	C₂³	1	2	yes	—
130	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
131	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
132	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
133	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
134	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
135	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
136	C₄²×C₄₇	C₂³	1	1	yes	characteristic
137	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
138	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
139	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
140	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
141	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
142	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
143	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
144	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
145	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
146	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
147	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₄₇	C₂³	1	2	yes	—
149	C₄⋊Dic₄₇	C₂³	1	4	yes	—
150	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₄₇	C₂³	1	2	yes	—
152	Dic₄₇⋊C₄	C₂³	1	2	yes	—
153	Dic₄₇⋊C₄	C₂³	1	2	yes	—
154	Dic₄₇⋊C₄	C₂³	1	2	yes	—
155	Dic₄₇⋊C₄	C₂³	1	4	yes	—
156	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
157	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
158	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
159	C₄×Dic₄₇	C₂³	1	2	yes	—
160	C₄×Dic₄₇	C₂³	1	2	yes	—
161	C₄×Dic₄₇	C₂³	1	2	yes	—
162	C₂³×C₄₇	—	2	8	no	—
163	C₂³×C₄₇	—	2	8	no	—
164	C₂³×C₄₇	—	4	4	no	—
165	C₂³×C₄₇	C₂⁴	1	4	yes	—
166	C₂³×C₄₇	C₂⁴	1	2	yes	—
167	C₂³×C₄₇	C₂⁴	1	2	yes	—
168	C₂²×D₄₇	—	2	4	no	—
169	C₂²×D₄₇	—	2	4	no	—
170	C₂²×D₄₇	—	4	2	no	—
171	C₂²×D₄₇	C₂⁴	1	2	yes	—
172	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
173	D₄×C₄₇	—	2	8	no	—
174	D₄×C₄₇	—	2	8	no	—
175	D₄×C₄₇	—	2	4	no	—
176	D₄×C₄₇	—	2	4	no	—
177	D₄×C₄₇	—	4	2	no	—
178	D₄×C₄₇	C₂×D₄	1	4	yes	complemented
179	D₄×C₄₇	#41	1	4	yes	complemented
180	C₂×C₄×C₄₇	—	2	4	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
183	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
185	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
187	C₂²⋊D₄₇	—	2	8	no	—
188	C₂²⋊D₄₇	—	2	4	no	—
189	C₂²⋊D₄₇	—	2	8	no	—
190	C₂²⋊D₄₇	—	2	8	no	—
191	C₂²⋊D₄₇	—	4	4	no	—
192	C₂²⋊D₄₇	C₂×D₄	1	8	yes	complemented
193	C₂×Dic₄₇	—	2	8	no	—
194	C₂×Dic₄₇	—	2	8	no	—
195	C₂×Dic₄₇	—	2	4	no	—
196	C₂×Dic₄₇	—	2	8	no	—
197	C₂×Dic₄₇	—	2	8	no	—
198	C₂×Dic₄₇	—	4	2	no	—
199	C₂×Dic₄₇	C₂×D₄	1	8	yes	complemented
200	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
201	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
202	C₂×Dic₄₇	C₂⁴	1	2	yes	—
203	C₂×Dic₄₇	C₂⁴	1	4	yes	—
204	C₂×Dic₄₇	C₂⁴	1	2	yes	—
205	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
206	C₂×Dic₄₇	C₂⁴	1	2	yes	—
207	D₁₈₈	—	2	2	no	—
208	C₄×D₄₇	—	2	4	no	—
209	C₄×D₄₇	—	2	4	no	—
210	C₄×D₄₇	—	2	2	no	—
211	C₄×D₄₇	—	2	4	no	—
212	C₄×D₄₇	—	4	1	no	—
213	C₄×D₄₇	C₂×D₄	1	4	yes	complemented
214	Dic₉₄	—	2	4	no	—
215	Dic₉₄	—	2	8	no	—
216	Dic₉₄	C₂×D₄	1	4	yes	complemented
217	C₂²×C₄₇	—	2	2	no	—
218	C₂²×C₄₇	—	2	2	no	—
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	2	4	no	—
222	C₂²×C₄₇	—	2	4	no	—
223	C₂²×C₄₇	—	2	4	no	—
224	C₂²×C₄₇	—	4	16	no	—
225	C₂²×C₄₇	C₂²×D₄	1	4	yes	—
226	C₂²×C₄₇	C₂×#41	1	4	yes	complemented
227	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
228	C₂×D₄₇	—	2	1	no	—
229	C₂×D₄₇	—	2	1	no	—
230	C₂×D₄₇	—	2	2	no	—
231	C₂×D₄₇	—	2	2	no	—
232	C₂×D₄₇	—	2	2	no	—
233	C₂×D₄₇	—	4	8	no	—
234	C₂×D₄₇	C₂²×D₄	1	2	yes	—
235	C₄×C₄₇	—	2	2	no	—
236	C₄×C₄₇	—	2	2	no	—
237	C₄×C₄₇	—	2	1	no	—
238	C₄×C₄₇	C₂²×D₄	1	2	yes	—
239	C₄×C₄₇	C₂×#41	1	2	yes	complemented
240	Dic₄₇	—	2	4	no	—
241	Dic₄₇	—	2	2	no	—
242	Dic₄₇	—	2	1	no	—
243	Dic₄₇	—	2	1	no	—
244	Dic₄₇	—	2	2	no	—
245	Dic₄₇	C₂²×D₄	1	4	yes	—
246	Dic₄₇	C₂²×D₄	1	2	yes	—
247	D₄×#41	—	47	1	no	maximal, Sylow
248	C₂×C₄₇	—	2	4	no	—
249	C₂×C₄₇	—	2	4	no	—
250	C₂×C₄₇	—	4	4	no	—
251	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
252	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
253	C₂×C₄₇	#585	1	1	yes	characteristic
254	D₄₇	—	2	2	no	—
255	D₄₇	—	4	2	no	—
256	C₂²×#41	—	47	2	no	—
257	#550	—	47	1	no	—
258	D₄×Q₈	—	47	1	no	—
259	#548	—	47	2	no	—
260	#547	—	47	2	no	—
261	#547	—	47	1	no	—
262	#546	—	47	2	no	—
263	#546	—	47	4	no	—
264	D₄²	—	47	2	no	—
265	D₄²	D₄₇	1	1	yes	characteristic, complemented
266	#532	—	47	1	no	—
267	#532	—	47	2	no	—
268	#525	—	47	2	no	—
269	#525	—	47	4	no	—
270	C₄×#41	—	47	1	no	—
271	C₂×C₄×D₄	—	47	2	no	—
272	C₂×C₄×D₄	—	47	1	no	—
273	C₄₇	D₄×#41	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	47	1	no	—
275	C₂×#41	—	47	4	no	—
276	C₂×#41	—	47	2	no	—
277	C₂×#41	—	47	2	no	—
278	C₂×#41	—	47	4	no	—
279	C₂×#41	—	47	2	no	—
280	C₂×#41	—	94	16	no	—
281	C₂²×Q₈	—	47	2	no	—
282	C₂²×D₄	—	47	4	no	—
283	C₂²×D₄	—	47	1	no	—
284	C₂²×D₄	C₂×D₄₇	1	2	yes	—
285	C₂²×D₄	C₂×D₄₇	1	2	yes	complemented
286	C₂³×C₄	—	47	4	no	—
287	C₂³×C₄	—	47	2	no	—
288	C₄⋊Q₈	—	47	2	no	—
289	C₄⋊Q₈	—	47	1	no	—
290	#127	—	47	2	no	—
291	#127	C₂×D₄₇	1	1	yes	characteristic, complemented
292	#124	—	47	2	no	—
293	#124	—	47	4	no	—
294	#123	—	47	4	no	—
295	#123	—	47	4	no	—
296	#123	—	47	4	no	—
297	C₂²⋊Q₈	—	47	2	no	—
298	C₂²⋊Q₈	—	47	2	no	—
299	C₂²⋊Q₈	—	47	4	no	—
300	C₂²⋊Q₈	—	47	4	no	—
301	#121	—	47	4	no	—
302	#121	—	47	2	no	—
303	#121	—	47	4	no	—
304	#121	—	47	2	no	—
305	#121	—	47	2	no	—
306	#121	—	47	4	no	—
307	#121	—	47	2	no	—
308	#121	C₂×D₄₇	1	2	yes	complemented
309	#121	C₂×D₄₇	1	2	yes	complemented
310	#120	—	47	4	no	—
311	#120	—	47	4	no	—
312	#120	C₂×D₄₇	1	4	yes	complemented
313	C₄×Q₈	—	47	1	no	—
314	C₄×Q₈	—	47	1	no	—
315	C₄×D₄	—	47	1	no	—
316	C₄×D₄	—	47	4	no	—
317	C₄×D₄	—	47	2	no	—
318	C₄×D₄	—	47	2	no	—
319	C₄×D₄	—	47	4	no	—
320	C₄×D₄	—	47	2	no	—
321	C₄×D₄	—	47	1	no	—
322	C₄×D₄	—	47	2	no	—
323	C₄×D₄	—	47	2	no	—
324	C₄×D₄	—	47	2	no	—
325	C₄×D₄	—	47	1	no	—
326	C₄×D₄	—	47	2	no	—
327	C₄×D₄	—	47	2	no	—
328	C₄×D₄	—	47	4	no	—
329	C₄×D₄	—	47	1	no	—
330	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
331	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
332	#117	—	47	1	no	—
333	#117	—	47	2	no	—
334	C₂×C₄⋊C₄	—	47	2	no	—
335	C₂×C₄⋊C₄	—	47	1	no	—
336	C₂×C₂²⋊C₄	—	47	4	no	—
337	C₂×C₂²⋊C₄	—	47	2	no	—
338	C₂×C₄²	—	47	2	no	—
339	C₂×C₄²	—	47	1	no	—
340	C₂⁴	—	47	2	no	—
341	C₂⁴	C₂²×D₄₇	1	4	yes	—
342	#41	—	47	8	no	—
343	#41	—	94	16	no	—
344	#41	—	94	8	no	—
345	#41	—	94	16	no	—
346	#41	—	94	8	no	—
347	#41	—	94	8	no	—
348	C₂×Q₈	—	47	1	no	—
349	C₂×Q₈	—	47	4	no	—
350	C₂×Q₈	—	47	2	no	—
351	C₂×Q₈	—	94	8	no	—
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	47	2	no	—
355	C₂×D₄	—	47	2	no	—
356	C₂×D₄	—	47	4	no	—
357	C₂×D₄	—	47	4	no	—
358	C₂×D₄	—	47	4	no	—
359	C₂×D₄	—	47	4	no	—
360	C₂×D₄	—	47	1	no	—
361	C₂×D₄	—	94	16	no	—
362	C₂×D₄	—	94	4	no	—
363	C₂×D₄	C₂²×D₄₇	1	4	yes	—
364	C₂×D₄	C₂²×D₄₇	1	2	yes	—
365	C₂×D₄	C₂²×D₄₇	1	4	yes	—
366	C₂×D₄	C₂²×D₄₇	1	2	yes	—
367	C₂×D₄	C₂²×D₄₇	1	2	yes	—
368	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
369	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
370	C₂²×C₄	—	47	2	no	—
371	C₂²×C₄	—	47	1	no	—
372	C₂²×C₄	—	47	4	no	—
373	C₂²×C₄	—	47	2	no	—
374	C₂²×C₄	—	47	4	no	—
375	C₂²×C₄	—	47	4	no	—
376	C₂²×C₄	—	47	4	no	—
377	C₂²×C₄	—	47	2	no	—
378	C₂²×C₄	—	47	1	no	—
379	C₂²×C₄	—	47	2	no	—
380	C₂²×C₄	—	47	2	no	—
381	C₂²×C₄	—	47	2	no	—
382	C₂²×C₄	—	47	1	no	—
383	C₂²×C₄	—	94	8	no	—
384	C₂²×C₄	—	94	16	no	—
385	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
386	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
387	C₄⋊C₄	—	47	2	no	—
388	C₄⋊C₄	—	47	2	no	—
389	C₄⋊C₄	—	47	2	no	—
390	C₄⋊C₄	—	47	4	no	—
391	C₄⋊C₄	—	47	1	no	—
392	C₄⋊C₄	—	47	2	no	—
393	C₄⋊C₄	—	47	4	no	—
394	C₄⋊C₄	—	47	1	no	—
395	C₄⋊C₄	—	47	2	no	—
396	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
398	C₂²⋊C₄	—	47	2	no	—
399	C₂²⋊C₄	—	47	4	no	—
400	C₂²⋊C₄	—	47	4	no	—
401	C₂²⋊C₄	—	47	4	no	—
402	C₂²⋊C₄	—	47	2	no	—
403	C₂²⋊C₄	—	47	4	no	—
404	C₂²⋊C₄	—	47	2	no	—
405	C₂²⋊C₄	—	47	2	no	—
406	C₂²⋊C₄	—	47	2	no	—
407	C₂²⋊C₄	—	47	4	no	—
408	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
409	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
410	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
411	C₄²	—	47	1	no	—
412	C₄²	—	47	2	no	—
413	C₄²	—	47	1	no	—
414	C₄²	—	47	2	no	—
415	C₄²	—	47	1	no	—
416	C₄²	—	47	2	no	—
417	C₄²	C₂²×D₄₇	1	1	yes	characteristic
418	C₂³	—	2	8	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	47	1	no	—
422	C₂³	—	47	2	no	—
423	C₂³	—	94	4	no	—
424	C₂³	—	94	4	no	—
425	C₂³	—	188	2	no	—
426	C₂³	C₂³×D₄₇	1	4	yes	—
427	C₂³	C₂³×D₄₇	1	2	yes	—
428	C₂³	C₂³×D₄₇	1	2	yes	—
429	Q₈	—	47	4	no	—
430	Q₈	—	94	8	no	—
431	Q₈	—	94	4	no	—
432	D₄	—	2	8	no	—
433	D₄	—	2	8	no	—
434	D₄	—	2	4	no	—
435	D₄	—	2	4	no	—
436	D₄	—	4	2	no	—
437	D₄	—	47	8	no	—
438	D₄	—	94	8	no	—
439	D₄	—	94	8	no	—
440	D₄	—	94	8	no	—
441	D₄	—	94	4	no	—
442	D₄	—	94	2	no	—
443	D₄	—	188	4	no	—
444	D₄	D₄×D₄₇	1	4	yes	complemented
445	D₄	#10625352	1	4	yes	direct product factor
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	47	8	no	—
449	C₂×C₄	—	47	1	no	—
450	C₂×C₄	—	47	2	no	—
451	C₂×C₄	—	47	4	no	—
452	C₂×C₄	—	47	1	no	—
453	C₂×C₄	—	47	1	no	—
454	C₂×C₄	—	47	2	no	—
455	C₂×C₄	—	47	2	no	—
456	C₂×C₄	—	47	4	no	—
457	C₂×C₄	—	94	4	no	—
458	C₂×C₄	—	94	4	no	—
459	C₂×C₄	—	94	4	no	—
460	C₂×C₄	—	94	8	no	—
461	C₂×C₄	—	94	8	no	—
462	C₂×C₄	—	94	8	no	—
463	C₂×C₄	—	94	8	no	—
464	C₂×C₄	—	94	4	no	—
465	C₂×C₄	—	94	2	no	—
466	C₂×C₄	—	188	1	no	—
467	C₂×C₄	—	188	2	no	—
468	C₂×C₄	C₂³×D₄₇	1	2	yes	—
469	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
470	C₂×C₄	C₂³×D₄₇	1	2	yes	—
471	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
472	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	16	no	—
481	C₂²	—	47	2	no	—
482	C₂²	—	94	1	no	—
483	C₂²	—	94	1	no	—
484	C₂²	—	94	2	no	—
485	C₂²	—	94	2	no	—
486	C₂²	—	94	2	no	—
487	C₂²	—	188	8	no	—
488	C₂²	C₂×D₄×D₄₇	1	4	yes	—
489	C₂²	C₂×#10625352	1	4	yes	complemented
490	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	1	no	—
494	C₄	—	47	2	no	—
495	C₄	—	47	4	no	—
496	C₄	—	94	2	no	—
497	C₄	—	94	4	no	—
498	C₄	—	94	1	no	—
499	C₄	—	94	1	no	—
500	C₄	—	94	2	no	—
501	C₄	C₂×D₄×D₄₇	1	2	yes	—
502	C₄	C₂×#10625352	1	2	yes	complemented
503	C₂	—	2	4	no	—
504	C₂	—	2	4	no	—
505	C₂	—	4	4	no	—
506	C₂	—	94	2	no	—
507	C₂	—	188	2	no	—
508	C₂	C₂²×D₄×D₄₇	1	1	yes	characteristic
509	C₂	C₂²×#10625352	1	1	yes	characteristic
510	C₂	#15689958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	D₄²×C₄₇	C₂
hypercenter	D₄²	D₄₇
hypocenter	C₄₇	D₄×#41
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×#10625352	C₂	semidirect
2. #15689793	C₂	semidirect
3. D₄×Dic₉₄	C₂	semidirect
4. #15689779	C₂	semidirect
5. #15689777	C₂	semidirect
6. #15689773	C₂	semidirect
7. #15689767	C₂	semidirect
8. #15689760	C₂	semidirect
9. D₄×C₂²⋊D₄₇	C₂	semidirect
10. #15689671	C₂	semidirect
11. #15689668	C₂	semidirect
12. #15689633	C₂	semidirect
13. #15689629	C₂	semidirect
14. C₄×#10625352	C₂	semidirect
15. C₂×D₄×Dic₄₇	C₂	semidirect
16. C₄×D₄×D₄₇	C₂	semidirect
17. D₄²×C₄₇	C₂	semidirect
20. C₂×#10625352	C₂²	semidirect
21. C₂×#10625352	C₂²	semidirect
22. C₂×#10625352	C₂²	semidirect
23. C₂×#10625352	C₂²	semidirect
24. C₂×#10625352	C₂²	semidirect
25. C₂²×Dic₉₄	C₂²	semidirect
26. C₂²×C₂²⋊D₄₇	C₂²	semidirect
28. C₂³×Dic₄₇	C₂²	semidirect
29. C₂²×C₄×D₄₇	C₂²	semidirect
30. #13094024	C₂²	semidirect
31. #13094023	C₂²	semidirect
32. #13094020	C₂²	semidirect
33. #13094011	C₂²	semidirect
34. #13094010	C₂²	semidirect
35. #13094008	C₂²	semidirect
36. #13094006	C₂²	semidirect
37. #13094005	C₂²	semidirect
38. #13094004	C₂²	semidirect
39. #13094003	C₂²	semidirect
40. #13094001	C₂²	semidirect
41. #13094001	C₂²	semidirect
42. #13093998	C₂²	semidirect
43. #13093996	C₂²	semidirect
44. #13093996	C₂²	semidirect
45. #13093996	C₂²	semidirect
46. #13093995	C₂²	semidirect
47. #13093995	C₂²	semidirect
48. #13093995	C₂²	semidirect
49. #13093993	C₂²	semidirect
50. #13093992	C₂²	semidirect
51. C₄×Dic₉₄	C₂²	semidirect
52. #13093989	C₂²	semidirect
53. C₄×D₁₈₈	C₂²	semidirect
56. D₄×Dic₄₇	C₂²	semidirect
57. D₄×Dic₄₇	C₂²	semidirect
58. D₄×Dic₄₇	C₂²	semidirect
59. D₄×Dic₄₇	C₂²	semidirect
60. D₄×Dic₄₇	C₂²	semidirect
61. D₄×Dic₄₇	C₂²	semidirect
62. #13093986	C₂²	semidirect
63. C₄×C₂²⋊D₄₇	C₂²	semidirect
64. C₄×C₂²⋊D₄₇	C₂²	semidirect
65. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
66. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
67. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
68. #13093982	C₂²	semidirect
69. #13093980	C₂²	semidirect
70. C₂×C₄⋊Dic₄₇	C₂²	semidirect
71. C₄⋊C₄×D₄₇	C₂²	semidirect
72. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
73. C₂²⋊C₄×D₄₇	C₂²	semidirect
74. C₂×C₄×Dic₄₇	C₂²	semidirect
75. C₄²×D₄₇	C₂²	semidirect
77. C₂²×D₄×C₄₇	C₂²	semidirect
78. #127×C₄₇	C₂²	semidirect
79. #121×C₄₇	C₂²	semidirect
80. #121×C₄₇	C₂²	semidirect
81. #120×C₄₇	C₂²	semidirect
83. C₄×D₄×C₄₇	C₂²	semidirect
117. #10625352	D₄	direct (N × H)
178. D₄×C₄₇	C₂×D₄	semidirect
179. D₄×C₄₇	#41	semidirect
192. C₂²⋊D₄₇	C₂×D₄	semidirect
199. C₂×Dic₄₇	C₂×D₄	semidirect
213. C₄×D₄₇	C₂×D₄	semidirect
216. Dic₉₄	C₂×D₄	semidirect
226. C₂²×C₄₇	C₂×#41	semidirect
239. C₄×C₄₇	C₂×#41	semidirect
265. D₄²	D₄₇	semidirect
273. C₄₇	D₄×#41	semidirect
285. C₂²×D₄	C₂×D₄₇	semidirect
291. #127	C₂×D₄₇	semidirect
308. #121	C₂×D₄₇	semidirect
309. #121	C₂×D₄₇	semidirect
312. #120	C₂×D₄₇	semidirect
331. C₄×D₄	C₂×D₄₇	semidirect
444. D₄	D₄×D₄₇	semidirect
445. D₄	#10625352	direct (N × H)
489. C₂²	C₂×#10625352	semidirect
502. C₄	C₂×#10625352	semidirect

Subgroups — D4×#10625352 #20256870

Conjugacy classes of subgroups

Complements

Subgroups — D₄×#10625352 #20256870