Subgroups — D₄×#13093951 #26231952

Order 12032.

1608 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13093951	C₂	1	2	yes	maximal, complemented
3	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244308	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244217	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243832	C₂	1	2	yes	maximal, complemented
7	#20243691	C₂	1	2	yes	maximal, complemented
8	#20243408	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243332	C₂	1	2	yes	maximal, complemented
10	C₄×#13093951	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	2	yes	complemented
13	C₂×D₄×Dic₄₇	—	2	1	no	—
14	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	complemented
15	#15689201	—	2	1	no	—
16	#15689195	—	2	2	no	—
17	D₄×C₄₇⋊C₈	—	2	1	no	—
18	#15689147	C₂²	1	1	yes	characteristic, complemented
19	C₂×#13093951	—	2	8	no	—
20	C₂×#13093951	C₂²	1	2	yes	—
21	C₂×#13093951	C₂²	1	1	yes	characteristic
22	C₂×#13093951	C₂²	1	1	yes	characteristic
23	C₂×#13093951	C₂²	1	2	yes	complemented
24	C₂×#13093951	C₂²	1	2	yes	complemented
25	C₂×#13093951	C₂²	1	2	yes	complemented
26	C₂×#13093951	C₂²	1	2	yes	complemented
27	#15689087	C₂²	1	2	yes	complemented
28	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
29	C₄⋊C₄×Dic₄₇	—	2	1	no	—
30	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
31	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
32	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
33	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
34	#15688882	C₂²	1	1	yes	characteristic, complemented
35	#15688882	C₂²	1	2	yes	complemented
36	#15688882	C₂²	1	1	yes	characteristic, complemented
37	C₂²×#41×C₄₇	C₂²	1	2	yes	—
38	C₄₇×#550	C₄	1	1	yes	characteristic, complemented
39	D₄×Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
40	C₄₇×#548	C₄	1	2	yes	complemented
41	C₄₇×#547	—	2	1	no	—
42	C₄₇×#547	C₄	1	1	yes	characteristic, complemented
43	C₄₇×#546	—	2	2	no	—
44	C₄₇×#546	C₄	1	2	yes	complemented
45	D₄²×C₄₇	—	2	1	no	—
46	D₄²×C₄₇	C₄	1	1	yes	characteristic, complemented
47	C₄₇×#532	—	2	1	no	—
48	C₄₇×#532	C₂²	1	1	yes	characteristic
49	C₄₇×#525	—	2	2	no	—
50	C₄₇×#525	C₂²	1	2	yes	—
51	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₄₇	—	2	1	no	—
53	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
54	C₂³×Dic₄₇	—	2	2	no	—
55	C₂×#10625329	—	2	2	no	—
56	C₂×#10625329	—	2	4	no	—
57	C₂×#10625329	—	4	2	no	—
58	C₂×#10625329	C₂³	1	1	yes	characteristic
59	C₂×#10625329	C₂³	1	2	yes	—
60	C₂×#10625329	C₂³	1	1	yes	characteristic
61	C₂²×C₄₇⋊C₈	—	2	2	no	—
62	D₄×Dic₄₇	—	2	8	no	—
63	C₂×C₄⋊Dic₄₇	—	2	1	no	—
64	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
65	C₂×C₄×Dic₄₇	—	2	1	no	—
66	C₂×C₄×Dic₄₇	—	2	4	no	—
67	C₂×C₄×Dic₄₇	—	2	1	no	—
68	C₂×C₄×Dic₄₇	—	2	2	no	—
69	C₂×C₄×Dic₄₇	—	4	2	no	—
70	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
72	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
73	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
74	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
75	#13093951	—	2	4	no	—
76	#13093951	—	2	2	no	—
77	#13093951	—	2	4	no	—
78	#13093951	—	2	4	no	—
79	#13093951	—	4	2	no	—
80	#13093951	—	4	2	no	—
81	#13093951	D₄	1	4	yes	direct product factor
82	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
83	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
84	#13093935	—	2	1	no	—
85	C₄×C₄₇⋊C₈	—	2	1	no	—
86	C₄₇⋊#95	—	2	2	no	—
87	C₄₇⋊#95	—	2	1	no	—
88	C₂×#41×C₄₇	—	2	2	no	—
89	C₂×#41×C₄₇	—	2	2	no	—
90	C₂×#41×C₄₇	—	2	4	no	—
91	C₂×#41×C₄₇	—	2	4	no	—
92	C₂×#41×C₄₇	—	4	2	no	—
93	C₂×#41×C₄₇	—	4	2	no	—
94	C₂×#41×C₄₇	C₂×C₄	1	2	yes	complemented
95	C₂×#41×C₄₇	C₂×C₄	1	2	yes	complemented
96	C₂×#41×C₄₇	C₂³	1	2	yes	—
97	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
99	C₂²×D₄×C₄₇	—	2	2	no	—
100	C₂²×D₄×C₄₇	—	2	1	no	—
101	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	complemented
102	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
103	C₂³×C₄×C₄₇	—	2	2	no	—
104	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₄₇	—	2	1	no	—
106	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
107	#127×C₄₇	—	2	1	no	—
108	#127×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
109	#124×C₄₇	—	2	2	no	—
110	#124×C₄₇	C₂×C₄	1	2	yes	complemented
111	#123×C₄₇	—	2	2	no	—
112	#123×C₄₇	—	2	2	no	—
113	#123×C₄₇	—	2	2	no	—
114	C₂²⋊Q₈×C₄₇	—	2	2	no	—
115	C₂²⋊Q₈×C₄₇	—	2	2	no	—
116	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
117	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
118	#121×C₄₇	—	2	2	no	—
119	#121×C₄₇	—	2	1	no	—
120	#121×C₄₇	—	2	1	no	—
121	#121×C₄₇	—	2	1	no	—
122	#121×C₄₇	—	2	1	no	—
123	#121×C₄₇	—	2	2	no	—
124	#121×C₄₇	—	2	2	no	—
125	#121×C₄₇	C₂×C₄	1	2	yes	complemented
126	#121×C₄₇	C₂×C₄	1	2	yes	complemented
127	#120×C₄₇	—	2	2	no	—
128	#120×C₄₇	—	2	2	no	—
129	#120×C₄₇	—	2	2	no	—
130	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
131	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
132	C₄×D₄×C₄₇	—	2	1	no	—
133	C₄×D₄×C₄₇	—	2	2	no	—
134	C₄×D₄×C₄₇	—	2	1	no	—
135	C₄×D₄×C₄₇	—	2	1	no	—
136	C₄×D₄×C₄₇	—	2	2	no	—
137	C₄×D₄×C₄₇	—	2	1	no	—
138	C₄×D₄×C₄₇	—	2	2	no	—
139	C₄×D₄×C₄₇	—	2	1	no	—
140	C₄×D₄×C₄₇	—	2	1	no	—
141	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
142	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
143	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
144	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
145	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
146	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
147	C₄×D₄×C₄₇	D₄	1	2	yes	—
148	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
149	#117×C₄₇	—	2	1	no	—
150	#117×C₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
152	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
154	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
155	C₂×C₄²×C₄₇	—	2	1	no	—
156	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
157	C₂⁴×C₄₇	—	2	2	no	—
158	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
159	#41×C₄₇	—	2	1	no	—
160	#41×C₄₇	—	2	1	no	—
161	#41×C₄₇	—	2	4	no	—
162	#41×C₄₇	—	2	4	no	—
163	#41×C₄₇	—	2	2	no	—
164	#41×C₄₇	—	2	2	no	—
165	#41×C₄₇	—	2	2	no	—
166	#41×C₄₇	—	2	2	no	—
167	#41×C₄₇	—	4	4	no	—
168	#41×C₄₇	—	4	4	no	—
169	#41×C₄₇	—	4	2	no	—
170	#41×C₄₇	—	4	2	no	—
171	#41×C₄₇	—	4	4	no	—
172	#41×C₄₇	—	4	4	no	—
173	#41×C₄₇	C₂×D₄	1	2	yes	—
174	#41×C₄₇	#41	1	2	yes	—
175	C₂×Q₈×C₄₇	—	2	2	no	—
176	C₂×Q₈×C₄₇	—	2	4	no	—
177	C₂×Q₈×C₄₇	—	4	2	no	—
178	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
179	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
180	C₂×D₄×C₄₇	—	2	1	no	—
181	C₂×D₄×C₄₇	—	2	4	no	—
182	C₂×D₄×C₄₇	—	2	4	no	—
183	C₂×D₄×C₄₇	—	2	2	no	—
184	C₂×D₄×C₄₇	—	2	2	no	—
185	C₂×D₄×C₄₇	—	2	2	no	—
186	C₂×D₄×C₄₇	—	2	2	no	—
187	C₂×D₄×C₄₇	—	2	2	no	—
188	C₂×D₄×C₄₇	—	2	1	no	—
189	C₂×D₄×C₄₇	—	2	2	no	—
190	C₂×D₄×C₄₇	—	2	1	no	—
191	C₂×D₄×C₄₇	—	4	2	no	—
192	C₂×D₄×C₄₇	—	4	4	no	—
193	C₂×D₄×C₄₇	—	4	4	no	—
194	C₂×D₄×C₄₇	—	4	4	no	—
195	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
196	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
197	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
198	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
199	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₄₇	—	2	1	no	—
201	C₂²×C₄×C₄₇	—	2	2	no	—
202	C₂²×C₄×C₄₇	—	2	2	no	—
203	C₂²×C₄×C₄₇	—	2	2	no	—
204	C₂²×C₄×C₄₇	—	2	2	no	—
205	C₂²×C₄×C₄₇	—	2	2	no	—
206	C₂²×C₄×C₄₇	—	2	1	no	—
207	C₂²×C₄×C₄₇	—	2	2	no	—
208	C₂²×C₄×C₄₇	—	2	2	no	—
209	C₂²×C₄×C₄₇	—	2	2	no	—
210	C₂²×C₄×C₄₇	—	2	1	no	—
211	C₂²×C₄×C₄₇	—	4	4	no	—
212	C₂²×C₄×C₄₇	—	4	4	no	—
213	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
214	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
215	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
221	C₂²×Dic₄₇	—	2	1	no	—
222	C₂²×Dic₄₇	—	2	8	no	—
223	C₂²×Dic₄₇	—	2	1	no	—
224	C₂²×Dic₄₇	—	2	2	no	—
225	C₂²×Dic₄₇	—	4	4	no	—
226	C₂²×Dic₄₇	—	4	4	no	—
227	C₄⋊C₄×C₄₇	—	2	1	no	—
228	C₄⋊C₄×C₄₇	—	2	2	no	—
229	C₄⋊C₄×C₄₇	—	2	1	no	—
230	C₄⋊C₄×C₄₇	—	2	1	no	—
231	C₄⋊C₄×C₄₇	—	2	1	no	—
232	C₄⋊C₄×C₄₇	—	2	2	no	—
233	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
234	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
235	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
236	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
237	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
238	C₂²⋊C₄×C₄₇	—	2	2	no	—
239	C₂²⋊C₄×C₄₇	—	2	2	no	—
240	C₂²⋊C₄×C₄₇	—	2	1	no	—
241	C₂²⋊C₄×C₄₇	—	2	2	no	—
242	C₂²⋊C₄×C₄₇	—	2	2	no	—
243	C₂²⋊C₄×C₄₇	—	2	1	no	—
244	C₂²⋊C₄×C₄₇	—	2	1	no	—
245	C₂²⋊C₄×C₄₇	—	2	2	no	—
246	C₂²⋊C₄×C₄₇	—	2	2	no	—
247	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
248	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
249	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
250	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
251	C₄²×C₄₇	—	2	1	no	—
252	C₄²×C₄₇	—	2	1	no	—
253	C₄²×C₄₇	—	2	1	no	—
254	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
255	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
256	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
257	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
258	C₂²⋊Dic₄₇	—	2	8	no	—
259	C₄⋊Dic₄₇	—	2	4	no	—
260	C₄×Dic₄₇	—	2	4	no	—
261	C₄×Dic₄₇	—	2	1	no	—
262	C₄×Dic₄₇	—	2	2	no	—
263	C₄×Dic₄₇	—	2	1	no	—
264	C₄×Dic₄₇	—	2	1	no	—
265	C₄×Dic₄₇	—	2	2	no	—
266	C₄×Dic₄₇	—	4	4	no	—
267	C₄×Dic₄₇	—	4	2	no	—
268	C₄×Dic₄₇	C₂×D₄	1	2	yes	complemented
269	#10625329	—	2	1	no	—
270	#10625329	—	2	2	no	—
271	#10625329	—	2	1	no	—
272	#10625329	—	2	1	no	—
273	#10625329	—	2	2	no	—
274	#10625329	—	4	4	no	—
275	#10625329	C₂×D₄	1	2	yes	complemented
276	C₂×C₄₇⋊C₈	—	2	1	no	—
277	C₂×C₄₇⋊C₈	—	2	1	no	—
278	C₂×C₄₇⋊C₈	—	2	2	no	—
279	C₂×C₄₇⋊C₈	—	4	4	no	—
280	C₂³×C₄₇	—	2	1	no	—
281	C₂³×C₄₇	—	2	2	no	—
282	C₂³×C₄₇	—	2	2	no	—
283	C₂³×C₄₇	—	2	4	no	—
284	C₂³×C₄₇	—	2	2	no	—
285	C₂³×C₄₇	—	4	2	no	—
286	C₂³×C₄₇	—	4	4	no	—
287	C₂³×C₄₇	—	4	4	no	—
288	C₂³×C₄₇	—	8	2	no	—
289	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
292	Q₈×C₄₇	—	2	1	no	—
293	Q₈×C₄₇	—	2	2	no	—
294	Q₈×C₄₇	—	2	2	no	—
295	Q₈×C₄₇	—	4	4	no	—
296	Q₈×C₄₇	C₄×D₄	1	2	yes	complemented
297	D₄×C₄₇	—	2	2	no	—
298	D₄×C₄₇	—	2	2	no	—
299	D₄×C₄₇	—	2	4	no	—
300	D₄×C₄₇	—	2	2	no	—
301	D₄×C₄₇	—	2	1	no	—
302	D₄×C₄₇	—	2	2	no	—
303	D₄×C₄₇	—	2	2	no	—
304	D₄×C₄₇	—	4	4	no	—
305	D₄×C₄₇	—	4	4	no	—
306	D₄×C₄₇	—	4	4	no	—
307	D₄×C₄₇	—	4	2	no	—
308	D₄×C₄₇	—	4	2	no	—
309	D₄×C₄₇	—	4	4	no	—
310	D₄×C₄₇	—	4	2	no	—
311	D₄×C₄₇	—	8	1	no	—
312	D₄×C₄₇	—	8	2	no	—
313	D₄×C₄₇	#104	1	4	yes	complemented
314	D₄×C₄₇	C₄×D₄	1	2	yes	complemented
315	C₂×C₄×C₄₇	—	2	1	no	—
316	C₂×C₄×C₄₇	—	2	2	no	—
317	C₂×C₄×C₄₇	—	2	2	no	—
318	C₂×C₄×C₄₇	—	2	2	no	—
319	C₂×C₄×C₄₇	—	2	2	no	—
320	C₂×C₄×C₄₇	—	2	2	no	—
321	C₂×C₄×C₄₇	—	2	2	no	—
322	C₂×C₄×C₄₇	—	2	2	no	—
323	C₂×C₄×C₄₇	—	2	2	no	—
324	C₂×C₄×C₄₇	—	2	2	no	—
325	C₂×C₄×C₄₇	—	2	2	no	—
326	C₂×C₄×C₄₇	—	2	2	no	—
327	C₂×C₄×C₄₇	—	2	2	no	—
328	C₂×C₄×C₄₇	—	2	2	no	—
329	C₂×C₄×C₄₇	—	2	1	no	—
330	C₂×C₄×C₄₇	—	2	1	no	—
331	C₂×C₄×C₄₇	—	2	2	no	—
332	C₂×C₄×C₄₇	—	4	1	no	—
333	C₂×C₄×C₄₇	—	4	4	no	—
334	C₂×C₄×C₄₇	—	4	4	no	—
335	C₂×C₄×C₄₇	—	4	4	no	—
336	C₂×C₄×C₄₇	—	4	2	no	—
337	C₂×C₄×C₄₇	—	4	2	no	—
338	C₂×C₄×C₄₇	—	4	2	no	—
339	C₂×C₄×C₄₇	—	8	1	no	—
340	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
341	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
342	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
344	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
345	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
346	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
347	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×Dic₄₇	—	2	2	no	—
353	C₂×Dic₄₇	—	2	2	no	—
354	C₂×Dic₄₇	—	2	2	no	—
355	C₂×Dic₄₇	—	2	2	no	—
356	C₂×Dic₄₇	—	2	4	no	—
357	C₂×Dic₄₇	—	4	16	no	—
358	C₂×Dic₄₇	—	4	1	no	—
359	C₂×Dic₄₇	—	4	2	no	—
360	C₂×Dic₄₇	—	4	2	no	—
361	C₂×Dic₄₇	—	4	1	no	—
362	C₄₇⋊C₈	—	2	2	no	—
363	C₄₇⋊C₈	—	4	2	no	—
364	C₄₇⋊C₈	—	4	1	no	—
365	D₄×#104	—	47	1	no	maximal, Sylow
366	C₂²×C₄₇	—	2	2	no	—
367	C₂²×C₄₇	—	2	1	no	—
368	C₂²×C₄₇	—	2	1	no	—
369	C₂²×C₄₇	—	2	2	no	—
370	C₂²×C₄₇	—	2	2	no	—
371	C₂²×C₄₇	—	2	2	no	—
372	C₂²×C₄₇	—	2	2	no	—
373	C₂²×C₄₇	—	2	2	no	—
374	C₂²×C₄₇	—	4	4	no	—
375	C₂²×C₄₇	—	4	4	no	—
376	C₂²×C₄₇	—	4	1	no	—
377	C₂²×C₄₇	—	4	1	no	—
378	C₂²×C₄₇	—	4	2	no	—
379	C₂²×C₄₇	—	4	2	no	—
380	C₂²×C₄₇	—	4	2	no	—
381	C₂²×C₄₇	—	8	8	no	—
382	C₂²×C₄₇	C₂×#104	1	4	yes	complemented
383	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
384	C₂²×C₄₇	D₄²	1	1	yes	characteristic
385	C₂²×C₄₇	#546	1	1	yes	characteristic
386	C₄×C₄₇	—	2	2	no	—
387	C₄×C₄₇	—	2	2	no	—
388	C₄×C₄₇	—	2	2	no	—
389	C₄×C₄₇	—	2	1	no	—
390	C₄×C₄₇	—	2	1	no	—
391	C₄×C₄₇	—	2	1	no	—
392	C₄×C₄₇	—	4	2	no	—
393	C₄×C₄₇	—	4	1	no	—
394	C₄×C₄₇	—	4	1	no	—
395	C₄×C₄₇	C₂×#104	1	2	yes	complemented
396	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
397	C₄×C₄₇	#518	1	1	yes	characteristic
398	C₄×C₄₇	D₄²	1	1	yes	characteristic
399	C₄×C₄₇	#546	1	1	yes	characteristic
400	Dic₄₇	—	2	4	no	—
401	Dic₄₇	—	4	2	no	—
402	Dic₄₇	—	4	4	no	—
403	D₄×#41	D₄₇	1	1	yes	characteristic
404	D₄×M₁₆	—	47	1	no	—
405	C₂²×#104	—	47	2	no	—
406	C₄²×D₄	—	47	1	no	—
407	#1980	—	47	1	no	—
408	#1962	—	47	1	no	—
409	#1896	—	47	2	no	—
410	#1871	—	47	2	no	—
411	#1806	—	47	1	no	—
412	#1789	—	47	2	no	—
413	C₄×#104	—	47	1	no	—
414	C₂×C₄₇	—	2	1	no	—
415	C₂×C₄₇	—	2	1	no	—
416	C₂×C₄₇	—	2	4	no	—
417	C₂×C₄₇	—	4	2	no	—
418	C₂×C₄₇	—	4	2	no	—
419	C₂×C₄₇	—	8	2	no	—
420	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
421	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
422	C₂×C₄₇	#2901	1	1	yes	characteristic
423	C₂²×#41	C₂×D₄₇	1	2	yes	—
424	C₂²×M₁₆	—	47	2	no	—
425	#550	Dic₄₇	1	1	yes	characteristic, complemented
426	D₄×Q₈	Dic₄₇	1	1	yes	characteristic, complemented
427	#548	Dic₄₇	1	2	yes	complemented
428	#547	—	2	1	no	—
429	#547	Dic₄₇	1	1	yes	characteristic, complemented
430	#546	—	2	2	no	—
431	#546	Dic₄₇	1	2	yes	complemented
432	D₄²	—	2	1	no	—
433	D₄²	Dic₄₇	1	1	yes	characteristic, complemented
434	#532	—	2	1	no	—
435	#532	C₂×D₄₇	1	1	yes	characteristic
436	#525	—	2	2	no	—
437	#525	C₂×D₄₇	1	2	yes	—
438	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
439	C₂×C₄×D₄	—	2	1	no	—
440	C₂×C₄×D₄	—	94	1	no	—
441	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
442	C₂²×C₄²	—	47	2	no	—
443	#436	—	94	1	no	—
444	#435	—	94	2	no	—
445	C₈×D₄	—	94	1	no	—
446	#423	—	47	1	no	—
447	C₂×#104	—	47	1	no	—
448	C₂×#104	—	47	2	no	—
449	C₂×#104	—	47	2	no	—
450	C₂×#104	—	47	2	no	—
451	C₂×#104	—	47	1	no	—
452	C₂×#104	—	47	2	no	—
453	C₂×#104	—	47	2	no	—
454	C₂×#104	—	94	8	no	—
455	#407	—	47	2	no	—
456	C₄×M₁₆	—	47	1	no	—
457	C₄×C₄⋊C₄	—	47	1	no	—
458	C₄×C₄⋊C₄	—	94	1	no	—
459	C₄×C₂²⋊C₄	—	47	2	no	—
460	C₄×C₂²⋊C₄	—	94	2	no	—
461	C₄³	—	47	1	no	—
462	#339	—	47	2	no	—
463	#339	—	47	1	no	—
464	#339	—	47	1	no	—
465	C₄₇	D₄×#104	1	1	yes	characteristic, complemented, Sylow
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	2	2	no	—
468	C₂×#41	—	2	4	no	—
469	C₂×#41	—	2	4	no	—
470	C₂×#41	—	4	2	no	—
471	C₂×#41	—	4	2	no	—
472	C₂×#41	C₂×Dic₄₇	1	2	yes	complemented
473	C₂×#41	C₂×Dic₄₇	1	2	yes	complemented
474	C₂×#41	C₂²×D₄₇	1	2	yes	—
475	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
476	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	complemented
477	C₂²×D₄	—	2	2	no	—
478	C₂²×D₄	—	2	1	no	—
479	C₂²×D₄	C₂×Dic₄₇	1	2	yes	complemented
480	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
481	C₂³×C₄	—	2	2	no	—
482	C₂³×C₄	—	94	2	no	—
483	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
484	C₂×M₁₆	—	47	1	no	—
485	C₂×M₁₆	—	47	2	no	—
486	C₂×M₁₆	—	47	1	no	—
487	C₂×M₁₆	—	94	2	no	—
488	C₂×M₁₆	—	94	4	no	—
489	C₂×M₁₆	—	188	2	no	—
490	C₂²×C₈	—	94	2	no	—
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
493	#127	—	2	1	no	—
494	#127	C₂×Dic₄₇	1	1	yes	characteristic, complemented
495	#124	—	2	2	no	—
496	#124	C₂×Dic₄₇	1	2	yes	complemented
497	#123	—	2	2	no	—
498	#123	—	2	2	no	—
499	#123	—	2	2	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
503	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
504	#121	—	2	2	no	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	1	no	—
509	#121	—	2	2	no	—
510	#121	—	2	2	no	—
511	#121	C₂×Dic₄₇	1	2	yes	complemented
512	#121	C₂×Dic₄₇	1	2	yes	complemented
513	#120	—	2	2	no	—
514	#120	—	2	2	no	—
515	#120	—	2	2	no	—
516	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
517	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
518	C₄×D₄	—	2	1	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	—	2	1	no	—
527	C₄×D₄	—	94	8	no	—
528	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
529	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
530	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
531	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic, complemented
532	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic, complemented
533	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
534	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
535	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
536	#117	—	2	1	no	—
537	#117	C₂²×D₄₇	1	1	yes	characteristic
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	94	1	no	—
540	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	—	2	2	no	—
542	C₂×C₂²⋊C₄	—	94	2	no	—
543	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
544	C₂×C₄²	—	2	1	no	—
545	C₂×C₄²	—	47	1	no	—
546	C₂×C₄²	—	47	1	no	—
547	C₂×C₄²	—	47	2	no	—
548	C₂×C₄²	—	94	4	no	—
549	C₂×C₄²	—	94	1	no	—
550	C₂×C₄²	—	94	1	no	—
551	C₂×C₄²	—	94	2	no	—
552	C₂×C₄²	—	188	2	no	—
553	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
554	C₄⋊C₈	—	94	1	no	—
555	C₄⋊C₈	—	94	1	no	—
556	#104	—	47	4	no	—
557	#104	—	94	4	no	—
558	#104	—	94	4	no	—
559	#104	—	94	4	no	—
560	#104	—	94	2	no	—
561	#104	—	188	2	no	—
562	#104	—	188	2	no	—
563	C₂²⋊C₈	—	94	2	no	—
564	C₂²⋊C₈	—	94	2	no	—
565	#97	—	94	1	no	—
566	C₄×C₈	—	94	1	no	—
567	#95	—	94	2	no	—
568	#95	—	94	1	no	—
569	C₂⁴	—	2	2	no	—
570	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
571	#41	—	2	1	no	—
572	#41	—	2	1	no	—
573	#41	—	2	4	no	—
574	#41	—	2	4	no	—
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	#41	—	2	2	no	—
578	#41	—	2	2	no	—
579	#41	—	4	4	no	—
580	#41	—	4	4	no	—
581	#41	—	4	2	no	—
582	#41	—	4	2	no	—
583	#41	—	4	4	no	—
584	#41	—	4	4	no	—
585	#41	D₄×D₄₇	1	2	yes	—
586	#41	#10625352	1	2	yes	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	—	4	2	no	—
590	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
591	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
608	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
609	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
610	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
611	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	—	94	1	no	—
626	C₂²×C₄	—	94	8	no	—
627	C₂²×C₄	—	94	1	no	—
628	C₂²×C₄	—	94	2	no	—
629	C₂²×C₄	—	188	4	no	—
630	C₂²×C₄	—	188	4	no	—
631	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
632	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
633	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
634	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
635	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
636	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
637	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
638	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
639	M₁₆	—	47	2	no	—
640	M₁₆	—	94	1	no	—
641	M₁₆	—	94	2	no	—
642	M₁₆	—	94	1	no	—
643	M₁₆	—	94	1	no	—
644	M₁₆	—	94	2	no	—
645	M₁₆	—	188	4	no	—
646	C₂×C₈	—	94	1	no	—
647	C₂×C₈	—	94	1	no	—
648	C₂×C₈	—	94	2	no	—
649	C₂×C₈	—	188	4	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	94	4	no	—
657	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
658	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
659	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
660	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
661	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	1	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	—	2	1	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	94	8	no	—
672	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
673	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
674	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
675	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
676	C₄²	—	2	1	no	—
677	C₄²	—	2	1	no	—
678	C₄²	—	2	1	no	—
679	C₄²	—	47	2	no	—
680	C₄²	—	94	4	no	—
681	C₄²	—	94	1	no	—
682	C₄²	—	94	2	no	—
683	C₄²	—	94	1	no	—
684	C₄²	—	94	1	no	—
685	C₄²	—	94	2	no	—
686	C₄²	—	188	4	no	—
687	C₄²	—	188	2	no	—
688	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
689	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
690	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
691	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	4	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	4	2	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	8	2	no	—
701	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
702	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
703	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
704	Q₈	—	2	1	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	4	4	no	—
708	Q₈	D₄×Dic₄₇	1	2	yes	complemented
709	D₄	—	2	2	no	—
710	D₄	—	2	2	no	—
711	D₄	—	2	4	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	1	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	2	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	2	no	—
720	D₄	—	4	2	no	—
721	D₄	—	4	4	no	—
722	D₄	—	4	2	no	—
723	D₄	—	8	1	no	—
724	D₄	—	8	2	no	—
725	D₄	#13093951	1	4	yes	direct product factor
726	D₄	D₄×Dic₄₇	1	2	yes	complemented
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	4	4	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	4	2	no	—
750	C₂×C₄	—	4	2	no	—
751	C₂×C₄	—	8	1	no	—
752	C₂×C₄	—	94	2	no	—
753	C₂×C₄	—	94	2	no	—
754	C₂×C₄	—	94	2	no	—
755	C₂×C₄	—	94	2	no	—
756	C₂×C₄	—	94	4	no	—
757	C₂×C₄	—	188	16	no	—
758	C₂×C₄	—	188	1	no	—
759	C₂×C₄	—	188	2	no	—
760	C₂×C₄	—	188	2	no	—
761	C₂×C₄	—	188	1	no	—
762	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
763	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
764	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
765	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
766	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
767	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
768	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
769	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
770	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
771	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
772	C₂×C₄	#13094069	1	1	yes	characteristic
773	C₂×C₄	#13094069	1	1	yes	characteristic
774	C₈	—	94	2	no	—
775	C₈	—	188	2	no	—
776	C₈	—	188	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	4	4	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	8	8	no	—
793	C₂²	C₂×#13093951	1	4	yes	complemented
794	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
795	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
796	C₂²	#15689767	1	1	yes	characteristic
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	1	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	2	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	1	no	—
805	C₄	—	4	2	no	—
806	C₄	—	94	4	no	—
807	C₄	—	188	4	no	—
808	C₄	—	188	2	no	—
809	C₄	C₂×#13093951	1	2	yes	complemented
810	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
811	C₄	#15689598	1	1	yes	characteristic
812	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
813	C₄	#15689767	1	1	yes	characteristic
814	C₂	—	2	1	no	—
815	C₂	—	2	1	no	—
816	C₂	—	2	4	no	—
817	C₂	—	4	2	no	—
818	C₂	—	4	2	no	—
819	C₂	—	8	2	no	—
820	C₂	D₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
821	C₂	C₂²×#13093951	1	1	yes	characteristic
822	C₂	#20251935	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	D₄×#41×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	D₄×#41	D₄₇
hypocenter	C₄₇	D₄×#104
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ D₄×#41

Complements

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

N	H ≅ G/N	type
1. D₄×#10625329	C₂	semidirect
2. C₂²×#13093951	C₂	semidirect
3. C₄×D₄×Dic₄₇	C₂	semidirect
4. #20244308	C₂	semidirect
5. #20244217	C₂	semidirect
6. #20243832	C₂	semidirect
7. #20243691	C₂	semidirect
8. #20243408	C₂	semidirect
9. #20243332	C₂	semidirect
10. C₄×#13093951	C₂	semidirect
12. C₂²×#10625329	C₂²	semidirect
14. C₂²×C₄×Dic₄₇	C₂²	semidirect
18. #15689147	C₂²	semidirect
23. C₂×#13093951	C₂²	semidirect
24. C₂×#13093951	C₂²	semidirect
25. C₂×#13093951	C₂²	semidirect
26. C₂×#13093951	C₂²	semidirect
27. #15689087	C₂²	semidirect
28. C₄×#10625329	C₂²	semidirect
30. C₄×C₄⋊Dic₄₇	C₂²	semidirect
32. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
33. C₄²×Dic₄₇	C₂²	semidirect
34. #15688882	C₂²	semidirect
35. #15688882	C₂²	semidirect
36. #15688882	C₂²	semidirect
38. C₄₇×#550	C₄	semidirect
39. D₄×Q₈×C₄₇	C₄	semidirect
40. C₄₇×#548	C₄	semidirect
42. C₄₇×#547	C₄	semidirect
44. C₄₇×#546	C₄	semidirect
46. D₄²×C₄₇	C₄	semidirect
81. #13093951	D₄	direct (N × H)
94. C₂×#41×C₄₇	C₂×C₄	semidirect
95. C₂×#41×C₄₇	C₂×C₄	semidirect
98. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
101. C₂²×D₄×C₄₇	C₂×C₄	semidirect
106. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
108. #127×C₄₇	C₂×C₄	semidirect
110. #124×C₄₇	C₂×C₄	semidirect
116. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
117. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
125. #121×C₄₇	C₂×C₄	semidirect
126. #121×C₄₇	C₂×C₄	semidirect
130. C₄×Q₈×C₄₇	C₂×C₄	semidirect
131. C₄×Q₈×C₄₇	C₂×C₄	semidirect
144. C₄×D₄×C₄₇	C₂×C₄	semidirect
145. C₄×D₄×C₄₇	C₂×C₄	semidirect
268. C₄×Dic₄₇	C₂×D₄	semidirect
275. #10625329	C₂×D₄	semidirect
296. Q₈×C₄₇	C₄×D₄	semidirect
313. D₄×C₄₇	#104	semidirect
314. D₄×C₄₇	C₄×D₄	semidirect
382. C₂²×C₄₇	C₂×#104	semidirect
395. C₄×C₄₇	C₂×#104	semidirect
425. #550	Dic₄₇	semidirect
426. D₄×Q₈	Dic₄₇	semidirect
427. #548	Dic₄₇	semidirect
429. #547	Dic₄₇	semidirect
431. #546	Dic₄₇	semidirect
433. D₄²	Dic₄₇	semidirect
465. C₄₇	D₄×#104	semidirect
472. C₂×#41	C₂×Dic₄₇	semidirect
473. C₂×#41	C₂×Dic₄₇	semidirect
476. C₂²×Q₈	C₂×Dic₄₇	semidirect
479. C₂²×D₄	C₂×Dic₄₇	semidirect
492. C₄⋊Q₈	C₂×Dic₄₇	semidirect
494. #127	C₂×Dic₄₇	semidirect
496. #124	C₂×Dic₄₇	semidirect
502. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
503. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
511. #121	C₂×Dic₄₇	semidirect
512. #121	C₂×Dic₄₇	semidirect
516. C₄×Q₈	C₂×Dic₄₇	semidirect
517. C₄×Q₈	C₂×Dic₄₇	semidirect
531. C₄×D₄	C₂×Dic₄₇	semidirect
532. C₄×D₄	C₂×Dic₄₇	semidirect
708. Q₈	D₄×Dic₄₇	semidirect
725. D₄	#13093951	direct (N × H)
726. D₄	D₄×Dic₄₇	semidirect
793. C₂²	C₂×#13093951	semidirect
809. C₄	C₂×#13093951	semidirect

Maximal subgroups

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

subgroup	index
D₄×#10625329	2
C₂²×#13093951	2
C₄×D₄×Dic₄₇	2
#20244308	2
#20244217	2
#20243832	2
#20243691	2
#20243408	2
#20243332	2
C₄×#13093951	2
D₄×#41×C₄₇	2
D₄×#104	47

Subgroups — D4×#13093951 #26231952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#13093951 #26231952