Subgroups — #20257060

Order 6016.

1522 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094071	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₉₄	C₂	1	2	yes	maximal, complemented
4	#15689782	C₂	1	2	yes	maximal, complemented
5	#15689778	C₂	1	2	yes	maximal, complemented
6	#15689771	C₂	1	4	yes	maximal, complemented
7	#15689769	C₂	1	2	yes	maximal, complemented
8	#15689760	C₂	1	4	yes	maximal, complemented
9	#15689702	C₂	1	2	yes	maximal, complemented
10	#15689701	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689699	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689696	C₂	1	2	yes	maximal, complemented
13	#15689633	C₂	1	2	yes	maximal, complemented
14	C₂×#13094003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²⋊Q₈×D₄₇	C₂	1	2	yes	maximal, complemented
16	#15689603	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	#13094071	—	2	8	no	—
19	C₂×#10625350	—	2	8	no	—
20	C₂×#10625350	C₂²	1	2	yes	—
21	C₂×#10625350	C₂²	1	1	yes	characteristic
22	C₂×#10625350	C₂²	1	1	yes	characteristic
23	C₂×#10625350	C₂²	1	2	yes	—
24	C₂×#10625350	C₂²	1	1	yes	characteristic
25	C₂×#10625350	C₂²	1	1	yes	characteristic
26	C₂×#10625350	C₂²	1	2	yes	complemented
27	C₂×#10625352	C₂²	1	4	yes	complemented
28	C₂×#10625352	C₂²	1	2	yes	complemented
29	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
30	C₂²×Dic₉₄	C₂²	1	2	yes	complemented
31	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×Q₈×D₄₇	C₂²	1	2	yes	complemented
33	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊D₄₇	C₂²	1	2	yes	—
35	C₂²×C₄×D₄₇	C₂²	1	2	yes	—
36	#13094024	C₂²	1	2	yes	complemented
37	#13094023	C₂²	1	4	yes	complemented
38	#13094012	C₂²	1	2	yes	complemented
39	#13094010	C₂²	1	4	yes	complemented
40	#13094009	C₂²	1	4	yes	complemented
41	#13094008	C₂²	1	4	yes	complemented
42	#13094006	C₂²	1	4	yes	complemented
43	#13094006	C₂²	1	4	yes	complemented
44	#13094004	C₂²	1	2	yes	complemented
45	#13094004	C₂²	1	2	yes	complemented
46	#13094003	C₂²	1	2	yes	—
47	#13094003	C₂²	1	2	yes	—
48	#13094003	C₂²	1	2	yes	complemented
49	#13094003	C₂²	1	2	yes	complemented
50	#13094003	C₂²	1	2	yes	complemented
51	#13094002	C₂²	1	4	yes	complemented
52	#13094001	C₂²	1	4	yes	—
53	#13094001	C₂²	1	4	yes	complemented
54	#13094000	C₂²	1	2	yes	complemented
55	#13093998	C₂²	1	2	yes	complemented
56	#13093997	C₂²	1	4	yes	complemented
57	#13093996	C₂²	1	4	yes	complemented
58	#13093996	C₂²	1	4	yes	complemented
59	#13093995	C₂²	1	4	yes	complemented
60	#13093995	C₂²	1	2	yes	complemented
61	#13093992	C₂²	1	4	yes	—
62	C₄×Dic₉₄	C₂²	1	2	yes	complemented
63	C₄×D₁₈₈	C₂²	1	2	yes	complemented
64	D₄×Dic₄₇	C₂²	1	4	yes	—
65	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
66	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
67	#13093982	C₂²	1	2	yes	complemented
68	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
69	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₄₇	C₂²	1	4	yes	complemented
71	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
72	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
74	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
75	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
76	#123×C₄₇	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
78	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
79	#121×C₄₇	C₂²	1	1	yes	characteristic
80	#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
81	#120×C₄₇	C₂²	1	2	yes	—
82	C₄×D₄×C₄₇	C₂²	1	2	yes	—
83	C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
84	#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
85	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
86	C₂³×D₄₇	C₂³	1	2	yes	—
87	#41×C₄₇	—	2	4	no	—
88	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₄₇	C₂³	1	2	yes	—
90	C₂×D₄×C₄₇	C₂³	1	2	yes	—
91	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×D₄×C₄₇	C₂³	1	2	yes	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊D₄₇	—	2	8	no	—
102	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
104	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
105	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
106	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
108	C₂²×Dic₄₇	C₂³	1	2	yes	—
109	C₂²×Dic₄₇	C₂³	1	4	yes	—
110	C₂²×Dic₄₇	C₂³	1	2	yes	—
111	C₂²×Dic₄₇	C₂³	1	2	yes	—
112	Q₈×D₄₇	—	2	8	no	—
113	#10625352	—	2	16	no	—
114	#10625352	—	2	8	no	—
115	#10625350	—	2	4	no	—
116	#10625350	—	2	8	no	—
117	#10625350	—	2	4	no	—
118	#10625350	—	2	8	no	—
119	#10625350	—	2	8	no	—
120	#10625350	—	2	4	no	—
121	#10625350	D₄	1	8	yes	complemented
122	C₂×D₁₈₈	—	2	4	no	—
123	C₂×D₁₈₈	C₂³	1	2	yes	—
124	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
125	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₄₇	—	2	8	no	—
127	C₂×C₄×D₄₇	C₂³	1	4	yes	—
128	C₂×C₄×D₄₇	C₂³	1	2	yes	—
129	C₂×C₄×D₄₇	C₂³	1	2	yes	—
130	C₂×C₄×D₄₇	C₂³	1	2	yes	—
131	C₂×C₄×D₄₇	C₂³	1	4	yes	—
132	C₂×C₄×D₄₇	C₂³	1	2	yes	—
133	C₂×Dic₉₄	—	2	4	no	—
134	C₂×Dic₉₄	—	2	4	no	—
135	C₂×Dic₉₄	—	2	8	no	—
136	C₂×Dic₉₄	C₂³	1	4	yes	—
137	C₂×Dic₉₄	C₂³	1	2	yes	—
138	C₂×Dic₉₄	C₂³	1	2	yes	—
139	C₂×Dic₉₄	C₂³	1	2	yes	—
140	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
141	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
145	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
151	C₄²×C₄₇	C₂³	1	2	yes	—
152	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
153	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
154	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
155	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
156	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
157	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
158	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
159	C₄⋊Dic₄₇	C₂³	1	2	yes	—
160	C₄⋊Dic₄₇	C₂³	1	4	yes	—
161	C₄⋊Dic₄₇	C₂³	1	2	yes	—
162	C₄⋊Dic₄₇	C₂³	1	4	yes	—
163	Dic₄₇⋊C₄	C₂³	1	4	yes	—
164	Dic₄₇⋊C₄	C₂³	1	4	yes	—
165	Dic₄₇⋊C₄	C₂³	1	4	yes	—
166	Dic₄₇⋊C₄	C₂³	1	4	yes	—
167	C₄×Dic₄₇	C₂³	1	4	yes	—
168	C₂³×C₄₇	—	2	2	no	—
169	C₂³×C₄₇	—	2	2	no	—
170	C₂³×C₄₇	—	4	1	no	—
171	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
172	C₂³×C₄₇	C₂⁴	1	2	yes	—
173	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
174	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
175	C₂²×D₄₇	—	2	4	no	—
176	C₂²×D₄₇	—	2	4	no	—
177	C₂²×D₄₇	—	4	2	no	—
178	C₂²×D₄₇	C₂⁴	1	2	yes	—
179	C₂²×D₄₇	C₂⁴	1	2	yes	—
180	Q₈×C₄₇	—	2	2	no	—
181	D₄×C₄₇	—	2	4	no	—
182	D₄×C₄₇	—	2	4	no	—
183	D₄×C₄₇	—	2	2	no	—
184	D₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	4	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
192	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
193	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
196	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
197	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
199	C₂²⋊D₄₇	—	2	4	no	—
200	C₂²⋊D₄₇	—	2	4	no	—
201	C₂²⋊D₄₇	—	2	8	no	—
202	C₂²⋊D₄₇	—	2	4	no	—
203	C₂²⋊D₄₇	—	4	4	no	—
204	C₂²⋊D₄₇	C₂×D₄	1	8	yes	—
205	C₂×Dic₄₇	—	2	4	no	—
206	C₂×Dic₄₇	—	2	4	no	—
207	C₂×Dic₄₇	—	2	8	no	—
208	C₂×Dic₄₇	—	4	2	no	—
209	C₂×Dic₄₇	C₂⁴	1	4	yes	—
210	C₂×Dic₄₇	C₂⁴	1	2	yes	—
211	C₂×Dic₄₇	C₂⁴	1	4	yes	—
212	C₂×Dic₄₇	C₂⁴	1	2	yes	—
213	D₁₈₈	—	2	4	no	—
214	D₁₈₈	—	2	2	no	—
215	D₁₈₈	C₂×D₄	1	4	yes	—
216	C₄×D₄₇	—	2	4	no	—
217	C₄×D₄₇	—	2	8	no	—
218	C₄×D₄₇	—	2	4	no	—
219	C₄×D₄₇	—	2	4	no	—
220	C₄×D₄₇	—	4	4	no	—
221	C₄×D₄₇	C₂×D₄	1	8	yes	—
222	Dic₉₄	—	2	4	no	—
223	Dic₉₄	—	2	2	no	—
224	Dic₉₄	—	2	4	no	—
225	Dic₉₄	—	2	4	no	—
226	Dic₉₄	—	2	8	no	—
227	Dic₉₄	C₂×D₄	1	4	yes	—
228	C₂²×C₄₇	—	2	1	no	—
229	C₂²×C₄₇	—	2	1	no	—
230	C₂²×C₄₇	—	2	1	no	—
231	C₂²×C₄₇	—	2	1	no	—
232	C₂²×C₄₇	—	2	2	no	—
233	C₂²×C₄₇	—	2	1	no	—
234	C₂²×C₄₇	—	2	2	no	—
235	C₂²×C₄₇	—	2	1	no	—
236	C₂²×C₄₇	—	2	2	no	—
237	C₂²×C₄₇	—	2	1	no	—
238	C₂²×C₄₇	—	4	4	no	—
239	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
240	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	complemented
241	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
242	C₂×D₄₇	—	2	2	no	—
243	C₂×D₄₇	—	2	2	no	—
244	C₂×D₄₇	—	2	2	no	—
245	C₂×D₄₇	—	2	2	no	—
246	C₂×D₄₇	—	2	2	no	—
247	C₂×D₄₇	—	4	8	no	—
248	C₂×D₄₇	C₂²×D₄	1	4	yes	—
249	C₄×C₄₇	—	2	2	no	—
250	C₄×C₄₇	—	2	1	no	—
251	C₄×C₄₇	—	2	1	no	—
252	C₄×C₄₇	—	2	2	no	—
253	C₄×C₄₇	—	2	2	no	—
254	C₄×C₄₇	C₂²×D₄	1	2	yes	—
255	C₄×C₄₇	C₂²×D₄	1	2	yes	—
256	Dic₄₇	—	2	4	no	—
257	Dic₄₇	—	2	2	no	—
258	Dic₄₇	—	2	4	no	—
259	Dic₄₇	C₂²×D₄	1	4	yes	—
260	#3489	—	47	1	no	maximal, Sylow
261	C₂×C₄₇	—	2	2	no	—
262	C₂×C₄₇	—	2	2	no	—
263	C₂×C₄₇	—	4	2	no	—
264	C₂×C₄₇	—	4	1	no	—
265	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
266	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
267	C₂×C₄₇	#585	1	1	yes	characteristic
268	D₄₇	—	2	4	no	—
269	D₄₇	—	4	2	no	—
270	C₂×2₋¹⁺⁴	—	47	1	no	—
271	C₂²×#41	—	47	1	no	—
272	D₄×Q₈	—	47	2	no	—
273	#548	—	47	2	no	—
274	#547	—	47	4	no	—
275	#547	—	47	2	no	—
276	#546	—	47	4	no	—
277	#546	—	47	2	no	—
278	#537	—	47	1	no	—
279	#537	—	47	2	no	—
280	#536	—	47	2	no	—
281	#536	—	47	1	no	—
282	#525	—	47	2	no	—
283	#525	D₄₇	1	1	yes	characteristic, complemented
284	C₂×C₂²⋊Q₈	—	47	1	no	—
285	C₂×C₂²⋊Q₈	—	47	2	no	—
286	#520	—	47	1	no	—
287	C₄₇	#3489	1	1	yes	characteristic, complemented, Sylow
288	2₋¹⁺⁴	—	94	8	no	—
289	C₂×#41	—	47	2	no	—
290	C₂×#41	—	47	4	no	—
291	C₂×#41	—	47	1	no	—
292	C₂×#41	—	47	2	no	—
293	C₂×#41	—	47	1	no	—
294	C₂×#41	—	47	2	no	—
295	C₂×#41	—	47	1	no	—
296	C₂×#41	—	47	2	no	—
297	C₂×#41	—	47	1	no	—
298	C₂×#41	—	94	8	no	—
299	C₂×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
300	C₂²×Q₈	—	47	2	no	—
301	C₂²×Q₈	—	47	1	no	—
302	C₂²×Q₈	—	47	2	no	—
303	C₂²×Q₈	—	47	1	no	—
304	C₂²×D₄	—	47	2	no	—
305	C₂²×D₄	—	47	1	no	—
306	C₂³×C₄	—	47	2	no	—
307	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
308	C₄⋊Q₈	—	47	4	no	—
309	C₄⋊Q₈	—	47	2	no	—
310	#124	—	47	4	no	—
311	#124	—	47	2	no	—
312	#123	—	47	4	no	—
313	#123	—	47	4	no	—
314	#123	—	47	4	no	—
315	#123	—	47	4	no	—
316	#123	C₂×D₄₇	1	2	yes	complemented
317	C₂²⋊Q₈	—	47	2	no	—
318	C₂²⋊Q₈	—	47	2	no	—
319	C₂²⋊Q₈	—	47	2	no	—
320	C₂²⋊Q₈	—	47	2	no	—
321	C₂²⋊Q₈	—	47	2	no	—
322	C₂²⋊Q₈	—	47	2	no	—
323	C₂²⋊Q₈	—	47	2	no	—
324	C₂²⋊Q₈	—	47	4	no	—
325	C₂²⋊Q₈	—	47	2	no	—
326	C₂²⋊Q₈	—	47	4	no	—
327	C₂²⋊Q₈	—	47	4	no	—
328	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
329	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
330	#121	—	47	2	no	—
331	#121	—	47	4	no	—
332	#121	—	47	4	no	—
333	#121	—	47	4	no	—
334	#121	—	47	2	no	—
335	#121	—	47	4	no	—
336	#121	C₂×D₄₇	1	1	yes	characteristic
337	#121	C₂×D₄₇	1	1	yes	characteristic, complemented
338	#120	—	47	4	no	—
339	#120	C₂×D₄₇	1	2	yes	—
340	C₄×Q₈	—	47	2	no	—
341	C₄×D₄	—	47	4	no	—
342	C₄×D₄	—	47	4	no	—
343	C₄×D₄	—	47	4	no	—
344	C₄×D₄	—	47	2	no	—
345	C₄×D₄	C₂×D₄₇	1	2	yes	—
346	C₄×D₄	C₂×D₄₇	1	2	yes	complemented
347	#117	—	47	2	no	—
348	#117	C₂×D₄₇	1	1	yes	characteristic, complemented
349	C₂×C₄⋊C₄	—	47	1	no	—
350	C₂×C₄⋊C₄	—	47	2	no	—
351	C₂×C₄⋊C₄	—	47	2	no	—
352	C₂×C₄⋊C₄	—	47	4	no	—
353	C₂×C₂²⋊C₄	—	47	2	no	—
354	C₂×C₂²⋊C₄	—	47	4	no	—
355	C₂⁴	—	47	2	no	—
356	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
357	#41	—	2	4	no	—
358	#41	—	47	8	no	—
359	#41	—	94	8	no	—
360	#41	—	94	8	no	—
361	#41	—	94	4	no	—
362	#41	—	94	8	no	—
363	#41	—	94	4	no	—
364	#41	—	94	8	no	—
365	#41	—	94	16	no	—
366	#41	—	94	4	no	—
367	C₂×Q₈	—	47	1	no	—
368	C₂×Q₈	—	47	2	no	—
369	C₂×Q₈	—	47	4	no	—
370	C₂×Q₈	—	47	2	no	—
371	C₂×Q₈	—	47	2	no	—
372	C₂×Q₈	—	47	1	no	—
373	C₂×Q₈	—	94	4	no	—
374	C₂×Q₈	—	94	8	no	—
375	C₂×Q₈	—	94	8	no	—
376	C₂×Q₈	—	94	4	no	—
377	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
378	C₂×D₄	—	47	2	no	—
379	C₂×D₄	—	47	4	no	—
380	C₂×D₄	—	47	2	no	—
381	C₂×D₄	—	47	2	no	—
382	C₂×D₄	—	47	2	no	—
383	C₂×D₄	—	47	4	no	—
384	C₂×D₄	—	47	1	no	—
385	C₂×D₄	—	47	2	no	—
386	C₂×D₄	—	47	1	no	—
387	C₂×D₄	—	94	4	no	—
388	C₂×D₄	—	94	8	no	—
389	C₂×D₄	C₂²×D₄₇	1	2	yes	—
390	C₂×D₄	C₂²×D₄₇	1	2	yes	—
391	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
392	C₂×D₄	C₂²×D₄₇	1	2	yes	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	47	2	no	—
395	C₂²×C₄	—	47	2	no	—
396	C₂²×C₄	—	47	4	no	—
397	C₂²×C₄	—	47	2	no	—
398	C₂²×C₄	—	47	2	no	—
399	C₂²×C₄	—	47	4	no	—
400	C₂²×C₄	—	47	2	no	—
401	C₂²×C₄	—	47	2	no	—
402	C₂²×C₄	—	47	2	no	—
403	C₂²×C₄	—	47	4	no	—
404	C₂²×C₄	—	94	8	no	—
405	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
406	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
407	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
408	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
409	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
410	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
411	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
412	C₄⋊C₄	—	47	4	no	—
413	C₄⋊C₄	—	47	4	no	—
414	C₄⋊C₄	—	47	4	no	—
415	C₄⋊C₄	—	47	4	no	—
416	C₄⋊C₄	—	47	2	no	—
417	C₄⋊C₄	—	47	2	no	—
418	C₄⋊C₄	—	47	4	no	—
419	C₄⋊C₄	—	47	4	no	—
420	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
421	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
422	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
423	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
424	C₂²⋊C₄	—	47	4	no	—
425	C₂²⋊C₄	—	47	4	no	—
426	C₂²⋊C₄	—	47	4	no	—
427	C₂²⋊C₄	—	47	4	no	—
428	C₂²⋊C₄	—	47	4	no	—
429	C₂²⋊C₄	—	47	4	no	—
430	C₂²⋊C₄	—	47	4	no	—
431	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
432	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
433	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
434	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
435	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
436	C₄²	—	47	4	no	—
437	C₄²	C₂²×D₄₇	1	2	yes	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	47	2	no	—
442	C₂³	—	47	2	no	—
443	C₂³	—	94	4	no	—
444	C₂³	—	94	4	no	—
445	C₂³	—	188	2	no	—
446	C₂³	C₂³×D₄₇	1	1	yes	characteristic
447	C₂³	C₂³×D₄₇	1	2	yes	—
448	C₂³	C₂³×D₄₇	1	1	yes	characteristic
449	C₂³	C₂³×D₄₇	1	1	yes	characteristic
450	Q₈	—	2	2	no	—
451	Q₈	—	47	4	no	—
452	Q₈	—	94	8	no	—
453	Q₈	—	94	4	no	—
454	Q₈	—	94	4	no	—
455	Q₈	—	94	4	no	—
456	Q₈	—	94	2	no	—
457	D₄	—	2	4	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	47	8	no	—
462	D₄	—	47	4	no	—
463	D₄	—	94	4	no	—
464	D₄	—	94	4	no	—
465	D₄	—	94	4	no	—
466	D₄	—	94	8	no	—
467	D₄	—	94	4	no	—
468	D₄	—	94	2	no	—
469	D₄	—	188	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	47	2	no	—
477	C₂×C₄	—	47	8	no	—
478	C₂×C₄	—	47	4	no	—
479	C₂×C₄	—	47	4	no	—
480	C₂×C₄	—	47	2	no	—
481	C₂×C₄	—	94	4	no	—
482	C₂×C₄	—	94	4	no	—
483	C₂×C₄	—	94	8	no	—
484	C₂×C₄	—	94	4	no	—
485	C₂×C₄	—	94	8	no	—
486	C₂×C₄	—	94	4	no	—
487	C₂×C₄	—	94	4	no	—
488	C₂×C₄	—	188	4	no	—
489	C₂×C₄	—	188	2	no	—
490	C₂×C₄	D₄×D₄₇	1	4	yes	—
491	C₂×C₄	C₂³×D₄₇	1	2	yes	—
492	C₂×C₄	C₂³×D₄₇	1	2	yes	—
493	C₂×C₄	C₂³×D₄₇	1	2	yes	—
494	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
495	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
496	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
497	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	47	4	no	—
510	C₂²	—	94	2	no	—
511	C₂²	—	94	2	no	—
512	C₂²	—	94	2	no	—
513	C₂²	—	94	2	no	—
514	C₂²	—	94	2	no	—
515	C₂²	—	188	8	no	—
516	C₂²	C₂×D₄×D₄₇	1	2	yes	—
517	C₂²	#13094071	1	2	yes	complemented
518	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	47	4	no	—
525	C₄	—	94	2	no	—
526	C₄	—	94	4	no	—
527	C₄	—	94	4	no	—
528	C₄	C₂×D₄×D₄₇	1	2	yes	—
529	C₄	C₂×D₄×D₄₇	1	2	yes	—
530	C₂	—	2	2	no	—
531	C₂	—	2	2	no	—
532	C₂	—	4	1	no	—
533	C₂	—	4	2	no	—
534	C₂	—	94	4	no	—
535	C₂	—	188	2	no	—
536	C₂	C₂²×D₄×D₄₇	1	1	yes	characteristic
537	C₂	C₂×#13094071	1	1	yes	characteristic
538	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#525	C₂
hypercenter	#525	D₄₇
hypocenter	C₄₇	#3489
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂×#13094071	C₂	semidirect
2. C₂²×#10625350	C₂	semidirect
3. D₄×Dic₉₄	C₂	semidirect
4. #15689782	C₂	semidirect
5. #15689778	C₂	semidirect
6. #15689771	C₂	semidirect
7. #15689769	C₂	semidirect
8. #15689760	C₂	semidirect
9. #15689702	C₂	semidirect
10. #15689701	C₂	semidirect
11. #15689699	C₂	semidirect
12. #15689696	C₂	semidirect
13. #15689633	C₂	semidirect
14. C₂×#13094003	C₂	semidirect
15. C₂²⋊Q₈×D₄₇	C₂	semidirect
16. #15689603	C₂	semidirect
17. C₄₇×#525	C₂	semidirect
26. C₂×#10625350	C₂²	semidirect
27. C₂×#10625352	C₂²	semidirect
28. C₂×#10625352	C₂²	semidirect
30. C₂²×Dic₉₄	C₂²	semidirect
31. C₂²×Dic₉₄	C₂²	semidirect
32. C₂×Q₈×D₄₇	C₂²	semidirect
36. #13094024	C₂²	semidirect
37. #13094023	C₂²	semidirect
38. #13094012	C₂²	semidirect
39. #13094010	C₂²	semidirect
40. #13094009	C₂²	semidirect
41. #13094008	C₂²	semidirect
42. #13094006	C₂²	semidirect
43. #13094006	C₂²	semidirect
44. #13094004	C₂²	semidirect
45. #13094004	C₂²	semidirect
48. #13094003	C₂²	semidirect
49. #13094003	C₂²	semidirect
50. #13094003	C₂²	semidirect
51. #13094002	C₂²	semidirect
53. #13094001	C₂²	semidirect
54. #13094000	C₂²	semidirect
55. #13093998	C₂²	semidirect
56. #13093997	C₂²	semidirect
57. #13093996	C₂²	semidirect
58. #13093996	C₂²	semidirect
59. #13093995	C₂²	semidirect
60. #13093995	C₂²	semidirect
62. C₄×Dic₉₄	C₂²	semidirect
63. C₄×D₁₈₈	C₂²	semidirect
65. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
66. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
67. #13093982	C₂²	semidirect
68. C₂×C₄⋊Dic₄₇	C₂²	semidirect
69. C₂×Dic₄₇⋊C₄	C₂²	semidirect
70. C₄⋊C₄×D₄₇	C₂²	semidirect
71. C₄⋊C₄×D₄₇	C₂²	semidirect
74. C₂×#41×C₄₇	C₂²	semidirect
76. #123×C₄₇	C₂²	semidirect
78. C₂²⋊Q₈×C₄₇	C₂²	semidirect
80. #121×C₄₇	C₂²	semidirect
83. C₄×D₄×C₄₇	C₂²	semidirect
84. #117×C₄₇	C₂²	semidirect
121. #10625350	D₄	semidirect
240. C₂²×C₄₇	2₋¹⁺⁴	semidirect
283. #525	D₄₇	semidirect
287. C₄₇	#3489	semidirect
299. C₂×#41	C₂×D₄₇	semidirect
316. #123	C₂×D₄₇	semidirect
329. C₂²⋊Q₈	C₂×D₄₇	semidirect
337. #121	C₂×D₄₇	semidirect
346. C₄×D₄	C₂×D₄₇	semidirect
348. #117	C₂×D₄₇	semidirect
517. C₂²	#13094071	semidirect