Subgroups — #20256774

Order 6016.

1040 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689743	C₂	1	2	yes	maximal, complemented
2	#15689739	C₂	1	2	yes	maximal, complemented
3	#15689732	C₂	1	2	yes	maximal, complemented
4	#15689725	C₂	1	2	yes	maximal, complemented
5	#15689720	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689717	C₂	1	2	yes	maximal, complemented
7	#15689713	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689710	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689706	C₂	1	2	yes	maximal, complemented
10	#15689675	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689668	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689659	C₂	1	2	yes	maximal, complemented
13	#15689658	C₂	1	2	yes	maximal, complemented
14	#15689656	C₂	1	2	yes	maximal, complemented
15	#15689650	C₂	1	2	yes	maximal, complemented
16	#15689631	C₂	1	2	yes	maximal, complemented
17	C₄×#10625352	C₂	1	2	yes	maximal, complemented
18	C₂×#13093982	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₇×#539	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10625352	C₂²	1	2	yes	—
21	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
22	#13094023	C₂²	1	1	yes	characteristic, complemented
23	#13094023	C₂²	1	1	yes	characteristic, complemented
24	#13094022	C₂²	1	1	yes	characteristic, complemented
25	#13094020	C₂²	1	1	yes	characteristic, complemented
26	#13094019	C₂²	1	2	yes	—
27	#13094019	C₂²	1	2	yes	—
28	#13094019	C₂²	1	2	yes	—
29	#13094019	C₂²	1	2	yes	complemented
30	#13094019	C₂²	1	2	yes	complemented
31	#13094018	C₂²	1	2	yes	—
32	#13094017	C₂²	1	2	yes	complemented
33	#13094015	C₂²	1	2	yes	complemented
34	#13094014	C₂²	1	2	yes	complemented
35	#13094014	C₂²	1	2	yes	complemented
36	#13094014	C₂²	1	2	yes	complemented
37	#13094013	C₂²	1	2	yes	—
38	#13094012	C₂²	1	2	yes	—
39	#13094010	C₂²	1	2	yes	—
40	#13094010	C₂²	1	2	yes	—
41	#13094010	C₂²	1	2	yes	complemented
42	#13094009	C₂²	1	2	yes	—
43	#13094009	C₂²	1	2	yes	—
44	#13094009	C₂²	1	2	yes	complemented
45	#13094008	C₂²	1	2	yes	—
46	#13094008	C₂²	1	2	yes	complemented
47	#13094007	C₂²	1	2	yes	—
48	#13094007	C₂²	1	2	yes	—
49	#13094006	C₂²	1	2	yes	complemented
50	#13094004	C₂²	1	2	yes	complemented
51	#13094003	C₂²	1	1	yes	characteristic
52	#13094002	C₂²	1	2	yes	—
53	#13094002	C₂²	1	2	yes	—
54	#13094002	C₂²	1	2	yes	complemented
55	#13094001	C₂²	1	2	yes	—
56	#13094001	C₂²	1	2	yes	complemented
57	#13093999	C₂²	1	2	yes	—
58	#13093998	C₂²	1	2	yes	—
59	#13093998	C₂²	1	1	yes	characteristic
60	#13093997	C₂²	1	2	yes	—
61	#13093997	C₂²	1	2	yes	—
62	#13093997	C₂²	1	2	yes	—
63	#13093996	C₂²	1	2	yes	—
64	#13093996	C₂²	1	2	yes	—
65	#13093994	C₂²	1	2	yes	—
66	#13093992	C₂²	1	2	yes	—
67	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
68	C₄×Dic₉₄	C₂²	1	2	yes	complemented
69	#13093989	C₂²	1	2	yes	complemented
70	#13093989	C₂²	1	2	yes	complemented
71	#13093989	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₄₇	C₂²	1	2	yes	—
73	D₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
74	#13093986	C₂²	1	2	yes	—
75	#13093986	C₂²	1	2	yes	—
76	#13093986	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
78	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
79	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
80	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
81	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
82	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
83	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
84	#13093982	C₂²	1	2	yes	—
85	#13093982	C₂²	1	2	yes	—
86	#13093982	C₂²	1	2	yes	—
87	#13093982	C₂²	1	2	yes	—
88	#13093982	C₂²	1	2	yes	complemented
89	#13093980	C₂²	1	2	yes	—
90	#13093980	C₂²	1	2	yes	complemented
91	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
92	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
93	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
94	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
95	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
96	C₂×C₄×Dic₄₇	C₂²	1	2	yes	complemented
97	C₄²×D₄₇	C₂²	1	2	yes	complemented
98	#126×C₄₇	C₂²	1	2	yes	complemented
99	#125×C₄₇	C₂²	1	2	yes	complemented
100	#123×C₄₇	C₂²	1	2	yes	—
101	#123×C₄₇	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
103	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
104	#121×C₄₇	C₂²	1	1	yes	characteristic
105	C₄×D₄×C₄₇	C₂²	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
107	C₂³×D₄₇	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₄₇	C₂³	1	2	yes	—
110	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
115	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
120	C₂²×Dic₄₇	C₂³	1	2	yes	—
121	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
122	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
123	C₂²×Dic₄₇	C₂³	1	2	yes	—
124	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
125	#10625352	—	2	8	no	—
126	C₂×D₁₈₈	C₂³	1	2	yes	—
127	C₂×D₁₈₈	C₂³	1	2	yes	—
128	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
129	C₂×C₄×D₄₇	—	2	4	no	—
130	C₂×C₄×D₄₇	C₂³	1	2	yes	—
131	C₂×C₄×D₄₇	C₂³	1	2	yes	—
132	C₂×C₄×D₄₇	C₂³	1	2	yes	—
133	C₂×C₄×D₄₇	C₂³	1	2	yes	—
134	C₂×C₄×D₄₇	C₂³	1	2	yes	—
135	C₂×Dic₉₄	C₂³	1	2	yes	—
136	C₂×Dic₉₄	C₂³	1	2	yes	—
137	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
139	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
140	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
141	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
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	2	yes	—
153	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
154	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
155	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
156	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
157	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
158	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
169	C₄⋊Dic₄₇	C₂³	1	2	yes	—
170	C₄⋊Dic₄₇	C₂³	1	2	yes	—
171	C₄⋊Dic₄₇	C₂³	1	2	yes	—
172	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₄₇	C₂³	1	2	yes	—
174	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
175	Dic₄₇⋊C₄	C₂³	1	2	yes	—
176	Dic₄₇⋊C₄	C₂³	1	2	yes	—
177	Dic₄₇⋊C₄	C₂³	1	2	yes	—
178	Dic₄₇⋊C₄	C₂³	1	2	yes	—
179	Dic₄₇⋊C₄	C₂³	1	2	yes	—
180	Dic₄₇⋊C₄	C₂³	1	2	yes	—
181	Dic₄₇⋊C₄	C₂³	1	2	yes	—
182	Dic₄₇⋊C₄	C₂³	1	2	yes	—
183	Dic₄₇⋊C₄	C₂³	1	2	yes	—
184	Dic₄₇⋊C₄	C₂³	1	2	yes	—
185	C₄×Dic₄₇	C₂³	1	2	yes	—
186	C₄×Dic₄₇	C₂³	1	2	yes	—
187	C₄×Dic₄₇	C₂³	1	2	yes	—
188	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
189	C₄×Dic₄₇	C₂³	1	2	yes	—
190	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
191	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
192	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
193	C₄×Dic₄₇	C₂³	1	2	yes	—
194	C₄×Dic₄₇	C₂³	1	2	yes	—
195	C₄×Dic₄₇	C₂³	1	2	yes	—
196	C₂³×C₄₇	C₂⁴	1	2	yes	—
197	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
198	C₂²×D₄₇	—	2	2	no	—
199	C₂²×D₄₇	—	4	1	no	—
200	C₂²×D₄₇	—	4	1	no	—
201	C₂²×D₄₇	C₂⁴	1	2	yes	—
202	C₂²×D₄₇	C₂⁴	1	2	yes	—
203	Q₈×C₄₇	—	4	1	no	—
204	D₄×C₄₇	—	2	4	no	—
205	D₄×C₄₇	—	4	1	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	—	4	2	no	—
210	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
211	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
212	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
215	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
216	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
217	C₂²⋊D₄₇	—	2	4	no	—
218	C₂²⋊D₄₇	—	2	4	no	—
219	C₂²⋊D₄₇	—	4	2	no	—
220	C₂²⋊D₄₇	—	4	2	no	—
221	C₂²⋊D₄₇	—	4	2	no	—
222	C₂×Dic₄₇	—	2	4	no	—
223	C₂×Dic₄₇	—	4	1	no	—
224	C₂×Dic₄₇	—	4	2	no	—
225	C₂×Dic₄₇	—	4	1	no	—
226	C₂×Dic₄₇	#41	1	4	yes	—
227	C₂×Dic₄₇	C₂⁴	1	2	yes	—
228	C₂×Dic₄₇	C₂⁴	1	2	yes	—
229	C₂×Dic₄₇	C₂⁴	1	2	yes	—
230	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
231	C₂×Dic₄₇	C₂⁴	1	2	yes	—
232	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
233	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
234	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
235	D₁₈₈	—	4	2	no	—
236	D₁₈₈	—	4	1	no	—
237	D₁₈₈	—	4	2	no	—
238	C₄×D₄₇	—	2	4	no	—
239	C₄×D₄₇	—	2	4	no	—
240	C₄×D₄₇	—	2	4	no	—
241	C₄×D₄₇	—	4	2	no	—
242	C₄×D₄₇	—	4	2	no	—
243	Dic₉₄	—	2	4	no	—
244	Dic₉₄	—	4	2	no	—
245	Dic₉₄	—	4	1	no	—
246	C₂²×C₄₇	—	2	1	no	—
247	C₂²×C₄₇	—	2	1	no	—
248	C₂²×C₄₇	—	2	2	no	—
249	C₂²×C₄₇	—	2	2	no	—
250	C₂²×C₄₇	—	2	2	no	—
251	C₂²×C₄₇	C₂×#41	1	2	yes	—
252	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
253	C₂×D₄₇	—	2	2	no	—
254	C₂×D₄₇	—	2	2	no	—
255	C₂×D₄₇	—	2	2	no	—
256	C₂×D₄₇	—	2	2	no	—
257	C₂×D₄₇	—	2	2	no	—
258	C₂×D₄₇	—	2	2	no	—
259	C₂×D₄₇	—	4	4	no	—
260	C₄×C₄₇	—	2	2	no	—
261	C₄×C₄₇	—	2	2	no	—
262	C₄×C₄₇	—	2	2	no	—
263	C₄×C₄₇	—	2	1	no	—
264	C₄×C₄₇	—	2	2	no	—
265	C₄×C₄₇	—	2	1	no	—
266	C₄×C₄₇	—	2	2	no	—
267	Dic₄₇	—	2	2	no	—
268	Dic₄₇	—	2	1	no	—
269	Dic₄₇	—	2	2	no	—
270	Dic₄₇	—	2	2	no	—
271	Dic₄₇	—	2	2	no	—
272	Dic₄₇	—	2	1	no	—
273	Dic₄₇	C₂×#41	1	2	yes	—
274	Dic₄₇	C₂×#41	1	2	yes	—
275	#3455	—	47	1	no	maximal, Sylow
276	C₂×C₄₇	—	2	2	no	—
277	C₂×C₄₇	—	4	2	no	—
278	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
279	C₂×C₄₇	#585	1	1	yes	characteristic
280	C₂×C₄₇	#585	1	1	yes	characteristic
281	D₄₇	—	4	2	no	—
282	D₄₇	—	4	2	no	—
283	#542	—	47	2	no	—
284	#542	—	47	2	no	—
285	#541	—	47	2	no	—
286	#540	—	47	2	no	—
287	#539	—	47	2	no	—
288	#539	—	47	1	no	—
289	#539	D₄₇	1	1	yes	characteristic, complemented
290	#538	—	47	1	no	—
291	#538	—	47	1	no	—
292	#538	—	47	2	no	—
293	#533	—	47	1	no	—
294	#532	—	47	1	no	—
295	#529	—	47	2	no	—
296	#529	—	47	2	no	—
297	#529	—	47	2	no	—
298	#529	—	47	2	no	—
299	#525	—	47	2	no	—
300	C₄×#41	—	47	2	no	—
301	C₂×#117	—	47	1	no	—
302	C₄₇	#3455	1	1	yes	characteristic, complemented, Sylow
303	C₂×#41	—	47	2	no	—
304	C₂³×C₄	—	47	1	no	—
305	C₄⋊Q₈	—	47	1	no	—
306	C₄⋊Q₈	—	47	1	no	—
307	C₄⋊Q₈	—	47	1	no	—
308	#127	—	47	1	no	—
309	#126	—	47	2	no	—
310	#126	—	47	2	no	—
311	#126	—	47	2	no	—
312	#126	—	47	2	no	—
313	#126	—	47	2	no	—
314	#126	—	47	2	no	—
315	#126	—	47	2	no	—
316	#126	C₂×D₄₇	1	2	yes	complemented
317	#125	—	47	2	no	—
318	#125	—	47	2	no	—
319	#125	—	47	2	no	—
320	#125	—	47	2	no	—
321	#125	C₂×D₄₇	1	2	yes	complemented
322	#124	—	47	2	no	—
323	#124	—	47	2	no	—
324	#124	—	47	2	no	—
325	#124	—	47	2	no	—
326	#124	—	47	2	no	—
327	#123	—	47	2	no	—
328	#123	—	47	2	no	—
329	#123	—	47	2	no	—
330	#123	—	47	2	no	—
331	#123	—	47	2	no	—
332	#123	—	47	2	no	—
333	#123	—	47	2	no	—
334	#123	—	47	2	no	—
335	#123	C₂×D₄₇	1	2	yes	—
336	#123	C₂×D₄₇	1	2	yes	complemented
337	C₂²⋊Q₈	—	47	1	no	—
338	C₂²⋊Q₈	—	47	2	no	—
339	C₂²⋊Q₈	—	47	2	no	—
340	C₂²⋊Q₈	—	47	2	no	—
341	C₂²⋊Q₈	—	47	2	no	—
342	C₂²⋊Q₈	—	47	2	no	—
343	C₂²⋊Q₈	—	47	2	no	—
344	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
345	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
346	#121	—	47	2	no	—
347	#121	—	47	2	no	—
348	#121	—	47	2	no	—
349	#121	—	47	1	no	—
350	#121	—	47	2	no	—
351	#121	—	47	2	no	—
352	#121	—	47	2	no	—
353	#121	—	47	2	no	—
354	#121	C₂×D₄₇	1	1	yes	characteristic
355	#120	—	47	2	no	—
356	#120	—	47	2	no	—
357	C₄×Q₈	—	47	1	no	—
358	C₄×Q₈	—	47	2	no	—
359	C₄×Q₈	—	47	1	no	—
360	C₄×Q₈	—	47	2	no	—
361	C₄×Q₈	—	47	2	no	—
362	C₄×D₄	—	47	2	no	—
363	C₄×D₄	—	47	1	no	—
364	C₄×D₄	—	47	2	no	—
365	C₄×D₄	—	47	2	no	—
366	C₄×D₄	—	47	2	no	—
367	C₄×D₄	—	47	2	no	—
368	C₄×D₄	—	47	1	no	—
369	C₄×D₄	—	47	2	no	—
370	C₄×D₄	—	47	2	no	—
371	C₄×D₄	—	47	2	no	—
372	C₄×D₄	—	47	2	no	—
373	C₄×D₄	—	47	2	no	—
374	C₄×D₄	C₂×D₄₇	1	2	yes	—
375	#117	—	47	2	no	—
376	#117	—	47	2	no	—
377	#117	—	47	2	no	—
378	#117	—	47	2	no	—
379	#117	—	47	2	no	—
380	#117	—	47	2	no	—
381	#117	—	47	2	no	—
382	C₂×C₄⋊C₄	—	47	1	no	—
383	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	—	47	1	no	—
385	C₂×C₂²⋊C₄	—	47	1	no	—
386	C₂×C₄²	—	47	1	no	—
387	C₂×C₄²	—	47	1	no	—
388	C₂×C₄²	—	47	2	no	—
389	C₂×C₄²	—	47	2	no	—
390	C₂⁴	—	47	1	no	—
391	#41	—	94	8	no	—
392	C₂×Q₈	—	47	2	no	—
393	C₂×Q₈	—	47	2	no	—
394	C₂×Q₈	—	47	1	no	—
395	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
396	C₂×D₄	—	47	2	no	—
397	C₂×D₄	—	47	2	no	—
398	C₂×D₄	—	47	2	no	—
399	C₂×D₄	—	47	2	no	—
400	C₂×D₄	—	47	2	no	—
401	C₂×D₄	—	47	2	no	—
402	C₂×D₄	—	47	2	no	—
403	C₂×D₄	—	47	1	no	—
404	C₂×D₄	C₂²×D₄₇	1	2	yes	—
405	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
406	C₂²×C₄	—	47	1	no	—
407	C₂²×C₄	—	47	2	no	—
408	C₂²×C₄	—	47	1	no	—
409	C₂²×C₄	—	47	1	no	—
410	C₂²×C₄	—	47	2	no	—
411	C₂²×C₄	—	47	2	no	—
412	C₂²×C₄	—	47	2	no	—
413	C₂²×C₄	—	47	2	no	—
414	C₂²×C₄	—	47	2	no	—
415	C₂²×C₄	—	47	2	no	—
416	C₂²×C₄	—	94	4	no	—
417	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
418	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
419	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
420	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
421	C₄⋊C₄	—	47	2	no	—
422	C₄⋊C₄	—	47	2	no	—
423	C₄⋊C₄	—	47	2	no	—
424	C₄⋊C₄	—	47	2	no	—
425	C₄⋊C₄	—	47	2	no	—
426	C₄⋊C₄	—	47	2	no	—
427	C₄⋊C₄	—	47	2	no	—
428	C₄⋊C₄	—	47	2	no	—
429	C₄⋊C₄	—	47	2	no	—
430	C₄⋊C₄	—	47	2	no	—
431	C₄⋊C₄	—	47	2	no	—
432	C₄⋊C₄	—	47	2	no	—
433	C₄⋊C₄	—	47	2	no	—
434	C₄⋊C₄	—	47	1	no	—
435	C₄⋊C₄	—	47	2	no	—
436	C₄⋊C₄	—	47	1	no	—
437	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
438	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
439	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
440	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
441	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
442	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
443	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
444	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
445	C₂²⋊C₄	—	47	2	no	—
446	C₂²⋊C₄	—	47	2	no	—
447	C₂²⋊C₄	—	47	2	no	—
448	C₂²⋊C₄	—	47	2	no	—
449	C₂²⋊C₄	—	47	2	no	—
450	C₂²⋊C₄	—	47	2	no	—
451	C₂²⋊C₄	—	47	2	no	—
452	C₂²⋊C₄	—	47	2	no	—
453	C₂²⋊C₄	—	47	2	no	—
454	C₂²⋊C₄	—	47	2	no	—
455	C₂²⋊C₄	—	47	2	no	—
456	C₂²⋊C₄	—	47	2	no	—
457	C₂²⋊C₄	—	47	2	no	—
458	C₂²⋊C₄	—	47	2	no	—
459	C₂²⋊C₄	—	47	2	no	—
460	C₂²⋊C₄	—	47	2	no	—
461	C₂²⋊C₄	—	47	2	no	—
462	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
463	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
464	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
465	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
466	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
467	C₄²	—	47	2	no	—
468	C₄²	—	47	1	no	—
469	C₄²	—	47	2	no	—
470	C₄²	—	47	2	no	—
471	C₄²	—	47	1	no	—
472	C₄²	—	47	2	no	—
473	C₄²	—	47	1	no	—
474	C₄²	—	47	1	no	—
475	C₄²	—	47	2	no	—
476	C₄²	—	47	2	no	—
477	C₄²	—	47	2	no	—
478	C₄²	C₂²×D₄₇	1	2	yes	—
479	C₂³	—	47	2	no	—
480	C₂³	—	47	2	no	—
481	C₂³	—	94	2	no	—
482	C₂³	—	188	1	no	—
483	C₂³	—	188	1	no	—
484	C₂³	C₂³×D₄₇	1	2	yes	—
485	C₂³	C₂³×D₄₇	1	1	yes	characteristic
486	Q₈	—	4	1	no	—
487	Q₈	—	94	4	no	—
488	Q₈	—	188	1	no	—
489	Q₈	—	188	2	no	—
490	D₄	—	2	4	no	—
491	D₄	—	4	1	no	—
492	D₄	—	94	4	no	—
493	D₄	—	94	4	no	—
494	D₄	—	188	1	no	—
495	D₄	—	188	2	no	—
496	D₄	—	188	2	no	—
497	D₄	—	188	2	no	—
498	D₄	—	188	2	no	—
499	D₄	—	188	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	47	4	no	—
505	C₂×C₄	—	47	1	no	—
506	C₂×C₄	—	47	1	no	—
507	C₂×C₄	—	47	2	no	—
508	C₂×C₄	—	47	1	no	—
509	C₂×C₄	—	47	2	no	—
510	C₂×C₄	—	47	2	no	—
511	C₂×C₄	—	47	2	no	—
512	C₂×C₄	—	47	1	no	—
513	C₂×C₄	—	94	4	no	—
514	C₂×C₄	—	94	4	no	—
515	C₂×C₄	—	94	4	no	—
516	C₂×C₄	—	94	4	no	—
517	C₂×C₄	—	188	2	no	—
518	C₂×C₄	—	188	2	no	—
519	C₂×C₄	—	188	1	no	—
520	C₂×C₄	—	188	2	no	—
521	C₂×C₄	—	188	1	no	—
522	C₂×C₄	C₂³×D₄₇	1	2	yes	—
523	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
524	C₂×C₄	C₂³×D₄₇	1	2	yes	—
525	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
526	C₂×C₄	C₂³×D₄₇	1	2	yes	—
527	C₂×C₄	C₂³×D₄₇	1	2	yes	—
528	C₂×C₄	C₂³×D₄₇	1	2	yes	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	94	2	no	—
535	C₂²	—	94	2	no	—
536	C₂²	—	94	2	no	—
537	C₂²	—	94	2	no	—
538	C₂²	—	94	2	no	—
539	C₂²	—	94	2	no	—
540	C₂²	—	188	4	no	—
541	C₂²	#41×D₄₇	1	2	yes	—
542	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	2	no	—
550	C₄	—	47	2	no	—
551	C₄	—	47	2	no	—
552	C₄	—	94	2	no	—
553	C₄	—	94	2	no	—
554	C₄	—	94	2	no	—
555	C₄	—	94	1	no	—
556	C₄	—	94	2	no	—
557	C₄	—	94	1	no	—
558	C₂	—	2	2	no	—
559	C₂	—	4	2	no	—
560	C₂	—	188	2	no	—
561	C₂	—	188	2	no	—
562	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
563	C₂	#15689958	1	1	yes	characteristic
564	C₂	#15689960	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#539	C₂
hypercenter	#539	D₄₇
hypocenter	C₄₇	#3455
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #15689743	C₂	semidirect
2. #15689739	C₂	semidirect
3. #15689732	C₂	semidirect
4. #15689725	C₂	semidirect
5. #15689720	C₂	semidirect
6. #15689717	C₂	semidirect
7. #15689713	C₂	semidirect
8. #15689710	C₂	semidirect
9. #15689706	C₂	semidirect
10. #15689675	C₂	semidirect
11. #15689668	C₂	semidirect
12. #15689659	C₂	semidirect
13. #15689658	C₂	semidirect
14. #15689656	C₂	semidirect
15. #15689650	C₂	semidirect
16. #15689631	C₂	semidirect
17. C₄×#10625352	C₂	semidirect
18. C₂×#13093982	C₂	semidirect
19. C₄₇×#539	C₂	semidirect
22. #13094023	C₂²	semidirect
23. #13094023	C₂²	semidirect
24. #13094022	C₂²	semidirect
25. #13094020	C₂²	semidirect
29. #13094019	C₂²	semidirect
30. #13094019	C₂²	semidirect
32. #13094017	C₂²	semidirect
33. #13094015	C₂²	semidirect
34. #13094014	C₂²	semidirect
35. #13094014	C₂²	semidirect
36. #13094014	C₂²	semidirect
41. #13094010	C₂²	semidirect
44. #13094009	C₂²	semidirect
46. #13094008	C₂²	semidirect
49. #13094006	C₂²	semidirect
50. #13094004	C₂²	semidirect
54. #13094002	C₂²	semidirect
56. #13094001	C₂²	semidirect
67. Q₈×Dic₄₇	C₂²	semidirect
68. C₄×Dic₉₄	C₂²	semidirect
69. #13093989	C₂²	semidirect
70. #13093989	C₂²	semidirect
71. #13093989	C₂²	semidirect
73. D₄×Dic₄₇	C₂²	semidirect
76. #13093986	C₂²	semidirect
78. C₄×C₂²⋊D₄₇	C₂²	semidirect
82. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
83. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
88. #13093982	C₂²	semidirect
90. #13093980	C₂²	semidirect
96. C₂×C₄×Dic₄₇	C₂²	semidirect
97. C₄²×D₄₇	C₂²	semidirect
98. #126×C₄₇	C₂²	semidirect
99. #125×C₄₇	C₂²	semidirect
101. #123×C₄₇	C₂²	semidirect
103. C₂²⋊Q₈×C₄₇	C₂²	semidirect
289. #539	D₄₇	semidirect
302. C₄₇	#3455	semidirect
316. #126	C₂×D₄₇	semidirect
321. #125	C₂×D₄₇	semidirect
336. #123	C₂×D₄₇	semidirect
345. C₂²⋊Q₈	C₂×D₄₇	semidirect