Subgroups — #20257300

Order 6016.

1104 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689845	C₂	1	2	yes	maximal, complemented
2	#15689836	C₂	1	2	yes	maximal, complemented
3	#15689829	C₂	1	2	yes	maximal, complemented
4	#15689826	C₂	1	2	yes	maximal, complemented
5	#15689817	C₂	1	2	yes	maximal, complemented
6	#15689785	C₂	1	2	yes	maximal, complemented
7	#15689783	C₂	1	2	yes	maximal, complemented
8	#15689775	C₂	1	2	yes	maximal, complemented
9	#15689746	C₂	1	2	yes	maximal, complemented
10	#15689745	C₂	1	2	yes	maximal, complemented
11	#15689703	C₂	1	2	yes	maximal, complemented
12	#15689678	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689674	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689674	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689673	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄⋊Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689605	C₂	1	2	yes	maximal, complemented
18	C₄×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10625354	C₂²	1	2	yes	—
21	C₂×#10625354	C₂²	1	2	yes	—
22	C₂×#10625350	C₂²	1	1	yes	characteristic
23	C₂×#10625350	C₂²	1	2	yes	—
24	C₂×Q₈×D₄₇	C₂²	1	2	yes	—
25	#13094024	C₂²	1	1	yes	characteristic
26	#13094023	C₂²	1	2	yes	—
27	#13094023	C₂²	1	2	yes	—
28	#13094022	C₂²	1	2	yes	—
29	#13094021	C₂²	1	1	yes	characteristic
30	#13094019	C₂²	1	4	yes	—
31	#13094018	C₂²	1	4	yes	—
32	#13094015	C₂²	1	2	yes	—
33	#13094013	C₂²	1	2	yes	—
34	#13094013	C₂²	1	2	yes	—
35	#13094012	C₂²	1	4	yes	—
36	#13094012	C₂²	1	2	yes	—
37	#13094010	C₂²	1	4	yes	—
38	#13094009	C₂²	1	4	yes	—
39	#13094006	C₂²	1	4	yes	—
40	#13094004	C₂²	1	4	yes	—
41	#13094004	C₂²	1	2	yes	—
42	#13094002	C₂²	1	4	yes	—
43	#13094002	C₂²	1	4	yes	—
44	#13094000	C₂²	1	2	yes	—
45	#13093999	C₂²	1	2	yes	—
46	#13093999	C₂²	1	2	yes	—
47	#13093999	C₂²	1	4	yes	—
48	#13093999	C₂²	1	2	yes	—
49	#13093999	C₂²	1	2	yes	—
50	#13093998	C₂²	1	2	yes	—
51	#13093998	C₂²	1	2	yes	—
52	#13093997	C₂²	1	4	yes	—
53	#13093997	C₂²	1	4	yes	—
54	Q₈×Dic₄₇	C₂²	1	2	yes	—
55	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
56	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
57	#13093989	C₂²	1	2	yes	—
58	C₄×D₁₈₈	C₂²	1	2	yes	—
59	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
60	C₄×D₁₈₈	C₂²	1	4	yes	—
61	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
62	C₄×D₁₈₈	C₂²	1	2	yes	—
63	#13093986	C₂²	1	2	yes	—
64	#13093986	C₂²	1	2	yes	—
65	#13093986	C₂²	1	4	yes	—
66	#13093986	C₂²	1	2	yes	—
67	#13093986	C₂²	1	2	yes	—
68	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
72	#13093983	C₂²	1	1	yes	characteristic
73	#13093982	C₂²	1	2	yes	—
74	#13093981	C₂²	1	1	yes	characteristic
75	#13093981	C₂²	1	4	yes	—
76	#13093981	C₂²	1	1	yes	characteristic
77	C₄⋊C₄×D₄₇	C₂²	1	4	yes	—
78	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
79	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
80	C₄²×D₄₇	C₂²	1	1	yes	characteristic
81	C₄²×D₄₇	C₂²	1	1	yes	characteristic
82	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
83	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
84	#125×C₄₇	C₂²	1	2	yes	—
85	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
86	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
87	C₄×Q₈×C₄₇	C₂²	1	2	yes	—
88	C₄×Q₈×C₄₇	C₂²	1	2	yes	—
89	#117×C₄₇	C₂²	1	2	yes	—
90	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
91	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
92	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
99	#10625354	—	2	8	no	—
100	#10625354	—	4	4	no	—
101	Q₈×D₄₇	—	4	4	no	—
102	#10625350	—	2	4	no	—
103	#10625350	—	4	4	no	—
104	C₂×D₁₈₈	C₂³	1	2	yes	—
105	C₂×D₁₈₈	C₂³	1	4	yes	—
106	C₂×D₁₈₈	C₂³	1	2	yes	—
107	C₂×D₁₈₈	C₂³	1	2	yes	—
108	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
109	C₂×D₁₈₈	C₂³	1	4	yes	—
110	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
112	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
114	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
115	C₂×C₄×D₄₇	C₂³	1	4	yes	—
116	C₂×C₄×D₄₇	C₂³	1	4	yes	—
117	C₂×C₄×D₄₇	C₂³	1	4	yes	—
118	C₂×C₄×D₄₇	C₂³	1	4	yes	—
119	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
120	C₂×Dic₉₄	C₂³	1	2	yes	—
121	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
122	C₂×Dic₉₄	C₂³	1	4	yes	—
123	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
124	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
125	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
126	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
127	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
128	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
129	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
130	C₄²×C₄₇	C₂³	1	1	yes	characteristic
131	C₄²×C₄₇	C₂³	1	1	yes	characteristic
132	C₄²×C₄₇	C₂³	1	1	yes	characteristic
133	C₄²×C₄₇	C₂³	1	1	yes	characteristic
134	C₄²×C₄₇	C₂³	1	4	yes	—
135	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
136	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
137	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
138	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
139	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
140	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
141	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
142	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
143	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
144	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
145	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
146	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
147	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
148	C₄⋊Dic₄₇	C₂³	1	2	yes	—
149	C₄⋊Dic₄₇	C₂³	1	2	yes	—
150	C₄⋊Dic₄₇	C₂³	1	4	yes	—
151	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
153	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
154	Dic₄₇⋊C₄	C₂³	1	4	yes	—
155	Dic₄₇⋊C₄	C₂³	1	4	yes	—
156	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
157	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
158	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
159	Dic₄₇⋊C₄	C₂³	1	4	yes	—
160	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
161	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
162	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
163	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
164	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
165	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
166	C₄×Dic₄₇	C₂³	1	4	yes	—
167	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
168	C₂²×D₄₇	C₂⁴	1	4	yes	—
169	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
170	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
171	Q₈×C₄₇	—	2	4	no	—
172	Q₈×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
177	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
180	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
184	C₂²⋊D₄₇	—	2	2	no	—
185	C₂²⋊D₄₇	—	2	2	no	—
186	C₂²⋊D₄₇	—	4	4	no	—
187	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
188	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
189	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
190	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
191	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₄₇	C₂⁴	1	4	yes	—
193	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
194	D₁₈₈	—	2	2	no	—
195	D₁₈₈	—	2	8	no	—
196	D₁₈₈	—	2	4	no	—
197	D₁₈₈	—	2	4	no	—
198	D₁₈₈	—	2	4	no	—
199	D₁₈₈	—	4	4	no	—
200	C₄×D₄₇	—	2	2	no	—
201	C₄×D₄₇	—	2	2	no	—
202	C₄×D₄₇	—	2	2	no	—
203	C₄×D₄₇	—	2	2	no	—
204	C₄×D₄₇	—	2	2	no	—
205	C₄×D₄₇	—	2	8	no	—
206	C₄×D₄₇	—	4	4	no	—
207	C₄×D₄₇	—	4	4	no	—
208	C₄×D₄₇	—	4	4	no	—
209	C₄×D₄₇	#41	1	4	yes	complemented
210	Dic₉₄	—	2	4	no	—
211	Dic₉₄	—	2	2	no	—
212	Dic₉₄	—	4	4	no	—
213	C₂²×C₄₇	—	2	1	no	—
214	C₂²×C₄₇	—	2	1	no	—
215	C₂²×C₄₇	—	2	1	no	—
216	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
217	C₂×D₄₇	—	2	1	no	—
218	C₂×D₄₇	—	2	1	no	—
219	C₂×D₄₇	—	2	4	no	—
220	C₂×D₄₇	—	2	1	no	—
221	C₂×D₄₇	—	2	1	no	—
222	C₂×D₄₇	—	2	4	no	—
223	C₂×D₄₇	—	2	1	no	—
224	C₂×D₄₇	—	2	4	no	—
225	C₂×D₄₇	C₂×#41	1	2	yes	—
226	C₄×C₄₇	—	2	1	no	—
227	C₄×C₄₇	—	2	4	no	—
228	C₄×C₄₇	—	2	4	no	—
229	C₄×C₄₇	—	2	1	no	—
230	C₄×C₄₇	—	2	1	no	—
231	C₄×C₄₇	C₂×#41	1	2	yes	—
232	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
233	C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
234	Dic₄₇	—	2	1	no	—
235	Dic₄₇	—	2	4	no	—
236	Dic₄₇	—	2	1	no	—
237	Dic₄₇	—	2	1	no	—
238	Dic₄₇	—	2	1	no	—
239	Dic₄₇	—	2	1	no	—
240	Dic₄₇	C₂×#41	1	2	yes	—
241	#3511	—	47	1	no	maximal, Sylow
242	C₂×C₄₇	—	4	1	no	—
243	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
244	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
246	D₄₇	—	2	2	no	—
247	D₄₇	—	4	4	no	—
248	D₄₇	—	4	1	no	—
249	#556	—	47	2	no	—
250	#555	—	47	2	no	—
251	#554	—	47	2	no	—
252	#553	—	47	2	no	—
253	#553	—	47	2	no	—
254	#548	—	47	2	no	—
255	#548	—	47	2	no	—
256	#547	—	47	2	no	—
257	#542	—	47	2	no	—
258	#542	—	47	2	no	—
259	#537	—	47	2	no	—
260	#533	—	47	1	no	—
261	#533	D₄₇	1	1	yes	characteristic, complemented
262	#532	—	47	1	no	—
263	#532	—	47	1	no	—
264	#532	—	47	1	no	—
265	C₂×C₄⋊Q₈	—	47	1	no	—
266	#520	—	47	2	no	—
267	C₄×#41	—	47	1	no	—
268	C₄₇	#3511	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	47	2	no	—
270	C₂×#41	—	47	2	no	—
271	C₂×#41	—	47	1	no	—
272	C₂×#41	—	47	2	no	—
273	C₂²×Q₈	—	47	2	no	—
274	C₄⋊Q₈	—	47	2	no	—
275	C₄⋊Q₈	—	47	2	no	—
276	C₄⋊Q₈	—	47	2	no	—
277	C₄⋊Q₈	—	47	1	no	—
278	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
279	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
280	#127	—	47	1	no	—
281	#126	—	47	4	no	—
282	#126	—	47	4	no	—
283	#125	—	47	2	no	—
284	#125	C₂×D₄₇	1	2	yes	—
285	#124	—	47	2	no	—
286	#124	—	47	2	no	—
287	#124	—	47	4	no	—
288	#124	—	47	2	no	—
289	#124	—	47	4	no	—
290	#123	—	47	4	no	—
291	#123	—	47	4	no	—
292	C₂²⋊Q₈	—	47	2	no	—
293	C₂²⋊Q₈	—	47	2	no	—
294	C₂²⋊Q₈	—	47	4	no	—
295	C₂²⋊Q₈	—	47	4	no	—
296	C₂²⋊Q₈	—	47	4	no	—
297	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
298	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
299	#121	—	47	2	no	—
300	#121	—	47	2	no	—
301	#121	—	47	2	no	—
302	#121	—	47	2	no	—
303	#121	—	47	2	no	—
304	#121	—	47	2	no	—
305	#121	—	47	4	no	—
306	#121	—	47	4	no	—
307	#121	—	47	4	no	—
308	C₄×Q₈	—	47	2	no	—
309	C₄×Q₈	—	47	2	no	—
310	C₄×Q₈	—	47	1	no	—
311	C₄×Q₈	—	47	1	no	—
312	C₄×Q₈	C₂×D₄₇	1	2	yes	—
313	C₄×Q₈	C₂×D₄₇	1	2	yes	—
314	C₄×D₄	—	47	1	no	—
315	C₄×D₄	—	47	1	no	—
316	C₄×D₄	—	47	1	no	—
317	C₄×D₄	—	47	1	no	—
318	C₄×D₄	—	47	2	no	—
319	C₄×D₄	—	47	4	no	—
320	C₄×D₄	—	47	2	no	—
321	C₄×D₄	—	47	2	no	—
322	C₄×D₄	—	47	2	no	—
323	C₄×D₄	—	47	1	no	—
324	C₄×D₄	—	47	1	no	—
325	C₄×D₄	—	47	2	no	—
326	C₄×D₄	—	47	4	no	—
327	C₄×D₄	—	47	2	no	—
328	#117	—	47	1	no	—
329	#117	—	47	2	no	—
330	#117	—	47	1	no	—
331	#117	—	47	1	no	—
332	#117	—	47	4	no	—
333	#117	C₂×D₄₇	1	2	yes	—
334	C₂×C₄⋊C₄	—	47	2	no	—
335	C₂×C₄⋊C₄	—	47	4	no	—
336	C₂×C₄⋊C₄	—	47	2	no	—
337	C₂×C₄²	—	47	1	no	—
338	C₂×C₄²	—	47	1	no	—
339	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
340	#41	—	94	4	no	—
341	#41	—	94	8	no	—
342	#41	—	188	4	no	—
343	#41	—	188	4	no	—
344	C₂×Q₈	—	47	1	no	—
345	C₂×Q₈	—	47	2	no	—
346	C₂×Q₈	—	47	4	no	—
347	C₂×Q₈	—	188	4	no	—
348	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
349	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
350	C₂×D₄	—	47	1	no	—
351	C₂×D₄	—	47	1	no	—
352	C₂×D₄	—	47	4	no	—
353	C₂×D₄	—	47	2	no	—
354	C₂×D₄	—	47	4	no	—
355	C₂×D₄	—	47	1	no	—
356	C₂×D₄	—	47	2	no	—
357	C₂×D₄	—	47	2	no	—
358	C₂×D₄	—	47	4	no	—
359	C₂²×C₄	—	47	1	no	—
360	C₂²×C₄	—	47	1	no	—
361	C₂²×C₄	—	47	1	no	—
362	C₂²×C₄	—	47	1	no	—
363	C₂²×C₄	—	47	1	no	—
364	C₂²×C₄	—	47	1	no	—
365	C₂²×C₄	—	47	4	no	—
366	C₂²×C₄	—	47	4	no	—
367	C₂²×C₄	—	47	4	no	—
368	C₂²×C₄	—	47	4	no	—
369	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
370	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
371	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
372	C₄⋊C₄	—	47	1	no	—
373	C₄⋊C₄	—	47	4	no	—
374	C₄⋊C₄	—	47	4	no	—
375	C₄⋊C₄	—	47	1	no	—
376	C₄⋊C₄	—	47	1	no	—
377	C₄⋊C₄	—	47	1	no	—
378	C₄⋊C₄	—	47	4	no	—
379	C₄⋊C₄	—	47	2	no	—
380	C₄⋊C₄	—	47	2	no	—
381	C₄⋊C₄	—	47	4	no	—
382	C₄⋊C₄	—	47	1	no	—
383	C₄⋊C₄	—	47	1	no	—
384	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
385	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
386	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
387	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
388	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
389	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
390	C₂²⋊C₄	—	47	1	no	—
391	C₂²⋊C₄	—	47	1	no	—
392	C₂²⋊C₄	—	47	1	no	—
393	C₂²⋊C₄	—	47	1	no	—
394	C₂²⋊C₄	—	47	4	no	—
395	C₂²⋊C₄	—	47	4	no	—
396	C₂²⋊C₄	—	47	1	no	—
397	C₂²⋊C₄	—	47	1	no	—
398	C₂²⋊C₄	—	47	4	no	—
399	C₂²⋊C₄	—	47	4	no	—
400	C₂²⋊C₄	—	47	4	no	—
401	C₂²⋊C₄	—	47	4	no	—
402	C₂²⋊C₄	—	47	4	no	—
403	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
404	C₄²	—	47	1	no	—
405	C₄²	—	47	1	no	—
406	C₄²	—	47	1	no	—
407	C₄²	—	47	1	no	—
408	C₄²	—	47	1	no	—
409	C₄²	—	47	1	no	—
410	C₄²	—	47	4	no	—
411	C₄²	C₂²×D₄₇	1	1	yes	characteristic
412	C₄²	C₂²×D₄₇	1	1	yes	characteristic
413	C₄²	C₂²×D₄₇	1	1	yes	characteristic
414	C₄²	C₂²×D₄₇	1	1	yes	characteristic
415	C₄²	C₂²×D₄₇	1	4	yes	—
416	C₂³	—	47	1	no	—
417	C₂³	—	47	1	no	—
418	C₂³	—	47	4	no	—
419	C₂³	C₂³×D₄₇	1	1	yes	characteristic
420	Q₈	—	2	4	no	—
421	Q₈	—	2	4	no	—
422	Q₈	—	94	2	no	—
423	Q₈	—	94	4	no	—
424	Q₈	—	188	4	no	—
425	D₄	—	94	2	no	—
426	D₄	—	94	8	no	—
427	D₄	—	94	2	no	—
428	D₄	—	94	2	no	—
429	D₄	—	94	4	no	—
430	D₄	—	94	4	no	—
431	D₄	—	94	4	no	—
432	D₄	—	188	4	no	—
433	D₄	—	188	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	47	1	no	—
438	C₂×C₄	—	47	4	no	—
439	C₂×C₄	—	47	1	no	—
440	C₂×C₄	—	47	1	no	—
441	C₂×C₄	—	47	1	no	—
442	C₂×C₄	—	47	1	no	—
443	C₂×C₄	—	47	1	no	—
444	C₂×C₄	—	47	4	no	—
445	C₂×C₄	—	94	8	no	—
446	C₂×C₄	—	94	2	no	—
447	C₂×C₄	—	94	2	no	—
448	C₂×C₄	—	94	2	no	—
449	C₂×C₄	—	94	2	no	—
450	C₂×C₄	—	94	2	no	—
451	C₂×C₄	—	188	4	no	—
452	C₂×C₄	—	188	4	no	—
453	C₂×C₄	—	188	4	no	—
454	C₂×C₄	C₂³×D₄₇	1	4	yes	—
455	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
456	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
457	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
458	C₂×C₄	C₂³×D₄₇	1	4	yes	—
459	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
460	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
461	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	47	2	no	—
466	C₂²	—	94	1	no	—
467	C₂²	—	94	1	no	—
468	C₂²	—	94	4	no	—
469	C₂²	—	94	1	no	—
470	C₂²	—	94	1	no	—
471	C₂²	—	94	4	no	—
472	C₂²	—	94	1	no	—
473	C₂²	—	94	4	no	—
474	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	4	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	1	no	—
480	C₄	—	47	2	no	—
481	C₄	—	94	1	no	—
482	C₄	—	94	1	no	—
483	C₄	—	94	1	no	—
484	C₄	—	94	4	no	—
485	C₄	—	94	1	no	—
486	C₄	—	94	1	no	—
487	C₄	#41×D₄₇	1	2	yes	—
488	C₄	#13094070	1	2	yes	—
489	C₄	#13094072	1	2	yes	—
490	C₂	—	4	1	no	—
491	C₂	—	94	2	no	—
492	C₂	—	188	1	no	—
493	C₂	—	188	4	no	—
494	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
495	C₂	C₂×#13094070	1	1	yes	characteristic
496	C₂	C₂×#13094072	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#533	C₂
hypercenter	#533	D₄₇
hypocenter	C₄₇	#3511
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #15689845	C₂	semidirect
2. #15689836	C₂	semidirect
3. #15689829	C₂	semidirect
4. #15689826	C₂	semidirect
5. #15689817	C₂	semidirect
6. #15689785	C₂	semidirect
7. #15689783	C₂	semidirect
8. #15689775	C₂	semidirect
9. #15689746	C₂	semidirect
10. #15689745	C₂	semidirect
11. #15689703	C₂	semidirect
12. #15689678	C₂	semidirect
13. #15689674	C₂	semidirect
14. #15689674	C₂	semidirect
15. #15689673	C₂	semidirect
16. C₄⋊Q₈×D₄₇	C₂	semidirect
17. #15689605	C₂	semidirect
18. C₄×#10625350	C₂	semidirect
19. C₄₇×#533	C₂	semidirect
209. C₄×D₄₇	#41	semidirect
261. #533	D₄₇	semidirect
268. C₄₇	#3511	semidirect