Subgroups — #27086132

Order 12032.

1878 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256777	C₂	1	2	yes	maximal, complemented
2	#20254044	C₂	1	2	yes	maximal, complemented
3	#20254035	C₂	1	2	yes	maximal, complemented
4	#20254024	C₂	1	4	yes	maximal, complemented
5	#20254013	C₂	1	4	yes	maximal, complemented
6	#20254002	C₂	1	4	yes	maximal, complemented
7	#20253902	C₂	1	1	yes	maximal, characteristic, complemented
8	#20253733	C₂	1	2	yes	maximal, complemented
9	#20252993	C₂	1	2	yes	maximal, complemented
10	#20252965	C₂	1	2	yes	maximal, complemented
11	#20252189	C₂	1	2	yes	maximal, complemented
12	#135×Dic₄₇	C₂	1	2	yes	maximal, complemented
13	C₂×#15689077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#10625324	C₂²	1	1	yes	characteristic
16	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
17	#15689742	C₂²	1	8	yes	—
18	#15689734	C₂²	1	4	yes	—
19	#15689727	C₂²	1	4	yes	—
20	#15689718	—	2	4	no	—
21	#15689710	—	2	4	no	—
22	#15689680	C₂²	1	2	yes	—
23	#15689653	—	2	8	no	—
24	#15689630	C₂²	1	4	yes	—
25	#41×Dic₄₇	C₂²	1	4	yes	—
26	C₂×#13093981	C₂²	1	1	yes	characteristic
27	#15689528	C₂²	1	2	yes	complemented
28	#15689525	C₂²	1	2	yes	complemented
29	#15689525	C₂²	1	2	yes	complemented
30	#15689521	C₂²	1	2	yes	complemented
31	#15689491	C₂²	1	4	yes	complemented
32	#15689487	C₂²	1	4	yes	complemented
33	#15689482	C₂²	1	8	yes	complemented
34	#15689378	C₂²	1	4	yes	—
35	#15689373	C₂²	1	4	yes	—
36	#15689366	C₂²	1	8	yes	—
37	#15689361	C₂²	1	4	yes	—
38	#15689356	C₂²	1	4	yes	—
39	#15689349	C₂²	1	8	yes	—
40	#15689235	C₂²	1	4	yes	complemented
41	#15689230	C₂²	1	4	yes	complemented
42	#15689224	C₂²	1	8	yes	complemented
43	Q₁₆×Dic₄₇	C₂²	1	4	yes	complemented
44	SD₁₆×Dic₄₇	C₂²	1	8	yes	complemented
45	D₈×Dic₄₇	C₂²	1	4	yes	complemented
46	#15689161	C₂²	1	2	yes	—
47	#15689161	C₂²	1	2	yes	—
48	#15689119	C₂²	1	4	yes	—
49	#15689119	C₂²	1	4	yes	—
50	#15689077	C₂²	1	2	yes	—
51	#15689077	C₂²	1	2	yes	—
52	#15689077	C₂²	1	2	yes	—
53	#15689077	C₂²	1	2	yes	—
54	C₂×#13093935	C₂²	1	1	yes	characteristic
55	C₂×#13093934	C₂²	1	1	yes	characteristic
56	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
57	C₂×#135×C₄₇	C₂²	1	2	yes	—
58	C₂×#135×C₄₇	C₂²	1	2	yes	—
59	C₄₇×#532	C₂²	1	2	yes	—
60	C₄₇×#495	C₂²	1	2	yes	complemented
61	C₄₇×#495	C₂²	1	2	yes	complemented
62	C₄₇×#494	C₂²	1	1	yes	characteristic, complemented
63	C₄₇×#493	C₂²	1	1	yes	characteristic, complemented
64	C₄₇×#492	C₂²	1	2	yes	complemented
65	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
66	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
67	C₂×#10625324	—	2	4	no	—
68	C₂×#10625324	C₂³	1	2	yes	—
69	C₂×#10625324	C₂³	1	2	yes	—
70	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
72	C₂×C₈×D₄₇	—	2	4	no	—
73	C₂×C₈×D₄₇	C₂³	1	2	yes	—
74	C₂×C₈×D₄₇	C₂³	1	2	yes	—
75	#13094024	C₂³	1	4	yes	—
76	#13094019	—	2	8	no	—
77	#13094017	—	2	8	no	—
78	#13094016	C₂³	1	4	yes	—
79	#13094014	—	2	8	no	—
80	#13094010	—	2	8	no	—
81	#13094008	—	2	8	no	—
82	#13094005	—	2	4	no	—
83	#13094005	—	2	8	no	—
84	#13094003	—	2	4	no	—
85	#13094001	—	2	8	no	—
86	#13094000	C₂³	1	8	yes	—
87	#13093996	—	2	8	no	—
88	#13093995	C₂³	1	8	yes	—
89	#13093992	—	2	4	no	—
90	Q₈×Dic₄₇	C₂³	1	8	yes	—
91	C₄×Dic₉₄	—	2	4	no	—
92	D₄×Dic₄₇	—	2	8	no	—
93	D₄×Dic₄₇	C₂³	1	8	yes	—
94	C₄×C₂²⋊D₄₇	—	2	8	no	—
95	#13093983	—	2	4	no	—
96	#13093983	C₂³	1	4	yes	—
97	#13093981	D₄	1	4	yes	—
98	#13093981	C₂³	1	2	yes	—
99	#13093981	C₂³	1	2	yes	—
100	C₂×Dic₄₇⋊C₄	D₄	1	2	yes	—
101	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
102	C₂×C₄×Dic₄₇	—	2	4	no	—
103	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
104	#13093958	C₂³	1	4	yes	—
105	#13093958	C₂³	1	4	yes	—
106	#13093956	C₂³	1	4	yes	—
107	#13093956	C₂³	1	4	yes	—
108	#13093948	C₂³	1	8	yes	—
109	#13093948	C₂³	1	8	yes	—
110	#13093945	C₂³	1	8	yes	—
111	#13093945	C₂³	1	8	yes	—
112	#13093935	C₂³	1	2	yes	—
113	#13093935	C₂³	1	2	yes	—
114	#13093934	C₂³	1	2	yes	—
115	#13093934	C₂³	1	2	yes	—
116	C₈×Dic₄₇	C₂³	1	2	yes	—
117	C₈×Dic₄₇	C₂³	1	2	yes	—
118	C₂×#41×C₄₇	C₂³	1	4	yes	—
119	#135×C₄₇	—	2	8	no	—
120	#135×C₄₇	—	2	8	no	—
121	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₄₇	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₄₇	C₂³	1	4	yes	—
125	C₂×D₈×C₄₇	C₂³	1	2	yes	—
126	C₂×D₈×C₄₇	C₂³	1	2	yes	—
127	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
129	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
130	#127×C₄₇	C₂³	1	2	yes	—
131	#124×C₄₇	C₂³	1	4	yes	—
132	#121×C₄₇	—	2	4	no	—
133	C₄×D₄×C₄₇	—	2	4	no	—
134	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
135	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
136	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
139	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
140	#41×C₄₇	—	2	8	no	—
141	#41×C₄₇	—	2	8	no	—
142	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
143	C₂×D₄×C₄₇	—	2	4	no	—
144	C₂×D₄×C₄₇	—	2	4	no	—
145	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₄₇	—	2	4	no	—
147	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
149	C₂×C₂²⋊D₄₇	—	2	8	no	—
150	C₂²×Dic₄₇	—	2	8	no	—
151	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
153	C₂×C₄×D₄₇	—	2	2	no	—
154	C₂×C₄×D₄₇	—	2	2	no	—
155	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
156	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
157	C₂×Dic₉₄	—	2	4	no	—
158	Q₁₆×C₄₇	—	2	4	no	—
159	Q₁₆×C₄₇	—	2	4	no	—
160	SD₁₆×C₄₇	—	2	8	no	—
161	SD₁₆×C₄₇	—	2	8	no	—
162	D₈×C₄₇	—	2	4	no	—
163	D₈×C₄₇	—	2	4	no	—
164	C₂×C₈×C₄₇	#41	1	4	yes	—
165	C₂×C₈×C₄₇	#41	1	4	yes	—
166	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
167	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
168	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₄⋊C₄×C₄₇	—	2	4	no	—
171	C₂²⋊C₄×C₄₇	—	2	8	no	—
172	C₄²×C₄₇	C₂×D₄	1	2	yes	—
173	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
174	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
175	C₂²⋊Dic₄₇	—	2	4	no	—
176	C₂²⋊Dic₄₇	—	2	8	no	—
177	C₂²⋊Dic₄₇	—	2	8	no	—
178	(C₂×D₄₇)⋊C₄	—	2	8	no	—
179	(C₂×D₄₇)⋊C₄	C₂×D₄	1	4	yes	—
180	(C₂×D₄₇)⋊C₄	C₂×D₄	1	4	yes	—
181	C₄⋊Dic₄₇	—	2	4	no	—
182	C₄⋊Dic₄₇	—	2	8	no	—
183	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
184	Dic₄₇⋊C₄	—	2	8	no	—
185	Dic₄₇⋊C₄	—	2	8	no	—
186	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
187	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
188	C₄×Dic₄₇	—	2	4	no	—
189	C₄×Dic₄₇	—	2	8	no	—
190	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
191	C₄×Dic₄₇	C₂⁴	1	2	yes	—
192	C₂×C₄₇⋊C₈	—	2	2	no	—
193	C₂×C₄₇⋊C₈	—	2	2	no	—
194	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
195	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
196	#10625324	—	2	4	no	—
197	#10625324	—	2	4	no	—
198	C₈×D₄₇	—	2	4	no	—
199	C₈×D₄₇	—	2	4	no	—
200	C₂³×C₄₇	—	2	4	no	—
201	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
202	C₂²×D₄₇	—	2	2	no	—
203	C₂²×D₄₇	—	4	2	no	—
204	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
205	Q₈×C₄₇	—	2	4	no	—
206	Q₈×C₄₇	—	2	4	no	—
207	D₄×C₄₇	—	2	4	no	—
208	D₄×C₄₇	—	2	4	no	—
209	D₄×C₄₇	—	4	8	no	—
210	D₄×C₄₇	—	8	4	no	—
211	C₂×C₄×C₄₇	—	2	4	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	8	no	—
214	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
218	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
219	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
220	C₂²⋊D₄₇	—	8	8	no	—
221	C₂×Dic₄₇	—	2	2	no	—
222	C₂×Dic₄₇	—	2	8	no	—
223	C₂×Dic₄₇	—	4	2	no	—
224	C₂×Dic₄₇	—	8	8	no	—
225	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
226	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
227	C₄×D₄₇	—	2	4	no	—
228	C₄×D₄₇	—	2	2	no	—
229	C₄×D₄₇	—	2	2	no	—
230	Dic₉₄	—	8	4	no	—
231	C₈×C₄₇	C₂×#41	1	2	yes	—
232	C₈×C₄₇	C₂×#41	1	2	yes	—
233	C₈×C₄₇	C₂×#41	1	2	yes	—
234	C₈×C₄₇	C₂×#41	1	2	yes	—
235	C₄₇⋊C₈	—	2	2	no	—
236	C₄₇⋊C₈	—	2	2	no	—
237	#60682	—	47	1	no	maximal, Sylow
238	C₂²×C₄₇	—	2	2	no	—
239	C₂²×C₄₇	—	4	8	no	—
240	C₂²×C₄₇	—	4	4	no	—
241	C₂²×C₄₇	#532	1	2	yes	—
242	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
243	C₂×D₄₇	—	2	4	no	—
244	C₂×D₄₇	—	2	2	no	—
245	C₂×D₄₇	—	4	4	no	—
246	C₄×C₄₇	—	2	2	no	—
247	C₄×C₄₇	—	2	2	no	—
248	C₄×C₄₇	—	4	4	no	—
249	C₄×C₄₇	#532	1	2	yes	—
250	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
251	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
252	Dic₄₇	—	2	4	no	—
253	Dic₄₇	—	2	2	no	—
254	Dic₄₇	—	4	8	no	—
255	#3455	—	47	2	no	—
256	#3177	—	47	2	no	—
257	#3176	—	47	2	no	—
258	#3175	—	47	4	no	—
259	#3174	—	47	4	no	—
260	#3173	—	47	4	no	—
261	#3160	—	47	1	no	—
262	#3147	D₄₇	1	1	yes	characteristic, complemented
263	#3135	—	47	2	no	—
264	#3054	—	47	2	no	—
265	#3050	—	47	2	no	—
266	#2943	—	47	2	no	—
267	C₄×#135	—	47	2	no	—
268	C₂×#405	—	47	1	no	—
269	C₂×C₄₇	—	2	2	no	—
270	C₂×C₄₇	—	8	4	no	—
271	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
272	C₂×C₄₇	#3584	1	2	yes	—
273	D₄₇	—	4	2	no	—
274	C₂×#135	C₂×D₄₇	1	2	yes	—
275	C₂×#135	C₂×D₄₇	1	2	yes	—
276	C₂²×M₁₆	—	47	1	no	—
277	C₂³×C₈	—	47	1	no	—
278	#542	—	47	8	no	—
279	#541	—	47	4	no	—
280	#540	—	47	4	no	—
281	#539	—	94	4	no	—
282	#538	—	94	4	no	—
283	#533	—	47	2	no	—
284	#532	C₂×D₄₇	1	2	yes	—
285	#529	—	94	8	no	—
286	#525	—	47	4	no	—
287	C₄×#41	—	47	4	no	—
288	C₂×#117	—	47	1	no	—
289	#500	—	47	2	no	—
290	#499	—	47	2	no	—
291	#499	—	47	2	no	—
292	#498	—	47	2	no	—
293	#495	C₂×D₄₇	1	2	yes	complemented
294	#495	C₂×D₄₇	1	2	yes	complemented
295	#494	C₂×D₄₇	1	1	yes	characteristic, complemented
296	#493	C₂×D₄₇	1	1	yes	characteristic, complemented
297	#492	C₂×D₄₇	1	2	yes	complemented
298	#491	—	47	4	no	—
299	#490	—	47	4	no	—
300	#489	—	47	8	no	—
301	#470	—	47	4	no	—
302	#469	—	47	4	no	—
303	#468	—	47	8	no	—
304	#467	—	47	4	no	—
305	#466	—	47	4	no	—
306	#465	—	47	8	no	—
307	#442	—	47	4	no	—
308	#441	—	47	4	no	—
309	#440	—	47	8	no	—
310	C₄×Q₁₆	—	47	4	no	—
311	C₄×SD₁₆	—	47	8	no	—
312	C₄×D₈	—	47	4	no	—
313	#427	—	47	2	no	—
314	#427	—	47	2	no	—
315	#416	—	47	4	no	—
316	#416	—	47	4	no	—
317	#405	—	47	2	no	—
318	#405	—	47	2	no	—
319	#405	—	47	2	no	—
320	#405	—	47	2	no	—
321	C₂×#97	—	47	1	no	—
322	C₂×#97	—	47	1	no	—
323	C₂×C₄×C₈	—	47	1	no	—
324	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
325	C₄₇	#60682	1	1	yes	characteristic, complemented, Sylow
326	C₂×#41	C₂²×D₄₇	1	4	yes	—
327	C₂³×C₄	—	47	1	no	—
328	#135	—	2	8	no	—
329	#135	—	2	8	no	—
330	C₂×Q₁₆	C₂²×D₄₇	1	2	yes	—
331	C₂×Q₁₆	C₂²×D₄₇	1	2	yes	—
332	C₂×SD₁₆	C₂²×D₄₇	1	4	yes	—
333	C₂×SD₁₆	C₂²×D₄₇	1	4	yes	—
334	C₂×D₈	C₂²×D₄₇	1	2	yes	—
335	C₂×D₈	C₂²×D₄₇	1	2	yes	—
336	C₂×M₁₆	—	47	2	no	—
337	C₂×M₁₆	—	47	2	no	—
338	C₂×M₁₆	—	94	4	no	—
339	C₂²×C₈	—	47	1	no	—
340	C₂²×C₈	—	47	1	no	—
341	C₂²×C₈	—	47	2	no	—
342	C₂²×C₈	—	47	2	no	—
343	C₂²×C₈	—	94	4	no	—
344	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
346	C₄⋊Q₈	—	47	4	no	—
347	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
348	#127	C₂²×D₄₇	1	2	yes	—
349	#126	—	94	8	no	—
350	#126	—	94	8	no	—
351	#125	—	47	4	no	—
352	#125	—	94	8	no	—
353	#124	—	94	8	no	—
354	#124	C₂²×D₄₇	1	4	yes	—
355	#123	—	94	8	no	—
356	#123	—	94	8	no	—
357	#123	—	94	4	no	—
358	C₂²⋊Q₈	—	47	8	no	—
359	C₂²⋊Q₈	—	94	8	no	—
360	C₂²⋊Q₈	—	94	4	no	—
361	#121	—	2	4	no	—
362	#121	—	47	8	no	—
363	#121	—	94	8	no	—
364	#120	—	94	4	no	—
365	C₄×Q₈	—	47	8	no	—
366	C₄×Q₈	—	94	4	no	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	—	47	8	no	—
369	C₄×D₄	—	94	8	no	—
370	C₄×D₄	—	94	8	no	—
371	#117	—	47	4	no	—
372	#117	—	47	2	no	—
373	#117	—	47	2	no	—
374	#117	—	47	4	no	—
375	#117	—	94	4	no	—
376	C₂×C₄⋊C₄	—	47	2	no	—
377	C₂×C₂²⋊C₄	—	47	2	no	—
378	C₂×C₄²	—	47	1	no	—
379	C₂×C₄²	—	94	4	no	—
380	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
381	#107	—	47	4	no	—
382	#107	—	47	4	no	—
383	#106	—	47	4	no	—
384	#106	—	47	4	no	—
385	#103	—	47	8	no	—
386	#103	—	47	8	no	—
387	#102	—	47	8	no	—
388	#102	—	47	8	no	—
389	#97	—	47	2	no	—
390	#97	—	47	2	no	—
391	#97	—	47	2	no	—
392	#97	—	47	2	no	—
393	C₄×C₈	—	47	2	no	—
394	C₄×C₈	—	47	2	no	—
395	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
396	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
397	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
398	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
399	C₂⁴	—	47	1	no	—
400	#41	—	2	8	no	—
401	#41	—	2	8	no	—
402	C₂×Q₈	—	94	4	no	—
403	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	94	8	no	—
407	C₂×D₄	C₂³×D₄₇	1	4	yes	—
408	C₂²×C₄	—	2	4	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	—	94	8	no	—
414	C₂²×C₄	—	94	2	no	—
415	C₂²×C₄	—	94	2	no	—
416	C₂²×C₄	D₄×D₄₇	1	2	yes	—
417	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
418	Q₁₆	—	2	4	no	—
419	Q₁₆	—	2	4	no	—
420	SD₁₆	—	2	8	no	—
421	SD₁₆	—	2	8	no	—
422	D₈	—	2	4	no	—
423	D₈	—	2	4	no	—
424	M₁₆	—	94	4	no	—
425	M₁₆	—	94	4	no	—
426	C₂×C₈	—	47	2	no	—
427	C₂×C₈	—	47	2	no	—
428	C₂×C₈	—	94	2	no	—
429	C₂×C₈	—	94	2	no	—
430	C₂×C₈	—	94	4	no	—
431	C₂×C₈	—	94	4	no	—
432	C₂×C₈	#10625352	1	4	yes	—
433	C₂×C₈	#10625352	1	4	yes	—
434	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
435	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
436	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
437	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	47	4	no	—
440	C₄⋊C₄	—	47	4	no	—
441	C₄⋊C₄	—	47	8	no	—
442	C₄⋊C₄	—	94	8	no	—
443	C₄⋊C₄	—	94	8	no	—
444	C₄⋊C₄	—	94	8	no	—
445	C₄⋊C₄	—	94	4	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₂²⋊C₄	—	47	4	no	—
448	C₂²⋊C₄	—	47	4	no	—
449	C₂²⋊C₄	—	94	8	no	—
450	C₂²⋊C₄	—	94	8	no	—
451	C₂²⋊C₄	—	94	8	no	—
452	C₂²⋊C₄	—	94	4	no	—
453	C₄²	—	47	2	no	—
454	C₄²	—	47	2	no	—
455	C₄²	—	94	8	no	—
456	C₄²	—	94	4	no	—
457	C₄²	D₄×D₄₇	1	2	yes	—
458	C₄²	C₂³×D₄₇	1	1	yes	characteristic
459	C₄²	C₂³×D₄₇	1	1	yes	characteristic
460	C₂³	—	2	4	no	—
461	C₂³	—	47	2	no	—
462	C₂³	—	94	2	no	—
463	C₂³	—	188	2	no	—
464	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
465	Q₈	—	2	4	no	—
466	Q₈	—	2	4	no	—
467	Q₈	—	376	4	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	4	no	—
470	D₄	—	4	8	no	—
471	D₄	—	8	4	no	—
472	D₄	—	376	8	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	8	no	—
476	C₂×C₄	—	47	4	no	—
477	C₂×C₄	—	47	2	no	—
478	C₂×C₄	—	94	2	no	—
479	C₂×C₄	—	94	4	no	—
480	C₂×C₄	—	94	2	no	—
481	C₂×C₄	—	94	2	no	—
482	C₂×C₄	—	94	8	no	—
483	C₂×C₄	—	376	8	no	—
484	C₂×C₄	—	188	2	no	—
485	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
486	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
487	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
488	C₂×C₄	C₂×#10625352	1	2	yes	—
489	C₂×C₄	C₂×#10625352	1	2	yes	—
490	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
491	C₈	—	94	2	no	—
492	C₈	—	94	2	no	—
493	C₈	C₂×#10625352	1	2	yes	—
494	C₈	C₂×#10625352	1	2	yes	—
495	C₈	C₂×#10625352	1	2	yes	—
496	C₈	C₂×#10625352	1	2	yes	—
497	C₂²	—	2	2	no	—
498	C₂²	—	4	8	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	94	4	no	—
501	C₂²	—	94	2	no	—
502	C₂²	—	188	4	no	—
503	C₂²	#15689671	1	2	yes	—
504	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	4	4	no	—
508	C₄	—	94	4	no	—
509	C₄	—	94	2	no	—
510	C₄	—	188	8	no	—
511	C₄	#15689671	1	2	yes	—
512	C₄	C₂²×#10625352	1	1	yes	characteristic
513	C₄	C₂²×#10625352	1	1	yes	characteristic
514	C₂	—	2	2	no	—
515	C₂	—	8	4	no	—
516	C₂	—	188	2	no	—
517	C₂	C₂×#15689671	1	1	yes	characteristic
518	C₂	#20258157	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3147	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3147	D₄₇
hypocenter	C₄₇	#60682
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3147

Complements

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

N	H ≅ G/N	type
1. #20256777	C₂	semidirect
2. #20254044	C₂	semidirect
3. #20254035	C₂	semidirect
4. #20254024	C₂	semidirect
5. #20254013	C₂	semidirect
6. #20254002	C₂	semidirect
7. #20253902	C₂	semidirect
8. #20253733	C₂	semidirect
9. #20252993	C₂	semidirect
10. #20252965	C₂	semidirect
11. #20252189	C₂	semidirect
12. #135×Dic₄₇	C₂	semidirect
13. C₂×#15689077	C₂	semidirect
14. C₄₇×#3147	C₂	semidirect
27. #15689528	C₂²	semidirect
28. #15689525	C₂²	semidirect
29. #15689525	C₂²	semidirect
30. #15689521	C₂²	semidirect
31. #15689491	C₂²	semidirect
32. #15689487	C₂²	semidirect
33. #15689482	C₂²	semidirect
40. #15689235	C₂²	semidirect
41. #15689230	C₂²	semidirect
42. #15689224	C₂²	semidirect
43. Q₁₆×Dic₄₇	C₂²	semidirect
44. SD₁₆×Dic₄₇	C₂²	semidirect
45. D₈×Dic₄₇	C₂²	semidirect
60. C₄₇×#495	C₂²	semidirect
61. C₄₇×#495	C₂²	semidirect
62. C₄₇×#494	C₂²	semidirect
63. C₄₇×#493	C₂²	semidirect
64. C₄₇×#492	C₂²	semidirect
262. #3147	D₄₇	semidirect
293. #495	C₂×D₄₇	semidirect
294. #495	C₂×D₄₇	semidirect
295. #494	C₂×D₄₇	semidirect
296. #493	C₂×D₄₇	semidirect
297. #492	C₂×D₄₇	semidirect
325. C₄₇	#60682	semidirect

Maximal subgroups

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

subgroup	index
#20256777	2
#20254044	2
#20254035	2
#20254024	2
#20254013	2
#20254002	2
#20253902	2
#20253733	2
#20252993	2
#20252965	2
#20252189	2
#135×Dic₄₇	2
C₂×#15689077	2
C₄₇×#3147	2
#60682	47