Subgroups — #27086135

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	#20256778	C₂	1	2	yes	maximal, complemented
2	#20254047	C₂	1	2	yes	maximal, complemented
3	#20254038	C₂	1	2	yes	maximal, complemented
4	#20254027	C₂	1	4	yes	maximal, complemented
5	#20254016	C₂	1	4	yes	maximal, complemented
6	#20254005	C₂	1	4	yes	maximal, complemented
7	#20253902	C₂	1	1	yes	maximal, characteristic, complemented
8	#20253816	C₂	1	1	yes	maximal, characteristic, complemented
9	#20253734	C₂	1	2	yes	maximal, complemented
10	#20252997	C₂	1	2	yes	maximal, complemented
11	#20252969	C₂	1	2	yes	maximal, complemented
12	#20252190	C₂	1	2	yes	maximal, complemented
13	C₄×#13094046	C₂	1	2	yes	maximal, complemented
14	C₂×C₄₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#13094046	C₂²	1	2	yes	—
16	C₂×#13094046	C₂²	1	2	yes	—
17	#15689744	C₂²	1	8	yes	—
18	#15689735	C₂²	1	4	yes	—
19	#15689728	C₂²	1	4	yes	—
20	#15689720	—	2	4	no	—
21	#15689711	—	2	4	no	—
22	#15689680	C₂²	1	2	yes	—
23	#15689673	C₂²	1	2	yes	—
24	#15689651	—	2	8	no	—
25	#15689634	C₂²	1	4	yes	—
26	C₄×#10625350	C₂²	1	4	yes	—
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	#15689507	C₂²	1	2	yes	complemented
32	#15689507	C₂²	1	2	yes	complemented
33	#15689503	C₂²	1	1	yes	characteristic, complemented
34	#15689500	C₂²	1	1	yes	characteristic, complemented
35	#15689496	C₂²	1	2	yes	complemented
36	#15689492	C₂²	1	4	yes	complemented
37	#15689488	C₂²	1	4	yes	complemented
38	#15689483	C₂²	1	8	yes	complemented
39	#15689381	C₂²	1	4	yes	—
40	#15689376	C₂²	1	4	yes	—
41	#15689369	C₂²	1	8	yes	—
42	#15689364	C₂²	1	4	yes	—
43	#15689359	C₂²	1	4	yes	—
44	#15689352	C₂²	1	8	yes	—
45	#15689236	C₂²	1	4	yes	complemented
46	#15689231	C₂²	1	4	yes	complemented
47	#15689225	C₂²	1	8	yes	complemented
48	C₄×Dic₁₈₈	C₂²	1	4	yes	complemented
49	C₄×#10625325	C₂²	1	8	yes	complemented
50	C₄×D₃₇₆	C₂²	1	4	yes	complemented
51	#15689161	C₂²	1	2	yes	—
52	#15689161	C₂²	1	2	yes	—
53	#15689120	C₂²	1	4	yes	—
54	#15689120	C₂²	1	4	yes	—
55	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
56	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
58	C₄₇×#405	C₂²	1	2	yes	—
59	C₄₇×#405	C₂²	1	2	yes	—
60	C₄₇×#405	C₂²	1	2	yes	—
61	C₄₇×#405	C₂²	1	2	yes	—
62	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
63	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
64	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
65	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
66	C₂×#10625350	C₂³	1	4	yes	—
67	#13094046	—	2	8	no	—
68	#13094046	—	2	8	no	—
69	C₂×Dic₁₈₈	C₂³	1	2	yes	—
70	C₂×Dic₁₈₈	C₂³	1	2	yes	—
71	C₂×#10625325	C₂³	1	4	yes	—
72	C₂×#10625325	C₂³	1	4	yes	—
73	C₂×D₃₇₆	C₂³	1	2	yes	—
74	C₂×D₃₇₆	C₂³	1	2	yes	—
75	#13094024	C₂³	1	2	yes	—
76	#13094024	C₂³	1	4	yes	—
77	#13094021	C₂³	1	2	yes	—
78	#13094019	—	2	8	no	—
79	#13094017	—	2	8	no	—
80	#13094016	C₂³	1	4	yes	—
81	#13094014	—	2	8	no	—
82	#13094012	C₂³	1	4	yes	—
83	#13094010	—	2	8	no	—
84	#13094009	—	2	8	no	—
85	#13094007	—	2	4	no	—
86	#13094006	—	2	8	no	—
87	#13094003	—	2	4	no	—
88	#13094003	C₂³	1	8	yes	—
89	#13094002	—	2	8	no	—
90	#13093998	—	2	4	no	—
91	#13093998	C₂³	1	8	yes	—
92	#13093997	—	2	8	no	—
93	#13093993	—	2	4	no	—
94	C₄×Dic₉₄	—	2	4	no	—
95	C₄×Dic₉₄	C₂³	1	8	yes	—
96	C₄×D₁₈₈	—	2	4	no	—
97	C₄×D₁₈₈	C₂³	1	8	yes	—
98	C₄×C₂²⋊D₄₇	—	2	8	no	—
99	C₄×C₂²⋊D₄₇	—	2	8	no	—
100	#13093983	C₂³	1	4	yes	—
101	#13093981	—	2	4	no	—
102	C₄²×D₄₇	—	2	4	no	—
103	#13093958	C₂³	1	4	yes	—
104	#13093958	C₂³	1	4	yes	—
105	#13093956	C₂³	1	4	yes	—
106	#13093956	C₂³	1	4	yes	—
107	#13093949	C₂³	1	8	yes	—
108	#13093949	C₂³	1	8	yes	—
109	#13093946	C₂³	1	8	yes	—
110	#13093946	C₂³	1	8	yes	—
111	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
112	C₂×M₁₆×C₄₇	—	2	4	no	—
113	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
114	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
115	C₂²×C₈×C₄₇	—	2	4	no	—
116	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
117	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
118	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
122	#117×C₄₇	D₄	1	4	yes	—
123	#117×C₄₇	C₂³	1	2	yes	—
124	#117×C₄₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
126	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
127	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	#97×C₄₇	C₂³	1	2	yes	—
130	#97×C₄₇	C₂³	1	2	yes	—
131	#97×C₄₇	C₂³	1	2	yes	—
132	#97×C₄₇	C₂³	1	2	yes	—
133	C₄×C₈×C₄₇	C₂³	1	2	yes	—
134	C₄×C₈×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	2	yes	—
139	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	—	2	2	no	—
141	C₂²×C₄×C₄₇	—	2	2	no	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
148	C₂×C₂²⋊D₄₇	—	2	4	no	—
149	C₂×C₂²⋊D₄₇	—	2	8	no	—
150	#10625350	—	2	8	no	—
151	#10625350	—	2	8	no	—
152	C₂×D₁₈₈	—	2	4	no	—
153	C₂×D₁₈₈	C₂⁴	1	4	yes	—
154	C₂×C₄×D₄₇	—	2	4	no	—
155	C₂×C₄×D₄₇	—	2	8	no	—
156	C₂×Dic₉₄	—	2	4	no	—
157	C₂×Dic₉₄	C₂⁴	1	4	yes	—
158	M₁₆×C₄₇	—	2	4	no	—
159	M₁₆×C₄₇	—	2	4	no	—
160	C₂×C₈×C₄₇	—	2	2	no	—
161	C₂×C₈×C₄₇	—	2	2	no	—
162	C₂×C₈×C₄₇	—	2	4	no	—
163	C₂×C₈×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	2	yes	—
167	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
168	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
172	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
173	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
174	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
175	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
176	C₄²×C₄₇	C₂×D₄	1	2	yes	—
177	C₄²×C₄₇	C₂×D₄	1	2	yes	—
178	C₄²×C₄₇	C₂⁴	1	2	yes	—
179	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
180	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
181	C₂²⋊Dic₄₇	—	2	4	no	—
182	C₂²⋊Dic₄₇	—	2	8	no	—
183	(C₂×D₄₇)⋊C₄	—	2	8	no	—
184	(C₂×D₄₇)⋊C₄	—	2	8	no	—
185	(C₂×D₄₇)⋊C₄	—	2	8	no	—
186	C₄⋊Dic₄₇	—	2	4	no	—
187	C₄⋊Dic₄₇	—	2	4	no	—
188	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
189	Dic₄₇⋊C₄	—	2	8	no	—
190	Dic₄₇⋊C₄	—	2	8	no	—
191	Dic₄₇⋊C₄	—	2	8	no	—
192	C₄×Dic₄₇	—	2	4	no	—
193	C₄×Dic₄₇	—	2	8	no	—
194	Dic₁₈₈	—	2	4	no	—
195	Dic₁₈₈	—	2	4	no	—
196	D₃₇₆	—	2	4	no	—
197	D₃₇₆	—	2	4	no	—
198	#10625325	—	2	8	no	—
199	#10625325	—	2	8	no	—
200	C₂³×C₄₇	—	2	2	no	—
201	C₂³×C₄₇	—	4	2	no	—
202	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
203	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
204	C₂²×D₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	4	2	no	—
210	C₂×C₄×C₄₇	—	4	2	no	—
211	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
217	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
218	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
219	C₂²⋊D₄₇	—	4	8	no	—
220	C₂²⋊D₄₇	—	8	8	no	—
221	C₂×Dic₄₇	—	2	4	no	—
222	C₂×Dic₄₇	—	2	8	no	—
223	D₁₈₈	—	2	4	no	—
224	D₁₈₈	—	2	4	no	—
225	D₁₈₈	—	8	4	no	—
226	C₄×D₄₇	—	4	8	no	—
227	C₄×D₄₇	—	8	8	no	—
228	Dic₉₄	—	2	4	no	—
229	Dic₉₄	—	2	4	no	—
230	Dic₉₄	—	8	4	no	—
231	C₈×C₄₇	—	2	2	no	—
232	C₈×C₄₇	—	2	2	no	—
233	C₈×C₄₇	C₂×#41	1	2	yes	—
234	C₈×C₄₇	C₂×#41	1	2	yes	—
235	C₈×C₄₇	C₂×#41	1	2	yes	—
236	C₈×C₄₇	C₂×#41	1	2	yes	—
237	#60682	—	47	1	no	maximal, Sylow
238	C₂²×C₄₇	—	2	2	no	—
239	C₂²×C₄₇	—	2	4	no	—
240	C₂²×C₄₇	—	2	2	no	—
241	C₂²×C₄₇	—	4	4	no	—
242	C₂²×C₄₇	#532	1	2	yes	—
243	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
244	C₂×D₄₇	—	4	8	no	—
245	C₂×D₄₇	—	4	4	no	—
246	C₄×C₄₇	—	2	2	no	—
247	C₄×C₄₇	—	2	4	no	—
248	C₄×C₄₇	—	2	2	no	—
249	C₄×C₄₇	—	2	2	no	—
250	C₄×C₄₇	#532	1	2	yes	—
251	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
252	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
253	Dic₄₇	—	4	8	no	—
254	Dic₄₇	—	4	4	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	—	47	1	no	—
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	D₄₇	1	1	yes	characteristic, complemented
269	C₂×C₄₇	—	2	2	no	—
270	C₂×C₄₇	—	4	2	no	—
271	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
272	C₂×C₄₇	#3584	1	2	yes	—
273	D₄₇	—	8	4	no	—
274	C₂×#135	—	47	2	no	—
275	C₂×#135	—	47	2	no	—
276	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
277	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
285	#529	—	94	8	no	—
286	#525	—	47	4	no	—
287	C₄×#41	—	47	4	no	—
288	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
289	#500	—	47	2	no	—
290	#499	—	47	2	no	—
291	#499	—	47	2	no	—
292	#498	—	47	2	no	—
293	#495	—	47	2	no	—
294	#495	—	47	2	no	—
295	#494	—	47	1	no	—
296	#493	—	47	1	no	—
297	#492	—	47	2	no	—
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	C₂×D₄₇	1	2	yes	—
318	#405	C₂×D₄₇	1	2	yes	—
319	#405	C₂×D₄₇	1	2	yes	—
320	#405	C₂×D₄₇	1	2	yes	—
321	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
322	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
323	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
324	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
325	C₄₇	#60682	1	1	yes	characteristic, complemented, Sylow
326	C₂×#41	—	47	4	no	—
327	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
328	#135	—	94	8	no	—
329	#135	—	94	8	no	—
330	C₂×Q₁₆	—	47	2	no	—
331	C₂×Q₁₆	—	47	2	no	—
332	C₂×SD₁₆	—	47	4	no	—
333	C₂×SD₁₆	—	47	4	no	—
334	C₂×D₈	—	47	2	no	—
335	C₂×D₈	—	47	2	no	—
336	C₂×M₁₆	—	2	4	no	—
337	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
338	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
339	C₂²×C₈	—	2	4	no	—
340	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
341	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
342	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
343	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
348	#127	—	47	2	no	—
349	#126	—	94	8	no	—
350	#126	—	94	8	no	—
351	#125	—	47	4	no	—
352	#125	—	94	8	no	—
353	#124	—	47	4	no	—
354	#124	—	94	8	no	—
355	#123	—	94	4	no	—
356	#123	—	94	8	no	—
357	#123	—	94	8	no	—
358	C₂²⋊Q₈	—	47	8	no	—
359	C₂²⋊Q₈	—	94	4	no	—
360	C₂²⋊Q₈	—	94	8	no	—
361	#121	—	47	8	no	—
362	#121	—	94	4	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	—	47	8	no	—
368	C₄×D₄	—	94	8	no	—
369	C₄×D₄	—	94	8	no	—
370	C₄×D₄	—	94	4	no	—
371	#117	—	47	4	no	—
372	#117	—	94	4	no	—
373	#117	D₁₈₈	1	4	yes	—
374	#117	C₂²×D₄₇	1	2	yes	—
375	#117	C₂²×D₄₇	1	2	yes	—
376	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
377	C₂×C₂²⋊C₄	D₁₈₈	1	2	yes	—
378	C₂×C₄²	—	94	4	no	—
379	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
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	C₂²×D₄₇	1	2	yes	—
390	#97	C₂²×D₄₇	1	2	yes	—
391	#97	C₂²×D₄₇	1	2	yes	—
392	#97	C₂²×D₄₇	1	2	yes	—
393	C₄×C₈	C₂²×D₄₇	1	2	yes	—
394	C₄×C₈	C₂²×D₄₇	1	2	yes	—
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	C₂×D₁₈₈	1	1	yes	characteristic
400	#41	—	94	8	no	—
401	#41	—	94	8	no	—
402	C₂×Q₈	—	47	4	no	—
403	C₂×Q₈	—	94	4	no	—
404	C₂×D₄	—	47	4	no	—
405	C₂×D₄	—	94	8	no	—
406	C₂×D₄	—	94	4	no	—
407	C₂×D₄	—	94	4	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	94	8	no	—
411	C₂²×C₄	—	94	4	no	—
412	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
414	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
415	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
416	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
417	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
418	Q₁₆	—	94	4	no	—
419	Q₁₆	—	94	4	no	—
420	SD₁₆	—	94	8	no	—
421	SD₁₆	—	94	8	no	—
422	D₈	—	94	4	no	—
423	D₈	—	94	4	no	—
424	M₁₆	—	2	4	no	—
425	M₁₆	—	2	4	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	#10625350	1	4	yes	—
431	C₂×C₈	#10625350	1	4	yes	—
432	C₂×C₈	C₂³×D₄₇	1	2	yes	—
433	C₂×C₈	C₂³×D₄₇	1	2	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	—	47	8	no	—
439	C₄⋊C₄	—	94	8	no	—
440	C₄⋊C₄	—	94	8	no	—
441	C₄⋊C₄	—	94	8	no	—
442	C₄⋊C₄	—	94	4	no	—
443	C₄⋊C₄	—	94	4	no	—
444	C₄⋊C₄	C₂×D₁₈₈	1	4	yes	—
445	C₄⋊C₄	C₂×D₁₈₈	1	4	yes	—
446	C₂²⋊C₄	—	94	4	no	—
447	C₂²⋊C₄	—	94	8	no	—
448	C₂²⋊C₄	—	94	8	no	—
449	C₂²⋊C₄	—	94	8	no	—
450	C₂²⋊C₄	—	94	8	no	—
451	C₂²⋊C₄	C₂×D₁₈₈	1	4	yes	—
452	C₂²⋊C₄	C₂×D₁₈₈	1	4	yes	—
453	C₄²	—	94	8	no	—
454	C₄²	—	94	4	no	—
455	C₄²	C₂×D₁₈₈	1	2	yes	—
456	C₄²	C₂×D₁₈₈	1	2	yes	—
457	C₄²	C₂³×D₄₇	1	2	yes	—
458	C₄²	C₂³×D₄₇	1	1	yes	characteristic
459	C₄²	C₂³×D₄₇	1	1	yes	characteristic
460	C₂³	—	2	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	94	4	no	—
463	C₂³	C₂²×D₁₈₈	1	2	yes	—
464	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
465	Q₈	—	94	4	no	—
466	Q₈	—	94	4	no	—
467	Q₈	—	376	4	no	—
468	D₄	—	94	4	no	—
469	D₄	—	94	4	no	—
470	D₄	—	376	4	no	—
471	D₄	—	376	8	no	—
472	D₄	—	188	8	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	94	8	no	—
480	C₂×C₄	—	94	4	no	—
481	C₂×C₄	—	376	8	no	—
482	C₂×C₄	—	188	8	no	—
483	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
484	C₂×C₄	C₂²×D₁₈₈	1	2	yes	—
485	C₂×C₄	C₂²×D₁₈₈	1	2	yes	—
486	C₂×C₄	C₂²×D₁₈₈	1	2	yes	—
487	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
488	C₂×C₄	C₂×#10625350	1	2	yes	—
489	C₂×C₄	C₂×#10625350	1	2	yes	—
490	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	C₂×#10625350	1	2	yes	—
494	C₈	C₂×#10625350	1	2	yes	—
495	C₈	C₂×#10625350	1	2	yes	—
496	C₈	C₂×#10625350	1	2	yes	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	188	8	no	—
502	C₂²	—	188	4	no	—
503	C₂²	#15689673	1	2	yes	—
504	C₂²	C₂³×D₁₈₈	1	1	yes	characteristic
505	C₄	—	2	4	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	188	8	no	—
510	C₄	—	188	4	no	—
511	C₄	#15689673	1	2	yes	—
512	C₄	C₂²×#10625350	1	1	yes	characteristic
513	C₄	C₂²×#10625350	1	1	yes	characteristic
514	C₂	—	2	2	no	—
515	C₂	—	4	2	no	—
516	C₂	—	376	4	no	—
517	C₂	C₂×#15689673	1	1	yes	characteristic
518	C₂	#20258162	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#405	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₂×#405	D₄₇
hypocenter	C₄₇	#60682
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
1. #20256778	C₂	semidirect
2. #20254047	C₂	semidirect
3. #20254038	C₂	semidirect
4. #20254027	C₂	semidirect
5. #20254016	C₂	semidirect
6. #20254005	C₂	semidirect
7. #20253902	C₂	semidirect
8. #20253816	C₂	semidirect
9. #20253734	C₂	semidirect
10. #20252997	C₂	semidirect
11. #20252969	C₂	semidirect
12. #20252190	C₂	semidirect
13. C₄×#13094046	C₂	semidirect
14. C₂×C₄₇×#405	C₂	semidirect
27. #15689528	C₂²	semidirect
28. #15689525	C₂²	semidirect
29. #15689525	C₂²	semidirect
30. #15689521	C₂²	semidirect
31. #15689507	C₂²	semidirect
32. #15689507	C₂²	semidirect
33. #15689503	C₂²	semidirect
34. #15689500	C₂²	semidirect
35. #15689496	C₂²	semidirect
36. #15689492	C₂²	semidirect
37. #15689488	C₂²	semidirect
38. #15689483	C₂²	semidirect
45. #15689236	C₂²	semidirect
46. #15689231	C₂²	semidirect
47. #15689225	C₂²	semidirect
48. C₄×Dic₁₈₈	C₂²	semidirect
49. C₄×#10625325	C₂²	semidirect
50. C₄×D₃₇₆	C₂²	semidirect
268. C₂×#405	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
#20256778	2
#20254047	2
#20254038	2
#20254027	2
#20254016	2
#20254005	2
#20253902	2
#20253816	2
#20253734	2
#20252997	2
#20252969	2
#20252190	2
C₄×#13094046	2
C₂×C₄₇×#405	2
#60682	47