Subgroups — #26184545

Order 12032.

900 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252408	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252402	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242026	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242019	C₂	1	2	yes	maximal, complemented
5	#20242008	C₂	1	2	yes	maximal, complemented
6	#20241995	C₂	1	2	yes	maximal, complemented
7	#20241986	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241986	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241983	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241976	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3510	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	1	no	—
13	Q₈×C₄₇⋊C₈	—	2	1	no	—
14	#15689201	—	2	2	no	—
15	#15689201	—	2	1	no	—
16	#15689195	—	2	2	no	—
17	D₄×C₄₇⋊C₈	—	2	1	no	—
18	#15689180	C₂²	1	1	yes	characteristic
19	#15689180	C₂²	1	1	yes	characteristic
20	#15689180	C₂²	1	2	yes	complemented
21	#15689180	C₂²	1	2	yes	complemented
22	C₄×#10625329	C₂²	1	1	yes	characteristic
23	C₄×#10625329	C₂²	1	1	yes	characteristic
24	C₄×#10625329	C₂²	1	2	yes	complemented
25	C₂×#13093935	C₂²	1	2	yes	complemented
26	#15688865	C₂²	1	1	yes	characteristic, complemented
27	#15688865	C₂²	1	2	yes	complemented
28	#15688865	C₂²	1	1	yes	characteristic, complemented
29	#15688865	C₂²	1	1	yes	characteristic, complemented
30	#15688865	C₂²	1	1	yes	characteristic, complemented
31	#15688865	C₂²	1	2	yes	complemented
32	#15688863	C₂²	1	2	yes	—
33	#15688863	C₂²	1	2	yes	—
34	#15688863	C₂²	1	2	yes	—
35	#15688863	C₂²	1	2	yes	—
36	C₄₇×#559	—	2	1	no	—
37	C₄₇×#559	—	2	1	no	—
38	C₄₇×#556	—	2	1	no	—
39	C₄₇×#556	—	2	1	no	—
40	C₄₇×#551	—	2	2	no	—
41	C₄₇×#551	—	2	2	no	—
42	C₄₇×#542	C₄	1	2	yes	—
43	C₄₇×#542	C₄	1	2	yes	—
44	C₄₇×#536	C₄	1	1	yes	characteristic
45	C₄₇×#535	C₄	1	1	yes	characteristic
46	C₄₇×#533	C₂²	1	1	yes	characteristic
47	C₄₇×#529	C₂²	1	2	yes	—
48	C₄₇×#529	C₂²	1	2	yes	—
49	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
50	C₄₇×#519	C₄	1	1	yes	characteristic
51	C₄₇×#518	C₄	1	1	yes	characteristic
52	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂×#10625329	—	2	2	no	—
56	C₂²×C₄₇⋊C₈	—	2	2	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
62	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
65	#13093935	—	2	2	no	—
66	#13093935	C₂³	1	1	yes	characteristic
67	#13093935	C₂³	1	2	yes	—
68	#13093935	C₂³	1	1	yes	characteristic
69	#13093935	C₂³	1	1	yes	characteristic
70	#13093935	C₂³	1	1	yes	characteristic
71	#13093935	C₂³	1	2	yes	—
72	C₄×C₄₇⋊C₈	—	2	1	no	—
73	C₄×C₄₇⋊C₈	—	2	2	no	—
74	C₄×C₄₇⋊C₈	—	2	1	no	—
75	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₄⋊Q₈×C₄₇	—	2	1	no	—
79	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
81	#127×C₄₇	—	2	1	no	—
82	#126×C₄₇	—	2	2	no	—
83	#126×C₄₇	—	2	2	no	—
84	#126×C₄₇	—	2	2	no	—
85	#126×C₄₇	—	2	2	no	—
86	#125×C₄₇	C₂³	1	1	yes	characteristic
87	#125×C₄₇	C₂³	1	1	yes	characteristic
88	#124×C₄₇	—	2	1	no	—
89	#124×C₄₇	—	2	1	no	—
90	#124×C₄₇	—	2	2	no	—
91	#124×C₄₇	—	2	2	no	—
92	#124×C₄₇	—	2	1	no	—
93	#124×C₄₇	—	2	1	no	—
94	#124×C₄₇	C₂×C₄	1	2	yes	—
95	#124×C₄₇	C₂³	1	2	yes	—
96	#123×C₄₇	—	2	2	no	—
97	#123×C₄₇	—	2	2	no	—
98	#123×C₄₇	—	2	2	no	—
99	#123×C₄₇	—	2	2	no	—
100	#123×C₄₇	—	2	2	no	—
101	C₂²⋊Q₈×C₄₇	—	2	1	no	—
102	C₂²⋊Q₈×C₄₇	—	2	1	no	—
103	C₂²⋊Q₈×C₄₇	—	2	2	no	—
104	C₂²⋊Q₈×C₄₇	—	2	2	no	—
105	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
106	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
107	#121×C₄₇	C₂×C₄	1	2	yes	—
108	#121×C₄₇	C₂×C₄	1	2	yes	—
109	#120×C₄₇	—	2	2	no	—
110	C₄×Q₈×C₄₇	—	2	1	no	—
111	C₄×Q₈×C₄₇	—	2	1	no	—
112	C₄×Q₈×C₄₇	—	2	1	no	—
113	C₄×Q₈×C₄₇	—	2	1	no	—
114	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
115	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
116	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
117	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
118	C₄×D₄×C₄₇	—	2	2	no	—
119	C₄×D₄×C₄₇	—	2	2	no	—
120	C₄×D₄×C₄₇	—	2	1	no	—
121	C₄×D₄×C₄₇	—	2	1	no	—
122	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
123	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
124	C₄×D₄×C₄₇	D₄	1	2	yes	—
125	C₄×D₄×C₄₇	D₄	1	2	yes	—
126	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
127	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
128	#117×C₄₇	—	2	2	no	—
129	#117×C₄₇	—	2	2	no	—
130	#117×C₄₇	—	2	2	no	—
131	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
132	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
133	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
134	#117×C₄₇	C₂×C₄	1	2	yes	—
135	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
138	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
140	C₂⁴×C₄₇	—	2	1	no	—
141	#41×C₄₇	—	4	2	no	—
142	C₂×Q₈×C₄₇	—	2	1	no	—
143	C₂×Q₈×C₄₇	—	2	1	no	—
144	C₂×Q₈×C₄₇	—	2	1	no	—
145	C₂×Q₈×C₄₇	—	4	2	no	—
146	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
148	C₂×D₄×C₄₇	—	2	2	no	—
149	C₂×D₄×C₄₇	—	2	2	no	—
150	C₂×D₄×C₄₇	—	2	1	no	—
151	C₂×D₄×C₄₇	—	4	2	no	—
152	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
154	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₄₇	—	2	1	no	—
156	C₂²×C₄×C₄₇	—	2	2	no	—
157	C₂²×C₄×C₄₇	—	2	2	no	—
158	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₄₇	—	2	2	no	—
165	C₄⋊C₄×C₄₇	—	2	2	no	—
166	C₄⋊C₄×C₄₇	—	2	2	no	—
167	C₄⋊C₄×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	—	2	1	no	—
169	C₄⋊C₄×C₄₇	—	2	1	no	—
170	C₄⋊C₄×C₄₇	—	2	1	no	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	—	2	1	no	—
173	C₄⋊C₄×C₄₇	—	2	1	no	—
174	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
175	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
176	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
177	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
178	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
182	C₂²⋊C₄×C₄₇	—	2	1	no	—
183	C₂²⋊C₄×C₄₇	—	2	1	no	—
184	C₂²⋊C₄×C₄₇	—	2	2	no	—
185	C₂²⋊C₄×C₄₇	—	2	2	no	—
186	C₂²⋊C₄×C₄₇	—	2	2	no	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₂²⋊C₄×C₄₇	—	2	2	no	—
189	C₂²⋊C₄×C₄₇	—	2	2	no	—
190	C₂²⋊C₄×C₄₇	—	2	2	no	—
191	C₂²⋊C₄×C₄₇	—	2	2	no	—
192	C₂²⋊C₄×C₄₇	—	2	2	no	—
193	C₂²⋊C₄×C₄₇	—	2	2	no	—
194	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
195	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
196	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
197	C₄²×C₄₇	—	2	2	no	—
198	C₄²×C₄₇	—	2	2	no	—
199	C₄²×C₄₇	—	2	1	no	—
200	C₄²×C₄₇	—	2	1	no	—
201	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
202	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₄₇	C₂×D₄	1	2	yes	—
204	C₄²×C₄₇	C₂×D₄	1	2	yes	—
205	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
208	#10625329	—	4	2	no	—
209	#10625329	—	4	2	no	—
210	#10625329	—	4	4	no	—
211	C₂×C₄₇⋊C₈	—	2	1	no	—
212	C₂×C₄₇⋊C₈	—	2	1	no	—
213	C₂×C₄₇⋊C₈	—	2	1	no	—
214	C₂×C₄₇⋊C₈	—	2	2	no	—
215	C₂×C₄₇⋊C₈	—	2	1	no	—
216	C₂×C₄₇⋊C₈	—	2	2	no	—
217	C₂×C₄₇⋊C₈	—	4	4	no	—
218	C₂³×C₄₇	—	2	2	no	—
219	C₂³×C₄₇	—	4	2	no	—
220	C₂³×C₄₇	—	8	1	no	—
221	C₂³×C₄₇	—	8	1	no	—
222	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
224	Q₈×C₄₇	—	2	2	no	—
225	Q₈×C₄₇	—	4	2	no	—
226	Q₈×C₄₇	—	4	2	no	—
227	Q₈×C₄₇	—	8	1	no	—
228	Q₈×C₄₇	—	8	1	no	—
229	D₄×C₄₇	—	2	2	no	—
230	D₄×C₄₇	—	4	2	no	—
231	D₄×C₄₇	—	4	2	no	—
232	D₄×C₄₇	—	4	2	no	—
233	D₄×C₄₇	—	8	2	no	—
234	D₄×C₄₇	—	8	2	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	2	1	no	—
238	C₂×C₄×C₄₇	—	2	2	no	—
239	C₂×C₄×C₄₇	—	2	1	no	—
240	C₂×C₄×C₄₇	—	2	1	no	—
241	C₂×C₄×C₄₇	—	4	2	no	—
242	C₂×C₄×C₄₇	—	4	2	no	—
243	C₂×C₄×C₄₇	—	4	1	no	—
244	C₂×C₄×C₄₇	—	4	1	no	—
245	C₂×C₄×C₄₇	—	4	2	no	—
246	C₂×C₄×C₄₇	—	4	2	no	—
247	C₂×C₄×C₄₇	—	8	2	no	—
248	C₂×C₄×C₄₇	—	8	2	no	—
249	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
250	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
251	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
254	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
258	C₄₇⋊C₈	—	2	2	no	—
259	C₄₇⋊C₈	—	2	2	no	—
260	C₄₇⋊C₈	—	4	2	no	—
261	C₄₇⋊C₈	—	4	1	no	—
262	C₄₇⋊C₈	—	4	1	no	—
263	C₄₇⋊C₈	—	4	2	no	—
264	#17691	—	47	1	no	maximal, Sylow
265	C₂²×C₄₇	—	2	1	no	—
266	C₂²×C₄₇	—	2	2	no	—
267	C₂²×C₄₇	—	2	2	no	—
268	C₂²×C₄₇	—	2	2	no	—
269	C₂²×C₄₇	—	2	1	no	—
270	C₂²×C₄₇	—	2	1	no	—
271	C₂²×C₄₇	—	4	2	no	—
272	C₂²×C₄₇	—	4	2	no	—
273	C₂²×C₄₇	—	4	2	no	—
274	C₂²×C₄₇	—	16	2	no	—
275	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
276	C₄×C₄₇	—	2	1	no	—
277	C₄×C₄₇	—	2	2	no	—
278	C₄×C₄₇	—	2	1	no	—
279	C₄×C₄₇	—	2	1	no	—
280	C₄×C₄₇	—	2	2	no	—
281	C₄×C₄₇	—	2	2	no	—
282	C₄×C₄₇	—	2	1	no	—
283	C₄×C₄₇	—	2	1	no	—
284	C₄×C₄₇	—	4	2	no	—
285	C₄×C₄₇	—	4	1	no	—
286	C₄×C₄₇	—	4	1	no	—
287	C₄×C₄₇	—	4	1	no	—
288	C₄×C₄₇	—	4	1	no	—
289	C₄×C₄₇	#413	1	2	yes	—
290	#3510	D₄₇	1	1	yes	characteristic
291	#2971	—	47	1	no	—
292	#2970	—	47	1	no	—
293	#1537	—	47	1	no	—
294	#1535	—	47	2	no	—
295	#1532	—	47	2	no	—
296	#1529	—	47	2	no	—
297	#1527	—	47	1	no	—
298	#1527	—	47	1	no	—
299	#1526	—	47	1	no	—
300	#1524	—	47	2	no	—
301	C₂×C₄₇	—	4	2	no	—
302	C₂×C₄₇	—	4	1	no	—
303	C₂×C₄₇	—	8	2	no	—
304	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
305	C₂×C₄₇	#2901	1	1	yes	characteristic
306	C₂×C₄₇	#2901	1	1	yes	characteristic
307	#559	—	2	1	no	—
308	#559	—	2	1	no	—
309	#556	—	2	1	no	—
310	#556	—	2	1	no	—
311	#551	—	2	2	no	—
312	#551	—	2	2	no	—
313	#542	Dic₄₇	1	2	yes	—
314	#542	Dic₄₇	1	2	yes	—
315	#536	Dic₄₇	1	1	yes	characteristic
316	#535	Dic₄₇	1	1	yes	characteristic
317	#533	C₂×D₄₇	1	1	yes	characteristic
318	#529	C₂×D₄₇	1	2	yes	—
319	#529	C₂×D₄₇	1	2	yes	—
320	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
321	#519	Dic₄₇	1	1	yes	characteristic
322	#518	Dic₄₇	1	1	yes	characteristic
323	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
324	#446	—	94	1	no	—
325	C₈×Q₈	—	94	1	no	—
326	#436	—	94	2	no	—
327	#436	—	94	1	no	—
328	#435	—	94	2	no	—
329	C₈×D₄	—	94	1	no	—
330	#432	—	47	1	no	—
331	#432	—	47	1	no	—
332	#432	—	47	2	no	—
333	#432	—	47	2	no	—
334	C₄×M₁₆	—	47	1	no	—
335	C₄×M₁₆	—	47	1	no	—
336	C₄×M₁₆	—	47	2	no	—
337	C₂×#97	—	47	2	no	—
338	#330	—	47	2	no	—
339	#330	—	47	2	no	—
340	#330	—	47	1	no	—
341	#330	—	47	1	no	—
342	#330	—	47	1	no	—
343	#330	—	47	1	no	—
344	#329	—	47	2	no	—
345	#329	—	47	2	no	—
346	#329	—	47	2	no	—
347	#329	—	47	2	no	—
348	C₄₇	#17691	1	1	yes	characteristic, complemented, Sylow
349	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
350	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
351	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
352	C₂×M₁₆	—	94	1	no	—
353	C₂×M₁₆	—	94	1	no	—
354	C₂×M₁₆	—	94	2	no	—
355	C₂²×C₈	—	94	2	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
358	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
359	#127	—	2	1	no	—
360	#126	—	2	2	no	—
361	#126	—	2	2	no	—
362	#126	—	2	2	no	—
363	#126	—	2	2	no	—
364	#125	C₂²×D₄₇	1	1	yes	characteristic
365	#125	C₂²×D₄₇	1	1	yes	characteristic
366	#124	—	2	1	no	—
367	#124	—	2	1	no	—
368	#124	—	2	2	no	—
369	#124	—	2	2	no	—
370	#124	—	2	1	no	—
371	#124	—	2	1	no	—
372	#124	C₂×Dic₄₇	1	2	yes	—
373	#124	C₂²×D₄₇	1	2	yes	—
374	#123	—	2	2	no	—
375	#123	—	2	2	no	—
376	#123	—	2	2	no	—
377	#123	—	2	2	no	—
378	#123	—	2	2	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
384	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
385	#121	C₂×Dic₄₇	1	2	yes	—
386	#121	C₂×Dic₄₇	1	2	yes	—
387	#120	—	2	2	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
393	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
394	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
395	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
401	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
402	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
403	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
404	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
405	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
406	#117	—	2	2	no	—
407	#117	—	2	2	no	—
408	#117	—	2	2	no	—
409	#117	C₂×Dic₄₇	1	1	yes	characteristic
410	#117	C₂×Dic₄₇	1	1	yes	characteristic
411	#117	C₂×Dic₄₇	1	1	yes	characteristic
412	#117	C₂×Dic₄₇	1	2	yes	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	2	no	—
416	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
417	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
418	C₄⋊C₈	—	94	1	no	—
419	C₄⋊C₈	—	94	2	no	—
420	C₄⋊C₈	—	94	2	no	—
421	C₄⋊C₈	—	94	1	no	—
422	C₂²⋊C₈	—	94	2	no	—
423	C₂²⋊C₈	—	94	1	no	—
424	C₂²⋊C₈	—	94	1	no	—
425	C₂²⋊C₈	—	94	2	no	—
426	#97	—	47	1	no	—
427	#97	—	47	2	no	—
428	#97	—	47	1	no	—
429	#97	—	47	1	no	—
430	#97	—	47	1	no	—
431	#97	—	47	2	no	—
432	#97	—	94	2	no	—
433	C₄×C₈	—	94	1	no	—
434	C₄×C₈	—	94	2	no	—
435	C₄×C₈	—	94	1	no	—
436	C₂⁴	—	2	1	no	—
437	#41	—	4	2	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	4	2	no	—
442	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
443	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	4	2	no	—
448	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
449	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
450	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
456	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
459	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
460	M₁₆	—	188	2	no	—
461	M₁₆	—	188	4	no	—
462	M₁₆	—	188	2	no	—
463	C₂×C₈	—	94	1	no	—
464	C₂×C₈	—	94	1	no	—
465	C₂×C₈	—	94	1	no	—
466	C₂×C₈	—	94	1	no	—
467	C₂×C₈	—	94	2	no	—
468	C₂×C₈	—	94	2	no	—
469	C₂×C₈	—	188	4	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
481	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
482	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
483	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
484	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
501	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
502	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	C₂²×Dic₄₇	1	2	yes	—
508	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
509	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
510	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
511	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
512	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
513	C₄²	C₂³×D₄₇	1	1	yes	characteristic
514	C₂³	—	2	2	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	8	1	no	—
517	C₂³	—	8	1	no	—
518	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
519	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
520	Q₈	—	2	2	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	8	1	no	—
524	Q₈	—	8	1	no	—
525	D₄	—	2	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	8	2	no	—
530	D₄	—	8	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
546	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
547	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
548	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
549	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
550	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
551	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
552	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
553	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
554	C₈	—	94	2	no	—
555	C₈	—	94	2	no	—
556	C₈	—	188	2	no	—
557	C₈	—	188	1	no	—
558	C₈	—	188	1	no	—
559	C₈	—	188	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	16	2	no	—
570	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	2	no	—
584	C₄	#15689107	1	2	yes	—
585	C₂	—	4	1	no	—
586	C₂	—	4	2	no	—
587	C₂	—	8	2	no	—
588	C₂	C₂×#15689107	1	1	yes	characteristic
589	C₂	#20251935	1	1	yes	characteristic
590	C₂	#20251935	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3510	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₄₇×#535	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3510	D₄₇
hypocenter	C₄₇	#17691
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3510

Complements

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

N	H ≅ G/N	type
1. #20252408	C₂	semidirect
2. #20252402	C₂	semidirect
3. #20242026	C₂	semidirect
4. #20242019	C₂	semidirect
5. #20242008	C₂	semidirect
6. #20241995	C₂	semidirect
7. #20241986	C₂	semidirect
8. #20241986	C₂	semidirect
9. #20241983	C₂	semidirect
10. #20241976	C₂	semidirect
20. #15689180	C₂²	semidirect
21. #15689180	C₂²	semidirect
24. C₄×#10625329	C₂²	semidirect
25. C₂×#13093935	C₂²	semidirect
26. #15688865	C₂²	semidirect
27. #15688865	C₂²	semidirect
28. #15688865	C₂²	semidirect
29. #15688865	C₂²	semidirect
30. #15688865	C₂²	semidirect
31. #15688865	C₂²	semidirect
348. C₄₇	#17691	semidirect

Maximal subgroups

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

subgroup	index
#20252408	2
#20252402	2
#20242026	2
#20242019	2
#20242008	2
#20241995	2
#20241986	2
#20241983	2
#20241976	2
C₄₇×#3510	2
#17691	47