Subgroups — #26223095

Order 12032.

914 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252994	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689238	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252082	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244280	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244138	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244102	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244098	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243837	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243834	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243428	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243268	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243227	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243223	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13094044	C₂²	1	1	yes	characteristic
17	C₂×#13094030	C₂²	1	1	yes	characteristic
18	C₂²×#10625329	C₂²	1	1	yes	characteristic
19	#15689634	C₂²	1	1	yes	characteristic
20	C₂×#13093983	C₂²	1	1	yes	characteristic
21	#15689379	C₄	1	2	yes	complemented
22	#15689374	C₄	1	2	yes	complemented
23	#15689371	C₄	1	2	yes	complemented
24	#15689367	C₄	1	2	yes	complemented
25	#15689238	—	2	4	no	—
26	#15689194	—	2	2	no	—
27	C₈×C₂²⋊D₄₇	—	2	2	no	—
28	C₂×#13093959	C₂²	1	1	yes	characteristic
29	C₂×#13093959	C₂²	1	1	yes	characteristic
30	#15689159	C₂²	1	1	yes	characteristic
31	#15689149	C₂²	1	1	yes	characteristic
32	C₂×#13093951	C₂²	1	1	yes	characteristic
33	C₂×#13093951	C₂²	1	1	yes	characteristic
34	C₂×#13093950	C₂²	1	1	yes	characteristic
35	C₂×#13093950	C₂²	1	1	yes	characteristic
36	#15689119	C₂²	1	1	yes	characteristic
37	#15689117	C₂²	1	1	yes	characteristic
38	#15689089	C₂²	1	1	yes	characteristic
39	#15689087	C₂²	1	1	yes	characteristic
40	#15689078	—	2	4	no	—
41	#15689078	C₂²	1	1	yes	characteristic
42	C₂×#13093934	C₂²	1	1	yes	characteristic
43	C₂×#13093934	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
45	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
46	#15688887	C₂²	1	1	yes	characteristic
47	#15688887	C₂²	1	1	yes	characteristic
48	#15688884	C₂²	1	1	yes	characteristic
49	#15688884	C₂²	1	1	yes	characteristic
50	#15688882	C₂²	1	1	yes	characteristic
51	#15688882	C₂²	1	1	yes	characteristic
52	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
53	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₄₇×#525	C₂²	1	1	yes	characteristic
55	C₄₇×#435	—	2	2	no	—
56	C₈×D₄×C₄₇	—	2	2	no	—
57	C₄₇×#424	C₂²	1	1	yes	characteristic
58	C₄₇×#408	C₂²	1	1	yes	characteristic
59	C₄₇×#407	C₂²	1	1	yes	characteristic
60	C₄₇×#405	C₂²	1	1	yes	characteristic
61	C₂×#10625350	C₂³	1	1	yes	characteristic
62	#13094044	—	2	2	no	—
63	#13094044	—	2	2	no	—
64	C₂×#10625337	C₂×C₄	1	1	yes	characteristic
65	C₂×#10625335	C₂×C₄	1	1	yes	characteristic
66	C₂×#10625336	C₂×C₄	1	1	yes	characteristic
67	C₂×#10625334	C₂×C₄	1	1	yes	characteristic
68	#13094030	—	2	2	no	—
69	#13094030	—	2	2	no	—
70	C₂×#10625329	—	2	2	no	—
71	C₂×#10625329	—	2	2	no	—
72	C₂×#10625329	C₂×C₄	1	2	yes	—
73	C₂×#10625329	C₂×C₄	1	2	yes	—
74	C₂×#10625329	C₂³	1	1	yes	characteristic
75	C₂×#10625329	C₂³	1	1	yes	characteristic
76	C₂×#10625324	—	2	1	no	—
77	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₄₇	—	2	1	no	—
80	#13094007	—	2	1	no	—
81	#13094003	C₂×C₄	1	2	yes	—
82	#13093998	C₂×C₄	1	2	yes	—
83	#13093993	—	2	1	no	—
84	C₄×C₂²⋊D₄₇	—	2	2	no	—
85	#13093983	—	2	2	no	—
86	#13093983	—	2	2	no	—
87	#13093983	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊Dic₄₇	—	2	1	no	—
89	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
90	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
92	#13093959	—	2	2	no	—
93	#13093959	—	2	2	no	—
94	#13093957	C₂×C₄	1	2	yes	—
95	#13093955	C₂×C₄	1	2	yes	—
96	Dic₄₇⋊C₈	—	2	2	no	—
97	#13093951	—	2	2	no	—
98	#13093951	—	2	2	no	—
99	#13093950	—	2	2	no	—
100	#13093950	—	2	2	no	—
101	#13093948	C₂×C₄	1	2	yes	—
102	#13093947	C₂×C₄	1	2	yes	—
103	#13093945	C₂×C₄	1	2	yes	—
104	#13093944	C₂×C₄	1	2	yes	—
105	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
106	(C₂×D₄₇)⋊C₈	—	2	2	no	—
107	#13093934	—	2	1	no	—
108	#13093934	—	2	2	no	—
109	#13093934	—	2	2	no	—
110	C₈×Dic₄₇	—	2	2	no	—
111	C₈×Dic₄₇	—	2	1	no	—
112	C₈×Dic₄₇	D₄	1	4	yes	complemented
113	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
115	#131×C₄₇	—	2	2	no	—
116	#131×C₄₇	—	2	2	no	—
117	C₂×M₁₆×C₄₇	—	2	1	no	—
118	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₄₇	—	2	2	no	—
121	C₂²×C₈×C₄₇	—	2	2	no	—
122	C₂²×C₈×C₄₇	—	2	1	no	—
123	C₂²×C₈×C₄₇	D₄	1	2	yes	—
124	C₂²×C₈×C₄₇	D₄	1	2	yes	—
125	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
127	#123×C₄₇	—	2	1	no	—
128	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
129	#121×C₄₇	C₂×C₄	1	2	yes	—
130	#120×C₄₇	—	2	1	no	—
131	C₄×D₄×C₄₇	—	2	2	no	—
132	#117×C₄₇	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₄₇	—	2	2	no	—
134	C₂²⋊C₈×C₄₇	—	2	2	no	—
135	C₂²⋊C₈×C₄₇	—	2	2	no	—
136	#97×C₄₇	—	2	1	no	—
137	C₄×C₈×C₄₇	—	2	1	no	—
138	C₂⁴×C₄₇	#41	1	1	yes	characteristic
139	#41×C₄₇	—	2	1	no	—
140	#41×C₄₇	—	2	1	no	—
141	#41×C₄₇	—	2	1	no	—
142	#41×C₄₇	—	2	1	no	—
143	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂×D₄×C₄₇	—	2	2	no	—
145	C₂×D₄×C₄₇	—	2	1	no	—
146	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	—	2	1	no	—
148	C₂²×C₄×C₄₇	—	2	1	no	—
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂²×C₄×C₄₇	—	2	1	no	—
152	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
156	C₂×C₂²⋊D₄₇	—	2	2	no	—
157	C₂×C₂²⋊D₄₇	—	2	1	no	—
158	C₂²×Dic₄₇	—	2	1	no	—
159	C₂²×Dic₄₇	—	2	1	no	—
160	#10625350	—	2	1	no	—
161	#10625350	—	2	1	no	—
162	#10625350	—	2	1	no	—
163	#10625350	—	2	1	no	—
164	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄×D₄₇	—	2	1	no	—
166	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
167	M₁₆×C₄₇	—	2	1	no	—
168	M₁₆×C₄₇	—	2	1	no	—
169	M₁₆×C₄₇	—	2	1	no	—
170	M₁₆×C₄₇	—	2	1	no	—
171	M₁₆×C₄₇	—	4	2	no	—
172	C₂×C₈×C₄₇	—	2	1	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	2	4	no	—
175	C₂×C₈×C₄₇	—	2	4	no	—
176	C₂×C₈×C₄₇	—	2	1	no	—
177	C₂×C₈×C₄₇	—	2	1	no	—
178	C₂×C₈×C₄₇	—	4	2	no	—
179	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
181	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₄₇	#41	1	2	yes	—
184	C₄⋊C₄×C₄₇	—	2	2	no	—
185	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
186	C₂²⋊C₄×C₄₇	—	2	2	no	—
187	C₂²⋊C₄×C₄₇	—	2	1	no	—
188	C₂²⋊C₄×C₄₇	—	2	2	no	—
189	C₄²×C₄₇	—	2	1	no	—
190	C₂²⋊Dic₄₇	—	2	4	no	—
191	C₂²⋊Dic₄₇	—	2	2	no	—
192	C₂²⋊Dic₄₇	—	2	1	no	—
193	#10625337	—	2	2	no	—
194	#10625336	—	2	2	no	—
195	#10625335	—	2	2	no	—
196	#10625334	—	2	2	no	—
197	(C₂×D₄₇)⋊C₄	—	2	2	no	—
198	C₄⋊Dic₄₇	—	2	4	no	—
199	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
200	Dic₄₇⋊C₄	—	2	2	no	—
201	C₄×Dic₄₇	—	2	1	no	—
202	C₄×Dic₄₇	—	2	1	no	—
203	C₄×Dic₄₇	—	2	1	no	—
204	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
205	C₄×Dic₄₇	#41	1	2	yes	—
206	#10625329	—	2	4	no	—
207	#10625329	—	2	4	no	—
208	#10625329	—	2	1	no	—
209	#10625329	—	2	1	no	—
210	#10625329	—	2	1	no	—
211	#10625329	—	2	1	no	—
212	C₂×C₄₇⋊C₈	—	2	1	no	—
213	C₂×C₄₇⋊C₈	—	2	1	no	—
214	C₂×C₄₇⋊C₈	—	2	1	no	—
215	C₂×C₄₇⋊C₈	—	2	1	no	—
216	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
217	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
220	C₂×C₄₇⋊C₈	#41	1	2	yes	—
221	#10625324	—	4	2	no	—
222	C₈×D₄₇	—	4	2	no	—
223	C₂³×C₄₇	—	2	1	no	—
224	C₂³×C₄₇	—	2	1	no	—
225	C₂³×C₄₇	—	2	1	no	—
226	C₂³×C₄₇	—	4	2	no	—
227	C₂³×C₄₇	C₄×D₄	1	2	yes	—
228	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
229	C₂²×D₄₇	—	2	1	no	—
230	Q₈×C₄₇	—	2	1	no	—
231	Q₈×C₄₇	—	2	1	no	—
232	D₄×C₄₇	—	2	1	no	—
233	D₄×C₄₇	—	2	1	no	—
234	D₄×C₄₇	—	4	4	no	—
235	D₄×C₄₇	—	4	1	no	—
236	D₄×C₄₇	—	4	1	no	—
237	C₂×C₄×C₄₇	—	2	1	no	—
238	C₂×C₄×C₄₇	—	2	1	no	—
239	C₂×C₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	2	2	no	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	2	2	no	—
244	C₂×C₄×C₄₇	—	2	1	no	—
245	C₂×C₄×C₄₇	—	4	1	no	—
246	C₂×C₄×C₄₇	—	4	1	no	—
247	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
248	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
254	C₂²⋊D₄₇	—	4	4	no	—
255	C₂²⋊D₄₇	—	4	1	no	—
256	C₂²⋊D₄₇	—	4	1	no	—
257	C₂×Dic₄₇	—	2	2	no	—
258	C₂×Dic₄₇	—	2	1	no	—
259	C₂×Dic₄₇	—	2	2	no	—
260	C₂×Dic₄₇	—	2	2	no	—
261	C₂×Dic₄₇	—	4	2	no	—
262	C₂×Dic₄₇	—	4	2	no	—
263	D₁₈₈	—	2	1	no	—
264	D₁₈₈	—	2	1	no	—
265	C₄×D₄₇	—	4	1	no	—
266	C₄×D₄₇	—	4	1	no	—
267	Dic₉₄	—	2	1	no	—
268	Dic₉₄	—	2	1	no	—
269	C₈×C₄₇	—	2	2	no	—
270	C₈×C₄₇	—	4	1	no	—
271	C₈×C₄₇	—	4	1	no	—
272	C₈×C₄₇	#121	1	2	yes	—
273	C₈×C₄₇	#121	1	2	yes	—
274	C₄₇⋊C₈	—	2	2	no	—
275	C₄₇⋊C₈	—	4	1	no	—
276	C₄₇⋊C₈	—	4	1	no	—
277	C₄₇⋊C₈	C₄×D₄	1	2	yes	—
278	C₄₇⋊C₈	C₄×D₄	1	2	yes	—
279	#21548	—	47	1	no	maximal, Sylow
280	C₂²×C₄₇	—	2	2	no	—
281	C₂²×C₄₇	—	2	2	no	—
282	C₂²×C₄₇	—	2	2	no	—
283	C₂²×C₄₇	—	2	2	no	—
284	C₂²×C₄₇	—	4	2	no	—
285	C₂²×C₄₇	—	4	2	no	—
286	C₂²×C₄₇	—	4	2	no	—
287	C₂²×C₄₇	—	4	1	no	—
288	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
289	C₂²×C₄₇	#525	1	1	yes	characteristic
290	C₂²×C₄₇	#529	1	1	yes	characteristic
291	C₂×D₄₇	—	4	2	no	—
292	C₂×D₄₇	—	4	1	no	—
293	C₄×C₄₇	—	2	2	no	—
294	C₄×C₄₇	—	4	2	no	—
295	C₄×C₄₇	—	4	1	no	—
296	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
297	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
298	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
299	C₄×C₄₇	#532	1	1	yes	characteristic
300	Dic₄₇	—	4	2	no	—
301	Dic₄₇	—	4	2	no	—
302	Dic₄₇	—	4	2	no	—
303	Dic₄₇	—	4	1	no	—
304	#3054	—	47	1	no	—
305	C₂×#443	—	47	1	no	—
306	#2929	—	47	1	no	—
307	#2929	D₄₇	1	1	yes	characteristic, complemented
308	C₂×#405	—	47	1	no	—
309	#1975	—	47	1	no	—
310	#1946	—	47	1	no	—
311	#1938	—	47	1	no	—
312	#1938	—	47	1	no	—
313	#1897	—	47	1	no	—
314	#1897	—	47	1	no	—
315	#1811	—	47	1	no	—
316	#1772	—	47	1	no	—
317	#1764	—	47	1	no	—
318	#1764	—	47	1	no	—
319	C₂×C₄₇	—	2	1	no	—
320	C₂×C₄₇	—	2	1	no	—
321	C₂×C₄₇	—	4	2	no	—
322	C₂×C₄₇	—	8	1	no	—
323	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
324	C₂×C₄₇	#2955	1	2	yes	—
325	D₄₇	—	8	1	no	—
326	C₂×#135	—	47	1	no	—
327	C₂×#131	—	47	1	no	—
328	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
329	C₂²×M₁₆	—	47	1	no	—
330	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
331	#525	—	47	1	no	—
332	#525	C₂×D₄₇	1	1	yes	characteristic
333	C₂×#117	—	47	1	no	—
334	#470	—	47	2	no	—
335	#469	—	47	2	no	—
336	#468	—	47	2	no	—
337	#468	—	47	2	no	—
338	#443	—	94	4	no	—
339	#435	—	2	2	no	—
340	#435	—	94	2	no	—
341	C₈×D₄	—	2	2	no	—
342	C₈×D₄	—	94	2	no	—
343	C₂×#108	—	47	1	no	—
344	C₂×#108	—	47	1	no	—
345	#427	—	47	1	no	—
346	#424	—	47	1	no	—
347	#424	C₂×D₄₇	1	1	yes	characteristic
348	C₂×#104	—	47	1	no	—
349	C₂×#104	—	47	1	no	—
350	C₂×#104	—	47	1	no	—
351	C₂×#104	—	47	1	no	—
352	#416	—	47	1	no	—
353	#416	—	47	1	no	—
354	#408	—	47	1	no	—
355	#408	C₂×D₄₇	1	1	yes	characteristic
356	#407	—	47	1	no	—
357	#407	C₂×D₄₇	1	1	yes	characteristic
358	#405	—	47	1	no	—
359	#405	—	94	4	no	—
360	#405	C₂×D₄₇	1	1	yes	characteristic
361	C₂×#97	—	47	1	no	—
362	C₂×#97	—	47	1	no	—
363	C₂×C₄×C₈	—	47	1	no	—
364	C₂×C₄×C₈	—	47	1	no	—
365	#341	—	47	1	no	—
366	#341	—	47	1	no	—
367	#339	—	47	1	no	—
368	#339	—	47	1	no	—
369	#339	—	47	1	no	—
370	#339	—	47	1	no	—
371	C₄₇	#21548	1	1	yes	characteristic, complemented, Sylow
372	C₂×#41	—	47	1	no	—
373	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
374	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
375	#135	—	94	2	no	—
376	#135	—	94	2	no	—
377	C₂×Q₁₆	—	47	1	no	—
378	C₂×SD₁₆	—	47	1	no	—
379	C₂×SD₁₆	—	47	1	no	—
380	C₂×D₈	—	47	1	no	—
381	#131	—	2	2	no	—
382	#131	—	2	2	no	—
383	#131	—	94	2	no	—
384	#131	—	94	2	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	47	2	no	—
387	C₂×M₁₆	—	47	2	no	—
388	C₂×M₁₆	—	47	1	no	—
389	C₂×M₁₆	—	47	1	no	—
390	C₂×M₁₆	—	94	2	no	—
391	C₂×M₁₆	—	94	2	no	—
392	C₂×M₁₆	—	94	1	no	—
393	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
394	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
395	C₂²×C₈	—	2	2	no	—
396	C₂²×C₈	—	2	2	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	—	47	1	no	—
399	C₂²×C₈	—	47	1	no	—
400	C₂²×C₈	—	94	1	no	—
401	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
402	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
403	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
404	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
405	#123	—	2	1	no	—
406	#123	—	94	1	no	—
407	C₂²⋊Q₈	—	47	2	no	—
408	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
409	#121	—	47	2	no	—
410	#121	C₄×D₄₇	1	2	yes	—
411	#120	—	2	1	no	—
412	#120	—	94	1	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	94	2	no	—
415	#117	—	47	1	no	—
416	#117	—	94	2	no	—
417	#117	—	94	2	no	—
418	#117	C₂²×D₄₇	1	1	yes	characteristic
419	C₂×C₄⋊C₄	—	94	1	no	—
420	C₂×C₂²⋊C₄	—	94	1	no	—
421	C₂×C₄²	—	47	1	no	—
422	C₂×C₄²	—	47	1	no	—
423	#108	—	94	2	no	—
424	#108	—	94	2	no	—
425	#107	—	47	2	no	—
426	#106	—	47	2	no	—
427	C₄⋊C₈	—	2	2	no	—
428	C₄⋊C₈	—	94	2	no	—
429	#104	—	94	2	no	—
430	#104	—	94	2	no	—
431	#104	—	94	2	no	—
432	#104	—	94	2	no	—
433	#103	—	47	2	no	—
434	#103	—	47	2	no	—
435	#102	—	47	2	no	—
436	#102	—	47	2	no	—
437	C₂²⋊C₈	—	2	2	no	—
438	C₂²⋊C₈	—	2	2	no	—
439	C₂²⋊C₈	—	94	2	no	—
440	C₂²⋊C₈	—	94	2	no	—
441	#97	—	2	1	no	—
442	#97	—	94	2	no	—
443	#97	—	94	2	no	—
444	#97	—	94	1	no	—
445	C₄×C₈	—	2	1	no	—
446	C₄×C₈	—	47	4	no	—
447	C₄×C₈	—	94	2	no	—
448	C₄×C₈	—	94	1	no	—
449	C₂⁴	#10625350	1	1	yes	characteristic
450	#41	—	2	1	no	—
451	#41	—	2	1	no	—
452	#41	—	2	1	no	—
453	#41	—	2	1	no	—
454	#41	—	94	1	no	—
455	#41	—	94	1	no	—
456	#41	—	94	1	no	—
457	#41	—	94	1	no	—
458	C₂×Q₈	—	47	1	no	—
459	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	47	1	no	—
463	C₂×D₄	—	94	2	no	—
464	C₂×D₄	—	94	1	no	—
465	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	94	1	no	—
472	C₂²×C₄	—	94	1	no	—
473	C₂²×C₄	—	94	1	no	—
474	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
475	C₂²×C₄	#10625350	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
477	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
478	Q₁₆	—	94	2	no	—
479	SD₁₆	—	94	2	no	—
480	SD₁₆	—	94	2	no	—
481	D₈	—	94	2	no	—
482	M₁₆	—	2	1	no	—
483	M₁₆	—	2	1	no	—
484	M₁₆	—	2	1	no	—
485	M₁₆	—	2	1	no	—
486	M₁₆	—	4	2	no	—
487	M₁₆	—	94	4	no	—
488	M₁₆	—	94	4	no	—
489	M₁₆	—	94	1	no	—
490	M₁₆	—	94	1	no	—
491	M₁₆	—	94	1	no	—
492	M₁₆	—	94	1	no	—
493	M₁₆	—	188	2	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	4	no	—
497	C₂×C₈	—	2	4	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	4	2	no	—
501	C₂×C₈	—	47	1	no	—
502	C₂×C₈	—	47	1	no	—
503	C₂×C₈	—	47	2	no	—
504	C₂×C₈	—	47	2	no	—
505	C₂×C₈	—	47	2	no	—
506	C₂×C₈	—	94	1	no	—
507	C₂×C₈	—	94	1	no	—
508	C₂×C₈	—	94	1	no	—
509	C₂×C₈	—	94	1	no	—
510	C₂×C₈	—	188	2	no	—
511	C₂×C₈	D₄×D₄₇	1	2	yes	—
512	C₂×C₈	#10625352	1	2	yes	—
513	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
514	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
515	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	47	2	no	—
518	C₄⋊C₄	—	94	4	no	—
519	C₄⋊C₄	—	94	2	no	—
520	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	94	4	no	—
525	C₂²⋊C₄	—	94	2	no	—
526	C₂²⋊C₄	—	94	1	no	—
527	C₂²⋊C₄	—	94	2	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	47	2	no	—
530	C₄²	—	47	2	no	—
531	C₄²	—	94	1	no	—
532	C₄²	—	94	1	no	—
533	C₄²	—	94	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	4	2	no	—
538	C₂³	—	94	1	no	—
539	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
540	C₂³	C₂×#10625350	1	1	yes	characteristic
541	Q₈	—	2	1	no	—
542	Q₈	—	2	1	no	—
543	Q₈	—	94	1	no	—
544	Q₈	—	94	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	94	1	no	—
551	D₄	—	94	1	no	—
552	D₄	—	188	4	no	—
553	D₄	—	188	1	no	—
554	D₄	—	188	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	94	2	no	—
566	C₂×C₄	—	94	1	no	—
567	C₂×C₄	—	94	2	no	—
568	C₂×C₄	—	94	2	no	—
569	C₂×C₄	—	188	2	no	—
570	C₂×C₄	—	188	2	no	—
571	C₂×C₄	—	188	1	no	—
572	C₂×C₄	—	188	1	no	—
573	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
574	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
575	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
576	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
577	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
578	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
579	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
580	C₈	—	2	2	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	47	2	no	—
584	C₈	—	47	2	no	—
585	C₈	—	94	2	no	—
586	C₈	—	188	1	no	—
587	C₈	—	188	1	no	—
588	C₈	#13093996	1	2	yes	—
589	C₈	#13093996	1	2	yes	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	188	2	no	—
599	C₂²	—	188	1	no	—
600	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
601	C₂²	#15689632	1	1	yes	characteristic
602	C₂²	#15689653	1	1	yes	characteristic
603	C₄	—	2	2	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	1	no	—
606	C₄	—	188	2	no	—
607	C₄	—	188	2	no	—
608	C₄	—	188	2	no	—
609	C₄	—	188	1	no	—
610	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
611	C₄	C₄×#10625352	1	1	yes	characteristic
612	C₄	C₂×#13093996	1	1	yes	characteristic
613	C₄	#15689669	1	1	yes	characteristic
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	4	2	no	—
617	C₂	—	8	1	no	—
618	C₂	—	376	1	no	—
619	C₂	C₄×#13093996	1	1	yes	characteristic
620	C₂	#20252289	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2929	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20252994	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2929	D₄₇
hypocenter	C₄₇	#21548
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ #2929

Complements

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

N	H ≅ G/N	type
2. C₂×#15689238	C₂	semidirect
3. #20252082	C₂	semidirect
4. C₂×#15689078	C₂	semidirect
5. #20244280	C₂	semidirect
6. #20244138	C₂	semidirect
7. #20244102	C₂	semidirect
8. #20244098	C₂	semidirect
9. #20243837	C₂	semidirect
10. #20243834	C₂	semidirect
11. #20243428	C₂	semidirect
12. #20243268	C₂	semidirect
13. #20243227	C₂	semidirect
14. #20243223	C₂	semidirect
15. C₄₇×#2929	C₂	semidirect
21. #15689379	C₄	semidirect
22. #15689374	C₄	semidirect
23. #15689371	C₄	semidirect
24. #15689367	C₄	semidirect
112. C₈×Dic₄₇	D₄	semidirect
307. #2929	D₄₇	semidirect
371. C₄₇	#21548	semidirect

Maximal subgroups

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

subgroup	index
#20252994	2
C₂×#15689238	2
#20252082	2
C₂×#15689078	2
#20244280	2
#20244138	2
#20244102	2
#20244098	2
#20243837	2
#20243834	2
#20243428	2
#20243268	2
#20243227	2
#20243223	2
C₄₇×#2929	2
#21548	47