Subgroups — #26221654

Order 12032.

1100 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689680	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
3	#20244376	C₂	1	2	yes	maximal, complemented
4	#20244231	C₂	1	2	yes	maximal, complemented
5	#20243854	C₂	1	4	yes	maximal
6	C₄×#13093942	C₂	1	4	yes	maximal, complemented
7	C₄₇×#2920	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10625329	C₂²	1	2	yes	—
9	#15689680	—	2	1	no	—
10	#15689680	—	2	1	no	—
11	#15689680	—	2	1	no	—
12	#15689680	—	2	1	no	—
13	#15689680	—	2	1	no	—
14	#15689680	—	2	1	no	—
15	#15689680	—	2	1	no	—
16	#15689680	—	2	1	no	—
17	C₂×#13094024	C₂²	1	1	yes	characteristic
18	C₂×#13094024	C₂²	1	1	yes	characteristic
19	C₂×#13094016	C₄	1	2	yes	—
20	C₂×#13094003	C₄	1	2	yes	—
21	C₂×#13094003	C₂²	1	2	yes	—
22	C₂×C₄×Dic₉₄	C₄	1	2	yes	—
23	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
24	C₂×#13093983	C₄	1	2	yes	—
25	C₂×#13093942	C₂²	1	8	yes	—
26	C₄×#10625329	—	2	1	no	—
27	C₄×#10625329	—	2	1	no	—
28	C₄×#10625329	C₂²	1	2	yes	—
29	C₄×#10625329	C₂²	1	2	yes	—
30	C₂×#13093935	—	2	1	no	—
31	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
32	#15688891	C₂²	1	8	yes	—
33	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#432	—	2	1	no	—
35	C₄₇×#432	—	2	1	no	—
36	C₄₇×#431	—	2	1	no	—
37	C₄₇×#431	—	2	1	no	—
38	C₄₇×#423	C₂²	1	2	yes	—
39	C₄₇×#407	C₂²	1	2	yes	—
40	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
41	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
42	C₂²×Dic₉₄	C₂³	1	2	yes	—
43	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	—	2	8	no	—
45	C₂×#10625329	C₂³	1	4	yes	—
46	C₂²×C₄₇⋊C₈	—	2	2	no	—
47	#13094024	—	2	1	no	—
48	#13094024	—	2	1	no	—
49	#13094024	—	2	1	no	—
50	#13094024	—	2	1	no	—
51	#13094024	—	2	1	no	—
52	#13094024	—	2	1	no	—
53	#13094024	—	2	1	no	—
54	#13094024	—	2	1	no	—
55	#13094016	—	2	2	no	—
56	#13094016	—	2	2	no	—
57	#13094016	—	2	2	no	—
58	#13094016	—	2	2	no	—
59	#13094003	—	2	2	no	—
60	#13094003	—	2	2	no	—
61	#13094003	—	2	2	no	—
62	#13094003	—	2	2	no	—
63	#13094003	—	2	2	no	—
64	#13094003	—	2	2	no	—
65	#13094003	—	2	2	no	—
66	#13094003	—	2	2	no	—
67	C₄×Dic₉₄	—	2	2	no	—
68	C₄×Dic₉₄	—	2	2	no	—
69	C₄×Dic₉₄	—	2	2	no	—
70	C₄×Dic₉₄	—	2	2	no	—
71	C₄×Dic₉₄	—	2	2	no	—
72	C₄×Dic₉₄	—	2	2	no	—
73	C₄×Dic₉₄	—	2	2	no	—
74	C₄×Dic₉₄	—	2	2	no	—
75	#13093983	—	2	2	no	—
76	#13093983	—	2	2	no	—
77	#13093983	—	2	2	no	—
78	#13093983	—	2	2	no	—
79	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
83	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
84	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
85	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
86	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
87	#13093942	—	2	16	no	—
88	#13093935	—	2	2	no	—
89	#13093935	—	2	2	no	—
90	C₄×C₄₇⋊C₈	—	2	2	no	—
91	C₄×C₄₇⋊C₈	—	2	2	no	—
92	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
96	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₄₇	—	2	2	no	—
109	C₄⋊C₈×C₄₇	—	2	2	no	—
110	C₂²⋊C₈×C₄₇	—	2	2	no	—
111	C₂²⋊C₈×C₄₇	—	2	2	no	—
112	#97×C₄₇	—	2	2	no	—
113	C₄×C₈×C₄₇	—	2	2	no	—
114	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	—	2	4	no	—
116	C₂²×C₄×C₄₇	—	2	4	no	—
117	C₂²×C₄×C₄₇	—	4	2	no	—
118	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
136	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
137	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
138	C₂×Dic₉₄	—	2	2	no	—
139	C₂×Dic₉₄	—	2	2	no	—
140	C₂×Dic₉₄	—	2	2	no	—
141	C₂×Dic₉₄	—	2	2	no	—
142	C₂×Dic₉₄	—	2	8	no	—
143	C₂×Dic₉₄	—	4	4	no	—
144	M₁₆×C₄₇	—	2	8	no	—
145	C₂×C₈×C₄₇	—	2	4	no	—
146	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
147	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
148	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
149	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
150	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
152	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
153	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
154	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₂²⋊Dic₄₇	—	2	4	no	—
163	C₂²⋊Dic₄₇	—	2	4	no	—
164	C₄⋊Dic₄₇	—	2	2	no	—
165	C₄⋊Dic₄₇	—	2	2	no	—
166	C₄⋊Dic₄₇	—	2	2	no	—
167	C₄⋊Dic₄₇	—	2	2	no	—
168	C₄⋊Dic₄₇	—	2	2	no	—
169	C₄⋊Dic₄₇	—	2	2	no	—
170	C₄⋊Dic₄₇	—	2	2	no	—
171	C₄⋊Dic₄₇	—	2	2	no	—
172	Dic₄₇⋊C₄	—	2	4	no	—
173	Dic₄₇⋊C₄	—	2	4	no	—
174	Dic₄₇⋊C₄	—	2	4	no	—
175	Dic₄₇⋊C₄	—	2	4	no	—
176	C₄×Dic₄₇	—	2	4	no	—
177	C₄×Dic₄₇	—	2	4	no	—
178	#10625329	—	2	8	no	—
179	#10625329	—	2	4	no	—
180	#10625329	#41	1	8	yes	—
181	C₂×C₄₇⋊C₈	—	2	8	no	—
182	C₂×C₄₇⋊C₈	—	2	4	no	—
183	C₂³×C₄₇	—	2	2	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	4	1	no	—
186	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	4	1	no	—
203	C₂×C₄×C₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	4	1	no	—
205	C₂×C₄×C₄₇	#101	1	4	yes	complemented
206	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
219	C₂×Dic₄₇	—	2	4	no	—
220	C₂×Dic₄₇	—	2	4	no	—
221	C₂×Dic₄₇	—	2	8	no	—
222	C₂×Dic₄₇	—	4	4	no	—
223	Dic₉₄	—	4	4	no	—
224	Dic₉₄	—	4	4	no	—
225	Dic₉₄	—	4	4	no	—
226	Dic₉₄	—	4	4	no	—
227	C₈×C₄₇	—	4	4	no	—
228	C₄₇⋊C₈	—	2	8	no	—
229	#21425	—	47	1	no	maximal, Sylow
230	C₂²×C₄₇	—	2	1	no	—
231	C₂²×C₄₇	—	2	1	no	—
232	C₂²×C₄₇	—	2	1	no	—
233	C₂²×C₄₇	—	2	1	no	—
234	C₂²×C₄₇	—	2	1	no	—
235	C₂²×C₄₇	—	2	1	no	—
236	C₂²×C₄₇	—	2	1	no	—
237	C₂²×C₄₇	—	4	4	no	—
238	C₂²×C₄₇	C₂×#101	1	2	yes	—
239	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₄₇	C₄×#41	1	2	yes	—
241	C₄×C₄₇	—	2	1	no	—
242	C₄×C₄₇	—	2	1	no	—
243	C₄×C₄₇	—	2	1	no	—
244	C₄×C₄₇	—	2	1	no	—
245	C₄×C₄₇	—	2	1	no	—
246	C₄×C₄₇	—	2	1	no	—
247	C₄×C₄₇	—	2	1	no	—
248	C₄×C₄₇	C₂×#101	1	2	yes	—
249	C₄×C₄₇	C₂×#101	1	2	yes	—
250	C₄×C₄₇	#413	1	2	yes	—
251	C₄×C₄₇	#525	1	2	yes	—
252	C₄×C₄₇	#532	1	2	yes	—
253	Dic₄₇	—	4	4	no	—
254	Dic₄₇	—	4	4	no	—
255	C₂×#533	—	47	1	no	—
256	#2920	D₄₇	1	1	yes	characteristic
257	C₂×C₄×M₁₆	—	47	1	no	—
258	#1997	—	47	2	no	—
259	#1966	—	47	2	no	—
260	#1901	—	47	4	no	—
261	C₄×#101	—	47	4	no	—
262	C₂×C₄₇	—	2	2	no	—
263	C₂×C₄₇	—	2	2	no	—
264	C₂×C₄₇	—	4	1	no	—
265	C₂×C₄₇	#2297	1	1	yes	characteristic
266	C₂×C₄₇	C₂²×#101	1	1	yes	characteristic
267	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
268	C₂²×M₁₆	—	47	2	no	—
269	#533	—	94	1	no	—
270	#533	—	94	1	no	—
271	#533	—	94	1	no	—
272	#533	—	94	1	no	—
273	#533	—	94	1	no	—
274	#533	—	94	1	no	—
275	#533	—	94	1	no	—
276	#533	—	94	1	no	—
277	C₂×C₄⋊Q₈	—	47	1	no	—
278	C₂×C₄⋊Q₈	—	47	1	no	—
279	C₂×#125	—	47	2	no	—
280	C₂×C₂²⋊Q₈	—	47	2	no	—
281	C₂×C₂²⋊Q₈	—	47	2	no	—
282	C₂×C₄×Q₈	—	47	2	no	—
283	C₂×C₄×Q₈	—	47	2	no	—
284	C₂×#117	—	47	2	no	—
285	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
286	#432	—	2	1	no	—
287	#432	—	2	1	no	—
288	#431	—	2	1	no	—
289	#431	—	2	1	no	—
290	#423	C₂×D₄₇	1	2	yes	—
291	C₂×#101	—	47	8	no	—
292	#407	C₂×D₄₇	1	2	yes	—
293	C₄×M₁₆	—	47	2	no	—
294	C₄×M₁₆	—	47	2	no	—
295	C₄×M₁₆	—	94	1	no	—
296	C₄×M₁₆	—	94	1	no	—
297	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
298	C₂×#97	—	94	1	no	—
299	C₂×C₄×C₈	—	94	1	no	—
300	#343	—	47	8	no	—
301	C₄₇	#21425	1	1	yes	characteristic, complemented, Sylow
302	C₂²×Q₈	—	47	2	no	—
303	C₂²×Q₈	—	47	2	no	—
304	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
305	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
306	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
307	C₂×M₁₆	—	47	4	no	—
308	C₂×M₁₆	—	94	8	no	—
309	C₂×M₁₆	—	94	2	no	—
310	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
311	C₂²×C₈	—	94	2	no	—
312	C₄⋊Q₈	—	94	1	no	—
313	C₄⋊Q₈	—	94	1	no	—
314	C₄⋊Q₈	—	94	1	no	—
315	C₄⋊Q₈	—	94	1	no	—
316	C₄⋊Q₈	—	94	1	no	—
317	C₄⋊Q₈	—	94	1	no	—
318	C₄⋊Q₈	—	94	1	no	—
319	C₄⋊Q₈	—	94	1	no	—
320	#125	—	94	2	no	—
321	#125	—	94	2	no	—
322	#125	—	94	2	no	—
323	#125	—	94	2	no	—
324	C₂²⋊Q₈	—	94	2	no	—
325	C₂²⋊Q₈	—	94	2	no	—
326	C₂²⋊Q₈	—	94	2	no	—
327	C₂²⋊Q₈	—	94	2	no	—
328	C₂²⋊Q₈	—	94	2	no	—
329	C₂²⋊Q₈	—	94	2	no	—
330	C₂²⋊Q₈	—	94	2	no	—
331	C₂²⋊Q₈	—	94	2	no	—
332	C₄×Q₈	—	94	2	no	—
333	C₄×Q₈	—	94	2	no	—
334	C₄×Q₈	—	94	2	no	—
335	C₄×Q₈	—	94	2	no	—
336	C₄×Q₈	—	94	2	no	—
337	C₄×Q₈	—	94	2	no	—
338	C₄×Q₈	—	94	2	no	—
339	C₄×Q₈	—	94	2	no	—
340	#117	—	94	2	no	—
341	#117	—	94	2	no	—
342	#117	—	94	2	no	—
343	#117	—	94	2	no	—
344	C₂×C₄⋊C₄	—	47	2	no	—
345	C₂×C₄⋊C₄	—	47	2	no	—
346	C₂×C₄⋊C₄	—	47	4	no	—
347	C₂×C₄⋊C₄	—	47	4	no	—
348	C₂×C₄⋊C₄	—	47	2	no	—
349	C₂×C₄⋊C₄	—	47	2	no	—
350	C₂×C₂²⋊C₄	—	47	4	no	—
351	C₂×C₄²	—	47	4	no	—
352	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
353	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
354	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
355	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
356	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
357	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
358	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
359	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
362	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
363	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
364	C₄⋊C₈	—	2	2	no	—
365	C₄⋊C₈	—	2	2	no	—
366	#101	—	94	16	no	—
367	C₂²⋊C₈	—	2	2	no	—
368	C₂²⋊C₈	—	2	2	no	—
369	#97	—	2	2	no	—
370	#97	—	94	2	no	—
371	#97	—	94	2	no	—
372	C₄×C₈	—	2	2	no	—
373	C₄×C₈	—	94	2	no	—
374	C₄×C₈	—	94	2	no	—
375	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
376	C₂×Q₈	—	94	2	no	—
377	C₂×Q₈	—	94	2	no	—
378	C₂×Q₈	—	94	2	no	—
379	C₂×Q₈	—	94	2	no	—
380	C₂×Q₈	—	94	8	no	—
381	C₂×Q₈	—	188	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	47	4	no	—
386	C₂²×C₄	—	47	4	no	—
387	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
388	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
389	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
390	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
391	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
392	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
393	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
394	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
398	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
399	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
403	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
404	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
405	M₁₆	—	2	8	no	—
406	M₁₆	—	47	8	no	—
407	M₁₆	—	94	8	no	—
408	M₁₆	—	94	4	no	—
409	C₂×C₈	—	2	4	no	—
410	C₂×C₈	—	94	8	no	—
411	C₂×C₈	—	94	4	no	—
412	C₄⋊C₄	—	94	4	no	—
413	C₄⋊C₄	—	94	4	no	—
414	C₄⋊C₄	—	94	4	no	—
415	C₄⋊C₄	—	94	4	no	—
416	C₄⋊C₄	—	94	2	no	—
417	C₄⋊C₄	—	94	2	no	—
418	C₄⋊C₄	—	94	2	no	—
419	C₄⋊C₄	—	94	2	no	—
420	C₄⋊C₄	—	94	2	no	—
421	C₄⋊C₄	—	94	2	no	—
422	C₄⋊C₄	—	94	2	no	—
423	C₄⋊C₄	—	94	2	no	—
424	C₂²⋊C₄	—	94	4	no	—
425	C₂²⋊C₄	—	94	4	no	—
426	C₄²	—	94	4	no	—
427	C₄²	—	94	4	no	—
428	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
429	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
430	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
431	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
432	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
433	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
434	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
435	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
436	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
437	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
438	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
439	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
440	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
441	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
442	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
443	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	4	1	no	—
447	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
448	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
449	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
450	Q₈	—	188	4	no	—
451	Q₈	—	188	4	no	—
452	Q₈	—	188	4	no	—
453	Q₈	—	188	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	94	4	no	—
471	C₂×C₄	—	94	4	no	—
472	C₂×C₄	—	94	8	no	—
473	C₂×C₄	—	188	4	no	—
474	C₂×C₄	#13093942	1	4	yes	complemented
475	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
476	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
477	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
478	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
479	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
480	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
481	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
482	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
483	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
484	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
487	C₂×C₄	#41×D₄₇	1	4	yes	—
488	C₈	—	4	4	no	—
489	C₈	—	94	8	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	4	4	no	—
498	C₂²	C₂×#13093942	1	2	yes	—
499	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
500	C₂²	#15689591	1	2	yes	—
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	188	4	no	—
509	C₄	—	188	4	no	—
510	C₄	C₂×#13093942	1	2	yes	—
511	C₄	C₂×#13093942	1	2	yes	—
512	C₄	#15689105	1	2	yes	—
513	C₄	#15689635	1	2	yes	—
514	C₄	#15689669	1	2	yes	—
515	C₂	—	2	2	no	—
516	C₂	—	2	2	no	—
517	C₂	—	4	1	no	—
518	C₂	#20245876	1	1	yes	characteristic
519	C₂	C₂²×#13093942	1	1	yes	characteristic
520	C₂	C₂×#15689105	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂³×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2920	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2920	D₄₇
hypocenter	C₄₇	#21425
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #20244376	C₂	semidirect
4. #20244231	C₂	semidirect
6. C₄×#13093942	C₂	semidirect
205. C₂×C₄×C₄₇	#101	semidirect
301. C₄₇	#21425	semidirect
474. C₂×C₄	#13093942	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689680	2
C₂×C₄×#10625329	2
#20244376	2
#20244231	2
#20243854	2
C₄×#13093942	2
C₄₇×#2920	2
#21425	47