Subgroups — #26121614

Order 12032.

1152 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689889	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689105	C₂	1	1	yes	maximal, characteristic
3	#20251832	C₂	1	1	yes	maximal, characteristic
4	#20243114	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₇⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1738	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625350	C₂²	1	1	yes	characteristic
9	#15689889	—	2	2	no	—
10	#15689889	—	2	2	no	—
11	#15689889	—	2	2	no	—
12	#15689889	C₄	1	4	yes	—
13	C₂×#13094032	—	2	2	no	—
14	C₂×#13094030	—	2	2	no	—
15	C₂²×#10625329	C₂²	1	1	yes	characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625329	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×D₄₇	—	2	2	no	—
19	#15689105	—	2	2	no	—
20	#15689105	—	2	2	no	—
21	C₂×#13093942	C₄	1	2	yes	—
22	C₂×#13093940	C₄	1	2	yes	—
23	#15689091	C₄	1	4	yes	—
24	#15689089	—	2	2	no	—
25	#15689086	—	2	2	no	—
26	#15688887	—	2	2	no	—
27	C₄₇⋊#338	—	2	2	no	—
28	C₄₇⋊#338	—	2	2	no	—
29	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#341	—	2	2	no	—
33	C₂×#10625350	—	2	1	no	—
34	C₂×#10625350	—	2	1	no	—
35	C₂×#10625350	—	2	1	no	—
36	C₂×#10625350	—	2	1	no	—
37	C₂×#10625350	—	2	1	no	—
38	C₂×#10625350	—	2	1	no	—
39	C₂×#10625350	—	2	1	no	—
40	C₂×#10625350	—	2	1	no	—
41	C₂×#10625350	C₂×C₄	1	2	yes	—
42	C₂×#10625350	C₂×C₄	1	2	yes	—
43	C₂×#10625350	D₄	1	2	yes	—
44	C₂×#10625350	D₄	1	2	yes	—
45	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₂²⋊D₄₇	Q₈	1	2	yes	—
48	C₂²×C₄×D₄₇	D₄	1	2	yes	—
49	#13094032	—	2	8	no	—
50	#13094032	—	2	8	no	—
51	#13094030	—	2	8	no	—
52	#13094030	—	2	8	no	—
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂×#10625329	—	2	1	no	—
57	C₂×#10625329	—	2	1	no	—
58	C₂×#10625329	—	2	1	no	—
59	C₂×#10625329	—	2	1	no	—
60	C₂×#10625329	—	2	1	no	—
61	C₂×#10625329	—	2	1	no	—
62	C₂×#10625329	—	2	1	no	—
63	C₂×#10625329	—	2	1	no	—
64	C₂×#10625329	—	2	1	no	—
65	C₂×#10625329	—	2	1	no	—
66	C₂×#10625329	—	2	1	no	—
67	C₂×#10625329	—	2	1	no	—
68	C₂×#10625329	C₂×C₄	1	2	yes	—
69	C₂×#10625329	C₂×C₄	1	2	yes	—
70	C₂×#10625329	D₄	1	2	yes	—
71	C₂×#10625324	—	2	4	no	—
72	M₁₆×D₄₇	—	2	8	no	—
73	M₁₆×D₄₇	—	2	8	no	—
74	C₂²×C₄₇⋊C₈	—	2	1	no	—
75	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
76	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
77	C₂×C₈×D₄₇	—	2	4	no	—
78	#13093942	—	2	4	no	—
79	#13093940	—	2	4	no	—
80	(C₂×D₄₇)⋊C₈	—	2	8	no	—
81	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₄₇	—	2	1	no	—
83	C₂×M₁₆×C₄₇	—	2	1	no	—
84	C₂×M₁₆×C₄₇	—	2	1	no	—
85	C₂×M₁₆×C₄₇	—	2	1	no	—
86	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	—	2	1	no	—
89	C₂×M₁₆×C₄₇	—	2	1	no	—
90	C₂×M₁₆×C₄₇	—	2	1	no	—
91	C₂×M₁₆×C₄₇	—	2	1	no	—
92	C₂×M₁₆×C₄₇	—	2	1	no	—
93	C₂×M₁₆×C₄₇	—	2	1	no	—
94	C₂×M₁₆×C₄₇	—	2	1	no	—
95	C₂×M₁₆×C₄₇	—	2	1	no	—
96	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
97	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
98	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
99	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
100	C₂²×C₈×C₄₇	—	2	1	no	—
101	C₂²×C₈×C₄₇	—	2	1	no	—
102	C₂²×C₈×C₄₇	D₄	1	2	yes	—
103	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
104	C₂³×D₄₇	C₄⋊C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
119	C₂×C₂²⋊D₄₇	—	2	2	no	—
120	C₂×C₂²⋊D₄₇	—	2	2	no	—
121	C₂×C₂²⋊D₄₇	—	2	2	no	—
122	C₂×C₂²⋊D₄₇	—	2	2	no	—
123	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	4	yes	—
124	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	4	yes	—
125	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
126	#10625350	—	2	2	no	—
127	#10625350	—	2	2	no	—
128	#10625350	—	2	2	no	—
129	#10625350	—	2	2	no	—
130	#10625350	—	2	2	no	—
131	#10625350	—	2	2	no	—
132	#10625350	—	2	2	no	—
133	#10625350	—	2	2	no	—
134	#10625350	—	2	2	no	—
135	#10625350	—	2	2	no	—
136	#10625350	—	2	2	no	—
137	#10625350	—	2	2	no	—
138	#10625350	—	2	2	no	—
139	#10625350	—	2	2	no	—
140	#10625350	—	2	2	no	—
141	#10625350	—	2	2	no	—
142	C₂×D₁₈₈	—	2	1	no	—
143	C₂×D₁₈₈	—	2	1	no	—
144	C₂×D₁₈₈	—	2	1	no	—
145	C₂×D₁₈₈	—	2	1	no	—
146	C₂×D₁₈₈	C₄²	1	2	yes	—
147	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×D₄₇	—	2	2	no	—
149	C₂×C₄×D₄₇	—	2	2	no	—
150	C₂×C₄×D₄₇	—	2	2	no	—
151	C₂×C₄×D₄₇	—	2	2	no	—
152	C₂×C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
153	C₂×C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
154	C₂×Dic₉₄	—	2	1	no	—
155	C₂×Dic₉₄	—	2	1	no	—
156	C₂×Dic₉₄	—	2	1	no	—
157	C₂×Dic₉₄	—	2	1	no	—
158	C₂×Dic₉₄	C₄²	1	2	yes	—
159	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
160	M₁₆×C₄₇	—	2	2	no	—
161	M₁₆×C₄₇	—	2	2	no	—
162	M₁₆×C₄₇	—	2	2	no	—
163	M₁₆×C₄₇	—	2	2	no	—
164	M₁₆×C₄₇	—	2	2	no	—
165	M₁₆×C₄₇	—	2	2	no	—
166	M₁₆×C₄₇	—	2	2	no	—
167	M₁₆×C₄₇	—	2	2	no	—
168	M₁₆×C₄₇	—	4	1	no	—
169	M₁₆×C₄₇	—	4	1	no	—
170	M₁₆×C₄₇	—	4	1	no	—
171	M₁₆×C₄₇	—	4	1	no	—
172	C₂×C₈×C₄₇	—	2	2	no	—
173	C₂×C₈×C₄₇	—	2	2	no	—
174	C₂×C₈×C₄₇	—	2	2	no	—
175	C₂×C₈×C₄₇	—	2	2	no	—
176	C₂×C₈×C₄₇	—	4	1	no	—
177	C₂×C₈×C₄₇	—	4	1	no	—
178	C₂×C₈×C₄₇	—	4	1	no	—
179	C₂×C₈×C₄₇	—	4	1	no	—
180	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
181	#10625329	—	2	2	no	—
182	#10625329	—	2	2	no	—
183	#10625329	—	2	2	no	—
184	#10625329	—	2	2	no	—
185	#10625329	—	2	2	no	—
186	#10625329	—	2	2	no	—
187	#10625329	—	4	1	no	—
188	#10625329	—	4	1	no	—
189	#10625329	—	4	1	no	—
190	#10625329	—	4	1	no	—
191	#10625329	—	4	1	no	—
192	#10625329	—	4	1	no	—
193	C₂×C₄₇⋊C₈	—	2	2	no	—
194	C₂×C₄₇⋊C₈	—	2	2	no	—
195	C₂×C₄₇⋊C₈	—	2	2	no	—
196	C₂×C₄₇⋊C₈	—	2	2	no	—
197	C₂×C₄₇⋊C₈	—	2	2	no	—
198	C₂×C₄₇⋊C₈	—	2	2	no	—
199	C₂×C₄₇⋊C₈	—	4	1	no	—
200	C₂×C₄₇⋊C₈	—	4	1	no	—
201	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
202	#10625324	—	2	16	no	—
203	C₈×D₄₇	—	2	16	no	—
204	C₂³×C₄₇	—	8	1	no	—
205	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
209	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
210	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
211	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
212	C₂²×D₄₇	—	2	2	no	—
213	C₂²×D₄₇	—	2	2	no	—
214	C₂²×D₄₇	—	8	2	no	—
215	C₂²×D₄₇	#95	1	4	yes	—
216	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
223	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
243	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
244	C₂²⋊D₄₇	—	2	4	no	—
245	C₂²⋊D₄₇	—	2	4	no	—
246	C₂²⋊D₄₇	—	2	4	no	—
247	C₂²⋊D₄₇	—	2	4	no	—
248	C₂×Dic₄₇	—	2	2	no	—
249	C₂×Dic₄₇	—	2	2	no	—
250	C₂×Dic₄₇	#95	1	4	yes	—
251	D₁₈₈	—	2	2	no	—
252	D₁₈₈	—	2	2	no	—
253	D₁₈₈	—	2	2	no	—
254	D₁₈₈	—	2	2	no	—
255	C₄×D₄₇	—	2	4	no	—
256	C₄×D₄₇	—	2	4	no	—
257	C₄×D₄₇	—	2	4	no	—
258	C₄×D₄₇	—	2	4	no	—
259	Dic₉₄	—	2	2	no	—
260	Dic₉₄	—	2	2	no	—
261	Dic₉₄	—	2	2	no	—
262	Dic₉₄	—	2	2	no	—
263	C₈×C₄₇	—	2	4	no	—
264	C₈×C₄₇	—	4	2	no	—
265	C₈×C₄₇	—	4	2	no	—
266	C₄₇⋊C₈	—	2	4	no	—
267	C₄₇⋊C₈	—	4	2	no	—
268	C₄₇⋊C₈	—	4	2	no	—
269	#10744	—	47	1	no	maximal, Sylow
270	C₂²×C₄₇	—	4	1	no	—
271	C₂²×C₄₇	—	4	1	no	—
272	C₂²×C₄₇	—	4	1	no	—
273	C₂²×C₄₇	—	4	1	no	—
274	C₂²×C₄₇	—	4	1	no	—
275	C₂²×C₄₇	—	4	1	no	—
276	C₂²×C₄₇	—	4	1	no	—
277	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
278	C₂²×C₄₇	#380	1	1	yes	characteristic
279	C₂²×C₄₇	#380	1	1	yes	characteristic
280	C₂²×C₄₇	#385	1	1	yes	characteristic
281	C₂²×C₄₇	#385	1	1	yes	characteristic
282	C₂²×C₄₇	#385	1	1	yes	characteristic
283	C₂²×C₄₇	#385	1	1	yes	characteristic
284	C₂×D₄₇	—	2	4	no	—
285	C₂×D₄₇	—	4	4	no	—
286	C₂×D₄₇	—	4	4	no	—
287	C₂×D₄₇	—	8	2	no	—
288	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
289	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
290	C₄×C₄₇	#379	1	1	yes	characteristic
291	C₄×C₄₇	#381	1	1	yes	characteristic
292	C₄×C₄₇	#386	1	1	yes	characteristic
293	C₄×C₄₇	#386	1	1	yes	characteristic
294	C₄×C₄₇	#386	1	1	yes	characteristic
295	C₄×C₄₇	#386	1	1	yes	characteristic
296	Dic₄₇	—	2	4	no	—
297	C₂×#568	—	47	1	no	—
298	C₂×#413	—	47	1	no	—
299	#2879	—	47	1	no	—
300	#1738	—	47	1	no	—
301	#1738	D₄₇	1	1	yes	characteristic, complemented
302	C₂×#338	—	47	1	no	—
303	C₂×#338	—	47	1	no	—
304	C₂×C₄₇	—	2	1	no	—
305	C₂×C₄₇	—	2	1	no	—
306	C₂×C₄₇	—	2	1	no	—
307	C₂×C₄₇	—	2	1	no	—
308	C₂×C₄₇	—	2	1	no	—
309	C₂×C₄₇	—	2	1	no	—
310	C₂×C₄₇	—	2	1	no	—
311	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
312	D₄₇	—	4	4	no	—
313	C₂²×#41	—	47	1	no	—
314	#568	—	47	4	no	—
315	#568	—	94	2	no	—
316	#568	—	94	2	no	—
317	#568	—	94	2	no	—
318	C₂×#131	—	94	2	no	—
319	C₂×#131	—	94	2	no	—
320	C₂²×M₁₆	—	47	1	no	—
321	C₂²×M₁₆	—	47	1	no	—
322	C₂²×M₁₆	—	47	1	no	—
323	C₂²×M₁₆	—	94	2	no	—
324	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
325	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
326	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
327	#413	—	94	2	no	—
328	#413	—	94	2	no	—
329	C₂×#101	—	47	2	no	—
330	C₂×#100	—	47	2	no	—
331	#408	—	47	4	no	—
332	#408	—	94	2	no	—
333	#407	—	94	2	no	—
334	#341	—	2	2	no	—
335	#341	—	94	2	no	—
336	#338	—	94	2	no	—
337	#338	—	94	2	no	—
338	C₄₇	#10744	1	1	yes	characteristic, complemented, Sylow
339	C₂×#41	—	47	2	no	—
340	C₂×#41	—	47	2	no	—
341	C₂×#41	—	47	2	no	—
342	C₂×#41	—	47	2	no	—
343	C₂×#41	—	94	1	no	—
344	C₂×#41	—	94	1	no	—
345	C₂×#41	—	94	1	no	—
346	C₂×#41	—	94	1	no	—
347	C₂×#41	—	94	1	no	—
348	C₂×#41	—	94	1	no	—
349	C₂×#41	—	94	1	no	—
350	C₂×#41	—	94	1	no	—
351	C₂²×Q₈	—	47	1	no	—
352	C₂²×D₄	—	47	2	no	—
353	C₂²×D₄	—	47	1	no	—
354	C₂³×C₄	—	47	2	no	—
355	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
356	#131	—	94	8	no	—
357	#131	—	94	8	no	—
358	#131	—	94	8	no	—
359	#131	—	94	8	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	47	2	no	—
375	C₂×M₁₆	—	47	2	no	—
376	C₂×M₁₆	—	47	2	no	—
377	C₂×M₁₆	—	94	4	no	—
378	C₂×M₁₆	—	94	8	no	—
379	C₂×M₁₆	—	94	8	no	—
380	C₂×M₁₆	—	94	1	no	—
381	C₂×M₁₆	—	94	1	no	—
382	C₂×M₁₆	—	94	1	no	—
383	C₂×M₁₆	—	94	1	no	—
384	C₂×M₁₆	—	94	1	no	—
385	C₂×M₁₆	—	94	1	no	—
386	C₂×M₁₆	—	94	1	no	—
387	C₂×M₁₆	—	94	1	no	—
388	C₂×M₁₆	—	94	1	no	—
389	C₂×M₁₆	—	94	1	no	—
390	C₂×M₁₆	—	94	1	no	—
391	C₂×M₁₆	—	94	1	no	—
392	C₂×M₁₆	—	94	1	no	—
393	C₂×M₁₆	—	94	1	no	—
394	C₂×M₁₆	—	94	1	no	—
395	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
396	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
397	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
398	C₂×M₁₆	D₁₈₈	1	2	yes	—
399	C₂²×C₈	—	2	1	no	—
400	C₂²×C₈	—	2	1	no	—
401	C₂²×C₈	—	47	2	no	—
402	C₂²×C₈	—	47	2	no	—
403	C₂²×C₈	—	94	4	no	—
404	C₂²×C₈	—	94	1	no	—
405	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
406	#101	—	94	4	no	—
407	#100	—	94	4	no	—
408	C₂²⋊C₈	—	94	8	no	—
409	C₂⁴	—	47	2	no	—
410	C₂⁴	Q₈×D₄₇	1	1	yes	characteristic
411	#41	—	94	2	no	—
412	#41	—	94	2	no	—
413	#41	—	94	2	no	—
414	#41	—	94	2	no	—
415	#41	—	94	2	no	—
416	#41	—	94	2	no	—
417	#41	—	94	2	no	—
418	#41	—	94	2	no	—
419	#41	—	94	2	no	—
420	#41	—	94	2	no	—
421	#41	—	94	2	no	—
422	#41	—	94	2	no	—
423	#41	—	94	2	no	—
424	#41	—	94	2	no	—
425	#41	—	94	2	no	—
426	#41	—	94	2	no	—
427	C₂×Q₈	—	47	2	no	—
428	C₂×Q₈	—	47	2	no	—
429	C₂×Q₈	—	94	1	no	—
430	C₂×Q₈	—	94	1	no	—
431	C₂×Q₈	—	94	1	no	—
432	C₂×Q₈	—	94	1	no	—
433	C₂×D₄	—	47	4	no	—
434	C₂×D₄	—	47	4	no	—
435	C₂×D₄	—	47	2	no	—
436	C₂×D₄	—	47	2	no	—
437	C₂×D₄	—	94	2	no	—
438	C₂×D₄	—	94	2	no	—
439	C₂×D₄	—	94	2	no	—
440	C₂×D₄	—	94	2	no	—
441	C₂×D₄	—	94	1	no	—
442	C₂×D₄	—	94	1	no	—
443	C₂×D₄	—	94	1	no	—
444	C₂×D₄	—	94	1	no	—
445	C₂²×C₄	—	47	2	no	—
446	C₂²×C₄	—	47	4	no	—
447	C₂²×C₄	—	47	4	no	—
448	C₂²×C₄	—	94	2	no	—
449	C₂²×C₄	—	94	2	no	—
450	C₂²×C₄	—	94	2	no	—
451	C₂²×C₄	—	94	2	no	—
452	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
456	C₂²×C₄	#10625350	1	1	yes	characteristic
457	C₂²×C₄	#10625350	1	1	yes	characteristic
458	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
459	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
460	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
461	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
462	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
463	C₂²×C₄	#10625352	1	1	yes	characteristic
464	C₂²×C₄	#10625354	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	2	2	no	—
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	4	1	no	—
475	M₁₆	—	4	1	no	—
476	M₁₆	—	4	1	no	—
477	M₁₆	—	4	1	no	—
478	M₁₆	—	94	16	no	—
479	M₁₆	—	94	2	no	—
480	M₁₆	—	94	2	no	—
481	M₁₆	—	94	2	no	—
482	M₁₆	—	94	2	no	—
483	M₁₆	—	94	2	no	—
484	M₁₆	—	94	2	no	—
485	M₁₆	—	188	1	no	—
486	M₁₆	—	188	1	no	—
487	M₁₆	—	188	1	no	—
488	M₁₆	—	188	1	no	—
489	M₁₆	—	188	1	no	—
490	M₁₆	—	188	1	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	4	1	no	—
496	C₂×C₈	—	4	1	no	—
497	C₂×C₈	—	4	1	no	—
498	C₂×C₈	—	4	1	no	—
499	C₂×C₈	—	47	4	no	—
500	C₂×C₈	—	94	16	no	—
501	C₂×C₈	—	94	2	no	—
502	C₂×C₈	—	94	2	no	—
503	C₂×C₈	—	94	2	no	—
504	C₂×C₈	—	94	2	no	—
505	C₂×C₈	—	94	2	no	—
506	C₂×C₈	—	94	2	no	—
507	C₂×C₈	—	188	1	no	—
508	C₂×C₈	—	188	1	no	—
509	C₂×C₈	(C₂×D₄₇)⋊C₄	1	4	yes	—
510	C₂³	—	8	1	no	—
511	C₂³	—	47	4	no	—
512	C₂³	—	94	2	no	—
513	C₂³	—	94	2	no	—
514	C₂³	—	376	2	no	—
515	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
516	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
517	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
518	C₂³	#13094000	1	1	yes	characteristic
519	C₂³	#13094002	1	1	yes	characteristic
520	C₂³	#13094002	1	1	yes	characteristic
521	C₂³	#13094004	1	1	yes	characteristic
522	Q₈	—	94	2	no	—
523	Q₈	—	94	2	no	—
524	Q₈	—	94	2	no	—
525	Q₈	—	94	2	no	—
526	D₄	—	94	4	no	—
527	D₄	—	94	4	no	—
528	D₄	—	94	4	no	—
529	D₄	—	94	4	no	—
530	D₄	—	94	2	no	—
531	D₄	—	94	2	no	—
532	D₄	—	94	2	no	—
533	D₄	—	94	2	no	—
534	C₂×C₄	—	47	4	no	—
535	C₂×C₄	—	94	2	no	—
536	C₂×C₄	—	94	2	no	—
537	C₂×C₄	—	94	4	no	—
538	C₂×C₄	—	94	4	no	—
539	C₂×C₄	—	94	4	no	—
540	C₂×C₄	—	94	4	no	—
541	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
542	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
543	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
544	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
545	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
546	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
547	C₂×C₄	#13093981	1	1	yes	characteristic
548	C₂×C₄	#13093982	1	1	yes	characteristic
549	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
550	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
551	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
552	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
553	C₂×C₄	#13093986	1	1	yes	characteristic
554	C₂×C₄	#13093986	1	1	yes	characteristic
555	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
556	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
557	C₂×C₄	#13093992	1	1	yes	characteristic
558	C₂×C₄	#13093992	1	1	yes	characteristic
559	C₂×C₄	#13093994	1	1	yes	characteristic
560	C₂×C₄	#13093994	1	1	yes	characteristic
561	C₂×C₄	#13093995	1	1	yes	characteristic
562	C₂×C₄	#13093997	1	1	yes	characteristic
563	C₂×C₄	#13093997	1	1	yes	characteristic
564	C₂×C₄	#13093999	1	1	yes	characteristic
565	C₂×C₄	#13094006	1	1	yes	characteristic
566	C₂×C₄	#13094006	1	1	yes	characteristic
567	C₂×C₄	#13094009	1	1	yes	characteristic
568	C₂×C₄	#13094009	1	1	yes	characteristic
569	C₈	—	2	4	no	—
570	C₈	—	4	2	no	—
571	C₈	—	4	2	no	—
572	C₈	—	94	4	no	—
573	C₈	—	188	2	no	—
574	C₈	—	188	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	94	4	no	—
583	C₂²	—	376	2	no	—
584	C₂²	—	188	4	no	—
585	C₂²	—	188	4	no	—
586	C₂²	#95×D₄₇	1	1	yes	characteristic
587	C₂²	#15688980	1	1	yes	characteristic
588	C₂²	#15688982	1	1	yes	characteristic
589	C₂²	#15688994	1	1	yes	characteristic
590	C₂²	#15688994	1	1	yes	characteristic
591	C₂²	#15688997	1	1	yes	characteristic
592	C₂²	#15688997	1	1	yes	characteristic
593	C₄	—	94	4	no	—
594	C₄	#15688970	1	1	yes	characteristic
595	C₄	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
596	C₄	#15688978	1	1	yes	characteristic
597	C₄	#15688985	1	1	yes	characteristic
598	C₄	#15688999	1	1	yes	characteristic
599	C₄	#15688999	1	1	yes	characteristic
600	C₄	#15689001	1	1	yes	characteristic
601	C₄	#15689001	1	1	yes	characteristic
602	C₂	—	2	1	no	—
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	2	1	no	—
609	C₂	—	188	4	no	—
610	C₂	(C₂×D₄₇)⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15688999
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#1738	C₂
socle	C₂×C₄₇	C₂²⋊#95
prime radical	C₂²×#10625350	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#1738	D₄₇
hypocenter	C₄₇	#10744
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1738

Complements

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

N	H ≅ G/N	type
4. #20243114	C₂	semidirect
5. C₂×C₄₇⋊#338	C₂	semidirect
6. C₂×C₄₇⋊#338	C₂	semidirect
7. C₄₇×#1738	C₂	semidirect
301. #1738	D₄₇	semidirect
338. C₄₇	#10744	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689889	2
C₂×#15689105	2
#20251832	2
#20243114	2
C₂×C₄₇⋊#338	2
C₄₇×#1738	2
#10744	47