Subgroups — #26121736

Order 12032.

1164 conjugacy classes of subgroups.

The subgroup lattice has 620 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	C₂×#15689096	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688894	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688893	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243126	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1742	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	—	2	2	no	—
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	C₂×M₁₆×D₄₇	C₄	1	4	yes	complemented
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	#15689105	—	2	2	no	—
20	#15689105	—	2	2	no	—
21	C₂×#13093942	C₄	1	2	yes	complemented
22	C₂×#13093940	C₄	1	2	yes	complemented
23	#15689096	—	2	2	no	—
24	#15689096	—	2	2	no	—
25	C₂×#13093938	C₄	1	4	yes	—
26	#15688894	—	2	2	no	—
27	#15688893	—	2	2	no	—
28	#15688891	—	2	2	no	—
29	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#343	—	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	D₄	1	2	yes	—
42	C₂×#10625350	D₄	1	2	yes	—
43	C₂×#10625350	D₄	1	2	yes	—
44	C₂×#10625350	Q₈	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	C₂×C₄	1	2	yes	—
48	C₂²×C₄×D₄₇	C₂×C₄	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	C₂×C₄	1	2	yes	—
62	C₂×#10625329	C₂×C₄	1	2	yes	—
63	C₂×#10625329	D₄	1	2	yes	—
64	C₂×#10625329	D₄	1	2	yes	—
65	C₂×#10625324	—	2	4	no	—
66	M₁₆×D₄₇	—	2	8	no	—
67	M₁₆×D₄₇	—	2	8	no	—
68	C₂²×C₄₇⋊C₈	—	2	1	no	—
69	C₂²×C₄₇⋊C₈	—	2	1	no	—
70	C₂×C₈×D₄₇	—	2	4	no	—
71	#13093983	—	2	1	no	—
72	#13093983	—	2	1	no	—
73	#13093983	—	2	1	no	—
74	#13093983	—	2	1	no	—
75	C₂×C₄⋊Dic₄₇	—	2	1	no	—
76	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₄×Dic₄₇	—	2	1	no	—
78	#13093942	—	2	4	no	—
79	#13093940	—	2	4	no	—
80	#13093938	—	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	C₂×C₄	1	2	yes	—
91	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
92	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
93	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
94	C₂²×C₈×C₄₇	—	2	1	no	—
95	C₂²×C₈×C₄₇	—	2	1	no	—
96	#117×C₄₇	—	2	1	no	—
97	#117×C₄₇	—	2	1	no	—
98	#117×C₄₇	—	2	1	no	—
99	#117×C₄₇	—	2	1	no	—
100	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
102	C₂×C₄²×C₄₇	—	2	1	no	—
103	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂³×D₄₇	C₄²	1	2	yes	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
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	C₂×Q₈	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	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
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	—	2	2	no	—
124	C₂×C₂²⋊D₄₇	C₂²⋊C₄	1	4	yes	—
125	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	4	yes	—
126	C₂²×Dic₄₇	—	2	2	no	—
127	C₂²×Dic₄₇	C₄²	1	2	yes	—
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	#10625350	—	2	2	no	—
143	#10625350	—	2	2	no	—
144	C₂×D₁₈₈	—	2	1	no	—
145	C₂×D₁₈₈	—	2	1	no	—
146	C₂×D₁₈₈	—	2	1	no	—
147	C₂×D₁₈₈	—	2	1	no	—
148	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
149	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
150	C₂×C₄×D₄₇	—	2	2	no	—
151	C₂×C₄×D₄₇	—	2	2	no	—
152	C₂×C₄×D₄₇	—	2	2	no	—
153	C₂×C₄×D₄₇	—	2	2	no	—
154	C₂×C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
155	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
156	C₂×Dic₉₄	—	2	1	no	—
157	C₂×Dic₉₄	—	2	1	no	—
158	C₂×Dic₉₄	—	2	1	no	—
159	C₂×Dic₉₄	—	2	1	no	—
160	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
161	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
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	—	4	1	no	—
168	M₁₆×C₄₇	—	4	1	no	—
169	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
170	C₂×C₈×C₄₇	—	2	2	no	—
171	C₂×C₈×C₄₇	—	2	2	no	—
172	C₂×C₈×C₄₇	—	2	2	no	—
173	C₂×C₈×C₄₇	—	2	2	no	—
174	C₂×C₈×C₄₇	—	4	1	no	—
175	C₂×C₈×C₄₇	—	4	1	no	—
176	C₄⋊C₄×C₄₇	—	4	1	no	—
177	C₄⋊C₄×C₄₇	—	4	1	no	—
178	C₂²⋊C₄×C₄₇	—	2	2	no	—
179	C₂²⋊C₄×C₄₇	—	2	2	no	—
180	C₄²×C₄₇	—	4	1	no	—
181	C₄²×C₄₇	—	4	1	no	—
182	C₂²⋊Dic₄₇	—	2	2	no	—
183	C₂²⋊Dic₄₇	—	2	2	no	—
184	C₄⋊Dic₄₇	—	4	1	no	—
185	C₄⋊Dic₄₇	—	4	1	no	—
186	C₄×Dic₄₇	—	4	1	no	—
187	C₄×Dic₄₇	—	4	1	no	—
188	#10625329	—	2	2	no	—
189	#10625329	—	2	2	no	—
190	#10625329	—	2	2	no	—
191	#10625329	—	2	2	no	—
192	#10625329	—	2	2	no	—
193	#10625329	—	4	1	no	—
194	#10625329	—	4	1	no	—
195	#10625329	C₂²⋊C₄	1	4	yes	—
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	—	2	2	no	—
200	C₂×C₄₇⋊C₈	—	4	1	no	—
201	C₂×C₄₇⋊C₈	—	4	1	no	—
202	#10625324	—	2	16	no	—
203	C₈×D₄₇	—	2	16	no	—
204	C₂³×C₄₇	—	8	1	no	—
205	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
206	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
209	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
210	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
211	C₂³×C₄₇	C₄×D₄	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	—	4	2	no	—
217	C₂×C₄×C₄₇	—	8	2	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
225	C₂×C₄×C₄₇	#117	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	#120	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#120	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	#121	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#121	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	C₂²⋊Q₈	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
243	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
244	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
245	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
246	C₂²⋊D₄₇	—	2	4	no	—
247	C₂²⋊D₄₇	—	2	4	no	—
248	C₂²⋊D₄₇	—	2	4	no	—
249	C₂²⋊D₄₇	—	2	4	no	—
250	C₂×Dic₄₇	—	2	2	no	—
251	C₂×Dic₄₇	—	2	2	no	—
252	C₂×Dic₄₇	—	4	2	no	—
253	C₂×Dic₄₇	—	8	2	no	—
254	C₂×Dic₄₇	#95	1	4	yes	—
255	D₁₈₈	—	2	2	no	—
256	D₁₈₈	—	2	2	no	—
257	D₁₈₈	—	2	2	no	—
258	D₁₈₈	—	2	2	no	—
259	C₄×D₄₇	—	2	4	no	—
260	C₄×D₄₇	—	2	4	no	—
261	C₄×D₄₇	—	2	4	no	—
262	C₄×D₄₇	—	2	4	no	—
263	Dic₉₄	—	2	2	no	—
264	Dic₉₄	—	2	2	no	—
265	Dic₉₄	—	2	2	no	—
266	Dic₉₄	—	2	2	no	—
267	C₈×C₄₇	—	2	4	no	—
268	C₈×C₄₇	—	4	2	no	—
269	C₄₇⋊C₈	—	2	4	no	—
270	C₄₇⋊C₈	—	4	2	no	—
271	#10771	—	47	1	no	maximal, Sylow
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	—	4	1	no	—
278	C₂²×C₄₇	—	4	1	no	—
279	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
280	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
281	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
282	C₂²×C₄₇	#385	1	1	yes	characteristic
283	C₂²×C₄₇	#385	1	1	yes	characteristic
284	C₂²×C₄₇	#386	1	1	yes	characteristic
285	C₂²×C₄₇	#386	1	1	yes	characteristic
286	C₂×D₄₇	—	2	4	no	—
287	C₂×D₄₇	—	4	4	no	—
288	C₂×D₄₇	—	8	2	no	—
289	C₂×D₄₇	—	8	2	no	—
290	C₄×C₄₇	—	8	2	no	—
291	C₄×C₄₇	#379	1	1	yes	characteristic
292	C₄×C₄₇	#380	1	1	yes	characteristic
293	C₄×C₄₇	#380	1	1	yes	characteristic
294	C₄×C₄₇	#381	1	1	yes	characteristic
295	C₄×C₄₇	#385	1	1	yes	characteristic
296	C₄×C₄₇	#385	1	1	yes	characteristic
297	C₄×C₄₇	#386	1	1	yes	characteristic
298	C₄×C₄₇	#386	1	1	yes	characteristic
299	Dic₄₇	—	2	4	no	—
300	Dic₄₇	—	8	2	no	—
301	C₂×#568	—	47	1	no	—
302	C₂×#413	—	47	1	no	—
303	C₂×#410	—	47	1	no	—
304	C₂×#344	—	47	1	no	—
305	C₂×#344	—	47	1	no	—
306	#1742	—	47	1	no	—
307	#1742	D₄₇	1	1	yes	characteristic, complemented
308	C₂×C₄₇	—	2	1	no	—
309	C₂×C₄₇	—	2	1	no	—
310	C₂×C₄₇	—	2	1	no	—
311	C₂×C₄₇	—	2	1	no	—
312	C₂×C₄₇	—	2	1	no	—
313	C₂×C₄₇	—	2	1	no	—
314	C₂×C₄₇	—	2	1	no	—
315	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
316	D₄₇	—	4	4	no	—
317	C₂²×#41	—	47	1	no	—
318	#568	—	94	2	no	—
319	#568	—	94	2	no	—
320	#568	—	94	2	no	—
321	#568	—	94	2	no	—
322	C₂×#131	—	94	2	no	—
323	C₂×#131	—	94	2	no	—
324	C₂²×M₁₆	—	47	1	no	—
325	C₂²×M₁₆	—	47	1	no	—
326	C₂²×M₁₆	—	47	4	no	—
327	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
328	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
329	C₂×#117	—	47	1	no	—
330	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
331	#413	—	94	2	no	—
332	#413	—	94	2	no	—
333	C₂×#101	—	47	2	no	—
334	C₂×#100	—	47	2	no	—
335	#410	—	94	2	no	—
336	#410	—	94	2	no	—
337	C₂×#99	—	47	4	no	—
338	#344	—	94	2	no	—
339	#344	—	94	2	no	—
340	#343	—	2	2	no	—
341	#343	—	94	2	no	—
342	C₄₇	#10771	1	1	yes	characteristic, complemented, Sylow
343	C₂×#41	—	47	2	no	—
344	C₂×#41	—	47	2	no	—
345	C₂×#41	—	47	2	no	—
346	C₂×#41	—	47	2	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	C₂×#41	—	94	1	no	—
352	C₂×#41	—	94	1	no	—
353	C₂×#41	—	94	1	no	—
354	C₂×#41	—	94	1	no	—
355	C₂²×Q₈	—	47	1	no	—
356	C₂²×D₄	—	47	2	no	—
357	C₂²×D₄	—	47	1	no	—
358	C₂³×C₄	—	47	2	no	—
359	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
360	#131	—	94	8	no	—
361	#131	—	94	8	no	—
362	#131	—	94	8	no	—
363	#131	—	94	8	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	—	47	2	no	—
373	C₂×M₁₆	—	47	2	no	—
374	C₂×M₁₆	—	47	2	no	—
375	C₂×M₁₆	—	47	2	no	—
376	C₂×M₁₆	—	94	4	no	—
377	C₂×M₁₆	—	94	8	no	—
378	C₂×M₁₆	—	94	1	no	—
379	C₂×M₁₆	—	94	1	no	—
380	C₂×M₁₆	—	94	1	no	—
381	C₂×M₁₆	—	94	8	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	C₄×D₄₇	1	2	yes	—
388	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
389	C₂×M₁₆	D₁₈₈	1	2	yes	—
390	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	94	4	no	—
394	C₂²×C₈	—	94	1	no	—
395	C₂²×C₈	—	94	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	94	1	no	—
401	#117	—	94	1	no	—
402	#117	—	94	1	no	—
403	#117	—	94	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	94	1	no	—
406	C₂×C₂²⋊C₄	—	47	2	no	—
407	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	—	94	1	no	—
410	#101	—	94	4	no	—
411	#100	—	94	4	no	—
412	#99	—	94	8	no	—
413	C₂⁴	—	47	2	no	—
414	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
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	#41	—	94	2	no	—
428	#41	—	94	2	no	—
429	#41	—	94	2	no	—
430	#41	—	94	2	no	—
431	C₂×Q₈	—	47	2	no	—
432	C₂×Q₈	—	47	2	no	—
433	C₂×Q₈	—	94	1	no	—
434	C₂×Q₈	—	94	1	no	—
435	C₂×Q₈	—	94	1	no	—
436	C₂×Q₈	—	94	1	no	—
437	C₂×D₄	—	47	4	no	—
438	C₂×D₄	—	47	4	no	—
439	C₂×D₄	—	47	2	no	—
440	C₂×D₄	—	47	2	no	—
441	C₂×D₄	—	94	2	no	—
442	C₂×D₄	—	94	2	no	—
443	C₂×D₄	—	94	2	no	—
444	C₂×D₄	—	94	2	no	—
445	C₂×D₄	—	94	1	no	—
446	C₂×D₄	—	94	1	no	—
447	C₂×D₄	—	94	1	no	—
448	C₂×D₄	—	94	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	47	2	no	—
451	C₂²×C₄	—	47	4	no	—
452	C₂²×C₄	—	47	4	no	—
453	C₂²×C₄	—	94	2	no	—
454	C₂²×C₄	—	94	2	no	—
455	C₂²×C₄	—	94	2	no	—
456	C₂²×C₄	—	94	2	no	—
457	C₂²×C₄	—	94	2	no	—
458	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
461	C₂²×C₄	#10625350	1	1	yes	characteristic
462	C₂²×C₄	#10625350	1	1	yes	characteristic
463	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
464	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
465	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
466	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
467	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
468	C₂²×C₄	#10625352	1	1	yes	characteristic
469	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
470	C₂²×C₄	#10625354	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	4	1	no	—
478	M₁₆	—	4	1	no	—
479	M₁₆	—	47	4	no	—
480	M₁₆	—	94	16	no	—
481	M₁₆	—	94	2	no	—
482	M₁₆	—	94	2	no	—
483	M₁₆	—	94	2	no	—
484	M₁₆	—	94	2	no	—
485	M₁₆	—	94	2	no	—
486	M₁₆	—	188	1	no	—
487	M₁₆	—	188	1	no	—
488	M₁₆	(C₂×D₄₇)⋊C₄	1	4	yes	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	4	1	no	—
494	C₂×C₈	—	4	1	no	—
495	C₂×C₈	—	94	16	no	—
496	C₂×C₈	—	94	2	no	—
497	C₂×C₈	—	94	2	no	—
498	C₂×C₈	—	94	2	no	—
499	C₂×C₈	—	94	2	no	—
500	C₂×C₈	—	188	1	no	—
501	C₂×C₈	—	188	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	—	188	1	no	—
505	C₄⋊C₄	—	188	1	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	94	2	no	—
509	C₂²⋊C₄	—	94	2	no	—
510	C₄²	—	4	1	no	—
511	C₄²	—	4	1	no	—
512	C₄²	—	188	1	no	—
513	C₄²	—	188	1	no	—
514	C₂³	—	8	1	no	—
515	C₂³	—	47	4	no	—
516	C₂³	—	94	2	no	—
517	C₂³	—	94	2	no	—
518	C₂³	—	376	2	no	—
519	C₂³	C₄²×D₄₇	1	1	yes	characteristic
520	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
521	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
522	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
523	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
524	C₂³	#13093986	1	1	yes	characteristic
525	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
526	Q₈	—	94	2	no	—
527	Q₈	—	94	2	no	—
528	Q₈	—	94	2	no	—
529	Q₈	—	94	2	no	—
530	D₄	—	94	4	no	—
531	D₄	—	94	4	no	—
532	D₄	—	94	4	no	—
533	D₄	—	94	4	no	—
534	D₄	—	94	2	no	—
535	D₄	—	94	2	no	—
536	D₄	—	94	2	no	—
537	D₄	—	94	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	—	47	4	no	—
541	C₂×C₄	—	94	2	no	—
542	C₂×C₄	—	94	2	no	—
543	C₂×C₄	—	94	4	no	—
544	C₂×C₄	—	94	4	no	—
545	C₂×C₄	—	94	4	no	—
546	C₂×C₄	—	94	4	no	—
547	C₂×C₄	—	376	2	no	—
548	C₂×C₄	—	188	2	no	—
549	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
550	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
551	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
552	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
553	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
554	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
555	C₂×C₄	#13093981	1	1	yes	characteristic
556	C₂×C₄	#13093982	1	1	yes	characteristic
557	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
558	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
559	C₂×C₄	#13093986	1	1	yes	characteristic
560	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
561	C₂×C₄	#13093992	1	1	yes	characteristic
562	C₂×C₄	#13093992	1	1	yes	characteristic
563	C₂×C₄	#13093994	1	1	yes	characteristic
564	C₂×C₄	#13093994	1	1	yes	characteristic
565	C₂×C₄	#13093995	1	1	yes	characteristic
566	C₂×C₄	#13093997	1	1	yes	characteristic
567	C₂×C₄	#13093997	1	1	yes	characteristic
568	C₂×C₄	#13093999	1	1	yes	characteristic
569	C₂×C₄	#13094000	1	1	yes	characteristic
570	C₂×C₄	#13094002	1	1	yes	characteristic
571	C₂×C₄	#13094002	1	1	yes	characteristic
572	C₂×C₄	#13094004	1	1	yes	characteristic
573	C₂×C₄	#13094006	1	1	yes	characteristic
574	C₂×C₄	#13094006	1	1	yes	characteristic
575	C₂×C₄	#13094009	1	1	yes	characteristic
576	C₂×C₄	#13094009	1	1	yes	characteristic
577	C₈	—	2	4	no	—
578	C₈	—	4	2	no	—
579	C₈	—	94	4	no	—
580	C₈	—	188	2	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	94	4	no	—
589	C₂²	—	376	2	no	—
590	C₂²	—	376	2	no	—
591	C₂²	—	188	4	no	—
592	C₂²	#95×D₄₇	1	1	yes	characteristic
593	C₂²	#15688970	1	1	yes	characteristic
594	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
595	C₂²	#15688994	1	1	yes	characteristic
596	C₂²	#15688997	1	1	yes	characteristic
597	C₂²	#15688999	1	1	yes	characteristic
598	C₂²	#15689001	1	1	yes	characteristic
599	C₄	—	8	2	no	—
600	C₄	—	94	4	no	—
601	C₄	—	376	2	no	—
602	C₄	#15688978	1	1	yes	characteristic
603	C₄	#15688980	1	1	yes	characteristic
604	C₄	#15688982	1	1	yes	characteristic
605	C₄	#15688985	1	1	yes	characteristic
606	C₄	#15688994	1	1	yes	characteristic
607	C₄	#15688997	1	1	yes	characteristic
608	C₄	#15688999	1	1	yes	characteristic
609	C₄	#15689001	1	1	yes	characteristic
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	188	4	no	—
618	C₂	(C₂×D₄₇)⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15688985
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#1742	C₂
socle	C₂×C₄₇	C₂²⋊#95
prime radical	C₂²×#10625350	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#1742	D₄₇
hypocenter	C₄₇	#10771
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1742

Complements

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

N	H ≅ G/N	type
4. C₂×#15688894	C₂	semidirect
5. C₂×#15688893	C₂	semidirect
6. #20243126	C₂	semidirect
7. C₄₇×#1742	C₂	semidirect
17. C₂×M₁₆×D₄₇	C₄	semidirect
21. C₂×#13093942	C₄	semidirect
22. C₂×#13093940	C₄	semidirect
307. #1742	D₄₇	semidirect
342. C₄₇	#10771	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
C₂×#15689096	2
C₂×#15688894	2
C₂×#15688893	2
#20243126	2
C₄₇×#1742	2
#10771	47