Subgroups — #26216148

Order 12032.

1244 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256589	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689105	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689105	C₂	1	1	yes	maximal, characteristic
4	#20243501	C₂	1	4	yes	maximal, complemented
5	#20243498	C₂	1	4	yes	maximal, complemented
6	C₂×#15688895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15688893	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₇×#344	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#10625350	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	#15689604	—	2	2	no	—
14	#15689603	—	2	2	no	—
15	#15689600	C₂²	1	2	yes	—
16	#15689597	C₂²	1	2	yes	—
17	#15689596	C₄	1	4	yes	—
18	C₄×#10625350	—	2	2	no	—
19	#15689591	—	2	2	no	—
20	C₂×#13093983	C₂²	1	1	yes	characteristic
21	#117×D₄₇	C₄	1	4	yes	—
22	#15689105	—	2	2	no	—
23	#15689105	—	2	2	no	—
24	#15689105	—	2	2	no	—
25	#15689105	—	2	2	no	—
26	C₂×#13093942	C₂²	1	2	yes	—
27	C₂×#13093942	C₂²	1	2	yes	—
28	C₂×#13093940	C₂²	1	2	yes	—
29	C₂×#13093940	C₂²	1	2	yes	—
30	#15688895	C₂²	1	4	yes	—
31	#15688894	C₂²	1	4	yes	—
32	#15688893	C₂²	1	4	yes	—
33	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#344	C₂²	1	4	yes	—
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	—	2	1	no	—
42	C₂×#10625350	—	2	1	no	—
43	C₂×#10625350	—	2	1	no	—
44	C₂×#10625350	—	2	1	no	—
45	C₂×#10625350	D₄	1	2	yes	—
46	C₂×#10625350	D₄	1	2	yes	—
47	C₂×#10625350	D₄	1	2	yes	—
48	C₂×#10625350	D₄	1	2	yes	—
49	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
50	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
51	C₂²×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
52	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
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	C₂³	1	2	yes	—
64	C₂×#10625329	C₂³	1	2	yes	—
65	C₂²×C₄₇⋊C₈	—	2	1	no	—
66	C₂²×C₄₇⋊C₈	—	2	1	no	—
67	C₄×Dic₉₄	—	2	4	no	—
68	#13093989	—	2	4	no	—
69	C₄×D₁₈₈	—	2	4	no	—
70	#13093986	—	2	4	no	—
71	C₄×C₂²⋊D₄₇	—	2	8	no	—
72	(C₂²⋊D₄₇)⋊C₄	—	2	8	no	—
73	#13093983	—	2	1	no	—
74	#13093983	—	2	1	no	—
75	#13093983	C₂×C₄	1	2	yes	—
76	#13093983	C₂³	1	2	yes	—
77	#13093982	—	2	4	no	—
78	#13093981	—	2	4	no	—
79	#13093980	C₂×C₄	1	8	yes	—
80	C₂×C₄⋊Dic₄₇	—	2	1	no	—
81	C₄⋊C₄×D₄₇	—	2	4	no	—
82	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
83	C₂²⋊C₄×D₄₇	C₂×C₄	1	8	yes	—
84	C₂×C₄×Dic₄₇	—	2	1	no	—
85	C₄²×D₄₇	—	2	4	no	—
86	#13093942	—	2	4	no	—
87	#13093942	—	2	4	no	—
88	#13093940	—	2	4	no	—
89	#13093940	—	2	4	no	—
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
97	C₂×M₁₆×C₄₇	—	2	1	no	—
98	C₂×M₁₆×C₄₇	—	2	1	no	—
99	C₂×M₁₆×C₄₇	—	2	1	no	—
100	C₂×M₁₆×C₄₇	—	2	1	no	—
101	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
102	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
103	C₂²×C₈×C₄₇	—	2	1	no	—
104	C₂²×C₈×C₄₇	—	2	1	no	—
105	#117×C₄₇	—	2	1	no	—
106	#117×C₄₇	—	2	1	no	—
107	#117×C₄₇	C₂×C₄	1	2	yes	—
108	#117×C₄₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
111	C₂×C₄²×C₄₇	—	2	1	no	—
112	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂³×D₄₇	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
129	C₂×C₂²⋊D₄₇	—	2	2	no	—
130	C₂×C₂²⋊D₄₇	—	2	2	no	—
131	C₂×C₂²⋊D₄₇	—	2	2	no	—
132	C₂×C₂²⋊D₄₇	—	2	2	no	—
133	C₂×C₂²⋊D₄₇	C₂²⋊C₄	1	4	yes	—
134	C₂×C₂²⋊D₄₇	C₂²⋊C₄	1	4	yes	—
135	C₂²×Dic₄₇	—	2	2	no	—
136	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
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	#10625350	—	2	2	no	—
145	#10625350	—	2	2	no	—
146	#10625350	—	2	2	no	—
147	#10625350	—	2	2	no	—
148	#10625350	—	2	2	no	—
149	#10625350	—	2	2	no	—
150	#10625350	—	2	2	no	—
151	#10625350	—	2	2	no	—
152	#10625350	—	2	2	no	—
153	C₂×D₁₈₈	—	2	1	no	—
154	C₂×D₁₈₈	—	2	1	no	—
155	C₂×D₁₈₈	—	2	1	no	—
156	C₂×D₁₈₈	—	2	1	no	—
157	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
158	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
159	C₂×C₄×D₄₇	—	2	2	no	—
160	C₂×C₄×D₄₇	—	2	2	no	—
161	C₂×C₄×D₄₇	—	2	2	no	—
162	C₂×C₄×D₄₇	—	2	2	no	—
163	C₂×C₄×D₄₇	—	2	8	no	—
164	C₂×C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
165	C₂×C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
166	C₂×Dic₉₄	—	2	1	no	—
167	C₂×Dic₉₄	—	2	1	no	—
168	C₂×Dic₉₄	—	2	1	no	—
169	C₂×Dic₉₄	—	2	1	no	—
170	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
171	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
172	M₁₆×C₄₇	—	2	2	no	—
173	M₁₆×C₄₇	—	2	2	no	—
174	M₁₆×C₄₇	—	2	2	no	—
175	M₁₆×C₄₇	—	2	2	no	—
176	M₁₆×C₄₇	—	4	1	no	—
177	M₁₆×C₄₇	—	4	1	no	—
178	M₁₆×C₄₇	—	4	1	no	—
179	M₁₆×C₄₇	—	4	1	no	—
180	C₂×C₈×C₄₇	—	2	2	no	—
181	C₂×C₈×C₄₇	—	2	2	no	—
182	C₂×C₈×C₄₇	—	4	1	no	—
183	C₂×C₈×C₄₇	—	4	1	no	—
184	C₂×C₈×C₄₇	—	4	1	no	—
185	C₂×C₈×C₄₇	—	4	1	no	—
186	C₄⋊C₄×C₄₇	—	2	2	no	—
187	C₄⋊C₄×C₄₇	—	2	2	no	—
188	C₂²⋊C₄×C₄₇	—	2	2	no	—
189	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
190	C₄²×C₄₇	—	2	2	no	—
191	C₄²×C₄₇	—	2	2	no	—
192	C₂²⋊Dic₄₇	—	2	2	no	—
193	C₂²⋊Dic₄₇	C₂²×C₄	1	4	yes	—
194	(C₂×D₄₇)⋊C₄	—	2	8	no	—
195	C₄⋊Dic₄₇	—	2	2	no	—
196	C₄⋊Dic₄₇	—	2	2	no	—
197	Dic₄₇⋊C₄	—	2	8	no	—
198	C₄×Dic₄₇	—	2	2	no	—
199	C₄×Dic₄₇	—	2	2	no	—
200	C₄×Dic₄₇	—	2	8	no	—
201	#10625329	—	2	2	no	—
202	#10625329	—	2	2	no	—
203	#10625329	—	2	2	no	—
204	#10625329	—	2	2	no	—
205	#10625329	—	4	1	no	—
206	#10625329	—	4	1	no	—
207	#10625329	—	4	1	no	—
208	#10625329	—	4	1	no	—
209	C₂×C₄₇⋊C₈	—	2	2	no	—
210	C₂×C₄₇⋊C₈	—	2	2	no	—
211	C₂×C₄₇⋊C₈	—	4	1	no	—
212	C₂×C₄₇⋊C₈	—	4	1	no	—
213	C₂×C₄₇⋊C₈	—	4	1	no	—
214	C₂×C₄₇⋊C₈	—	4	1	no	—
215	C₂³×C₄₇	—	8	1	no	—
216	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂³×C₄₇	#117	1	1	yes	characteristic
219	C₂³×C₄₇	#117	1	1	yes	characteristic
220	C₂³×C₄₇	#117	1	1	yes	characteristic
221	C₂³×C₄₇	#117	1	1	yes	characteristic
222	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
223	C₂²×D₄₇	—	2	2	no	—
224	C₂²×D₄₇	—	2	2	no	—
225	C₂²×D₄₇	—	8	2	no	—
226	C₂²×D₄₇	C₂×C₂²⋊C₄	1	4	yes	—
227	C₂×C₄×C₄₇	—	2	4	no	—
228	C₂×C₄×C₄₇	—	8	2	no	—
229	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
232	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#123	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	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
245	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
246	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
247	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
248	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
249	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
250	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
257	C₂²⋊D₄₇	—	2	4	no	—
258	C₂²⋊D₄₇	—	2	4	no	—
259	C₂²⋊D₄₇	—	2	4	no	—
260	C₂²⋊D₄₇	—	2	4	no	—
261	C₂×Dic₄₇	—	2	2	no	—
262	C₂×Dic₄₇	—	2	2	no	—
263	C₂×Dic₄₇	—	2	4	no	—
264	C₂×Dic₄₇	—	8	2	no	—
265	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	4	yes	—
266	D₁₈₈	—	2	2	no	—
267	D₁₈₈	—	2	2	no	—
268	D₁₈₈	—	2	2	no	—
269	D₁₈₈	—	2	2	no	—
270	C₄×D₄₇	—	2	4	no	—
271	C₄×D₄₇	—	2	4	no	—
272	C₄×D₄₇	—	2	4	no	—
273	C₄×D₄₇	—	2	4	no	—
274	C₄×D₄₇	—	8	8	no	—
275	Dic₉₄	—	2	2	no	—
276	Dic₉₄	—	2	2	no	—
277	Dic₉₄	—	2	2	no	—
278	Dic₉₄	—	2	2	no	—
279	C₈×C₄₇	—	4	2	no	—
280	C₈×C₄₇	—	4	2	no	—
281	C₄₇⋊C₈	—	4	2	no	—
282	C₄₇⋊C₈	—	4	2	no	—
283	#20713	—	47	1	no	maximal, Sylow
284	C₂²×C₄₇	—	4	1	no	—
285	C₂²×C₄₇	—	4	1	no	—
286	C₂²×C₄₇	—	4	1	no	—
287	C₂²×C₄₇	—	4	1	no	—
288	C₂²×C₄₇	—	4	1	no	—
289	C₂²×C₄₇	—	4	1	no	—
290	C₂²×C₄₇	—	4	1	no	—
291	C₂²×C₄₇	#381	1	1	yes	characteristic
292	C₂²×C₄₇	#381	1	1	yes	characteristic
293	C₂²×C₄₇	#381	1	1	yes	characteristic
294	C₂²×C₄₇	#381	1	1	yes	characteristic
295	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
296	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
297	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
298	C₂×D₄₇	—	2	4	no	—
299	C₂×D₄₇	—	4	4	no	—
300	C₂×D₄₇	—	8	2	no	—
301	C₂×D₄₇	—	8	2	no	—
302	C₄×C₄₇	—	4	4	no	—
303	C₄×C₄₇	#381	1	1	yes	characteristic
304	C₄×C₄₇	#381	1	1	yes	characteristic
305	C₄×C₄₇	#381	1	1	yes	characteristic
306	C₄×C₄₇	#381	1	1	yes	characteristic
307	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
308	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
309	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
310	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
311	Dic₄₇	—	2	4	no	—
312	Dic₄₇	—	4	4	no	—
313	#3428	—	47	1	no	—
314	C₂×#413	—	47	1	no	—
315	C₂×#413	—	47	1	no	—
316	#1830	—	47	4	no	—
317	#1829	—	47	4	no	—
318	C₂×#344	—	47	1	no	—
319	C₂×#344	—	47	1	no	—
320	C₂×#344	—	47	1	no	—
321	C₂×#344	D₄₇	1	1	yes	characteristic, complemented
322	C₂×C₄₇	—	2	1	no	—
323	C₂×C₄₇	—	2	1	no	—
324	C₂×C₄₇	—	2	1	no	—
325	C₂×C₄₇	—	2	1	no	—
326	C₂×C₄₇	—	2	1	no	—
327	C₂×C₄₇	—	2	1	no	—
328	C₂×C₄₇	—	2	1	no	—
329	C₂×C₄₇	C₂×#381	1	1	yes	characteristic
330	D₄₇	—	4	4	no	—
331	C₂²×#41	—	47	1	no	—
332	C₂²×M₁₆	—	47	1	no	—
333	C₂²×M₁₆	—	47	1	no	—
334	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
335	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
336	#520	—	94	2	no	—
337	#520	—	94	2	no	—
338	#519	—	47	2	no	—
339	#518	—	47	2	no	—
340	#518	—	47	4	no	—
341	C₄×#41	—	94	2	no	—
342	C₄×#41	—	94	2	no	—
343	C₂×#117	—	47	1	no	—
344	C₂×#117	—	47	4	no	—
345	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
346	#413	—	94	2	no	—
347	#413	—	94	2	no	—
348	#413	—	94	2	no	—
349	#413	—	94	2	no	—
350	C₂×#101	—	47	2	no	—
351	C₂×#101	—	47	2	no	—
352	C₂×#100	—	47	2	no	—
353	C₂×#100	—	47	2	no	—
354	#344	—	47	4	no	—
355	#344	—	47	4	no	—
356	#344	—	47	4	no	—
357	#344	C₂×D₄₇	1	4	yes	—
358	C₄₇	#20713	1	1	yes	characteristic, complemented, Sylow
359	C₂×#41	—	47	2	no	—
360	C₂×#41	—	47	2	no	—
361	C₂×#41	—	47	2	no	—
362	C₂×#41	—	47	2	no	—
363	C₂×#41	—	94	1	no	—
364	C₂×#41	—	94	1	no	—
365	C₂×#41	—	94	1	no	—
366	C₂×#41	—	94	1	no	—
367	C₂×#41	—	94	1	no	—
368	C₂×#41	—	94	1	no	—
369	C₂×#41	—	94	1	no	—
370	C₂×#41	—	94	1	no	—
371	C₂²×Q₈	—	47	1	no	—
372	C₂²×D₄	—	47	2	no	—
373	C₂²×D₄	—	47	1	no	—
374	C₂³×C₄	—	47	2	no	—
375	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	47	2	no	—
387	C₂×M₁₆	—	47	2	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	—	94	1	no	—
396	C₂×M₁₆	—	94	1	no	—
397	C₂×M₁₆	—	94	1	no	—
398	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
399	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
400	C₂²×C₈	—	2	1	no	—
401	C₂²×C₈	—	2	1	no	—
402	C₂²×C₈	—	94	1	no	—
403	C₂²×C₈	—	94	1	no	—
404	C₄×Q₈	—	94	4	no	—
405	C₄×Q₈	—	94	4	no	—
406	C₄×D₄	—	94	4	no	—
407	C₄×D₄	—	94	8	no	—
408	C₄×D₄	—	94	4	no	—
409	C₄×D₄	—	94	8	no	—
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	#117	—	47	2	no	—
413	#117	—	47	2	no	—
414	#117	—	47	8	no	—
415	#117	—	94	4	no	—
416	#117	—	94	4	no	—
417	#117	—	94	1	no	—
418	#117	—	94	1	no	—
419	#117	C₄×D₄₇	1	2	yes	—
420	#117	C₂²×D₄₇	1	2	yes	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	94	4	no	—
423	C₂×C₄⋊C₄	—	94	1	no	—
424	C₂×C₂²⋊C₄	—	47	2	no	—
425	C₂×C₂²⋊C₄	—	47	8	no	—
426	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	94	4	no	—
429	C₂×C₄²	—	94	1	no	—
430	#101	—	94	4	no	—
431	#101	—	94	4	no	—
432	#100	—	94	4	no	—
433	#100	—	94	4	no	—
434	C₂⁴	—	47	2	no	—
435	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
436	#41	—	94	2	no	—
437	#41	—	94	2	no	—
438	#41	—	94	2	no	—
439	#41	—	94	2	no	—
440	#41	—	94	2	no	—
441	#41	—	94	2	no	—
442	#41	—	94	2	no	—
443	#41	—	94	2	no	—
444	#41	—	94	2	no	—
445	#41	—	94	2	no	—
446	#41	—	94	2	no	—
447	#41	—	94	2	no	—
448	#41	—	94	2	no	—
449	#41	—	94	2	no	—
450	#41	—	94	2	no	—
451	#41	—	94	2	no	—
452	C₂×Q₈	—	47	2	no	—
453	C₂×Q₈	—	47	2	no	—
454	C₂×Q₈	—	94	1	no	—
455	C₂×Q₈	—	94	1	no	—
456	C₂×Q₈	—	94	1	no	—
457	C₂×Q₈	—	94	1	no	—
458	C₂×D₄	—	47	4	no	—
459	C₂×D₄	—	47	4	no	—
460	C₂×D₄	—	47	2	no	—
461	C₂×D₄	—	47	2	no	—
462	C₂×D₄	—	94	2	no	—
463	C₂×D₄	—	94	2	no	—
464	C₂×D₄	—	94	2	no	—
465	C₂×D₄	—	94	2	no	—
466	C₂×D₄	—	94	1	no	—
467	C₂×D₄	—	94	1	no	—
468	C₂×D₄	—	94	1	no	—
469	C₂×D₄	—	94	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	47	2	no	—
472	C₂²×C₄	—	47	4	no	—
473	C₂²×C₄	—	47	4	no	—
474	C₂²×C₄	—	94	8	no	—
475	C₂²×C₄	—	94	2	no	—
476	C₂²×C₄	—	94	2	no	—
477	C₂²×C₄	—	94	2	no	—
478	C₂²×C₄	—	94	2	no	—
479	C₂²×C₄	—	94	2	no	—
480	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
481	C₂²×C₄	#10625350	1	1	yes	characteristic
482	C₂²×C₄	#10625350	1	1	yes	characteristic
483	C₂²×C₄	#10625350	1	1	yes	characteristic
484	C₂²×C₄	#10625350	1	1	yes	characteristic
485	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
486	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
487	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
488	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
489	C₂²×C₄	#10625352	1	1	yes	characteristic
490	C₂²×C₄	#10625352	1	1	yes	characteristic
491	C₂²×C₄	#10625354	1	1	yes	characteristic
492	C₂²×C₄	#10625354	1	1	yes	characteristic
493	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	2	2	no	—
497	M₁₆	—	2	2	no	—
498	M₁₆	—	4	1	no	—
499	M₁₆	—	4	1	no	—
500	M₁₆	—	4	1	no	—
501	M₁₆	—	4	1	no	—
502	M₁₆	—	94	2	no	—
503	M₁₆	—	94	2	no	—
504	M₁₆	—	94	2	no	—
505	M₁₆	—	94	2	no	—
506	M₁₆	—	188	1	no	—
507	M₁₆	—	188	1	no	—
508	M₁₆	—	188	1	no	—
509	M₁₆	—	188	1	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	2	2	no	—
512	C₂×C₈	—	4	1	no	—
513	C₂×C₈	—	4	1	no	—
514	C₂×C₈	—	4	1	no	—
515	C₂×C₈	—	4	1	no	—
516	C₂×C₈	—	94	2	no	—
517	C₂×C₈	—	94	2	no	—
518	C₂×C₈	—	188	1	no	—
519	C₂×C₈	—	188	1	no	—
520	C₂×C₈	—	188	1	no	—
521	C₂×C₈	—	188	1	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	94	8	no	—
525	C₄⋊C₄	—	94	2	no	—
526	C₄⋊C₄	—	94	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	47	4	no	—
529	C₂²⋊C₄	—	94	8	no	—
530	C₂²⋊C₄	—	94	2	no	—
531	C₂²⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	94	8	no	—
535	C₄²	—	94	2	no	—
536	C₄²	—	94	2	no	—
537	C₂³	—	8	1	no	—
538	C₂³	—	47	4	no	—
539	C₂³	—	94	2	no	—
540	C₂³	—	94	2	no	—
541	C₂³	—	376	2	no	—
542	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
543	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
544	C₂³	#13093981	1	1	yes	characteristic
545	C₂³	#13093981	1	1	yes	characteristic
546	C₂³	#13093982	1	1	yes	characteristic
547	C₂³	#13093982	1	1	yes	characteristic
548	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
549	Q₈	—	94	2	no	—
550	Q₈	—	94	2	no	—
551	Q₈	—	94	2	no	—
552	Q₈	—	94	2	no	—
553	D₄	—	94	4	no	—
554	D₄	—	94	4	no	—
555	D₄	—	94	4	no	—
556	D₄	—	94	4	no	—
557	D₄	—	94	2	no	—
558	D₄	—	94	2	no	—
559	D₄	—	94	2	no	—
560	D₄	—	94	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	8	2	no	—
563	C₂×C₄	—	47	4	no	—
564	C₂×C₄	—	94	2	no	—
565	C₂×C₄	—	94	2	no	—
566	C₂×C₄	—	94	4	no	—
567	C₂×C₄	—	94	4	no	—
568	C₂×C₄	—	94	4	no	—
569	C₂×C₄	—	94	4	no	—
570	C₂×C₄	—	94	4	no	—
571	C₂×C₄	—	376	8	no	—
572	C₂×C₄	—	376	2	no	—
573	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
574	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
575	C₂×C₄	#13093981	1	1	yes	characteristic
576	C₂×C₄	#13093981	1	1	yes	characteristic
577	C₂×C₄	#13093982	1	1	yes	characteristic
578	C₂×C₄	#13093982	1	1	yes	characteristic
579	C₂×C₄	#13094006	1	1	yes	characteristic
580	C₂×C₄	#13094006	1	1	yes	characteristic
581	C₂×C₄	#13094006	1	1	yes	characteristic
582	C₂×C₄	#13094006	1	1	yes	characteristic
583	C₂×C₄	#13094006	1	1	yes	characteristic
584	C₂×C₄	#13094006	1	1	yes	characteristic
585	C₂×C₄	#13094006	1	1	yes	characteristic
586	C₂×C₄	#13094006	1	1	yes	characteristic
587	C₂×C₄	#13094009	1	1	yes	characteristic
588	C₂×C₄	#13094009	1	1	yes	characteristic
589	C₂×C₄	#13094009	1	1	yes	characteristic
590	C₂×C₄	#13094009	1	1	yes	characteristic
591	C₂×C₄	#13094009	1	1	yes	characteristic
592	C₂×C₄	#13094009	1	1	yes	characteristic
593	C₂×C₄	#13094009	1	1	yes	characteristic
594	C₂×C₄	#13094009	1	1	yes	characteristic
595	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
596	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
597	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
598	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
599	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
600	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
601	C₈	—	4	2	no	—
602	C₈	—	4	2	no	—
603	C₈	—	188	2	no	—
604	C₈	—	188	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	94	4	no	—
613	C₂²	—	376	2	no	—
614	C₂²	—	376	2	no	—
615	C₂²	—	188	4	no	—
616	C₂²	#15688985	1	1	yes	characteristic
617	C₂²	#15688985	1	1	yes	characteristic
618	C₂²	#15688985	1	1	yes	characteristic
619	C₂²	#15688985	1	1	yes	characteristic
620	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
621	C₂²	C₂×#13093981	1	1	yes	characteristic
622	C₂²	C₂×#13093982	1	1	yes	characteristic
623	C₄	—	4	4	no	—
624	C₄	—	94	4	no	—
625	C₄	—	188	4	no	—
626	C₄	#15688985	1	1	yes	characteristic
627	C₄	#15688985	1	1	yes	characteristic
628	C₄	#15688985	1	1	yes	characteristic
629	C₄	#15688985	1	1	yes	characteristic
630	C₄	C₂×#13094006	1	1	yes	characteristic
631	C₄	C₂×#13094006	1	1	yes	characteristic
632	C₄	C₂×#13094009	1	1	yes	characteristic
633	C₄	C₂×#13094009	1	1	yes	characteristic
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	188	4	no	—
642	C₂	C₂×#15688985	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15688985
commutator	C₂³×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#344	C₂
socle	C₂×C₄₇	C₂×#381
prime radical	C₂²×#10625350	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#344	D₄₇
hypocenter	C₄₇	#20713
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
4. #20243501	C₂	semidirect
5. #20243498	C₂	semidirect
6. C₂×#15688895	C₂	semidirect
7. C₂×#15688894	C₂	semidirect
8. C₂×#15688893	C₂	semidirect
9. C₂×C₄₇×#344	C₂	semidirect
321. C₂×#344	D₄₇	semidirect
358. C₄₇	#20713	semidirect

Maximal subgroups

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

subgroup	index
#20256589	2
C₂×#15689105	2
#20243501	2
#20243498	2
C₂×#15688895	2
C₂×#15688894	2
C₂×#15688893	2
C₂×C₄₇×#344	2
#20713	47