Subgroups — #26368985

Order 12032.

1114 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258099	C₂	1	1	yes	maximal, characteristic
2	#20256490	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689541	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245015	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245014	C₂	1	4	yes	maximal, complemented
6	C₂×#15688908	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688907	C₂	1	1	yes	maximal, characteristic, complemented
8	#350×D₄₇	C₂	1	4	yes	maximal, complemented
9	C₄₇×#2117	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689959	C₄	1	1	yes	characteristic
11	#15689890	C₄	1	1	yes	characteristic
12	#15689889	—	2	2	no	—
13	#15689889	C₄	1	1	yes	characteristic
14	#15689889	C₄	1	1	yes	characteristic
15	#15689888	—	2	2	no	—
16	#15689888	C₄	1	4	yes	—
17	C₂×#13094030	—	2	2	no	—
18	C₂×#13094030	C₂²	1	1	yes	characteristic
19	C₂×#13094030	C₂²	1	1	yes	characteristic
20	#131×D₄₇	—	2	2	no	—
21	#131×D₄₇	C₂²	1	4	yes	—
22	#15689541	—	2	2	no	—
23	#15689541	—	2	2	no	—
24	#15689541	—	2	2	no	—
25	#15689539	—	2	2	no	—
26	C₂×#13093964	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13093963	C₂²	1	2	yes	complemented
28	M₃₂×D₄₇	C₂²	1	4	yes	complemented
29	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₆×D₄₇	C₂²	1	2	yes	complemented
31	#15688908	C₂²	1	2	yes	complemented
32	#15688908	C₂²	1	2	yes	complemented
33	#15688907	C₂²	1	2	yes	complemented
34	#15688907	C₂²	1	2	yes	complemented
35	#15688906	C₂²	1	4	yes	complemented
36	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic, complemented
39	C₄₇×#350	C₂²	1	4	yes	complemented
40	#13094072	C₈	1	2	yes	—
41	#13094071	—	2	1	no	—
42	#13094071	C₈	1	2	yes	—
43	#13094070	—	2	1	no	—
44	#13094070	C₈	1	2	yes	—
45	#13094069	—	2	2	no	—
46	#13094069	C₈	1	2	yes	—
47	C₂×#10625350	—	2	2	no	—
48	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
49	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
50	#41×D₄₇	—	2	2	no	—
51	#41×D₄₇	C₂×C₄	1	4	yes	—
52	#13094032	—	2	2	no	—
53	#13094032	—	2	4	no	—
54	#13094032	—	2	4	no	—
55	#13094032	C₂×C₄	1	4	yes	—
56	#13094031	—	2	2	no	—
57	#13094031	C₂×C₄	1	4	yes	—
58	#13094030	—	2	2	no	—
59	#13094030	—	2	1	no	—
60	#13094030	—	2	1	no	—
61	#13094030	—	2	2	no	—
62	#13094030	—	2	4	no	—
63	#13094030	—	2	4	no	—
64	#13094030	C₂×C₄	1	2	yes	—
65	#13094030	D₄	1	2	yes	—
66	#13094030	D₄	1	2	yes	—
67	#13094030	D₄	1	2	yes	—
68	#13094030	D₄	1	2	yes	—
69	#13094030	C₂³	1	2	yes	—
70	C₂×#10625329	—	2	2	no	—
71	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
72	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
73	C₂×#10625324	—	2	1	no	—
74	C₂×#10625324	—	2	4	no	—
75	C₂×#10625324	C₂×C₄	1	2	yes	—
76	M₁₆×D₄₇	—	2	2	no	—
77	M₁₆×D₄₇	—	2	4	no	—
78	M₁₆×D₄₇	—	2	4	no	—
79	M₁₆×D₄₇	C₂×C₄	1	4	yes	—
80	C₂×C₈×D₄₇	—	2	1	no	—
81	C₂×C₈×D₄₇	—	2	4	no	—
82	C₂×C₈×D₄₇	C₂³	1	2	yes	—
83	#13093964	—	2	1	no	—
84	#13093964	C₂³	1	2	yes	—
85	#13093963	—	2	4	no	—
86	#13093963	—	2	4	no	—
87	C₂×C₄₇⋊C₁₆	—	2	1	no	—
88	C₂×C₄₇⋊C₁₆	—	2	1	no	—
89	C₂×C₄₇⋊C₁₆	—	2	1	no	—
90	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
92	C₁₆×D₄₇	—	2	4	no	—
93	C₁₆×D₄₇	—	2	4	no	—
94	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
95	#131×C₄₇	—	2	1	no	—
96	#131×C₄₇	—	2	1	no	—
97	#131×C₄₇	C₂×C₄	1	2	yes	—
98	#131×C₄₇	C₂³	1	2	yes	—
99	C₂×M₁₆×C₄₇	—	2	1	no	—
100	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
101	C₂²×C₈×C₄₇	—	2	1	no	—
102	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	M₃₂×C₄₇	—	2	1	no	—
104	M₃₂×C₄₇	—	2	1	no	—
105	M₃₂×C₄₇	—	2	1	no	—
106	M₃₂×C₄₇	C₂³	1	2	yes	—
107	C₂×C₁₆×C₄₇	—	2	1	no	—
108	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
109	#41×C₄₇	—	2	1	no	—
110	#41×C₄₇	—	2	1	no	—
111	#41×C₄₇	C₂×C₈	1	2	yes	—
112	#41×C₄₇	C₂²×C₄	1	2	yes	—
113	C₂×Q₈×C₄₇	C₂×C₈	1	1	yes	characteristic
114	C₂×D₄×C₄₇	—	2	1	no	—
115	C₂×D₄×C₄₇	C₂×C₈	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊D₄₇	—	2	1	no	—
119	C₂×C₂²⋊D₄₇	—	2	4	no	—
120	C₂×C₂²⋊D₄₇	M₁₆	1	2	yes	—
121	#10625354	—	2	2	no	—
122	#10625354	C₂×C₈	1	4	yes	—
123	Q₈×D₄₇	—	2	2	no	—
124	Q₈×D₄₇	C₂×C₈	1	4	yes	—
125	#10625352	—	2	4	no	—
126	#10625352	—	2	4	no	—
127	#10625352	—	2	2	no	—
128	#10625352	C₂×C₈	1	4	yes	—
129	D₄×D₄₇	—	2	4	no	—
130	D₄×D₄₇	—	2	4	no	—
131	D₄×D₄₇	—	2	2	no	—
132	D₄×D₄₇	C₂×C₈	1	4	yes	—
133	#10625350	—	2	1	no	—
134	#10625350	—	2	1	no	—
135	#10625350	—	2	4	no	—
136	#10625350	—	2	2	no	—
137	#10625350	—	2	4	no	—
138	#10625350	—	2	2	no	—
139	#10625350	C₂²⋊C₄	1	2	yes	—
140	#10625350	C₂²⋊C₄	1	2	yes	—
141	#10625350	C₂×C₈	1	2	yes	—
142	#10625350	C₂×C₈	1	2	yes	—
143	#10625350	C₂×C₈	1	2	yes	—
144	#10625350	C₂²×C₄	1	2	yes	—
145	C₂×D₁₈₈	—	2	2	no	—
146	C₂×D₁₈₈	C₂×C₈	1	1	yes	characteristic
147	C₂×D₁₈₈	M₁₆	1	1	yes	characteristic
148	C₂×C₄×D₄₇	—	2	1	no	—
149	C₂×C₄×D₄₇	—	2	4	no	—
150	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
151	C₂×Dic₉₄	—	2	2	no	—
152	C₂×Dic₉₄	C₂×C₈	1	1	yes	characteristic
153	C₂×Dic₉₄	M₁₆	1	1	yes	characteristic
154	M₁₆×C₄₇	—	2	1	no	—
155	M₁₆×C₄₇	—	2	2	no	—
156	M₁₆×C₄₇	—	2	2	no	—
157	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
158	C₂×C₈×C₄₇	—	2	1	no	—
159	C₂×C₈×C₄₇	—	2	2	no	—
160	C₂×C₈×C₄₇	—	2	2	no	—
161	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
167	#10625329	—	2	1	no	—
168	#10625329	—	2	4	no	—
169	#10625329	C₂²⋊C₄	1	2	yes	—
170	#10625329	C₂²⋊C₄	1	2	yes	—
171	#10625329	C₂²×C₄	1	2	yes	—
172	C₂×C₄₇⋊C₈	—	2	1	no	—
173	C₂×C₄₇⋊C₈	—	2	4	no	—
174	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
175	#10625324	—	2	4	no	—
176	#10625324	—	2	2	no	—
177	#10625324	—	2	2	no	—
178	#10625324	—	2	4	no	—
179	#10625324	C₂²⋊C₄	1	4	yes	—
180	#10625324	C₂²⋊C₄	1	4	yes	—
181	C₈×D₄₇	—	2	4	no	—
182	C₈×D₄₇	—	2	2	no	—
183	C₈×D₄₇	—	2	2	no	—
184	C₈×D₄₇	—	2	4	no	—
185	C₈×D₄₇	C₂×D₄	1	4	yes	—
186	C₈×D₄₇	C₂×D₄	1	4	yes	—
187	C₁₆×C₄₇	—	2	2	no	—
188	C₁₆×C₄₇	—	2	2	no	—
189	C₄₇⋊C₁₆	—	2	1	no	—
190	C₄₇⋊C₁₆	—	2	2	no	—
191	C₄₇⋊C₁₆	—	2	1	no	—
192	C₂³×C₄₇	—	2	1	no	—
193	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
194	C₂²×D₄₇	—	2	1	no	—
195	C₂²×D₄₇	—	2	4	no	—
196	C₂²×D₄₇	C₂×M₁₆	1	2	yes	—
197	Q₈×C₄₇	—	2	1	no	—
198	Q₈×C₄₇	C₂²×C₈	1	2	yes	—
199	D₄×C₄₇	—	2	2	no	—
200	D₄×C₄₇	—	2	2	no	—
201	D₄×C₄₇	—	2	1	no	—
202	D₄×C₄₇	C₂²×C₈	1	2	yes	—
203	C₂×C₄×C₄₇	—	2	1	no	—
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
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	C₂²×C₈	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
212	C₂²⋊D₄₇	—	2	2	no	—
213	C₂²⋊D₄₇	—	2	2	no	—
214	C₂²⋊D₄₇	—	2	4	no	—
215	C₂²⋊D₄₇	—	2	4	no	—
216	C₂²⋊D₄₇	C₂²⋊C₈	1	4	yes	—
217	C₂²⋊D₄₇	C₂²⋊C₈	1	4	yes	—
218	C₂×Dic₄₇	—	2	1	no	—
219	C₂×Dic₄₇	—	2	4	no	—
220	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
221	D₁₈₈	—	2	4	no	—
222	D₁₈₈	—	2	1	no	—
223	D₁₈₈	C₂²⋊C₈	1	2	yes	—
224	D₁₈₈	C₂²⋊C₈	1	2	yes	—
225	D₁₈₈	C₂²×C₈	1	2	yes	—
226	C₄×D₄₇	—	2	4	no	—
227	C₄×D₄₇	—	2	2	no	—
228	C₄×D₄₇	—	2	2	no	—
229	C₄×D₄₇	—	2	4	no	—
230	C₄×D₄₇	C₂×C₂²⋊C₄	1	4	yes	—
231	C₄×D₄₇	C₂²×C₈	1	4	yes	—
232	Dic₉₄	—	2	1	no	—
233	Dic₉₄	—	2	4	no	—
234	Dic₉₄	C₂²⋊C₈	1	2	yes	—
235	Dic₉₄	C₂²⋊C₈	1	2	yes	—
236	Dic₉₄	C₂²×C₈	1	2	yes	—
237	C₈×C₄₇	—	2	2	no	—
238	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
241	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
242	C₄₇⋊C₈	—	2	2	no	—
243	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	4	yes	—
244	#33340	—	47	1	no	maximal, Sylow
245	C₂²×C₄₇	—	2	2	no	—
246	C₂²×C₄₇	—	4	1	no	—
247	C₂²×C₄₇	—	8	1	no	—
248	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
249	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
250	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
251	C₂×D₄₇	—	2	2	no	—
252	C₂×D₄₇	—	4	2	no	—
253	C₂×D₄₇	—	8	4	no	—
254	C₂×D₄₇	—	8	1	no	—
255	C₂×D₄₇	C₂×C₂²⋊C₈	1	4	yes	—
256	C₄×C₄₇	—	2	2	no	—
257	C₄×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
258	C₄×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
259	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
260	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
261	Dic₄₇	—	2	2	no	—
262	Dic₄₇	C₂×C₂²⋊C₈	1	4	yes	—
263	#3573	—	47	1	no	—
264	#3407	—	47	1	no	—
265	C₂×#504	—	47	1	no	—
266	#2117	—	47	1	no	—
267	#2117	—	47	4	no	—
268	#2117	D₄₇	1	1	yes	characteristic, complemented
269	C₂×#350	—	47	1	no	—
270	C₂×#350	—	47	4	no	—
271	C₂×#350	—	47	1	no	—
272	C₂×C₄₇	—	2	1	no	—
273	C₂×C₄₇	—	2	1	no	—
274	C₂×C₄₇	—	2	1	no	—
275	C₂×C₄₇	—	4	2	no	—
276	C₂×C₄₇	C₂²×C₂²⋊C₈	1	1	yes	characteristic
277	D₄₇	—	2	4	no	—
278	D₄₇	—	4	2	no	—
279	#585	—	47	1	no	—
280	#568	—	47	1	no	—
281	#568	—	47	1	no	—
282	#568	—	47	4	no	—
283	#568	—	47	1	no	—
284	#568	—	94	2	no	—
285	#568	—	94	2	no	—
286	C₂×#131	—	47	1	no	—
287	C₂×#131	—	47	4	no	—
288	C₂×#131	—	47	1	no	—
289	C₂×#131	—	94	2	no	—
290	C₂×#131	—	94	2	no	—
291	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
292	#504	—	94	2	no	—
293	#504	—	94	2	no	—
294	#504	—	94	2	no	—
295	#504	—	94	2	no	—
296	C₂×M₃₂	—	47	2	no	—
297	C₂×M₃₂	—	47	1	no	—
298	C₂×M₃₂	—	47	4	no	—
299	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic, complemented
300	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic, complemented
301	C₂²×C₁₆	—	47	1	no	—
302	C₂²×C₁₆	—	47	2	no	—
303	#350	—	47	2	no	—
304	#350	—	47	2	no	—
305	#350	—	47	2	no	—
306	#350	—	47	2	no	—
307	#350	—	47	4	no	—
308	#350	C₂×D₄₇	1	4	yes	complemented
309	C₄₇	#33340	1	1	yes	characteristic, complemented, Sylow
310	2₋¹⁺⁴	—	47	2	no	—
311	2₋¹⁺⁴	—	47	2	no	—
312	2₋¹⁺⁴	—	94	1	no	—
313	H(5,𝔽₂)	—	47	2	no	—
314	H(5,𝔽₂)	—	47	2	no	—
315	H(5,𝔽₂)	—	94	2	no	—
316	H(5,𝔽₂)	—	94	1	no	—
317	C₂×#41	—	47	1	no	—
318	C₂×#41	—	47	4	no	—
319	C₂×#41	—	47	1	no	—
320	C₂×#41	—	94	2	no	—
321	C₂×#41	—	94	2	no	—
322	C₂×#41	C₄×D₄₇	1	1	yes	characteristic
323	#131	—	2	1	no	—
324	#131	—	2	1	no	—
325	#131	—	47	2	no	—
326	#131	—	47	2	no	—
327	#131	—	47	2	no	—
328	#131	—	47	2	no	—
329	#131	—	47	4	no	—
330	#131	—	47	4	no	—
331	#131	—	47	2	no	—
332	#131	—	47	2	no	—
333	#131	—	94	4	no	—
334	#131	—	94	2	no	—
335	#131	—	94	4	no	—
336	#131	—	94	2	no	—
337	#131	—	94	4	no	—
338	#131	—	94	4	no	—
339	#131	—	94	2	no	—
340	#131	—	94	2	no	—
341	#131	—	94	1	no	—
342	#131	—	94	1	no	—
343	#131	C₄×D₄₇	1	2	yes	—
344	#131	C₂²×D₄₇	1	2	yes	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	47	1	no	—
347	C₂×M₁₆	—	47	2	no	—
348	C₂×M₁₆	—	47	1	no	—
349	C₂×M₁₆	—	47	4	no	—
350	C₂×M₁₆	—	94	4	no	—
351	C₂×M₁₆	—	94	4	no	—
352	C₂×M₁₆	—	94	2	no	—
353	C₂×M₁₆	—	94	4	no	—
354	C₂×M₁₆	—	94	2	no	—
355	C₂×M₁₆	—	94	1	no	—
356	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	47	2	no	—
359	C₂²×C₈	—	94	4	no	—
360	C₂²×C₈	—	94	1	no	—
361	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
362	M₃₂	—	2	1	no	—
363	M₃₂	—	2	1	no	—
364	M₃₂	—	2	1	no	—
365	M₃₂	—	47	2	no	—
366	M₃₂	—	94	4	no	—
367	M₃₂	—	94	4	no	—
368	M₃₂	—	94	1	no	—
369	M₃₂	C₂²×D₄₇	1	2	yes	—
370	C₂×C₁₆	—	2	1	no	—
371	C₂×C₁₆	—	47	1	no	—
372	C₂×C₁₆	—	47	1	no	—
373	C₂×C₁₆	—	94	4	no	—
374	C₂×C₁₆	—	94	4	no	—
375	C₂×C₁₆	—	94	1	no	—
376	C₂×C₁₆	—	94	1	no	—
377	C₂×C₁₆	—	94	1	no	—
378	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
379	#41	—	2	1	no	—
380	#41	—	2	1	no	—
381	#41	—	47	2	no	—
382	#41	—	47	2	no	—
383	#41	—	47	2	no	—
384	#41	—	47	2	no	—
385	#41	—	47	4	no	—
386	#41	—	47	4	no	—
387	#41	—	47	2	no	—
388	#41	—	47	2	no	—
389	#41	—	94	4	no	—
390	#41	—	94	4	no	—
391	#41	—	94	2	no	—
392	#41	—	94	2	no	—
393	#41	—	94	4	no	—
394	#41	—	94	4	no	—
395	#41	—	94	2	no	—
396	#41	—	94	2	no	—
397	#41	—	94	1	no	—
398	#41	—	94	1	no	—
399	#41	C₈×D₄₇	1	2	yes	—
400	#41	C₂×C₄×D₄₇	1	2	yes	—
401	C₂×Q₈	—	47	1	no	—
402	C₂×Q₈	—	47	4	no	—
403	C₂×Q₈	—	47	1	no	—
404	C₂×Q₈	—	94	2	no	—
405	C₂×Q₈	—	94	2	no	—
406	C₂×Q₈	C₈×D₄₇	1	1	yes	characteristic
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	47	2	no	—
409	C₂×D₄	—	47	4	no	—
410	C₂×D₄	—	47	1	no	—
411	C₂×D₄	—	47	1	no	—
412	C₂×D₄	—	94	2	no	—
413	C₂×D₄	—	94	4	no	—
414	C₂×D₄	—	94	2	no	—
415	C₂×D₄	—	94	4	no	—
416	C₂×D₄	—	94	4	no	—
417	C₂×D₄	—	94	1	no	—
418	C₂×D₄	C₈×D₄₇	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	47	2	no	—
421	C₂²×C₄	—	94	4	no	—
422	C₂²×C₄	—	94	1	no	—
423	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
424	M₁₆	—	2	1	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	—	47	2	no	—
428	M₁₆	—	47	2	no	—
429	M₁₆	—	47	4	no	—
430	M₁₆	—	47	4	no	—
431	M₁₆	—	47	2	no	—
432	M₁₆	—	94	4	no	—
433	M₁₆	—	94	4	no	—
434	M₁₆	—	94	4	no	—
435	M₁₆	—	94	1	no	—
436	M₁₆	—	94	2	no	—
437	M₁₆	—	94	2	no	—
438	M₁₆	C₂×C₄×D₄₇	1	2	yes	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	47	2	no	—
443	C₂×C₈	—	47	4	no	—
444	C₂×C₈	—	47	4	no	—
445	C₂×C₈	—	94	4	no	—
446	C₂×C₈	—	94	4	no	—
447	C₂×C₈	—	94	4	no	—
448	C₂×C₈	—	94	1	no	—
449	C₂×C₈	—	94	2	no	—
450	C₂×C₈	—	94	2	no	—
451	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
452	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
453	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
454	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
455	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
456	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
457	C₁₆	—	2	2	no	—
458	C₁₆	—	2	2	no	—
459	C₁₆	—	94	1	no	—
460	C₁₆	—	94	1	no	—
461	C₁₆	—	94	2	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	47	2	no	—
464	C₂³	—	94	4	no	—
465	C₂³	—	94	1	no	—
466	C₂³	M₁₆×D₄₇	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	47	2	no	—
469	Q₈	—	47	2	no	—
470	Q₈	—	47	2	no	—
471	Q₈	—	94	4	no	—
472	Q₈	—	94	1	no	—
473	Q₈	C₂×C₈×D₄₇	1	2	yes	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	1	no	—
477	D₄	—	47	4	no	—
478	D₄	—	47	4	no	—
479	D₄	—	47	2	no	—
480	D₄	—	47	2	no	—
481	D₄	—	47	2	no	—
482	D₄	—	94	4	no	—
483	D₄	—	94	4	no	—
484	D₄	—	94	4	no	—
485	D₄	—	94	2	no	—
486	D₄	—	94	2	no	—
487	D₄	—	94	1	no	—
488	D₄	C₂×C₈×D₄₇	1	2	yes	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	47	2	no	—
493	C₂×C₄	—	47	4	no	—
494	C₂×C₄	—	47	4	no	—
495	C₂×C₄	—	94	4	no	—
496	C₂×C₄	—	94	4	no	—
497	C₂×C₄	—	94	4	no	—
498	C₂×C₄	—	94	1	no	—
499	C₂×C₄	—	94	2	no	—
500	C₂×C₄	—	94	2	no	—
501	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
502	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
503	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
504	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
505	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
506	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
507	C₈	—	2	2	no	—
508	C₈	—	47	4	no	—
509	C₈	—	94	2	no	—
510	C₈	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
511	C₈	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
512	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
513	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
514	C₂²	—	2	2	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	—	47	4	no	—
518	C₂²	—	94	2	no	—
519	C₂²	—	376	1	no	—
520	C₂²	—	376	4	no	—
521	C₂²	—	188	2	no	—
522	C₂²	C₂²⋊C₈×D₄₇	1	1	yes	characteristic
523	C₂²	C₂²⋊C₈×D₄₇	1	1	yes	characteristic
524	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	47	4	no	—
527	C₄	—	94	2	no	—
528	C₄	C₂²⋊C₈×D₄₇	1	1	yes	characteristic
529	C₄	C₂²⋊C₈×D₄₇	1	1	yes	characteristic
530	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
531	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
532	C₂	—	2	1	no	—
533	C₂	—	2	1	no	—
534	C₂	—	2	1	no	—
535	C₂	—	4	2	no	—
536	C₂	—	94	4	no	—
537	C₂	—	188	2	no	—
538	C₂	C₂×C₂²⋊C₈×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#2117	C₂
socle	C₂×C₄₇	C₂²×C₂²⋊C₈
prime radical	#15689959	C₄
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	#2117	D₄₇
hypocenter	C₄₇	#33340
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2117

Complements

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

N	H ≅ G/N	type
2. #20256490	C₂	semidirect
3. C₂×#15689541	C₂	semidirect
4. #20245015	C₂	semidirect
5. #20245014	C₂	semidirect
6. C₂×#15688908	C₂	semidirect
7. C₂×#15688907	C₂	semidirect
8. #350×D₄₇	C₂	semidirect
9. C₄₇×#2117	C₂	semidirect
26. C₂×#13093964	C₂²	semidirect
27. C₂×#13093963	C₂²	semidirect
28. M₃₂×D₄₇	C₂²	semidirect
29. C₂²×C₄₇⋊C₁₆	C₂²	semidirect
30. C₂×C₁₆×D₄₇	C₂²	semidirect
31. #15688908	C₂²	semidirect
32. #15688908	C₂²	semidirect
33. #15688907	C₂²	semidirect
34. #15688907	C₂²	semidirect
35. #15688906	C₂²	semidirect
37. C₂×M₃₂×C₄₇	C₂²	semidirect
38. C₂×M₃₂×C₄₇	C₂²	semidirect
39. C₄₇×#350	C₂²	semidirect
268. #2117	D₄₇	semidirect
299. C₂×M₃₂	C₂×D₄₇	semidirect
300. C₂×M₃₂	C₂×D₄₇	semidirect
308. #350	C₂×D₄₇	semidirect
309. C₄₇	#33340	semidirect

Maximal subgroups

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

subgroup	index
#20258099	2
#20256490	2
C₂×#15689541	2
#20245015	2
#20245014	2
C₂×#15688908	2
C₂×#15688907	2
#350×D₄₇	2
C₄₇×#2117	2
#33340	47