Subgroups — #27122806

Order 12032.

2038 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258157	C₂	1	2	yes	maximal, complemented
2	#20256538	C₂	1	2	yes	maximal, complemented
3	#20256537	C₂	1	2	yes	maximal, complemented
4	#20256531	C₂	1	4	yes	maximal, complemented
5	#20256530	C₂	1	4	yes	maximal, complemented
6	#20256526	C₂	1	2	yes	maximal, complemented
7	#20256525	C₂	1	2	yes	maximal, complemented
8	#20256522	C₂	1	2	yes	maximal, complemented
9	#20256521	C₂	1	4	yes	maximal, complemented
10	C₂×#15689555	C₂	1	1	yes	maximal, characteristic, complemented
11	#508×D₄₇	C₂	1	4	yes	maximal, complemented
12	C₂×#15689539	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₇×#508	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689959	—	2	2	no	—
15	#15689937	C₂²	1	4	yes	complemented
16	#15689936	C₂²	1	4	yes	complemented
17	#15689930	—	2	4	no	—
18	#15689929	—	2	4	no	—
19	#15689925	C₂²	1	4	yes	complemented
20	#15689924	C₂²	1	4	yes	complemented
21	#15689921	—	2	2	no	—
22	#15689920	—	2	4	no	—
23	C₂×#13094046	C₂²	1	2	yes	complemented
24	#135×D₄₇	C₂²	1	8	yes	complemented
25	C₂×#13094030	C₂²	1	1	yes	characteristic
26	#15689565	C₂²	1	8	yes	complemented
27	#15689564	C₂²	1	4	yes	complemented
28	#15689563	C₂²	1	4	yes	complemented
29	#15689562	C₂²	1	8	yes	complemented
30	#15689560	C₂²	1	8	yes	complemented
31	#15689559	C₂²	1	4	yes	complemented
32	#15689558	C₂²	1	4	yes	complemented
33	#15689557	C₂²	1	8	yes	complemented
34	#15689556	C₂²	1	4	yes	complemented
35	#15689555	C₂²	1	2	yes	complemented
36	#15689555	C₂²	1	2	yes	complemented
37	#15689555	C₂²	1	2	yes	complemented
38	#15689555	C₂²	1	2	yes	complemented
39	#15689554	C₂²	1	8	yes	complemented
40	#15689553	C₂²	1	8	yes	complemented
41	#15689552	C₂²	1	4	yes	complemented
42	C₂×Dic₃₇₆	C₂²	1	1	yes	characteristic, complemented
43	Q₃₂×D₄₇	C₂²	1	4	yes	complemented
44	C₂×#13093969	C₂²	1	2	yes	complemented
45	SD₃₂×D₄₇	C₂²	1	8	yes	complemented
46	C₂×D₇₅₂	C₂²	1	1	yes	characteristic, complemented
47	D₁₆×D₄₇	C₂²	1	4	yes	complemented
48	#15689539	C₂²	1	2	yes	complemented
49	#15689539	C₂²	1	2	yes	complemented
50	#15689539	C₂²	1	2	yes	complemented
51	#15689539	C₂²	1	2	yes	complemented
52	C₂×#13093964	C₂²	1	1	yes	characteristic, complemented
53	C₂×#13093963	C₂²	1	2	yes	complemented
54	C₂×C₁₆×D₄₇	C₂²	1	2	yes	complemented
55	C₂×#135×C₄₇	C₂²	1	2	yes	complemented
56	C₄₇×#508	C₂²	1	2	yes	complemented
57	C₄₇×#508	C₂²	1	2	yes	complemented
58	C₄₇×#508	C₂²	1	2	yes	complemented
59	C₄₇×#508	C₂²	1	2	yes	complemented
60	C₂×Q₃₂×C₄₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×SD₃₂×C₄₇	C₂²	1	2	yes	complemented
62	C₂×D₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
64	#13094072	—	2	4	no	—
65	#13094071	—	2	4	no	—
66	#13094071	—	4	2	no	—
67	#13094070	—	2	4	no	—
68	#13094070	—	4	2	no	—
69	#13094069	—	2	4	no	—
70	#13094069	—	4	4	no	—
71	C₂×#10625350	—	2	2	no	—
72	C₂×#10625350	—	4	4	no	—
73	C₂×#10625350	D₄	1	1	yes	characteristic
74	#41×D₄₇	—	2	8	no	—
75	#41×D₄₇	—	4	4	no	—
76	#13094056	—	2	8	no	—
77	#13094055	—	2	4	no	—
78	#13094054	—	2	4	no	—
79	#13094053	—	2	8	no	—
80	#13094051	—	2	8	no	—
81	#13094050	—	2	4	no	—
82	#13094049	—	2	4	no	—
83	#13094048	—	2	8	no	—
84	#13094047	C₂³	1	8	yes	—
85	#13094046	—	2	2	no	—
86	#13094046	—	2	2	no	—
87	#13094046	C₂³	1	4	yes	—
88	#13094046	C₂³	1	4	yes	—
89	#13094045	—	2	8	no	—
90	#13094044	—	2	8	no	—
91	#13094043	C₂³	1	8	yes	—
92	C₂×Dic₁₈₈	C₂³	1	2	yes	—
93	Q₁₆×D₄₇	C₂³	1	8	yes	—
94	C₂×#10625325	—	2	2	no	—
95	SD₁₆×D₄₇	—	2	8	no	—
96	C₂×D₃₇₆	C₂³	1	2	yes	—
97	D₈×D₄₇	C₂³	1	8	yes	—
98	#13094030	D₄	1	2	yes	—
99	#13094030	D₄	1	2	yes	—
100	#13094030	C₂³	1	2	yes	—
101	#13094030	C₂³	1	2	yes	—
102	C₂×#10625329	D₄	1	1	yes	characteristic
103	C₂×#10625324	D₄	1	2	yes	—
104	C₂×C₈×D₄₇	C₂³	1	2	yes	—
105	Dic₃₇₆	C₂³	1	2	yes	—
106	Dic₃₇₆	C₂³	1	2	yes	—
107	#13093970	C₂³	1	8	yes	—
108	#13093969	C₂³	1	4	yes	—
109	#13093969	C₂³	1	4	yes	—
110	#13093968	C₂³	1	8	yes	—
111	#13093967	C₂³	1	8	yes	—
112	D₇₅₂	C₂³	1	2	yes	—
113	D₇₅₂	C₂³	1	2	yes	—
114	#13093965	C₂³	1	8	yes	—
115	#13093964	C₂³	1	2	yes	—
116	#13093964	C₂³	1	2	yes	—
117	#13093963	C₂³	1	4	yes	—
118	#13093963	C₂³	1	4	yes	—
119	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
120	C₁₆×D₄₇	C₂³	1	4	yes	—
121	C₁₆×D₄₇	C₂³	1	4	yes	—
122	C₂×#41×C₄₇	—	2	2	no	—
123	#135×C₄₇	—	2	2	no	—
124	#135×C₄₇	—	2	2	no	—
125	#135×C₄₇	C₂³	1	4	yes	—
126	#135×C₄₇	C₂³	1	4	yes	—
127	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₄₇	—	2	2	no	—
129	C₂×D₈×C₄₇	C₂³	1	2	yes	—
130	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
131	Q₃₂×C₄₇	C₂³	1	2	yes	—
132	Q₃₂×C₄₇	C₂³	1	2	yes	—
133	SD₃₂×C₄₇	C₂³	1	4	yes	—
134	SD₃₂×C₄₇	C₂³	1	4	yes	—
135	D₁₆×C₄₇	C₂³	1	2	yes	—
136	D₁₆×C₄₇	C₂³	1	2	yes	—
137	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
138	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
139	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
140	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
141	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
143	#41×C₄₇	—	2	4	no	—
144	#41×C₄₇	—	2	4	no	—
145	#41×C₄₇	—	4	2	no	—
146	#41×C₄₇	—	4	2	no	—
147	C₂×Q₈×C₄₇	—	2	2	no	—
148	C₂×D₄×C₄₇	—	2	2	no	—
149	C₂×D₄×C₄₇	—	4	2	no	—
150	C₂²×C₄×C₄₇	—	4	2	no	—
151	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₂²⋊D₄₇	—	4	2	no	—
153	C₂×C₂²⋊D₄₇	—	4	8	no	—
154	C₂×C₂²⋊D₄₇	D₈	1	2	yes	—
155	#10625354	—	2	8	no	—
156	#10625354	—	4	4	no	—
157	Q₈×D₄₇	—	2	8	no	—
158	Q₈×D₄₇	—	4	4	no	—
159	#10625352	—	2	8	no	—
160	#10625352	—	4	8	no	—
161	#10625352	—	4	8	no	—
162	#10625352	—	4	4	no	—
163	D₄×D₄₇	—	2	8	no	—
164	D₄×D₄₇	—	4	8	no	—
165	D₄×D₄₇	—	4	8	no	—
166	D₄×D₄₇	—	4	4	no	—
167	#10625350	—	2	4	no	—
168	#10625350	—	2	4	no	—
169	#10625350	—	4	2	no	—
170	#10625350	—	4	2	no	—
171	#10625350	—	4	8	no	—
172	#10625350	—	4	4	no	—
173	#10625350	—	4	8	no	—
174	#10625350	—	4	4	no	—
175	#10625350	D₈	1	2	yes	—
176	#10625350	D₈	1	2	yes	—
177	#10625350	C₂×D₄	1	2	yes	—
178	#10625350	C₂×D₄	1	2	yes	—
179	C₂×D₁₈₈	—	2	2	no	—
180	C₂×D₁₈₈	—	4	4	no	—
181	C₂×D₁₈₈	D₈	1	1	yes	characteristic
182	C₂×C₄×D₄₇	—	4	2	no	—
183	C₂×C₄×D₄₇	—	4	8	no	—
184	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
185	C₂×Dic₉₄	—	2	2	no	—
186	C₂×Dic₉₄	—	4	4	no	—
187	C₂×Dic₉₄	D₈	1	1	yes	characteristic
188	Q₁₆×C₄₇	—	2	2	no	—
189	Q₁₆×C₄₇	C₂⁴	1	4	yes	—
190	SD₁₆×C₄₇	—	2	4	no	—
191	SD₁₆×C₄₇	—	2	4	no	—
192	D₈×C₄₇	—	2	2	no	—
193	D₈×C₄₇	C₂⁴	1	4	yes	—
194	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
198	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
199	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
200	#10625337	—	2	8	no	—
201	#10625336	—	2	8	no	—
202	#10625335	—	2	8	no	—
203	#10625334	—	2	8	no	—
204	#10625329	C₂×D₄	1	2	yes	—
205	#10625329	C₂×D₄	1	2	yes	—
206	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
207	Dic₁₈₈	—	2	2	no	—
208	Dic₁₈₈	C₂⁴	1	4	yes	—
209	D₃₇₆	—	2	2	no	—
210	D₃₇₆	C₂⁴	1	4	yes	—
211	#10625325	—	2	4	no	—
212	#10625325	—	2	4	no	—
213	#10625324	C₂×D₄	1	4	yes	—
214	#10625324	C₂×D₄	1	4	yes	—
215	C₈×D₄₇	C₂×D₄	1	4	yes	—
216	C₈×D₄₇	C₂⁴	1	4	yes	—
217	C₁₆×C₄₇	C₂⁴	1	1	yes	characteristic
218	C₁₆×C₄₇	C₂⁴	1	1	yes	characteristic
219	C₁₆×C₄₇	C₂⁴	1	1	yes	characteristic
220	C₁₆×C₄₇	C₂⁴	1	1	yes	characteristic
221	C₄₇⋊C₁₆	C₂⁴	1	4	yes	—
222	C₂³×C₄₇	—	4	2	no	—
223	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
224	C₂²×D₄₇	—	4	2	no	—
225	C₂²×D₄₇	—	4	8	no	—
226	C₂²×D₄₇	C₂×D₈	1	2	yes	—
227	Q₈×C₄₇	—	2	4	no	—
228	Q₈×C₄₇	—	4	2	no	—
229	D₄×C₄₇	—	2	4	no	—
230	D₄×C₄₇	—	4	4	no	—
231	D₄×C₄₇	—	4	4	no	—
232	D₄×C₄₇	—	4	2	no	—
233	C₂×C₄×C₄₇	—	4	2	no	—
234	C₂×C₄×C₄₇	—	4	4	no	—
235	C₂×C₄×C₄₇	—	4	4	no	—
236	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
242	C₂²⋊D₄₇	—	4	4	no	—
243	C₂²⋊D₄₇	—	4	4	no	—
244	C₂²⋊D₄₇	—	4	8	no	—
245	C₂²⋊D₄₇	—	4	8	no	—
246	C₂²⋊D₄₇	C₂×D₈	1	4	yes	—
247	C₂²⋊D₄₇	C₂×D₈	1	4	yes	—
248	C₂×Dic₄₇	—	4	2	no	—
249	C₂×Dic₄₇	—	4	8	no	—
250	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
251	D₁₈₈	—	2	4	no	—
252	D₁₈₈	—	4	8	no	—
253	D₁₈₈	—	4	2	no	—
254	D₁₈₈	C₂×D₈	1	2	yes	—
255	D₁₈₈	C₂×D₈	1	2	yes	—
256	C₄×D₄₇	—	4	8	no	—
257	C₄×D₄₇	—	4	4	no	—
258	C₄×D₄₇	—	4	4	no	—
259	C₄×D₄₇	—	4	8	no	—
260	C₄×D₄₇	C₂×D₈	1	4	yes	—
261	C₄×D₄₇	C₂²×D₄	1	4	yes	—
262	Dic₉₄	—	2	4	no	—
263	Dic₉₄	—	4	2	no	—
264	Dic₉₄	—	4	8	no	—
265	Dic₉₄	C₂×D₈	1	2	yes	—
266	Dic₉₄	C₂×D₈	1	2	yes	—
267	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
268	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
269	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
270	C₈×C₄₇	C₂⁵	1	1	yes	characteristic
271	C₄₇⋊C₈	C₂²×D₄	1	4	yes	—
272	#62635	—	47	1	no	maximal, Sylow
273	C₂²×C₄₇	—	4	1	no	—
274	C₂²×C₄₇	—	4	4	no	—
275	C₂²×C₄₇	—	16	2	no	—
276	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
277	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
278	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
279	C₂×D₄₇	—	4	2	no	—
280	C₂×D₄₇	—	4	4	no	—
281	C₂×D₄₇	—	16	8	no	—
282	C₂×D₄₇	—	16	2	no	—
283	C₂×D₄₇	C₂²×D₈	1	4	yes	—
284	C₄×C₄₇	—	4	4	no	—
285	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
286	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
287	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
288	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
289	Dic₄₇	—	4	4	no	—
290	Dic₄₇	C₂²×D₈	1	4	yes	—
291	#3584	—	47	2	no	—
292	#3417	—	47	2	no	—
293	#3417	—	47	2	no	—
294	#3416	—	47	4	no	—
295	#3416	—	47	4	no	—
296	#3415	—	47	2	no	—
297	#3415	—	47	2	no	—
298	#3414	—	47	4	no	—
299	#3414	—	47	2	no	—
300	C₂×#508	—	47	4	no	—
301	C₂×#508	—	47	1	no	—
302	C₂×#508	D₄₇	1	1	yes	characteristic, complemented
303	C₂×#504	—	47	1	no	—
304	C₂×C₄₇	—	2	1	no	—
305	C₂×C₄₇	—	2	1	no	—
306	C₂×C₄₇	—	2	1	no	—
307	C₂×C₄₇	—	8	4	no	—
308	C₂×C₄₇	C₂³×D₈	1	1	yes	characteristic
309	D₄₇	—	2	4	no	—
310	D₄₇	—	8	4	no	—
311	#585	—	94	2	no	—
312	#578	—	47	4	no	—
313	#578	—	47	4	no	—
314	#577	—	94	4	no	—
315	#577	—	94	4	no	—
316	#576	—	47	4	no	—
317	#576	—	47	4	no	—
318	#575	—	94	4	no	—
319	#575	—	94	2	no	—
320	C₂×#135	—	47	8	no	—
321	C₂×#135	—	47	2	no	—
322	C₂×#135	C₂×D₄₇	1	2	yes	complemented
323	C₂×#131	—	47	1	no	—
324	#510	—	47	4	no	—
325	#510	—	47	4	no	—
326	#510	—	47	8	no	—
327	#510	—	47	8	no	—
328	#509	—	47	4	no	—
329	#509	—	47	4	no	—
330	#509	—	47	8	no	—
331	#509	—	47	8	no	—
332	#508	—	47	8	no	—
333	#508	—	47	4	no	—
334	#508	—	47	8	no	—
335	#508	—	47	4	no	—
336	#508	—	47	2	no	—
337	#508	—	47	2	no	—
338	#508	—	47	2	no	—
339	#508	—	47	2	no	—
340	#508	C₂×D₄₇	1	2	yes	complemented
341	#508	C₂×D₄₇	1	2	yes	complemented
342	#508	C₂×D₄₇	1	2	yes	complemented
343	#508	C₂×D₄₇	1	2	yes	complemented
344	C₂×Q₃₂	—	47	4	no	—
345	C₂×Q₃₂	—	47	1	no	—
346	C₂×Q₃₂	C₂×D₄₇	1	1	yes	characteristic, complemented
347	C₂×SD₃₂	—	47	8	no	—
348	C₂×SD₃₂	—	47	2	no	—
349	C₂×SD₃₂	C₂×D₄₇	1	2	yes	complemented
350	C₂×D₁₆	—	47	4	no	—
351	C₂×D₁₆	—	47	1	no	—
352	C₂×D₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
353	#504	—	47	2	no	—
354	#504	—	47	2	no	—
355	#504	—	47	2	no	—
356	#504	—	47	2	no	—
357	C₂×M₃₂	—	47	1	no	—
358	C₂×M₃₂	—	47	2	no	—
359	C₂²×C₁₆	—	47	2	no	—
360	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
361	C₄₇	#62635	1	1	yes	characteristic, complemented, Sylow
362	2₋¹⁺⁴	—	94	4	no	—
363	2₋¹⁺⁴	—	94	4	no	—
364	2₋¹⁺⁴	—	188	2	no	—
365	H(5,𝔽₂)	—	94	4	no	—
366	H(5,𝔽₂)	—	94	4	no	—
367	H(5,𝔽₂)	—	188	4	no	—
368	H(5,𝔽₂)	—	188	2	no	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	47	1	no	—
371	C₂×#41	—	94	8	no	—
372	C₂×#41	—	94	2	no	—
373	C₂×#41	—	188	4	no	—
374	C₂×#41	—	188	4	no	—
375	#137	—	94	8	no	—
376	#137	—	94	8	no	—
377	#137	—	94	4	no	—
378	#137	—	94	4	no	—
379	AGL(1,ℤ/8)	—	94	8	no	—
380	AGL(1,ℤ/8)	—	94	8	no	—
381	AGL(1,ℤ/8)	—	94	4	no	—
382	AGL(1,ℤ/8)	—	94	4	no	—
383	#135	—	2	2	no	—
384	#135	—	2	2	no	—
385	#135	—	47	8	no	—
386	#135	—	47	8	no	—
387	#135	—	47	4	no	—
388	#135	—	47	4	no	—
389	#135	—	94	8	no	—
390	#135	—	94	8	no	—
391	#135	—	94	2	no	—
392	#135	—	94	2	no	—
393	#135	C₂²×D₄₇	1	4	yes	—
394	#135	C₂²×D₄₇	1	4	yes	—
395	C₂×Q₁₆	—	47	8	no	—
396	C₂×Q₁₆	—	47	2	no	—
397	C₂×Q₁₆	C₂²×D₄₇	1	2	yes	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	94	8	no	—
400	C₂×SD₁₆	—	94	2	no	—
401	C₂×D₈	—	47	8	no	—
402	C₂×D₈	—	47	2	no	—
403	C₂×D₈	C₂²×D₄₇	1	2	yes	—
404	#131	—	47	2	no	—
405	#131	—	47	2	no	—
406	#131	—	47	2	no	—
407	#131	—	47	2	no	—
408	C₂×M₁₆	—	47	1	no	—
409	C₂×M₁₆	—	47	2	no	—
410	C₂²×C₈	—	47	2	no	—
411	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
412	Q₃₂	—	47	8	no	—
413	Q₃₂	—	47	2	no	—
414	Q₃₂	—	47	2	no	—
415	Q₃₂	C₂²×D₄₇	1	2	yes	—
416	Q₃₂	C₂²×D₄₇	1	2	yes	—
417	SD₃₂	—	47	8	no	—
418	SD₃₂	—	47	8	no	—
419	SD₃₂	—	47	4	no	—
420	SD₃₂	—	47	4	no	—
421	SD₃₂	C₂²×D₄₇	1	4	yes	—
422	SD₃₂	C₂²×D₄₇	1	4	yes	—
423	D₁₆	—	47	8	no	—
424	D₁₆	—	47	2	no	—
425	D₁₆	—	47	2	no	—
426	D₁₆	C₂²×D₄₇	1	2	yes	—
427	D₁₆	C₂²×D₄₇	1	2	yes	—
428	M₃₂	—	47	2	no	—
429	M₃₂	—	47	2	no	—
430	M₃₂	—	47	4	no	—
431	M₃₂	—	47	4	no	—
432	C₂×C₁₆	—	47	2	no	—
433	C₂×C₁₆	—	47	4	no	—
434	C₂×C₁₆	—	47	4	no	—
435	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
436	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
437	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
438	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
439	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
440	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
441	#41	—	2	4	no	—
442	#41	—	2	4	no	—
443	#41	—	4	2	no	—
444	#41	—	4	2	no	—
445	#41	—	47	2	no	—
446	#41	—	47	2	no	—
447	#41	—	47	2	no	—
448	#41	—	47	2	no	—
449	#41	—	94	8	no	—
450	#41	—	94	8	no	—
451	#41	—	94	4	no	—
452	#41	—	94	4	no	—
453	#41	—	188	8	no	—
454	#41	—	188	8	no	—
455	#41	—	188	4	no	—
456	#41	—	188	4	no	—
457	#41	—	188	8	no	—
458	#41	—	188	8	no	—
459	#41	—	188	4	no	—
460	#41	—	188	4	no	—
461	#41	—	188	2	no	—
462	#41	—	188	2	no	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×Q₈	—	47	1	no	—
465	C₂×Q₈	—	94	8	no	—
466	C₂×Q₈	—	94	2	no	—
467	C₂×Q₈	—	188	4	no	—
468	C₂×Q₈	—	188	4	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	47	2	no	—
472	C₂×D₄	—	47	1	no	—
473	C₂×D₄	—	94	8	no	—
474	C₂×D₄	—	94	2	no	—
475	C₂×D₄	—	188	4	no	—
476	C₂×D₄	—	188	8	no	—
477	C₂×D₄	—	188	4	no	—
478	C₂×D₄	—	188	8	no	—
479	C₂×D₄	—	188	8	no	—
480	C₂×D₄	—	188	2	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	47	2	no	—
483	C₂²×C₄	—	188	8	no	—
484	C₂²×C₄	—	188	2	no	—
485	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
486	Q₁₆	—	2	2	no	—
487	Q₁₆	—	47	4	no	—
488	Q₁₆	—	94	8	no	—
489	Q₁₆	—	94	2	no	—
490	Q₁₆	C₂³×D₄₇	1	4	yes	—
491	SD₁₆	—	2	4	no	—
492	SD₁₆	—	2	4	no	—
493	SD₁₆	—	94	8	no	—
494	SD₁₆	—	94	8	no	—
495	SD₁₆	—	94	4	no	—
496	SD₁₆	—	94	4	no	—
497	D₈	—	2	2	no	—
498	D₈	—	47	4	no	—
499	D₈	—	94	8	no	—
500	D₈	—	94	2	no	—
501	D₈	C₂³×D₄₇	1	4	yes	—
502	M₁₆	—	47	2	no	—
503	M₁₆	—	47	2	no	—
504	M₁₆	—	47	4	no	—
505	M₁₆	—	47	4	no	—
506	C₂×C₈	—	47	2	no	—
507	C₂×C₈	—	47	4	no	—
508	C₂×C₈	—	47	4	no	—
509	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
510	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
511	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
512	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
513	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
514	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
515	C₁₆	—	47	4	no	—
516	C₁₆	C₂³×D₄₇	1	1	yes	characteristic
517	C₁₆	C₂³×D₄₇	1	1	yes	characteristic
518	C₁₆	C₂³×D₄₇	1	1	yes	characteristic
519	C₁₆	C₂³×D₄₇	1	1	yes	characteristic
520	C₂³	—	4	2	no	—
521	C₂³	—	47	2	no	—
522	C₂³	—	188	8	no	—
523	C₂³	—	188	2	no	—
524	C₂³	D₈×D₄₇	1	1	yes	characteristic
525	Q₈	—	2	4	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	47	2	no	—
528	Q₈	—	47	2	no	—
529	Q₈	—	94	4	no	—
530	Q₈	—	188	8	no	—
531	Q₈	—	188	2	no	—
532	D₄	—	2	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	4	no	—
535	D₄	—	4	2	no	—
536	D₄	—	47	4	no	—
537	D₄	—	47	4	no	—
538	D₄	—	47	2	no	—
539	D₄	—	47	2	no	—
540	D₄	—	94	4	no	—
541	D₄	—	188	8	no	—
542	D₄	—	188	8	no	—
543	D₄	—	188	8	no	—
544	D₄	—	188	4	no	—
545	D₄	—	188	4	no	—
546	D₄	—	188	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	47	2	no	—
551	C₂×C₄	—	47	4	no	—
552	C₂×C₄	—	47	4	no	—
553	C₂×C₄	—	188	8	no	—
554	C₂×C₄	—	188	8	no	—
555	C₂×C₄	—	188	8	no	—
556	C₂×C₄	—	188	2	no	—
557	C₂×C₄	—	188	4	no	—
558	C₂×C₄	—	188	4	no	—
559	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
560	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
561	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
562	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
563	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
564	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
565	C₈	—	47	4	no	—
566	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
567	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
568	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
569	C₈	C₂⁴×D₄₇	1	1	yes	characteristic
570	C₂²	—	4	1	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	16	2	no	—
573	C₂²	—	47	4	no	—
574	C₂²	—	188	2	no	—
575	C₂²	—	188	4	no	—
576	C₂²	—	752	2	no	—
577	C₂²	—	752	8	no	—
578	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
579	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
580	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
581	C₄	—	4	4	no	—
582	C₄	—	47	4	no	—
583	C₄	—	188	4	no	—
584	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
585	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
586	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
587	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	8	4	no	—
592	C₂	—	94	4	no	—
593	C₂	—	376	4	no	—
594	C₂	C₂²×D₈×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₈×D₄₇
commutator, cosocle	C₈×C₄₇	C₂⁵
Frattini	C₈	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#508	C₂
socle	C₂×C₄₇	C₂³×D₈
hypercenter	C₂×#508	D₄₇
hypocenter	C₄₇	#62635
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#508

Complements

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

N	H ≅ G/N	type
1. #20258157	C₂	semidirect
2. #20256538	C₂	semidirect
3. #20256537	C₂	semidirect
4. #20256531	C₂	semidirect
5. #20256530	C₂	semidirect
6. #20256526	C₂	semidirect
7. #20256525	C₂	semidirect
8. #20256522	C₂	semidirect
9. #20256521	C₂	semidirect
10. C₂×#15689555	C₂	semidirect
11. #508×D₄₇	C₂	semidirect
12. C₂×#15689539	C₂	semidirect
13. C₂×C₄₇×#508	C₂	semidirect
15. #15689937	C₂²	semidirect
16. #15689936	C₂²	semidirect
19. #15689925	C₂²	semidirect
20. #15689924	C₂²	semidirect
23. C₂×#13094046	C₂²	semidirect
24. #135×D₄₇	C₂²	semidirect
26. #15689565	C₂²	semidirect
27. #15689564	C₂²	semidirect
28. #15689563	C₂²	semidirect
29. #15689562	C₂²	semidirect
30. #15689560	C₂²	semidirect
31. #15689559	C₂²	semidirect
32. #15689558	C₂²	semidirect
33. #15689557	C₂²	semidirect
34. #15689556	C₂²	semidirect
35. #15689555	C₂²	semidirect
36. #15689555	C₂²	semidirect
37. #15689555	C₂²	semidirect
38. #15689555	C₂²	semidirect
39. #15689554	C₂²	semidirect
40. #15689553	C₂²	semidirect
41. #15689552	C₂²	semidirect
42. C₂×Dic₃₇₆	C₂²	semidirect
43. Q₃₂×D₄₇	C₂²	semidirect
44. C₂×#13093969	C₂²	semidirect
45. SD₃₂×D₄₇	C₂²	semidirect
46. C₂×D₇₅₂	C₂²	semidirect
47. D₁₆×D₄₇	C₂²	semidirect
48. #15689539	C₂²	semidirect
49. #15689539	C₂²	semidirect
50. #15689539	C₂²	semidirect
51. #15689539	C₂²	semidirect
52. C₂×#13093964	C₂²	semidirect
53. C₂×#13093963	C₂²	semidirect
54. C₂×C₁₆×D₄₇	C₂²	semidirect
55. C₂×#135×C₄₇	C₂²	semidirect
56. C₄₇×#508	C₂²	semidirect
57. C₄₇×#508	C₂²	semidirect
58. C₄₇×#508	C₂²	semidirect
59. C₄₇×#508	C₂²	semidirect
60. C₂×Q₃₂×C₄₇	C₂²	semidirect
61. C₂×SD₃₂×C₄₇	C₂²	semidirect
62. C₂×D₁₆×C₄₇	C₂²	semidirect
63. C₂²×C₁₆×C₄₇	C₂²	semidirect
302. C₂×#508	D₄₇	semidirect
322. C₂×#135	C₂×D₄₇	semidirect
340. #508	C₂×D₄₇	semidirect
341. #508	C₂×D₄₇	semidirect
342. #508	C₂×D₄₇	semidirect
343. #508	C₂×D₄₇	semidirect
346. C₂×Q₃₂	C₂×D₄₇	semidirect
349. C₂×SD₃₂	C₂×D₄₇	semidirect
352. C₂×D₁₆	C₂×D₄₇	semidirect
360. C₂²×C₁₆	C₂×D₄₇	semidirect
361. C₄₇	#62635	semidirect

Maximal subgroups

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

subgroup	index
#20258157	2
#20256538	2
#20256537	2
#20256531	2
#20256530	2
#20256526	2
#20256525	2
#20256522	2
#20256521	2
C₂×#15689555	2
#508×D₄₇	2
C₂×#15689539	2
C₂×C₄₇×#508	2
#62635	47