Subgroups — #26223210

Order 12032.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253108	C₂	1	1	yes	maximal, characteristic
2	#20252287	C₂	1	2	yes	maximal, complemented
3	C₂×#15689239	C₂	1	1	yes	maximal, characteristic, complemented
4	#131×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244284	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244176	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244055	C₂	1	2	yes	maximal, complemented
8	#20243887	C₂	1	2	yes	maximal, complemented
9	#20243269	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243187	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1814	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689921	C₂²	1	2	yes	—
13	C₂×#13094046	C₂²	1	1	yes	characteristic
14	C₂×#13094032	C₂²	1	2	yes	—
15	C₂×#13094031	C₂²	1	1	yes	characteristic
16	#41×Dic₄₇	C₂²	1	1	yes	characteristic
17	#15689398	C₄	1	2	yes	complemented
18	#15689393	C₄	1	2	yes	complemented
19	#15689386	C₄	1	4	yes	complemented
20	#15689242	—	2	4	no	—
21	#15689239	—	2	1	no	—
22	#15689239	—	2	1	no	—
23	#15689239	—	2	1	no	—
24	#15689239	—	2	1	no	—
25	#15689237	—	2	4	no	—
26	#15689171	C₂²	1	2	yes	—
27	C₂×#13093960	C₂²	1	1	yes	characteristic
28	#15689141	C₂²	1	2	yes	—
29	C₂×#13093950	C₂²	1	2	yes	—
30	#15689105	C₂²	1	2	yes	—
31	#15689096	C₂²	1	2	yes	—
32	#15689081	—	2	1	no	—
33	#15689081	C₂²	1	1	yes	characteristic
34	#15689079	C₂²	1	2	yes	—
35	#15689078	—	2	1	no	—
36	#15689078	C₂²	1	1	yes	characteristic
37	M₁₆×Dic₄₇	—	2	1	no	—
38	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₈×Dic₄₇	—	2	1	no	—
40	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
41	#15688894	C₂²	1	2	yes	—
42	#15688882	C₂²	1	2	yes	—
43	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#427	C₂²	1	1	yes	characteristic
46	C₄₇×#421	C₂²	1	2	yes	—
47	C₄₇×#344	C₂²	1	2	yes	—
48	C₂×#10625350	C₂³	1	2	yes	—
49	#13094055	—	2	2	no	—
50	#13094054	C₂×C₄	1	4	yes	—
51	#13094050	—	2	2	no	—
52	#13094049	C₂×C₄	1	4	yes	—
53	#13094046	—	2	1	no	—
54	#13094046	—	2	1	no	—
55	#13094046	—	2	1	no	—
56	#13094046	—	2	1	no	—
57	#13094044	—	2	4	no	—
58	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂×#10625325	C₂×C₄	1	2	yes	complemented
60	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic, complemented
61	#13094032	—	2	2	no	—
62	#13094032	—	2	2	no	—
63	#13094032	—	2	2	no	—
64	#13094032	—	2	2	no	—
65	#13094031	—	2	1	no	—
66	#13094031	—	2	1	no	—
67	#13094031	D₄	1	2	yes	—
68	#13094031	D₄	1	2	yes	—
69	C₂×#10625329	—	2	1	no	—
70	C₂×#10625329	C₂³	1	2	yes	—
71	C₂×#10625329	C₂³	1	1	yes	characteristic
72	C₂×#10625324	—	2	2	no	—
73	C₂²×C₄₇⋊C₈	—	2	1	no	—
74	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₂×C₈×D₄₇	—	2	2	no	—
76	Q₈×Dic₄₇	—	2	1	no	—
77	D₄×Dic₄₇	—	2	1	no	—
78	D₄×Dic₄₇	—	2	2	no	—
79	#13093983	—	2	1	no	—
80	#13093983	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₄₇	—	2	1	no	—
82	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
83	#13093960	C₂×C₄	1	2	yes	complemented
84	#13093960	C₂×C₄	1	2	yes	complemented
85	#13093959	—	2	4	no	—
86	#13093952	—	2	4	no	—
87	#13093950	—	2	2	no	—
88	#13093950	—	2	2	no	—
89	#13093942	C₂×C₄	1	4	yes	complemented
90	#13093940	C₂×C₄	1	4	yes	complemented
91	#13093938	—	2	4	no	—
92	#13093935	—	2	2	no	—
93	#13093934	—	2	1	no	—
94	#13093934	—	2	1	no	—
95	#13093934	—	2	1	no	—
96	C₄×C₄₇⋊C₈	—	2	2	no	—
97	C₈×Dic₄₇	—	2	1	no	—
98	C₈×Dic₄₇	—	2	1	no	—
99	C₈×Dic₄₇	—	2	1	no	—
100	C₈×Dic₄₇	D₄	1	1	yes	characteristic
101	C₈×Dic₄₇	D₄	1	1	yes	characteristic
102	C₈×Dic₄₇	D₄	1	1	yes	characteristic
103	C₈×Dic₄₇	D₄	1	1	yes	characteristic
104	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
105	#131×C₄₇	—	2	1	no	—
106	#131×C₄₇	—	2	1	no	—
107	#131×C₄₇	C₂×C₄	1	2	yes	—
108	#131×C₄₇	C₂×C₄	1	2	yes	—
109	C₂×M₁₆×C₄₇	—	2	1	no	—
110	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
111	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₄₇	—	2	1	no	—
113	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	#117×C₄₇	C₂³	1	2	yes	—
115	#108×C₄₇	—	2	1	no	—
116	#108×C₄₇	—	2	1	no	—
117	#107×C₄₇	—	2	1	no	—
118	#106×C₄₇	—	2	1	no	—
119	#104×C₄₇	—	2	4	no	—
120	#41×C₄₇	—	2	1	no	—
121	#41×C₄₇	—	2	1	no	—
122	#41×C₄₇	C₂²×C₄	1	2	yes	—
123	#41×C₄₇	C₂×D₄	1	2	yes	—
124	C₂×Q₈×C₄₇	#41	1	1	yes	characteristic
125	C₂×D₄×C₄₇	—	2	1	no	—
126	C₂×D₄×C₄₇	#41	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	—	2	1	no	—
128	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
129	C₂×C₂²⋊D₄₇	—	2	2	no	—
130	C₂²×Dic₄₇	—	2	2	no	—
131	C₂²×Dic₄₇	—	2	1	no	—
132	#10625350	—	2	2	no	—
133	#10625350	—	2	2	no	—
134	#10625350	—	2	2	no	—
135	#10625350	—	2	2	no	—
136	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
137	C₂×C₄×D₄₇	—	2	2	no	—
138	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
139	M₁₆×C₄₇	—	2	1	no	—
140	M₁₆×C₄₇	—	2	2	no	—
141	M₁₆×C₄₇	—	2	2	no	—
142	M₁₆×C₄₇	—	2	2	no	—
143	M₁₆×C₄₇	—	2	2	no	—
144	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₄₇	—	2	1	no	—
146	C₂×C₈×C₄₇	—	2	2	no	—
147	C₂×C₈×C₄₇	—	2	2	no	—
148	C₂×C₈×C₄₇	—	2	2	no	—
149	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
154	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
155	C₄⋊C₄×C₄₇	—	2	2	no	—
156	C₂²⋊C₄×C₄₇	—	2	2	no	—
157	C₄²×C₄₇	—	2	2	no	—
158	C₂²⋊Dic₄₇	—	2	2	no	—
159	C₂²⋊Dic₄₇	#41	1	2	yes	—
160	#10625337	—	2	4	no	—
161	#10625336	—	2	4	no	—
162	#10625335	—	2	4	no	—
163	#10625334	—	2	4	no	—
164	C₄⋊Dic₄₇	—	2	2	no	—
165	C₄⋊Dic₄₇	—	2	1	no	—
166	C₄×Dic₄₇	—	2	2	no	—
167	C₄×Dic₄₇	—	2	1	no	—
168	C₄×Dic₄₇	—	2	1	no	—
169	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
170	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
171	#10625329	—	2	1	no	—
172	#10625329	—	2	2	no	—
173	#10625329	—	2	2	no	—
174	#10625329	—	2	2	no	—
175	#10625329	C₂²×C₄	1	4	yes	—
176	#10625329	C₂×D₄	1	2	yes	—
177	C₂×C₄₇⋊C₈	—	2	1	no	—
178	C₂×C₄₇⋊C₈	—	2	2	no	—
179	C₂×C₄₇⋊C₈	—	2	2	no	—
180	C₂×C₄₇⋊C₈	—	2	2	no	—
181	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
182	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
183	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
185	C₂×C₄₇⋊C₈	#41	1	1	yes	characteristic
186	C₂×C₄₇⋊C₈	#41	1	1	yes	characteristic
187	Dic₁₈₈	—	2	1	no	—
188	Dic₁₈₈	—	2	1	no	—
189	D₃₇₆	—	2	1	no	—
190	D₃₇₆	—	2	1	no	—
191	#10625325	—	2	2	no	—
192	#10625325	—	2	2	no	—
193	#10625324	—	4	2	no	—
194	#10625324	—	4	2	no	—
195	C₈×D₄₇	—	4	2	no	—
196	C₈×D₄₇	—	4	2	no	—
197	C₂³×C₄₇	—	2	1	no	—
198	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂²×D₄₇	—	2	2	no	—
200	Q₈×C₄₇	—	2	1	no	—
201	Q₈×C₄₇	C₄×D₄	1	2	yes	—
202	D₄×C₄₇	—	2	2	no	—
203	D₄×C₄₇	—	2	2	no	—
204	D₄×C₄₇	—	2	1	no	—
205	D₄×C₄₇	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₄₇	—	2	1	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	4	2	no	—
210	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
216	C₂²⋊D₄₇	—	4	2	no	—
217	C₂²⋊D₄₇	—	4	2	no	—
218	C₂×Dic₄₇	—	2	1	no	—
219	C₂×Dic₄₇	—	2	2	no	—
220	C₂×Dic₄₇	—	2	2	no	—
221	C₂×Dic₄₇	—	2	1	no	—
222	C₂×Dic₄₇	—	4	2	no	—
223	C₂×Dic₄₇	—	4	4	no	—
224	D₁₈₈	—	2	2	no	—
225	D₁₈₈	—	2	2	no	—
226	C₄×D₄₇	—	4	2	no	—
227	C₄×D₄₇	—	4	2	no	—
228	Dic₉₄	—	2	2	no	—
229	Dic₉₄	—	2	2	no	—
230	C₈×C₄₇	—	2	2	no	—
231	C₈×C₄₇	—	4	2	no	—
232	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
233	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
234	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
235	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
236	C₄₇⋊C₈	—	2	4	no	—
237	C₄₇⋊C₈	—	2	2	no	—
238	C₄₇⋊C₈	#121	1	1	yes	characteristic
239	C₄₇⋊C₈	#121	1	1	yes	characteristic
240	C₄₇⋊C₈	#121	1	1	yes	characteristic
241	C₄₇⋊C₈	#121	1	1	yes	characteristic
242	#21558	—	47	1	no	maximal, Sylow
243	C₂²×C₄₇	—	2	2	no	—
244	C₂²×C₄₇	—	4	1	no	—
245	C₂²×C₄₇	—	4	2	no	—
246	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
247	C₂²×C₄₇	#525	1	1	yes	characteristic
248	C₂²×C₄₇	#532	1	1	yes	characteristic
249	C₂×D₄₇	—	4	2	no	—
250	C₂×D₄₇	—	8	2	no	—
251	C₄×C₄₇	—	2	2	no	—
252	C₄×C₄₇	—	8	2	no	—
253	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
254	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
256	C₄×C₄₇	#529	1	1	yes	characteristic
257	Dic₄₇	—	2	2	no	—
258	Dic₄₇	—	4	2	no	—
259	Dic₄₇	—	4	1	no	—
260	Dic₄₇	—	4	2	no	—
261	#3067	—	47	1	no	—
262	#2955	—	47	2	no	—
263	C₂×#443	—	47	1	no	—
264	C₄×#131	—	47	1	no	—
265	#1976	—	47	1	no	—
266	#1953	—	47	1	no	—
267	#1932	—	47	2	no	—
268	#1906	—	47	2	no	—
269	#1814	D₄₇	1	1	yes	characteristic, complemented
270	#1772	—	47	1	no	—
271	#1757	—	47	2	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	C₄×#121	1	1	yes	characteristic
277	D₄₇	—	8	2	no	—
278	#575	—	47	2	no	—
279	C₂×#135	—	47	1	no	—
280	C₂×#131	—	47	1	no	—
281	C₂×#131	—	47	2	no	—
282	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
283	C₄×#41	—	47	1	no	—
284	#473	—	47	2	no	—
285	#472	—	47	2	no	—
286	#471	—	47	4	no	—
287	#444	—	94	4	no	—
288	#443	—	94	1	no	—
289	#443	—	94	1	no	—
290	#443	—	94	1	no	—
291	#443	—	94	1	no	—
292	#443	—	94	4	no	—
293	#430	—	47	2	no	—
294	C₂×#108	—	47	1	no	—
295	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
296	#427	C₂×D₄₇	1	1	yes	characteristic
297	#421	—	47	2	no	—
298	#421	C₂×D₄₇	1	2	yes	—
299	C₂×#104	—	47	2	no	—
300	#413	—	47	2	no	—
301	#410	—	47	2	no	—
302	#405	—	47	1	no	—
303	#405	—	47	1	no	—
304	#405	—	47	2	no	—
305	#405	—	94	1	no	—
306	#405	—	94	1	no	—
307	C₄×M₁₆	—	47	1	no	—
308	C₄×M₁₆	—	94	1	no	—
309	C₂×C₄×C₈	—	47	1	no	—
310	C₂×C₄×C₈	—	94	1	no	—
311	#344	—	47	2	no	—
312	#344	C₂×D₄₇	1	2	yes	—
313	#339	—	47	2	no	—
314	C₄₇	#21558	1	1	yes	characteristic, complemented, Sylow
315	C₂×#41	—	47	2	no	—
316	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
317	#137	—	47	4	no	—
318	#137	—	94	2	no	—
319	AGL(1,ℤ/8)	—	47	4	no	—
320	AGL(1,ℤ/8)	—	94	2	no	—
321	#135	—	94	4	no	—
322	#135	—	94	1	no	—
323	#135	—	94	1	no	—
324	#135	—	94	1	no	—
325	#135	—	94	1	no	—
326	C₂×Q₁₆	—	47	1	no	—
327	C₂×SD₁₆	—	47	2	no	—
328	C₂×D₈	—	47	1	no	—
329	#131	—	2	1	no	—
330	#131	—	2	1	no	—
331	#131	—	47	2	no	—
332	#131	—	47	2	no	—
333	#131	—	94	1	no	—
334	#131	—	94	1	no	—
335	#131	—	94	2	no	—
336	#131	—	94	2	no	—
337	#131	—	94	2	no	—
338	#131	—	94	2	no	—
339	#131	C₄×D₄₇	1	2	yes	—
340	#131	C₄×D₄₇	1	2	yes	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	47	1	no	—
343	C₂×M₁₆	—	47	2	no	—
344	C₂×M₁₆	—	94	2	no	—
345	C₂×M₁₆	—	94	1	no	—
346	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
347	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	47	1	no	—
350	C₂²×C₈	—	94	2	no	—
351	C₂²×C₈	—	94	1	no	—
352	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
353	C₄×Q₈	—	94	1	no	—
354	C₄×D₄	—	94	2	no	—
355	C₄×D₄	—	94	1	no	—
356	#117	—	47	1	no	—
357	#117	—	94	1	no	—
358	#117	C₂²×D₄₇	1	2	yes	—
359	C₂×C₄²	—	47	1	no	—
360	C₂×C₄²	—	94	1	no	—
361	#108	—	2	1	no	—
362	#108	—	2	1	no	—
363	#108	—	47	2	no	—
364	#108	—	47	2	no	—
365	#108	—	94	4	no	—
366	#107	—	2	1	no	—
367	#106	—	2	1	no	—
368	#104	—	2	4	no	—
369	#104	—	94	4	no	—
370	#104	—	94	2	no	—
371	#104	—	94	2	no	—
372	#101	—	47	4	no	—
373	#100	—	47	4	no	—
374	#99	—	94	4	no	—
375	#97	—	94	2	no	—
376	#97	—	94	1	no	—
377	#97	—	94	1	no	—
378	#97	—	94	1	no	—
379	C₄×C₈	—	47	1	no	—
380	C₄×C₈	—	47	1	no	—
381	C₄×C₈	—	47	1	no	—
382	C₄×C₈	—	47	1	no	—
383	C₄×C₈	—	94	2	no	—
384	C₄×C₈	—	94	1	no	—
385	C₄×C₈	—	94	1	no	—
386	C₄×C₈	—	94	1	no	—
387	#41	—	2	1	no	—
388	#41	—	2	1	no	—
389	#41	—	94	2	no	—
390	#41	—	94	2	no	—
391	#41	—	94	2	no	—
392	#41	—	94	2	no	—
393	#41	C₂×C₄×D₄₇	1	2	yes	—
394	#41	D₄×D₄₇	1	2	yes	—
395	C₂×Q₈	—	47	2	no	—
396	C₂×Q₈	#10625354	1	1	yes	characteristic
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	47	2	no	—
399	C₂×D₄	—	94	2	no	—
400	C₂×D₄	#10625354	1	1	yes	characteristic
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	94	2	no	—
403	C₂²×C₄	—	94	1	no	—
404	C₂²×C₄	—	94	2	no	—
405	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
406	Q₁₆	—	94	4	no	—
407	Q₁₆	—	94	1	no	—
408	Q₁₆	—	94	1	no	—
409	SD₁₆	—	94	4	no	—
410	SD₁₆	—	94	4	no	—
411	SD₁₆	—	94	2	no	—
412	SD₁₆	—	94	2	no	—
413	D₈	—	94	4	no	—
414	D₈	—	94	1	no	—
415	D₈	—	94	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	47	4	no	—
422	M₁₆	—	47	2	no	—
423	M₁₆	—	94	2	no	—
424	M₁₆	—	94	2	no	—
425	M₁₆	—	94	1	no	—
426	M₁₆	—	94	2	no	—
427	M₁₆	—	188	2	no	—
428	M₁₆	—	188	2	no	—
429	M₁₆	C₂×C₄×D₄₇	1	2	yes	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	47	1	no	—
435	C₂×C₈	—	47	1	no	—
436	C₂×C₈	—	47	1	no	—
437	C₂×C₈	—	47	1	no	—
438	C₂×C₈	—	47	1	no	—
439	C₂×C₈	—	47	1	no	—
440	C₂×C₈	—	94	2	no	—
441	C₂×C₈	—	94	2	no	—
442	C₂×C₈	—	94	1	no	—
443	C₂×C₈	—	94	2	no	—
444	C₂×C₈	—	188	2	no	—
445	C₂×C₈	—	188	2	no	—
446	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
447	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
448	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
449	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
450	C₂×C₈	#10625352	1	1	yes	characteristic
451	C₂×C₈	#10625352	1	1	yes	characteristic
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	94	2	no	—
454	C₄⋊C₄	—	94	1	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	47	2	no	—
457	C₂²⋊C₄	—	94	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	47	1	no	—
460	C₄²	—	47	1	no	—
461	C₄²	—	94	2	no	—
462	C₄²	—	94	1	no	—
463	C₄²	—	94	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	94	2	no	—
466	C₂³	#41×D₄₇	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	94	2	no	—
469	Q₈	—	94	2	no	—
470	Q₈	#13093986	1	2	yes	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	1	no	—
474	D₄	—	94	2	no	—
475	D₄	—	94	2	no	—
476	D₄	—	188	2	no	—
477	D₄	—	188	2	no	—
478	D₄	#13093986	1	2	yes	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	94	1	no	—
484	C₂×C₄	—	94	2	no	—
485	C₂×C₄	—	94	1	no	—
486	C₂×C₄	—	94	2	no	—
487	C₂×C₄	—	188	2	no	—
488	C₂×C₄	—	188	4	no	—
489	C₂×C₄	—	188	2	no	—
490	C₂×C₄	—	188	2	no	—
491	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
494	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
495	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
496	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	4	2	no	—
499	C₈	—	47	1	no	—
500	C₈	—	47	1	no	—
501	C₈	—	47	1	no	—
502	C₈	—	47	1	no	—
503	C₈	—	94	4	no	—
504	C₈	—	94	2	no	—
505	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
506	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
507	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
508	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	376	2	no	—
513	C₂²	—	188	2	no	—
514	C₂²	#15689591	1	1	yes	characteristic
515	C₂²	#15689636	1	1	yes	characteristic
516	C₂²	#15689668	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	8	2	no	—
519	C₄	—	94	2	no	—
520	C₄	—	188	1	no	—
521	C₄	—	188	2	no	—
522	C₄	—	188	2	no	—
523	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
524	C₄	C₂×#13093986	1	1	yes	characteristic
525	C₄	#121×D₄₇	1	1	yes	characteristic
526	C₄	#15689659	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	376	2	no	—
532	C₂	#20245894	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1814	C₂
socle	C₂×C₄₇	C₄×#121
prime radical	#20253108	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1814	D₄₇
hypocenter	C₄₇	#21558
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1814

Complements

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

N	H ≅ G/N	type
2. #20252287	C₂	semidirect
3. C₂×#15689239	C₂	semidirect
4. #131×Dic₄₇	C₂	semidirect
5. #20244284	C₂	semidirect
6. #20244176	C₂	semidirect
7. #20244055	C₂	semidirect
8. #20243887	C₂	semidirect
9. #20243269	C₂	semidirect
10. #20243187	C₂	semidirect
11. C₄₇×#1814	C₂	semidirect
17. #15689398	C₄	semidirect
18. #15689393	C₄	semidirect
19. #15689386	C₄	semidirect
58. C₂×Dic₁₈₈	C₂×C₄	semidirect
59. C₂×#10625325	C₂×C₄	semidirect
60. C₂×D₃₇₆	C₂×C₄	semidirect
83. #13093960	C₂×C₄	semidirect
84. #13093960	C₂×C₄	semidirect
89. #13093942	C₂×C₄	semidirect
90. #13093940	C₂×C₄	semidirect
269. #1814	D₄₇	semidirect
314. C₄₇	#21558	semidirect

Maximal subgroups

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

subgroup	index
#20253108	2
#20252287	2
C₂×#15689239	2
#131×Dic₄₇	2
#20244284	2
#20244176	2
#20244055	2
#20243887	2
#20243269	2
#20243187	2
C₄₇×#1814	2
#21558	47