Subgroups — #26234763

Order 12032.

846 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689238	C₂	1	1	yes	maximal, characteristic
2	#20252267	C₂	1	2	yes	maximal
3	#20251988	C₂	1	1	yes	maximal, characteristic, complemented
4	#20251984	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244167	C₂	1	2	yes	maximal, complemented
6	#20243624	C₂	1	2	yes	maximal, complemented
7	#20243619	C₂	1	2	yes	maximal, complemented
8	#20243551	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243449	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243270	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1816	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094044	C₂²	1	1	yes	characteristic
13	C₂×#13094030	C₂²	1	1	yes	characteristic
14	#15689606	C₂²	1	2	yes	—
15	#15689604	C₂²	1	2	yes	—
16	#15689238	C₄	1	8	yes	complemented
17	#15689232	—	2	2	no	—
18	#15689227	—	2	2	no	—
19	#15689214	—	2	2	no	—
20	#15689208	—	2	2	no	—
21	C₂×#13093959	C₂²	1	1	yes	characteristic
22	#15689165	—	2	2	no	—
23	#15689165	C₂²	1	2	yes	—
24	#15689164	—	2	2	no	—
25	#15689163	C₂²	1	2	yes	—
26	#15689161	—	2	1	no	—
27	#15689161	C₂²	1	1	yes	characteristic
28	#15689160	—	2	1	no	—
29	C₂×#13093958	—	2	1	no	—
30	C₂×#13093958	C₂²	1	1	yes	characteristic
31	#107×D₄₇	—	2	1	no	—
32	C₂×#13093955	C₂²	1	2	yes	—
33	C₂×#13093951	C₂²	1	1	yes	characteristic
34	C₂×#13093950	C₂²	1	1	yes	characteristic
35	#15689125	C₂²	1	2	yes	—
36	#15689081	C₂²	1	2	yes	—
37	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
38	#15688988	C₂²	1	2	yes	—
39	#15688891	C₂²	1	2	yes	—
40	#15688884	C₂²	1	2	yes	—
41	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#417	C₂²	1	2	yes	—
45	C₄₇×#343	C₂²	1	2	yes	—
46	C₂×#10625350	C₂³	1	1	yes	characteristic
47	#13094044	C₂×C₄	1	4	yes	—
48	#13094044	Q₈	1	4	yes	—
49	C₂×#10625337	D₄	1	1	yes	characteristic
50	C₂×#10625335	D₄	1	1	yes	characteristic
51	C₂×#10625336	D₄	1	1	yes	characteristic
52	C₂×#10625334	D₄	1	1	yes	characteristic
53	#13094030	—	2	2	no	—
54	#13094030	C₂×C₄	1	4	yes	complemented
55	C₂×#10625329	C₂³	1	1	yes	characteristic
56	C₂×#10625324	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₄₇	—	2	1	no	—
59	Q₈×Dic₄₇	—	2	2	no	—
60	#13093989	—	2	2	no	—
61	D₄×Dic₄₇	—	2	2	no	—
62	D₄×Dic₄₇	—	4	2	no	—
63	#13093986	—	2	2	no	—
64	C₄×C₂²⋊D₄₇	—	4	2	no	—
65	#13093983	—	2	2	no	—
66	#13093983	C₂³	1	2	yes	—
67	#13093982	—	2	2	no	—
68	C₂×C₄⋊Dic₄₇	—	2	2	no	—
69	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
70	C₄⋊C₄×D₄₇	—	2	2	no	—
71	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	#13093959	C₂×C₄	1	4	yes	complemented
73	#13093958	—	2	1	no	—
74	#13093958	—	2	1	no	—
75	#13093958	—	2	2	no	—
76	#13093958	D₄	1	1	yes	characteristic
77	#13093958	D₄	1	1	yes	characteristic
78	#13093957	—	2	2	no	—
79	#13093956	—	2	2	no	—
80	#13093956	D₄	1	2	yes	—
81	#13093955	—	2	2	no	—
82	#13093955	—	2	2	no	—
83	#13093955	—	2	2	no	—
84	#13093951	C₂×C₄	1	4	yes	complemented
85	#13093950	C₂×C₄	1	4	yes	complemented
86	#13093949	—	2	2	no	—
87	#13093946	—	2	2	no	—
88	#13093934	—	2	2	no	—
89	C₈×Dic₄₇	—	2	2	no	—
90	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
91	C₄₇⋊#95	—	4	2	no	—
92	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
93	#131×C₄₇	—	2	2	no	—
94	#131×C₄₇	C₂×C₄	1	4	yes	complemented
95	C₂×M₁₆×C₄₇	—	2	1	no	—
96	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
97	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₄₇	—	2	1	no	—
99	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
101	#108×C₄₇	—	2	2	no	—
102	#107×C₄₇	—	2	1	no	—
103	#107×C₄₇	—	2	1	no	—
104	#103×C₄₇	—	2	2	no	—
105	#102×C₄₇	—	2	2	no	—
106	#41×C₄₇	—	2	1	no	—
107	#41×C₄₇	—	2	1	no	—
108	#41×C₄₇	C₂²×C₄	1	2	yes	—
109	#41×C₄₇	C₂×Q₈	1	2	yes	—
110	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₂²⋊D₄₇	—	2	1	no	—
117	C₂²×Dic₄₇	—	2	1	no	—
118	C₂²×Dic₄₇	—	2	2	no	—
119	C₂²×Dic₄₇	—	4	2	no	—
120	#10625350	—	2	1	no	—
121	#10625350	—	2	1	no	—
122	#10625350	C₂²×C₄	1	2	yes	—
123	#10625350	C₂×Q₈	1	2	yes	—
124	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×D₄₇	—	2	1	no	—
126	C₂×C₄×D₄₇	—	4	2	no	—
127	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
128	M₁₆×C₄₇	—	2	1	no	—
129	M₁₆×C₄₇	—	2	4	no	—
130	M₁₆×C₄₇	—	2	2	no	—
131	M₁₆×C₄₇	—	2	2	no	—
132	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₇	—	2	1	no	—
134	C₂×C₈×C₄₇	—	2	4	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₄₇	#41	1	2	yes	—
140	C₄⋊C₄×C₄₇	—	2	2	no	—
141	C₄⋊C₄×C₄₇	—	2	2	no	—
142	C₂²⋊Dic₄₇	—	2	2	no	—
143	C₂²⋊Dic₄₇	—	4	2	no	—
144	#10625337	C₄⋊C₄	1	4	yes	—
145	#10625336	C₄⋊C₄	1	4	yes	—
146	#10625335	C₄⋊C₄	1	4	yes	—
147	#10625334	C₄⋊C₄	1	4	yes	—
148	(C₂×D₄₇)⋊C₄	—	4	2	no	—
149	C₄⋊Dic₄₇	—	2	2	no	—
150	C₄⋊Dic₄₇	—	2	2	no	—
151	C₄⋊Dic₄₇	—	4	2	no	—
152	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
153	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
154	Dic₄₇⋊C₄	—	4	2	no	—
155	C₄×Dic₄₇	—	2	2	no	—
156	C₄×Dic₄₇	—	2	1	no	—
157	C₄×Dic₄₇	—	4	2	no	—
158	C₄×Dic₄₇	—	4	2	no	—
159	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
160	#10625329	—	2	1	no	—
161	#10625329	C₂²×C₄	1	2	yes	—
162	C₂×C₄₇⋊C₈	—	2	1	no	—
163	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
164	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
167	#10625324	—	2	4	no	—
168	C₈×D₄₇	—	2	4	no	—
169	C₂³×C₄₇	—	2	1	no	—
170	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂²×D₄₇	—	2	1	no	—
172	Q₈×C₄₇	—	2	1	no	—
173	Q₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
174	D₄×C₄₇	—	2	2	no	—
175	D₄×C₄₇	—	2	2	no	—
176	D₄×C₄₇	—	2	1	no	—
177	D₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	8	2	no	—
183	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂²⋊D₄₇	—	2	2	no	—
190	C₂²⋊D₄₇	—	2	2	no	—
191	C₂×Dic₄₇	—	2	1	no	—
192	C₂×Dic₄₇	—	2	2	no	—
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	—	2	2	no	—
195	C₂×Dic₄₇	—	4	1	no	—
196	C₂×Dic₄₇	—	4	1	no	—
197	C₂×Dic₄₇	—	4	2	no	—
198	C₂×Dic₄₇	—	8	2	no	—
199	C₂×Dic₄₇	—	16	2	no	—
200	D₁₈₈	—	2	1	no	—
201	D₁₈₈	C₂×C₄⋊C₄	1	2	yes	—
202	C₄×D₄₇	—	2	2	no	—
203	C₄×D₄₇	—	2	2	no	—
204	C₄×D₄₇	—	16	2	no	—
205	Dic₉₄	—	2	1	no	—
206	Dic₉₄	C₂×C₄⋊C₄	1	2	yes	—
207	C₈×C₄₇	—	2	2	no	—
208	C₈×C₄₇	—	4	2	no	—
209	C₈×C₄₇	C₄×D₄	1	2	yes	—
210	C₈×C₄₇	C₄×D₄	1	2	yes	—
211	C₄₇⋊C₈	—	2	2	no	—
212	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
213	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
214	#22691	—	47	1	no	maximal, Sylow
215	C₂²×C₄₇	—	2	1	no	—
216	C₂²×C₄₇	—	2	1	no	—
217	C₂²×C₄₇	—	2	2	no	—
218	C₂²×C₄₇	—	4	1	no	—
219	C₂²×C₄₇	—	4	1	no	—
220	C₂²×C₄₇	#520	1	1	yes	characteristic
221	C₂²×C₄₇	D₄²	1	1	yes	characteristic
222	C₂²×C₄₇	#554	1	1	yes	characteristic
223	C₂×D₄₇	—	2	2	no	—
224	C₂×D₄₇	—	4	1	no	—
225	C₂×D₄₇	—	4	1	no	—
226	C₄×C₄₇	—	2	2	no	—
227	C₄×C₄₇	—	8	2	no	—
228	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
229	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
230	C₄×C₄₇	#547	1	1	yes	characteristic
231	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
232	Dic₄₇	—	2	2	no	—
233	Dic₄₇	—	4	2	no	—
234	Dic₄₇	—	4	2	no	—
235	Dic₄₇	—	4	2	no	—
236	Dic₄₇	—	8	2	no	—
237	C₂×#443	—	47	1	no	—
238	#2952	—	47	2	no	—
239	#2913	—	47	1	no	—
240	#2913	—	47	1	no	—
241	#1951	—	47	2	no	—
242	#1860	—	47	2	no	—
243	#1860	—	47	2	no	—
244	#1846	—	47	1	no	—
245	#1816	—	47	1	no	—
246	#1816	D₄₇	1	1	yes	characteristic, complemented
247	#1772	—	47	1	no	—
248	C₂×C₄₇	—	2	1	no	—
249	C₂×C₄₇	—	2	1	no	—
250	C₂×C₄₇	—	4	2	no	—
251	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
252	C₂×C₄₇	#3290	1	1	yes	characteristic
253	C₂×C₄₇	#3290	1	1	yes	characteristic
254	D₄₇	—	4	2	no	—
255	C₂×#135	—	47	1	no	—
256	C₂×#131	—	47	1	no	—
257	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
258	#520	—	47	2	no	—
259	#520	—	47	2	no	—
260	#443	—	47	8	no	—
261	#442	—	94	2	no	—
262	#441	—	94	2	no	—
263	C₄×SD₁₆	—	94	2	no	—
264	C₄×SD₁₆	—	94	2	no	—
265	C₂×#108	—	47	1	no	—
266	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
267	#428	—	47	2	no	—
268	#428	—	47	2	no	—
269	#428	—	94	2	no	—
270	#428	—	94	2	no	—
271	#427	—	47	1	no	—
272	#427	—	94	1	no	—
273	#427	—	94	1	no	—
274	C₂×#107	—	47	1	no	—
275	C₂×#107	—	94	1	no	—
276	C₂×#107	—	94	1	no	—
277	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
278	C₂×#106	—	47	2	no	—
279	C₂×#104	—	47	1	no	—
280	C₂×#104	—	47	1	no	—
281	#417	—	47	2	no	—
282	#417	C₂×D₄₇	1	2	yes	—
283	#405	—	47	2	no	—
284	C₂×C₄×C₈	—	47	1	no	—
285	#382	—	47	2	no	—
286	#343	—	47	2	no	—
287	#343	C₂×D₄₇	1	2	yes	—
288	#339	—	47	2	no	—
289	C₄₇	#22691	1	1	yes	characteristic, complemented, Sylow
290	C₂×#41	—	47	1	no	—
291	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
292	#135	—	47	4	no	—
293	#135	—	47	4	no	—
294	C₂×Q₁₆	—	47	1	no	—
295	C₂×SD₁₆	—	47	1	no	—
296	C₂×SD₁₆	—	47	1	no	—
297	C₂×D₈	—	47	1	no	—
298	#131	—	2	2	no	—
299	#131	—	47	4	no	—
300	#131	—	94	2	no	—
301	#131	C₄×D₄₇	1	4	yes	complemented
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	47	1	no	—
304	C₂×M₁₆	—	94	1	no	—
305	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
306	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	47	1	no	—
309	C₂²×C₈	—	94	1	no	—
310	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
311	C₄×Q₈	—	94	2	no	—
312	C₄×Q₈	—	94	2	no	—
313	C₄×D₄	—	94	2	no	—
314	C₄×D₄	—	94	2	no	—
315	C₄×D₄	—	188	2	no	—
316	C₄×D₄	—	188	2	no	—
317	#117	—	47	2	no	—
318	#117	—	94	2	no	—
319	#117	—	94	2	no	—
320	C₂×C₄⋊C₄	—	47	2	no	—
321	C₂×C₄⋊C₄	—	94	2	no	—
322	C₂×C₄⋊C₄	—	94	2	no	—
323	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
324	C₂×C₄²	—	47	1	no	—
325	#108	—	2	2	no	—
326	#108	—	47	4	no	—
327	#107	—	2	1	no	—
328	#107	—	2	1	no	—
329	#107	—	47	1	no	—
330	#107	—	47	1	no	—
331	#107	—	94	2	no	—
332	#107	—	94	2	no	—
333	#107	—	94	1	no	—
334	#107	—	94	1	no	—
335	#106	—	47	2	no	—
336	#106	—	94	2	no	—
337	#106	—	94	2	no	—
338	#106	—	94	2	no	—
339	#106	—	94	2	no	—
340	#104	—	47	4	no	—
341	#104	—	47	4	no	—
342	#103	—	2	2	no	—
343	#103	—	94	2	no	—
344	#102	—	2	2	no	—
345	#102	—	94	2	no	—
346	#97	—	94	2	no	—
347	C₄×C₈	—	47	4	no	—
348	C₄×C₈	—	94	2	no	—
349	#95	—	188	2	no	—
350	#41	—	2	1	no	—
351	#41	—	2	1	no	—
352	#41	—	47	2	no	—
353	#41	—	47	2	no	—
354	#41	—	94	1	no	—
355	#41	—	94	1	no	—
356	#41	C₂×C₄×D₄₇	1	2	yes	—
357	#41	Q₈×D₄₇	1	2	yes	—
358	C₂×Q₈	—	47	1	no	—
359	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	47	1	no	—
362	C₂×D₄	—	94	1	no	—
363	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	94	1	no	—
367	C₂²×C₄	—	94	1	no	—
368	C₂²×C₄	—	94	2	no	—
369	C₂²×C₄	—	188	2	no	—
370	C₂²×C₄	—	188	2	no	—
371	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
372	Q₁₆	—	47	4	no	—
373	SD₁₆	—	47	4	no	—
374	SD₁₆	—	47	4	no	—
375	D₈	—	47	4	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	4	no	—
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	47	2	no	—
381	M₁₆	—	94	1	no	—
382	M₁₆	—	94	4	no	—
383	M₁₆	C₂×C₄×D₄₇	1	2	yes	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	47	2	no	—
388	C₂×C₈	—	47	1	no	—
389	C₂×C₈	—	47	1	no	—
390	C₂×C₈	—	47	2	no	—
391	C₂×C₈	—	94	1	no	—
392	C₂×C₈	—	94	4	no	—
393	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
394	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
395	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
396	C₂×C₈	#10625352	1	2	yes	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	47	2	no	—
400	C₄⋊C₄	—	47	2	no	—
401	C₄⋊C₄	—	94	2	no	—
402	C₄⋊C₄	—	94	2	no	—
403	C₄⋊C₄	—	188	2	no	—
404	C₄⋊C₄	—	188	2	no	—
405	C₂²⋊C₄	—	94	2	no	—
406	C₂²⋊C₄	—	188	2	no	—
407	C₂²⋊C₄	—	188	2	no	—
408	C₄²	—	47	2	no	—
409	C₄²	—	94	2	no	—
410	C₄²	—	94	1	no	—
411	C₄²	—	188	2	no	—
412	C₄²	—	188	2	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	94	1	no	—
415	C₂³	#13094070	1	1	yes	characteristic
416	Q₈	—	2	1	no	—
417	Q₈	—	47	2	no	—
418	Q₈	—	94	1	no	—
419	Q₈	C₄⋊C₄×D₄₇	1	2	yes	—
420	D₄	—	2	2	no	—
421	D₄	—	2	2	no	—
422	D₄	—	2	1	no	—
423	D₄	—	47	2	no	—
424	D₄	—	94	2	no	—
425	D₄	—	94	2	no	—
426	D₄	—	94	1	no	—
427	D₄	C₄⋊C₄×D₄₇	1	2	yes	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	94	1	no	—
434	C₂×C₄	—	94	2	no	—
435	C₂×C₄	—	94	2	no	—
436	C₂×C₄	—	94	2	no	—
437	C₂×C₄	—	94	2	no	—
438	C₂×C₄	—	94	2	no	—
439	C₂×C₄	—	376	2	no	—
440	C₂×C₄	—	188	2	no	—
441	C₂×C₄	—	188	1	no	—
442	C₂×C₄	—	188	1	no	—
443	C₂×C₄	—	752	2	no	—
444	C₂×C₄	—	752	2	no	—
445	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
446	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
447	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
448	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
449	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
450	C₂×C₄	#13094071	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	4	2	no	—
453	C₈	—	47	2	no	—
454	C₈	—	47	2	no	—
455	C₈	—	94	2	no	—
456	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
457	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	94	2	no	—
464	C₂²	—	188	1	no	—
465	C₂²	—	188	1	no	—
466	C₂²	#15689603	1	1	yes	characteristic
467	C₂²	#15689757	1	1	yes	characteristic
468	C₂²	#15689831	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	8	2	no	—
471	C₄	—	94	2	no	—
472	C₄	—	376	2	no	—
473	C₄	—	188	2	no	—
474	C₄	—	188	2	no	—
475	C₄	—	188	2	no	—
476	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
477	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
478	C₄	#15689773	1	1	yes	characteristic
479	C₄	#15689786	1	1	yes	characteristic
480	C₂	—	2	1	no	—
481	C₂	—	2	1	no	—
482	C₂	—	4	2	no	—
483	C₂	—	188	2	no	—
484	C₂	#20246284	1	1	yes	characteristic
485	C₂	#20255169	1	1	yes	characteristic
486	C₂	#20255177	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15689757
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1816	C₂
socle	C₂²×C₄₇	D₄²
prime radical	C₂×#13094044	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1816	D₄₇
hypocenter	C₄₇	#22691
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1816

Complements

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

N	H ≅ G/N	type
3. #20251988	C₂	semidirect
4. #20251984	C₂	semidirect
5. #20244167	C₂	semidirect
6. #20243624	C₂	semidirect
7. #20243619	C₂	semidirect
8. #20243551	C₂	semidirect
9. #20243449	C₂	semidirect
10. #20243270	C₂	semidirect
11. C₄₇×#1816	C₂	semidirect
16. #15689238	C₄	semidirect
54. #13094030	C₂×C₄	semidirect
72. #13093959	C₂×C₄	semidirect
84. #13093951	C₂×C₄	semidirect
85. #13093950	C₂×C₄	semidirect
90. C₈×Dic₄₇	C₂×C₄	semidirect
94. #131×C₄₇	C₂×C₄	semidirect
246. #1816	D₄₇	semidirect
289. C₄₇	#22691	semidirect
301. #131	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689238	2
#20252267	2
#20251988	2
#20251984	2
#20244167	2
#20243624	2
#20243619	2
#20243551	2
#20243449	2
#20243270	2
C₄₇×#1816	2
#22691	47