Subgroups — #26185807

Order 12032.

688 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252349	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252344	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13094046	C₂	1	1	yes	maximal, characteristic
4	#20242237	C₂	1	2	yes	maximal, complemented
5	#20242230	C₂	1	2	yes	maximal, complemented
6	#20242223	C₂	1	2	yes	maximal, complemented
7	#20242216	C₂	1	2	yes	maximal, complemented
8	#20241768	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241768	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688845	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₄	1	1	yes	characteristic
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	C₄×#10625350	C₂²	1	1	yes	characteristic
15	#15689250	C₂²	1	2	yes	—
16	#15689247	C₂²	1	2	yes	—
17	C₄×Dic₁₈₈	C₄	1	1	yes	characteristic
18	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic
19	C₄×#10625325	C₄	1	1	yes	characteristic
20	C₄×#10625325	C₄	1	1	yes	characteristic
21	C₄×#10625325	C₂²	1	1	yes	characteristic
22	C₄×#10625325	C₂²	1	1	yes	characteristic
23	C₄×D₃₇₆	C₄	1	1	yes	characteristic
24	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
25	#15689200	C₂²	1	2	yes	—
26	#15689191	—	2	2	no	—
27	#15689188	C₂²	1	2	yes	—
28	(C₂²⋊D₄₇)⋊C₈	—	2	2	no	—
29	#15689174	—	2	1	no	—
30	#15689174	—	2	1	no	—
31	#15689161	C₄	1	1	yes	characteristic
32	#15689120	C₄	1	1	yes	characteristic
33	#15689120	C₄	1	1	yes	characteristic
34	C₄×#10625324	—	2	1	no	—
35	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
37	C₄×C₈×D₄₇	—	2	1	no	—
38	#15688853	C₂²	1	2	yes	—
39	#15688853	C₂²	1	2	yes	—
40	#15688850	C₂²	1	2	yes	—
41	#15688850	C₂²	1	2	yes	—
42	#15688845	C₂²	1	2	yes	—
43	#15688845	C₂²	1	2	yes	—
44	C₄₇×#431	C₂²	1	1	yes	characteristic
45	C₄₇×#431	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#335	C₂²	1	2	yes	—
48	C₄₇×#334	C₂²	1	2	yes	—
49	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
50	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
51	#13094046	—	2	4	no	—
52	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
53	C₂×#10625325	C₂×C₄	1	1	yes	characteristic
54	C₂×#10625325	C₂×C₄	1	1	yes	characteristic
55	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
56	C₂×#10625324	—	2	2	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
59	C₂×C₈×D₄₇	—	2	2	no	—
60	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
63	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
64	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
65	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
66	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
67	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
68	C₄×C₂²⋊D₄₇	—	2	1	no	—
69	C₄×C₂²⋊D₄₇	—	2	1	no	—
70	C₄×C₂²⋊D₄₇	—	2	1	no	—
71	C₄×C₂²⋊D₄₇	—	2	1	no	—
72	#13093983	C₂×C₄	1	1	yes	characteristic
73	#13093983	C₂×C₄	1	1	yes	characteristic
74	#13093981	—	2	1	no	—
75	#13093981	—	2	1	no	—
76	C₄²×D₄₇	—	2	1	no	—
77	C₄²×D₄₇	—	2	1	no	—
78	#13093958	C₂×C₄	1	1	yes	characteristic
79	#13093958	C₂×C₄	1	1	yes	characteristic
80	#13093956	C₂×C₄	1	1	yes	characteristic
81	#13093956	C₂×C₄	1	1	yes	characteristic
82	Dic₄₇⋊C₈	—	2	2	no	—
83	Dic₄₇⋊C₈	—	2	2	no	—
84	#13093949	C₂×C₄	1	1	yes	characteristic
85	#13093949	C₂×C₄	1	1	yes	characteristic
86	#13093949	C₂×C₄	1	1	yes	characteristic
87	#13093949	C₂×C₄	1	1	yes	characteristic
88	#13093946	C₂×C₄	1	1	yes	characteristic
89	#13093946	C₂×C₄	1	1	yes	characteristic
90	#13093946	C₂×C₄	1	1	yes	characteristic
91	#13093946	C₂×C₄	1	1	yes	characteristic
92	(C₂×D₄₇)⋊C₈	—	2	2	no	—
93	(C₂×D₄₇)⋊C₈	—	2	2	no	—
94	#13093934	—	2	2	no	—
95	C₄×C₄₇⋊C₈	—	2	1	no	—
96	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
97	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
98	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
99	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
100	C₈×Dic₄₇	—	2	2	no	—
101	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
102	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
105	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
106	C₂²⋊C₈×C₄₇	—	2	1	no	—
107	C₂²⋊C₈×C₄₇	—	2	1	no	—
108	C₄×C₈×C₄₇	—	2	1	no	—
109	C₄×C₈×C₄₇	—	2	1	no	—
110	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
111	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
112	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	C₂×C₂²⋊D₄₇	—	2	1	no	—
118	C₂×C₂²⋊D₄₇	—	2	1	no	—
119	#10625350	—	2	2	no	—
120	#10625350	—	2	2	no	—
121	#10625350	—	2	2	no	—
122	#10625350	M₁₆	1	4	yes	complemented
123	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₄₇	—	2	1	no	—
126	C₂×C₄×D₄₇	—	2	1	no	—
127	C₂×C₄×D₄₇	—	2	1	no	—
128	C₂×C₄×D₄₇	—	2	1	no	—
129	C₂×C₄×D₄₇	—	2	1	no	—
130	C₂×C₄×D₄₇	—	2	1	no	—
131	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
132	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	—	2	2	no	—
137	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₄₇	#41	1	1	yes	characteristic
144	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₂²⋊Dic₄₇	—	2	1	no	—
146	C₂²⋊Dic₄₇	—	2	1	no	—
147	(C₂×D₄₇)⋊C₄	—	2	1	no	—
148	(C₂×D₄₇)⋊C₄	—	2	1	no	—
149	(C₂×D₄₇)⋊C₄	—	2	1	no	—
150	(C₂×D₄₇)⋊C₄	—	2	1	no	—
151	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
155	Dic₄₇⋊C₄	—	2	1	no	—
156	Dic₄₇⋊C₄	—	2	1	no	—
157	Dic₄₇⋊C₄	—	2	1	no	—
158	Dic₄₇⋊C₄	—	2	1	no	—
159	C₄×Dic₄₇	—	2	1	no	—
160	C₄×Dic₄₇	—	2	1	no	—
161	C₄×Dic₄₇	—	2	1	no	—
162	C₄×Dic₄₇	—	2	1	no	—
163	C₄×Dic₄₇	—	2	1	no	—
164	C₄×Dic₄₇	—	2	1	no	—
165	C₂×C₄₇⋊C₈	—	2	4	no	—
166	C₂×C₄₇⋊C₈	—	2	2	no	—
167	C₂×C₄₇⋊C₈	—	4	2	no	—
168	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
169	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
170	Dic₁₈₈	—	2	2	no	—
171	D₃₇₆	—	2	2	no	—
172	#10625325	—	2	2	no	—
173	#10625325	—	2	2	no	—
174	#10625324	—	4	4	no	—
175	C₈×D₄₇	—	4	4	no	—
176	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
177	C₂²×D₄₇	—	2	1	no	—
178	C₂²×D₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
185	C₂×C₄×C₄₇	#131	1	2	yes	—
186	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂²⋊D₄₇	—	2	4	no	—
190	C₂²⋊D₄₇	—	4	2	no	—
191	C₂×Dic₄₇	—	2	1	no	—
192	C₂×Dic₄₇	—	2	1	no	—
193	C₂×Dic₄₇	—	2	1	no	—
194	C₂×Dic₄₇	—	2	1	no	—
195	C₂×Dic₄₇	—	2	1	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	D₁₈₈	—	2	1	no	—
198	D₁₈₈	—	2	1	no	—
199	D₁₈₈	—	2	1	no	—
200	D₁₈₈	C₂×M₁₆	1	2	yes	—
201	C₄×D₄₇	—	2	4	no	—
202	C₄×D₄₇	—	4	2	no	—
203	C₄×D₄₇	—	4	2	no	—
204	C₄×D₄₇	—	4	2	no	—
205	C₄×D₄₇	—	4	2	no	—
206	C₄×D₄₇	—	4	2	no	—
207	Dic₉₄	—	2	1	no	—
208	Dic₉₄	—	2	1	no	—
209	Dic₉₄	—	2	1	no	—
210	Dic₉₄	C₂×M₁₆	1	2	yes	—
211	C₈×C₄₇	—	2	1	no	—
212	C₈×C₄₇	—	2	1	no	—
213	C₈×C₄₇	—	2	1	no	—
214	C₈×C₄₇	—	2	1	no	—
215	C₈×C₄₇	—	4	2	no	—
216	C₈×C₄₇	—	4	2	no	—
217	C₄₇⋊C₈	—	2	2	no	—
218	C₄₇⋊C₈	—	4	2	no	—
219	C₄₇⋊C₈	#135	1	4	yes	complemented
220	#17863	—	47	1	no	maximal, Sylow
221	C₂²×C₄₇	—	2	1	no	—
222	C₂²×C₄₇	—	2	1	no	—
223	C₂²×C₄₇	#435	1	2	yes	—
224	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂×D₄₇	—	2	2	no	—
226	C₂×D₄₇	—	4	1	no	—
227	C₂×D₄₇	—	4	1	no	—
228	C₂×D₄₇	—	4	1	no	—
229	C₂×D₄₇	—	4	1	no	—
230	C₂×D₄₇	—	4	1	no	—
231	C₄×C₄₇	—	2	1	no	—
232	C₄×C₄₇	—	2	1	no	—
233	C₄×C₄₇	#435	1	2	yes	—
234	C₄×C₄₇	#444	1	2	yes	—
235	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
236	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
237	C₄×C₄₇	C₂×#135	1	2	yes	—
238	Dic₄₇	—	2	2	no	—
239	Dic₄₇	—	4	1	no	—
240	Dic₄₇	—	4	1	no	—
241	Dic₄₇	—	4	1	no	—
242	Dic₄₇	—	4	1	no	—
243	Dic₄₇	—	4	1	no	—
244	#2965	—	47	1	no	—
245	C₈×#41	—	47	1	no	—
246	C₄×#135	—	47	1	no	—
247	#1584	—	47	2	no	—
248	#1583	—	47	2	no	—
249	#1582	—	47	2	no	—
250	#1581	—	47	2	no	—
251	#1564	D₄₇	1	1	yes	characteristic, complemented
252	#1476	—	47	1	no	—
253	#1476	—	47	1	no	—
254	C₂×#322	—	47	1	no	—
255	C₂×C₄₇	—	2	2	no	—
256	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
257	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
258	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
259	D₄₇	—	4	2	no	—
260	D₄₇	—	8	1	no	—
261	C₂×#135	—	47	1	no	—
262	C₄×#41	—	47	1	no	—
263	C₄×#41	—	47	1	no	—
264	#446	—	47	2	no	—
265	C₈×Q₈	—	47	2	no	—
266	C₄×Q₁₆	—	47	1	no	—
267	C₄×Q₁₆	—	47	1	no	—
268	C₄×SD₁₆	—	47	1	no	—
269	C₄×SD₁₆	—	47	1	no	—
270	C₄×SD₁₆	—	47	1	no	—
271	C₄×SD₁₆	—	47	1	no	—
272	C₄×D₈	—	47	1	no	—
273	C₄×D₈	—	47	1	no	—
274	#436	—	47	2	no	—
275	#435	—	94	2	no	—
276	C₈×D₄	—	47	2	no	—
277	C₈×D₄	—	94	2	no	—
278	#431	—	94	1	no	—
279	#431	—	94	1	no	—
280	#431	C₂×D₄₇	1	1	yes	characteristic
281	#431	C₂×D₄₇	1	1	yes	characteristic
282	#427	—	47	1	no	—
283	#416	—	47	1	no	—
284	#416	—	47	1	no	—
285	C₄×M₁₆	—	94	1	no	—
286	C₂×C₄×C₈	—	47	1	no	—
287	C₂×C₄×C₈	—	47	1	no	—
288	C₂×C₄×C₈	—	94	1	no	—
289	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
290	#335	C₂×D₄₇	1	2	yes	—
291	#334	C₂×D₄₇	1	2	yes	—
292	Q₈⋊C₈	—	47	2	no	—
293	Q₈⋊C₈	—	47	2	no	—
294	D₄⋊C₈	—	47	2	no	—
295	D₄⋊C₈	—	47	2	no	—
296	#322	—	47	2	no	—
297	#322	—	47	2	no	—
298	C₄₇	#17863	1	1	yes	characteristic, complemented, Sylow
299	C₂×#41	—	47	1	no	—
300	C₂×#41	—	47	1	no	—
301	#135	—	94	4	no	—
302	C₂×Q₁₆	—	47	1	no	—
303	C₂×SD₁₆	—	47	1	no	—
304	C₂×SD₁₆	—	47	1	no	—
305	C₂×D₈	—	47	1	no	—
306	C₂×M₁₆	—	94	2	no	—
307	C₂²×C₈	—	47	2	no	—
308	C₂²×C₈	—	94	2	no	—
309	C₂²×C₈	—	94	1	no	—
310	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
311	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
312	C₄×Q₈	—	47	1	no	—
313	C₄×Q₈	—	47	1	no	—
314	C₄×Q₈	—	47	1	no	—
315	C₄×Q₈	—	47	1	no	—
316	C₄×D₄	—	47	1	no	—
317	C₄×D₄	—	47	1	no	—
318	C₄×D₄	—	47	1	no	—
319	C₄×D₄	—	47	1	no	—
320	C₄×D₄	—	94	1	no	—
321	C₄×D₄	—	94	1	no	—
322	C₄×D₄	—	94	1	no	—
323	C₄×D₄	—	94	1	no	—
324	#117	—	47	1	no	—
325	#117	—	47	1	no	—
326	#117	—	94	1	no	—
327	#117	—	94	1	no	—
328	C₂×C₄²	—	94	1	no	—
329	C₂×C₄²	—	94	1	no	—
330	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
331	#107	—	47	1	no	—
332	#107	—	47	1	no	—
333	#106	—	47	1	no	—
334	#106	—	47	1	no	—
335	C₄⋊C₈	—	94	2	no	—
336	C₄⋊C₈	—	94	2	no	—
337	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
338	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
339	#103	—	47	1	no	—
340	#103	—	47	1	no	—
341	#103	—	47	1	no	—
342	#103	—	47	1	no	—
343	#102	—	47	1	no	—
344	#102	—	47	1	no	—
345	#102	—	47	1	no	—
346	#102	—	47	1	no	—
347	C₂²⋊C₈	—	2	1	no	—
348	C₂²⋊C₈	—	2	1	no	—
349	C₂²⋊C₈	—	94	2	no	—
350	C₂²⋊C₈	—	94	2	no	—
351	#97	—	94	2	no	—
352	C₄×C₈	—	2	1	no	—
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	—	47	1	no	—
355	C₄×C₈	—	47	1	no	—
356	C₄×C₈	—	47	2	no	—
357	C₄×C₈	—	47	2	no	—
358	C₄×C₈	—	94	2	no	—
359	C₄×C₈	—	94	1	no	—
360	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
361	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
362	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
363	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
364	#41	—	47	4	no	—
365	#41	—	94	2	no	—
366	#41	—	94	2	no	—
367	#41	—	94	2	no	—
368	C₂×Q₈	—	47	1	no	—
369	C₂×Q₈	—	47	1	no	—
370	C₂×D₄	—	47	1	no	—
371	C₂×D₄	—	47	1	no	—
372	C₂×D₄	—	94	1	no	—
373	C₂×D₄	—	94	1	no	—
374	C₂²×C₄	—	94	1	no	—
375	C₂²×C₄	—	94	1	no	—
376	C₂²×C₄	—	94	1	no	—
377	C₂²×C₄	—	94	1	no	—
378	C₂²×C₄	—	94	1	no	—
379	C₂²×C₄	—	94	1	no	—
380	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
381	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
382	C₂²×C₄	#10625354	1	1	yes	characteristic
383	Q₁₆	—	94	2	no	—
384	SD₁₆	—	94	2	no	—
385	SD₁₆	—	94	2	no	—
386	D₈	—	94	2	no	—
387	M₁₆	—	188	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	47	2	no	—
393	C₂×C₈	—	47	2	no	—
394	C₂×C₈	—	94	4	no	—
395	C₂×C₈	—	94	2	no	—
396	C₂×C₈	—	188	4	no	—
397	C₂×C₈	—	188	2	no	—
398	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
399	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
400	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
401	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
402	C₄⋊C₄	—	47	1	no	—
403	C₄⋊C₄	—	47	1	no	—
404	C₄⋊C₄	—	47	1	no	—
405	C₄⋊C₄	—	47	1	no	—
406	C₄⋊C₄	—	94	1	no	—
407	C₄⋊C₄	—	94	1	no	—
408	C₄⋊C₄	—	94	1	no	—
409	C₄⋊C₄	—	94	1	no	—
410	C₂²⋊C₄	—	94	1	no	—
411	C₂²⋊C₄	—	94	1	no	—
412	C₂²⋊C₄	—	94	1	no	—
413	C₂²⋊C₄	—	94	1	no	—
414	C₂²⋊C₄	—	94	1	no	—
415	C₂²⋊C₄	—	94	1	no	—
416	C₄²	—	94	1	no	—
417	C₄²	—	94	1	no	—
418	C₄²	—	94	1	no	—
419	C₄²	—	94	1	no	—
420	C₄²	—	94	1	no	—
421	C₄²	—	94	1	no	—
422	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
423	C₄²	D₄×D₄₇	1	1	yes	characteristic
424	C₄²	#10625354	1	1	yes	characteristic
425	C₄²	C₂³×D₄₇	1	1	yes	characteristic
426	C₂³	—	94	1	no	—
427	C₂³	—	94	1	no	—
428	C₂³	#13093986	1	1	yes	characteristic
429	Q₈	—	47	2	no	—
430	Q₈	—	94	1	no	—
431	Q₈	—	94	1	no	—
432	Q₈	—	94	1	no	—
433	D₄	—	47	2	no	—
434	D₄	—	94	4	no	—
435	D₄	—	94	1	no	—
436	D₄	—	94	1	no	—
437	D₄	—	94	1	no	—
438	D₄	—	188	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	94	1	no	—
442	C₂×C₄	—	94	4	no	—
443	C₂×C₄	—	94	1	no	—
444	C₂×C₄	—	94	1	no	—
445	C₂×C₄	—	94	1	no	—
446	C₂×C₄	—	94	1	no	—
447	C₂×C₄	—	94	1	no	—
448	C₂×C₄	—	188	2	no	—
449	C₂×C₄	—	188	2	no	—
450	C₂×C₄	—	188	2	no	—
451	C₂×C₄	—	188	2	no	—
452	C₂×C₄	—	188	2	no	—
453	C₂×C₄	#13093986	1	1	yes	characteristic
454	C₂×C₄	#13093986	1	1	yes	characteristic
455	C₂×C₄	#13093986	1	1	yes	characteristic
456	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
457	C₂×C₄	#13094030	1	2	yes	—
458	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
459	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
460	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	1	no	—
464	C₈	—	2	1	no	—
465	C₈	—	4	2	no	—
466	C₈	—	4	2	no	—
467	C₈	—	47	4	no	—
468	C₈	—	94	2	no	—
469	C₈	—	188	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	94	2	no	—
473	C₂²	—	188	1	no	—
474	C₂²	—	188	1	no	—
475	C₂²	—	188	1	no	—
476	C₂²	—	188	1	no	—
477	C₂²	—	188	1	no	—
478	C₂²	#15689193	1	2	yes	—
479	C₂²	C₂×#13093986	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	94	2	no	—
483	C₄	—	188	1	no	—
484	C₄	—	188	1	no	—
485	C₄	—	188	1	no	—
486	C₄	—	188	1	no	—
487	C₄	—	188	1	no	—
488	C₄	#15689193	1	2	yes	—
489	C₄	#15689244	1	2	yes	—
490	C₄	C₂×M₁₆×D₄₇	1	1	yes	characteristic
491	C₄	C₂×#13094030	1	1	yes	characteristic
492	C₄	#135×D₄₇	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	376	1	no	—
495	C₂	—	188	2	no	—
496	C₂	C₂×#15689193	1	1	yes	characteristic
497	C₂	#20252159	1	1	yes	characteristic
498	C₂	C₂×#15689244	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1564	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094046	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1564	D₄₇
hypocenter	C₄₇	#17863
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
1. #20252349	C₂	semidirect
2. #20252344	C₂	semidirect
4. #20242237	C₂	semidirect
5. #20242230	C₂	semidirect
6. #20242223	C₂	semidirect
7. #20242216	C₂	semidirect
8. #20241768	C₂	semidirect
9. #20241768	C₂	semidirect
10. C₂×#15688845	C₂	semidirect
11. C₄₇×#1564	C₂	semidirect
122. #10625350	M₁₆	semidirect
219. C₄₇⋊C₈	#135	semidirect
251. #1564	D₄₇	semidirect
298. C₄₇	#17863	semidirect

Maximal subgroups

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

subgroup	index
#20252349	2
#20252344	2
C₄×#13094046	2
#20242237	2
#20242230	2
#20242223	2
#20242216	2
#20241768	2
C₂×#15688845	2
C₄₇×#1564	2
#17863	47