Subgroups — #26223111

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689240	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252092	C₂	1	2	yes	maximal, complemented
3	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244282	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244142	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244094	C₂	1	2	yes	maximal, complemented
7	#20243832	C₂	1	2	yes	maximal, complemented
8	#20243430	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243269	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243235	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3054	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	2	yes	—
13	C₂²×#10625329	C₂²	1	1	yes	characteristic
14	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
15	#15689240	—	2	4	no	—
16	#15689201	—	2	4	no	—
17	#15689195	—	2	4	no	—
18	C₂×#13093960	C₂²	1	1	yes	characteristic
19	C₂×#13093960	C₂²	1	1	yes	characteristic
20	#15689150	C₂²	1	2	yes	—
21	C₂×#13093951	C₂²	1	2	yes	—
22	C₂×#13093951	C₂²	1	2	yes	—
23	#15689090	C₂²	1	2	yes	—
24	#15689087	C₂²	1	2	yes	—
25	#15689079	C₂²	1	2	yes	—
26	M₁₆×Dic₄₇	—	2	4	no	—
27	C₂×#13093934	C₂²	1	1	yes	characteristic
28	C₂×#13093934	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688888	C₂²	1	2	yes	—
32	#15688882	C₂²	1	2	yes	—
33	#15688882	C₂²	1	2	yes	—
34	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#525	C₂²	1	2	yes	—
37	C₄₇×#470	C₄	1	2	yes	complemented
38	C₄₇×#469	C₄	1	2	yes	complemented
39	C₄₇×#468	C₄	1	4	yes	complemented
40	C₄₇×#427	C₂²	1	1	yes	characteristic
41	C₄₇×#416	C₂²	1	2	yes	—
42	C₂³×Dic₄₇	—	2	1	no	—
43	#13094031	—	2	4	no	—
44	#13094031	—	2	4	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂×#10625329	—	2	2	no	—
47	C₂×#10625329	—	2	2	no	—
48	C₂×#10625329	D₄	1	2	yes	—
49	C₂×#10625329	D₄	1	2	yes	—
50	C₂×#10625329	C₂³	1	2	yes	—
51	C₂×#10625329	C₂³	1	2	yes	—
52	C₂²×C₄₇⋊C₈	—	2	2	no	—
53	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	—	2	1	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	—	2	2	no	—
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	#13093960	—	2	2	no	—
61	#13093960	—	2	2	no	—
62	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
63	#13093951	—	2	4	no	—
64	#13093951	—	2	4	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
67	#13093935	—	2	2	no	—
68	#13093934	—	2	2	no	—
69	#13093934	—	2	2	no	—
70	C₄×C₄₇⋊C₈	—	2	2	no	—
71	C₈×Dic₄₇	—	2	2	no	—
72	C₈×Dic₄₇	D₄	1	4	yes	complemented
73	C₂×#41×C₄₇	C₂³	1	2	yes	—
74	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
75	#135×C₄₇	—	2	2	no	—
76	#135×C₄₇	—	2	2	no	—
77	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
79	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
80	C₂×M₁₆×C₄₇	—	2	2	no	—
81	C₂×M₁₆×C₄₇	—	2	2	no	—
82	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
83	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	#123×C₄₇	—	2	2	no	—
87	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
88	#121×C₄₇	C₂×C₄	1	4	yes	—
89	#120×C₄₇	—	2	2	no	—
90	C₄×D₄×C₄₇	—	2	4	no	—
91	#117×C₄₇	C₂³	1	2	yes	—
92	#107×C₄₇	C₂×C₄	1	2	yes	complemented
93	#106×C₄₇	C₂×C₄	1	2	yes	complemented
94	#103×C₄₇	C₂×C₄	1	4	yes	complemented
95	#102×C₄₇	C₂×C₄	1	4	yes	complemented
96	C₂⁴×C₄₇	#41	1	1	yes	characteristic
97	#41×C₄₇	—	2	2	no	—
98	#41×C₄₇	—	2	2	no	—
99	#41×C₄₇	—	2	2	no	—
100	#41×C₄₇	—	2	2	no	—
101	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	4	no	—
104	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₄₇	—	2	1	no	—
115	C₂²×Dic₄₇	—	2	4	no	—
116	C₂²×Dic₄₇	—	2	1	no	—
117	C₂²×Dic₄₇	—	4	4	no	—
118	Q₁₆×C₄₇	—	2	2	no	—
119	SD₁₆×C₄₇	—	2	4	no	—
120	D₈×C₄₇	—	2	2	no	—
121	M₁₆×C₄₇	—	2	4	no	—
122	M₁₆×C₄₇	—	2	4	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₄₇	#41	1	2	yes	—
130	C₄⋊C₄×C₄₇	—	2	4	no	—
131	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
132	C₂²⋊C₄×C₄₇	—	2	4	no	—
133	C₂²⋊C₄×C₄₇	—	2	2	no	—
134	C₂²⋊C₄×C₄₇	—	2	4	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄×Dic₄₇	—	2	4	no	—
137	C₄×Dic₄₇	—	2	1	no	—
138	C₄×Dic₄₇	—	2	1	no	—
139	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
140	C₄×Dic₄₇	#41	1	2	yes	—
141	#10625329	—	2	4	no	—
142	#10625329	—	2	4	no	—
143	#10625329	—	2	2	no	—
144	#10625329	—	2	2	no	—
145	#10625329	—	2	2	no	—
146	#10625329	—	2	2	no	—
147	#10625329	—	4	4	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	4	4	no	—
153	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
155	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄₇⋊C₈	#41	1	2	yes	—
158	C₂³×C₄₇	—	2	1	no	—
159	C₂³×C₄₇	—	2	1	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	C₄×D₄	1	2	yes	—
163	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
164	Q₈×C₄₇	—	2	2	no	—
165	Q₈×C₄₇	—	2	2	no	—
166	D₄×C₄₇	—	2	2	no	—
167	D₄×C₄₇	—	2	2	no	—
168	D₄×C₄₇	—	4	2	no	—
169	D₄×C₄₇	—	4	2	no	—
170	D₄×C₄₇	—	8	4	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	4	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₄₇	—	2	4	no	—
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	2	2	no	—
191	C₂×Dic₄₇	—	4	8	no	—
192	C₂×Dic₄₇	—	4	2	no	—
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	C₄×D₄	1	2	yes	—
195	C₈×C₄₇	C₄×D₄	1	2	yes	—
196	C₄₇⋊C₈	—	2	2	no	—
197	C₄₇⋊C₈	—	4	2	no	—
198	C₄₇⋊C₈	—	4	2	no	—
199	C₄₇⋊C₈	#121	1	2	yes	—
200	C₄₇⋊C₈	#121	1	2	yes	—
201	#21549	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	2	4	no	—
204	C₂²×C₄₇	—	2	2	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	—	4	2	no	—
207	C₂²×C₄₇	—	4	4	no	—
208	C₂²×C₄₇	—	4	2	no	—
209	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂²×C₄₇	#525	1	1	yes	characteristic
211	C₂²×C₄₇	#529	1	1	yes	characteristic
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	4	4	no	—
214	C₄×C₄₇	—	4	2	no	—
215	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
217	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
218	C₄×C₄₇	#532	1	1	yes	characteristic
219	Dic₄₇	—	2	4	no	—
220	Dic₄₇	—	4	2	no	—
221	#3054	D₄₇	1	1	yes	characteristic
222	C₂×#443	—	47	1	no	—
223	#2930	—	47	2	no	—
224	C₂×C₄×M₁₆	—	47	1	no	—
225	#1975	—	47	1	no	—
226	#1946	—	47	1	no	—
227	#1937	—	47	2	no	—
228	#1896	—	47	2	no	—
229	#1811	—	47	1	no	—
230	#1772	—	47	1	no	—
231	#1765	—	47	2	no	—
232	C₂×C₄₇	—	2	1	no	—
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	—	4	2	no	—
235	C₂×C₄₇	—	8	2	no	—
236	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
237	C₂×C₄₇	#2956	1	2	yes	—
238	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
239	C₂×#131	—	47	2	no	—
240	C₂²×M₁₆	—	47	1	no	—
241	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
242	#525	C₂×D₄₇	1	2	yes	—
243	C₂²×C₄²	—	47	1	no	—
244	#470	Dic₄₇	1	2	yes	complemented
245	#469	Dic₄₇	1	2	yes	complemented
246	#468	Dic₄₇	1	4	yes	complemented
247	#443	—	94	4	no	—
248	#436	—	94	4	no	—
249	#435	—	94	4	no	—
250	C₂×#108	—	47	1	no	—
251	C₂×#108	—	47	1	no	—
252	#427	C₂×D₄₇	1	1	yes	characteristic
253	#424	—	47	2	no	—
254	C₂×#104	—	47	2	no	—
255	C₂×#104	—	47	2	no	—
256	#416	C₂×D₄₇	1	2	yes	—
257	#408	—	47	2	no	—
258	#407	—	47	2	no	—
259	#405	—	47	2	no	—
260	C₄×M₁₆	—	94	4	no	—
261	C₂×#97	—	47	1	no	—
262	C₂×#97	—	47	1	no	—
263	C₂×C₄×C₈	—	47	1	no	—
264	C₂×C₄×C₈	—	47	1	no	—
265	#341	—	47	2	no	—
266	#339	—	47	2	no	—
267	#339	—	47	2	no	—
268	C₄₇	#21549	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	C₂²×D₄₇	1	2	yes	—
270	C₂³×C₄	—	94	1	no	—
271	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
272	#135	—	2	2	no	—
273	#135	—	2	2	no	—
274	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic, complemented
275	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	complemented
276	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
277	#131	—	94	4	no	—
278	#131	—	94	4	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	47	2	no	—
282	C₂×M₁₆	—	47	2	no	—
283	C₂×M₁₆	—	47	2	no	—
284	C₂×M₁₆	—	47	2	no	—
285	C₂×M₁₆	—	94	2	no	—
286	C₂×M₁₆	—	94	2	no	—
287	C₂×M₁₆	—	94	2	no	—
288	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
289	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
290	C₂²×C₈	—	47	1	no	—
291	C₂²×C₈	—	47	1	no	—
292	C₂²×C₈	—	94	2	no	—
293	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
294	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
295	#123	—	2	2	no	—
296	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
297	#121	C₂×Dic₄₇	1	4	yes	—
298	#120	—	2	2	no	—
299	C₄×D₄	—	2	4	no	—
300	#117	C₂²×D₄₇	1	2	yes	—
301	C₂×C₄²	—	47	1	no	—
302	C₂×C₄²	—	47	1	no	—
303	C₂×C₄²	—	94	2	no	—
304	C₂×C₄²	—	94	2	no	—
305	C₂×C₄²	—	94	1	no	—
306	#108	—	94	2	no	—
307	#108	—	94	2	no	—
308	#107	C₂×Dic₄₇	1	2	yes	complemented
309	#106	C₂×Dic₄₇	1	2	yes	complemented
310	C₄⋊C₈	—	94	4	no	—
311	#104	—	94	4	no	—
312	#104	—	94	4	no	—
313	#103	C₂×Dic₄₇	1	4	yes	complemented
314	#102	C₂×Dic₄₇	1	4	yes	complemented
315	C₂²⋊C₈	—	94	4	no	—
316	C₂²⋊C₈	—	94	4	no	—
317	#97	—	94	2	no	—
318	#97	—	94	2	no	—
319	#97	—	94	2	no	—
320	C₄×C₈	—	47	4	no	—
321	C₄×C₈	—	94	2	no	—
322	C₄×C₈	—	94	2	no	—
323	C₂⁴	#10625352	1	1	yes	characteristic
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	94	1	no	—
338	C₂²×C₄	—	94	4	no	—
339	C₂²×C₄	—	94	1	no	—
340	C₂²×C₄	—	188	4	no	—
341	C₂²×C₄	D₄×D₄₇	1	2	yes	—
342	C₂²×C₄	#10625352	1	1	yes	characteristic
343	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
344	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
345	Q₁₆	—	2	2	no	—
346	SD₁₆	—	2	4	no	—
347	D₈	—	2	2	no	—
348	M₁₆	—	2	4	no	—
349	M₁₆	—	2	4	no	—
350	M₁₆	—	94	4	no	—
351	M₁₆	—	94	4	no	—
352	M₁₆	—	94	2	no	—
353	M₁₆	—	94	2	no	—
354	M₁₆	—	94	2	no	—
355	M₁₆	—	94	2	no	—
356	M₁₆	—	188	4	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	47	2	no	—
360	C₂×C₈	—	47	1	no	—
361	C₂×C₈	—	47	1	no	—
362	C₂×C₈	—	47	2	no	—
363	C₂×C₈	—	47	2	no	—
364	C₂×C₈	—	94	1	no	—
365	C₂×C₈	—	94	1	no	—
366	C₂×C₈	—	94	2	no	—
367	C₂×C₈	—	94	2	no	—
368	C₂×C₈	—	188	4	no	—
369	C₂×C₈	D₄×D₄₇	1	2	yes	—
370	C₂×C₈	#10625352	1	2	yes	—
371	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
372	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
373	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	47	2	no	—
381	C₄²	—	47	2	no	—
382	C₄²	—	94	4	no	—
383	C₄²	—	94	1	no	—
384	C₄²	—	94	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	D₄×Dic₄₇	1	2	yes	—
390	C₂³	C₂×#10625352	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	8	4	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	94	4	no	—
409	C₂×C₄	—	94	2	no	—
410	C₂×C₄	—	94	2	no	—
411	C₂×C₄	—	188	8	no	—
412	C₂×C₄	—	188	2	no	—
413	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
414	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
417	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
418	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	47	2	no	—
422	C₈	—	47	2	no	—
423	C₈	—	94	2	no	—
424	C₈	—	188	2	no	—
425	C₈	—	188	2	no	—
426	C₈	D₄×Dic₄₇	1	2	yes	—
427	C₈	D₄×Dic₄₇	1	2	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
436	C₂²	#15689633	1	1	yes	characteristic
437	C₂²	#15689654	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	2	no	—
441	C₄	—	94	4	no	—
442	C₄	—	188	2	no	—
443	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
444	C₄	#41×Dic₄₇	1	1	yes	characteristic
445	C₄	#121×D₄₇	1	1	yes	characteristic
446	C₄	#15689668	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	4	2	no	—
450	C₂	—	8	2	no	—
451	C₂	#121×Dic₄₇	1	1	yes	characteristic
452	C₂	#20252298	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3054	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3054	D₄₇
hypocenter	C₄₇	#21549
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3054

Complements

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

N	H ≅ G/N	type
1. C₂×#15689240	C₂	semidirect
2. #20252092	C₂	semidirect
3. C₂×M₁₆×Dic₄₇	C₂	semidirect
4. #20244282	C₂	semidirect
5. #20244142	C₂	semidirect
6. #20244094	C₂	semidirect
7. #20243832	C₂	semidirect
8. #20243430	C₂	semidirect
9. #20243269	C₂	semidirect
10. #20243235	C₂	semidirect
37. C₄₇×#470	C₄	semidirect
38. C₄₇×#469	C₄	semidirect
39. C₄₇×#468	C₄	semidirect
72. C₈×Dic₄₇	D₄	semidirect
77. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
78. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
79. C₂×D₈×C₄₇	C₂×C₄	semidirect
92. #107×C₄₇	C₂×C₄	semidirect
93. #106×C₄₇	C₂×C₄	semidirect
94. #103×C₄₇	C₂×C₄	semidirect
95. #102×C₄₇	C₂×C₄	semidirect
244. #470	Dic₄₇	semidirect
245. #469	Dic₄₇	semidirect
246. #468	Dic₄₇	semidirect
268. C₄₇	#21549	semidirect
274. C₂×Q₁₆	C₂×Dic₄₇	semidirect
275. C₂×SD₁₆	C₂×Dic₄₇	semidirect
276. C₂×D₈	C₂×Dic₄₇	semidirect
308. #107	C₂×Dic₄₇	semidirect
309. #106	C₂×Dic₄₇	semidirect
313. #103	C₂×Dic₄₇	semidirect
314. #102	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689240	2
#20252092	2
C₂×M₁₆×Dic₄₇	2
#20244282	2
#20244142	2
#20244094	2
#20243832	2
#20243430	2
#20243269	2
#20243235	2
C₄₇×#3054	2
#21549	47