Subgroups — #26220495

Order 12032.

974 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#20245850	C₂	1	2	yes	maximal, complemented
3	#20244255	C₂	1	1	yes	maximal, characteristic
4	#20244121	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244119	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244074	C₂	1	2	yes	maximal, complemented
7	#20244068	C₂	1	2	yes	maximal, complemented
8	#107×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#102×Dic₄₇	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1970	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
13	C₂×#13093980	—	2	2	no	—
14	D₈×Dic₄₇	C₄	1	8	yes	complemented
15	C₂×#13093958	C₂²	1	1	yes	characteristic
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093945	C₂²	1	2	yes	—
18	C₂×#13093945	C₂²	1	2	yes	—
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	#15689026	C₂²	1	2	yes	—
25	#15689021	C₂²	1	2	yes	—
26	#15689019	C₂²	1	2	yes	—
27	#15689017	—	2	2	no	—
28	#15689011	—	2	2	no	—
29	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
30	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
31	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688886	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#102×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#390	C₂²	1	2	yes	—
40	C₂³×Dic₄₇	—	2	2	no	—
41	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	D₄×Dic₄₇	—	2	4	no	—
44	D₄×Dic₄₇	C₂×C₄	1	8	yes	—
45	#13093980	—	4	8	no	—
46	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
48	C₂×Dic₄₇⋊C₄	—	2	2	no	—
49	C₂×Dic₄₇⋊C₄	—	2	2	no	—
50	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
51	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
52	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	—	2	2	no	—
54	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	#13093958	—	2	2	no	—
61	#13093958	C₂×C₄	1	4	yes	—
62	#13093945	—	2	4	no	—
63	#13093945	C₂×C₄	1	8	yes	—
64	C₄×C₄₇⋊C₈	—	2	2	no	—
65	C₈×Dic₄₇	—	2	2	no	—
66	C₈×Dic₄₇	—	2	2	no	—
67	C₈×Dic₄₇	—	2	2	no	—
68	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
73	C₂×D₈×C₄₇	—	2	2	no	—
74	C₂×D₈×C₄₇	—	2	2	no	—
75	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	#107×C₄₇	—	2	2	no	—
83	#102×C₄₇	—	2	4	no	—
84	C₄×C₈×C₄₇	—	2	2	no	—
85	C₂⁴×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₂²×Dic₄₇	—	2	8	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	—	4	4	no	—
100	C₂²×Dic₄₇	—	4	4	no	—
101	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
105	D₈×C₄₇	—	2	8	no	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	—	2	1	no	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₄₇	#41	1	2	yes	—
110	C₂×C₈×C₄₇	#41	1	2	yes	—
111	C₂×C₈×C₄₇	#41	1	2	yes	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₂²⋊C₄×C₄₇	—	4	4	no	—
115	C₂²⋊C₄×C₄₇	—	4	4	no	—
116	C₄²×C₄₇	—	2	1	no	—
117	C₄²×C₄₇	—	2	1	no	—
118	C₂²⋊Dic₄₇	—	2	8	no	—
119	C₂²⋊Dic₄₇	—	4	4	no	—
120	C₂²⋊Dic₄₇	—	4	4	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
125	Dic₄₇⋊C₄	—	4	4	no	—
126	Dic₄₇⋊C₄	—	4	4	no	—
127	C₄×Dic₄₇	—	2	2	no	—
128	C₄×Dic₄₇	—	2	1	no	—
129	C₄×Dic₄₇	—	2	1	no	—
130	C₄×Dic₄₇	—	2	2	no	—
131	C₄×Dic₄₇	—	2	2	no	—
132	C₄×Dic₄₇	—	4	4	no	—
133	C₄×Dic₄₇	D₈	1	4	yes	complemented
134	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
135	C₄×Dic₄₇	#41	1	2	yes	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₄₇⋊C₈	#41	1	2	yes	—
142	C₂³×C₄₇	—	2	4	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	—	4	2	no	—
145	C₂³×C₄₇	—	4	2	no	—
146	C₂³×C₄₇	—	4	2	no	—
147	C₂³×C₄₇	—	4	2	no	—
148	C₂³×C₄₇	—	4	2	no	—
149	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	D₄×C₄₇	—	2	4	no	—
151	D₄×C₄₇	—	2	4	no	—
152	D₄×C₄₇	—	4	2	no	—
153	D₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
162	C₂×C₄×C₄₇	#135	1	2	yes	—
163	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₂×Dic₄₇	—	2	1	no	—
170	C₂×Dic₄₇	—	2	1	no	—
171	C₂×Dic₄₇	—	2	1	no	—
172	C₂×Dic₄₇	—	2	1	no	—
173	C₂×Dic₄₇	—	2	1	no	—
174	C₂×Dic₄₇	—	2	1	no	—
175	C₂×Dic₄₇	—	2	4	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	16	no	—
179	C₂×Dic₄₇	—	4	2	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
183	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
184	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
185	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
186	C₂×Dic₄₇	#135	1	2	yes	—
187	C₂×Dic₄₇	#135	1	2	yes	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	#117	1	4	yes	complemented
190	C₄₇⋊C₈	—	2	2	no	—
191	C₄₇⋊C₈	—	2	2	no	—
192	#21275	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	—	4	4	no	—
194	C₂²×C₄₇	—	4	4	no	—
195	C₂²×C₄₇	—	4	4	no	—
196	C₂²×C₄₇	—	8	2	no	—
197	C₂²×C₄₇	—	8	2	no	—
198	C₂²×C₄₇	—	8	2	no	—
199	C₂²×C₄₇	—	8	2	no	—
200	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂²×C₄₇	#532	1	1	yes	characteristic
202	C₂²×C₄₇	#532	1	1	yes	characteristic
203	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	8	2	no	—
210	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
211	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
212	C₄×C₄₇	#529	1	1	yes	characteristic
213	C₄×C₄₇	#529	1	1	yes	characteristic
214	Dic₄₇	—	2	2	no	—
215	Dic₄₇	—	2	2	no	—
216	Dic₄₇	—	2	2	no	—
217	Dic₄₇	—	4	4	no	—
218	Dic₄₇	—	8	2	no	—
219	Dic₄₇	C₄×D₈	1	4	yes	—
220	C₂×C₄×D₈	—	47	1	no	—
221	#2293	—	47	2	no	—
222	#1970	—	47	1	no	—
223	#1970	D₄₇	1	1	yes	characteristic
224	#1942	—	47	1	no	—
225	#1942	—	47	1	no	—
226	#1934	—	47	2	no	—
227	#1934	—	47	2	no	—
228	C₄×#107	—	47	1	no	—
229	C₄×#102	—	47	2	no	—
230	C₄²×C₈	—	47	1	no	—
231	C₂×C₄₇	—	8	4	no	—
232	C₂×C₄₇	#2293	1	1	yes	characteristic
233	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
234	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
235	C₂×C₄₇	#3168	1	1	yes	characteristic
236	C₂×C₄₇	#3168	1	1	yes	characteristic
237	C₂×C₄₇	#3169	1	1	yes	characteristic
238	C₂×C₄₇	#3169	1	1	yes	characteristic
239	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
240	C₂×C₄×D₄	—	47	2	no	—
241	C₂×#117	—	94	2	no	—
242	C₄×D₈	—	47	8	no	—
243	C₂×#107	—	47	1	no	—
244	C₂×#107	—	47	1	no	—
245	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
246	C₂×#102	—	47	2	no	—
247	C₂×#102	—	47	2	no	—
248	C₂×#102	C₂×D₄₇	1	2	yes	—
249	C₂×C₄×C₈	—	47	1	no	—
250	C₂×C₄×C₈	—	47	1	no	—
251	C₂×C₄×C₈	—	47	1	no	—
252	C₂×C₄×C₈	—	47	1	no	—
253	C₂×C₄×C₈	—	47	1	no	—
254	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
255	#390	—	47	2	no	—
256	#390	C₂×D₄₇	1	2	yes	—
257	#389	—	47	2	no	—
258	#389	—	47	2	no	—
259	#388	—	94	2	no	—
260	#388	—	94	2	no	—
261	C₄×C₄⋊C₄	—	47	2	no	—
262	C₄×C₂²⋊C₄	—	94	2	no	—
263	C₄³	—	47	1	no	—
264	#340	—	47	2	no	—
265	#340	—	47	2	no	—
266	#340	—	47	2	no	—
267	C₄₇	#21275	1	1	yes	characteristic, complemented, Sylow
268	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
269	C₂³×C₄	—	94	2	no	—
270	C₂×D₈	—	2	2	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂×D₈	C₄×D₄₇	1	4	yes	—
273	C₂²×C₈	—	47	1	no	—
274	C₂²×C₈	—	47	1	no	—
275	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
276	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
277	C₄×D₄	—	47	8	no	—
278	C₄×D₄	—	94	4	no	—
279	#117	—	188	8	no	—
280	C₂×C₄⋊C₄	—	47	2	no	—
281	C₂×C₄⋊C₄	—	47	2	no	—
282	C₂×C₄⋊C₄	—	94	2	no	—
283	C₂×C₄⋊C₄	—	94	2	no	—
284	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	94	2	no	—
288	C₂×C₂²⋊C₄	—	94	2	no	—
289	C₂×C₂²⋊C₄	—	94	2	no	—
290	C₂×C₄²	—	47	1	no	—
291	C₂×C₄²	—	47	1	no	—
292	C₂×C₄²	—	47	1	no	—
293	C₂×C₄²	—	47	1	no	—
294	C₂×C₄²	—	47	1	no	—
295	C₂×C₄²	—	47	1	no	—
296	C₂×C₄²	—	94	2	no	—
297	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
298	#107	—	2	2	no	—
299	#107	—	47	4	no	—
300	#107	—	94	2	no	—
301	#102	—	2	4	no	—
302	#102	—	47	8	no	—
303	#102	—	94	4	no	—
304	C₄×C₈	—	2	2	no	—
305	C₄×C₈	—	47	4	no	—
306	C₄×C₈	—	94	2	no	—
307	C₄×C₈	—	94	2	no	—
308	C₄×C₈	—	94	2	no	—
309	C₄×C₈	—	94	2	no	—
310	#95	—	94	2	no	—
311	#95	—	94	2	no	—
312	#95	—	94	2	no	—
313	C₂⁴	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	C₂×C₄×D₄₇	1	4	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	47	1	no	—
322	C₂²×C₄	—	47	1	no	—
323	C₂²×C₄	—	47	1	no	—
324	C₂²×C₄	—	47	1	no	—
325	C₂²×C₄	—	94	8	no	—
326	C₂²×C₄	—	94	2	no	—
327	C₂²×C₄	—	94	2	no	—
328	C₂²×C₄	—	188	4	no	—
329	C₂²×C₄	—	188	4	no	—
330	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	D₈	—	2	8	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	47	2	no	—
337	C₂×C₈	—	47	2	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	—	94	1	no	—
340	C₂×C₈	—	94	1	no	—
341	C₂×C₈	—	94	1	no	—
342	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
343	C₂×C₈	#10625352	1	2	yes	—
344	C₂×C₈	#10625352	1	2	yes	—
345	C₂×C₈	#10625352	1	2	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	47	4	no	—
349	C₄⋊C₄	—	94	2	no	—
350	C₄⋊C₄	—	94	2	no	—
351	C₄⋊C₄	—	94	2	no	—
352	C₄⋊C₄	—	188	4	no	—
353	C₄⋊C₄	—	188	4	no	—
354	C₂²⋊C₄	—	4	4	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	94	8	no	—
357	C₂²⋊C₄	—	188	4	no	—
358	C₂²⋊C₄	—	188	4	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	47	4	no	—
362	C₄²	—	47	2	no	—
363	C₄²	—	47	2	no	—
364	C₄²	—	94	2	no	—
365	C₄²	—	94	2	no	—
366	C₄²	—	94	2	no	—
367	C₄²	—	94	1	no	—
368	C₄²	—	94	1	no	—
369	C₄²	—	188	4	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
378	D₄	—	2	4	no	—
379	D₄	—	2	4	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	47	2	no	—
390	C₂×C₄	—	47	2	no	—
391	C₂×C₄	—	47	2	no	—
392	C₂×C₄	—	47	2	no	—
393	C₂×C₄	—	47	2	no	—
394	C₂×C₄	—	47	2	no	—
395	C₂×C₄	—	94	1	no	—
396	C₂×C₄	—	94	1	no	—
397	C₂×C₄	—	94	1	no	—
398	C₂×C₄	—	94	1	no	—
399	C₂×C₄	—	94	1	no	—
400	C₂×C₄	—	94	1	no	—
401	C₂×C₄	—	94	4	no	—
402	C₂×C₄	—	188	16	no	—
403	C₂×C₄	—	188	2	no	—
404	C₂×C₄	—	188	2	no	—
405	C₂×C₄	—	188	2	no	—
406	C₂×C₄	—	188	2	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	D₈×D₄₇	1	2	yes	—
409	C₂×C₄	#13094043	1	2	yes	—
410	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
411	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
412	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
414	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
415	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	94	2	no	—
418	C₈	—	94	2	no	—
419	C₈	#13093980	1	4	yes	complemented
420	C₂²	—	4	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
428	C₂²	#15689668	1	1	yes	characteristic
429	C₂²	#15689671	1	1	yes	characteristic
430	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
431	C₂²	#135×D₄₇	1	1	yes	characteristic
432	C₂²	#135×D₄₇	1	1	yes	characteristic
433	C₂²	C₂×#13094043	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	8	2	no	—
437	C₄	—	47	4	no	—
438	C₄	—	94	2	no	—
439	C₄	—	94	2	no	—
440	C₄	—	94	2	no	—
441	C₄	—	376	2	no	—
442	C₄	—	188	4	no	—
443	C₄	C₂×#13093980	1	1	yes	characteristic
444	C₄	C₄×#10625352	1	1	yes	characteristic
445	C₄	#15689652	1	1	yes	characteristic
446	C₄	#15689654	1	1	yes	characteristic
447	C₂	—	8	4	no	—
448	C₂	#20245850	1	1	yes	characteristic
449	C₂	C₄×D₈×D₄₇	1	1	yes	characteristic
450	C₂	C₄×#13094043	1	1	yes	characteristic
451	C₂	#20253953	1	1	yes	characteristic
452	C₂	#20253955	1	1	yes	characteristic
453	C₂	#20253962	1	1	yes	characteristic
454	C₂	#20253965	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1970	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₈×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1970	D₄₇
hypocenter	C₄₇	#21275
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1970

Complements

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

N	H ≅ G/N	type
2. #20245850	C₂	semidirect
4. #20244121	C₂	semidirect
5. #20244119	C₂	semidirect
6. #20244074	C₂	semidirect
7. #20244068	C₂	semidirect
8. #107×Dic₄₇	C₂	semidirect
9. #102×Dic₄₇	C₂	semidirect
10. C₄×C₈×Dic₄₇	C₂	semidirect
14. D₈×Dic₄₇	C₄	semidirect
133. C₄×Dic₄₇	D₈	semidirect
189. C₈×C₄₇	#117	semidirect
267. C₄₇	#21275	semidirect
419. C₈	#13093980	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×Dic₄₇	2
#20245850	2
#20244255	2
#20244121	2
#20244119	2
#20244074	2
#20244068	2
#107×Dic₄₇	2
#102×Dic₄₇	2
C₄×C₈×Dic₄₇	2
C₄₇×#1970	2
#21275	47