Subgroups — #26222993

Order 12032.

1002 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊Q₈×Dic₄₇	C₂	1	2	yes	maximal
4	#20244250	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244117	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244066	C₂	1	2	yes	maximal, complemented
7	#20243822	C₂	1	2	yes	maximal
8	#20243421	C₂	1	1	yes	maximal, characteristic
9	#20243288	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243220	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#470	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
15	#15689230	—	2	4	no	—
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093956	C₂²	1	1	yes	characteristic
18	C₂×#13093948	C₂²	1	2	yes	—
19	C₂×#13093948	C₂²	1	2	yes	—
20	M₁₆×Dic₄₇	—	2	4	no	—
21	C₂×#13093934	C₂²	1	1	yes	characteristic
22	C₂×#13093934	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	#15689030	C₂²	1	2	yes	—
26	#15689022	C₂²	1	2	yes	—
27	#15689009	—	2	2	no	—
28	#15688998	—	2	2	no	—
29	#15688983	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₇	—	2	2	no	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
32	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
33	#15688886	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
37	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#470	C₄	1	8	yes	complemented
40	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#103×C₄₇	C₂²	1	2	yes	—
42	C₂³×Dic₄₇	D₄	1	2	yes	—
43	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	—	2	2	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	Q₈×Dic₄₇	—	2	4	no	—
49	Q₈×Dic₄₇	—	2	4	no	—
50	C₂×C₄⋊Dic₄₇	—	2	2	no	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
54	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
55	C₂×C₄×Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	—	2	2	no	—
58	C₂×C₄×Dic₄₇	—	2	2	no	—
59	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
62	#13093958	—	2	2	no	—
63	#13093956	—	2	2	no	—
64	#13093948	—	2	4	no	—
65	#13093948	—	2	4	no	—
66	#13093934	—	2	2	no	—
67	#13093934	D₄	1	4	yes	—
68	C₈×Dic₄₇	—	2	2	no	—
69	C₈×Dic₄₇	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×Q₁₆×C₄₇	—	2	2	no	—
78	C₂×Q₁₆×C₄₇	—	2	2	no	—
79	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
80	C₂×M₁₆×C₄₇	—	2	2	no	—
81	C₂×M₁₆×C₄₇	—	2	2	no	—
82	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²⋊Q₈×C₄₇	—	2	4	no	—
86	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
87	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
90	#106×C₄₇	C₂×C₄	1	4	yes	complemented
91	#103×C₄₇	C₂×C₄	1	8	yes	complemented
92	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	2	4	no	—
110	C₂²×Dic₄₇	—	2	4	no	—
111	C₂²×Dic₄₇	—	2	2	no	—
112	C₂²×Dic₄₇	—	2	2	no	—
113	C₂²×Dic₄₇	—	4	2	no	—
114	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
115	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
116	Q₁₆×C₄₇	—	2	8	no	—
117	M₁₆×C₄₇	—	2	8	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₇	#41	1	2	yes	—
124	C₄⋊C₄×C₄₇	—	2	8	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
127	C₂²⋊C₄×C₄₇	—	2	8	no	—
128	C₂²⋊Dic₄₇	—	4	4	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	—	2	2	no	—
133	C₄⋊Dic₄₇	—	4	4	no	—
134	C₄⋊Dic₄₇	—	4	4	no	—
135	C₄×Dic₄₇	—	2	1	no	—
136	C₄×Dic₄₇	—	2	1	no	—
137	C₄×Dic₄₇	—	2	4	no	—
138	C₄×Dic₄₇	—	4	4	no	—
139	C₄×Dic₄₇	—	4	4	no	—
140	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
141	C₄×Dic₄₇	#41	1	2	yes	—
142	#10625329	—	2	8	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
148	C₂×C₄₇⋊C₈	#41	1	2	yes	—
149	C₂³×C₄₇	—	2	1	no	—
150	C₂³×C₄₇	—	2	1	no	—
151	C₂³×C₄₇	—	2	2	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	C₄×D₄	1	2	yes	—
154	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₇	—	2	4	no	—
156	Q₈×C₄₇	—	2	4	no	—
157	Q₈×C₄₇	—	4	2	no	—
158	Q₈×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	4	8	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	C₂×Dic₄₇	—	4	2	no	—
187	C₂×Dic₄₇	—	4	2	no	—
188	C₂×Dic₄₇	—	4	2	no	—
189	C₂×Dic₄₇	#121	1	4	yes	—
190	C₂×Dic₄₇	#137	1	4	yes	—
191	C₈×C₄₇	—	2	2	no	—
192	C₈×C₄₇	C₄×D₄	1	4	yes	—
193	C₄₇⋊C₈	—	2	2	no	—
194	C₄₇⋊C₈	—	2	2	no	—
195	#21539	—	47	1	no	maximal, Sylow
196	C₂²×C₄₇	—	2	4	no	—
197	C₂²×C₄₇	—	2	2	no	—
198	C₂²×C₄₇	—	4	1	no	—
199	C₂²×C₄₇	—	4	1	no	—
200	C₂²×C₄₇	—	4	2	no	—
201	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
203	C₂²×C₄₇	#532	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#137	1	2	yes	—
205	C₂²×C₄₇	#575	1	2	yes	—
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	4	4	no	—
208	C₄×C₄₇	—	4	4	no	—
209	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
211	C₄×C₄₇	#525	1	1	yes	characteristic
212	C₄×C₄₇	#529	1	1	yes	characteristic
213	Dic₄₇	—	2	4	no	—
214	Dic₄₇	—	2	4	no	—
215	Dic₄₇	—	8	2	no	—
216	Dic₄₇	—	8	2	no	—
217	C₂×#470	D₄₇	1	1	yes	characteristic
218	C₂×#441	—	47	1	no	—
219	C₂×C₄×M₁₆	—	47	1	no	—
220	C₄×C₂²⋊Q₈	—	47	2	no	—
221	#1969	—	47	1	no	—
222	#1941	—	47	1	no	—
223	#1933	—	47	2	no	—
224	#1894	—	47	2	no	—
225	#1809	—	47	1	no	—
226	#1776	—	47	1	no	—
227	#1763	—	47	2	no	—
228	C₂×C₄₇	—	4	2	no	—
229	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
230	C₂×C₄₇	C₄×#137	1	2	yes	—
231	C₂×C₄₇	#3056	1	2	yes	—
232	C₂×C₄₇	#3183	1	1	yes	characteristic
233	C₂×C₄₇	#3185	1	1	yes	characteristic
234	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
235	C₂²×M₁₆	—	47	1	no	—
236	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
237	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
238	C₂×C₄×Q₈	—	47	2	no	—
239	C₂²×C₄²	—	47	1	no	—
240	#470	Dic₄₇	1	8	yes	complemented
241	#441	—	94	4	no	—
242	C₂×#107	—	47	1	no	—
243	C₂×#106	—	47	1	no	—
244	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
245	C₂×#103	—	47	2	no	—
246	C₂×#103	—	47	2	no	—
247	C₂×#103	C₂×D₄₇	1	2	yes	—
248	C₄×M₁₆	—	94	4	no	—
249	C₂×#97	—	47	1	no	—
250	C₂×#97	—	47	1	no	—
251	C₂×C₄×C₈	—	47	1	no	—
252	C₂×C₄×C₈	—	47	1	no	—
253	#391	—	47	2	no	—
254	#389	—	47	2	no	—
255	#387	—	94	2	no	—
256	#385	—	94	2	no	—
257	#380	—	47	2	no	—
258	C₄×C₄⋊C₄	—	47	2	no	—
259	C₄×C₄⋊C₄	—	94	2	no	—
260	C₄×C₂²⋊C₄	—	94	2	no	—
261	#340	—	47	2	no	—
262	#340	—	47	2	no	—
263	#340	—	47	2	no	—
264	C₄₇	#21539	1	1	yes	characteristic, complemented, Sylow
265	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
266	C₂³×C₄	—	47	2	no	—
267	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	—	2	2	no	—
270	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	complemented
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	94	2	no	—
274	C₂×M₁₆	—	94	2	no	—
275	C₂×M₁₆	—	94	2	no	—
276	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
277	C₂²×C₈	—	47	1	no	—
278	C₂²×C₈	—	47	1	no	—
279	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
280	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
283	C₄×Q₈	—	94	4	no	—
284	C₄×Q₈	—	94	4	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	47	2	no	—
287	C₂×C₄⋊C₄	—	47	2	no	—
288	C₂×C₄⋊C₄	—	94	2	no	—
289	C₂×C₄⋊C₄	—	94	2	no	—
290	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	94	2	no	—
293	C₂×C₄²	—	47	1	no	—
294	C₂×C₄²	—	47	2	no	—
295	C₂×C₄²	—	47	1	no	—
296	C₂×C₄²	—	94	2	no	—
297	C₂×C₄²	—	94	2	no	—
298	C₂×C₄²	—	94	2	no	—
299	C₂×C₄²	—	94	2	no	—
300	#107	—	94	2	no	—
301	#106	—	94	2	no	—
302	#106	C₂×Dic₄₇	1	4	yes	complemented
303	#103	—	94	4	no	—
304	#103	—	94	4	no	—
305	#103	C₂×Dic₄₇	1	8	yes	complemented
306	#97	—	47	4	no	—
307	#97	—	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	#95	—	94	2	no	—
314	#95	—	94	2	no	—
315	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	47	2	no	—
329	C₂²×C₄	—	47	2	no	—
330	C₂²×C₄	—	94	4	no	—
331	C₂²×C₄	—	94	4	no	—
332	C₂²×C₄	—	94	2	no	—
333	C₂²×C₄	—	94	2	no	—
334	C₂²×C₄	—	188	2	no	—
335	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
336	C₂²×C₄	#10625352	1	2	yes	—
337	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
338	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
339	Q₁₆	—	2	8	no	—
340	M₁₆	—	2	8	no	—
341	M₁₆	—	94	8	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	47	2	no	—
345	C₂×C₈	—	47	2	no	—
346	C₂×C₈	—	94	1	no	—
347	C₂×C₈	—	94	1	no	—
348	C₂×C₈	—	94	1	no	—
349	C₂×C₈	—	94	1	no	—
350	C₂×C₈	D₄×D₄₇	1	2	yes	—
351	C₂×C₈	#10625352	1	2	yes	—
352	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
353	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
354	C₄⋊C₄	—	2	8	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	94	2	no	—
357	C₄⋊C₄	—	94	2	no	—
358	C₄⋊C₄	—	94	2	no	—
359	C₄⋊C₄	—	94	2	no	—
360	C₄⋊C₄	—	188	4	no	—
361	C₄⋊C₄	—	188	4	no	—
362	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	188	4	no	—
365	C₄²	—	47	2	no	—
366	C₄²	—	47	2	no	—
367	C₄²	—	94	4	no	—
368	C₄²	—	94	1	no	—
369	C₄²	—	94	1	no	—
370	C₄²	—	188	4	no	—
371	C₄²	—	188	4	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	1	no	—
376	C₂³	D₄×Dic₄₇	1	2	yes	—
377	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
378	Q₈	—	2	4	no	—
379	Q₈	—	2	4	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	47	4	no	—
395	C₂×C₄	—	47	4	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	—	94	2	no	—
398	C₂×C₄	—	94	2	no	—
399	C₂×C₄	—	94	2	no	—
400	C₂×C₄	—	188	8	no	—
401	C₂×C₄	—	188	2	no	—
402	C₂×C₄	—	188	2	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	D₄×Dic₄₇	1	2	yes	—
408	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
409	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
410	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
411	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
413	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	94	2	no	—
416	C₈	—	94	2	no	—
417	C₈	D₄×Dic₄₇	1	4	yes	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
424	C₂²	#121×D₄₇	1	1	yes	characteristic
425	C₂²	#15689668	1	1	yes	characteristic
426	C₂²	#137×D₄₇	1	2	yes	—
427	C₂²	#15689922	1	2	yes	—
428	C₄	—	2	2	no	—
429	C₄	—	4	4	no	—
430	C₄	—	4	4	no	—
431	C₄	—	94	4	no	—
432	C₄	—	94	4	no	—
433	C₄	—	376	2	no	—
434	C₄	—	376	2	no	—
435	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
436	C₄	#41×Dic₄₇	1	1	yes	characteristic
437	C₄	#15689633	1	1	yes	characteristic
438	C₄	#15689654	1	1	yes	characteristic
439	C₂	—	4	2	no	—
440	C₂	#121×Dic₄₇	1	1	yes	characteristic
441	C₂	#137×Dic₄₇	1	2	yes	—
442	C₂	#20253017	1	2	yes	—
443	C₂	#20254118	1	1	yes	characteristic
444	C₂	#20254128	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#470	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#470	D₄₇
hypocenter	C₄₇	#21539
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#470

Complements

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

N	H ≅ G/N	type
1. C₂×#15689230	C₂	semidirect
4. #20244250	C₂	semidirect
5. #20244117	C₂	semidirect
6. #20244066	C₂	semidirect
9. #20243288	C₂	semidirect
10. #20243220	C₂	semidirect
39. C₄₇×#470	C₄	semidirect
79. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
90. #106×C₄₇	C₂×C₄	semidirect
91. #103×C₄₇	C₂×C₄	semidirect
240. #470	Dic₄₇	semidirect
264. C₄₇	#21539	semidirect
270. C₂×Q₁₆	C₂×Dic₄₇	semidirect
302. #106	C₂×Dic₄₇	semidirect
305. #103	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×#15689230	2
C₂×M₁₆×Dic₄₇	2
C₂²⋊Q₈×Dic₄₇	2
#20244250	2
#20244117	2
#20244066	2
#20243822	2
#20243421	2
#20243288	2
#20243220	2
C₂×C₄₇×#470	2
#21539	47