Subgroups — #26223777

Order 12032.

842 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×C₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#20246656	C₂	1	1	yes	maximal, characteristic
3	#20244328	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244111	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243945	C₂	1	2	yes	maximal, complemented
6	#20243566	C₂	1	2	yes	maximal
7	#20243372	C₂	1	1	yes	maximal, characteristic
8	#20243264	C₂	1	2	yes	maximal, complemented
9	#20243255	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243169	C₂	1	2	yes	maximal
11	C₂×C₄₇×#405	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
13	C₈×Dic₉₄	—	2	4	no	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×#13093934	C₂²	1	2	yes	—
20	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
21	#15689062	C₄	1	1	yes	characteristic
22	#15689059	C₄	1	1	yes	characteristic
23	#15689056	C₄	1	2	yes	—
24	#15689046	C₄	1	2	yes	—
25	#15689043	C₄	1	1	yes	characteristic
26	#15689035	C₄	1	1	yes	characteristic
27	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
30	#15688878	C₂²	1	2	yes	—
31	#15688877	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#405	—	2	4	no	—
39	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₄×Dic₉₄	—	2	2	no	—
47	C₄×Dic₉₄	—	2	2	no	—
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
50	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
57	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	Dic₄₇⋊C₈	—	2	4	no	—
60	Dic₄₇⋊C₈	—	2	4	no	—
61	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
62	#13093934	—	2	4	no	—
63	C₈×Dic₄₇	—	2	4	no	—
64	C₄₇⋊#95	C₂×C₄	1	2	yes	—
65	C₄₇⋊#95	C₂×C₄	1	2	yes	—
66	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
67	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
68	C₄₇⋊#95	C₂×C₄	1	2	yes	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₄₇	—	2	2	no	—
72	C₂×M₁₆×C₄₇	—	2	2	no	—
73	C₂×M₁₆×C₄₇	Q₈	1	4	yes	complemented
74	C₂²×C₈×C₄₇	—	2	2	no	—
75	C₂²×C₈×C₄₇	—	2	2	no	—
76	C₂²×C₈×C₄₇	—	2	2	no	—
77	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	#117×C₄₇	—	2	2	no	—
82	#117×C₄₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	#97×C₄₇	—	2	2	no	—
90	#97×C₄₇	—	2	2	no	—
91	C₄×C₈×C₄₇	—	2	2	no	—
92	C₄×C₈×C₄₇	D₄	1	4	yes	—
93	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₄₇	#41	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
110	C₂×Dic₉₄	—	2	2	no	—
111	C₂×Dic₉₄	—	2	4	no	—
112	M₁₆×C₄₇	—	2	8	no	—
113	C₂×C₈×C₄₇	—	2	8	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	—	2	1	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
123	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
124	C₂×C₈×C₄₇	#41	1	2	yes	—
125	C₂×C₈×C₄₇	#41	1	2	yes	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₂²⋊C₄×C₄₇	—	2	2	no	—
129	C₂²⋊C₄×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	1	no	—
131	C₄²×C₄₇	—	2	1	no	—
132	C₄²×C₄₇	C₂×D₄	1	2	yes	—
133	C₄²×C₄₇	#41	1	2	yes	—
134	C₂²⋊Dic₄₇	—	2	4	no	—
135	C₂²⋊Dic₄₇	—	4	2	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	4	2	no	—
138	Dic₄₇⋊C₄	—	2	4	no	—
139	Dic₄₇⋊C₄	—	2	4	no	—
140	Dic₄₇⋊C₄	—	4	2	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂³×C₄₇	—	2	1	no	—
152	C₂³×C₄₇	—	2	1	no	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
156	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	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	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×Q₈	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	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	2	2	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	2	2	no	—
189	C₂×Dic₄₇	#131	1	4	yes	—
190	Dic₉₄	—	2	8	no	—
191	C₈×C₄₇	—	2	2	no	—
192	C₈×C₄₇	—	2	2	no	—
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	C₂²⋊Q₈	1	4	yes	—
195	C₄₇⋊C₈	—	4	2	no	—
196	C₄₇⋊C₈	—	4	2	no	—
197	#21602	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	—	2	4	no	—
199	C₂²×C₄₇	—	2	2	no	—
200	C₂²×C₄₇	—	4	1	no	—
201	C₂²×C₄₇	—	4	1	no	—
202	C₂²×C₄₇	—	4	2	no	—
203	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
205	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×#131	1	2	yes	—
207	C₂²×C₄₇	#568	1	2	yes	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	2	2	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	4	1	no	—
212	C₄×C₄₇	—	4	1	no	—
213	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
214	C₄×C₄₇	#525	1	1	yes	characteristic
215	C₄×C₄₇	#529	1	1	yes	characteristic
216	C₄×C₄₇	#533	1	1	yes	characteristic
217	Dic₄₇	—	2	4	no	—
218	Dic₄₇	—	4	2	no	—
219	Dic₄₇	—	4	2	no	—
220	Dic₄₇	—	4	2	no	—
221	C₂×C₈×Q₈	—	47	1	no	—
222	C₂×#405	D₄₇	1	1	yes	characteristic
223	#2396	—	47	1	no	—
224	#1985	—	47	1	no	—
225	#1940	—	47	1	no	—
226	#1916	—	47	2	no	—
227	#1850	—	47	2	no	—
228	#1798	—	47	1	no	—
229	#1771	—	47	2	no	—
230	#1770	—	47	1	no	—
231	#1753	—	47	2	no	—
232	C₂×C₄₇	—	4	2	no	—
233	C₂×C₄₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
234	C₂×C₄₇	#2929	1	1	yes	characteristic
235	C₂×C₄₇	#2932	1	1	yes	characteristic
236	C₂×C₄₇	#2962	1	2	yes	—
237	C₂×C₄₇	#2969	1	2	yes	—
238	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
239	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
240	C₂×C₄×Q₈	—	47	1	no	—
241	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
242	C₈×Q₈	—	94	4	no	—
243	C₂×C₄⋊C₈	—	47	2	no	—
244	C₂×C₄⋊C₈	—	47	2	no	—
245	C₂×C₄⋊C₈	—	47	1	no	—
246	C₂×C₄⋊C₈	—	47	1	no	—
247	C₂×C₂²⋊C₈	—	47	2	no	—
248	#405	—	2	4	no	—
249	C₂×#97	—	47	2	no	—
250	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
251	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
252	C₂×C₄×C₈	—	47	2	no	—
253	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
254	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
255	#400	—	47	1	no	—
256	#399	—	47	1	no	—
257	#398	—	47	2	no	—
258	#396	—	47	2	no	—
259	#395	—	47	1	no	—
260	#393	—	47	1	no	—
261	C₄×C₄⋊C₄	—	47	1	no	—
262	C₄×C₄⋊C₄	—	47	2	no	—
263	C₄×C₂²⋊C₄	—	47	2	no	—
264	#336	—	47	2	no	—
265	#336	—	47	2	no	—
266	#336	—	47	2	no	—
267	#336	—	47	2	no	—
268	#336	—	47	2	no	—
269	C₄₇	#21602	1	1	yes	characteristic, complemented, Sylow
270	C₂²×Q₈	—	47	1	no	—
271	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	Dic₉₄	1	4	yes	complemented
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	47	2	no	—
279	C₂²×C₈	—	47	2	no	—
280	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
282	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
284	C₄×Q₈	—	94	2	no	—
285	C₄×Q₈	—	94	2	no	—
286	#117	—	2	2	no	—
287	#117	—	2	2	no	—
288	C₂×C₄⋊C₄	—	47	2	no	—
289	C₂×C₄⋊C₄	—	47	1	no	—
290	C₂×C₄⋊C₄	—	47	2	no	—
291	C₂×C₄⋊C₄	—	47	2	no	—
292	C₂×C₄⋊C₄	—	47	2	no	—
293	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	47	2	no	—
296	C₂×C₂²⋊C₄	—	47	2	no	—
297	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
299	C₂×C₄²	—	47	2	no	—
300	C₂×C₄²	—	47	2	no	—
301	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
302	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
303	C₄⋊C₈	—	94	4	no	—
304	C₄⋊C₈	—	94	4	no	—
305	C₄⋊C₈	—	94	2	no	—
306	C₄⋊C₈	—	94	2	no	—
307	C₂²⋊C₈	—	94	4	no	—
308	#97	—	2	2	no	—
309	#97	—	2	2	no	—
310	#97	—	94	4	no	—
311	C₄×C₈	—	2	2	no	—
312	C₄×C₈	—	94	4	no	—
313	C₄×C₈	C₂²⋊D₄₇	1	4	yes	—
314	#95	—	47	2	no	—
315	#95	—	47	2	no	—
316	#95	—	47	2	no	—
317	#95	—	47	1	no	—
318	#95	—	47	1	no	—
319	#95	—	47	2	no	—
320	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
321	C₂×Q₈	—	94	4	no	—
322	C₂×Q₈	—	94	2	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	47	2	no	—
328	C₂²×C₄	—	47	2	no	—
329	C₂²×C₄	—	47	2	no	—
330	C₂²×C₄	—	47	2	no	—
331	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
332	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
337	C₂²×C₄	#10625350	1	2	yes	—
338	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
339	M₁₆	—	2	8	no	—
340	C₂×C₈	—	2	8	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	94	2	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	94	2	no	—
350	C₂×C₈	—	94	2	no	—
351	C₂×C₈	—	94	2	no	—
352	C₂×C₈	—	94	2	no	—
353	C₂×C₈	C₂×Dic₉₄	1	2	yes	—
354	C₂×C₈	C₂×Dic₉₄	1	2	yes	—
355	C₂×C₈	#10625350	1	2	yes	—
356	C₂×C₈	#10625350	1	2	yes	—
357	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
358	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	94	4	no	—
362	C₄⋊C₄	—	94	4	no	—
363	C₄⋊C₄	—	94	2	no	—
364	C₄⋊C₄	—	188	2	no	—
365	C₄⋊C₄	—	188	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	94	4	no	—
369	C₂²⋊C₄	—	188	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	94	2	no	—
373	C₄²	—	94	2	no	—
374	C₄²	—	94	2	no	—
375	C₄²	—	94	2	no	—
376	C₄²	#10625350	1	2	yes	—
377	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	C₄×Dic₉₄	1	2	yes	—
383	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
384	Q₈	—	94	8	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	47	4	no	—
398	C₂×C₄	—	94	2	no	—
399	C₂×C₄	—	94	2	no	—
400	C₂×C₄	—	94	2	no	—
401	C₂×C₄	—	94	2	no	—
402	C₂×C₄	—	94	2	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	94	2	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	94	2	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	2	no	—
409	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
410	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
411	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
412	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
414	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
415	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
416	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
417	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	2	no	—
421	C₈	—	188	2	no	—
422	C₈	—	188	2	no	—
423	C₈	#13094003	1	4	yes	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
430	C₂²	C₂×C₄×Dic₉₄	1	1	yes	characteristic
431	C₂²	C₄×#10625350	1	1	yes	characteristic
432	C₂²	#131×D₄₇	1	2	yes	—
433	C₂²	#15689888	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	94	4	no	—
440	C₄	—	188	2	no	—
441	C₄	—	188	2	no	—
442	C₄	—	188	2	no	—
443	C₄	C₂×#13094003	1	1	yes	characteristic
444	C₄	#15689634	1	1	yes	characteristic
445	C₄	#15689657	1	1	yes	characteristic
446	C₄	#15689680	1	1	yes	characteristic
447	C₂	—	4	2	no	—
448	C₂	C₄×#13094003	1	1	yes	characteristic
449	C₂	#20252080	1	1	yes	characteristic
450	C₂	#20252104	1	1	yes	characteristic
451	C₂	#20252332	1	2	yes	—
452	C₂	#20252388	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₂×C₄₇×#405	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#405	D₄₇
hypocenter	C₄₇	#21602
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×Dic₉₄	C₂	semidirect
3. #20244328	C₂	semidirect
4. #20244111	C₂	semidirect
5. #20243945	C₂	semidirect
8. #20243264	C₂	semidirect
9. #20243255	C₂	semidirect
73. C₂×M₁₆×C₄₇	Q₈	semidirect
269. C₄₇	#21602	semidirect
274. C₂×M₁₆	Dic₉₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Dic₉₄	2
#20246656	2
#20244328	2
#20244111	2
#20243945	2
#20243566	2
#20243372	2
#20243264	2
#20243255	2
#20243169	2
C₂×C₄₇×#405	2
#21602	47