Subgroups — #26123252

Order 12032.

1070 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13093951	C₂	1	2	yes	maximal
3	C₂×#15688882	C₂	1	2	yes	maximal, complemented
4	C₄×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2297	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
8	#15689147	—	2	4	no	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
10	C₂×#13093951	—	2	4	no	—
11	C₂×#13093951	—	2	4	no	—
12	C₂×#13093951	—	2	4	no	—
13	C₂×C₄₇⋊#95	—	2	2	no	—
14	#15688882	—	2	4	no	—
15	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#391	C₄	1	1	yes	characteristic, complemented
19	C₄₇×#391	C₄	1	1	yes	characteristic, complemented
20	C₄₇×#390	C₄	1	1	yes	characteristic, complemented
21	C₄₇×#390	C₄	1	1	yes	characteristic, complemented
22	C₄₇×#386	—	2	2	no	—
23	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
24	C₂³×Dic₄₇	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	D₄	1	4	yes	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₂×C₄×Dic₄₇	—	2	2	no	—
33	C₂×C₄×Dic₄₇	—	2	2	no	—
34	C₂×C₄×Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	2	2	no	—
37	C₂×C₄×Dic₄₇	D₄	1	4	yes	—
38	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
39	#13093951	—	2	16	no	—
40	C₄₇⋊#95	—	2	8	no	—
41	C₂×#41×C₄₇	—	2	1	no	—
42	C₂×#41×C₄₇	—	2	1	no	—
43	C₂×#41×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	—	2	2	no	—
45	C₂×#41×C₄₇	—	2	2	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	D₄	1	2	yes	—
48	C₂×#41×C₄₇	Q₈	1	2	yes	—
49	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₄₇	—	2	1	no	—
51	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	—	2	1	no	—
53	C₂³×C₄×C₄₇	D₄	1	2	yes	—
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	#117×C₄₇	—	2	2	no	—
56	#117×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	—	2	2	no	—
63	C₂×C₄²×C₄₇	—	2	2	no	—
64	C₂×C₄²×C₄₇	—	2	1	no	—
65	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	D₄	1	2	yes	—
68	#95×C₄₇	—	2	2	no	—
69	#95×C₄₇	—	2	2	no	—
70	C₂⁴×C₄₇	—	2	1	no	—
71	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
72	#41×C₄₇	—	2	4	no	—
73	#41×C₄₇	—	2	4	no	—
74	#41×C₄₇	—	2	4	no	—
75	#41×C₄₇	—	2	4	no	—
76	#41×C₄₇	—	4	2	no	—
77	#41×C₄₇	—	4	2	no	—
78	#41×C₄₇	—	4	2	no	—
79	#41×C₄₇	—	4	2	no	—
80	C₂×Q₈×C₄₇	—	2	1	no	—
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
84	C₂×D₄×C₄₇	—	2	2	no	—
85	C₂×D₄×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	2	1	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	4	2	no	—
90	C₂×D₄×C₄₇	—	4	2	no	—
91	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	—	2	1	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	4	2	no	—
100	C₂²×C₄×C₄₇	—	4	1	no	—
101	C₂²×C₄×C₄₇	—	4	1	no	—
102	C₂²×C₄×C₄₇	—	4	1	no	—
103	C₂²×C₄×C₄₇	—	4	1	no	—
104	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	#41	1	2	yes	—
115	C₂²×C₄×C₄₇	#41	1	2	yes	—
116	C₂²×Dic₄₇	—	2	8	no	—
117	C₂²×Dic₄₇	—	2	4	no	—
118	C₂²×Dic₄₇	—	4	4	no	—
119	C₂²×Dic₄₇	—	4	2	no	—
120	C₂²×Dic₄₇	—	4	2	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₂²⋊C₄×C₄₇	—	4	4	no	—
124	C₂²⋊C₄×C₄₇	—	4	2	no	—
125	C₂²⋊C₄×C₄₇	—	4	4	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	4	1	no	—
131	C₄²×C₄₇	—	4	1	no	—
132	C₄×Dic₄₇	—	2	4	no	—
133	C₄×Dic₄₇	—	2	4	no	—
134	C₄×Dic₄₇	—	4	2	no	—
135	C₄×Dic₄₇	—	4	2	no	—
136	#10625329	—	2	4	no	—
137	#10625329	—	2	4	no	—
138	#10625329	—	4	2	no	—
139	#10625329	—	4	2	no	—
140	C₂×C₄₇⋊C₈	—	2	4	no	—
141	C₂×C₄₇⋊C₈	—	4	2	no	—
142	C₂×C₄₇⋊C₈	—	4	2	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	—	2	2	no	—
146	C₂³×C₄₇	—	4	1	no	—
147	C₂³×C₄₇	—	4	1	no	—
148	C₂³×C₄₇	—	4	2	no	—
149	C₂³×C₄₇	—	4	2	no	—
150	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂³×C₄₇	#121	1	2	yes	—
152	C₂³×C₄₇	#121	1	2	yes	—
153	C₂³×C₄₇	#121	1	1	yes	characteristic
154	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
155	Q₈×C₄₇	—	2	4	no	—
156	Q₈×C₄₇	—	4	2	no	—
157	D₄×C₄₇	—	2	4	no	—
158	D₄×C₄₇	—	4	4	no	—
159	D₄×C₄₇	—	4	4	no	—
160	D₄×C₄₇	—	4	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	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	4	8	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	#104	1	4	yes	complemented
179	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
184	C₂×C₄×C₄₇	#120	1	2	yes	—
185	C₂×C₄×C₄₇	#121	1	2	yes	—
186	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
188	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
189	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
191	C₂×C₄×C₄₇	#123	1	2	yes	—
192	C₂×C₄×C₄₇	#123	1	2	yes	—
193	C₂×C₄×C₄₇	#124	1	2	yes	—
194	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
195	C₂×C₄×C₄₇	#126	1	2	yes	—
196	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
197	C₂×Dic₄₇	—	2	8	no	—
198	C₂×Dic₄₇	—	4	8	no	—
199	C₂×Dic₄₇	—	4	8	no	—
200	C₂×Dic₄₇	—	4	4	no	—
201	C₂×Dic₄₇	—	4	4	no	—
202	C₄₇⋊C₈	—	4	4	no	—
203	#11053	—	47	1	no	maximal, Sylow
204	C₂²×C₄₇	—	2	2	no	—
205	C₂²×C₄₇	—	2	2	no	—
206	C₂²×C₄₇	—	2	4	no	—
207	C₂²×C₄₇	—	2	2	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	4	4	no	—
210	C₂²×C₄₇	—	4	2	no	—
211	C₂²×C₄₇	—	8	2	no	—
212	C₂²×C₄₇	—	8	1	no	—
213	C₂²×C₄₇	—	8	1	no	—
214	C₂²×C₄₇	#380	1	1	yes	characteristic
215	C₂²×C₄₇	#386	1	1	yes	characteristic
216	C₂²×C₄₇	#390	1	1	yes	characteristic
217	C₂²×C₄₇	#394	1	2	yes	—
218	C₂²×C₄₇	#396	1	2	yes	—
219	C₂²×C₄₇	C₂×#104	1	2	yes	—
220	C₂²×C₄₇	#421	1	2	yes	—
221	C₄×C₄₇	—	2	4	no	—
222	C₄×C₄₇	—	4	2	no	—
223	C₄×C₄₇	—	4	2	no	—
224	C₄×C₄₇	—	8	1	no	—
225	C₄×C₄₇	—	8	1	no	—
226	C₄×C₄₇	#385	1	2	yes	—
227	C₄×C₄₇	#388	1	2	yes	—
228	C₄×C₄₇	#392	1	1	yes	characteristic
229	C₄×C₄₇	#393	1	1	yes	characteristic
230	C₄×C₄₇	#397	1	1	yes	characteristic
231	C₄×C₄₇	#399	1	1	yes	characteristic
232	Dic₄₇	—	4	8	no	—
233	C₂×#423	—	47	1	no	—
234	C₂²×#104	—	47	2	no	—
235	#2297	D₄₇	1	1	yes	characteristic
236	C₂×#339	—	47	2	no	—
237	C₄×#95	—	47	1	no	—
238	C₂×C₄₇	—	2	2	no	—
239	C₂×C₄₇	—	2	2	no	—
240	C₂×C₄₇	—	8	2	no	—
241	C₂×C₄₇	#1439	1	1	yes	characteristic
242	C₂×C₄₇	#1806	1	2	yes	—
243	C₂×C₄₇	#1871	1	2	yes	—
244	C₂×C₄₇	#1962	1	1	yes	characteristic
245	C₂×C₄₇	#1963	1	1	yes	characteristic
246	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
247	C₂²×M₁₆	—	47	2	no	—
248	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
249	C₂²×C₄²	—	47	2	no	—
250	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
251	#423	—	94	4	no	—
252	C₂×C₄⋊C₈	—	94	2	no	—
253	C₂×#104	—	94	4	no	—
254	C₂×#104	—	94	4	no	—
255	C₂×#104	—	94	4	no	—
256	#391	Dic₄₇	1	1	yes	characteristic, complemented
257	#391	Dic₄₇	1	1	yes	characteristic, complemented
258	#390	Dic₄₇	1	1	yes	characteristic, complemented
259	#390	Dic₄₇	1	1	yes	characteristic, complemented
260	#386	—	2	2	no	—
261	C₄×C₂²⋊C₄	—	2	2	no	—
262	C₂×#95	—	94	2	no	—
263	#339	—	94	4	no	—
264	C₄₇	#11053	1	1	yes	characteristic, complemented, Sylow
265	C₂×#41	—	2	1	no	—
266	C₂×#41	—	2	1	no	—
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	Dic₉₄	1	2	yes	—
272	C₂×#41	D₁₈₈	1	2	yes	—
273	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
276	C₂³×C₄	—	2	1	no	—
277	C₂³×C₄	—	94	2	no	—
278	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
279	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
280	C₂×M₁₆	—	47	4	no	—
281	C₂×M₁₆	—	94	2	no	—
282	C₂×M₁₆	—	94	2	no	—
283	C₂×M₁₆	—	94	2	no	—
284	C₂×M₁₆	—	94	2	no	—
285	C₂×M₁₆	—	94	2	no	—
286	C₂²×C₈	—	94	2	no	—
287	#117	—	2	2	no	—
288	#117	—	2	2	no	—
289	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	47	4	no	—
298	C₂×C₄²	—	94	2	no	—
299	C₂×C₄²	—	94	2	no	—
300	C₂×C₄²	—	94	2	no	—
301	C₂×C₄²	—	94	2	no	—
302	C₂×C₄²	—	94	2	no	—
303	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
304	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
305	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
306	C₄⋊C₈	—	94	8	no	—
307	#104	—	94	16	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	94	8	no	—
311	C₂⁴	—	2	1	no	—
312	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
313	#41	—	2	4	no	—
314	#41	—	2	4	no	—
315	#41	—	2	4	no	—
316	#41	—	2	4	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	#41	—	4	2	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	94	8	no	—
346	C₂²×C₄	—	94	4	no	—
347	C₂²×C₄	—	188	4	no	—
348	C₂²×C₄	—	188	2	no	—
349	C₂²×C₄	—	188	2	no	—
350	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
351	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
352	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
354	C₂²×C₄	#10625350	1	1	yes	characteristic
355	C₂²×C₄	#10625350	1	1	yes	characteristic
356	C₂²×C₄	D₄×D₄₇	1	2	yes	—
357	C₂²×C₄	D₄×D₄₇	1	2	yes	—
358	C₂²×C₄	#10625352	1	2	yes	—
359	C₂²×C₄	#10625352	1	2	yes	—
360	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
362	M₁₆	—	94	4	no	—
363	M₁₆	—	94	4	no	—
364	M₁₆	—	188	2	no	—
365	M₁₆	—	188	2	no	—
366	C₂×C₈	—	94	4	no	—
367	C₂×C₈	—	188	2	no	—
368	C₂×C₈	—	188	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	4	1	no	—
379	C₄²	—	4	1	no	—
380	C₄²	—	94	4	no	—
381	C₄²	—	94	4	no	—
382	C₄²	—	188	2	no	—
383	C₄²	—	188	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
392	C₂³	#13093995	1	2	yes	—
393	C₂³	#13093996	1	2	yes	—
394	C₂³	#13093998	1	1	yes	characteristic
395	C₂³	#13094003	1	1	yes	characteristic
396	Q₈	—	2	4	no	—
397	Q₈	—	4	2	no	—
398	D₄	—	2	4	no	—
399	D₄	—	4	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	8	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	94	8	no	—
420	C₂×C₄	—	188	8	no	—
421	C₂×C₄	—	188	8	no	—
422	C₂×C₄	—	188	4	no	—
423	C₂×C₄	—	188	4	no	—
424	C₂×C₄	#13093951	1	4	yes	complemented
425	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
426	C₂×C₄	#13093983	1	1	yes	characteristic
427	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
428	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
429	C₂×C₄	#13093992	1	1	yes	characteristic
430	C₂×C₄	#13093994	1	2	yes	—
431	C₂×C₄	#13093997	1	2	yes	—
432	C₂×C₄	#13093998	1	1	yes	characteristic
433	C₂×C₄	#13094001	1	2	yes	—
434	C₂×C₄	#13094001	1	2	yes	—
435	C₂×C₄	#13094003	1	1	yes	characteristic
436	C₂×C₄	#13094005	1	1	yes	characteristic
437	C₂×C₄	#13094006	1	2	yes	—
438	C₂×C₄	#13094008	1	2	yes	—
439	C₂×C₄	#13094010	1	2	yes	—
440	C₂×C₄	#13094011	1	1	yes	characteristic
441	C₂×C₄	#13094017	1	2	yes	—
442	C₂×C₄	#13094020	1	1	yes	characteristic
443	C₈	—	188	4	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	#15688983	1	1	yes	characteristic
455	C₂²	#15689003	1	1	yes	characteristic
456	C₂²	#15689026	1	1	yes	characteristic
457	C₂²	#15689039	1	2	yes	—
458	C₂²	#15689046	1	2	yes	—
459	C₂²	C₂×#13093951	1	2	yes	—
460	C₂²	#15689140	1	2	yes	—
461	C₄	—	2	4	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	1	no	—
466	C₄	—	188	8	no	—
467	C₄	#15688998	1	2	yes	—
468	C₄	#15689016	1	2	yes	—
469	C₄	#15689032	1	1	yes	characteristic
470	C₄	#15689035	1	1	yes	characteristic
471	C₄	#15689048	1	1	yes	characteristic
472	C₄	#15689059	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	—	2	2	no	—
475	C₂	—	8	2	no	—
476	C₂	#20241633	1	1	yes	characteristic
477	C₂	#20243408	1	2	yes	—
478	C₂	#20243691	1	2	yes	—
479	C₂	#20244217	1	1	yes	characteristic
480	C₂	#20244221	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#2297	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#2297	D₄₇
hypocenter	C₄₇	#11053
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ #2297

Complements

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

N	H ≅ G/N	type
1. C₂×#15689147	C₂	semidirect
3. C₂×#15688882	C₂	semidirect
4. C₄×C₄₇⋊#95	C₂	semidirect
18. C₄₇×#391	C₄	semidirect
19. C₄₇×#391	C₄	semidirect
20. C₄₇×#390	C₄	semidirect
21. C₄₇×#390	C₄	semidirect
178. C₂×C₄×C₄₇	#104	semidirect
256. #391	Dic₄₇	semidirect
257. #391	Dic₄₇	semidirect
258. #390	Dic₄₇	semidirect
259. #390	Dic₄₇	semidirect
264. C₄₇	#11053	semidirect
424. C₂×C₄	#13093951	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₂²×#13093951	2
C₂×#15688882	2
C₄×C₄₇⋊#95	2
C₄₇×#2297	2
#11053	47