Subgroups — #26236061

Order 12032.

846 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625336	C₂	1	1	yes	maximal, characteristic
2	#20246335	C₂	1	1	yes	maximal, characteristic
3	#20244272	C₂	1	2	yes	maximal
4	#20244026	C₂	1	2	yes	maximal, complemented
5	#20244008	C₂	1	2	yes	maximal
6	#20243547	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243393	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243385	C₂	1	1	yes	maximal, characteristic
9	#20243286	C₂	1	2	yes	maximal, complemented
10	#20243257	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625336	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
14	C₂×#13093982	—	2	1	no	—
15	C₄×#10625336	C₄	1	8	yes	complemented
16	C₂×#13093957	C₂²	1	2	yes	—
17	C₂×#13093957	C₂²	1	2	yes	—
18	C₂×#13093955	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093948	C₂²	1	2	yes	—
21	C₂×#13093948	C₂²	1	1	yes	characteristic
22	C₂×#13093944	C₂²	1	2	yes	—
23	C₂×#13093944	C₂²	1	1	yes	characteristic
24	C₂×#13093935	C₂²	1	2	yes	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	#15689025	C₂²	1	2	yes	—
27	#15689015	—	2	2	no	—
28	#15688993	C₂²	1	1	yes	characteristic
29	#15688980	—	2	1	no	—
30	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	#15688878	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#391	C₂²	1	2	yes	—
36	C₄₇×#387	—	2	2	no	—
37	C₄₇×#384	C₂²	1	1	yes	characteristic
38	C₄₇×#382	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄×D₄₇	—	2	1	no	—
44	C₂×#10625336	—	2	2	no	—
45	C₂×#10625336	—	2	2	no	—
46	C₂×#10625336	C₂×C₄	1	4	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₄×D₁₈₈	—	2	2	no	—
51	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
52	#13093982	—	4	4	no	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₂×C₄⋊Dic₄₇	—	2	1	no	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
57	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
59	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
60	C₂×C₄×Dic₄₇	—	2	2	no	—
61	#13093957	—	2	4	no	—
62	#13093957	—	4	2	no	—
63	#13093955	C₂×C₄	1	4	yes	—
64	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
65	#13093948	—	4	2	no	—
66	#13093948	C₂×C₄	1	4	yes	—
67	#13093944	—	4	2	no	—
68	#13093944	C₂×C₄	1	4	yes	—
69	#13093935	—	2	4	no	—
70	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₄×Q₈×C₄₇	—	2	2	no	—
74	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	—	2	1	no	—
83	C₂×C₄²×C₄₇	—	2	2	no	—
84	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	#95×C₄₇	—	2	2	no	—
87	#95×C₄₇	—	2	2	no	—
88	#95×C₄₇	—	2	2	no	—
89	#95×C₄₇	D₄	1	2	yes	—
90	C₂³×D₄₇	—	2	1	no	—
91	C₂×Q₈×C₄₇	—	2	1	no	—
92	C₂×Q₈×C₄₇	—	2	1	no	—
93	C₂×Q₈×C₄₇	—	2	1	no	—
94	C₂×Q₈×C₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	—	2	1	no	—
106	C₂²×Dic₄₇	—	2	2	no	—
107	C₂×D₁₈₈	—	2	1	no	—
108	C₂×D₁₈₈	—	2	1	no	—
109	C₂×D₁₈₈	—	2	1	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	—	2	1	no	—
112	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₄₇	—	2	4	no	—
114	C₂×C₄×D₄₇	—	4	2	no	—
115	C₂×C₄×D₄₇	—	4	2	no	—
116	C₄⋊C₄×C₄₇	—	2	4	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	4	2	no	—
123	C₄⋊C₄×C₄₇	—	8	1	no	—
124	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
125	C₄²×C₄₇	—	2	4	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	8	2	no	—
129	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
130	C₄²×C₄₇	#41	1	2	yes	—
131	#10625336	—	2	8	no	—
132	(C₂×D₄₇)⋊C₄	—	2	4	no	—
133	(C₂×D₄₇)⋊C₄	—	4	4	no	—
134	(C₂×D₄₇)⋊C₄	—	8	2	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	4	2	no	—
139	C₄⋊Dic₄₇	—	8	1	no	—
140	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
141	C₄×Dic₄₇	—	4	4	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
148	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₄₇⋊C₈	#41	1	2	yes	—
150	C₂×C₄₇⋊C₈	#41	1	2	yes	—
151	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
152	C₂²×D₄₇	—	2	2	no	—
153	C₂²×D₄₇	—	4	1	no	—
154	C₂²×D₄₇	—	4	1	no	—
155	C₂²×D₄₇	—	4	1	no	—
156	C₂²×D₄₇	—	4	1	no	—
157	C₂²×D₄₇	—	4	1	no	—
158	C₂²×D₄₇	—	4	1	no	—
159	Q₈×C₄₇	—	2	2	no	—
160	Q₈×C₄₇	—	2	2	no	—
161	Q₈×C₄₇	—	4	1	no	—
162	Q₈×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
183	C₂×C₄×C₄₇	#137	1	2	yes	—
184	C₂×C₄×C₄₇	C₂³×C₄	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×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
190	C₂×Dic₄₇	—	2	2	no	—
191	C₂×Dic₄₇	—	4	1	no	—
192	C₂×Dic₄₇	—	4	1	no	—
193	C₂×Dic₄₇	—	4	2	no	—
194	C₂×Dic₄₇	—	4	2	no	—
195	C₂×Dic₄₇	—	4	2	no	—
196	D₁₈₈	—	2	2	no	—
197	D₁₈₈	—	2	2	no	—
198	D₁₈₈	—	4	1	no	—
199	D₁₈₈	—	4	1	no	—
200	C₄×D₄₇	—	4	8	no	—
201	C₄₇⋊C₈	—	2	2	no	—
202	C₄₇⋊C₈	—	4	2	no	—
203	C₄₇⋊C₈	#117	1	4	yes	complemented
204	#22811	—	47	1	no	maximal, Sylow
205	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂²×C₄₇	#547	1	1	yes	characteristic
207	C₂²×C₄₇	#550	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
210	C₂²×C₄₇	#576	1	1	yes	characteristic
211	C₂²×C₄₇	#578	1	1	yes	characteristic
212	C₂×D₄₇	—	4	2	no	—
213	C₂×D₄₇	—	4	2	no	—
214	C₂×D₄₇	—	4	2	no	—
215	C₂×D₄₇	—	8	1	no	—
216	C₂×D₄₇	—	8	1	no	—
217	C₂×D₄₇	—	8	1	no	—
218	C₂×D₄₇	—	8	1	no	—
219	C₄×C₄₇	—	2	2	no	—
220	C₄×C₄₇	—	4	2	no	—
221	C₄×C₄₇	—	4	2	no	—
222	C₄×C₄₇	—	4	2	no	—
223	C₄×C₄₇	—	4	2	no	—
224	C₄×C₄₇	—	8	2	no	—
225	C₄×C₄₇	#440	1	4	yes	—
226	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
227	C₄×C₄₇	#520	1	1	yes	characteristic
228	C₄×C₄₇	#555	1	1	yes	characteristic
229	C₄×C₄₇	#556	1	1	yes	characteristic
230	Dic₄₇	—	4	2	no	—
231	Dic₄₇	—	8	2	no	—
232	C₂×C₄×SD₁₆	—	47	1	no	—
233	#2355	D₄₇	1	1	yes	characteristic, complemented
234	#2354	—	47	1	no	—
235	#1973	—	47	2	no	—
236	#1928	—	47	2	no	—
237	#1925	—	47	2	no	—
238	#1845	—	47	1	no	—
239	#1803	—	47	1	no	—
240	#1802	—	47	1	no	—
241	#1776	—	47	2	no	—
242	#1770	—	47	1	no	—
243	C₂×C₄₇	#2354	1	1	yes	characteristic
244	C₂×C₄₇	C₂×#440	1	1	yes	characteristic
245	C₂×C₄₇	#2951	1	1	yes	characteristic
246	C₂×C₄₇	#3353	1	1	yes	characteristic
247	C₂×C₄₇	#3357	1	1	yes	characteristic
248	C₂×C₄₇	#3398	1	1	yes	characteristic
249	C₂×C₄₇	#3399	1	1	yes	characteristic
250	D₄₇	—	8	2	no	—
251	C₂²×SD₁₆	—	47	1	no	—
252	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
253	C₂×C₄×D₄	—	47	1	no	—
254	C₂×#117	—	94	1	no	—
255	C₄×SD₁₆	—	47	8	no	—
256	C₂×#107	—	47	2	no	—
257	C₂×#107	—	47	2	no	—
258	C₂×#106	—	47	1	no	—
259	C₂×C₄⋊C₈	—	47	1	no	—
260	C₂×#103	—	47	1	no	—
261	C₂×#103	—	47	2	no	—
262	C₂×#102	—	47	1	no	—
263	C₂×#102	—	47	2	no	—
264	C₂×#97	—	47	2	no	—
265	C₂×C₄×C₈	—	47	1	no	—
266	#391	C₂×D₄₇	1	2	yes	—
267	#390	—	47	2	no	—
268	#388	—	94	2	no	—
269	#387	—	2	2	no	—
270	#384	—	47	1	no	—
271	#384	C₂×D₄₇	1	1	yes	characteristic
272	#382	—	2	1	no	—
273	#380	—	94	1	no	—
274	C₄×C₄⋊C₄	—	2	1	no	—
275	C₄×C₄⋊C₄	—	47	2	no	—
276	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
277	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
278	#340	—	47	2	no	—
279	#340	—	47	2	no	—
280	#336	—	47	2	no	—
281	C₄₇	#22811	1	1	yes	characteristic, complemented, Sylow
282	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
283	C₂²×D₄	—	47	1	no	—
284	C₂³×C₄	—	94	1	no	—
285	C₂×SD₁₆	—	47	4	no	—
286	C₂×SD₁₆	—	94	2	no	—
287	C₂×SD₁₆	—	94	2	no	—
288	C₂²×C₈	—	47	1	no	—
289	C₂²×C₈	—	47	1	no	—
290	C₂²×C₈	—	47	2	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	C₄×D₄₇	1	4	yes	—
293	C₄×D₄	—	47	4	no	—
294	C₄×D₄	—	94	2	no	—
295	#117	—	188	4	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	47	1	no	—
300	C₂×C₄⋊C₄	—	47	2	no	—
301	C₂×C₄⋊C₄	—	94	1	no	—
302	C₂×C₄⋊C₄	—	94	1	no	—
303	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
306	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	94	1	no	—
308	C₂×C₂²⋊C₄	—	94	2	no	—
309	C₂×C₂²⋊C₄	—	94	2	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	—	94	2	no	—
313	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
314	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
315	#107	—	94	4	no	—
316	#107	—	188	2	no	—
317	#106	—	47	4	no	—
318	C₄⋊C₈	—	94	2	no	—
319	#103	—	47	4	no	—
320	#103	—	188	2	no	—
321	#102	—	47	4	no	—
322	#102	—	188	2	no	—
323	#97	—	94	4	no	—
324	C₄×C₈	—	47	4	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	#95	—	94	2	no	—
329	#95	C₂²⋊D₄₇	1	2	yes	—
330	C₂⁴	—	94	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
337	C₂×D₄	—	47	2	no	—
338	C₂×D₄	—	94	1	no	—
339	C₂×D₄	—	94	1	no	—
340	C₂×D₄	—	94	1	no	—
341	C₂×D₄	—	94	1	no	—
342	C₂×D₄	—	94	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	94	1	no	—
347	C₂²×C₄	—	94	4	no	—
348	C₂²×C₄	—	94	2	no	—
349	C₂²×C₄	—	188	2	no	—
350	C₂²×C₄	—	188	2	no	—
351	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
352	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
355	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
356	SD₁₆	—	94	8	no	—
357	C₂×C₈	—	47	2	no	—
358	C₂×C₈	—	47	2	no	—
359	C₂×C₈	—	47	2	no	—
360	C₂×C₈	—	47	2	no	—
361	C₂×C₈	—	94	1	no	—
362	C₂×C₈	—	94	1	no	—
363	C₂×C₈	—	94	2	no	—
364	C₂×C₈	—	94	2	no	—
365	C₂×C₈	—	94	2	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	8	1	no	—
374	C₄⋊C₄	—	47	2	no	—
375	C₄⋊C₄	—	94	1	no	—
376	C₄⋊C₄	—	94	2	no	—
377	C₄⋊C₄	—	94	2	no	—
378	C₄⋊C₄	—	376	1	no	—
379	C₄⋊C₄	—	188	2	no	—
380	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
381	C₂²⋊C₄	—	94	4	no	—
382	C₂²⋊C₄	—	376	2	no	—
383	C₂²⋊C₄	—	188	4	no	—
384	C₄²	—	2	4	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	8	2	no	—
388	C₄²	—	188	4	no	—
389	C₄²	C₂×C₄×D₄₇	1	2	yes	—
390	C₄²	#10625350	1	2	yes	—
391	C₂³	—	94	2	no	—
392	C₂³	—	188	1	no	—
393	C₂³	—	188	1	no	—
394	C₂³	—	188	1	no	—
395	C₂³	—	188	1	no	—
396	C₂³	—	188	1	no	—
397	C₂³	—	188	1	no	—
398	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
399	Q₈	—	2	2	no	—
400	Q₈	—	2	2	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	4	1	no	—
403	D₄	—	94	2	no	—
404	D₄	—	94	2	no	—
405	D₄	—	188	1	no	—
406	D₄	—	188	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	94	2	no	—
425	C₂×C₄	—	188	2	no	—
426	C₂×C₄	—	188	2	no	—
427	C₂×C₄	—	188	2	no	—
428	C₂×C₄	—	188	1	no	—
429	C₂×C₄	—	188	1	no	—
430	C₂×C₄	—	188	8	no	—
431	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
432	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
433	C₂×C₄	#13094049	1	2	yes	—
434	C₂×C₄	#13094055	1	2	yes	—
435	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
436	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
437	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
438	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
439	C₂×C₄	#13094070	1	1	yes	characteristic
440	C₂×C₄	#13094071	1	1	yes	characteristic
441	C₈	—	47	4	no	—
442	C₈	—	94	2	no	—
443	C₈	—	188	2	no	—
444	C₂²	—	376	1	no	—
445	C₂²	—	376	1	no	—
446	C₂²	—	376	1	no	—
447	C₂²	—	376	1	no	—
448	C₂²	—	188	2	no	—
449	C₂²	—	188	2	no	—
450	C₂²	—	188	2	no	—
451	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
452	C₂²	#15689772	1	1	yes	characteristic
453	C₂²	#15689792	1	1	yes	characteristic
454	C₂²	C₂×#13094049	1	1	yes	characteristic
455	C₂²	C₂×#13094055	1	1	yes	characteristic
456	C₂²	#15689926	1	1	yes	characteristic
457	C₂²	#15689938	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	8	2	no	—
464	C₄	—	376	2	no	—
465	C₄	—	188	2	no	—
466	C₄	#15689221	1	4	yes	—
467	C₄	#117×D₄₇	1	1	yes	characteristic
468	C₄	#15689603	1	1	yes	characteristic
469	C₄	#15689836	1	1	yes	characteristic
470	C₄	#15689841	1	1	yes	characteristic
471	C₂	—	376	2	no	—
472	C₂	#20246338	1	1	yes	characteristic
473	C₂	C₂×#15689221	1	1	yes	characteristic
474	C₂	#20252261	1	1	yes	characteristic
475	C₂	#20255966	1	1	yes	characteristic
476	C₂	#20256014	1	1	yes	characteristic
477	C₂	#20256415	1	1	yes	characteristic
478	C₂	#20256426	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2355	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2355	D₄₇
hypocenter	C₄₇	#22811
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2355

Complements

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

N	H ≅ G/N	type
4. #20244026	C₂	semidirect
6. #20243547	C₂	semidirect
7. #20243393	C₂	semidirect
9. #20243286	C₂	semidirect
10. #20243257	C₂	semidirect
11. C₄₇×#2355	C₂	semidirect
15. C₄×#10625336	C₄	semidirect
203. C₄₇⋊C₈	#117	semidirect
233. #2355	D₄₇	semidirect
281. C₄₇	#22811	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625336	2
#20246335	2
#20244272	2
#20244026	2
#20244008	2
#20243547	2
#20243393	2
#20243385	2
#20243286	2
#20243257	2
C₄₇×#2355	2
#22811	47