Subgroups — #26266126

Order 12032.

838 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689473	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689325	C₂	1	1	yes	maximal, characteristic
3	#20248557	C₂	1	1	yes	maximal, characteristic
4	#20244806	C₂	1	2	yes	maximal, complemented
5	#20244703	C₂	1	2	yes	maximal
6	#20244336	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243743	C₂	1	2	yes	maximal
9	#20243403	C₂	1	2	yes	maximal, complemented
10	C₄×#13093944	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625336	C₂²	1	2	yes	—
13	C₂×#13094024	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	#15689473	—	2	4	no	—
16	#15689325	—	2	4	no	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×#13093948	C₂²	1	2	yes	—
20	C₂×#13093948	C₂²	1	2	yes	—
21	C₂×#13093948	C₂²	1	2	yes	—
22	C₂×#13093944	C₂²	1	1	yes	characteristic
23	C₂×#13093944	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15689036	—	2	2	no	—
26	#15689025	C₂²	1	2	yes	—
27	#15688989	C₂²	1	2	yes	—
28	#15688980	—	2	1	no	—
29	#15688980	—	2	1	no	—
30	#15688885	C₂²	1	1	yes	characteristic
31	#15688885	C₂²	1	1	yes	characteristic
32	#15688885	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688878	C₂²	1	2	yes	—
35	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
37	C₄₇×#391	C₂²	1	2	yes	—
38	C₄₇×#389	—	2	1	no	—
39	C₄₇×#387	—	2	2	no	—
40	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×Dic₉₄	—	2	1	no	—
44	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	—	2	1	no	—
46	C₂×#10625336	—	2	4	no	—
47	C₂×#10625336	—	2	4	no	—
48	C₂×#10625336	—	4	2	no	—
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
52	#13094024	—	2	2	no	—
53	#13094024	—	2	2	no	—
54	C₄×D₁₈₈	—	2	2	no	—
55	C₄×D₁₈₈	—	2	2	no	—
56	C₂×C₄⋊Dic₄₇	—	2	1	no	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
59	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
60	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
61	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
62	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
63	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
64	#13093948	—	2	4	no	—
65	#13093948	—	2	4	no	—
66	#13093948	—	2	4	no	—
67	#13093944	—	2	2	no	—
68	#13093944	—	2	2	no	—
69	C₄×C₄₇⋊C₈	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
73	C₄⋊Q₈×C₄₇	—	2	2	no	—
74	C₄⋊Q₈×C₄₇	D₄	1	4	yes	—
75	C₄×Q₈×C₄₇	—	2	4	no	—
76	C₄×Q₈×C₄₇	—	4	2	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
80	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	—	2	2	no	—
85	C₂×C₄²×C₄₇	—	2	1	no	—
86	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	#95×C₄₇	—	2	2	no	—
89	#95×C₄₇	—	2	1	no	—
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	D₄	1	2	yes	—
92	C₂³×D₄₇	—	2	1	no	—
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	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₂²×Dic₄₇	—	2	1	no	—
108	C₂²×Dic₄₇	—	2	2	no	—
109	C₂×D₁₈₈	—	2	1	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	—	2	1	no	—
112	C₂×D₁₈₈	—	2	1	no	—
113	C₂×D₁₈₈	—	2	1	no	—
114	C₂×D₁₈₈	#41	1	2	yes	—
115	C₂×C₄×D₄₇	—	4	2	no	—
116	C₂×C₄×D₄₇	—	4	2	no	—
117	C₂×C₄×D₄₇	—	4	2	no	—
118	C₂×Dic₉₄	—	4	2	no	—
119	C₂×Dic₉₄	—	8	1	no	—
120	C₂×Dic₉₄	—	8	1	no	—
121	C₄⋊C₄×C₄₇	—	2	4	no	—
122	C₄⋊C₄×C₄₇	—	2	4	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	4	4	no	—
129	C₄⋊C₄×C₄₇	#41	1	2	yes	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	4	4	no	—
133	C₄²×C₄₇	—	4	2	no	—
134	C₄²×C₄₇	C₂×D₄	1	2	yes	—
135	C₄²×C₄₇	#41	1	2	yes	—
136	#10625336	—	4	8	no	—
137	(C₂×D₄₇)⋊C₄	—	4	2	no	—
138	(C₂×D₄₇)⋊C₄	—	8	2	no	—
139	(C₂×D₄₇)⋊C₄	—	8	2	no	—
140	C₄⋊Dic₄₇	—	2	1	no	—
141	C₄⋊Dic₄₇	—	2	2	no	—
142	C₄⋊Dic₄₇	—	2	1	no	—
143	C₄⋊Dic₄₇	—	2	2	no	—
144	C₄⋊Dic₄₇	—	4	2	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂²×D₄₇	—	2	2	no	—
156	C₂²×D₄₇	—	4	1	no	—
157	C₂²×D₄₇	—	4	1	no	—
158	C₂²×D₄₇	—	4	1	no	—
159	C₂²×D₄₇	—	4	1	no	—
160	C₂²×D₄₇	—	4	1	no	—
161	C₂²×D₄₇	—	4	1	no	—
162	Q₈×C₄₇	—	2	4	no	—
163	Q₈×C₄₇	—	2	4	no	—
164	Q₈×C₄₇	—	4	2	no	—
165	Q₈×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	4	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	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	#121	1	2	yes	—
184	C₂×C₄×C₄₇	#121	1	2	yes	—
185	C₂×C₄×C₄₇	#135	1	2	yes	—
186	C₂×C₄×C₄₇	#137	1	2	yes	—
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
193	C₂×Dic₄₇	—	4	2	no	—
194	C₂×Dic₄₇	—	4	1	no	—
195	C₂×Dic₄₇	—	4	1	no	—
196	C₂×Dic₄₇	—	4	1	no	—
197	C₂×Dic₄₇	—	4	2	no	—
198	C₂×Dic₄₇	—	4	2	no	—
199	D₁₈₈	—	2	2	no	—
200	D₁₈₈	—	2	2	no	—
201	D₁₈₈	—	4	1	no	—
202	D₁₈₈	—	4	1	no	—
203	C₄×D₄₇	—	8	4	no	—
204	Dic₉₄	—	8	4	no	—
205	C₄₇⋊C₈	—	4	1	no	—
206	C₄₇⋊C₈	—	4	2	no	—
207	C₄₇⋊C₈	—	4	1	no	—
208	#25319	—	47	1	no	maximal, Sylow
209	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
210	C₂²×C₄₇	#546	1	1	yes	characteristic
211	C₂²×C₄₇	#548	1	1	yes	characteristic
212	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
214	C₂²×C₄₇	#577	1	1	yes	characteristic
215	C₂²×C₄₇	#577	1	1	yes	characteristic
216	C₂×D₄₇	—	4	2	no	—
217	C₂×D₄₇	—	4	2	no	—
218	C₂×D₄₇	—	4	2	no	—
219	C₂×D₄₇	—	8	1	no	—
220	C₂×D₄₇	—	8	1	no	—
221	C₂×D₄₇	—	8	1	no	—
222	C₂×D₄₇	—	8	1	no	—
223	C₄×C₄₇	—	2	2	no	—
224	C₄×C₄₇	—	4	2	no	—
225	C₄×C₄₇	—	4	4	no	—
226	C₄×C₄₇	—	4	2	no	—
227	C₄×C₄₇	—	4	2	no	—
228	C₄×C₄₇	—	8	1	no	—
229	C₄×C₄₇	#464	1	4	yes	—
230	C₄×C₄₇	#529	1	1	yes	characteristic
231	C₄×C₄₇	#542	1	1	yes	characteristic
232	C₄×C₄₇	#546	1	1	yes	characteristic
233	C₄×C₄₇	#547	1	1	yes	characteristic
234	Dic₄₇	—	8	1	no	—
235	Dic₄₇	—	8	2	no	—
236	C₂×#487	—	47	1	no	—
237	C₂×#461	—	47	1	no	—
238	#2563	—	47	1	no	—
239	#2365	D₄₇	1	1	yes	characteristic, complemented
240	#2074	—	47	2	no	—
241	#2055	—	47	2	no	—
242	#1987	—	47	1	no	—
243	#1939	—	47	1	no	—
244	#1880	—	47	2	no	—
245	#1805	—	47	2	no	—
246	C₄×#102	—	47	1	no	—
247	C₂×C₄₇	#2427	1	1	yes	characteristic
248	C₂×C₄₇	C₂×#464	1	1	yes	characteristic
249	C₂×C₄₇	#3043	1	1	yes	characteristic
250	C₂×C₄₇	#3303	1	1	yes	characteristic
251	C₂×C₄₇	#3329	1	1	yes	characteristic
252	C₂×C₄₇	#3360	1	1	yes	characteristic
253	C₂×C₄₇	#3372	1	1	yes	characteristic
254	D₄₇	—	8	2	no	—
255	C₂²×SD₁₆	—	47	2	no	—
256	C₂×C₄⋊Q₈	—	47	1	no	—
257	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
258	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
259	C₂×C₄×D₄	—	47	1	no	—
260	#487	—	94	4	no	—
261	#461	—	94	4	no	—
262	C₂×C₄⋊C₈	—	47	1	no	—
263	C₂×C₄⋊C₈	—	47	2	no	—
264	C₂×#103	—	47	2	no	—
265	C₂×#103	—	47	2	no	—
266	C₂×#103	—	47	2	no	—
267	C₂×#102	—	47	1	no	—
268	C₂×#102	—	47	1	no	—
269	C₂×C₄×C₈	—	47	1	no	—
270	#393	—	94	2	no	—
271	#391	C₂×D₄₇	1	2	yes	—
272	#390	—	47	2	no	—
273	#389	—	2	1	no	—
274	#387	—	2	2	no	—
275	#382	—	47	2	no	—
276	#380	—	94	1	no	—
277	#380	—	94	1	no	—
278	C₄×C₄⋊C₄	—	2	1	no	—
279	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
280	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
281	#340	—	47	2	no	—
282	#340	—	47	1	no	—
283	#340	—	47	2	no	—
284	#340	—	47	1	no	—
285	#336	—	47	2	no	—
286	C₄₇	#25319	1	1	yes	characteristic, complemented, Sylow
287	C₂²×Q₈	—	94	1	no	—
288	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
289	C₂²×D₄	—	47	1	no	—
290	C₂³×C₄	—	94	1	no	—
291	C₂×SD₁₆	—	94	4	no	—
292	C₂×SD₁₆	—	94	4	no	—
293	C₂×SD₁₆	—	188	2	no	—
294	C₂²×C₈	—	47	2	no	—
295	C₂²×C₈	—	47	1	no	—
296	C₂²×C₈	—	47	1	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₄⋊Q₈	—	94	2	no	—
299	C₄⋊Q₈	—	94	2	no	—
300	C₄⋊Q₈	D₁₈₈	1	4	yes	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	—	4	2	no	—
303	C₄×D₄	—	94	2	no	—
304	C₄×D₄	—	94	2	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	47	1	no	—
309	C₂×C₄⋊C₄	—	47	2	no	—
310	C₂×C₄⋊C₄	—	94	1	no	—
311	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	—	94	2	no	—
316	C₂×C₂²⋊C₄	—	94	2	no	—
317	C₂×C₂²⋊C₄	—	94	1	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
321	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
322	C₄⋊C₈	—	94	2	no	—
323	C₄⋊C₈	—	188	2	no	—
324	#103	—	94	4	no	—
325	#103	—	94	4	no	—
326	#103	—	94	4	no	—
327	#102	—	94	2	no	—
328	#102	—	94	2	no	—
329	C₄×C₈	—	94	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	1	no	—
332	#95	—	2	2	no	—
333	#95	—	94	2	no	—
334	#95	—	94	2	no	—
335	#95	C₂²⋊D₄₇	1	2	yes	—
336	C₂⁴	—	94	1	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	376	1	no	—
343	C₂×Q₈	—	376	1	no	—
344	C₂×Q₈	—	188	2	no	—
345	C₂×Q₈	C₂×D₁₈₈	1	4	yes	—
346	C₂×D₄	—	47	2	no	—
347	C₂×D₄	—	94	1	no	—
348	C₂×D₄	—	94	1	no	—
349	C₂×D₄	—	94	1	no	—
350	C₂×D₄	—	94	1	no	—
351	C₂×D₄	—	94	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	94	1	no	—
356	C₂²×C₄	—	94	2	no	—
357	C₂²×C₄	—	188	2	no	—
358	C₂²×C₄	—	188	2	no	—
359	C₂²×C₄	—	188	2	no	—
360	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
361	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
362	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
364	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
365	SD₁₆	—	188	8	no	—
366	C₂×C₈	—	94	1	no	—
367	C₂×C₈	—	94	1	no	—
368	C₂×C₈	—	94	2	no	—
369	C₂×C₈	—	94	1	no	—
370	C₂×C₈	—	94	2	no	—
371	C₂×C₈	—	94	1	no	—
372	C₂×C₈	—	94	1	no	—
373	C₂×C₈	—	94	2	no	—
374	C₂×C₈	—	94	1	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	94	1	no	—
384	C₄⋊C₄	—	94	2	no	—
385	C₄⋊C₄	—	94	1	no	—
386	C₄⋊C₄	—	94	2	no	—
387	C₄⋊C₄	—	188	2	no	—
388	C₄⋊C₄	#10625352	1	2	yes	—
389	C₂²⋊C₄	—	376	2	no	—
390	C₂²⋊C₄	—	376	2	no	—
391	C₂²⋊C₄	—	188	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	4	4	no	—
395	C₄²	—	4	2	no	—
396	C₄²	C₂×D₁₈₈	1	2	yes	—
397	C₄²	#10625350	1	2	yes	—
398	C₂³	—	94	2	no	—
399	C₂³	—	188	1	no	—
400	C₂³	—	188	1	no	—
401	C₂³	—	188	1	no	—
402	C₂³	—	188	1	no	—
403	C₂³	—	188	1	no	—
404	C₂³	—	188	1	no	—
405	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	376	4	no	—
411	D₄	—	94	2	no	—
412	D₄	—	94	2	no	—
413	D₄	—	188	1	no	—
414	D₄	—	188	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	376	4	no	—
433	C₂×C₄	—	188	1	no	—
434	C₂×C₄	—	188	2	no	—
435	C₂×C₄	—	188	1	no	—
436	C₂×C₄	—	188	1	no	—
437	C₂×C₄	—	188	2	no	—
438	C₂×C₄	—	188	2	no	—
439	C₂×C₄	#13093998	1	2	yes	—
440	C₂×C₄	#13093998	1	2	yes	—
441	C₂×C₄	#13094044	1	2	yes	—
442	C₂×C₄	#13094055	1	2	yes	—
443	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
444	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
445	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
446	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
447	C₂×C₄	#13094069	1	1	yes	characteristic
448	C₂×C₄	#13094071	1	1	yes	characteristic
449	C₈	—	188	1	no	—
450	C₈	—	188	2	no	—
451	C₈	—	188	1	no	—
452	C₂²	—	376	1	no	—
453	C₂²	—	376	1	no	—
454	C₂²	—	376	1	no	—
455	C₂²	—	376	1	no	—
456	C₂²	—	188	2	no	—
457	C₂²	—	188	2	no	—
458	C₂²	—	188	2	no	—
459	C₂²	C₂×#13093998	1	1	yes	characteristic
460	C₂²	#15689767	1	1	yes	characteristic
461	C₂²	#15689780	1	1	yes	characteristic
462	C₂²	C₂×#13094044	1	1	yes	characteristic
463	C₂²	C₂×#13094055	1	1	yes	characteristic
464	C₂²	#15689931	1	1	yes	characteristic
465	C₂²	#15689931	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	1	no	—
472	C₄	—	376	1	no	—
473	C₄	—	376	2	no	—
474	C₄	#15689345	1	4	yes	—
475	C₄	#15689655	1	1	yes	characteristic
476	C₄	#15689738	1	1	yes	characteristic
477	C₄	#15689768	1	1	yes	characteristic
478	C₄	#15689777	1	1	yes	characteristic
479	C₂	—	376	2	no	—
480	C₂	#20246959	1	1	yes	characteristic
481	C₂	C₂×#15689345	1	1	yes	characteristic
482	C₂	#20252909	1	1	yes	characteristic
483	C₂	#20255316	1	1	yes	characteristic
484	C₂	#20255682	1	1	yes	characteristic
485	C₂	#20256033	1	1	yes	characteristic
486	C₂	#20256165	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2365	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
hypercenter	#2365	D₄₇
hypocenter	C₄₇	#25319
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2365

Complements

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

N	H ≅ G/N	type
1. C₂×#15689473	C₂	semidirect
4. #20244806	C₂	semidirect
6. #20244336	C₂	semidirect
7. #20244107	C₂	semidirect
9. #20243403	C₂	semidirect
11. C₄₇×#2365	C₂	semidirect
239. #2365	D₄₇	semidirect
286. C₄₇	#25319	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689473	2
C₂×#15689325	2
#20248557	2
#20244806	2
#20244703	2
#20244336	2
#20244107	2
#20243743	2
#20243403	2
C₄×#13093944	2
C₄₇×#2365	2
#25319	47