Subgroups — #26266137

Order 12032.

894 conjugacy classes of subgroups.

The subgroup lattice has 496 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	#20248337	C₂	1	1	yes	maximal, characteristic
4	#20244796	C₂	1	2	yes	maximal, complemented
5	#20244703	C₂	1	2	yes	maximal
6	#20244340	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243743	C₂	1	2	yes	maximal
9	#20243393	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×#13094004	—	2	1	no	—
15	C₂×#13094004	—	2	1	no	—
16	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
17	#15689473	—	2	4	no	—
18	#15689325	—	2	4	no	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
21	C₂×#13093948	C₂²	1	2	yes	—
22	C₂×#13093948	C₂²	1	2	yes	—
23	C₂×#13093948	C₂²	1	2	yes	—
24	C₂×#13093944	C₂²	1	1	yes	characteristic
25	C₂×#13093944	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	#15689060	—	2	2	no	—
28	#15689025	C₂²	1	2	yes	—
29	#15688993	C₂²	1	2	yes	—
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	#13094004	—	4	4	no	—
55	#13094004	—	4	4	no	—
56	C₄×D₁₈₈	—	2	2	no	—
57	C₄×D₁₈₈	—	2	2	no	—
58	C₂×C₄⋊Dic₄₇	—	2	2	no	—
59	C₂×C₄⋊Dic₄₇	—	2	2	no	—
60	C₂×C₄⋊Dic₄₇	—	2	1	no	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
63	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
65	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
66	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
68	#13093948	—	2	4	no	—
69	#13093948	—	2	4	no	—
70	#13093948	—	2	4	no	—
71	#13093944	—	2	2	no	—
72	#13093944	—	2	2	no	—
73	C₄×C₄₇⋊C₈	—	2	2	no	—
74	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
75	C₄⋊Q₈×C₄₇	—	2	2	no	—
76	C₄⋊Q₈×C₄₇	D₄	1	4	yes	—
77	C₄×Q₈×C₄₇	—	2	4	no	—
78	C₄×Q₈×C₄₇	—	4	2	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	—	2	2	no	—
87	C₂×C₄²×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	1	no	—
92	#95×C₄₇	—	2	2	no	—
93	#95×C₄₇	D₄	1	2	yes	—
94	C₂³×D₄₇	—	2	1	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	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	2	2	no	—
110	C₂²×Dic₄₇	—	2	1	no	—
111	C₂×D₁₈₈	—	2	1	no	—
112	C₂×D₁₈₈	—	2	1	no	—
113	C₂×D₁₈₈	—	2	1	no	—
114	C₂×D₁₈₈	—	2	1	no	—
115	C₂×D₁₈₈	—	2	1	no	—
116	C₂×D₁₈₈	#41	1	2	yes	—
117	C₂×C₄×D₄₇	—	4	2	no	—
118	C₂×C₄×D₄₇	—	4	2	no	—
119	C₂×C₄×D₄₇	—	4	2	no	—
120	C₂×Dic₉₄	—	4	2	no	—
121	C₂×Dic₉₄	—	4	2	no	—
122	C₂×Dic₉₄	—	4	2	no	—
123	C₄⋊C₄×C₄₇	—	2	4	no	—
124	C₄⋊C₄×C₄₇	—	2	4	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	4	4	no	—
130	C₄⋊C₄×C₄₇	SD₁₆	1	4	yes	complemented
131	C₄⋊C₄×C₄₇	#41	1	2	yes	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	—	4	4	no	—
135	C₄²×C₄₇	—	4	2	no	—
136	C₄²×C₄₇	C₂×D₄	1	2	yes	—
137	C₄²×C₄₇	#41	1	2	yes	—
138	#10625336	—	4	8	no	—
139	(C₂×D₄₇)⋊C₄	—	4	4	no	—
140	(C₂×D₄₇)⋊C₄	—	4	2	no	—
141	(C₂×D₄₇)⋊C₄	—	4	4	no	—
142	C₄⋊Dic₄₇	—	2	1	no	—
143	C₄⋊Dic₄₇	—	2	2	no	—
144	C₄⋊Dic₄₇	—	2	1	no	—
145	C₄⋊Dic₄₇	—	2	2	no	—
146	C₄⋊Dic₄₇	—	4	4	no	—
147	C₄⋊Dic₄₇	—	4	2	no	—
148	C₄⋊Dic₄₇	—	4	4	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	1	no	—
158	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	C₂²×D₄₇	—	2	2	no	—
160	C₂²×D₄₇	—	4	1	no	—
161	C₂²×D₄₇	—	4	1	no	—
162	C₂²×D₄₇	—	4	1	no	—
163	C₂²×D₄₇	—	4	1	no	—
164	C₂²×D₄₇	—	4	1	no	—
165	C₂²×D₄₇	—	4	1	no	—
166	Q₈×C₄₇	—	2	4	no	—
167	Q₈×C₄₇	—	2	4	no	—
168	Q₈×C₄₇	—	4	2	no	—
169	Q₈×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	#121	1	2	yes	—
187	C₂×C₄×C₄₇	#121	1	2	yes	—
188	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
189	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
190	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
191	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
197	C₂×Dic₄₇	—	4	2	no	—
198	C₂×Dic₄₇	—	4	1	no	—
199	C₂×Dic₄₇	—	4	1	no	—
200	C₂×Dic₄₇	—	4	2	no	—
201	C₂×Dic₄₇	—	4	1	no	—
202	C₂×Dic₄₇	—	4	2	no	—
203	D₁₈₈	—	2	2	no	—
204	D₁₈₈	—	2	2	no	—
205	D₁₈₈	—	4	1	no	—
206	D₁₈₈	—	4	1	no	—
207	C₄×D₄₇	—	8	4	no	—
208	Dic₉₄	—	8	4	no	—
209	C₄₇⋊C₈	—	4	1	no	—
210	C₄₇⋊C₈	—	4	2	no	—
211	C₄₇⋊C₈	—	4	1	no	—
212	#25320	—	47	1	no	maximal, Sylow
213	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
214	C₂²×C₄₇	#546	1	1	yes	characteristic
215	C₂²×C₄₇	#548	1	1	yes	characteristic
216	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
217	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂²×C₄₇	#578	1	1	yes	characteristic
219	C₂²×C₄₇	#578	1	1	yes	characteristic
220	C₂×D₄₇	—	4	2	no	—
221	C₂×D₄₇	—	4	2	no	—
222	C₂×D₄₇	—	4	2	no	—
223	C₂×D₄₇	—	8	1	no	—
224	C₂×D₄₇	—	8	1	no	—
225	C₂×D₄₇	—	8	1	no	—
226	C₂×D₄₇	—	8	1	no	—
227	C₄×C₄₇	—	2	4	no	—
228	C₄×C₄₇	—	2	2	no	—
229	C₄×C₄₇	—	4	2	no	—
230	C₄×C₄₇	—	4	2	no	—
231	C₄×C₄₇	—	4	4	no	—
232	C₄×C₄₇	—	8	1	no	—
233	C₄×C₄₇	#460	1	4	yes	—
234	C₄×C₄₇	#529	1	1	yes	characteristic
235	C₄×C₄₇	#542	1	1	yes	characteristic
236	C₄×C₄₇	#546	1	1	yes	characteristic
237	C₄×C₄₇	#547	1	1	yes	characteristic
238	Dic₄₇	—	8	2	no	—
239	Dic₄₇	—	8	1	no	—
240	C₂×#487	—	47	1	no	—
241	C₂×#461	—	47	1	no	—
242	#2542	—	47	1	no	—
243	#2365	D₄₇	1	1	yes	characteristic, complemented
244	#2072	—	47	2	no	—
245	#2055	—	47	2	no	—
246	#1988	—	47	1	no	—
247	#1939	—	47	1	no	—
248	#1880	—	47	2	no	—
249	#1803	—	47	2	no	—
250	C₄×#102	—	47	1	no	—
251	C₂×C₄₇	#2427	1	1	yes	characteristic
252	C₂×C₄₇	C₂×#460	1	1	yes	characteristic
253	C₂×C₄₇	#3044	1	1	yes	characteristic
254	C₂×C₄₇	#3298	1	1	yes	characteristic
255	C₂×C₄₇	#3330	1	1	yes	characteristic
256	C₂×C₄₇	#3359	1	1	yes	characteristic
257	C₂×C₄₇	#3367	1	1	yes	characteristic
258	D₄₇	—	8	2	no	—
259	C₂²×SD₁₆	—	47	2	no	—
260	C₂×C₄⋊Q₈	—	47	1	no	—
261	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
262	C₂×C₂²⋊Q₈	—	94	1	no	—
263	C₂×C₂²⋊Q₈	—	94	1	no	—
264	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
265	C₂×C₄×D₄	—	47	1	no	—
266	#487	—	94	4	no	—
267	#461	—	94	4	no	—
268	C₂×C₄⋊C₈	—	47	1	no	—
269	C₂×C₄⋊C₈	—	47	2	no	—
270	C₂×#103	—	47	2	no	—
271	C₂×#103	—	47	2	no	—
272	C₂×#103	—	47	2	no	—
273	C₂×#102	—	47	1	no	—
274	C₂×#102	—	47	1	no	—
275	C₂×C₄×C₈	—	47	1	no	—
276	#399	—	94	2	no	—
277	#391	C₂×D₄₇	1	2	yes	—
278	#390	—	47	2	no	—
279	#389	—	2	1	no	—
280	#387	—	2	2	no	—
281	#384	—	47	2	no	—
282	C₄×C₄⋊C₄	—	2	1	no	—
283	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
284	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
285	#340	—	47	2	no	—
286	#340	—	47	1	no	—
287	#340	—	47	2	no	—
288	#340	—	47	1	no	—
289	#336	—	47	2	no	—
290	C₄₇	#25320	1	1	yes	characteristic, complemented, Sylow
291	C₂²×Q₈	—	94	1	no	—
292	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
293	C₂²×D₄	—	47	1	no	—
294	C₂³×C₄	—	94	1	no	—
295	C₂×SD₁₆	—	94	4	no	—
296	C₂×SD₁₆	—	94	4	no	—
297	C₂×SD₁₆	—	188	2	no	—
298	C₂²×C₈	—	47	2	no	—
299	C₂²×C₈	—	47	1	no	—
300	C₂²×C₈	—	47	1	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	94	2	no	—
303	C₄⋊Q₈	—	94	2	no	—
304	C₄⋊Q₈	D₁₈₈	1	4	yes	—
305	C₂²⋊Q₈	—	188	4	no	—
306	C₂²⋊Q₈	—	188	4	no	—
307	C₄×Q₈	—	2	4	no	—
308	C₄×Q₈	—	4	2	no	—
309	C₄×D₄	—	94	2	no	—
310	C₄×D₄	—	94	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	47	1	no	—
315	C₂×C₄⋊C₄	—	47	2	no	—
316	C₂×C₄⋊C₄	—	94	2	no	—
317	C₂×C₄⋊C₄	—	94	2	no	—
318	C₂×C₄⋊C₄	—	94	1	no	—
319	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	94	1	no	—
324	C₂×C₂²⋊C₄	—	94	2	no	—
325	C₂×C₂²⋊C₄	—	94	2	no	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
329	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
330	C₄⋊C₈	—	94	2	no	—
331	C₄⋊C₈	—	188	2	no	—
332	#103	—	94	4	no	—
333	#103	—	94	4	no	—
334	#103	—	94	4	no	—
335	#102	—	94	2	no	—
336	#102	—	94	2	no	—
337	C₄×C₈	—	94	2	no	—
338	#95	—	2	2	no	—
339	#95	—	2	1	no	—
340	#95	—	2	2	no	—
341	#95	C₂²⋊D₄₇	1	2	yes	—
342	C₂⁴	—	94	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	188	2	no	—
349	C₂×Q₈	—	188	2	no	—
350	C₂×Q₈	—	188	2	no	—
351	C₂×Q₈	C₂×D₁₈₈	1	4	yes	—
352	C₂×D₄	—	47	2	no	—
353	C₂×D₄	—	94	1	no	—
354	C₂×D₄	—	94	1	no	—
355	C₂×D₄	—	94	1	no	—
356	C₂×D₄	—	94	1	no	—
357	C₂×D₄	—	94	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	94	2	no	—
362	C₂²×C₄	—	94	1	no	—
363	C₂²×C₄	—	188	2	no	—
364	C₂²×C₄	—	188	2	no	—
365	C₂²×C₄	—	188	2	no	—
366	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
367	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
369	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
370	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
371	SD₁₆	—	188	8	no	—
372	C₂×C₈	—	94	1	no	—
373	C₂×C₈	—	94	1	no	—
374	C₂×C₈	—	94	2	no	—
375	C₂×C₈	—	94	1	no	—
376	C₂×C₈	—	94	2	no	—
377	C₂×C₈	—	94	1	no	—
378	C₂×C₈	—	94	1	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	94	1	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	94	1	no	—
389	C₄⋊C₄	—	94	2	no	—
390	C₄⋊C₄	—	94	1	no	—
391	C₄⋊C₄	—	94	2	no	—
392	C₄⋊C₄	—	188	4	no	—
393	C₄⋊C₄	—	188	2	no	—
394	C₄⋊C₄	—	188	4	no	—
395	C₄⋊C₄	#10625336	1	4	yes	complemented
396	C₄⋊C₄	#10625352	1	2	yes	—
397	C₂²⋊C₄	—	188	4	no	—
398	C₂²⋊C₄	—	188	2	no	—
399	C₂²⋊C₄	—	188	4	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	4	4	no	—
403	C₄²	—	4	2	no	—
404	C₄²	C₂×D₁₈₈	1	2	yes	—
405	C₄²	#10625350	1	2	yes	—
406	C₂³	—	94	2	no	—
407	C₂³	—	188	1	no	—
408	C₂³	—	188	1	no	—
409	C₂³	—	188	1	no	—
410	C₂³	—	188	1	no	—
411	C₂³	—	188	1	no	—
412	C₂³	—	188	1	no	—
413	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
414	Q₈	—	2	4	no	—
415	Q₈	—	2	4	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	376	4	no	—
419	D₄	—	94	2	no	—
420	D₄	—	94	2	no	—
421	D₄	—	188	1	no	—
422	D₄	—	188	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	376	4	no	—
440	C₂×C₄	—	188	1	no	—
441	C₂×C₄	—	188	2	no	—
442	C₂×C₄	—	188	2	no	—
443	C₂×C₄	—	188	1	no	—
444	C₂×C₄	—	188	2	no	—
445	C₂×C₄	—	188	1	no	—
446	C₂×C₄	#13093998	1	2	yes	—
447	C₂×C₄	#13093998	1	2	yes	—
448	C₂×C₄	C₂×#10625336	1	4	yes	—
449	C₂×C₄	C₂×#10625336	1	2	yes	—
450	C₂×C₄	#13094049	1	2	yes	—
451	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
452	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
454	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
455	C₂×C₄	#13094069	1	1	yes	characteristic
456	C₂×C₄	#13094071	1	1	yes	characteristic
457	C₈	—	188	1	no	—
458	C₈	—	188	2	no	—
459	C₈	—	188	1	no	—
460	C₂²	—	376	1	no	—
461	C₂²	—	376	1	no	—
462	C₂²	—	376	1	no	—
463	C₂²	—	376	1	no	—
464	C₂²	—	188	2	no	—
465	C₂²	—	188	2	no	—
466	C₂²	—	188	2	no	—
467	C₂²	C₂×#13093998	1	1	yes	characteristic
468	C₂²	#15689767	1	1	yes	characteristic
469	C₂²	#15689780	1	1	yes	characteristic
470	C₂²	C₂²×#10625336	1	1	yes	characteristic
471	C₂²	C₂×#13094049	1	1	yes	characteristic
472	C₂²	#15689938	1	1	yes	characteristic
473	C₂²	#15689938	1	1	yes	characteristic
474	C₄	—	2	4	no	—
475	C₄	—	2	2	no	—
476	C₄	—	4	4	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	1	no	—
480	C₄	—	376	1	no	—
481	C₄	—	376	2	no	—
482	C₄	#15689323	1	4	yes	—
483	C₄	#15689655	1	1	yes	characteristic
484	C₄	#15689738	1	1	yes	characteristic
485	C₄	#15689768	1	1	yes	characteristic
486	C₄	#15689777	1	1	yes	characteristic
487	C₂	—	376	2	no	—
488	C₂	#20246959	1	1	yes	characteristic
489	C₂	C₂×#15689323	1	1	yes	characteristic
490	C₂	#20252918	1	1	yes	characteristic
491	C₂	#20255253	1	1	yes	characteristic
492	C₂	#20255693	1	1	yes	characteristic
493	C₂	#20256026	1	1	yes	characteristic
494	C₂	#20256102	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	#25320
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. #20244796	C₂	semidirect
6. #20244340	C₂	semidirect
7. #20244107	C₂	semidirect
9. #20243393	C₂	semidirect
11. C₄₇×#2365	C₂	semidirect
130. C₄⋊C₄×C₄₇	SD₁₆	semidirect
243. #2365	D₄₇	semidirect
290. C₄₇	#25320	semidirect
395. C₄⋊C₄	#10625336	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
#20248337	2
#20244796	2
#20244703	2
#20244340	2
#20244107	2
#20243743	2
#20243393	2
C₄×#13093944	2
C₄₇×#2365	2
#25320	47