Subgroups — #26228322

Order 12032.

848 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689410	C₂	1	1	yes	maximal, characteristic
2	#20245852	C₂	1	1	yes	maximal, characteristic
3	#20244337	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244149	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244113	C₂	1	2	yes	maximal, complemented
6	#20244070	C₂	1	2	yes	maximal
7	#20244015	C₂	1	2	yes	maximal
8	#20243966	C₂	1	2	yes	maximal, complemented
9	#20243385	C₂	1	1	yes	maximal, characteristic
10	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
13	C₂×#13093981	—	2	1	no	—
14	#15689410	C₄	1	8	yes	complemented
15	C₂×#13093955	C₂²	1	2	yes	—
16	C₂×#13093955	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#13093944	C₂²	1	2	yes	—
20	C₂×#13093944	C₂²	1	2	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
22	#15689025	C₂²	1	1	yes	characteristic
23	#15689025	C₂²	1	1	yes	characteristic
24	#15689021	C₂²	1	1	yes	characteristic
25	#15689021	C₂²	1	1	yes	characteristic
26	#15689014	—	2	1	no	—
27	#15689014	—	2	1	no	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
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	—	2	1	no	—
37	C₄₇×#391	—	2	1	no	—
38	C₄₇×#389	—	2	1	no	—
39	C₄₇×#389	C₂²	1	2	yes	—
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
43	C₄³×C₄₇	C₂²	1	1	yes	characteristic
44	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	—	2	1	no	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₄×D₁₈₈	—	2	2	no	—
49	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
50	#13093981	—	4	4	no	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
54	C₂×Dic₄₇⋊C₄	—	2	1	no	—
55	C₂×Dic₄₇⋊C₄	—	2	1	no	—
56	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
57	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
59	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
60	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	#13093955	—	4	2	no	—
63	#13093955	C₂×C₄	1	8	yes	—
64	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
66	#13093944	—	4	2	no	—
67	#13093944	C₂×C₄	1	8	yes	—
68	C₄×C₄₇⋊C₈	—	4	2	no	—
69	C₄₇⋊#95	—	2	1	no	—
70	C₄₇⋊#95	—	2	1	no	—
71	C₄₇⋊#95	—	2	1	no	—
72	C₂²×Q₈×C₄₇	—	2	1	no	—
73	C₄⋊Q₈×C₄₇	—	2	2	no	—
74	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
75	C₄×Q₈×C₄₇	—	4	4	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₇	—	2	2	no	—
83	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	2	no	—
92	C₂³×D₄₇	—	2	1	no	—
93	C₂×Q₈×C₄₇	—	2	4	no	—
94	C₂×Q₈×C₄₇	—	4	2	no	—
95	C₂×Q₈×C₄₇	—	4	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	1	no	—
107	C₂²×Dic₄₇	—	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	—	2	1	no	—
113	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₄₇	—	2	4	no	—
115	C₂×C₄×D₄₇	—	4	2	no	—
116	C₂×C₄×D₄₇	—	4	2	no	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	4	2	no	—
122	C₄⋊C₄×C₄₇	—	4	2	no	—
123	C₄⋊C₄×C₄₇	—	4	4	no	—
124	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	2	1	no	—
128	C₄²×C₄₇	—	2	1	no	—
129	C₄²×C₄₇	—	2	1	no	—
130	C₄²×C₄₇	—	2	1	no	—
131	C₄²×C₄₇	—	4	1	no	—
132	C₄²×C₄₇	—	4	4	no	—
133	C₄²×C₄₇	SD₁₆	1	4	yes	—
134	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
135	C₄²×C₄₇	#41	1	2	yes	—
136	(C₂×D₄₇)⋊C₄	—	2	4	no	—
137	(C₂×D₄₇)⋊C₄	—	4	2	no	—
138	(C₂×D₄₇)⋊C₄	—	4	2	no	—
139	(C₂×D₄₇)⋊C₄	—	4	2	no	—
140	(C₂×D₄₇)⋊C₄	—	4	2	no	—
141	C₄⋊Dic₄₇	—	2	1	no	—
142	C₄⋊Dic₄₇	—	2	1	no	—
143	C₄⋊Dic₄₇	—	2	1	no	—
144	C₄⋊Dic₄₇	—	2	1	no	—
145	C₄⋊Dic₄₇	—	2	1	no	—
146	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
147	Dic₄₇⋊C₄	—	4	2	no	—
148	Dic₄₇⋊C₄	—	4	2	no	—
149	C₄×Dic₄₇	—	4	2	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
156	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
157	C₂²×D₄₇	—	2	2	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	C₂²×D₄₇	—	4	1	no	—
163	C₂²×D₄₇	—	4	1	no	—
164	Q₈×C₄₇	—	4	8	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	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	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
187	C₂×C₄×C₄₇	#135	1	2	yes	—
188	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₄₇	C₂³×C₄	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×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
194	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
195	C₂×Dic₄₇	—	2	2	no	—
196	C₂×Dic₄₇	—	4	1	no	—
197	C₂×Dic₄₇	—	4	1	no	—
198	C₂×Dic₄₇	—	4	1	no	—
199	C₂×Dic₄₇	—	4	1	no	—
200	C₂×Dic₄₇	—	4	1	no	—
201	C₂×Dic₄₇	—	4	1	no	—
202	C₂×Dic₄₇	—	4	1	no	—
203	C₂×Dic₄₇	—	4	1	no	—
204	D₁₈₈	—	2	2	no	—
205	D₁₈₈	—	2	2	no	—
206	D₁₈₈	—	4	1	no	—
207	D₁₈₈	—	4	1	no	—
208	C₄×D₄₇	—	4	8	no	—
209	C₄₇⋊C₈	—	2	4	no	—
210	C₄₇⋊C₈	—	4	2	no	—
211	#22111	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂²×C₄₇	#536	1	1	yes	characteristic
214	C₂²×C₄₇	#537	1	1	yes	characteristic
215	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
216	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
217	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂²×C₄₇	#575	1	1	yes	characteristic
219	C₂×D₄₇	—	4	2	no	—
220	C₂×D₄₇	—	4	2	no	—
221	C₂×D₄₇	—	4	2	no	—
222	C₂×D₄₇	—	8	1	no	—
223	C₂×D₄₇	—	8	1	no	—
224	C₂×D₄₇	—	8	1	no	—
225	C₂×D₄₇	—	8	1	no	—
226	C₄×C₄₇	—	2	2	no	—
227	C₄×C₄₇	—	2	2	no	—
228	C₄×C₄₇	—	2	2	no	—
229	C₄×C₄₇	—	2	2	no	—
230	C₄×C₄₇	—	4	4	no	—
231	C₄×C₄₇	—	4	1	no	—
232	C₄×C₄₇	—	8	2	no	—
233	C₄×C₄₇	C₄×SD₁₆	1	4	yes	—
234	C₄×C₄₇	#519	1	1	yes	characteristic
235	C₄×C₄₇	#520	1	1	yes	characteristic
236	C₄×C₄₇	#541	1	1	yes	characteristic
237	C₄×C₄₇	#542	1	1	yes	characteristic
238	Dic₄₇	—	4	2	no	—
239	Dic₄₇	—	8	1	no	—
240	Dic₄₇	—	8	1	no	—
241	C₂×#476	—	47	1	no	—
242	C₄×C₄⋊Q₈	D₄₇	1	1	yes	characteristic, complemented
243	#2293	—	47	1	no	—
244	#1987	—	47	1	no	—
245	#1948	—	47	1	no	—
246	#1941	—	47	2	no	—
247	#1934	—	47	2	no	—
248	#1926	—	47	2	no	—
249	#1919	—	47	2	no	—
250	#1802	—	47	1	no	—
251	C₄×C₄⋊C₈	—	47	1	no	—
252	C₂×C₄₇	#2323	1	1	yes	characteristic
253	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
254	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₂×C₄₇	#3227	1	1	yes	characteristic
256	C₂×C₄₇	#3233	1	1	yes	characteristic
257	C₂×C₄₇	#3246	1	1	yes	characteristic
258	C₂×C₄₇	#3247	1	1	yes	characteristic
259	D₄₇	—	8	2	no	—
260	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
261	C₂×C₄×Q₈	—	2	1	no	—
262	C₂×C₄×D₄	—	47	1	no	—
263	C₂×#117	—	94	1	no	—
264	#476	—	47	8	no	—
265	C₂×#106	—	47	2	no	—
266	C₂×#106	—	47	2	no	—
267	C₂×C₄⋊C₈	—	47	1	no	—
268	C₂×C₄⋊C₈	—	47	1	no	—
269	C₂×#102	—	47	2	no	—
270	C₂×#102	—	47	2	no	—
271	C₂×C₄×C₈	—	47	2	no	—
272	#391	—	2	1	no	—
273	#390	—	47	1	no	—
274	#390	—	47	1	no	—
275	#389	—	2	1	no	—
276	#389	—	47	1	no	—
277	#389	—	47	1	no	—
278	#389	C₂×D₄₇	1	2	yes	—
279	#388	—	94	1	no	—
280	#388	—	94	1	no	—
281	#384	C₂×D₄₇	1	1	yes	characteristic
282	C₄×C₄⋊C₄	—	2	1	no	—
283	C₄×C₄⋊C₄	—	47	1	no	—
284	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
285	C₄×C₂²⋊C₄	—	94	1	no	—
286	C₄³	C₂×D₄₇	1	1	yes	characteristic
287	#340	—	47	2	no	—
288	#340	—	47	2	no	—
289	#340	—	47	2	no	—
290	#340	—	47	2	no	—
291	#336	—	47	2	no	—
292	C₄₇	#22111	1	1	yes	characteristic, complemented, Sylow
293	C₂²×Q₈	—	2	1	no	—
294	C₂²×D₄	—	47	1	no	—
295	C₂³×C₄	—	94	1	no	—
296	C₂²×C₈	—	47	2	no	—
297	C₂²×C₈	—	47	2	no	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	C₄×D₄₇	1	4	yes	—
300	C₄×Q₈	—	4	4	no	—
301	C₄×D₄	—	47	4	no	—
302	C₄×D₄	—	94	2	no	—
303	#117	—	188	4	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	47	1	no	—
309	C₂×C₄⋊C₄	—	47	1	no	—
310	C₂×C₄⋊C₄	—	47	1	no	—
311	C₂×C₄⋊C₄	—	94	1	no	—
312	C₂×C₄⋊C₄	—	94	1	no	—
313	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
314	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
315	C₂×C₂²⋊C₄	—	94	1	no	—
316	C₂×C₂²⋊C₄	—	94	1	no	—
317	C₂×C₂²⋊C₄	—	94	1	no	—
318	C₂×C₂²⋊C₄	—	94	1	no	—
319	C₂×C₂²⋊C₄	—	94	1	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	94	1	no	—
322	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
324	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
325	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
326	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
327	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
328	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
329	#106	—	47	8	no	—
330	#106	—	188	2	no	—
331	C₄⋊C₈	—	47	4	no	—
332	C₄⋊C₈	—	94	2	no	—
333	#102	—	47	8	no	—
334	#102	—	188	2	no	—
335	C₄×C₈	—	188	2	no	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	#95	—	94	1	no	—
339	#95	—	94	1	no	—
340	#95	—	94	1	no	—
341	C₂⁴	—	94	1	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×D₄	—	47	2	no	—
346	C₂×D₄	—	94	1	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	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	94	1	no	—
354	C₂²×C₄	—	94	4	no	—
355	C₂²×C₄	—	94	1	no	—
356	C₂²×C₄	—	94	1	no	—
357	C₂²×C₄	—	188	2	no	—
358	C₂²×C₄	—	188	2	no	—
359	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
366	C₂×C₈	—	47	4	no	—
367	C₂×C₈	—	94	2	no	—
368	C₂×C₈	—	94	2	no	—
369	C₂×C₈	—	94	2	no	—
370	C₂×C₈	—	94	2	no	—
371	C₂×C₈	—	94	2	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	47	2	no	—
380	C₄⋊C₄	—	94	1	no	—
381	C₄⋊C₄	—	94	1	no	—
382	C₄⋊C₄	—	94	1	no	—
383	C₄⋊C₄	—	94	1	no	—
384	C₄⋊C₄	—	94	1	no	—
385	C₄⋊C₄	—	188	2	no	—
386	C₄⋊C₄	—	188	2	no	—
387	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
388	C₂²⋊C₄	—	94	4	no	—
389	C₂²⋊C₄	—	188	2	no	—
390	C₂²⋊C₄	—	188	2	no	—
391	C₂²⋊C₄	—	188	2	no	—
392	C₂²⋊C₄	—	188	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	4	1	no	—
400	C₄²	—	4	4	no	—
401	C₄²	—	188	2	no	—
402	C₄²	#10625336	1	4	yes	—
403	C₄²	C₂×C₄×D₄₇	1	2	yes	—
404	C₄²	#10625350	1	2	yes	—
405	C₂³	—	94	2	no	—
406	C₂³	—	188	1	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	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
413	Q₈	—	4	8	no	—
414	D₄	—	94	2	no	—
415	D₄	—	94	2	no	—
416	D₄	—	188	1	no	—
417	D₄	—	188	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	94	2	no	—
436	C₂×C₄	—	188	1	no	—
437	C₂×C₄	—	188	1	no	—
438	C₂×C₄	—	188	1	no	—
439	C₂×C₄	—	188	1	no	—
440	C₂×C₄	—	188	1	no	—
441	C₂×C₄	—	188	1	no	—
442	C₂×C₄	—	188	1	no	—
443	C₂×C₄	—	188	1	no	—
444	C₂×C₄	—	188	8	no	—
445	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
446	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
447	C₂×C₄	C₂×#10625336	1	2	yes	—
448	C₂×C₄	C₂×#10625336	1	2	yes	—
449	C₂×C₄	C₂×#10625336	1	2	yes	—
450	C₂×C₄	#13094044	1	2	yes	—
451	C₂×C₄	#13094050	1	2	yes	—
452	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
454	C₂×C₄	#13094070	1	1	yes	characteristic
455	C₂×C₄	#13094071	1	1	yes	characteristic
456	C₂×C₄	#13094072	1	1	yes	characteristic
457	C₂×C₄	#13094072	1	1	yes	characteristic
458	C₈	—	94	4	no	—
459	C₈	—	188	2	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×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
468	C₂²	#15689697	1	1	yes	characteristic
469	C₂²	#15689701	1	1	yes	characteristic
470	C₂²	C₂²×#10625336	1	1	yes	characteristic
471	C₂²	C₂×#13094044	1	1	yes	characteristic
472	C₂²	C₂×#13094050	1	1	yes	characteristic
473	C₂²	#15689921	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	1	no	—
480	C₄	—	8	2	no	—
481	C₄	—	376	1	no	—
482	C₄	—	376	1	no	—
483	C₄	—	188	2	no	—
484	C₄	C₄×#10625336	1	4	yes	—
485	C₄	#15689599	1	1	yes	characteristic
486	C₄	#15689605	1	1	yes	characteristic
487	C₄	#15689731	1	1	yes	characteristic
488	C₄	#15689745	1	1	yes	characteristic
489	C₂	—	376	2	no	—
490	C₂	#20246064	1	1	yes	characteristic
491	C₂	C₂×C₄×#10625336	1	1	yes	characteristic
492	C₂	C₄×#13094050	1	1	yes	characteristic
493	C₂	#20254516	1	1	yes	characteristic
494	C₂	#20254567	1	1	yes	characteristic
495	C₂	#20254700	1	1	yes	characteristic
496	C₂	#20254708	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×C₄⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	#22111
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
3. #20244337	C₂	semidirect
4. #20244149	C₂	semidirect
5. #20244113	C₂	semidirect
8. #20243966	C₂	semidirect
10. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
11. C₄×C₄⋊Q₈×C₄₇	C₂	semidirect
14. #15689410	C₄	semidirect
242. C₄×C₄⋊Q₈	D₄₇	semidirect
292. C₄₇	#22111	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689410	2
#20245852	2
#20244337	2
#20244149	2
#20244113	2
#20244070	2
#20244015	2
#20243966	2
#20243385	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₄×C₄⋊Q₈×C₄₇	2
#22111	47