Subgroups — C₄×#15689330 #26222481

Order 12032.

984 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689330	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625337	C₂	1	2	yes	maximal
3	C₄²×Dic₉₄	C₂	1	1	yes	maximal, characteristic
4	#20244312	C₂	1	1	yes	maximal, characteristic
5	#20244144	C₂	1	1	yes	maximal, characteristic
6	#20244026	C₂	1	2	yes	maximal
7	#20243732	C₂	1	2	yes	maximal
8	#20243390	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093948	C₂	1	2	yes	maximal
11	C₄×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625337	C₂²	1	2	yes	—
13	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
16	#15689330	C₄	1	8	yes	direct product factor
17	C₄×#10625337	—	2	8	no	—
18	C₂×#13093957	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#13093948	C₂²	1	2	yes	—
22	C₂×#13093948	C₂²	1	2	yes	—
23	C₂×#13093948	C₂²	1	2	yes	—
24	C₂×#13093947	C₂²	1	2	yes	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
26	C₄×Dic₄₇⋊C₄	—	2	1	no	—
27	C₄×Dic₄₇⋊C₄	—	2	1	no	—
28	C₄×Dic₄₇⋊C₄	—	2	1	no	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	C₄²×Dic₄₇	—	2	1	no	—
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688878	C₂²	1	2	yes	—
36	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
38	C₄₇×#391	C₂²	1	2	yes	—
39	C₄₇×#389	—	2	1	no	—
40	C₄₇×#389	—	2	1	no	—
41	C₄₇×#384	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
43	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
44	C₄³×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
46	C₂×#10625337	—	2	4	no	—
47	C₂×#10625337	—	2	4	no	—
48	C₂×#10625337	C₂×C₄	1	8	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	C₄×Dic₉₄	—	2	2	no	—
52	C₄×Dic₉₄	—	2	2	no	—
53	C₄×Dic₉₄	—	2	2	no	—
54	C₄×Dic₉₄	—	2	2	no	—
55	C₄×Dic₉₄	C₂×C₄	1	4	yes	—
56	C₄×Dic₉₄	D₄	1	4	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×Dic₄₇⋊C₄	—	2	1	no	—
61	C₂×Dic₄₇⋊C₄	—	2	1	no	—
62	C₂×Dic₄₇⋊C₄	—	2	1	no	—
63	C₂×C₄×Dic₄₇	—	2	1	no	—
64	C₂×C₄×Dic₄₇	—	2	1	no	—
65	C₂×C₄×Dic₄₇	—	2	1	no	—
66	C₂×C₄×Dic₄₇	—	2	1	no	—
67	C₂×C₄×Dic₄₇	—	2	1	no	—
68	C₂×C₄×Dic₄₇	—	2	1	no	—
69	#13093957	—	2	4	no	—
70	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
71	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
72	#13093948	—	2	4	no	—
73	#13093948	—	2	4	no	—
74	#13093948	C₂×C₄	1	8	yes	—
75	#13093947	—	2	4	no	—
76	C₄×C₄₇⋊C₈	—	2	4	no	—
77	C₄₇⋊#95	—	2	1	no	—
78	C₄₇⋊#95	—	2	1	no	—
79	C₄₇⋊#95	—	2	1	no	—
80	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
81	C₄⋊Q₈×C₄₇	—	2	2	no	—
82	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
83	C₄×Q₈×C₄₇	—	2	4	no	—
84	C₄×Q₈×C₄₇	—	2	4	no	—
85	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
91	C₂×C₄²×C₄₇	—	2	2	no	—
92	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	#95×C₄₇	—	2	2	no	—
100	#95×C₄₇	—	2	2	no	—
101	C₂×Q₈×C₄₇	—	2	2	no	—
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂²×Dic₄₇	—	2	1	no	—
117	C₂²×Dic₄₇	—	2	1	no	—
118	C₂²×Dic₄₇	—	2	1	no	—
119	C₂²×Dic₄₇	—	2	1	no	—
120	C₂×Dic₉₄	—	2	1	no	—
121	C₂×Dic₉₄	—	2	1	no	—
122	C₂×Dic₉₄	—	2	1	no	—
123	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
124	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
125	C₂×Dic₉₄	#41	1	2	yes	—
126	C₄⋊C₄×C₄₇	—	2	4	no	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	4	2	no	—
131	C₄⋊C₄×C₄₇	—	4	4	no	—
132	C₄⋊C₄×C₄₇	—	4	2	no	—
133	C₄²×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	1	no	—
136	C₄²×C₄₇	—	2	1	no	—
137	C₄²×C₄₇	—	4	1	no	—
138	C₄²×C₄₇	—	4	4	no	—
139	C₄²×C₄₇	Q₁₆	1	4	yes	complemented
140	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
141	C₄²×C₄₇	C₂×D₄	1	2	yes	—
142	C₄²×C₄₇	#41	1	2	yes	—
143	C₄²×C₄₇	#41	1	2	yes	—
144	#10625337	—	2	16	no	—
145	C₄⋊Dic₄₇	—	2	1	no	—
146	C₄⋊Dic₄₇	—	2	1	no	—
147	C₄⋊Dic₄₇	—	2	1	no	—
148	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
149	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
150	C₄⋊Dic₄₇	#41	1	2	yes	—
151	Dic₄₇⋊C₄	—	2	4	no	—
152	Dic₄₇⋊C₄	—	2	4	no	—
153	Dic₄₇⋊C₄	—	2	4	no	—
154	C₄×Dic₄₇	—	2	4	no	—
155	C₄×Dic₄₇	—	2	4	no	—
156	C₄×Dic₄₇	—	2	4	no	—
157	C₄×Dic₄₇	—	4	2	no	—
158	C₄×Dic₄₇	—	4	2	no	—
159	C₄×Dic₄₇	—	4	2	no	—
160	C₂×C₄₇⋊C₈	—	2	2	no	—
161	C₂×C₄₇⋊C₈	—	2	2	no	—
162	C₂×C₄₇⋊C₈	—	2	2	no	—
163	C₂×C₄₇⋊C₈	—	2	2	no	—
164	C₂×C₄₇⋊C₈	—	2	2	no	—
165	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
166	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₄₇	—	2	4	no	—
168	Q₈×C₄₇	—	2	4	no	—
169	Q₈×C₄₇	—	4	2	no	—
170	Q₈×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	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	—	2	4	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₄₇	#121	1	2	yes	—
189	C₂×C₄×C₄₇	#121	1	2	yes	—
190	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
192	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
193	C₂×C₄×C₄₇	#135	1	2	yes	—
194	C₂×C₄×C₄₇	#137	1	2	yes	—
195	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
201	C₂×Dic₄₇	—	2	2	no	—
202	C₂×Dic₄₇	—	2	2	no	—
203	C₂×Dic₄₇	—	2	2	no	—
204	C₂×Dic₄₇	—	2	2	no	—
205	C₂×Dic₄₇	—	2	2	no	—
206	C₂×Dic₄₇	—	2	2	no	—
207	C₂×Dic₄₇	—	4	1	no	—
208	C₂×Dic₄₇	—	4	1	no	—
209	C₂×Dic₄₇	—	4	1	no	—
210	C₂×Dic₄₇	—	4	1	no	—
211	C₂×Dic₄₇	—	4	1	no	—
212	C₂×Dic₄₇	—	4	1	no	—
213	Dic₉₄	—	2	2	no	—
214	Dic₉₄	—	2	2	no	—
215	Dic₉₄	—	2	2	no	—
216	Dic₉₄	C₄×D₄	1	4	yes	—
217	C₄₇⋊C₈	—	2	4	no	—
218	C₄₇⋊C₈	—	4	2	no	—
219	C₄×#462	—	47	1	no	maximal, Sylow
220	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
222	C₂²×C₄₇	#525	1	1	yes	characteristic
223	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
224	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
225	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
226	C₂²×C₄₇	#575	1	1	yes	characteristic
227	C₄×C₄₇	—	2	2	no	—
228	C₄×C₄₇	—	2	2	no	—
229	C₄×C₄₇	—	2	2	no	—
230	C₄×C₄₇	—	4	1	no	—
231	C₄×C₄₇	—	4	4	no	—
232	C₄×C₄₇	—	8	2	no	—
233	C₄×C₄₇	C₄×Q₁₆	1	4	yes	complemented
234	C₄×C₄₇	#462	1	4	yes	complemented
235	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
236	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
237	C₄×C₄₇	#529	1	1	yes	characteristic
238	C₄×C₄₇	#532	1	1	yes	characteristic
239	Dic₄₇	—	2	4	no	—
240	Dic₄₇	—	4	2	no	—
241	Dic₄₇	—	4	2	no	—
242	Dic₄₇	—	4	2	no	—
243	C₂×#462	—	47	1	no	—
244	C₂×C₄×Q₁₆	—	47	2	no	—
245	C₄×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
246	C₄²×Q₈	—	47	1	no	—
247	#1981	—	47	1	no	—
248	#1947	—	47	1	no	—
249	#1928	—	47	2	no	—
250	#1878	—	47	2	no	—
251	#1803	—	47	1	no	—
252	C₄×C₄⋊C₈	—	47	1	no	—
253	C₄×#103	—	47	2	no	—
254	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
255	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
256	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
257	C₂×C₄₇	C₂×#462	1	1	yes	characteristic
258	C₂×C₄₇	#3035	1	1	yes	characteristic
259	C₂×C₄₇	#3104	1	1	yes	characteristic
260	C₂×C₄₇	#3107	1	1	yes	characteristic
261	C₂²×Q₁₆	—	47	2	no	—
262	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
263	C₂×C₄×Q₈	—	47	1	no	—
264	C₂×C₄×Q₈	—	47	1	no	—
265	C₂×C₄×Q₈	—	47	1	no	—
266	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
267	#462	—	47	8	no	—
268	C₄×Q₁₆	—	94	8	no	—
269	C₂×#107	—	47	2	no	—
270	C₂×C₄⋊C₈	—	47	1	no	—
271	C₂×C₄⋊C₈	—	47	1	no	—
272	C₂×#103	—	47	2	no	—
273	C₂×#103	—	47	2	no	—
274	C₂×#103	—	47	2	no	—
275	C₂×#103	—	47	2	no	—
276	C₂×C₄×C₈	—	47	2	no	—
277	#391	C₂×D₄₇	1	2	yes	—
278	#389	—	2	1	no	—
279	#389	—	2	1	no	—
280	#384	C₂×D₄₇	1	1	yes	characteristic
281	C₄×C₄⋊C₄	—	2	1	no	—
282	C₄×C₄⋊C₄	—	2	1	no	—
283	C₄×C₄⋊C₄	—	47	1	no	—
284	C₄×C₄⋊C₄	—	47	1	no	—
285	C₄×C₄⋊C₄	—	47	1	no	—
286	C₄×C₄⋊C₄	—	94	1	no	—
287	C₄×C₄⋊C₄	—	94	1	no	—
288	C₄×C₄⋊C₄	—	94	1	no	—
289	C₄³	—	94	1	no	—
290	C₄³	C₂×D₄₇	1	1	yes	characteristic
291	#340	—	47	2	no	—
292	#340	—	47	2	no	—
293	#336	—	47	2	no	—
294	C₄₇	C₄×#462	1	1	yes	characteristic, complemented, Sylow
295	C₂²×Q₈	—	47	1	no	—
296	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
297	C₂×Q₁₆	—	47	8	no	—
298	C₂×Q₁₆	—	94	4	no	—
299	C₂×Q₁₆	—	94	4	no	—
300	C₂²×C₈	—	47	2	no	—
301	C₂²×C₈	—	47	2	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	C₄×D₄₇	1	4	yes	—
304	C₄×Q₈	—	2	4	no	—
305	C₄×Q₈	—	2	4	no	—
306	C₄×Q₈	—	47	4	no	—
307	C₄×Q₈	—	47	4	no	—
308	C₄×Q₈	—	94	2	no	—
309	C₄×Q₈	—	94	2	no	—
310	C₄×Q₈	—	94	2	no	—
311	C₄×Q₈	—	94	2	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	47	1	no	—
318	C₂×C₄⋊C₄	—	47	1	no	—
319	C₂×C₄⋊C₄	—	47	1	no	—
320	C₂×C₄⋊C₄	—	94	1	no	—
321	C₂×C₄⋊C₄	—	94	1	no	—
322	C₂×C₄⋊C₄	—	94	1	no	—
323	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	—	94	1	no	—
326	C₂×C₄²	—	94	1	no	—
327	C₂×C₄²	—	94	1	no	—
328	C₂×C₄²	—	94	1	no	—
329	C₂×C₄²	—	94	1	no	—
330	C₂×C₄²	—	94	1	no	—
331	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
332	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
333	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
334	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
335	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
336	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
337	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
338	#107	—	94	4	no	—
339	C₄⋊C₈	—	47	4	no	—
340	C₄⋊C₈	—	94	2	no	—
341	#103	—	47	8	no	—
342	#103	—	94	4	no	—
343	#103	—	94	4	no	—
344	#103	—	94	4	no	—
345	C₄×C₈	—	94	4	no	—
346	#95	—	2	2	no	—
347	#95	—	2	2	no	—
348	#95	—	94	1	no	—
349	#95	—	94	1	no	—
350	#95	—	94	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	47	2	no	—
357	C₂×Q₈	—	47	2	no	—
358	C₂×Q₈	—	47	2	no	—
359	C₂×Q₈	—	94	1	no	—
360	C₂×Q₈	—	94	1	no	—
361	C₂×Q₈	—	94	1	no	—
362	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	94	1	no	—
366	C₂²×C₄	—	94	1	no	—
367	C₂²×C₄	—	94	1	no	—
368	C₂²×C₄	—	94	1	no	—
369	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
375	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
376	Q₁₆	—	94	16	no	—
377	C₂×C₈	—	47	4	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	94	2	no	—
381	C₂×C₈	—	94	2	no	—
382	C₂×C₈	—	94	2	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	47	2	no	—
391	C₄⋊C₄	—	47	2	no	—
392	C₄⋊C₄	—	47	2	no	—
393	C₄⋊C₄	—	94	4	no	—
394	C₄⋊C₄	—	94	4	no	—
395	C₄⋊C₄	—	94	4	no	—
396	C₄⋊C₄	—	94	1	no	—
397	C₄⋊C₄	—	94	1	no	—
398	C₄⋊C₄	—	94	1	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	4	1	no	—
404	C₄²	—	4	4	no	—
405	C₄²	—	94	4	no	—
406	C₄²	—	94	4	no	—
407	C₄²	—	94	4	no	—
408	C₄²	—	188	2	no	—
409	C₄²	—	188	2	no	—
410	C₄²	—	188	2	no	—
411	C₄²	#10625337	1	4	yes	complemented
412	C₄²	C₂×C₄×D₄₇	1	2	yes	—
413	C₄²	#10625350	1	2	yes	—
414	C₄²	D₄×D₄₇	1	2	yes	—
415	C₄²	#10625352	1	2	yes	—
416	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
417	Q₈	—	2	4	no	—
418	Q₈	—	2	4	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	Q₈	—	47	4	no	—
422	Q₈	—	94	2	no	—
423	Q₈	—	94	2	no	—
424	Q₈	—	94	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	94	2	no	—
441	C₂×C₄	—	94	2	no	—
442	C₂×C₄	—	94	2	no	—
443	C₂×C₄	—	94	2	no	—
444	C₂×C₄	—	94	2	no	—
445	C₂×C₄	—	94	2	no	—
446	C₂×C₄	—	188	1	no	—
447	C₂×C₄	—	188	1	no	—
448	C₂×C₄	—	188	1	no	—
449	C₂×C₄	—	188	1	no	—
450	C₂×C₄	—	188	1	no	—
451	C₂×C₄	—	188	1	no	—
452	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
453	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
454	C₂×C₄	#13093995	1	2	yes	—
455	C₂×C₄	#13093995	1	2	yes	—
456	C₂×C₄	C₂×#10625337	1	2	yes	—
457	C₂×C₄	C₂×#10625337	1	2	yes	—
458	C₂×C₄	C₂×#10625337	1	2	yes	—
459	C₂×C₄	#13094044	1	2	yes	—
460	C₂×C₄	#13094055	1	2	yes	—
461	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
462	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
463	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
464	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
465	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
466	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
467	C₈	—	94	4	no	—
468	C₈	—	188	2	no	—
469	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
470	C₂²	C₂×#13093995	1	1	yes	characteristic
471	C₂²	#15689630	1	1	yes	characteristic
472	C₂²	C₂²×#10625337	1	1	yes	characteristic
473	C₂²	C₂×#13094044	1	1	yes	characteristic
474	C₂²	C₂×#13094055	1	1	yes	characteristic
475	C₂²	#15689921	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	4	no	—
481	C₄	—	8	2	no	—
482	C₄	—	94	4	no	—
483	C₄	—	188	2	no	—
484	C₄	—	188	2	no	—
485	C₄	—	188	2	no	—
486	C₄	C₄×#10625337	1	4	yes	complemented
487	C₄	#15689330	1	4	yes	direct product factor
488	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
489	C₄	C₄×#10625352	1	1	yes	characteristic
490	C₄	#15689655	1	1	yes	characteristic
491	C₄	#15689670	1	1	yes	characteristic
492	C₂	C₄×#13093995	1	1	yes	characteristic
493	C₂	C₂×C₄×#10625337	1	1	yes	characteristic
494	C₂	C₄×#13094055	1	1	yes	characteristic
495	C₂	C₂×#15689330	1	1	yes	characteristic
496	C₂	#20252837	1	1	yes	characteristic
497	C₂	#20253423	1	1	yes	characteristic
498	C₂	#20253453	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×C₄⋊Q₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	C₄×#462
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
16. #15689330	C₄	direct (N × H)
139. C₄²×C₄₇	Q₁₆	semidirect
233. C₄×C₄₇	C₄×Q₁₆	semidirect
234. C₄×C₄₇	#462	semidirect
294. C₄₇	C₄×#462	semidirect
411. C₄²	#10625337	semidirect
486. C₄	C₄×#10625337	semidirect
487. C₄	#15689330	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689330	2
C₂×C₄×#10625337	2
C₄²×Dic₉₄	2
#20244312	2
#20244144	2
#20244026	2
#20243732	2
#20243390	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₄×#13093948	2
C₄×C₄⋊Q₈×C₄₇	2
C₄×#462	47

Subgroups — C4×#15689330 #26222481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689330 #26222481