Subgroups — #26183469

Order 12032.

1194 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256684	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241914	C₂	1	4	yes	maximal, complemented
4	#20241893	C₂	1	4	yes	maximal, complemented
5	#20241888	C₂	1	2	yes	maximal, complemented
6	#20241884	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689680	C₄	1	1	yes	characteristic, complemented
9	#15689680	C₄	1	1	yes	characteristic, complemented
10	#15689680	C₂²	1	1	yes	characteristic
11	#15689673	C₄	1	1	yes	characteristic, complemented
12	#15689673	C₄	1	1	yes	characteristic, complemented
13	#15689673	C₂²	1	1	yes	characteristic
14	#15689657	—	2	1	no	—
15	#15689657	—	2	1	no	—
16	#15689657	—	2	1	no	—
17	#15689657	—	2	1	no	—
18	#15689657	C₄	1	2	yes	complemented
19	#15689657	C₂²	1	2	yes	—
20	#15689634	—	2	1	no	—
21	#15689634	—	2	1	no	—
22	#15689634	C₂²	1	2	yes	—
23	C₄×#10625350	—	2	1	no	—
24	C₄×#10625350	—	2	1	no	—
25	C₄×#10625350	C₄	1	2	yes	complemented
26	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
27	C₂²×C₄×Dic₄₇	—	2	1	no	—
28	C₄×C₄⋊Dic₄₇	—	2	1	no	—
29	C₄×C₄⋊Dic₄₇	—	2	1	no	—
30	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
31	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
32	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
33	#15688861	C₂²	1	8	yes	—
34	#15688858	C₂²	1	8	yes	—
35	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#432	—	2	1	no	—
37	C₄₇×#432	C₂²	1	2	yes	—
38	C₄₇×#431	—	2	1	no	—
39	C₄₇×#431	C₂²	1	2	yes	—
40	C₄₇×#423	—	2	1	no	—
41	C₄₇×#407	C₂²	1	2	yes	—
42	C₄×M₁₆×C₄₇	—	2	1	no	—
43	C₂×#10625350	—	2	1	no	—
44	C₂×#10625350	—	2	1	no	—
45	C₂×#10625350	C₂×C₄	1	2	yes	—
46	C₂³×Dic₄₇	—	2	2	no	—
47	#13094024	C₂×C₄	1	1	yes	characteristic, complemented
48	#13094024	C₂×C₄	1	1	yes	characteristic, complemented
49	#13094024	C₂×C₄	1	1	yes	characteristic, complemented
50	#13094021	C₂×C₄	1	1	yes	characteristic, complemented
51	#13094018	—	2	2	no	—
52	#13094018	—	2	2	no	—
53	#13094016	—	2	1	no	—
54	#13094016	—	2	1	no	—
55	#13094016	C₂×C₄	1	2	yes	complemented
56	#13094012	—	2	1	no	—
57	#13094012	—	2	1	no	—
58	#13094012	C₂×C₄	1	2	yes	complemented
59	#13094007	—	2	2	no	—
60	#13094007	—	2	2	no	—
61	#13094007	—	2	2	no	—
62	#13094003	—	2	1	no	—
63	#13094003	—	2	1	no	—
64	#13094003	—	2	1	no	—
65	#13094003	—	2	1	no	—
66	#13094003	C₂×C₄	1	2	yes	—
67	#13094003	C₂³	1	2	yes	—
68	#13093998	—	2	1	no	—
69	#13093998	—	2	1	no	—
70	#13093998	—	2	1	no	—
71	#13093998	—	2	1	no	—
72	#13093998	C₂×C₄	1	2	yes	—
73	#13093998	C₂³	1	2	yes	—
74	#13093993	—	2	2	no	—
75	C₄×Dic₉₄	—	2	1	no	—
76	C₄×Dic₉₄	—	2	1	no	—
77	C₄×Dic₉₄	—	2	1	no	—
78	C₄×Dic₉₄	—	2	1	no	—
79	C₄×Dic₉₄	C₂×C₄	1	2	yes	complemented
80	C₄×Dic₉₄	C₂×C₄	1	2	yes	complemented
81	C₄×D₁₈₈	—	2	1	no	—
82	C₄×D₁₈₈	—	2	1	no	—
83	C₄×D₁₈₈	—	2	1	no	—
84	C₄×D₁₈₈	—	2	1	no	—
85	C₄×D₁₈₈	C₂×C₄	1	2	yes	complemented
86	C₄×D₁₈₈	C₂×C₄	1	2	yes	complemented
87	C₄×C₂²⋊D₄₇	—	2	2	no	—
88	C₄×C₂²⋊D₄₇	—	2	2	no	—
89	C₄×C₂²⋊D₄₇	—	2	2	no	—
90	C₄×C₂²⋊D₄₇	—	2	2	no	—
91	C₄×C₂²⋊D₄₇	—	2	2	no	—
92	C₄×C₂²⋊D₄₇	—	2	2	no	—
93	#13093983	—	2	1	no	—
94	#13093983	—	2	1	no	—
95	#13093983	C₂×C₄	1	2	yes	—
96	#13093981	—	2	2	no	—
97	#13093981	—	2	2	no	—
98	#13093981	—	2	2	no	—
99	C₂×C₄⋊Dic₄₇	—	2	8	no	—
100	C₂×C₄⋊Dic₄₇	—	2	2	no	—
101	C₂×C₄⋊Dic₄₇	—	2	2	no	—
102	C₂×C₄×Dic₄₇	—	2	2	no	—
103	C₂×C₄×Dic₄₇	—	2	2	no	—
104	C₂×C₄×Dic₄₇	—	4	4	no	—
105	C₄²×D₄₇	—	2	2	no	—
106	C₄₇⋊#95	—	2	2	no	—
107	C₄₇⋊#95	C₂³	1	4	yes	—
108	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
109	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
110	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₄₇	—	2	2	no	—
112	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₄₇	—	2	2	no	—
125	C₄⋊C₈×C₄₇	—	2	2	no	—
126	C₂²⋊C₈×C₄₇	—	2	2	no	—
127	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
128	#97×C₄₇	—	2	2	no	—
129	C₄×C₈×C₄₇	—	2	2	no	—
130	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	—	2	4	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	4	2	no	—
135	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
153	C₂×C₂²⋊D₄₇	—	2	2	no	—
154	C₂×C₂²⋊D₄₇	—	2	2	no	—
155	C₂×C₂²⋊D₄₇	—	2	2	no	—
156	C₂²×Dic₄₇	—	2	8	no	—
157	C₂²×Dic₄₇	—	2	4	no	—
158	C₂²×Dic₄₇	—	4	4	no	—
159	C₂²×Dic₄₇	—	4	4	no	—
160	#10625350	—	4	4	no	—
161	#10625350	—	4	2	no	—
162	#10625350	—	4	2	no	—
163	#10625350	—	4	4	no	—
164	C₂×D₁₈₈	—	2	1	no	—
165	C₂×D₁₈₈	—	2	1	no	—
166	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
167	C₂×C₄×D₄₇	—	2	2	no	—
168	C₂×C₄×D₄₇	—	2	2	no	—
169	C₂×C₄×D₄₇	—	2	2	no	—
170	C₂×Dic₉₄	—	2	1	no	—
171	C₂×Dic₉₄	—	2	1	no	—
172	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
173	M₁₆×C₄₇	—	4	4	no	—
174	C₂×C₈×C₄₇	—	2	4	no	—
175	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
181	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
182	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
183	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
185	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
191	C₂²⋊Dic₄₇	—	2	2	no	—
192	C₂²⋊Dic₄₇	—	2	2	no	—
193	C₂²⋊Dic₄₇	—	2	2	no	—
194	(C₂×D₄₇)⋊C₄	—	2	2	no	—
195	(C₂×D₄₇)⋊C₄	—	2	2	no	—
196	(C₂×D₄₇)⋊C₄	—	2	2	no	—
197	(C₂×D₄₇)⋊C₄	—	2	2	no	—
198	(C₂×D₄₇)⋊C₄	—	2	2	no	—
199	(C₂×D₄₇)⋊C₄	—	2	2	no	—
200	C₄⋊Dic₄₇	—	2	8	no	—
201	C₄⋊Dic₄₇	—	2	8	no	—
202	C₄⋊Dic₄₇	—	2	1	no	—
203	C₄⋊Dic₄₇	—	2	1	no	—
204	C₄⋊Dic₄₇	—	2	1	no	—
205	C₄⋊Dic₄₇	—	2	1	no	—
206	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
207	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
208	Dic₄₇⋊C₄	—	2	2	no	—
209	Dic₄₇⋊C₄	—	2	2	no	—
210	Dic₄₇⋊C₄	—	2	2	no	—
211	Dic₄₇⋊C₄	—	2	2	no	—
212	Dic₄₇⋊C₄	—	2	2	no	—
213	Dic₄₇⋊C₄	—	2	2	no	—
214	C₄×Dic₄₇	—	2	2	no	—
215	C₄×Dic₄₇	—	2	2	no	—
216	C₄×Dic₄₇	—	2	2	no	—
217	C₄×Dic₄₇	—	4	4	no	—
218	C₄×Dic₄₇	—	4	4	no	—
219	C₂³×C₄₇	—	2	1	no	—
220	C₂³×C₄₇	—	2	1	no	—
221	C₂³×C₄₇	—	2	2	no	—
222	C₂³×C₄₇	—	2	2	no	—
223	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
226	C₂²×D₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	1	no	—
228	C₂×C₄×C₄₇	—	2	1	no	—
229	C₂×C₄×C₄₇	—	2	2	no	—
230	C₂×C₄×C₄₇	—	2	2	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	—	2	2	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	2	2	no	—
237	C₂×C₄×C₄₇	—	2	2	no	—
238	C₂×C₄×C₄₇	—	2	2	no	—
239	C₂×C₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	4	1	no	—
241	C₂×C₄×C₄₇	—	4	1	no	—
242	C₂×C₄×C₄₇	—	4	1	no	—
243	C₂×C₄×C₄₇	—	4	1	no	—
244	C₂×C₄×C₄₇	#104	1	4	yes	—
245	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
256	C₂×C₄×C₄₇	#137	1	2	yes	—
257	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
259	C₂²⋊D₄₇	—	4	2	no	—
260	C₂²⋊D₄₇	—	4	2	no	—
261	C₂²⋊D₄₇	—	4	4	no	—
262	C₂²⋊D₄₇	—	4	4	no	—
263	C₂×Dic₄₇	—	2	8	no	—
264	C₂×Dic₄₇	—	2	2	no	—
265	C₂×Dic₄₇	—	2	2	no	—
266	C₂×Dic₄₇	—	2	2	no	—
267	C₂×Dic₄₇	—	4	16	no	—
268	C₂×Dic₄₇	—	4	4	no	—
269	C₂×Dic₄₇	—	4	4	no	—
270	D₁₈₈	—	4	2	no	—
271	D₁₈₈	—	4	2	no	—
272	D₁₈₈	—	4	2	no	—
273	C₄×D₄₇	—	4	4	no	—
274	C₄×D₄₇	—	4	4	no	—
275	C₄×D₄₇	—	4	4	no	—
276	Dic₉₄	—	4	2	no	—
277	Dic₉₄	—	4	2	no	—
278	Dic₉₄	—	4	2	no	—
279	C₈×C₄₇	—	4	4	no	—
280	#17546	—	47	1	no	maximal, Sylow
281	C₂²×C₄₇	—	2	4	no	—
282	C₂²×C₄₇	—	2	4	no	—
283	C₂²×C₄₇	—	2	1	no	—
284	C₂²×C₄₇	—	2	1	no	—
285	C₂²×C₄₇	—	2	1	no	—
286	C₂²×C₄₇	—	2	1	no	—
287	C₂²×C₄₇	—	2	1	no	—
288	C₂²×C₄₇	—	2	1	no	—
289	C₂²×C₄₇	#410	1	2	yes	—
290	C₂²×C₄₇	C₂×#104	1	2	yes	—
291	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
292	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
293	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
294	C₂×D₄₇	—	4	2	no	—
295	C₂×D₄₇	—	4	2	no	—
296	C₂×D₄₇	—	4	2	no	—
297	C₄×C₄₇	—	2	1	no	—
298	C₄×C₄₇	—	2	1	no	—
299	C₄×C₄₇	—	2	1	no	—
300	C₄×C₄₇	—	2	1	no	—
301	C₄×C₄₇	—	2	1	no	—
302	C₄×C₄₇	—	2	1	no	—
303	C₄×C₄₇	—	2	1	no	—
304	C₄×C₄₇	—	2	1	no	—
305	C₄×C₄₇	#417	1	2	yes	—
306	C₄×C₄₇	#417	1	2	yes	—
307	C₄×C₄₇	C₂×#104	1	2	yes	—
308	C₄×C₄₇	C₂×#104	1	2	yes	—
309	Dic₄₇	—	4	8	no	—
310	Dic₄₇	—	4	2	no	—
311	Dic₄₇	—	4	2	no	—
312	Dic₄₇	—	4	2	no	—
313	#3444	—	47	1	no	—
314	#2920	D₄₇	1	1	yes	characteristic, complemented
315	C₂×C₄×C₄⋊C₄	—	47	1	no	—
316	#1509	—	47	4	no	—
317	#1504	—	47	4	no	—
318	#1503	—	47	2	no	—
319	#1502	—	47	2	no	—
320	C₂×C₄₇	—	2	1	no	—
321	C₂×C₄₇	—	2	1	no	—
322	C₂×C₄₇	—	2	2	no	—
323	C₂×C₄₇	—	2	2	no	—
324	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
325	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
326	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
327	D₄₇	—	8	2	no	—
328	#533	—	47	1	no	—
329	#533	—	47	1	no	—
330	#533	—	47	1	no	—
331	#532	—	47	1	no	—
332	#532	—	47	1	no	—
333	#532	—	47	1	no	—
334	#529	—	47	2	no	—
335	#529	—	47	2	no	—
336	#529	—	94	1	no	—
337	#529	—	94	1	no	—
338	#529	—	94	1	no	—
339	#529	—	94	1	no	—
340	#525	—	47	2	no	—
341	#525	—	94	1	no	—
342	#525	—	94	1	no	—
343	C₄×#41	—	47	2	no	—
344	C₄×#41	—	94	1	no	—
345	C₄×#41	—	94	1	no	—
346	C₂²×C₄⋊C₄	—	94	1	no	—
347	C₂²×C₄²	—	94	1	no	—
348	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
349	#432	—	2	1	no	—
350	#432	C₂×D₄₇	1	2	yes	—
351	#431	—	2	1	no	—
352	#431	C₂×D₄₇	1	2	yes	—
353	#423	—	2	1	no	—
354	#407	C₂×D₄₇	1	2	yes	—
355	C₄×M₁₆	—	2	1	no	—
356	C₄×C₄⋊C₄	—	47	2	no	—
357	C₄×C₄⋊C₄	—	47	2	no	—
358	C₄×C₄⋊C₄	—	94	1	no	—
359	C₄×C₄⋊C₄	—	94	1	no	—
360	C₂×#95	—	47	2	no	—
361	#328	—	47	8	no	—
362	#327	—	47	8	no	—
363	C₄₇	#17546	1	1	yes	characteristic, complemented, Sylow
364	C₂×#41	—	47	2	no	—
365	C₂×#41	—	94	1	no	—
366	C₂×#41	—	94	1	no	—
367	C₂³×C₄	—	94	2	no	—
368	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
369	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
370	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
371	C₂×M₁₆	—	2	2	no	—
372	C₄⋊Q₈	—	47	1	no	—
373	C₄⋊Q₈	—	47	1	no	—
374	C₄⋊Q₈	—	47	1	no	—
375	#127	—	47	1	no	—
376	#126	—	94	2	no	—
377	#126	—	94	2	no	—
378	#125	—	47	2	no	—
379	#125	—	94	1	no	—
380	#125	—	94	1	no	—
381	#124	—	47	2	no	—
382	#124	—	94	1	no	—
383	#124	—	94	1	no	—
384	#123	—	94	2	no	—
385	#123	—	94	2	no	—
386	#123	—	94	2	no	—
387	C₂²⋊Q₈	—	47	2	no	—
388	C₂²⋊Q₈	—	47	2	no	—
389	C₂²⋊Q₈	—	94	1	no	—
390	C₂²⋊Q₈	—	94	1	no	—
391	C₂²⋊Q₈	—	94	1	no	—
392	C₂²⋊Q₈	—	94	1	no	—
393	#121	—	47	2	no	—
394	#121	—	47	2	no	—
395	#121	—	94	1	no	—
396	#121	—	94	1	no	—
397	#121	—	94	1	no	—
398	#121	—	94	1	no	—
399	#120	—	94	2	no	—
400	C₄×Q₈	—	47	2	no	—
401	C₄×Q₈	—	47	2	no	—
402	C₄×Q₈	—	94	1	no	—
403	C₄×Q₈	—	94	1	no	—
404	C₄×Q₈	—	94	1	no	—
405	C₄×Q₈	—	94	1	no	—
406	C₄×D₄	—	47	2	no	—
407	C₄×D₄	—	47	2	no	—
408	C₄×D₄	—	94	2	no	—
409	C₄×D₄	—	94	2	no	—
410	C₄×D₄	—	94	2	no	—
411	C₄×D₄	—	94	2	no	—
412	C₄×D₄	—	94	2	no	—
413	C₄×D₄	—	94	2	no	—
414	C₄×D₄	—	94	1	no	—
415	C₄×D₄	—	94	1	no	—
416	C₄×D₄	—	94	1	no	—
417	C₄×D₄	—	94	1	no	—
418	#117	—	47	2	no	—
419	#117	—	94	1	no	—
420	#117	—	94	1	no	—
421	#117	—	94	2	no	—
422	#117	—	94	2	no	—
423	#117	—	94	2	no	—
424	C₂×C₄⋊C₄	—	94	8	no	—
425	C₂×C₄⋊C₄	—	94	2	no	—
426	C₂×C₄⋊C₄	—	94	2	no	—
427	C₂×C₄²	—	94	2	no	—
428	C₂×C₄²	—	94	2	no	—
429	C₂×C₄²	—	94	2	no	—
430	C₂×C₄²	—	188	4	no	—
431	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
432	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
433	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
434	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
435	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
436	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
437	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
438	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
439	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
440	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
441	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
442	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
443	C₄⋊C₈	—	2	2	no	—
444	C₄⋊C₈	—	2	2	no	—
445	C₂²⋊C₈	—	2	2	no	—
446	C₂²⋊C₈	C₂²×D₄₇	1	4	yes	—
447	#97	—	2	2	no	—
448	C₄×C₈	—	2	2	no	—
449	#95	—	47	4	no	—
450	#95	—	94	2	no	—
451	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
452	#41	—	188	4	no	—
453	#41	—	188	4	no	—
454	#41	—	188	2	no	—
455	#41	—	188	2	no	—
456	C₂×Q₈	—	47	2	no	—
457	C₂×Q₈	—	94	1	no	—
458	C₂×Q₈	—	94	1	no	—
459	C₂×D₄	—	47	2	no	—
460	C₂×D₄	—	94	2	no	—
461	C₂×D₄	—	94	2	no	—
462	C₂×D₄	—	94	2	no	—
463	C₂×D₄	—	94	1	no	—
464	C₂×D₄	—	94	1	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	4	2	no	—
469	C₂²×C₄	—	94	8	no	—
470	C₂²×C₄	—	94	4	no	—
471	C₂²×C₄	—	94	2	no	—
472	C₂²×C₄	—	94	2	no	—
473	C₂²×C₄	—	94	2	no	—
474	C₂²×C₄	—	188	4	no	—
475	C₂²×C₄	—	188	4	no	—
476	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
477	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
478	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
479	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
480	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
481	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
482	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
483	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
484	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
491	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
492	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
493	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
494	M₁₆	—	4	4	no	—
495	C₂×C₈	—	2	4	no	—
496	C₄⋊C₄	—	47	2	no	—
497	C₄⋊C₄	—	47	2	no	—
498	C₄⋊C₄	—	94	8	no	—
499	C₄⋊C₄	—	94	8	no	—
500	C₄⋊C₄	—	94	2	no	—
501	C₄⋊C₄	—	94	2	no	—
502	C₄⋊C₄	—	94	2	no	—
503	C₄⋊C₄	—	94	2	no	—
504	C₄⋊C₄	—	94	2	no	—
505	C₄⋊C₄	—	94	1	no	—
506	C₄⋊C₄	—	94	1	no	—
507	C₄⋊C₄	—	94	1	no	—
508	C₄⋊C₄	—	94	1	no	—
509	C₄⋊C₄	—	94	2	no	—
510	C₂²⋊C₄	—	94	2	no	—
511	C₂²⋊C₄	—	94	2	no	—
512	C₂²⋊C₄	—	94	2	no	—
513	C₂²⋊C₄	—	94	2	no	—
514	C₂²⋊C₄	—	94	2	no	—
515	C₂²⋊C₄	—	94	2	no	—
516	C₂²⋊C₄	—	94	2	no	—
517	C₂²⋊C₄	—	94	2	no	—
518	C₂²⋊C₄	—	94	2	no	—
519	C₄²	—	94	2	no	—
520	C₄²	—	94	2	no	—
521	C₄²	—	94	2	no	—
522	C₄²	—	188	4	no	—
523	C₄²	—	188	4	no	—
524	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
525	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
526	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
527	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
528	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
529	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
530	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
531	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
532	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
533	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
534	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
535	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
536	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
537	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
538	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
539	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	94	2	no	—
545	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
546	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
547	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
548	Q₈	—	188	2	no	—
549	Q₈	—	188	2	no	—
550	Q₈	—	188	2	no	—
551	D₄	—	188	2	no	—
552	D₄	—	188	4	no	—
553	D₄	—	188	4	no	—
554	D₄	—	188	2	no	—
555	D₄	—	188	2	no	—
556	D₄	—	188	2	no	—
557	D₄	—	188	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	94	8	no	—
576	C₂×C₄	—	94	2	no	—
577	C₂×C₄	—	94	2	no	—
578	C₂×C₄	—	94	2	no	—
579	C₂×C₄	—	188	4	no	—
580	C₂×C₄	—	188	16	no	—
581	C₂×C₄	—	188	4	no	—
582	C₂×C₄	—	188	4	no	—
583	C₂×C₄	—	188	4	no	—
584	C₂×C₄	—	188	4	no	—
585	C₂×C₄	#13093950	1	4	yes	—
586	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
587	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
588	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
589	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
590	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
591	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
592	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
593	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
594	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
595	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
596	C₂×C₄	#13094052	1	2	yes	—
597	C₂×C₄	#13094057	1	2	yes	—
598	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
599	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
600	C₈	—	4	4	no	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	188	2	no	—
610	C₂²	—	188	2	no	—
611	C₂²	—	188	2	no	—
612	C₂²	#15689096	1	2	yes	—
613	C₂²	C₂×#13093950	1	2	yes	—
614	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
615	C₂²	C₂×#13094052	1	1	yes	characteristic
616	C₂²	C₂×#13094057	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	188	8	no	—
626	C₄	—	188	2	no	—
627	C₄	—	188	2	no	—
628	C₄	—	188	2	no	—
629	C₄	#15689125	1	2	yes	—
630	C₄	#15689125	1	2	yes	—
631	C₄	C₂×#13093950	1	2	yes	—
632	C₄	C₂×#13093950	1	2	yes	—
633	C₂	—	2	1	no	—
634	C₂	—	2	2	no	—
635	C₂	—	2	2	no	—
636	C₂	—	2	1	no	—
637	C₂	—	376	2	no	—
638	C₂	C₂×#15689096	1	1	yes	characteristic
639	C₂	C₂×#15689125	1	1	yes	characteristic
640	C₂	C₂²×#13093950	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2920	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	#20256684	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2920	D₄₇
hypocenter	C₄₇	#17546
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
3. #20241914	C₂	semidirect
4. #20241893	C₂	semidirect
5. #20241888	C₂	semidirect
6. #20241884	C₂	semidirect
7. C₄₇×#2920	C₂	semidirect
8. #15689680	C₄	semidirect
9. #15689680	C₄	semidirect
11. #15689673	C₄	semidirect
12. #15689673	C₄	semidirect
18. #15689657	C₄	semidirect
25. C₄×#10625350	C₄	semidirect
47. #13094024	C₂×C₄	semidirect
48. #13094024	C₂×C₄	semidirect
49. #13094024	C₂×C₄	semidirect
50. #13094021	C₂×C₄	semidirect
55. #13094016	C₂×C₄	semidirect
58. #13094012	C₂×C₄	semidirect
79. C₄×Dic₉₄	C₂×C₄	semidirect
80. C₄×Dic₉₄	C₂×C₄	semidirect
85. C₄×D₁₈₈	C₂×C₄	semidirect
86. C₄×D₁₈₈	C₂×C₄	semidirect
314. #2920	D₄₇	semidirect
363. C₄₇	#17546	semidirect

Maximal subgroups

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

subgroup	index
#20256684	2
C₂×C₄×C₄⋊Dic₄₇	2
#20241914	2
#20241893	2
#20241888	2
#20241884	2
C₄₇×#2920	2
#17546	47