Subgroups — #26221306

Order 12032.

1256 conjugacy classes of subgroups.

The subgroup lattice has 626 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	C₄×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244332	C₂	1	2	yes	maximal, complemented
4	#20244307	C₂	1	2	yes	maximal, complemented
5	#20243690	C₂	1	4	yes	maximal, complemented
6	C₄×#13093950	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×M₁₆×C₄₇	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	C₄	1	2	yes	complemented
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	C₂²	1	2	yes	—
26	C₂×#13093983	—	2	1	no	—
27	C₂×#13093950	C₂²	1	8	yes	—
28	C₄×C₄⋊Dic₄₇	—	2	1	no	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
30	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
31	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
32	#15688969	—	2	1	no	—
33	C₄²×Dic₄₇	C₂²	1	2	yes	—
34	#15688884	C₂²	1	8	yes	—
35	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
36	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₄₇	—	2	1	no	—
38	C₄×M₁₆×C₄₇	—	2	1	no	—
39	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
40	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
41	C₂×#97×C₄₇	—	2	1	no	—
42	C₂×C₄×C₈×C₄₇	—	2	1	no	—
43	C₂×#10625350	—	2	1	no	—
44	C₂×#10625350	—	2	1	no	—
45	C₂×#10625350	C₂³	1	2	yes	—
46	#13094024	C₂×C₄	1	1	yes	characteristic
47	#13094024	C₂×C₄	1	1	yes	characteristic
48	#13094024	C₂×C₄	1	1	yes	characteristic
49	#13094021	C₂×C₄	1	1	yes	characteristic
50	#13094018	—	2	2	no	—
51	#13094018	—	2	2	no	—
52	#13094016	—	2	1	no	—
53	#13094016	—	2	1	no	—
54	#13094016	C₂×C₄	1	2	yes	—
55	#13094012	—	2	1	no	—
56	#13094012	—	2	1	no	—
57	#13094012	C₂×C₄	1	2	yes	—
58	#13094007	—	2	2	no	—
59	#13094007	—	2	2	no	—
60	#13094007	—	2	2	no	—
61	#13094003	—	2	1	no	—
62	#13094003	—	2	1	no	—
63	#13094003	—	2	1	no	—
64	#13094003	—	2	1	no	—
65	#13094003	C₂×C₄	1	2	yes	—
66	#13094003	C₂×C₄	1	2	yes	—
67	#13093998	—	2	1	no	—
68	#13093998	—	2	1	no	—
69	#13093998	—	2	1	no	—
70	#13093998	—	2	1	no	—
71	#13093998	C₂×C₄	1	2	yes	—
72	#13093998	C₂×C₄	1	2	yes	—
73	#13093993	—	2	2	no	—
74	C₄×Dic₉₄	—	2	1	no	—
75	C₄×Dic₉₄	—	2	1	no	—
76	C₄×Dic₉₄	—	2	1	no	—
77	C₄×Dic₉₄	—	2	1	no	—
78	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
79	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
80	C₄×D₁₈₈	—	2	1	no	—
81	C₄×D₁₈₈	—	2	1	no	—
82	C₄×D₁₈₈	—	2	1	no	—
83	C₄×D₁₈₈	—	2	1	no	—
84	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
85	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
86	C₄×C₂²⋊D₄₇	—	2	2	no	—
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	#13093983	—	2	8	no	—
93	#13093983	—	2	1	no	—
94	#13093983	—	2	1	no	—
95	#13093983	C₂³	1	2	yes	—
96	#13093981	—	2	2	no	—
97	#13093981	—	2	2	no	—
98	#13093981	—	2	2	no	—
99	C₂×C₄⋊Dic₄₇	—	2	2	no	—
100	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
101	C₂×C₄×Dic₄₇	—	2	2	no	—
102	C₂×C₄×Dic₄₇	—	2	2	no	—
103	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
104	C₄²×D₄₇	—	2	2	no	—
105	#13093950	—	2	16	no	—
106	C₄₇⋊#95	—	2	2	no	—
107	C₄₇⋊#95	—	2	2	no	—
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×M₁₆×C₄₇	—	2	8	no	—
113	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
114	C₂²×C₈×C₄₇	—	2	2	no	—
115	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄²×C₄₇	C₂×C₄	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	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
127	#97×C₄₇	—	2	2	no	—
128	#97×C₄₇	—	2	2	no	—
129	C₄×C₈×C₄₇	—	2	2	no	—
130	C₄×C₈×C₄₇	—	2	2	no	—
131	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	—	2	4	no	—
133	C₂²×C₄×C₄₇	—	2	4	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	4	no	—
157	#10625350	—	2	8	no	—
158	#10625350	—	4	4	no	—
159	#10625350	—	4	4	no	—
160	C₂×D₁₈₈	—	2	1	no	—
161	C₂×D₁₈₈	—	2	1	no	—
162	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
163	C₂×C₄×D₄₇	—	2	2	no	—
164	C₂×C₄×D₄₇	—	2	2	no	—
165	C₂×C₄×D₄₇	—	2	2	no	—
166	C₂×Dic₉₄	—	2	1	no	—
167	C₂×Dic₉₄	—	2	1	no	—
168	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
169	M₁₆×C₄₇	—	2	8	no	—
170	M₁₆×C₄₇	—	2	4	no	—
171	M₁₆×C₄₇	#41	1	8	yes	complemented
172	C₂×C₈×C₄₇	—	2	8	no	—
173	C₂×C₈×C₄₇	—	2	4	no	—
174	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×D₄	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	C₂²⋊Dic₄₇	—	2	8	no	—
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	1	no	—
202	C₄⋊Dic₄₇	—	2	1	no	—
203	C₄⋊Dic₄₇	—	2	1	no	—
204	C₄⋊Dic₄₇	—	2	1	no	—
205	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
206	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
207	Dic₄₇⋊C₄	—	2	2	no	—
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	C₄×Dic₄₇	—	2	8	no	—
214	C₄×Dic₄₇	—	2	2	no	—
215	C₄×Dic₄₇	—	2	2	no	—
216	C₄×Dic₄₇	—	2	2	no	—
217	C₄×Dic₄₇	—	2	8	no	—
218	C₄×Dic₄₇	—	4	4	no	—
219	C₂³×C₄₇	—	2	2	no	—
220	C₂³×C₄₇	—	2	2	no	—
221	C₂³×C₄₇	—	4	1	no	—
222	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
225	C₂²×D₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	2	2	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	—	4	1	no	—
240	C₂×C₄×C₄₇	—	4	1	no	—
241	C₂×C₄×C₄₇	—	4	1	no	—
242	C₂×C₄×C₄₇	#104	1	4	yes	complemented
243	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
256	C₂²⋊D₄₇	—	4	4	no	—
257	C₂²⋊D₄₇	—	4	4	no	—
258	C₂²⋊D₄₇	—	4	4	no	—
259	C₂×Dic₄₇	—	2	8	no	—
260	C₂×Dic₄₇	—	2	2	no	—
261	C₂×Dic₄₇	—	2	2	no	—
262	C₂×Dic₄₇	—	2	2	no	—
263	C₂×Dic₄₇	—	4	4	no	—
264	C₂×Dic₄₇	—	4	4	no	—
265	D₁₈₈	—	2	4	no	—
266	D₁₈₈	—	4	2	no	—
267	D₁₈₈	—	4	2	no	—
268	C₄×D₄₇	—	4	4	no	—
269	C₄×D₄₇	—	4	4	no	—
270	C₄×D₄₇	—	4	4	no	—
271	Dic₉₄	—	2	4	no	—
272	Dic₉₄	—	4	2	no	—
273	Dic₉₄	—	4	2	no	—
274	C₈×C₄₇	—	2	8	no	—
275	#21382	—	47	1	no	maximal, Sylow
276	C₂²×C₄₇	—	2	1	no	—
277	C₂²×C₄₇	—	2	1	no	—
278	C₂²×C₄₇	—	2	1	no	—
279	C₂²×C₄₇	—	2	1	no	—
280	C₂²×C₄₇	—	2	1	no	—
281	C₂²×C₄₇	—	2	1	no	—
282	C₂²×C₄₇	—	2	1	no	—
283	C₂²×C₄₇	—	4	4	no	—
284	C₂²×C₄₇	C₂×#104	1	2	yes	—
285	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
286	C₂²×C₄₇	#532	1	2	yes	—
287	C₂×D₄₇	—	4	2	no	—
288	C₂×D₄₇	—	4	2	no	—
289	C₂×D₄₇	—	4	2	no	—
290	C₄×C₄₇	—	2	1	no	—
291	C₄×C₄₇	—	2	1	no	—
292	C₄×C₄₇	—	2	1	no	—
293	C₄×C₄₇	—	2	1	no	—
294	C₄×C₄₇	—	2	1	no	—
295	C₄×C₄₇	—	2	1	no	—
296	C₄×C₄₇	—	2	1	no	—
297	C₄×C₄₇	C₂×#104	1	2	yes	—
298	C₄×C₄₇	C₂×#104	1	2	yes	—
299	C₄×C₄₇	#421	1	2	yes	—
300	C₄×C₄₇	C₄×#41	1	2	yes	—
301	C₄×C₄₇	#525	1	2	yes	—
302	Dic₄₇	—	4	8	no	—
303	Dic₄₇	—	4	2	no	—
304	Dic₄₇	—	4	2	no	—
305	Dic₄₇	—	4	2	no	—
306	#3444	—	47	1	no	—
307	C₂×C₄×M₁₆	D₄₇	1	1	yes	characteristic, complemented
308	C₄×#117	—	47	1	no	—
309	#1986	—	47	2	no	—
310	#1980	—	47	2	no	—
311	#1871	—	47	4	no	—
312	C₄×#104	—	47	4	no	—
313	C₂×C₄₇	—	2	2	no	—
314	C₂×C₄₇	—	2	2	no	—
315	C₂×C₄₇	—	4	1	no	—
316	C₂×C₄₇	#2297	1	1	yes	characteristic
317	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
318	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
319	D₄₇	—	8	2	no	—
320	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
321	#533	—	47	1	no	—
322	#533	—	47	1	no	—
323	#533	—	47	1	no	—
324	#532	—	47	1	no	—
325	#532	—	47	1	no	—
326	#532	—	47	1	no	—
327	#529	—	47	2	no	—
328	#529	—	47	2	no	—
329	#529	—	94	1	no	—
330	#529	—	94	1	no	—
331	#529	—	94	1	no	—
332	#529	—	94	1	no	—
333	#525	—	47	2	no	—
334	#525	—	94	1	no	—
335	#525	—	94	1	no	—
336	C₄×#41	—	47	2	no	—
337	C₄×#41	—	94	1	no	—
338	C₄×#41	—	94	1	no	—
339	C₂×#117	—	94	1	no	—
340	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
341	C₂×#104	—	47	8	no	—
342	C₄×M₁₆	—	2	1	no	—
343	C₄×M₁₆	—	2	1	no	—
344	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
345	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
346	C₂×#97	—	2	1	no	—
347	C₂×C₄×C₈	—	2	1	no	—
348	C₄×C₄⋊C₄	—	47	2	no	—
349	C₄×C₄⋊C₄	—	94	1	no	—
350	C₄×C₂²⋊C₄	—	47	2	no	—
351	C₄×C₂²⋊C₄	—	94	1	no	—
352	#376	—	94	1	no	—
353	C₄³	—	47	2	no	—
354	#339	—	47	8	no	—
355	C₄₇	#21382	1	1	yes	characteristic, complemented, Sylow
356	C₂×#41	—	47	2	no	—
357	C₂×#41	—	94	1	no	—
358	C₂×#41	—	94	1	no	—
359	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
360	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
361	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
362	C₂×M₁₆	—	2	2	no	—
363	C₂×M₁₆	—	2	8	no	—
364	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
365	C₂²×C₈	—	2	2	no	—
366	C₄⋊Q₈	—	47	1	no	—
367	C₄⋊Q₈	—	47	1	no	—
368	C₄⋊Q₈	—	47	1	no	—
369	#127	—	47	1	no	—
370	#126	—	94	2	no	—
371	#126	—	94	2	no	—
372	#125	—	47	2	no	—
373	#125	—	94	1	no	—
374	#125	—	94	1	no	—
375	#124	—	47	2	no	—
376	#124	—	94	1	no	—
377	#124	—	94	1	no	—
378	#123	—	94	2	no	—
379	#123	—	94	2	no	—
380	#123	—	94	2	no	—
381	C₂²⋊Q₈	—	47	2	no	—
382	C₂²⋊Q₈	—	47	2	no	—
383	C₂²⋊Q₈	—	94	1	no	—
384	C₂²⋊Q₈	—	94	1	no	—
385	C₂²⋊Q₈	—	94	1	no	—
386	C₂²⋊Q₈	—	94	1	no	—
387	#121	—	47	2	no	—
388	#121	—	47	2	no	—
389	#121	—	94	1	no	—
390	#121	—	94	1	no	—
391	#121	—	94	1	no	—
392	#121	—	94	1	no	—
393	#120	—	94	2	no	—
394	C₄×Q₈	—	47	2	no	—
395	C₄×Q₈	—	47	2	no	—
396	C₄×Q₈	—	94	1	no	—
397	C₄×Q₈	—	94	1	no	—
398	C₄×Q₈	—	94	1	no	—
399	C₄×Q₈	—	94	1	no	—
400	C₄×D₄	—	47	2	no	—
401	C₄×D₄	—	47	2	no	—
402	C₄×D₄	—	94	2	no	—
403	C₄×D₄	—	94	2	no	—
404	C₄×D₄	—	94	2	no	—
405	C₄×D₄	—	94	2	no	—
406	C₄×D₄	—	94	2	no	—
407	C₄×D₄	—	94	2	no	—
408	C₄×D₄	—	94	1	no	—
409	C₄×D₄	—	94	1	no	—
410	C₄×D₄	—	94	1	no	—
411	C₄×D₄	—	94	1	no	—
412	#117	—	47	2	no	—
413	#117	—	94	8	no	—
414	#117	—	94	1	no	—
415	#117	—	94	1	no	—
416	#117	—	94	2	no	—
417	#117	—	94	2	no	—
418	#117	—	94	2	no	—
419	C₂×C₄⋊C₄	—	94	2	no	—
420	C₂×C₂²⋊C₄	—	94	2	no	—
421	C₂×C₄²	—	47	4	no	—
422	C₂×C₄²	—	94	2	no	—
423	C₂×C₄²	—	94	2	no	—
424	C₂×C₄²	—	94	2	no	—
425	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
426	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
427	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
428	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
430	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
431	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
432	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
433	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
434	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
435	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
436	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
437	#104	—	94	16	no	—
438	#97	—	2	2	no	—
439	#97	—	2	2	no	—
440	C₄×C₈	—	2	2	no	—
441	C₄×C₈	—	2	2	no	—
442	#95	—	94	2	no	—
443	#95	—	94	2	no	—
444	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
445	#41	—	94	8	no	—
446	#41	—	188	4	no	—
447	#41	—	188	4	no	—
448	C₂×Q₈	—	47	2	no	—
449	C₂×Q₈	—	94	1	no	—
450	C₂×Q₈	—	94	1	no	—
451	C₂×D₄	—	47	2	no	—
452	C₂×D₄	—	94	2	no	—
453	C₂×D₄	—	94	2	no	—
454	C₂×D₄	—	94	2	no	—
455	C₂×D₄	—	94	1	no	—
456	C₂×D₄	—	94	1	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	94	4	no	—
461	C₂²×C₄	—	94	2	no	—
462	C₂²×C₄	—	94	2	no	—
463	C₂²×C₄	—	94	2	no	—
464	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
465	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
466	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
467	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
468	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
469	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
470	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
471	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
481	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
482	M₁₆	—	2	8	no	—
483	M₁₆	—	2	4	no	—
484	M₁₆	#10625350	1	8	yes	complemented
485	C₂×C₈	—	2	8	no	—
486	C₂×C₈	—	2	4	no	—
487	C₄⋊C₄	—	47	2	no	—
488	C₄⋊C₄	—	47	2	no	—
489	C₄⋊C₄	—	94	8	no	—
490	C₄⋊C₄	—	94	2	no	—
491	C₄⋊C₄	—	94	2	no	—
492	C₄⋊C₄	—	94	2	no	—
493	C₄⋊C₄	—	94	2	no	—
494	C₄⋊C₄	—	94	2	no	—
495	C₄⋊C₄	—	94	2	no	—
496	C₄⋊C₄	—	94	1	no	—
497	C₄⋊C₄	—	94	1	no	—
498	C₄⋊C₄	—	94	1	no	—
499	C₄⋊C₄	—	94	1	no	—
500	C₂²⋊C₄	—	94	8	no	—
501	C₂²⋊C₄	—	94	2	no	—
502	C₂²⋊C₄	—	94	2	no	—
503	C₂²⋊C₄	—	94	2	no	—
504	C₂²⋊C₄	—	94	2	no	—
505	C₂²⋊C₄	—	94	2	no	—
506	C₂²⋊C₄	—	94	2	no	—
507	C₂²⋊C₄	—	94	2	no	—
508	C₂²⋊C₄	—	94	2	no	—
509	C₂²⋊C₄	—	94	2	no	—
510	C₄²	—	94	8	no	—
511	C₄²	—	94	2	no	—
512	C₄²	—	94	2	no	—
513	C₄²	—	94	2	no	—
514	C₄²	—	94	8	no	—
515	C₄²	—	188	4	no	—
516	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
517	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
518	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
519	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
520	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
521	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
522	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
523	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
524	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
525	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
526	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
527	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
528	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
529	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
530	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
531	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
532	C₂³	—	2	2	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	94	2	no	—
536	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
537	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
538	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
539	Q₈	—	94	4	no	—
540	Q₈	—	188	2	no	—
541	Q₈	—	188	2	no	—
542	D₄	—	94	4	no	—
543	D₄	—	188	2	no	—
544	D₄	—	188	4	no	—
545	D₄	—	188	4	no	—
546	D₄	—	188	4	no	—
547	D₄	—	188	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	94	8	no	—
565	C₂×C₄	—	94	2	no	—
566	C₂×C₄	—	94	2	no	—
567	C₂×C₄	—	94	2	no	—
568	C₂×C₄	—	188	4	no	—
569	C₂×C₄	—	188	4	no	—
570	C₂×C₄	—	188	4	no	—
571	C₂×C₄	—	188	4	no	—
572	C₂×C₄	—	188	4	no	—
573	C₂×C₄	#13093950	1	4	yes	complemented
574	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
575	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
576	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
577	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
578	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
579	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
580	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
581	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
582	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
583	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
584	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
585	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
586	C₂×C₄	C₂×#10625350	1	4	yes	—
587	C₈	—	2	8	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	188	2	no	—
597	C₂²	—	188	2	no	—
598	C₂²	—	188	2	no	—
599	C₂²	C₂×#13093950	1	2	yes	—
600	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
601	C₂²	#15689673	1	2	yes	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	188	8	no	—
610	C₄	—	188	2	no	—
611	C₄	—	188	2	no	—
612	C₄	—	188	2	no	—
613	C₄	C₂×#13093950	1	2	yes	—
614	C₄	C₂×#13093950	1	2	yes	—
615	C₄	#15689139	1	2	yes	—
616	C₄	C₄×#10625350	1	2	yes	—
617	C₄	#15689634	1	2	yes	—
618	C₂	—	2	2	no	—
619	C₂	—	2	2	no	—
620	C₂	—	4	1	no	—
621	C₂	—	376	2	no	—
622	C₂	#20245878	1	1	yes	characteristic
623	C₂	C₂²×#13093950	1	1	yes	characteristic
624	C₂	C₂×#15689139	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	#20256684	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₄₇
hypocenter	C₄₇	#21382
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×#13093983	C₂	semidirect
3. #20244332	C₂	semidirect
4. #20244307	C₂	semidirect
5. #20243690	C₂	semidirect
6. C₄×#13093950	C₂	semidirect
7. C₂×C₄×M₁₆×C₄₇	C₂	semidirect
8. #15689680	C₄	semidirect
9. #15689680	C₄	semidirect
11. #15689673	C₄	semidirect
12. #15689673	C₄	semidirect
18. #15689657	C₄	semidirect
19. #15689657	C₄	semidirect
171. M₁₆×C₄₇	#41	semidirect
242. C₂×C₄×C₄₇	#104	semidirect
307. C₂×C₄×M₁₆	D₄₇	semidirect
355. C₄₇	#21382	semidirect
484. M₁₆	#10625350	semidirect
573. C₂×C₄	#13093950	semidirect

Maximal subgroups

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

subgroup	index
#20256684	2
C₄×#13093983	2
#20244332	2
#20244307	2
#20243690	2
C₄×#13093950	2
C₂×C₄×M₁₆×C₄₇	2
#21382	47