Subgroups — #26184272

Order 12032.

964 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252402	C₂	1	1	yes	maximal, characteristic, complemented
2	#20251816	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242008	C₂	1	2	yes	maximal, complemented
4	#20242003	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241995	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241990	C₂	1	2	yes	maximal, complemented
7	#20241983	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241976	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241976	C₂	1	2	yes	maximal, complemented
10	C₂×#15688865	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3515	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	—	2	1	no	—
13	#15689254	—	2	1	no	—
14	#15689195	—	2	2	no	—
15	D₄×C₄₇⋊C₈	—	2	1	no	—
16	#15689180	C₂²	1	2	yes	—
17	#15689180	C₂²	1	1	yes	characteristic
18	#15689079	—	2	1	no	—
19	#15689079	—	2	2	no	—
20	C₄×#10625329	C₂²	1	1	yes	characteristic
21	C₄×#10625329	C₂²	1	2	yes	—
22	C₄×#10625329	C₂²	1	1	yes	characteristic
23	C₂×#13093935	C₂²	1	2	yes	—
24	C₂×#13093935	C₂²	1	2	yes	—
25	C₂×#13093935	C₂²	1	1	yes	characteristic
26	#15688865	C₂²	1	1	yes	characteristic
27	#15688865	C₂²	1	2	yes	—
28	#15688865	C₂²	1	2	yes	—
29	#15688865	C₂²	1	2	yes	—
30	#15688865	C₂²	1	1	yes	characteristic
31	#15688865	C₂²	1	2	yes	—
32	#15688865	C₂²	1	2	yes	—
33	#15688863	C₂²	1	1	yes	characteristic
34	#15688863	C₂²	1	2	yes	—
35	#15688863	C₂²	1	1	yes	characteristic
36	C₄₇×#557	C₄	1	1	yes	characteristic
37	C₄₇×#554	C₄	1	1	yes	characteristic
38	C₄₇×#554	C₄	1	1	yes	characteristic
39	C₄₇×#553	C₄	1	2	yes	—
40	C₄₇×#552	—	2	2	no	—
41	C₄₇×#552	—	2	1	no	—
42	C₄₇×#552	C₄	1	2	yes	—
43	C₄₇×#547	—	2	1	no	—
44	C₄₇×#547	C₄	1	1	yes	characteristic
45	C₄₇×#541	—	2	1	no	—
46	C₄₇×#539	—	2	2	no	—
47	C₄₇×#533	C₂²	1	1	yes	characteristic
48	C₄₇×#529	C₂²	1	1	yes	characteristic
49	C₄₇×#529	C₂²	1	2	yes	—
50	C₂×#125×C₄₇	C₂²	1	2	yes	—
51	C₄₇×#520	—	2	1	no	—
52	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
53	#13094031	—	2	8	no	—
54	C₂×#10625329	—	2	2	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂×#10625329	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	2	no	—
58	C₂²×C₄₇⋊C₈	—	2	1	no	—
59	C₂²×C₄₇⋊C₈	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
64	#13093935	—	2	2	no	—
65	#13093935	—	2	2	no	—
66	#13093935	—	2	1	no	—
67	#13093935	C₂³	1	1	yes	characteristic
68	#13093935	C₂³	1	1	yes	characteristic
69	#13093935	C₂³	1	2	yes	—
70	#13093935	C₂³	1	1	yes	characteristic
71	#13093935	C₂³	1	2	yes	—
72	#13093935	C₂³	1	1	yes	characteristic
73	C₄×C₄₇⋊C₈	—	2	1	no	—
74	C₄×C₄₇⋊C₈	—	2	2	no	—
75	C₄×C₄₇⋊C₈	—	2	1	no	—
76	C₂×#41×C₄₇	—	2	1	no	—
77	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
78	C₄⋊Q₈×C₄₇	—	2	1	no	—
79	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
81	#126×C₄₇	—	2	2	no	—
82	#126×C₄₇	—	2	2	no	—
83	#126×C₄₇	—	2	2	no	—
84	#126×C₄₇	—	2	1	no	—
85	#125×C₄₇	—	2	2	no	—
86	#125×C₄₇	—	2	2	no	—
87	#125×C₄₇	—	2	1	no	—
88	#125×C₄₇	—	2	2	no	—
89	#125×C₄₇	—	2	2	no	—
90	#125×C₄₇	C₂×C₄	1	2	yes	—
91	#125×C₄₇	C₂×C₄	1	2	yes	—
92	#125×C₄₇	C₂³	1	1	yes	characteristic
93	#125×C₄₇	C₂³	1	2	yes	—
94	#124×C₄₇	C₂³	1	1	yes	characteristic
95	#123×C₄₇	—	2	2	no	—
96	#123×C₄₇	—	2	1	no	—
97	#123×C₄₇	—	2	2	no	—
98	#123×C₄₇	—	2	2	no	—
99	#123×C₄₇	—	2	2	no	—
100	C₂²⋊Q₈×C₄₇	—	2	1	no	—
101	C₂²⋊Q₈×C₄₇	—	2	1	no	—
102	C₂²⋊Q₈×C₄₇	—	2	1	no	—
103	C₂²⋊Q₈×C₄₇	—	2	2	no	—
104	C₂²⋊Q₈×C₄₇	—	2	1	no	—
105	C₂²⋊Q₈×C₄₇	—	2	2	no	—
106	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
108	#121×C₄₇	—	2	2	no	—
109	#121×C₄₇	C₂×C₄	1	2	yes	—
110	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
111	C₄×Q₈×C₄₇	—	2	1	no	—
112	C₄×Q₈×C₄₇	—	2	1	no	—
113	C₄×Q₈×C₄₇	—	2	1	no	—
114	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
115	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
116	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
117	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
118	C₄×D₄×C₄₇	—	2	1	no	—
119	C₄×D₄×C₄₇	—	2	2	no	—
120	C₄×D₄×C₄₇	—	2	1	no	—
121	C₄×D₄×C₄₇	—	2	2	no	—
122	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
123	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
124	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
125	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
126	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
127	C₄×D₄×C₄₇	D₄	1	2	yes	—
128	#117×C₄₇	—	2	2	no	—
129	#117×C₄₇	—	2	1	no	—
130	#117×C₄₇	—	2	2	no	—
131	#117×C₄₇	C₂×C₄	1	2	yes	—
132	#117×C₄₇	D₄	1	1	yes	characteristic
133	#117×C₄₇	D₄	1	2	yes	—
134	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
135	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
138	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
139	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
141	#41×C₄₇	—	2	4	no	—
142	#41×C₄₇	—	4	4	no	—
143	C₂×Q₈×C₄₇	—	2	1	no	—
144	C₂×Q₈×C₄₇	—	2	1	no	—
145	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₄₇	—	2	2	no	—
148	C₂×D₄×C₄₇	—	2	1	no	—
149	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
150	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	—	2	2	no	—
153	C₂²×C₄×C₄₇	—	2	2	no	—
154	C₂²×C₄×C₄₇	—	2	1	no	—
155	C₂²×C₄×C₄₇	—	2	2	no	—
156	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₄⋊C₄×C₄₇	—	2	2	no	—
163	C₄⋊C₄×C₄₇	—	2	1	no	—
164	C₄⋊C₄×C₄₇	—	2	2	no	—
165	C₄⋊C₄×C₄₇	—	2	2	no	—
166	C₄⋊C₄×C₄₇	—	2	2	no	—
167	C₄⋊C₄×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	—	2	2	no	—
169	C₄⋊C₄×C₄₇	—	2	1	no	—
170	C₄⋊C₄×C₄₇	—	2	2	no	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	—	2	1	no	—
173	C₄⋊C₄×C₄₇	—	2	2	no	—
174	C₄⋊C₄×C₄₇	—	2	1	no	—
175	C₄⋊C₄×C₄₇	—	2	1	no	—
176	C₄⋊C₄×C₄₇	—	2	2	no	—
177	C₄⋊C₄×C₄₇	—	2	2	no	—
178	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
179	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
181	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
182	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
183	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
184	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
185	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
186	C₂²⋊C₄×C₄₇	—	2	2	no	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₂²⋊C₄×C₄₇	—	2	1	no	—
189	C₂²⋊C₄×C₄₇	—	2	1	no	—
190	C₂²⋊C₄×C₄₇	—	2	2	no	—
191	C₂²⋊C₄×C₄₇	—	2	2	no	—
192	C₂²⋊C₄×C₄₇	—	2	1	no	—
193	C₂²⋊C₄×C₄₇	—	2	1	no	—
194	C₂²⋊C₄×C₄₇	—	2	1	no	—
195	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
196	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
197	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
198	C₄²×C₄₇	—	2	2	no	—
199	C₄²×C₄₇	—	2	2	no	—
200	C₄²×C₄₇	—	2	1	no	—
201	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
202	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₄₇	C₂×D₄	1	2	yes	—
204	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₄₇	C₂×D₄	1	2	yes	—
207	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
208	#10625329	—	2	8	no	—
209	#10625329	—	2	4	no	—
210	#10625329	—	4	2	no	—
211	C₂×C₄₇⋊C₈	—	2	8	no	—
212	C₂×C₄₇⋊C₈	—	2	4	no	—
213	C₂×C₄₇⋊C₈	—	2	1	no	—
214	C₂×C₄₇⋊C₈	—	2	2	no	—
215	C₂×C₄₇⋊C₈	—	2	1	no	—
216	C₂×C₄₇⋊C₈	—	2	1	no	—
217	C₂×C₄₇⋊C₈	—	2	1	no	—
218	C₂×C₄₇⋊C₈	—	2	2	no	—
219	C₂×C₄₇⋊C₈	—	4	4	no	—
220	C₂³×C₄₇	—	2	1	no	—
221	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
223	Q₈×C₄₇	—	2	2	no	—
224	Q₈×C₄₇	—	4	1	no	—
225	Q₈×C₄₇	—	4	2	no	—
226	Q₈×C₄₇	—	8	1	no	—
227	D₄×C₄₇	—	2	4	no	—
228	D₄×C₄₇	—	4	1	no	—
229	D₄×C₄₇	—	4	4	no	—
230	D₄×C₄₇	—	8	1	no	—
231	D₄×C₄₇	#104	1	4	yes	—
232	C₂×C₄×C₄₇	—	2	4	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	1	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	2	2	no	—
237	C₂×C₄×C₄₇	—	2	1	no	—
238	C₂×C₄×C₄₇	—	2	1	no	—
239	C₂×C₄×C₄₇	—	4	2	no	—
240	C₂×C₄×C₄₇	—	4	1	no	—
241	C₂×C₄×C₄₇	—	4	2	no	—
242	C₂×C₄×C₄₇	—	4	1	no	—
243	C₂×C₄×C₄₇	—	4	4	no	—
244	C₂×C₄×C₄₇	—	4	2	no	—
245	C₂×C₄×C₄₇	—	8	2	no	—
246	C₂×C₄×C₄₇	—	8	2	no	—
247	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
249	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
251	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
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	C₂²×D₄	1	1	yes	characteristic
256	C₄₇⋊C₈	—	2	2	no	—
257	C₄₇⋊C₈	—	2	4	no	—
258	C₄₇⋊C₈	—	2	2	no	—
259	C₄₇⋊C₈	—	2	2	no	—
260	C₄₇⋊C₈	—	4	2	no	—
261	C₄₇⋊C₈	—	4	1	no	—
262	#17653	—	47	1	no	maximal, Sylow
263	C₂²×C₄₇	—	2	2	no	—
264	C₂²×C₄₇	—	2	2	no	—
265	C₂²×C₄₇	—	2	1	no	—
266	C₂²×C₄₇	—	2	1	no	—
267	C₂²×C₄₇	—	2	1	no	—
268	C₂²×C₄₇	—	4	1	no	—
269	C₂²×C₄₇	—	4	1	no	—
270	C₂²×C₄₇	—	4	1	no	—
271	C₂²×C₄₇	C₂×#104	1	4	yes	—
272	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
273	C₄×C₄₇	—	2	1	no	—
274	C₄×C₄₇	—	2	1	no	—
275	C₄×C₄₇	—	2	2	no	—
276	C₄×C₄₇	—	2	1	no	—
277	C₄×C₄₇	—	2	2	no	—
278	C₄×C₄₇	—	2	1	no	—
279	C₄×C₄₇	—	2	2	no	—
280	C₄×C₄₇	—	2	1	no	—
281	C₄×C₄₇	—	4	1	no	—
282	C₄×C₄₇	—	4	1	no	—
283	C₄×C₄₇	—	4	2	no	—
284	C₄×C₄₇	—	4	1	no	—
285	C₄×C₄₇	—	4	2	no	—
286	C₄×C₄₇	C₂×#104	1	2	yes	—
287	#3515	D₄₇	1	1	yes	characteristic
288	#2970	—	47	1	no	—
289	#2875	—	47	1	no	—
290	#1532	—	47	2	no	—
291	#1531	—	47	1	no	—
292	#1529	—	47	1	no	—
293	#1528	—	47	2	no	—
294	#1526	—	47	1	no	—
295	#1524	—	47	1	no	—
296	#1524	—	47	2	no	—
297	C₂×#330	—	47	2	no	—
298	C₂×C₄₇	—	2	4	no	—
299	C₂×C₄₇	—	4	1	no	—
300	C₂×C₄₇	—	8	1	no	—
301	C₂×C₄₇	#2889	1	1	yes	characteristic
302	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
303	C₂×C₄₇	#2901	1	1	yes	characteristic
304	C₂×#131	—	94	1	no	—
305	#557	Dic₄₇	1	1	yes	characteristic
306	#554	Dic₄₇	1	1	yes	characteristic
307	#554	Dic₄₇	1	1	yes	characteristic
308	#553	Dic₄₇	1	2	yes	—
309	#552	—	2	2	no	—
310	#552	—	2	1	no	—
311	#552	Dic₄₇	1	2	yes	—
312	#547	—	2	1	no	—
313	#547	Dic₄₇	1	1	yes	characteristic
314	#541	—	2	1	no	—
315	#539	—	2	2	no	—
316	#533	C₂×D₄₇	1	1	yes	characteristic
317	#529	C₂×D₄₇	1	1	yes	characteristic
318	#529	C₂×D₄₇	1	2	yes	—
319	C₂×#125	C₂×D₄₇	1	2	yes	—
320	#520	—	2	1	no	—
321	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
322	#446	—	94	1	no	—
323	#435	—	94	2	no	—
324	C₈×D₄	—	94	1	no	—
325	#432	—	47	2	no	—
326	#432	—	47	1	no	—
327	#405	—	94	1	no	—
328	#405	—	94	2	no	—
329	C₄×M₁₆	—	47	2	no	—
330	C₄×M₁₆	—	47	1	no	—
331	C₄×M₁₆	—	47	1	no	—
332	C₂×#97	—	47	2	no	—
333	C₂×#97	—	47	1	no	—
334	C₂×#97	—	47	2	no	—
335	#330	—	47	1	no	—
336	#330	—	47	2	no	—
337	#330	—	47	2	no	—
338	#330	—	47	2	no	—
339	#330	—	47	1	no	—
340	#330	—	47	2	no	—
341	#330	—	47	2	no	—
342	#329	—	47	1	no	—
343	#329	—	47	2	no	—
344	#329	—	47	1	no	—
345	C₄₇	#17653	1	1	yes	characteristic, complemented, Sylow
346	C₂×#41	—	2	1	no	—
347	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
348	#131	—	94	8	no	—
349	C₂×M₁₆	—	94	2	no	—
350	C₂×M₁₆	—	94	1	no	—
351	C₂×M₁₆	—	94	1	no	—
352	C₂²×C₈	—	94	2	no	—
353	C₂²×C₈	—	94	1	no	—
354	C₂²×C₈	—	94	2	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
357	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
358	#126	—	2	2	no	—
359	#126	—	2	2	no	—
360	#126	—	2	2	no	—
361	#126	—	2	1	no	—
362	#125	—	2	2	no	—
363	#125	—	2	2	no	—
364	#125	—	2	1	no	—
365	#125	—	2	2	no	—
366	#125	—	2	2	no	—
367	#125	C₂×Dic₄₇	1	2	yes	—
368	#125	C₂×Dic₄₇	1	2	yes	—
369	#125	C₂²×D₄₇	1	1	yes	characteristic
370	#125	C₂²×D₄₇	1	2	yes	—
371	#124	C₂²×D₄₇	1	1	yes	characteristic
372	#123	—	2	2	no	—
373	#123	—	2	1	no	—
374	#123	—	2	2	no	—
375	#123	—	2	2	no	—
376	#123	—	2	2	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
384	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
385	#121	—	2	2	no	—
386	#121	C₂×Dic₄₇	1	2	yes	—
387	#121	C₂×Dic₄₇	1	1	yes	characteristic
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
392	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
393	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
394	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
400	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
401	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
402	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
403	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
404	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
405	#117	—	2	2	no	—
406	#117	—	2	1	no	—
407	#117	—	2	2	no	—
408	#117	C₂×Dic₄₇	1	2	yes	—
409	#117	C₂²⋊D₄₇	1	1	yes	characteristic
410	#117	C₂²⋊D₄₇	1	2	yes	—
411	C₂×C₄⋊C₄	—	2	2	no	—
412	C₂×C₄⋊C₄	—	2	2	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
415	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
416	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
417	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
418	C₄⋊C₈	—	94	1	no	—
419	C₄⋊C₈	—	94	2	no	—
420	C₂²⋊C₈	—	94	2	no	—
421	C₂²⋊C₈	—	94	1	no	—
422	#97	—	47	1	no	—
423	#97	—	47	1	no	—
424	#97	—	47	1	no	—
425	#97	—	47	2	no	—
426	#97	—	47	2	no	—
427	#97	—	47	1	no	—
428	#97	—	94	2	no	—
429	#97	—	94	1	no	—
430	#97	—	94	2	no	—
431	C₄×C₈	—	94	2	no	—
432	C₄×C₈	—	94	1	no	—
433	C₄×C₈	—	94	1	no	—
434	#41	—	2	4	no	—
435	#41	—	4	4	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
439	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
443	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
444	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
450	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
452	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
454	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
455	M₁₆	—	94	8	no	—
456	M₁₆	—	94	4	no	—
457	M₁₆	—	188	2	no	—
458	C₂×C₈	—	94	8	no	—
459	C₂×C₈	—	94	4	no	—
460	C₂×C₈	—	94	1	no	—
461	C₂×C₈	—	94	2	no	—
462	C₂×C₈	—	94	1	no	—
463	C₂×C₈	—	94	1	no	—
464	C₂×C₈	—	94	1	no	—
465	C₂×C₈	—	94	2	no	—
466	C₂×C₈	—	188	4	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
484	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
485	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
486	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
487	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
490	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
501	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
502	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	2	1	no	—
506	C₄²	C₂²×Dic₄₇	1	2	yes	—
507	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
508	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
509	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
510	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
511	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
512	C₄²	C₂³×D₄₇	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
515	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
516	Q₈	—	2	2	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	2	no	—
519	Q₈	—	8	1	no	—
520	D₄	—	2	4	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	4	no	—
523	D₄	—	8	1	no	—
524	D₄	#13093951	1	4	yes	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
541	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
542	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
543	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
544	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
545	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
546	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
547	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
548	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
549	C₈	—	94	2	no	—
550	C₈	—	94	4	no	—
551	C₈	—	94	2	no	—
552	C₈	—	94	2	no	—
553	C₈	—	188	2	no	—
554	C₈	—	188	1	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	C₂×#13093951	1	4	yes	—
564	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
565	C₄	—	2	1	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	1	no	—
578	C₄	C₂×#13093951	1	2	yes	—
579	C₂	—	2	4	no	—
580	C₂	—	4	1	no	—
581	C₂	—	8	1	no	—
582	C₂	#20251871	1	1	yes	characteristic
583	C₂	C₂²×#13093951	1	1	yes	characteristic
584	C₂	#20251935	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3515	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3515	D₄₇
hypocenter	C₄₇	#17653
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3515

Complements

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

N	H ≅ G/N	type
1. #20252402	C₂	semidirect
2. #20251816	C₂	semidirect
3. #20242008	C₂	semidirect
4. #20242003	C₂	semidirect
5. #20241995	C₂	semidirect
6. #20241990	C₂	semidirect
7. #20241983	C₂	semidirect
8. #20241976	C₂	semidirect
9. #20241976	C₂	semidirect
10. C₂×#15688865	C₂	semidirect
345. C₄₇	#17653	semidirect

Maximal subgroups

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

subgroup	index
#20252402	2
#20251816	2
#20242008	2
#20242003	2
#20241995	2
#20241990	2
#20241983	2
#20241976	2
C₂×#15688865	2
C₄₇×#3515	2
#17653	47