Subgroups — #26184261

Order 12032.

1028 conjugacy classes of subgroups.

The subgroup lattice has 616 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	#20241999	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241995	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241986	C₂	1	2	yes	maximal, complemented
7	#20241980	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×#15688863	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3514	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	complemented
17	#15689180	C₂²	1	1	yes	characteristic, complemented
18	#15689079	—	2	2	no	—
19	#15689079	—	2	1	no	—
20	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
21	C₄×#10625329	C₂²	1	2	yes	complemented
22	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13093935	C₂²	1	2	yes	complemented
24	C₂×#13093935	C₂²	1	2	yes	complemented
25	C₂×#13093935	C₂²	1	1	yes	characteristic, complemented
26	#15688865	C₂²	1	1	yes	characteristic, complemented
27	#15688865	C₂²	1	2	yes	complemented
28	#15688865	C₂²	1	1	yes	characteristic, complemented
29	#15688863	C₂²	1	1	yes	characteristic
30	#15688863	C₂²	1	2	yes	—
31	#15688863	C₂²	1	1	yes	characteristic
32	#15688863	C₂²	1	2	yes	complemented
33	#15688863	C₂²	1	2	yes	complemented
34	#15688863	C₂²	1	2	yes	complemented
35	#15688863	C₂²	1	2	yes	complemented
36	C₄₇×#559	C₄	1	1	yes	characteristic
37	C₄₇×#556	C₄	1	1	yes	characteristic
38	C₄₇×#555	—	2	1	no	—
39	C₄₇×#551	—	2	2	no	—
40	D₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
41	C₄₇×#548	C₄	1	2	yes	—
42	C₄₇×#546	—	2	1	no	—
43	C₄₇×#546	C₄	1	2	yes	—
44	D₄²×C₄₇	C₄	1	1	yes	characteristic
45	C₄₇×#542	—	2	1	no	—
46	C₄₇×#538	—	2	2	no	—
47	C₄₇×#532	C₂²	1	1	yes	characteristic
48	C₄₇×#529	C₂²	1	1	yes	characteristic
49	C₄₇×#529	C₂²	1	2	yes	—
50	C₂×#124×C₄₇	C₂²	1	2	yes	—
51	C₄₇×#518	—	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	C₂×C₄	1	2	yes	—
77	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
78	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
79	C₂²×D₄×C₄₇	—	2	1	no	—
80	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
81	C₄⋊Q₈×C₄₇	—	2	1	no	—
82	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
83	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
84	#126×C₄₇	—	2	2	no	—
85	#126×C₄₇	—	2	2	no	—
86	#126×C₄₇	—	2	1	no	—
87	#125×C₄₇	C₂³	1	1	yes	characteristic
88	#124×C₄₇	—	2	1	no	—
89	#124×C₄₇	—	2	2	no	—
90	#124×C₄₇	—	2	2	no	—
91	#124×C₄₇	—	2	2	no	—
92	#124×C₄₇	C₂×C₄	1	2	yes	—
93	#124×C₄₇	C₂×C₄	1	2	yes	—
94	#124×C₄₇	C₂³	1	1	yes	characteristic
95	#124×C₄₇	C₂³	1	2	yes	—
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	2	no	—
102	C₂²⋊Q₈×C₄₇	—	2	2	no	—
103	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
104	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
105	#121×C₄₇	—	2	2	no	—
106	#121×C₄₇	—	2	1	no	—
107	#121×C₄₇	—	2	1	no	—
108	#121×C₄₇	—	2	1	no	—
109	#121×C₄₇	—	2	2	no	—
110	#121×C₄₇	C₂×C₄	1	2	yes	—
111	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
112	#120×C₄₇	—	2	2	no	—
113	#120×C₄₇	—	2	2	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	1	no	—
122	C₄×D₄×C₄₇	—	2	2	no	—
123	C₄×D₄×C₄₇	—	2	1	no	—
124	C₄×D₄×C₄₇	—	2	1	no	—
125	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
126	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
127	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
128	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
129	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
130	C₄×D₄×C₄₇	D₄	1	2	yes	—
131	#117×C₄₇	—	2	1	no	—
132	#117×C₄₇	—	2	1	no	—
133	#117×C₄₇	—	2	2	no	—
134	#117×C₄₇	D₄	1	2	yes	—
135	#117×C₄₇	D₄	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
137	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
138	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
139	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
141	C₂⁴×C₄₇	—	2	2	no	—
142	#41×C₄₇	—	2	4	no	—
143	#41×C₄₇	—	8	2	no	—
144	C₂×Q₈×C₄₇	—	2	2	no	—
145	C₂×Q₈×C₄₇	—	8	2	no	—
146	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₄₇	—	2	2	no	—
150	C₂×D₄×C₄₇	—	2	1	no	—
151	C₂×D₄×C₄₇	—	2	2	no	—
152	C₂×D₄×C₄₇	—	2	1	no	—
153	C₂×D₄×C₄₇	—	2	1	no	—
154	C₂×D₄×C₄₇	—	2	2	no	—
155	C₂×D₄×C₄₇	—	4	4	no	—
156	C₂×D₄×C₄₇	—	8	2	no	—
157	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
158	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
160	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₄₇	—	2	2	no	—
162	C₂²×C₄×C₄₇	—	2	1	no	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	2	2	no	—
165	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	2	no	—
176	C₄⋊C₄×C₄₇	—	2	1	no	—
177	C₄⋊C₄×C₄₇	—	2	1	no	—
178	C₄⋊C₄×C₄₇	—	2	1	no	—
179	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
181	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
182	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
183	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
184	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
185	C₂²⋊C₄×C₄₇	—	2	2	no	—
186	C₂²⋊C₄×C₄₇	—	2	1	no	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₂²⋊C₄×C₄₇	—	2	1	no	—
189	C₂²⋊C₄×C₄₇	—	2	2	no	—
190	C₂²⋊C₄×C₄₇	—	2	2	no	—
191	C₂²⋊C₄×C₄₇	—	2	2	no	—
192	C₂²⋊C₄×C₄₇	—	2	2	no	—
193	C₂²⋊C₄×C₄₇	—	2	1	no	—
194	C₂²⋊C₄×C₄₇	—	2	2	no	—
195	C₂²⋊C₄×C₄₇	—	2	1	no	—
196	C₂²⋊C₄×C₄₇	—	2	1	no	—
197	C₂²⋊C₄×C₄₇	—	2	2	no	—
198	C₂²⋊C₄×C₄₇	—	2	2	no	—
199	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
200	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
201	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
202	C₄²×C₄₇	—	2	2	no	—
203	C₄²×C₄₇	—	2	1	no	—
204	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
205	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₄₇	C₂×D₄	1	2	yes	—
207	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₄₇	C₂×D₄	1	2	yes	—
210	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
211	#10625329	—	2	8	no	—
212	#10625329	—	2	4	no	—
213	#10625329	—	4	2	no	—
214	C₂×C₄₇⋊C₈	—	2	8	no	—
215	C₂×C₄₇⋊C₈	—	2	4	no	—
216	C₂×C₄₇⋊C₈	—	2	1	no	—
217	C₂×C₄₇⋊C₈	—	2	2	no	—
218	C₂×C₄₇⋊C₈	—	2	1	no	—
219	C₂×C₄₇⋊C₈	—	2	1	no	—
220	C₂×C₄₇⋊C₈	—	2	1	no	—
221	C₂×C₄₇⋊C₈	—	2	2	no	—
222	C₂×C₄₇⋊C₈	—	4	4	no	—
223	C₂³×C₄₇	—	2	1	no	—
224	C₂³×C₄₇	—	2	2	no	—
225	C₂³×C₄₇	—	4	4	no	—
226	C₂³×C₄₇	—	8	2	no	—
227	C₂³×C₄₇	—	8	2	no	—
228	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
230	Q₈×C₄₇	—	2	2	no	—
231	Q₈×C₄₇	—	4	1	no	—
232	Q₈×C₄₇	—	4	2	no	—
233	Q₈×C₄₇	—	8	2	no	—
234	D₄×C₄₇	—	2	4	no	—
235	D₄×C₄₇	—	4	1	no	—
236	D₄×C₄₇	—	4	2	no	—
237	D₄×C₄₇	—	4	4	no	—
238	D₄×C₄₇	—	4	2	no	—
239	D₄×C₄₇	—	8	1	no	—
240	D₄×C₄₇	—	8	2	no	—
241	D₄×C₄₇	—	8	1	no	—
242	D₄×C₄₇	—	8	2	no	—
243	D₄×C₄₇	#104	1	4	yes	—
244	C₂×C₄×C₄₇	—	2	4	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	2	1	no	—
247	C₂×C₄×C₄₇	—	2	1	no	—
248	C₂×C₄×C₄₇	—	2	1	no	—
249	C₂×C₄×C₄₇	—	2	2	no	—
250	C₂×C₄×C₄₇	—	4	2	no	—
251	C₂×C₄×C₄₇	—	4	1	no	—
252	C₂×C₄×C₄₇	—	4	2	no	—
253	C₂×C₄×C₄₇	—	4	1	no	—
254	C₂×C₄×C₄₇	—	4	2	no	—
255	C₂×C₄×C₄₇	—	8	2	no	—
256	C₂×C₄×C₄₇	—	8	2	no	—
257	C₂×C₄×C₄₇	—	8	2	no	—
258	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
259	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
265	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
267	C₄₇⋊C₈	—	2	2	no	—
268	C₄₇⋊C₈	—	2	4	no	—
269	C₄₇⋊C₈	—	2	2	no	—
270	C₄₇⋊C₈	—	2	2	no	—
271	C₄₇⋊C₈	—	4	2	no	—
272	C₄₇⋊C₈	—	4	1	no	—
273	#17652	—	47	1	no	maximal, Sylow
274	C₂²×C₄₇	—	2	2	no	—
275	C₂²×C₄₇	—	2	2	no	—
276	C₂²×C₄₇	—	2	1	no	—
277	C₂²×C₄₇	—	2	1	no	—
278	C₂²×C₄₇	—	2	1	no	—
279	C₂²×C₄₇	—	4	2	no	—
280	C₂²×C₄₇	—	4	1	no	—
281	C₂²×C₄₇	—	4	1	no	—
282	C₂²×C₄₇	—	4	2	no	—
283	C₂²×C₄₇	—	4	2	no	—
284	C₂²×C₄₇	—	4	1	no	—
285	C₂²×C₄₇	—	16	4	no	—
286	C₂²×C₄₇	C₂×#104	1	4	yes	—
287	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
288	C₄×C₄₇	—	2	1	no	—
289	C₄×C₄₇	—	2	1	no	—
290	C₄×C₄₇	—	2	2	no	—
291	C₄×C₄₇	—	2	1	no	—
292	C₄×C₄₇	—	2	2	no	—
293	C₄×C₄₇	—	2	1	no	—
294	C₄×C₄₇	—	2	2	no	—
295	C₄×C₄₇	—	2	1	no	—
296	C₄×C₄₇	—	4	2	no	—
297	C₄×C₄₇	—	4	1	no	—
298	C₄×C₄₇	—	4	1	no	—
299	C₄×C₄₇	—	4	1	no	—
300	C₄×C₄₇	C₂×#104	1	2	yes	—
301	#3514	D₄₇	1	1	yes	characteristic
302	#2970	—	47	1	no	—
303	#2875	—	47	1	no	—
304	#1532	—	47	2	no	—
305	#1530	—	47	1	no	—
306	#1529	—	47	1	no	—
307	#1527	—	47	2	no	—
308	#1525	—	47	1	no	—
309	#1524	—	47	1	no	—
310	#1524	—	47	2	no	—
311	C₂×#329	—	47	2	no	—
312	C₂×C₄₇	—	2	4	no	—
313	C₂×C₄₇	—	4	1	no	—
314	C₂×C₄₇	—	8	2	no	—
315	C₂×C₄₇	—	8	1	no	—
316	C₂×C₄₇	#2888	1	1	yes	characteristic
317	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
318	C₂×C₄₇	#2901	1	1	yes	characteristic
319	C₂×#131	—	94	1	no	—
320	#559	Dic₄₇	1	1	yes	characteristic
321	#556	Dic₄₇	1	1	yes	characteristic
322	#555	—	2	1	no	—
323	#551	—	2	2	no	—
324	D₄×Q₈	Dic₄₇	1	1	yes	characteristic
325	#548	Dic₄₇	1	2	yes	—
326	#546	—	2	1	no	—
327	#546	Dic₄₇	1	2	yes	—
328	D₄²	Dic₄₇	1	1	yes	characteristic
329	#542	—	2	1	no	—
330	#538	—	2	2	no	—
331	#532	C₂×D₄₇	1	1	yes	characteristic
332	#529	C₂×D₄₇	1	1	yes	characteristic
333	#529	C₂×D₄₇	1	2	yes	—
334	C₂×#124	C₂×D₄₇	1	2	yes	—
335	#518	—	2	1	no	—
336	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
337	#446	—	94	1	no	—
338	#435	—	94	2	no	—
339	C₈×D₄	—	94	1	no	—
340	#432	—	47	2	no	—
341	#432	—	47	1	no	—
342	#405	—	94	2	no	—
343	#405	—	94	1	no	—
344	C₄×M₁₆	—	47	2	no	—
345	C₄×M₁₆	—	47	1	no	—
346	C₄×M₁₆	—	47	1	no	—
347	C₂×#97	—	47	2	no	—
348	C₂×#97	—	47	1	no	—
349	C₂×#97	—	47	2	no	—
350	#330	—	47	1	no	—
351	#330	—	47	2	no	—
352	#330	—	47	1	no	—
353	#329	—	47	1	no	—
354	#329	—	47	2	no	—
355	#329	—	47	1	no	—
356	#329	—	47	2	no	—
357	#329	—	47	2	no	—
358	#329	—	47	2	no	—
359	#329	—	47	2	no	—
360	C₄₇	#17652	1	1	yes	characteristic, complemented, Sylow
361	C₂×#41	C₂×Dic₄₇	1	2	yes	—
362	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
363	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
366	#131	—	94	8	no	—
367	C₂×M₁₆	—	94	2	no	—
368	C₂×M₁₆	—	94	1	no	—
369	C₂×M₁₆	—	94	1	no	—
370	C₂²×C₈	—	94	2	no	—
371	C₂²×C₈	—	94	1	no	—
372	C₂²×C₈	—	94	2	no	—
373	C₄⋊Q₈	—	2	1	no	—
374	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
375	#127	C₂×Dic₄₇	1	1	yes	characteristic
376	#126	—	2	2	no	—
377	#126	—	2	2	no	—
378	#126	—	2	1	no	—
379	#125	C₂²×D₄₇	1	1	yes	characteristic
380	#124	—	2	1	no	—
381	#124	—	2	2	no	—
382	#124	—	2	2	no	—
383	#124	—	2	2	no	—
384	#124	C₂×Dic₄₇	1	2	yes	—
385	#124	C₂×Dic₄₇	1	2	yes	—
386	#124	C₂²×D₄₇	1	1	yes	characteristic
387	#124	C₂²×D₄₇	1	2	yes	—
388	#123	—	2	1	no	—
389	#123	—	2	2	no	—
390	#123	—	2	2	no	—
391	#123	—	2	2	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
396	C₂²⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
397	#121	—	2	2	no	—
398	#121	—	2	1	no	—
399	#121	—	2	1	no	—
400	#121	—	2	1	no	—
401	#121	—	2	2	no	—
402	#121	C₂×Dic₄₇	1	2	yes	—
403	#121	C₂×Dic₄₇	1	1	yes	characteristic
404	#120	—	2	2	no	—
405	#120	—	2	2	no	—
406	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
407	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
408	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
409	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
418	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
419	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
420	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
421	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
422	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
423	#117	—	2	1	no	—
424	#117	—	2	1	no	—
425	#117	—	2	2	no	—
426	#117	C₂²⋊D₄₇	1	2	yes	—
427	#117	C₂²⋊D₄₇	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	—	2	2	no	—
429	C₂×C₂²⋊C₄	—	2	2	no	—
430	C₂×C₂²⋊C₄	—	2	2	no	—
431	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
432	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
433	C₄⋊C₈	—	94	1	no	—
434	C₄⋊C₈	—	94	2	no	—
435	C₂²⋊C₈	—	94	2	no	—
436	C₂²⋊C₈	—	94	1	no	—
437	#97	—	47	1	no	—
438	#97	—	47	1	no	—
439	#97	—	47	2	no	—
440	#97	—	47	1	no	—
441	#97	—	47	2	no	—
442	#97	—	47	1	no	—
443	#97	—	94	2	no	—
444	#97	—	94	1	no	—
445	#97	—	94	2	no	—
446	C₄×C₈	—	94	2	no	—
447	C₄×C₈	—	94	1	no	—
448	C₄×C₈	—	94	1	no	—
449	C₂⁴	—	2	2	no	—
450	#41	—	2	4	no	—
451	#41	—	8	2	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	8	2	no	—
454	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
455	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
456	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	4	4	no	—
464	C₂×D₄	—	8	2	no	—
465	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
466	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
467	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
468	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
474	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
476	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
478	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
479	M₁₆	—	94	8	no	—
480	M₁₆	—	94	4	no	—
481	M₁₆	—	188	2	no	—
482	C₂×C₈	—	94	8	no	—
483	C₂×C₈	—	94	4	no	—
484	C₂×C₈	—	94	1	no	—
485	C₂×C₈	—	94	2	no	—
486	C₂×C₈	—	94	1	no	—
487	C₂×C₈	—	94	1	no	—
488	C₂×C₈	—	94	1	no	—
489	C₂×C₈	—	94	2	no	—
490	C₂×C₈	—	188	4	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
500	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
501	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
502	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
503	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
520	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
521	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	1	no	—
524	C₄²	C₂²×Dic₄₇	1	2	yes	—
525	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
526	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
527	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
528	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
529	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
530	C₄²	C₂³×D₄₇	1	1	yes	characteristic
531	C₂³	—	2	1	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	4	4	no	—
534	C₂³	—	8	2	no	—
535	C₂³	—	8	2	no	—
536	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
537	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
538	Q₈	—	2	2	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	8	2	no	—
542	D₄	—	2	4	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	4	no	—
546	D₄	—	4	2	no	—
547	D₄	—	8	1	no	—
548	D₄	—	8	2	no	—
549	D₄	—	8	1	no	—
550	D₄	—	8	2	no	—
551	D₄	#13093951	1	4	yes	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	2	no	—
565	C₂×C₄	—	8	2	no	—
566	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
567	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
568	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
569	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
570	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
571	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
572	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
573	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
574	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
575	C₈	—	94	2	no	—
576	C₈	—	94	4	no	—
577	C₈	—	94	2	no	—
578	C₈	—	94	2	no	—
579	C₈	—	188	2	no	—
580	C₈	—	188	1	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	16	4	no	—
593	C₂²	C₂×#13093951	1	4	yes	—
594	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
595	C₄	—	2	1	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	2	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	1	no	—
607	C₄	C₂×#13093951	1	2	yes	—
608	C₂	—	2	4	no	—
609	C₂	—	4	1	no	—
610	C₂	—	8	1	no	—
611	C₂	—	8	2	no	—
612	C₂	#20251867	1	1	yes	characteristic
613	C₂	C₂²×#13093951	1	1	yes	characteristic
614	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×#3514	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3514	D₄₇
hypocenter	C₄₇	#17652
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3514

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. #20241999	C₂	semidirect
5. #20241995	C₂	semidirect
6. #20241986	C₂	semidirect
7. #20241980	C₂	semidirect
8. #20241976	C₂	semidirect
9. #20241976	C₂	semidirect
10. C₂×#15688863	C₂	semidirect
16. #15689180	C₂²	semidirect
17. #15689180	C₂²	semidirect
20. C₄×#10625329	C₂²	semidirect
21. C₄×#10625329	C₂²	semidirect
22. C₄×#10625329	C₂²	semidirect
23. C₂×#13093935	C₂²	semidirect
24. C₂×#13093935	C₂²	semidirect
25. C₂×#13093935	C₂²	semidirect
26. #15688865	C₂²	semidirect
27. #15688865	C₂²	semidirect
28. #15688865	C₂²	semidirect
32. #15688863	C₂²	semidirect
33. #15688863	C₂²	semidirect
34. #15688863	C₂²	semidirect
35. #15688863	C₂²	semidirect
360. C₄₇	#17652	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
#20241999	2
#20241995	2
#20241986	2
#20241980	2
#20241976	2
C₂×#15688863	2
C₄₇×#3514	2
#17652	47