Subgroups — #26184234

Order 12032.

1036 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689680	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
3	#20242004	C₂	1	4	yes	maximal, complemented
4	#20241991	C₂	1	4	yes	maximal, complemented
5	#20241982	C₂	1	4	yes	maximal, complemented
6	C₄₇×#2920	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	—	2	1	no	—
8	#15689680	—	2	1	no	—
9	#15689680	—	2	1	no	—
10	#15689680	—	2	1	no	—
11	#15689680	—	2	1	no	—
12	#15689680	C₄	1	2	yes	—
13	#15689680	C₄	1	2	yes	—
14	#15689680	C₂²	1	2	yes	—
15	#15689680	C₂²	1	2	yes	—
16	C₂×#13094024	C₄	1	1	yes	characteristic
17	C₂×#13094024	C₄	1	1	yes	characteristic
18	C₂×#13094016	C₂²	1	2	yes	—
19	C₂×#13094003	—	2	1	no	—
20	C₂×#13094003	—	2	1	no	—
21	C₂×C₄×Dic₉₄	—	2	1	no	—
22	C₂×C₄×Dic₉₄	—	2	1	no	—
23	C₂×#13093983	C₄	1	2	yes	—
24	C₄×#10625329	—	2	1	no	—
25	C₄×#10625329	—	2	1	no	—
26	C₄×#10625329	C₂²	1	2	yes	—
27	C₄×#10625329	C₂²	1	2	yes	—
28	C₂×#13093935	C₂²	1	2	yes	—
29	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
30	#15688864	C₂²	1	16	yes	complemented
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#432	C₂²	1	2	yes	—
33	C₄₇×#432	C₂²	1	2	yes	—
34	C₄₇×#431	—	2	1	no	—
35	C₄₇×#431	—	2	1	no	—
36	C₄₇×#423	—	2	1	no	—
37	C₄₇×#407	—	2	1	no	—
38	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
39	C₂²×Dic₉₄	—	2	1	no	—
40	C₂²×Dic₉₄	—	2	1	no	—
41	C₂×#10625329	—	2	8	no	—
42	C₂×#10625329	—	2	2	no	—
43	C₂×#10625329	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	—	2	2	no	—
45	#13094024	—	2	1	no	—
46	#13094024	—	2	1	no	—
47	#13094024	—	2	1	no	—
48	#13094024	—	2	1	no	—
49	#13094024	C₂×C₄	1	2	yes	—
50	#13094024	C₂×C₄	1	2	yes	—
51	#13094024	C₂×C₄	1	2	yes	—
52	#13094024	C₂×C₄	1	2	yes	—
53	#13094016	—	2	2	no	—
54	#13094016	—	2	2	no	—
55	#13094016	C₂×C₄	1	4	yes	—
56	#13094016	C₂³	1	4	yes	—
57	#13094003	—	2	2	no	—
58	#13094003	—	2	2	no	—
59	#13094003	—	2	2	no	—
60	#13094003	—	2	2	no	—
61	#13094003	—	2	2	no	—
62	#13094003	—	2	2	no	—
63	#13094003	—	2	2	no	—
64	#13094003	—	2	2	no	—
65	C₄×Dic₉₄	—	2	2	no	—
66	C₄×Dic₉₄	—	2	2	no	—
67	C₄×Dic₉₄	—	2	2	no	—
68	C₄×Dic₉₄	—	2	2	no	—
69	C₄×Dic₉₄	—	2	2	no	—
70	C₄×Dic₉₄	—	2	2	no	—
71	C₄×Dic₉₄	—	2	2	no	—
72	C₄×Dic₉₄	—	2	2	no	—
73	#13093983	—	2	2	no	—
74	#13093983	—	2	2	no	—
75	#13093983	C₂×C₄	1	4	yes	—
76	#13093983	C₂×C₄	1	4	yes	—
77	C₂×C₄⋊Dic₄₇	—	2	1	no	—
78	C₂×C₄⋊Dic₄₇	—	2	1	no	—
79	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
81	C₂×Dic₄₇⋊C₄	—	2	2	no	—
82	C₂×Dic₄₇⋊C₄	—	2	2	no	—
83	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
84	C₂×C₄×Dic₄₇	—	2	2	no	—
85	#13093935	—	2	2	no	—
86	#13093935	C₂³	1	4	yes	—
87	C₄×C₄₇⋊C₈	—	2	2	no	—
88	C₄×C₄₇⋊C₈	—	2	2	no	—
89	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
91	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
92	C₂×M₁₆×C₄₇	—	2	2	no	—
93	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₄₇	—	2	2	no	—
106	C₄⋊C₈×C₄₇	—	2	2	no	—
107	C₂²⋊C₈×C₄₇	—	2	2	no	—
108	C₂²⋊C₈×C₄₇	—	2	2	no	—
109	#97×C₄₇	C₂³	1	4	yes	—
110	C₄×C₈×C₄₇	—	2	2	no	—
111	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	2	4	no	—
114	C₂²×C₄×C₄₇	—	4	2	no	—
115	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×Dic₄₇	—	2	2	no	—
134	C₂²×Dic₄₇	—	2	2	no	—
135	C₂×Dic₉₄	—	2	2	no	—
136	C₂×Dic₉₄	—	2	2	no	—
137	C₂×Dic₉₄	—	2	2	no	—
138	C₂×Dic₉₄	—	2	2	no	—
139	C₂×Dic₉₄	—	4	4	no	—
140	C₂×Dic₉₄	—	4	4	no	—
141	M₁₆×C₄₇	—	4	4	no	—
142	C₂×C₈×C₄₇	—	2	4	no	—
143	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
144	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
145	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
146	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
147	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
148	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
149	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
159	C₂²⋊Dic₄₇	—	2	4	no	—
160	C₂²⋊Dic₄₇	—	2	4	no	—
161	C₄⋊Dic₄₇	—	2	2	no	—
162	C₄⋊Dic₄₇	—	2	2	no	—
163	C₄⋊Dic₄₇	—	2	2	no	—
164	C₄⋊Dic₄₇	—	2	2	no	—
165	C₄⋊Dic₄₇	—	2	2	no	—
166	C₄⋊Dic₄₇	—	2	2	no	—
167	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
168	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
169	Dic₄₇⋊C₄	—	2	4	no	—
170	Dic₄₇⋊C₄	—	2	4	no	—
171	Dic₄₇⋊C₄	—	2	4	no	—
172	Dic₄₇⋊C₄	—	2	4	no	—
173	C₄×Dic₄₇	—	2	4	no	—
174	C₄×Dic₄₇	—	2	4	no	—
175	#10625329	—	2	8	no	—
176	#10625329	—	2	8	no	—
177	C₂×C₄₇⋊C₈	—	2	8	no	—
178	C₂×C₄₇⋊C₈	—	2	4	no	—
179	C₂³×C₄₇	—	2	2	no	—
180	C₂³×C₄₇	—	2	2	no	—
181	C₂³×C₄₇	—	4	1	no	—
182	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	4	1	no	—
199	C₂×C₄×C₄₇	—	4	1	no	—
200	C₂×C₄×C₄₇	—	4	1	no	—
201	C₂×C₄×C₄₇	#101	1	4	yes	—
202	C₂×C₄×C₄₇	#104	1	4	yes	—
203	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×Dic₄₇	—	2	4	no	—
216	C₂×Dic₄₇	—	2	4	no	—
217	C₂×Dic₄₇	—	4	4	no	—
218	C₂×Dic₄₇	—	4	4	no	—
219	Dic₉₄	—	4	4	no	—
220	Dic₉₄	—	4	4	no	—
221	Dic₉₄	—	4	4	no	—
222	Dic₉₄	—	4	4	no	—
223	C₈×C₄₇	—	4	4	no	—
224	C₄₇⋊C₈	—	2	8	no	—
225	#17648	—	47	1	no	maximal, Sylow
226	C₂²×C₄₇	—	2	1	no	—
227	C₂²×C₄₇	—	2	1	no	—
228	C₂²×C₄₇	—	2	1	no	—
229	C₂²×C₄₇	—	2	1	no	—
230	C₂²×C₄₇	—	2	1	no	—
231	C₂²×C₄₇	—	2	1	no	—
232	C₂²×C₄₇	—	2	1	no	—
233	C₂²×C₄₇	—	4	4	no	—
234	C₂²×C₄₇	C₂×#101	1	2	yes	—
235	C₂²×C₄₇	C₂×#104	1	2	yes	—
236	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
237	C₄×C₄₇	—	2	1	no	—
238	C₄×C₄₇	—	2	1	no	—
239	C₄×C₄₇	—	2	1	no	—
240	C₄×C₄₇	—	2	1	no	—
241	C₄×C₄₇	—	2	1	no	—
242	C₄×C₄₇	—	2	1	no	—
243	C₄×C₄₇	—	2	1	no	—
244	C₄×C₄₇	C₂×#101	1	2	yes	—
245	C₄×C₄₇	C₂×#101	1	2	yes	—
246	C₄×C₄₇	C₂×#104	1	2	yes	—
247	C₄×C₄₇	C₂×#104	1	2	yes	—
248	C₄×C₄₇	#421	1	2	yes	—
249	Dic₄₇	—	4	4	no	—
250	Dic₄₇	—	4	4	no	—
251	C₂×#533	—	47	1	no	—
252	#2920	D₄₇	1	1	yes	characteristic
253	C₂×C₄×M₁₆	—	47	1	no	—
254	#1531	—	47	4	no	—
255	#1528	—	47	4	no	—
256	#1526	—	47	4	no	—
257	C₂×C₄₇	—	2	2	no	—
258	C₂×C₄₇	—	2	2	no	—
259	C₂×C₄₇	—	4	1	no	—
260	C₂×C₄₇	C₂²×#101	1	1	yes	characteristic
261	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
262	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
263	C₂²×M₁₆	—	94	1	no	—
264	#533	—	47	2	no	—
265	#533	—	47	2	no	—
266	#533	—	47	2	no	—
267	#533	—	47	2	no	—
268	#533	—	94	1	no	—
269	#533	—	94	1	no	—
270	#533	—	94	1	no	—
271	#533	—	94	1	no	—
272	C₂×C₄⋊Q₈	—	47	1	no	—
273	C₂×C₄⋊Q₈	—	47	1	no	—
274	C₂×#125	—	47	2	no	—
275	C₂×C₂²⋊Q₈	—	94	1	no	—
276	C₂×C₂²⋊Q₈	—	94	1	no	—
277	C₂×C₄×Q₈	—	94	1	no	—
278	C₂×C₄×Q₈	—	94	1	no	—
279	C₂×#117	—	47	2	no	—
280	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
281	#432	C₂×D₄₇	1	2	yes	—
282	#432	C₂×D₄₇	1	2	yes	—
283	#431	—	2	1	no	—
284	#431	—	2	1	no	—
285	#423	—	2	1	no	—
286	#407	—	2	1	no	—
287	C₄×M₁₆	—	47	2	no	—
288	C₄×M₁₆	—	47	2	no	—
289	C₄×M₁₆	—	94	1	no	—
290	C₄×M₁₆	—	94	1	no	—
291	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
292	C₂×#97	—	47	2	no	—
293	C₂×C₄×C₈	—	94	1	no	—
294	#330	—	47	16	no	—
295	C₄₇	#17648	1	1	yes	characteristic, complemented, Sylow
296	C₂²×Q₈	—	94	1	no	—
297	C₂²×Q₈	—	94	1	no	—
298	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
299	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
300	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	—	94	8	no	—
303	C₂×M₁₆	—	94	2	no	—
304	C₂×M₁₆	—	94	2	no	—
305	C₂²×C₈	—	94	2	no	—
306	C₄⋊Q₈	—	47	2	no	—
307	C₄⋊Q₈	—	47	2	no	—
308	C₄⋊Q₈	—	47	2	no	—
309	C₄⋊Q₈	—	47	2	no	—
310	C₄⋊Q₈	—	94	1	no	—
311	C₄⋊Q₈	—	94	1	no	—
312	C₄⋊Q₈	—	94	1	no	—
313	C₄⋊Q₈	—	94	1	no	—
314	#125	—	47	4	no	—
315	#125	—	47	4	no	—
316	#125	—	94	2	no	—
317	#125	—	94	2	no	—
318	C₂²⋊Q₈	—	94	2	no	—
319	C₂²⋊Q₈	—	94	2	no	—
320	C₂²⋊Q₈	—	94	2	no	—
321	C₂²⋊Q₈	—	94	2	no	—
322	C₂²⋊Q₈	—	94	2	no	—
323	C₂²⋊Q₈	—	94	2	no	—
324	C₂²⋊Q₈	—	94	2	no	—
325	C₂²⋊Q₈	—	94	2	no	—
326	C₄×Q₈	—	94	2	no	—
327	C₄×Q₈	—	94	2	no	—
328	C₄×Q₈	—	94	2	no	—
329	C₄×Q₈	—	94	2	no	—
330	C₄×Q₈	—	94	2	no	—
331	C₄×Q₈	—	94	2	no	—
332	C₄×Q₈	—	94	2	no	—
333	C₄×Q₈	—	94	2	no	—
334	#117	—	47	4	no	—
335	#117	—	47	4	no	—
336	#117	—	94	2	no	—
337	#117	—	94	2	no	—
338	C₂×C₄⋊C₄	—	47	2	no	—
339	C₂×C₄⋊C₄	—	47	2	no	—
340	C₂×C₄⋊C₄	—	94	1	no	—
341	C₂×C₄⋊C₄	—	94	1	no	—
342	C₂×C₄⋊C₄	—	94	2	no	—
343	C₂×C₄⋊C₄	—	94	2	no	—
344	C₂×C₂²⋊C₄	—	94	2	no	—
345	C₂×C₄²	—	94	2	no	—
346	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
347	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
348	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
349	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
350	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
351	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
352	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
354	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
355	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
356	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
357	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
358	C₄⋊C₈	—	2	2	no	—
359	C₄⋊C₈	—	2	2	no	—
360	C₂²⋊C₈	—	2	2	no	—
361	C₂²⋊C₈	—	2	2	no	—
362	#97	—	47	4	no	—
363	#97	—	94	2	no	—
364	#97	C₂²×D₄₇	1	4	yes	—
365	C₄×C₈	—	2	2	no	—
366	C₄×C₈	—	94	2	no	—
367	C₄×C₈	—	94	2	no	—
368	C₂⁴	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
369	C₂×Q₈	—	94	2	no	—
370	C₂×Q₈	—	94	2	no	—
371	C₂×Q₈	—	94	2	no	—
372	C₂×Q₈	—	94	2	no	—
373	C₂×Q₈	—	188	4	no	—
374	C₂×Q₈	—	188	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	94	2	no	—
379	C₂²×C₄	—	94	2	no	—
380	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
381	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
382	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
383	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
384	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
385	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
386	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
387	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
388	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
398	M₁₆	—	4	4	no	—
399	M₁₆	—	94	8	no	—
400	M₁₆	—	94	8	no	—
401	C₂×C₈	—	2	4	no	—
402	C₂×C₈	—	94	8	no	—
403	C₂×C₈	—	94	4	no	—
404	C₄⋊C₄	—	47	4	no	—
405	C₄⋊C₄	—	47	4	no	—
406	C₄⋊C₄	—	94	4	no	—
407	C₄⋊C₄	—	94	4	no	—
408	C₄⋊C₄	—	94	2	no	—
409	C₄⋊C₄	—	94	2	no	—
410	C₄⋊C₄	—	94	2	no	—
411	C₄⋊C₄	—	94	2	no	—
412	C₄⋊C₄	—	94	2	no	—
413	C₄⋊C₄	—	94	2	no	—
414	C₄⋊C₄	—	94	4	no	—
415	C₄⋊C₄	—	94	4	no	—
416	C₂²⋊C₄	—	94	4	no	—
417	C₂²⋊C₄	—	94	4	no	—
418	C₄²	—	94	4	no	—
419	C₄²	—	94	4	no	—
420	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
421	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
422	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
423	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
424	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
425	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
426	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
427	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
428	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
429	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
430	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
431	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
432	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
433	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
434	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
435	C₄²	C₂³×D₄₇	1	1	yes	characteristic
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	4	1	no	—
439	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
440	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
441	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
442	Q₈	—	188	4	no	—
443	Q₈	—	188	4	no	—
444	Q₈	—	188	4	no	—
445	Q₈	—	188	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	94	4	no	—
463	C₂×C₄	—	94	4	no	—
464	C₂×C₄	—	188	4	no	—
465	C₂×C₄	—	188	4	no	—
466	C₂×C₄	#13093942	1	4	yes	—
467	C₂×C₄	#13093950	1	4	yes	—
468	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
469	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
470	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
471	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
472	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
473	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
474	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
475	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
476	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
477	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
478	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
480	C₈	—	4	4	no	—
481	C₈	—	94	8	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	4	4	no	—
490	C₂²	C₂×#13093942	1	2	yes	—
491	C₂²	C₂×#13093950	1	2	yes	—
492	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	188	4	no	—
501	C₄	—	188	4	no	—
502	C₄	C₂×#13093942	1	2	yes	—
503	C₄	C₂×#13093942	1	2	yes	—
504	C₄	C₂×#13093950	1	2	yes	—
505	C₄	C₂×#13093950	1	2	yes	—
506	C₄	#15689141	1	2	yes	—
507	C₂	—	2	2	no	—
508	C₂	—	2	2	no	—
509	C₂	—	4	1	no	—
510	C₂	C₂²×#13093942	1	1	yes	characteristic
511	C₂	C₂²×#13093950	1	1	yes	characteristic
512	C₂	C₂×#15689141	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#2920	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#2920	D₄₇
hypocenter	C₄₇	#17648
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
3. #20242004	C₂	semidirect
4. #20241991	C₂	semidirect
5. #20241982	C₂	semidirect
30. #15688864	C₂²	semidirect
295. C₄₇	#17648	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689680	2
C₂×C₄×#10625329	2
#20242004	2
#20241991	2
#20241982	2
C₄₇×#2920	2
#17648	47