Subgroups — #26225737

Order 12032.

1194 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094024	C₂	1	1	yes	maximal, characteristic
2	#20252021	C₂	1	1	yes	maximal, characteristic
3	#20244377	C₂	1	4	yes	maximal, complemented
4	#20244376	C₂	1	4	yes	maximal, complemented
5	#20243466	C₂	1	4	yes	maximal
6	C₄₇×#2920	C₂	1	1	yes	maximal, characteristic
7	C₂³×Dic₉₄	C₄	1	2	yes	—
8	C₂×#13094024	—	2	1	no	—
9	C₂×#13094024	—	2	1	no	—
10	C₂×#13094024	—	2	1	no	—
11	C₂×#13094024	—	2	1	no	—
12	C₂×#13094024	—	2	1	no	—
13	C₂×#13094024	—	2	1	no	—
14	C₂×#13094024	—	2	1	no	—
15	C₂×#13094024	—	2	1	no	—
16	C₂×#13094024	C₄	1	2	yes	—
17	C₂×#13094024	C₄	1	2	yes	—
18	C₂×#13094024	C₂²	1	2	yes	—
19	C₂×#13094024	C₂²	1	2	yes	—
20	C₂²×C₄⋊Dic₄₇	C₄	1	2	yes	—
21	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
22	#15689180	—	2	1	no	—
23	#15689180	—	2	1	no	—
24	#15689176	—	2	1	no	—
25	#15689176	—	2	1	no	—
26	#15689147	C₂²	1	2	yes	—
27	#15689087	C₂²	1	2	yes	—
28	C₄×#10625329	C₂²	1	2	yes	—
29	#15688891	C₂²	1	16	yes	—
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#432	—	2	1	no	—
32	C₄₇×#432	—	2	1	no	—
33	C₄₇×#431	—	2	1	no	—
34	C₄₇×#431	—	2	1	no	—
35	C₄₇×#423	C₂²	1	2	yes	—
36	C₄₇×#407	C₂²	1	2	yes	—
37	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
38	C₂²×Dic₉₄	—	2	2	no	—
39	C₂²×Dic₉₄	—	2	2	no	—
40	C₂²×Dic₉₄	—	2	2	no	—
41	C₂²×Dic₉₄	—	2	2	no	—
42	C₂²×Dic₉₄	—	4	8	no	—
43	C₂²×Dic₉₄	C₂×C₄	1	4	yes	—
44	C₂²×Dic₉₄	C₂×C₄	1	4	yes	—
45	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
46	C₂×#10625329	C₂³	1	4	yes	—
47	#13094024	—	2	2	no	—
48	#13094024	—	2	2	no	—
49	#13094024	—	2	2	no	—
50	#13094024	—	2	2	no	—
51	#13094024	—	2	2	no	—
52	#13094024	—	2	2	no	—
53	#13094024	—	2	2	no	—
54	#13094024	—	2	2	no	—
55	#13094024	—	2	2	no	—
56	#13094024	—	2	2	no	—
57	#13094024	—	2	2	no	—
58	#13094024	—	2	2	no	—
59	#13094024	—	2	2	no	—
60	#13094024	—	2	2	no	—
61	#13094024	—	2	2	no	—
62	#13094024	—	2	2	no	—
63	C₂×C₄⋊Dic₄₇	—	2	2	no	—
64	C₂×C₄⋊Dic₄₇	—	2	2	no	—
65	C₂×C₄⋊Dic₄₇	—	2	2	no	—
66	C₂×C₄⋊Dic₄₇	—	2	2	no	—
67	C₂×C₄⋊Dic₄₇	—	2	2	no	—
68	C₂×C₄⋊Dic₄₇	—	2	2	no	—
69	C₂×C₄⋊Dic₄₇	—	2	2	no	—
70	C₂×C₄⋊Dic₄₇	—	2	2	no	—
71	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
72	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
73	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
74	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
75	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
76	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
79	#13093935	—	2	2	no	—
80	C₄×C₄₇⋊C₈	—	2	2	no	—
81	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
85	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₄₇	—	2	2	no	—
98	C₄⋊C₈×C₄₇	—	2	2	no	—
99	C₂²⋊C₈×C₄₇	—	2	2	no	—
100	C₂²⋊C₈×C₄₇	—	2	2	no	—
101	#97×C₄₇	—	2	2	no	—
102	C₄×C₈×C₄₇	—	2	2	no	—
103	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	4	no	—
107	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂²×Dic₄₇	—	2	4	no	—
126	C₂²×Dic₄₇	—	2	4	no	—
127	C₂²×Dic₄₇	—	4	8	no	—
128	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
129	C₂×Dic₉₄	—	2	4	no	—
130	C₂×Dic₉₄	—	2	4	no	—
131	C₂×Dic₉₄	—	2	4	no	—
132	C₂×Dic₉₄	—	2	4	no	—
133	C₂×Dic₉₄	—	4	8	no	—
134	C₂×Dic₉₄	—	4	8	no	—
135	C₂×Dic₉₄	—	4	8	no	—
136	C₂×Dic₉₄	—	4	8	no	—
137	C₂×Dic₉₄	—	4	8	no	—
138	C₂×Dic₉₄	—	4	8	no	—
139	M₁₆×C₄₇	—	2	8	no	—
140	C₂×C₈×C₄₇	—	2	4	no	—
141	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
142	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₄₇	C₂×D₄	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	C₄⋊Dic₄₇	—	2	4	no	—
158	C₄⋊Dic₄₇	—	2	4	no	—
159	C₄⋊Dic₄₇	—	2	4	no	—
160	C₄⋊Dic₄₇	—	2	4	no	—
161	C₄⋊Dic₄₇	—	2	4	no	—
162	C₄⋊Dic₄₇	—	2	4	no	—
163	C₄⋊Dic₄₇	—	2	4	no	—
164	C₄⋊Dic₄₇	—	2	4	no	—
165	#10625329	—	2	8	no	—
166	C₂×C₄₇⋊C₈	—	2	4	no	—
167	C₂³×C₄₇	—	2	2	no	—
168	C₂³×C₄₇	—	2	2	no	—
169	C₂³×C₄₇	—	2	2	no	—
170	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
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	#100	1	4	yes	—
189	C₂×C₄×C₄₇	#101	1	4	yes	—
190	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₇	2₋¹⁺⁴	1	4	yes	—
203	C₂×Dic₄₇	—	2	8	no	—
204	C₂×Dic₄₇	—	4	8	no	—
205	C₂×Dic₄₇	—	4	8	no	—
206	C₂×Dic₄₇	—	4	8	no	—
207	Dic₉₄	—	4	8	no	—
208	Dic₉₄	—	4	8	no	—
209	Dic₉₄	—	4	8	no	—
210	Dic₉₄	—	4	8	no	—
211	C₈×C₄₇	—	4	4	no	—
212	C₄₇⋊C₈	—	4	4	no	—
213	#21829	—	47	1	no	maximal, Sylow
214	C₂²×C₄₇	—	2	8	no	—
215	C₂²×C₄₇	—	2	1	no	—
216	C₂²×C₄₇	—	2	1	no	—
217	C₂²×C₄₇	—	2	1	no	—
218	C₂²×C₄₇	—	2	1	no	—
219	C₂²×C₄₇	—	2	1	no	—
220	C₂²×C₄₇	—	2	1	no	—
221	C₂²×C₄₇	C₂×#100	1	2	yes	—
222	C₂²×C₄₇	C₂×#101	1	2	yes	—
223	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
224	C₂²×C₄₇	#519	1	2	yes	—
225	C₄×C₄₇	—	2	1	no	—
226	C₄×C₄₇	—	2	1	no	—
227	C₄×C₄₇	—	2	1	no	—
228	C₄×C₄₇	—	2	1	no	—
229	C₄×C₄₇	—	2	1	no	—
230	C₄×C₄₇	—	2	1	no	—
231	C₄×C₄₇	C₂×#100	1	2	yes	—
232	C₄×C₄₇	C₂×#100	1	2	yes	—
233	C₄×C₄₇	C₂×#101	1	2	yes	—
234	C₄×C₄₇	C₂×#101	1	2	yes	—
235	C₄×C₄₇	#536	1	2	yes	—
236	C₄×C₄₇	#536	1	2	yes	—
237	Dic₄₇	—	4	8	no	—
238	C₂²×C₄⋊Q₈	—	47	1	no	—
239	#2920	—	47	1	no	—
240	#2920	D₄₇	1	1	yes	characteristic
241	#1997	—	47	4	no	—
242	#1997	—	47	4	no	—
243	#1821	—	47	4	no	—
244	C₂×C₄₇	—	2	2	no	—
245	C₂×C₄₇	—	2	2	no	—
246	C₂×C₄₇	—	2	2	no	—
247	C₂×C₄₇	#2310	1	1	yes	characteristic
248	C₂×C₄₇	C₂²×#100	1	1	yes	characteristic
249	C₂×C₄₇	C₂²×#101	1	1	yes	characteristic
250	C₂³×Q₈	—	47	2	no	—
251	C₂×C₄⋊Q₈	—	47	2	no	—
252	C₂×C₄⋊Q₈	—	47	2	no	—
253	C₂×C₄⋊Q₈	—	47	2	no	—
254	C₂×C₄⋊Q₈	—	47	2	no	—
255	C₂×C₄⋊Q₈	—	94	1	no	—
256	C₂×C₄⋊Q₈	—	94	1	no	—
257	C₂×C₄⋊Q₈	—	94	1	no	—
258	C₂×C₄⋊Q₈	—	94	1	no	—
259	C₂×C₄⋊Q₈	—	94	1	no	—
260	C₂×C₄⋊Q₈	—	94	1	no	—
261	C₂×C₄⋊Q₈	—	94	1	no	—
262	C₂×C₄⋊Q₈	—	94	1	no	—
263	C₂²×C₄⋊C₄	—	47	2	no	—
264	C₂²×C₄⋊C₄	—	47	2	no	—
265	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
266	#432	—	2	1	no	—
267	#432	—	2	1	no	—
268	#432	—	94	1	no	—
269	#432	—	94	1	no	—
270	#431	—	2	1	no	—
271	#431	—	2	1	no	—
272	#431	—	94	1	no	—
273	#431	—	94	1	no	—
274	#423	—	47	2	no	—
275	#423	C₂×D₄₇	1	2	yes	—
276	#407	—	47	2	no	—
277	#407	C₂×D₄₇	1	2	yes	—
278	C₄×M₁₆	—	47	2	no	—
279	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
280	#343	—	47	16	no	—
281	C₄₇	#21829	1	1	yes	characteristic, complemented, Sylow
282	C₂²×Q₈	—	47	4	no	—
283	C₂²×Q₈	—	47	4	no	—
284	C₂²×Q₈	—	94	2	no	—
285	C₂²×Q₈	—	94	2	no	—
286	C₂²×Q₈	—	94	2	no	—
287	C₂²×Q₈	—	94	2	no	—
288	C₂²×Q₈	—	188	8	no	—
289	C₂³×C₄	—	47	4	no	—
290	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
291	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
292	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
293	C₂×M₁₆	—	47	4	no	—
294	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
295	C₄⋊Q₈	—	94	2	no	—
296	C₄⋊Q₈	—	94	2	no	—
297	C₄⋊Q₈	—	94	2	no	—
298	C₄⋊Q₈	—	94	2	no	—
299	C₄⋊Q₈	—	94	2	no	—
300	C₄⋊Q₈	—	94	2	no	—
301	C₄⋊Q₈	—	94	2	no	—
302	C₄⋊Q₈	—	94	2	no	—
303	C₄⋊Q₈	—	94	2	no	—
304	C₄⋊Q₈	—	94	2	no	—
305	C₄⋊Q₈	—	94	2	no	—
306	C₄⋊Q₈	—	94	2	no	—
307	C₄⋊Q₈	—	94	2	no	—
308	C₄⋊Q₈	—	94	2	no	—
309	C₄⋊Q₈	—	94	2	no	—
310	C₄⋊Q₈	—	94	2	no	—
311	C₂×C₄⋊C₄	—	47	4	no	—
312	C₂×C₄⋊C₄	—	47	4	no	—
313	C₂×C₄⋊C₄	—	47	4	no	—
314	C₂×C₄⋊C₄	—	47	4	no	—
315	C₂×C₄⋊C₄	—	94	2	no	—
316	C₂×C₄⋊C₄	—	94	2	no	—
317	C₂×C₄⋊C₄	—	94	2	no	—
318	C₂×C₄⋊C₄	—	94	2	no	—
319	C₂×C₄⋊C₄	—	94	2	no	—
320	C₂×C₄⋊C₄	—	94	2	no	—
321	C₂×C₄⋊C₄	—	94	2	no	—
322	C₂×C₄⋊C₄	—	94	2	no	—
323	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
324	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
325	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
326	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
327	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
328	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
329	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
330	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
331	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
332	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
334	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	—	2	2	no	—
337	C₄⋊C₈	—	94	2	no	—
338	C₄⋊C₈	—	94	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₂²⋊C₈	—	2	2	no	—
341	C₂²⋊C₈	—	94	2	no	—
342	C₂²⋊C₈	—	94	2	no	—
343	#97	—	2	2	no	—
344	#97	—	94	2	no	—
345	C₄×C₈	—	2	2	no	—
346	C₄×C₈	—	94	2	no	—
347	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
348	C₂×Q₈	—	94	4	no	—
349	C₂×Q₈	—	94	4	no	—
350	C₂×Q₈	—	94	4	no	—
351	C₂×Q₈	—	94	4	no	—
352	C₂×Q₈	—	188	8	no	—
353	C₂×Q₈	—	188	8	no	—
354	C₂×Q₈	—	188	8	no	—
355	C₂×Q₈	—	188	8	no	—
356	C₂×Q₈	—	188	8	no	—
357	C₂×Q₈	—	188	8	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	47	8	no	—
362	C₂²×C₄	—	94	4	no	—
363	C₂²×C₄	—	94	4	no	—
364	C₂²×C₄	—	188	8	no	—
365	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
366	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
367	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
368	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
369	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
370	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
371	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
372	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
382	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
383	M₁₆	—	2	8	no	—
384	M₁₆	—	94	8	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	94	4	no	—
387	C₄⋊C₄	—	94	4	no	—
388	C₄⋊C₄	—	94	4	no	—
389	C₄⋊C₄	—	94	4	no	—
390	C₄⋊C₄	—	94	4	no	—
391	C₄⋊C₄	—	94	4	no	—
392	C₄⋊C₄	—	94	4	no	—
393	C₄⋊C₄	—	94	4	no	—
394	C₄⋊C₄	—	94	4	no	—
395	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
396	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
397	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
398	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
399	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
400	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
401	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
402	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
403	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
404	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
405	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
406	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
407	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
408	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
409	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
410	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
415	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
416	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
417	Q₈	—	188	8	no	—
418	Q₈	—	188	8	no	—
419	Q₈	—	188	8	no	—
420	Q₈	—	188	8	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	94	8	no	—
437	C₂×C₄	—	188	8	no	—
438	C₂×C₄	—	188	8	no	—
439	C₂×C₄	—	188	8	no	—
440	C₂×C₄	#13093940	1	4	yes	—
441	C₂×C₄	#13093942	1	4	yes	—
442	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
443	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
444	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
445	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
446	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
447	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
448	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
449	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
450	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
451	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
454	C₂×C₄	#13094071	1	4	yes	—
455	C₈	—	4	4	no	—
456	C₈	—	188	4	no	—
457	C₂²	—	2	8	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	C₂×#13093940	1	2	yes	—
465	C₂²	C₂×#13093942	1	2	yes	—
466	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
467	C₂²	#15689600	1	2	yes	—
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	188	8	no	—
475	C₄	C₂×#13093940	1	2	yes	—
476	C₄	C₂×#13093940	1	2	yes	—
477	C₄	C₂×#13093942	1	2	yes	—
478	C₄	C₂×#13093942	1	2	yes	—
479	C₄	#15689694	1	2	yes	—
480	C₄	#15689699	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	2	2	no	—
483	C₂	—	2	2	no	—
484	C₂	#20245972	1	1	yes	characteristic
485	C₂	C₂²×#13093940	1	1	yes	characteristic
486	C₂	C₂²×#13093942	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×(C₂×D₄₇)⋊C₄
commutator	C₂³×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2920	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2920	D₄₇
hypocenter	C₄₇	#21829
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #20244377	C₂	semidirect
4. #20244376	C₂	semidirect
281. C₄₇	#21829	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13094024	2
#20252021	2
#20244377	2
#20244376	2
#20243466	2
C₄₇×#2920	2
#21829	47