Subgroups — #26108970

Order 12032.

688 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13093986	C₂	1	1	yes	maximal, characteristic
2	#20243504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15688852	C₂	1	1	yes	maximal, characteristic
5	C₂×#15688850	C₂	1	1	yes	maximal, characteristic
6	#20241229	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#13093986	C₄	1	1	yes	characteristic
10	C₂×#13093986	C₄	1	1	yes	characteristic
11	C₂×C₄²×D₄₇	—	2	1	no	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₇⋊C₈	—	2	1	no	—
14	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
16	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
17	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
18	#15688970	—	2	1	no	—
19	#15688970	—	2	1	no	—
20	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
21	#15688877	—	2	1	no	—
22	#15688877	—	2	1	no	—
23	#15688877	—	2	1	no	—
24	#15688852	—	2	2	no	—
25	#15688850	—	2	2	no	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₇	—	2	1	no	—
31	C₂²×C₄×D₄₇	—	2	1	no	—
32	C₂²×C₄×D₄₇	—	2	1	no	—
33	C₂²×C₄₇⋊C₈	—	2	1	no	—
34	C₂²×C₄₇⋊C₈	—	2	1	no	—
35	C₄×D₁₈₈	—	2	1	no	—
36	C₄×D₁₈₈	—	2	1	no	—
37	C₄×D₁₈₈	D₄	1	2	yes	—
38	C₄×D₁₈₈	Q₈	1	2	yes	—
39	#13093986	—	2	2	no	—
40	#13093986	—	2	2	no	—
41	#13093986	—	2	2	no	—
42	#13093986	C₈	1	4	yes	complemented
43	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
45	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
46	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
47	C₂×C₄×Dic₄₇	—	2	1	no	—
48	C₂×C₄×Dic₄₇	—	2	1	no	—
49	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
55	C₄²×D₄₇	—	4	2	no	—
56	C₄²×D₄₇	—	4	2	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
59	Dic₄₇⋊C₈	—	2	4	no	—
60	C₄×C₄₇⋊C₈	—	2	1	no	—
61	C₄×C₄₇⋊C₈	—	2	1	no	—
62	C₄₇⋊#95	—	2	1	no	—
63	C₄₇⋊#95	—	2	1	no	—
64	C₂²×C₈×C₄₇	—	2	1	no	—
65	C₂²×C₈×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	—	2	1	no	—
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₄₇	—	2	1	no	—
71	C₄⋊C₈×C₄₇	—	2	1	no	—
72	C₄×C₈×C₄₇	—	2	1	no	—
73	C₄×C₈×C₄₇	—	2	1	no	—
74	#95×C₄₇	—	2	1	no	—
75	C₂³×D₄₇	—	2	1	no	—
76	C₂²×C₄×C₄₇	—	2	1	no	—
77	C₂²×C₄×C₄₇	—	2	1	no	—
78	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×Dic₄₇	—	2	1	no	—
82	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×D₁₈₈	—	2	1	no	—
87	C₂×D₁₈₈	—	2	1	no	—
88	C₂×D₁₈₈	—	2	1	no	—
89	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
90	C₂×D₁₈₈	C₂×C₈	1	2	yes	—
91	C₂×D₁₈₈	M₁₆	1	2	yes	—
92	C₂×C₄×D₄₇	—	2	4	no	—
93	C₂×C₄×D₄₇	—	2	2	no	—
94	C₂×C₄×D₄₇	—	2	2	no	—
95	C₂×C₄×D₄₇	—	2	4	no	—
96	C₂×C₄×D₄₇	—	4	2	no	—
97	C₂×C₄×D₄₇	—	4	2	no	—
98	C₂×C₄×D₄₇	—	4	2	no	—
99	C₂×C₄×D₄₇	—	4	1	no	—
100	C₂×C₄×D₄₇	—	4	1	no	—
101	C₂×C₄×D₄₇	—	4	1	no	—
102	C₂×C₄×D₄₇	—	4	1	no	—
103	C₂×C₄×D₄₇	—	4	2	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	4	1	no	—
106	C₂×C₈×C₄₇	—	4	1	no	—
107	C₂×C₈×C₄₇	—	4	1	no	—
108	C₂×C₈×C₄₇	—	4	1	no	—
109	C₂×C₈×C₄₇	—	4	1	no	—
110	C₄⋊C₄×C₄₇	—	2	1	no	—
111	C₄⋊C₄×C₄₇	—	2	1	no	—
112	C₄⋊C₄×C₄₇	C₂×C₈	1	2	yes	—
113	C₄⋊C₄×C₄₇	M₁₆	1	2	yes	—
114	C₄²×C₄₇	—	4	1	no	—
115	C₄²×C₄₇	—	4	1	no	—
116	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
118	C₄²×C₄₇	#41	1	1	yes	characteristic
119	C₄²×C₄₇	#41	1	1	yes	characteristic
120	(C₂×D₄₇)⋊C₄	—	2	4	no	—
121	(C₂×D₄₇)⋊C₄	—	2	2	no	—
122	(C₂×D₄₇)⋊C₄	—	2	2	no	—
123	(C₂×D₄₇)⋊C₄	—	2	4	no	—
124	C₄⋊Dic₄₇	—	2	1	no	—
125	C₄⋊Dic₄₇	C₄⋊C₄	1	2	yes	—
126	C₄×Dic₄₇	—	2	1	no	—
127	C₄×Dic₄₇	—	2	1	no	—
128	C₄×Dic₄₇	—	2	1	no	—
129	C₄×Dic₄₇	—	2	1	no	—
130	C₄×Dic₄₇	—	2	1	no	—
131	C₄×Dic₄₇	—	2	1	no	—
132	C₄×Dic₄₇	—	2	2	no	—
133	C₄×Dic₄₇	—	4	1	no	—
134	C₄×Dic₄₇	—	4	2	no	—
135	C₄×Dic₄₇	—	4	2	no	—
136	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
137	C₄×Dic₄₇	M₁₆	1	2	yes	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	4	1	no	—
140	C₂×C₄₇⋊C₈	—	4	1	no	—
141	C₂×C₄₇⋊C₈	—	4	1	no	—
142	C₂×C₄₇⋊C₈	—	4	1	no	—
143	C₂×C₄₇⋊C₈	—	4	1	no	—
144	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×D₄₇	—	2	2	no	—
146	C₂²×D₄₇	—	2	2	no	—
147	C₂²×D₄₇	—	2	2	no	—
148	C₂²×D₄₇	—	4	1	no	—
149	C₂²×D₄₇	—	4	1	no	—
150	C₂²×D₄₇	—	4	1	no	—
151	C₂²×D₄₇	—	4	1	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	4	1	no	—
157	C₂×C₄×C₄₇	—	4	1	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
170	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
171	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
172	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂×Dic₄₇	—	2	1	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	1	no	—
183	C₂×Dic₄₇	—	2	1	no	—
184	C₂×Dic₄₇	—	4	1	no	—
185	C₂×Dic₄₇	—	4	1	no	—
186	C₂×Dic₄₇	C₂²⋊C₈	1	2	yes	—
187	C₂×Dic₄₇	C₂²⋊C₈	1	2	yes	—
188	C₂×Dic₄₇	#104	1	2	yes	—
189	D₁₈₈	—	2	2	no	—
190	D₁₈₈	—	2	2	no	—
191	D₁₈₈	—	2	2	no	—
192	D₁₈₈	C₄⋊C₈	1	4	yes	complemented
193	C₄×D₄₇	—	4	8	no	—
194	C₄×D₄₇	—	4	8	no	—
195	C₄×D₄₇	—	4	2	no	—
196	C₄×D₄₇	—	4	2	no	—
197	C₄×D₄₇	—	4	2	no	—
198	C₄×D₄₇	—	4	2	no	—
199	C₈×C₄₇	—	4	2	no	—
200	C₈×C₄₇	—	8	1	no	—
201	C₄₇⋊C₈	—	4	2	no	—
202	C₄₇⋊C₈	—	8	1	no	—
203	#8565	—	47	1	no	maximal, Sylow
204	C₂²×C₄₇	#380	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
206	C₂²×C₄₇	#407	1	1	yes	characteristic
207	C₂²×C₄₇	#416	1	1	yes	characteristic
208	C₂²×C₄₇	#418	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
210	C₂²×C₄₇	#421	1	1	yes	characteristic
211	C₂×D₄₇	—	2	4	no	—
212	C₂×D₄₇	—	4	2	no	—
213	C₂×D₄₇	—	4	2	no	—
214	C₂×D₄₇	—	4	2	no	—
215	C₂×D₄₇	—	4	2	no	—
216	C₂×D₄₇	—	4	2	no	—
217	C₂×D₄₇	—	4	2	no	—
218	C₄×C₄₇	—	2	1	no	—
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	4	2	no	—
221	C₄×C₄₇	—	4	2	no	—
222	C₄×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
223	C₄×C₄₇	#423	1	1	yes	characteristic
224	C₄×C₄₇	#431	1	1	yes	characteristic
225	C₄×C₄₇	#432	1	1	yes	characteristic
226	C₄×C₄₇	#463	1	1	yes	characteristic
227	C₄×C₄₇	#463	1	1	yes	characteristic
228	C₄×C₄₇	#478	1	1	yes	characteristic
229	C₄×C₄₇	#478	1	1	yes	characteristic
230	Dic₄₇	—	2	2	no	—
231	Dic₄₇	—	2	2	no	—
232	Dic₄₇	—	2	2	no	—
233	Dic₄₇	—	4	2	no	—
234	Dic₄₇	—	4	1	no	—
235	C₄²×D₄	—	47	1	no	—
236	#1831	—	47	1	no	—
237	C₄×C₄⋊C₈	—	47	1	no	—
238	C₂×D₄⋊C₈	—	47	1	no	—
239	C₂×D₄⋊C₈	—	47	1	no	—
240	#1279	—	47	1	no	—
241	#1279	D₄₇	1	1	yes	characteristic, complemented
242	C₂×C₄₇	#1476	1	1	yes	characteristic
243	C₂×C₄₇	#1478	1	1	yes	characteristic
244	C₂×C₄₇	#1488	1	1	yes	characteristic
245	C₂×C₄₇	#1490	1	1	yes	characteristic
246	C₂×C₄₇	#1797	1	1	yes	characteristic
247	C₂×C₄₇	#1804	1	1	yes	characteristic
248	C₂×C₄₇	#1806	1	1	yes	characteristic
249	D₄₇	—	4	4	no	—
250	C₂×C₄×D₄	—	47	1	no	—
251	C₂×C₄×D₄	—	47	1	no	—
252	C₂×C₄×D₄	—	47	1	no	—
253	C₂²×C₄²	—	94	1	no	—
254	C₂×C₄⋊C₈	—	47	1	no	—
255	C₂×C₄⋊C₈	—	94	1	no	—
256	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
257	C₂×C₄×C₈	—	47	1	no	—
258	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
259	C₄×C₄⋊C₄	—	47	1	no	—
260	C₄×C₄⋊C₄	—	47	1	no	—
261	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
262	C₄×C₂²⋊C₄	—	94	1	no	—
263	C₄×C₂²⋊C₄	—	94	1	no	—
264	C₄×C₂²⋊C₄	—	94	1	no	—
265	C₄³	—	47	1	no	—
266	#336	—	94	1	no	—
267	#336	—	94	1	no	—
268	#336	—	94	1	no	—
269	D₄⋊C₈	—	94	2	no	—
270	D₄⋊C₈	—	94	2	no	—
271	C₄₇	#8565	1	1	yes	characteristic, complemented, Sylow
272	C₂²×D₄	—	47	1	no	—
273	C₂³×C₄	—	94	1	no	—
274	C₂³×C₄	—	94	1	no	—
275	C₂³×C₄	—	94	1	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	94	1	no	—
279	C₂²×C₈	—	94	1	no	—
280	C₄×D₄	—	47	4	no	—
281	C₄×D₄	—	47	2	no	—
282	C₄×D₄	—	47	2	no	—
283	C₄×D₄	—	94	2	no	—
284	C₄×D₄	—	94	2	no	—
285	C₄×D₄	—	94	2	no	—
286	C₄×D₄	—	94	1	no	—
287	C₄×D₄	—	94	1	no	—
288	C₂×C₄⋊C₄	—	47	1	no	—
289	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	—	94	1	no	—
292	C₂×C₂²⋊C₄	—	94	1	no	—
293	C₂×C₂²⋊C₄	—	94	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	47	1	no	—
296	C₂×C₄²	—	47	1	no	—
297	C₂×C₄²	—	47	1	no	—
298	C₂×C₄²	—	47	1	no	—
299	C₂×C₄²	—	47	1	no	—
300	C₂×C₄²	—	47	1	no	—
301	C₂×C₄²	—	94	1	no	—
302	C₂×C₄²	—	94	1	no	—
303	C₂×C₄²	—	188	2	no	—
304	C₂×C₄²	—	188	2	no	—
305	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	94	4	no	—
309	C₄⋊C₈	—	94	1	no	—
310	C₄⋊C₈	—	94	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	94	1	no	—
314	C₄×C₈	—	94	1	no	—
315	#95	—	2	1	no	—
316	#95	—	94	1	no	—
317	#95	—	94	1	no	—
318	C₂⁴	—	94	1	no	—
319	C₂×D₄	—	47	2	no	—
320	C₂×D₄	—	47	2	no	—
321	C₂×D₄	—	47	2	no	—
322	C₂×D₄	—	94	1	no	—
323	C₂×D₄	—	94	1	no	—
324	C₂×D₄	—	94	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	47	1	no	—
328	C₂²×C₄	—	47	1	no	—
329	C₂²×C₄	—	47	1	no	—
330	C₂²×C₄	—	47	1	no	—
331	C₂²×C₄	—	94	4	no	—
332	C₂²×C₄	—	94	4	no	—
333	C₂²×C₄	—	94	1	no	—
334	C₂²×C₄	—	94	2	no	—
335	C₂²×C₄	—	94	2	no	—
336	C₂²×C₄	—	188	2	no	—
337	C₂²×C₄	—	188	2	no	—
338	C₂²×C₄	—	188	2	no	—
339	C₂²×C₄	—	188	2	no	—
340	C₂²×C₄	—	188	1	no	—
341	C₂²×C₄	—	188	1	no	—
342	C₂²×C₄	—	188	1	no	—
343	C₂²×C₄	—	188	1	no	—
344	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	94	2	no	—
354	C₂×C₈	—	188	1	no	—
355	C₂×C₈	—	188	1	no	—
356	C₂×C₈	—	188	1	no	—
357	C₂×C₈	—	188	1	no	—
358	C₂×C₈	—	188	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	47	2	no	—
362	C₄⋊C₄	—	94	1	no	—
363	C₄⋊C₄	C₈×D₄₇	1	2	yes	—
364	C₄⋊C₄	#10625324	1	2	yes	—
365	C₂²⋊C₄	—	94	4	no	—
366	C₂²⋊C₄	—	94	4	no	—
367	C₂²⋊C₄	—	94	2	no	—
368	C₂²⋊C₄	—	94	2	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₄²	—	47	2	no	—
372	C₄²	—	47	2	no	—
373	C₄²	—	94	2	no	—
374	C₄²	—	94	1	no	—
375	C₄²	—	94	1	no	—
376	C₄²	—	94	1	no	—
377	C₄²	—	94	1	no	—
378	C₄²	—	94	1	no	—
379	C₄²	—	94	1	no	—
380	C₄²	—	188	1	no	—
381	C₄²	—	188	2	no	—
382	C₄²	—	188	2	no	—
383	C₄²	#10625350	1	1	yes	characteristic
384	C₄²	#10625350	1	1	yes	characteristic
385	C₄²	D₄×D₄₇	1	1	yes	characteristic
386	C₄²	Q₈×D₄₇	1	1	yes	characteristic
387	C₂³	—	94	2	no	—
388	C₂³	—	94	2	no	—
389	C₂³	—	94	2	no	—
390	C₂³	—	188	1	no	—
391	C₂³	—	188	1	no	—
392	C₂³	—	188	1	no	—
393	C₂³	—	188	1	no	—
394	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
395	D₄	—	47	4	no	—
396	D₄	—	94	2	no	—
397	D₄	—	94	2	no	—
398	D₄	—	94	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	47	2	no	—
408	C₂×C₄	—	47	2	no	—
409	C₂×C₄	—	47	2	no	—
410	C₂×C₄	—	94	1	no	—
411	C₂×C₄	—	94	1	no	—
412	C₂×C₄	—	94	1	no	—
413	C₂×C₄	—	94	1	no	—
414	C₂×C₄	—	94	1	no	—
415	C₂×C₄	—	94	1	no	—
416	C₂×C₄	—	94	2	no	—
417	C₂×C₄	—	94	1	no	—
418	C₂×C₄	—	94	1	no	—
419	C₂×C₄	—	94	1	no	—
420	C₂×C₄	—	188	8	no	—
421	C₂×C₄	—	188	8	no	—
422	C₂×C₄	—	188	1	no	—
423	C₂×C₄	—	188	1	no	—
424	C₂×C₄	—	188	2	no	—
425	C₂×C₄	—	188	2	no	—
426	C₂×C₄	—	188	2	no	—
427	C₂×C₄	—	188	2	no	—
428	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	#13093981	1	1	yes	characteristic
430	C₂×C₄	#13093997	1	1	yes	characteristic
431	C₂×C₄	#13093997	1	1	yes	characteristic
432	C₂×C₄	#13094002	1	1	yes	characteristic
433	C₂×C₄	#13094002	1	1	yes	characteristic
434	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
435	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
436	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
437	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
438	C₂×C₄	#13094045	1	1	yes	characteristic
439	C₂×C₄	#13094047	1	1	yes	characteristic
440	C₂×C₄	#13094048	1	1	yes	characteristic
441	C₂×C₄	#13094051	1	1	yes	characteristic
442	C₈	—	4	2	no	—
443	C₈	—	8	1	no	—
444	C₈	—	376	1	no	—
445	C₈	—	188	2	no	—
446	C₂²	—	94	4	no	—
447	C₂²	—	188	2	no	—
448	C₂²	—	188	2	no	—
449	C₂²	—	188	2	no	—
450	C₂²	—	188	2	no	—
451	C₂²	—	188	2	no	—
452	C₂²	—	188	2	no	—
453	C₂²	#15688982	1	1	yes	characteristic
454	C₂²	C₂²⋊C₈×D₄₇	1	1	yes	characteristic
455	C₂²	#15689085	1	1	yes	characteristic
456	C₂²	#15689118	1	1	yes	characteristic
457	C₂²	#15689126	1	1	yes	characteristic
458	C₂²	#104×D₄₇	1	1	yes	characteristic
459	C₂²	#15689138	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	94	2	no	—
465	C₄	—	94	2	no	—
466	C₄	—	94	2	no	—
467	C₄	—	188	1	no	—
468	C₄	—	188	2	no	—
469	C₄	C₄⋊C₈×D₄₇	1	1	yes	characteristic
470	C₄	#15689145	1	1	yes	characteristic
471	C₄	#15689174	1	1	yes	characteristic
472	C₄	#15689178	1	1	yes	characteristic
473	C₄	#15689337	1	1	yes	characteristic
474	C₄	#15689341	1	1	yes	characteristic
475	C₄	#15689422	1	1	yes	characteristic
476	C₄	#15689426	1	1	yes	characteristic
477	C₂	—	188	4	no	—
478	C₂	#20241769	1	1	yes	characteristic
479	C₂	#20241777	1	1	yes	characteristic
480	C₂	#20241821	1	1	yes	characteristic
481	C₂	#20241829	1	1	yes	characteristic
482	C₂	#20243367	1	1	yes	characteristic
483	C₂	#20243397	1	1	yes	characteristic
484	C₂	#20243407	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1279	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1279	D₄₇
hypocenter	C₄₇	#8565
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. #20243504	C₂	semidirect
3. C₄×Dic₄₇⋊C₈	C₂	semidirect
6. #20241229	C₂	semidirect
7. C₄₇×#1279	C₂	semidirect
42. #13093986	C₈	semidirect
192. D₁₈₈	C₄⋊C₈	semidirect
241. #1279	D₄₇	semidirect
271. C₄₇	#8565	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13093986	2
#20243504	2
C₄×Dic₄₇⋊C₈	2
C₂×#15688852	2
C₂×#15688850	2
#20241229	2
C₄₇×#1279	2
#8565	47