Subgroups — #26111912

Order 12032.

644 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20251741	C₂	1	1	yes	maximal, characteristic
3	#20243365	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688871	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688871	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241271	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₄₇	—	2	1	no	—
9	C₂×#13094024	C₂²	1	1	yes	characteristic
10	C₂×#13094004	C₄	1	2	yes	—
11	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×Dic₄₇⋊C₈	—	2	1	no	—
15	C₄⋊C₈×D₄₇	—	2	2	no	—
16	C₄⋊C₈×D₄₇	—	2	2	no	—
17	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
18	#15689028	C₄	1	2	yes	—
19	#15689022	—	2	1	no	—
20	#15689022	—	2	1	no	—
21	#15688980	—	2	1	no	—
22	#15688980	—	2	1	no	—
23	#15688877	—	2	1	no	—
24	#15688871	—	2	2	no	—
25	#15688871	—	2	2	no	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#384	C₂²	1	1	yes	characteristic
29	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
30	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
33	C₂²×C₄₇⋊C₈	—	2	1	no	—
34	C₂²×C₄₇⋊C₈	—	2	1	no	—
35	C₂×C₈×D₄₇	—	2	4	no	—
36	C₂×C₈×D₄₇	—	4	2	no	—
37	C₂×C₈×D₄₇	—	4	2	no	—
38	#13094024	—	2	1	no	—
39	#13094024	—	2	1	no	—
40	#13094024	—	2	1	no	—
41	#13094024	—	2	1	no	—
42	#13094004	—	4	4	no	—
43	C₂×C₄⋊Dic₄₇	—	2	1	no	—
44	C₂×C₄⋊Dic₄₇	—	2	1	no	—
45	C₂×C₄⋊Dic₄₇	—	2	2	no	—
46	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
47	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
50	C₄²×D₄₇	—	2	1	no	—
51	C₄²×D₄₇	—	2	1	no	—
52	C₄²×D₄₇	—	2	1	no	—
53	C₄²×D₄₇	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
57	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
58	Dic₄₇⋊C₈	—	2	4	no	—
59	(C₂×D₄₇)⋊C₈	—	4	2	no	—
60	C₄₇⋊#95	—	2	2	no	—
61	C₄₇⋊#95	—	2	2	no	—
62	C₂²×C₈×C₄₇	—	2	1	no	—
63	C₂²×C₈×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₇	—	2	1	no	—
69	C₄⋊C₈×C₄₇	—	2	1	no	—
70	C₄⋊C₈×C₄₇	—	2	1	no	—
71	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
72	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×Dic₄₇	—	2	2	no	—
78	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₄₇	—	2	1	no	—
82	C₂×C₄×D₄₇	—	2	1	no	—
83	C₂×C₄×D₄₇	—	2	1	no	—
84	C₂×C₄×D₄₇	—	2	1	no	—
85	C₂×C₄×D₄₇	—	2	1	no	—
86	C₂×C₄×D₄₇	—	2	1	no	—
87	C₂×C₄×D₄₇	—	2	1	no	—
88	C₂×C₄×D₄₇	—	2	1	no	—
89	C₂×C₄×D₄₇	—	2	2	no	—
90	C₂×C₄×D₄₇	—	2	1	no	—
91	C₂×C₄×D₄₇	—	2	1	no	—
92	C₂×C₄×D₄₇	—	4	1	no	—
93	C₂×C₄×D₄₇	SD₁₆	1	2	yes	—
94	C₂×C₄×D₄₇	SD₁₆	1	2	yes	—
95	C₂×C₄×D₄₇	Q₁₆	1	2	yes	—
96	C₂×C₄×D₄₇	Q₁₆	1	2	yes	—
97	C₂×Dic₉₄	—	2	2	no	—
98	C₂×Dic₉₄	—	2	2	no	—
99	C₂×Dic₉₄	—	4	2	no	—
100	C₂×Dic₉₄	—	4	2	no	—
101	C₂×C₈×C₄₇	—	2	2	no	—
102	C₂×C₈×C₄₇	—	4	1	no	—
103	C₂×C₈×C₄₇	—	4	1	no	—
104	C₂×C₈×C₄₇	—	4	1	no	—
105	C₂×C₈×C₄₇	—	4	1	no	—
106	C₂×C₈×C₄₇	—	4	1	no	—
107	C₄⋊C₄×C₄₇	—	4	2	no	—
108	C₄⋊C₄×C₄₇	—	4	1	no	—
109	C₄⋊C₄×C₄₇	—	4	1	no	—
110	C₄⋊C₄×C₄₇	—	4	1	no	—
111	C₄⋊C₄×C₄₇	—	4	1	no	—
112	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₄₇	#41	1	1	yes	characteristic
115	C₄²×C₄₇	#41	1	1	yes	characteristic
116	(C₂×D₄₇)⋊C₄	—	4	4	no	—
117	C₄⋊Dic₄₇	—	4	4	no	—
118	C₄⋊Dic₄₇	—	4	1	no	—
119	C₄⋊Dic₄₇	—	4	1	no	—
120	C₄⋊Dic₄₇	—	4	1	no	—
121	C₄⋊Dic₄₇	—	4	1	no	—
122	C₄×Dic₄₇	—	2	1	no	—
123	C₄×Dic₄₇	—	2	1	no	—
124	C₄×Dic₄₇	—	2	1	no	—
125	C₄×Dic₄₇	—	2	1	no	—
126	C₄×Dic₄₇	—	2	1	no	—
127	C₄×Dic₄₇	—	2	1	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	4	1	no	—
130	C₂×C₄₇⋊C₈	—	4	1	no	—
131	C₂×C₄₇⋊C₈	—	4	1	no	—
132	C₂×C₄₇⋊C₈	—	4	1	no	—
133	C₂×C₄₇⋊C₈	—	4	1	no	—
134	C₈×D₄₇	—	4	8	no	—
135	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×D₄₇	—	2	1	no	—
137	C₂²×D₄₇	—	2	1	no	—
138	C₂²×D₄₇	—	2	1	no	—
139	C₂²×D₄₇	—	2	1	no	—
140	C₂²×D₄₇	#100	1	2	yes	—
141	C₂²×D₄₇	#103	1	2	yes	—
142	C₂²×D₄₇	#103	1	2	yes	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
152	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
160	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
162	C₂×Dic₄₇	—	2	1	no	—
163	C₂×Dic₄₇	—	2	1	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	2	1	no	—
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	2	1	no	—
168	C₂×Dic₄₇	—	2	1	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	#103	1	2	yes	—
173	C₂×Dic₄₇	#103	1	2	yes	—
174	C₄×D₄₇	—	2	2	no	—
175	C₄×D₄₇	—	2	2	no	—
176	C₄×D₄₇	—	2	2	no	—
177	C₄×D₄₇	—	2	2	no	—
178	C₄×D₄₇	—	2	2	no	—
179	C₄×D₄₇	—	2	2	no	—
180	C₄×D₄₇	—	2	2	no	—
181	C₄×D₄₇	—	2	2	no	—
182	C₄×D₄₇	—	4	2	no	—
183	C₄×D₄₇	—	4	2	no	—
184	Dic₉₄	—	8	2	no	—
185	Dic₉₄	—	8	2	no	—
186	C₈×C₄₇	—	4	2	no	—
187	C₈×C₄₇	—	8	1	no	—
188	C₄₇⋊C₈	—	4	2	no	—
189	C₄₇⋊C₈	—	8	1	no	—
190	#9127	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	#386	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
193	C₂²×C₄₇	#413	1	1	yes	characteristic
194	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
196	C₂²×C₄₇	#416	1	1	yes	characteristic
197	C₂²×C₄₇	#417	1	1	yes	characteristic
198	C₂×D₄₇	—	2	2	no	—
199	C₂×D₄₇	—	2	2	no	—
200	C₂×D₄₇	—	2	2	no	—
201	C₂×D₄₇	—	2	2	no	—
202	C₂×D₄₇	—	2	2	no	—
203	C₂×D₄₇	—	2	2	no	—
204	C₂×D₄₇	#333	1	4	yes	complemented
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	8	2	no	—
208	C₄×C₄₇	#450	1	1	yes	characteristic
209	C₄×C₄₇	#451	1	1	yes	characteristic
210	C₄×C₄₇	#465	1	1	yes	characteristic
211	C₄×C₄₇	#465	1	1	yes	characteristic
212	C₄×C₄₇	#467	1	1	yes	characteristic
213	C₄×C₄₇	#467	1	1	yes	characteristic
214	C₄×C₄₇	#483	1	1	yes	characteristic
215	C₄×C₄₇	#484	1	1	yes	characteristic
216	Dic₄₇	—	2	2	no	—
217	Dic₄₇	—	2	2	no	—
218	Dic₄₇	—	4	1	no	—
219	Dic₄₇	—	8	2	no	—
220	C₂²×C₄⋊C₈	—	47	1	no	—
221	#2857	—	47	1	no	—
222	#1797	—	47	1	no	—
223	C₂×#333	—	47	1	no	—
224	C₂×#333	—	47	1	no	—
225	#1296	—	47	1	no	—
226	#1296	D₄₇	1	1	yes	characteristic, complemented
227	C₂×C₄₇	C₂×#333	1	1	yes	characteristic
228	C₂×C₄₇	#1542	1	1	yes	characteristic
229	C₂×C₄₇	#1550	1	1	yes	characteristic
230	C₂×C₄₇	#1551	1	1	yes	characteristic
231	C₂×C₄₇	#1872	1	1	yes	characteristic
232	C₂×C₄₇	#1892	1	1	yes	characteristic
233	C₂×C₄₇	#1900	1	1	yes	characteristic
234	D₄₇	—	2	4	no	—
235	C₂³×C₈	—	94	1	no	—
236	C₂×C₄⋊Q₈	—	47	1	no	—
237	C₂×C₂²⋊Q₈	—	47	2	no	—
238	C₂²×C₄²	—	47	1	no	—
239	C₂×C₄⋊C₈	—	47	1	no	—
240	C₂×C₄⋊C₈	—	47	1	no	—
241	C₂×C₄⋊C₈	—	94	2	no	—
242	C₂×C₄⋊C₈	—	94	1	no	—
243	C₂×C₄⋊C₈	—	94	2	no	—
244	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
246	C₂×C₂²⋊C₈	—	94	1	no	—
247	#391	—	47	2	no	—
248	#389	—	94	1	no	—
249	#389	—	94	1	no	—
250	#384	C₂×D₄₇	1	1	yes	characteristic
251	#380	—	94	1	no	—
252	#380	—	94	1	no	—
253	#336	—	94	1	no	—
254	#333	—	94	2	no	—
255	#333	—	94	2	no	—
256	C₄₇	#9127	1	1	yes	characteristic, complemented, Sylow
257	C₂²×Q₈	—	47	2	no	—
258	C₂³×C₄	—	47	1	no	—
259	C₂³×C₄	—	47	1	no	—
260	C₂³×C₄	—	47	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	94	4	no	—
264	C₂²×C₈	—	94	1	no	—
265	C₂²×C₈	—	94	1	no	—
266	C₂²×C₈	—	188	2	no	—
267	C₂²×C₈	—	188	2	no	—
268	C₄⋊Q₈	—	94	1	no	—
269	C₄⋊Q₈	—	94	1	no	—
270	C₄⋊Q₈	—	94	1	no	—
271	C₄⋊Q₈	—	94	1	no	—
272	C₂²⋊Q₈	—	188	4	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	94	2	no	—
276	C₂×C₄⋊C₄	—	94	1	no	—
277	C₂×C₄⋊C₄	—	94	1	no	—
278	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
279	C₂×C₂²⋊C₄	—	94	2	no	—
280	C₂×C₄²	—	47	1	no	—
281	C₂×C₄²	—	47	1	no	—
282	C₂×C₄²	—	47	1	no	—
283	C₂×C₄²	—	94	1	no	—
284	C₂×C₄²	—	94	1	no	—
285	C₂×C₄²	—	94	1	no	—
286	C₂×C₄²	—	94	1	no	—
287	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	47	2	no	—
292	C₄⋊C₈	—	94	4	no	—
293	C₄⋊C₈	—	94	1	no	—
294	C₄⋊C₈	—	94	1	no	—
295	C₄⋊C₈	—	94	1	no	—
296	C₄⋊C₈	D₁₈₈	1	2	yes	—
297	C₂²⋊C₈	—	188	2	no	—
298	#95	—	94	2	no	—
299	#95	—	94	2	no	—
300	C₂⁴	—	47	1	no	—
301	C₂×Q₈	—	94	2	no	—
302	C₂×Q₈	—	94	2	no	—
303	C₂×Q₈	—	188	2	no	—
304	C₂×Q₈	—	188	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	47	1	no	—
307	C₂²×C₄	—	47	1	no	—
308	C₂²×C₄	—	47	2	no	—
309	C₂²×C₄	—	47	2	no	—
310	C₂²×C₄	—	47	2	no	—
311	C₂²×C₄	—	47	2	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	94	2	no	—
314	C₂²×C₄	—	94	1	no	—
315	C₂²×C₄	—	94	1	no	—
316	C₂²×C₄	—	94	1	no	—
317	C₂²×C₄	—	94	1	no	—
318	C₂²×C₄	—	94	1	no	—
319	C₂²×C₄	—	94	1	no	—
320	C₂²×C₄	—	94	1	no	—
321	C₂²×C₄	—	94	1	no	—
322	C₂²×C₄	—	94	1	no	—
323	C₂²×C₄	—	94	1	no	—
324	C₂²×C₄	—	94	2	no	—
325	C₂²×C₄	—	188	1	no	—
326	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
328	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	94	2	no	—
336	C₂×C₈	—	188	8	no	—
337	C₂×C₈	—	188	1	no	—
338	C₂×C₈	—	188	1	no	—
339	C₂×C₈	—	188	1	no	—
340	C₂×C₈	—	188	1	no	—
341	C₂×C₈	—	188	1	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	188	4	no	—
348	C₄⋊C₄	—	188	1	no	—
349	C₄⋊C₄	—	188	1	no	—
350	C₄⋊C₄	—	188	1	no	—
351	C₄⋊C₄	—	188	1	no	—
352	C₂²⋊C₄	—	188	4	no	—
353	C₄²	—	94	1	no	—
354	C₄²	—	94	1	no	—
355	C₄²	—	94	1	no	—
356	C₄²	—	94	1	no	—
357	C₄²	—	94	1	no	—
358	C₄²	—	94	1	no	—
359	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
360	C₄²	#10625350	1	1	yes	characteristic
361	C₄²	D₄×D₄₇	1	1	yes	characteristic
362	C₄²	#10625354	1	1	yes	characteristic
363	C₂³	—	47	2	no	—
364	C₂³	—	47	2	no	—
365	C₂³	—	47	2	no	—
366	C₂³	—	94	1	no	—
367	C₂³	—	94	1	no	—
368	C₂³	—	94	1	no	—
369	C₂³	—	94	1	no	—
370	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
371	Q₈	—	376	2	no	—
372	Q₈	—	376	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	47	2	no	—
379	C₂×C₄	—	47	2	no	—
380	C₂×C₄	—	94	1	no	—
381	C₂×C₄	—	94	1	no	—
382	C₂×C₄	—	94	1	no	—
383	C₂×C₄	—	94	1	no	—
384	C₂×C₄	—	94	2	no	—
385	C₂×C₄	—	94	2	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	2	no	—
388	C₂×C₄	—	94	2	no	—
389	C₂×C₄	—	94	2	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	94	2	no	—
392	C₂×C₄	—	94	1	no	—
393	C₂×C₄	—	94	1	no	—
394	C₂×C₄	—	94	1	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	—	188	2	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	#13093986	1	1	yes	characteristic
401	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
402	C₂×C₄	#13093994	1	1	yes	characteristic
403	C₂×C₄	#13093997	1	1	yes	characteristic
404	C₂×C₄	#13093999	1	1	yes	characteristic
405	C₂×C₄	#13094009	1	1	yes	characteristic
406	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
407	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
408	C₂×C₄	Q₁₆×D₄₇	1	1	yes	characteristic
409	C₂×C₄	Q₁₆×D₄₇	1	1	yes	characteristic
410	C₂×C₄	#13094043	1	1	yes	characteristic
411	C₂×C₄	#13094045	1	1	yes	characteristic
412	C₂×C₄	#13094048	1	1	yes	characteristic
413	C₂×C₄	#13094053	1	1	yes	characteristic
414	C₈	—	4	2	no	—
415	C₈	—	8	1	no	—
416	C₈	—	376	1	no	—
417	C₈	—	188	2	no	—
418	C₂²	—	47	4	no	—
419	C₂²	—	94	2	no	—
420	C₂²	—	94	2	no	—
421	C₂²	—	94	2	no	—
422	C₂²	—	94	2	no	—
423	C₂²	—	94	2	no	—
424	C₂²	—	94	2	no	—
425	C₂²	#15689001	1	1	yes	characteristic
426	C₂²	#100×D₄₇	1	1	yes	characteristic
427	C₂²	#15689106	1	1	yes	characteristic
428	C₂²	#103×D₄₇	1	1	yes	characteristic
429	C₂²	#103×D₄₇	1	1	yes	characteristic
430	C₂²	#15689116	1	1	yes	characteristic
431	C₂²	#15689121	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	8	2	no	—
435	C₄	—	94	2	no	—
436	C₄	—	94	2	no	—
437	C₄	—	376	2	no	—
438	C₄	—	188	1	no	—
439	C₄	#15689275	1	1	yes	characteristic
440	C₄	#15689280	1	1	yes	characteristic
441	C₄	#15689351	1	1	yes	characteristic
442	C₄	#15689353	1	1	yes	characteristic
443	C₄	#15689363	1	1	yes	characteristic
444	C₄	#15689365	1	1	yes	characteristic
445	C₄	#15689455	1	1	yes	characteristic
446	C₄	#15689460	1	1	yes	characteristic
447	C₂	—	94	4	no	—
448	C₂	#333×D₄₇	1	1	yes	characteristic
449	C₂	#20242044	1	1	yes	characteristic
450	C₂	#20242077	1	1	yes	characteristic
451	C₂	#20242080	1	1	yes	characteristic
452	C₂	#20243694	1	1	yes	characteristic
453	C₂	#20243810	1	1	yes	characteristic
454	C₂	#20243850	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1296	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1296	D₄₇
hypocenter	C₄₇	#9127
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
4. C₂×#15688871	C₂	semidirect
5. C₂×#15688871	C₂	semidirect
6. #20241271	C₂	semidirect
7. C₄₇×#1296	C₂	semidirect
204. C₂×D₄₇	#333	semidirect
226. #1296	D₄₇	semidirect
256. C₄₇	#9127	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₈×D₄₇	2
#20251741	2
#20243365	2
C₂×#15688871	2
#20241271	2
C₄₇×#1296	2
#9127	47