Subgroups — #26111972

Order 12032.

612 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689145	C₂	1	1	yes	maximal, characteristic
2	#20251741	C₂	1	1	yes	maximal, characteristic
3	#20243365	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688870	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688868	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×#10625324	—	2	1	no	—
9	C₂×#13094024	C₂²	1	1	yes	characteristic
10	C₂×#13094004	—	2	1	no	—
11	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
12	#15689145	—	2	2	no	—
13	#15689145	—	2	2	no	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₇⋊C₈	—	2	1	no	—
17	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
18	#15689028	—	2	1	no	—
19	#15689022	—	2	1	no	—
20	#15689022	C₄	1	2	yes	—
21	#15688980	—	2	1	no	—
22	#15688980	C₄	1	2	yes	—
23	#15688877	—	2	1	no	—
24	#15688870	—	2	2	no	—
25	#15688868	—	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	—	2	1	no	—
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	C₂×#10625324	—	2	4	no	—
34	C₂×#10625324	—	4	2	no	—
35	C₂×#10625324	—	4	2	no	—
36	C₂²×C₄₇⋊C₈	—	2	1	no	—
37	C₂²×C₄₇⋊C₈	—	2	1	no	—
38	#13094024	—	2	1	no	—
39	#13094024	—	2	1	no	—
40	#13094024	—	2	1	no	—
41	#13094024	—	2	1	no	—
42	#13094004	—	4	2	no	—
43	#13094004	—	4	2	no	—
44	C₂×C₄⋊Dic₄₇	—	2	1	no	—
45	C₂×C₄⋊Dic₄₇	—	2	2	no	—
46	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
47	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
48	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
51	C₄²×D₄₇	—	2	1	no	—
52	C₄²×D₄₇	—	2	1	no	—
53	C₄²×D₄₇	—	2	1	no	—
54	C₄²×D₄₇	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
59	Dic₄₇⋊C₈	—	2	4	no	—
60	(C₂×D₄₇)⋊C₈	—	4	2	no	—
61	C₄₇⋊#95	—	2	2	no	—
62	C₄₇⋊#95	—	2	2	no	—
63	C₂²×C₈×C₄₇	—	2	1	no	—
64	C₂²×C₈×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₄₇	—	2	1	no	—
70	C₄⋊C₈×C₄₇	—	2	1	no	—
71	C₄⋊C₈×C₄₇	—	2	1	no	—
72	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
73	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×Dic₄₇	—	2	2	no	—
79	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	1	no	—
90	C₂×C₄×D₄₇	—	2	1	no	—
91	C₂×C₄×D₄₇	—	2	1	no	—
92	C₂×C₄×D₄₇	—	2	1	no	—
93	C₂×C₄×D₄₇	—	2	1	no	—
94	C₂×C₄×D₄₇	—	2	2	no	—
95	C₂×C₄×D₄₇	—	4	1	no	—
96	C₂×C₄×D₄₇	D₈	1	2	yes	—
97	C₂×C₄×D₄₇	SD₁₆	1	2	yes	—
98	C₂×Dic₉₄	—	4	1	no	—
99	C₂×Dic₉₄	—	4	1	no	—
100	C₂×Dic₉₄	—	4	1	no	—
101	C₂×Dic₉₄	—	4	1	no	—
102	C₂×Dic₉₄	—	4	1	no	—
103	C₂×Dic₉₄	—	4	1	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	—	4	2	no	—
111	C₄⋊C₄×C₄₇	—	4	1	no	—
112	C₄⋊C₄×C₄₇	—	4	1	no	—
113	C₄⋊C₄×C₄₇	—	4	1	no	—
114	C₄⋊C₄×C₄₇	—	4	1	no	—
115	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₇	#41	1	1	yes	characteristic
118	C₄²×C₄₇	#41	1	1	yes	characteristic
119	(C₂×D₄₇)⋊C₄	—	4	4	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	4	1	no	—
123	C₄⋊Dic₄₇	—	4	1	no	—
124	C₄⋊Dic₄₇	—	4	4	no	—
125	C₄×Dic₄₇	—	2	1	no	—
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	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	4	1	no	—
133	C₂×C₄₇⋊C₈	—	4	1	no	—
134	C₂×C₄₇⋊C₈	—	4	1	no	—
135	C₂×C₄₇⋊C₈	—	4	1	no	—
136	C₂×C₄₇⋊C₈	—	4	1	no	—
137	#10625324	—	4	8	no	—
138	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×D₄₇	—	2	1	no	—
140	C₂²×D₄₇	—	2	1	no	—
141	C₂²×D₄₇	—	2	1	no	—
142	C₂²×D₄₇	—	2	1	no	—
143	C₂²×D₄₇	—	2	1	no	—
144	C₂²×D₄₇	—	2	1	no	—
145	C₂²×D₄₇	#102	1	2	yes	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
156	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
159	C₂×C₄×C₄₇	AGL(1,ℤ/8)	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×C₄×C₄₇	#137	1	1	yes	characteristic
163	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
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	—	2	1	no	—
170	C₂×Dic₄₇	—	2	1	no	—
171	C₂×Dic₄₇	—	2	1	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	#101	1	2	yes	—
176	C₂×Dic₄₇	#102	1	2	yes	—
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	—	4	2	no	—
182	C₄×D₄₇	—	4	2	no	—
183	C₄×D₄₇	—	4	1	no	—
184	C₄×D₄₇	—	4	1	no	—
185	C₄×D₄₇	—	4	1	no	—
186	C₄×D₄₇	—	4	1	no	—
187	Dic₉₄	—	8	1	no	—
188	Dic₉₄	—	8	1	no	—
189	Dic₉₄	—	8	1	no	—
190	Dic₉₄	—	8	1	no	—
191	C₈×C₄₇	—	4	2	no	—
192	C₈×C₄₇	—	8	1	no	—
193	C₄₇⋊C₈	—	4	2	no	—
194	C₄₇⋊C₈	—	8	1	no	—
195	#9139	—	47	1	no	maximal, Sylow
196	C₂²×C₄₇	#386	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
198	C₂²×C₄₇	#413	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
200	C₂²×C₄₇	#417	1	1	yes	characteristic
201	C₂²×C₄₇	#417	1	1	yes	characteristic
202	C₂²×C₄₇	#419	1	1	yes	characteristic
203	C₂×D₄₇	—	2	2	no	—
204	C₂×D₄₇	—	2	2	no	—
205	C₂×D₄₇	—	2	2	no	—
206	C₂×D₄₇	—	4	1	no	—
207	C₂×D₄₇	—	4	1	no	—
208	C₂×D₄₇	—	4	1	no	—
209	C₂×D₄₇	—	4	1	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	8	2	no	—
213	C₄×C₄₇	#447	1	1	yes	characteristic
214	C₄×C₄₇	#448	1	1	yes	characteristic
215	C₄×C₄₇	#468	1	1	yes	characteristic
216	C₄×C₄₇	#468	1	1	yes	characteristic
217	C₄×C₄₇	#470	1	1	yes	characteristic
218	C₄×C₄₇	#470	1	1	yes	characteristic
219	C₄×C₄₇	#480	1	1	yes	characteristic
220	C₄×C₄₇	#481	1	1	yes	characteristic
221	Dic₄₇	—	2	2	no	—
222	Dic₄₇	—	2	2	no	—
223	Dic₄₇	—	4	1	no	—
224	Dic₄₇	—	8	2	no	—
225	C₂×#423	—	47	1	no	—
226	#2857	—	47	1	no	—
227	#1797	—	47	1	no	—
228	C₂×#332	—	47	1	no	—
229	C₂×#332	—	47	1	no	—
230	#1296	—	47	1	no	—
231	#1296	D₄₇	1	1	yes	characteristic, complemented
232	C₂×C₄₇	#1546	1	1	yes	characteristic
233	C₂×C₄₇	#1547	1	1	yes	characteristic
234	C₂×C₄₇	#1559	1	1	yes	characteristic
235	C₂×C₄₇	#1561	1	1	yes	characteristic
236	C₂×C₄₇	#1874	1	1	yes	characteristic
237	C₂×C₄₇	#1894	1	1	yes	characteristic
238	C₂×C₄₇	#1901	1	1	yes	characteristic
239	D₄₇	—	4	2	no	—
240	C₂²×M₁₆	—	94	1	no	—
241	C₂×C₄⋊Q₈	—	47	1	no	—
242	C₂×C₂²⋊Q₈	—	94	1	no	—
243	C₂²×C₄²	—	47	1	no	—
244	#423	—	94	2	no	—
245	#423	—	94	2	no	—
246	C₂×C₄⋊C₈	—	47	1	no	—
247	C₂×C₄⋊C₈	—	47	1	no	—
248	C₂×C₄⋊C₈	—	94	1	no	—
249	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	—	94	1	no	—
252	#391	—	94	1	no	—
253	#389	—	47	2	no	—
254	#389	—	94	1	no	—
255	#384	C₂×D₄₇	1	1	yes	characteristic
256	#380	—	47	2	no	—
257	#380	—	94	1	no	—
258	#336	—	94	1	no	—
259	#332	—	94	2	no	—
260	#332	—	94	2	no	—
261	C₄₇	#9139	1	1	yes	characteristic, complemented, Sylow
262	C₂²×Q₈	—	94	1	no	—
263	C₂³×C₄	—	47	1	no	—
264	C₂³×C₄	—	47	1	no	—
265	C₂³×C₄	—	47	1	no	—
266	C₂×M₁₆	—	94	4	no	—
267	C₂×M₁₆	—	188	2	no	—
268	C₂×M₁₆	—	188	2	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	94	1	no	—
272	C₂²×C₈	—	94	1	no	—
273	C₄⋊Q₈	—	94	1	no	—
274	C₄⋊Q₈	—	94	1	no	—
275	C₄⋊Q₈	—	94	1	no	—
276	C₄⋊Q₈	—	94	1	no	—
277	C₂²⋊Q₈	—	188	2	no	—
278	C₂²⋊Q₈	—	188	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	47	2	no	—
282	C₂×C₄⋊C₄	—	94	2	no	—
283	C₂×C₄⋊C₄	—	94	1	no	—
284	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
285	C₂×C₂²⋊C₄	—	94	2	no	—
286	C₂×C₄²	—	47	1	no	—
287	C₂×C₄²	—	47	1	no	—
288	C₂×C₄²	—	47	1	no	—
289	C₂×C₄²	—	94	1	no	—
290	C₂×C₄²	—	94	1	no	—
291	C₂×C₄²	—	94	1	no	—
292	C₂×C₄²	—	94	1	no	—
293	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	47	2	no	—
298	C₄⋊C₈	—	94	4	no	—
299	C₄⋊C₈	—	94	1	no	—
300	C₄⋊C₈	—	94	1	no	—
301	C₄⋊C₈	—	94	1	no	—
302	C₄⋊C₈	D₁₈₈	1	2	yes	—
303	C₂²⋊C₈	—	188	2	no	—
304	#95	—	94	2	no	—
305	#95	—	94	2	no	—
306	C₂⁴	—	47	1	no	—
307	C₂×Q₈	—	188	1	no	—
308	C₂×Q₈	—	188	1	no	—
309	C₂×Q₈	—	188	1	no	—
310	C₂×Q₈	—	188	1	no	—
311	C₂×Q₈	—	188	1	no	—
312	C₂×Q₈	—	188	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	47	1	no	—
315	C₂²×C₄	—	47	1	no	—
316	C₂²×C₄	—	47	2	no	—
317	C₂²×C₄	—	47	2	no	—
318	C₂²×C₄	—	47	1	no	—
319	C₂²×C₄	—	94	2	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	1	no	—
325	C₂²×C₄	—	94	1	no	—
326	C₂²×C₄	—	94	1	no	—
327	C₂²×C₄	—	94	1	no	—
328	C₂²×C₄	—	94	1	no	—
329	C₂²×C₄	—	94	1	no	—
330	C₂²×C₄	—	94	1	no	—
331	C₂²×C₄	—	94	1	no	—
332	C₂²×C₄	—	94	2	no	—
333	C₂²×C₄	—	188	1	no	—
334	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
337	M₁₆	—	188	8	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	188	1	no	—
346	C₂×C₈	—	188	1	no	—
347	C₂×C₈	—	188	1	no	—
348	C₂×C₈	—	188	1	no	—
349	C₂×C₈	—	188	1	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	94	2	no	—
356	C₄⋊C₄	—	94	2	no	—
357	C₄⋊C₄	—	188	4	no	—
358	C₄⋊C₄	—	188	1	no	—
359	C₄⋊C₄	—	188	1	no	—
360	C₂²⋊C₄	—	188	4	no	—
361	C₄²	—	94	1	no	—
362	C₄²	—	94	1	no	—
363	C₄²	—	94	1	no	—
364	C₄²	—	94	1	no	—
365	C₄²	—	94	1	no	—
366	C₄²	—	94	1	no	—
367	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
368	C₄²	#10625350	1	1	yes	characteristic
369	C₄²	D₄×D₄₇	1	1	yes	characteristic
370	C₄²	#10625354	1	1	yes	characteristic
371	C₂³	—	47	2	no	—
372	C₂³	—	94	1	no	—
373	C₂³	—	94	1	no	—
374	C₂³	—	94	1	no	—
375	C₂³	—	94	1	no	—
376	C₂³	—	94	1	no	—
377	C₂³	—	94	1	no	—
378	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
379	Q₈	—	376	1	no	—
380	Q₈	—	376	1	no	—
381	Q₈	—	376	1	no	—
382	Q₈	—	376	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	47	2	no	—
389	C₂×C₄	—	47	2	no	—
390	C₂×C₄	—	94	1	no	—
391	C₂×C₄	—	94	1	no	—
392	C₂×C₄	—	94	1	no	—
393	C₂×C₄	—	94	1	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	94	2	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	—	94	2	no	—
398	C₂×C₄	—	94	1	no	—
399	C₂×C₄	—	94	1	no	—
400	C₂×C₄	—	94	1	no	—
401	C₂×C₄	—	188	2	no	—
402	C₂×C₄	—	188	2	no	—
403	C₂×C₄	—	188	2	no	—
404	C₂×C₄	—	188	2	no	—
405	C₂×C₄	—	188	2	no	—
406	C₂×C₄	—	188	1	no	—
407	C₂×C₄	—	188	1	no	—
408	C₂×C₄	—	188	1	no	—
409	C₂×C₄	—	188	1	no	—
410	C₂×C₄	#13093986	1	1	yes	characteristic
411	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
412	C₂×C₄	#13093994	1	1	yes	characteristic
413	C₂×C₄	#13093997	1	1	yes	characteristic
414	C₂×C₄	#13093999	1	1	yes	characteristic
415	C₂×C₄	#13094009	1	1	yes	characteristic
416	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
417	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
418	C₂×C₄	#13094048	1	1	yes	characteristic
419	C₂×C₄	#13094051	1	1	yes	characteristic
420	C₂×C₄	#13094053	1	1	yes	characteristic
421	C₂×C₄	#13094053	1	1	yes	characteristic
422	C₂×C₄	#13094056	1	1	yes	characteristic
423	C₂×C₄	#13094056	1	1	yes	characteristic
424	C₈	—	4	2	no	—
425	C₈	—	8	1	no	—
426	C₈	—	376	1	no	—
427	C₈	—	188	2	no	—
428	C₂²	—	94	2	no	—
429	C₂²	—	94	2	no	—
430	C₂²	—	94	2	no	—
431	C₂²	—	188	1	no	—
432	C₂²	—	188	1	no	—
433	C₂²	—	188	1	no	—
434	C₂²	—	188	1	no	—
435	C₂²	#15689001	1	1	yes	characteristic
436	C₂²	#101×D₄₇	1	1	yes	characteristic
437	C₂²	#15689104	1	1	yes	characteristic
438	C₂²	#102×D₄₇	1	1	yes	characteristic
439	C₂²	#15689121	1	1	yes	characteristic
440	C₂²	#15689123	1	1	yes	characteristic
441	C₂²	#15689130	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	8	2	no	—
445	C₄	—	94	2	no	—
446	C₄	—	94	2	no	—
447	C₄	—	376	2	no	—
448	C₄	—	188	1	no	—
449	C₄	#15689258	1	1	yes	characteristic
450	C₄	#15689263	1	1	yes	characteristic
451	C₄	#15689368	1	1	yes	characteristic
452	C₄	#15689370	1	1	yes	characteristic
453	C₄	#15689380	1	1	yes	characteristic
454	C₄	#15689382	1	1	yes	characteristic
455	C₄	#15689438	1	1	yes	characteristic
456	C₄	#15689443	1	1	yes	characteristic
457	C₂	—	188	2	no	—
458	C₂	#20242058	1	1	yes	characteristic
459	C₂	#20242062	1	1	yes	characteristic
460	C₂	#20242115	1	1	yes	characteristic
461	C₂	#20242124	1	1	yes	characteristic
462	C₂	#20243704	1	1	yes	characteristic
463	C₂	#20243820	1	1	yes	characteristic
464	C₂	#20243855	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	#9139
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×#15688870	C₂	semidirect
5. C₂×#15688868	C₂	semidirect
6. #20241271	C₂	semidirect
7. C₄₇×#1296	C₂	semidirect
231. #1296	D₄₇	semidirect
261. C₄₇	#9139	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689145	2
#20251741	2
#20243365	2
C₂×#15688870	2
C₂×#15688868	2
#20241271	2
C₄₇×#1296	2
#9139	47