Subgroups — #26111920

Order 12032.

644 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×C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20251735	C₂	1	1	yes	maximal, characteristic
3	#20243365	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688869	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241272	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241272	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₄₇	—	2	1	no	—
9	C₂×#13094000	—	2	1	no	—
10	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₇⋊C₈	—	2	1	no	—
14	C₄⋊C₈×D₄₇	—	2	2	no	—
15	C₄⋊C₈×D₄₇	—	2	2	no	—
16	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
17	#15689030	—	2	1	no	—
18	#15689019	—	2	1	no	—
19	#15689019	C₄	1	2	yes	—
20	#15688993	C₂²	1	1	yes	characteristic
21	#15688980	—	2	1	no	—
22	#15688980	C₄	1	2	yes	—
23	#15688877	—	2	1	no	—
24	#15688869	—	2	2	no	—
25	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#332	—	2	2	no	—
29	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
32	C₂²×C₄₇⋊C₈	—	2	1	no	—
33	C₂²×C₄₇⋊C₈	—	2	1	no	—
34	C₂×C₈×D₄₇	—	2	4	no	—
35	C₂×C₈×D₄₇	—	4	2	no	—
36	C₂×C₈×D₄₇	—	4	2	no	—
37	#13094000	—	4	2	no	—
38	#13094000	—	4	2	no	—
39	C₂×C₄⋊Dic₄₇	—	2	1	no	—
40	C₂×C₄⋊Dic₄₇	—	2	1	no	—
41	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
42	C₂×Dic₄₇⋊C₄	—	2	2	no	—
43	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
44	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
46	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
47	C₄²×D₄₇	—	2	1	no	—
48	C₄²×D₄₇	—	2	1	no	—
49	C₄²×D₄₇	—	2	1	no	—
50	C₄²×D₄₇	—	2	1	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
55	Dic₄₇⋊C₈	—	2	4	no	—
56	(C₂×D₄₇)⋊C₈	—	4	2	no	—
57	C₄₇⋊#95	—	2	2	no	—
58	C₄₇⋊#95	—	2	2	no	—
59	C₂²×Q₈×C₄₇	—	2	1	no	—
60	C₂²×C₈×C₄₇	—	2	1	no	—
61	C₂²×C₈×C₄₇	—	2	1	no	—
62	C₄⋊Q₈×C₄₇	—	2	1	no	—
63	C₄⋊Q₈×C₄₇	—	2	1	no	—
64	C₄⋊Q₈×C₄₇	—	2	1	no	—
65	C₄⋊Q₈×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	C₂×Q₈×C₄₇	—	4	1	no	—
75	C₂×Q₈×C₄₇	—	4	1	no	—
76	C₂×Q₈×C₄₇	—	4	1	no	—
77	C₂×Q₈×C₄₇	—	4	1	no	—
78	C₂×Q₈×C₄₇	—	4	1	no	—
79	C₂×Q₈×C₄₇	—	4	1	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×Dic₄₇	—	2	2	no	—
85	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	1	no	—
95	C₂×C₄×D₄₇	—	2	1	no	—
96	C₂×C₄×D₄₇	—	2	2	no	—
97	C₂×C₄×D₄₇	—	2	1	no	—
98	C₂×C₄×D₄₇	—	2	1	no	—
99	C₂×C₄×D₄₇	—	4	1	no	—
100	C₂×C₄×D₄₇	D₈	1	2	yes	—
101	C₂×C₄×D₄₇	SD₁₆	1	2	yes	—
102	C₂×C₄×D₄₇	SD₁₆	1	2	yes	—
103	C₂×C₄×D₄₇	Q₁₆	1	2	yes	—
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	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	4	1	no	—
113	C₄⋊C₄×C₄₇	—	4	1	no	—
114	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₄₇	#41	1	1	yes	characteristic
117	C₄²×C₄₇	#41	1	1	yes	characteristic
118	(C₂×D₄₇)⋊C₄	—	4	4	no	—
119	C₄⋊Dic₄₇	—	4	1	no	—
120	C₄⋊Dic₄₇	—	4	1	no	—
121	C₄⋊Dic₄₇	—	4	1	no	—
122	C₄⋊Dic₄₇	—	4	1	no	—
123	C₄⋊Dic₄₇	—	4	2	no	—
124	Dic₄₇⋊C₄	—	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	C₈×D₄₇	—	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	#101	1	2	yes	—
144	C₂²×D₄₇	#102	1	2	yes	—
145	C₂²×D₄₇	#103	1	2	yes	—
146	Q₈×C₄₇	—	8	1	no	—
147	Q₈×C₄₇	—	8	1	no	—
148	Q₈×C₄₇	—	8	1	no	—
149	Q₈×C₄₇	—	8	1	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
167	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
169	C₂×Dic₄₇	—	2	1	no	—
170	C₂×Dic₄₇	—	2	1	no	—
171	C₂×Dic₄₇	—	2	1	no	—
172	C₂×Dic₄₇	—	2	1	no	—
173	C₂×Dic₄₇	—	2	1	no	—
174	C₂×Dic₄₇	—	2	1	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	C₂×Dic₄₇	#102	1	2	yes	—
180	C₂×Dic₄₇	#103	1	2	yes	—
181	C₄×D₄₇	—	2	2	no	—
182	C₄×D₄₇	—	2	2	no	—
183	C₄×D₄₇	—	2	2	no	—
184	C₄×D₄₇	—	2	2	no	—
185	C₄×D₄₇	—	2	2	no	—
186	C₄×D₄₇	—	2	2	no	—
187	C₄×D₄₇	—	2	2	no	—
188	C₄×D₄₇	—	2	2	no	—
189	C₄×D₄₇	—	4	2	no	—
190	C₄×D₄₇	—	4	2	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	#9129	—	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	C₂×#103	1	1	yes	characteristic
201	C₂²×C₄₇	#416	1	1	yes	characteristic
202	C₂²×C₄₇	#417	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	—	2	2	no	—
207	C₂×D₄₇	—	2	2	no	—
208	C₂×D₄₇	—	2	2	no	—
209	C₂×D₄₇	#332	1	4	yes	complemented
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	8	2	no	—
213	C₄×C₄₇	#450	1	1	yes	characteristic
214	C₄×C₄₇	#451	1	1	yes	characteristic
215	C₄×C₄₇	#465	1	1	yes	characteristic
216	C₄×C₄₇	#465	1	1	yes	characteristic
217	C₄×C₄₇	#466	1	1	yes	characteristic
218	C₄×C₄₇	#466	1	1	yes	characteristic
219	C₄×C₄₇	#483	1	1	yes	characteristic
220	C₄×C₄₇	#484	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	C₂²×C₄⋊C₈	—	47	1	no	—
226	#2857	—	47	1	no	—
227	#1797	—	47	1	no	—
228	C₂×#332	—	47	1	no	—
229	C₂×#332	D₄₇	1	1	yes	characteristic, complemented
230	#1296	—	47	1	no	—
231	#1296	—	47	1	no	—
232	C₂×C₄₇	C₂×#332	1	1	yes	characteristic
233	C₂×C₄₇	#1542	1	1	yes	characteristic
234	C₂×C₄₇	#1547	1	1	yes	characteristic
235	C₂×C₄₇	#1552	1	1	yes	characteristic
236	C₂×C₄₇	#1872	1	1	yes	characteristic
237	C₂×C₄₇	#1893	1	1	yes	characteristic
238	C₂×C₄₇	#1901	1	1	yes	characteristic
239	D₄₇	—	2	4	no	—
240	C₂³×C₈	—	94	1	no	—
241	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
242	C₂×C₂²⋊Q₈	—	94	1	no	—
243	C₂²×C₄²	—	47	1	no	—
244	C₂×C₄⋊C₈	—	47	1	no	—
245	C₂×C₄⋊C₈	—	47	1	no	—
246	C₂×C₄⋊C₈	—	94	2	no	—
247	C₂×C₄⋊C₈	—	94	1	no	—
248	C₂×C₄⋊C₈	—	94	2	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	—	47	1	no	—
256	#380	—	47	2	no	—
257	#380	—	94	1	no	—
258	#336	—	94	1	no	—
259	#332	—	2	2	no	—
260	#332	—	94	2	no	—
261	C₄₇	#9129	1	1	yes	characteristic, complemented, Sylow
262	C₂²×Q₈	—	2	1	no	—
263	C₂³×C₄	—	47	1	no	—
264	C₂³×C₄	—	47	1	no	—
265	C₂³×C₄	—	47	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	94	4	no	—
269	C₂²×C₈	—	94	1	no	—
270	C₂²×C₈	—	94	1	no	—
271	C₂²×C₈	—	188	2	no	—
272	C₂²×C₈	—	188	2	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	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	—	47	2	no	—
281	C₂×C₄⋊C₄	—	94	2	no	—
282	C₂×C₄⋊C₄	—	94	1	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	C₂²⋊D₄₇	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	—	4	1	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×Q₈	—	4	1	no	—
310	C₂×Q₈	—	4	1	no	—
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	—	4	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	2	no	—
319	C₂²×C₄	—	47	2	no	—
320	C₂²×C₄	—	47	1	no	—
321	C₂²×C₄	—	94	2	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	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	1	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	—	94	2	no	—
344	C₂×C₈	—	188	8	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	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	188	2	no	—
355	C₄⋊C₄	—	188	4	no	—
356	C₄⋊C₄	—	188	1	no	—
357	C₄⋊C₄	—	188	1	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	#10625350	1	1	yes	characteristic
368	C₄²	D₄×D₄₇	1	1	yes	characteristic
369	C₄²	#10625352	1	1	yes	characteristic
370	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
371	C₂³	—	47	2	no	—
372	C₂³	—	47	2	no	—
373	C₂³	—	47	2	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	—	8	1	no	—
380	Q₈	—	8	1	no	—
381	Q₈	—	8	1	no	—
382	Q₈	—	8	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	2	no	—
399	C₂×C₄	—	94	2	no	—
400	C₂×C₄	—	94	2	no	—
401	C₂×C₄	—	94	2	no	—
402	C₂×C₄	—	94	1	no	—
403	C₂×C₄	—	94	1	no	—
404	C₂×C₄	—	94	1	no	—
405	C₂×C₄	—	188	2	no	—
406	C₂×C₄	—	188	2	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	—	188	2	no	—
409	C₂×C₄	—	188	2	no	—
410	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
411	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
412	C₂×C₄	#13093992	1	1	yes	characteristic
413	C₂×C₄	#13093995	1	1	yes	characteristic
414	C₂×C₄	#13093997	1	1	yes	characteristic
415	C₂×C₄	#13094006	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	SD₁₆×D₄₇	1	1	yes	characteristic
419	C₂×C₄	Q₁₆×D₄₇	1	1	yes	characteristic
420	C₂×C₄	#13094043	1	1	yes	characteristic
421	C₂×C₄	#13094045	1	1	yes	characteristic
422	C₂×C₄	#13094051	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	—	47	4	no	—
429	C₂²	—	94	2	no	—
430	C₂²	—	94	2	no	—
431	C₂²	—	94	2	no	—
432	C₂²	—	94	2	no	—
433	C₂²	—	94	2	no	—
434	C₂²	—	94	2	no	—
435	C₂²	#15688999	1	1	yes	characteristic
436	C₂²	#101×D₄₇	1	1	yes	characteristic
437	C₂²	#15689106	1	1	yes	characteristic
438	C₂²	#102×D₄₇	1	1	yes	characteristic
439	C₂²	#103×D₄₇	1	1	yes	characteristic
440	C₂²	#15689116	1	1	yes	characteristic
441	C₂²	#15689123	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	#15689272	1	1	yes	characteristic
450	C₄	#15689277	1	1	yes	characteristic
451	C₄	#15689349	1	1	yes	characteristic
452	C₄	#15689351	1	1	yes	characteristic
453	C₄	#15689356	1	1	yes	characteristic
454	C₄	#15689358	1	1	yes	characteristic
455	C₄	#15689452	1	1	yes	characteristic
456	C₄	#15689457	1	1	yes	characteristic
457	C₂	—	94	4	no	—
458	C₂	#332×D₄₇	1	1	yes	characteristic
459	C₂	#20242044	1	1	yes	characteristic
460	C₂	#20242064	1	1	yes	characteristic
461	C₂	#20242085	1	1	yes	characteristic
462	C₂	#20243692	1	1	yes	characteristic
463	C₂	#20243813	1	1	yes	characteristic
464	C₂	#20243853	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#332	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#332	D₄₇
hypocenter	C₄₇	#9129
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#332

Complements

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

N	H ≅ G/N	type
4. C₂×#15688869	C₂	semidirect
5. #20241272	C₂	semidirect
6. #20241272	C₂	semidirect
7. C₂×C₄₇×#332	C₂	semidirect
209. C₂×D₄₇	#332	semidirect
229. C₂×#332	D₄₇	semidirect
261. C₄₇	#9129	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
#20251735	2
#20243365	2
C₂×#15688869	2
#20241272	2
C₂×C₄₇×#332	2
#9129	47