Subgroups — #26186248

Order 12032.

720 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253435	C₂	1	1	yes	maximal, characteristic
2	#20252363	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242252	C₂	1	2	yes	maximal, complemented
4	#20242245	C₂	1	2	yes	maximal, complemented
5	C₈×#10625335	C₂	1	2	yes	maximal, complemented
6	C₈×#10625334	C₂	1	2	yes	maximal, complemented
7	#20242171	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241831	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241799	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689657	C₂²	1	1	yes	characteristic
13	#15689458	C₄	1	1	yes	characteristic
14	#15689441	C₄	1	1	yes	characteristic
15	#15689423	C₄	1	2	yes	—
16	#15689338	C₄	1	2	yes	—
17	#15689274	C₄	1	1	yes	characteristic
18	#15689257	C₄	1	1	yes	characteristic
19	#15689253	C₂²	1	1	yes	characteristic, complemented
20	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
21	C₄×#10625335	C₂²	1	2	yes	—
22	C₄×#10625334	C₂²	1	2	yes	—
23	#15689202	C₂²	1	1	yes	characteristic, complemented
24	#15689194	—	2	1	no	—
25	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
26	C₈×C₂²⋊D₄₇	—	2	1	no	—
27	#15689182	—	2	1	no	—
28	#15689180	C₂²	1	1	yes	characteristic
29	#15689176	C₂²	1	1	yes	characteristic
30	#15689077	—	2	1	no	—
31	C₄×#10625329	C₂²	1	1	yes	characteristic
32	#15688875	C₂²	1	2	yes	complemented
33	#15688873	C₂²	1	2	yes	complemented
34	#15688853	C₂²	1	2	yes	complemented
35	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
36	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
37	#15688850	C₂²	1	2	yes	complemented
38	#15688845	C₂²	1	2	yes	complemented
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
40	C₂³×C₈×C₄₇	—	2	1	no	—
41	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₄₇	—	2	1	no	—
43	C₈×D₄×C₄₇	—	2	1	no	—
44	C₈×D₄×C₄₇	C₂²	1	2	yes	—
45	C₈×D₄×C₄₇	C₂²	1	2	yes	—
46	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
48	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#10625335	C₂×C₄	1	2	yes	—
50	C₂×#10625334	C₂×C₄	1	2	yes	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625324	—	2	1	no	—
53	C₂×C₈×D₄₇	—	2	1	no	—
54	#13094018	—	2	1	no	—
55	#13094016	C₂×C₄	1	1	yes	characteristic
56	#13094012	C₂×C₄	1	1	yes	characteristic
57	#13094007	—	2	1	no	—
58	#13094003	C₂×C₄	1	1	yes	characteristic
59	#13093998	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
61	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
62	C₄×C₂²⋊D₄₇	—	2	1	no	—
63	#13093981	—	2	1	no	—
64	#13093957	C₂×C₄	1	2	yes	—
65	#13093955	C₂×C₄	1	2	yes	—
66	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
69	Dic₄₇⋊C₈	—	2	1	no	—
70	Dic₄₇⋊C₈	—	2	1	no	—
71	#13093947	C₂×C₄	1	2	yes	—
72	#13093945	C₂×C₄	1	2	yes	—
73	#13093945	C₂×C₄	1	2	yes	—
74	#13093944	C₂×C₄	1	2	yes	—
75	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
76	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
77	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
78	(C₂×D₄₇)⋊C₈	—	2	1	no	—
79	(C₂×D₄₇)⋊C₈	—	2	1	no	—
80	#13093935	—	2	1	no	—
81	#13093935	—	2	1	no	—
82	#13093934	—	2	1	no	—
83	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
84	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
85	C₈×Dic₄₇	—	2	1	no	—
86	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₈×C₄₇	—	2	1	no	—
89	C₂²×C₈×C₄₇	—	2	2	no	—
90	C₂²×C₈×C₄₇	—	2	2	no	—
91	C₂²×C₈×C₄₇	—	4	4	no	—
92	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
94	C₄×D₄×C₄₇	—	2	1	no	—
95	C₄×D₄×C₄₇	—	2	1	no	—
96	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
97	C₄×D₄×C₄₇	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₄₇	—	2	1	no	—
102	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
103	C₂²⋊C₈×C₄₇	—	2	2	no	—
104	C₂²⋊C₈×C₄₇	—	2	2	no	—
105	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
107	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
109	C₂⁴×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	2	4	no	—
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	4	2	no	—
117	C₂²×C₄×C₄₇	—	4	2	no	—
118	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
121	C₂×C₂²⋊D₄₇	—	2	1	no	—
122	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₄₇	—	2	1	no	—
124	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	4	1	no	—
128	C₂×C₈×C₄₇	—	4	4	no	—
129	C₂×C₈×C₄₇	—	4	2	no	—
130	C₂×C₈×C₄₇	—	4	4	no	—
131	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂²⋊C₄×C₄₇	—	2	2	no	—
138	C₂²⋊C₄×C₄₇	—	2	2	no	—
139	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₇	#41	1	1	yes	characteristic
142	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
143	C₂²⋊Dic₄₇	—	2	1	no	—
144	#10625335	—	2	4	no	—
145	#10625334	—	2	4	no	—
146	(C₂×D₄₇)⋊C₄	—	2	1	no	—
147	(C₂×D₄₇)⋊C₄	—	2	1	no	—
148	(C₂×D₄₇)⋊C₄	—	2	1	no	—
149	(C₂×D₄₇)⋊C₄	—	2	1	no	—
150	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
152	Dic₄₇⋊C₄	—	2	1	no	—
153	Dic₄₇⋊C₄	—	2	1	no	—
154	Dic₄₇⋊C₄	—	2	1	no	—
155	Dic₄₇⋊C₄	—	2	1	no	—
156	C₄×Dic₄₇	—	2	1	no	—
157	#10625329	—	2	4	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	1	no	—
160	C₂×C₄₇⋊C₈	—	2	1	no	—
161	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
162	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
163	#10625324	—	4	2	no	—
164	C₈×D₄₇	—	4	2	no	—
165	C₂³×C₄₇	—	2	4	no	—
166	C₂³×C₄₇	—	2	2	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	—	4	2	no	—
169	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
170	C₂²×D₄₇	—	2	1	no	—
171	D₄×C₄₇	—	2	4	no	—
172	D₄×C₄₇	—	2	2	no	—
173	D₄×C₄₇	#131	1	4	yes	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	4	4	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂²⋊D₄₇	—	4	2	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	1	no	—
192	C₂×Dic₄₇	—	2	1	no	—
193	D₁₈₈	—	2	2	no	—
194	C₄×D₄₇	—	4	1	no	—
195	C₄×D₄₇	—	4	1	no	—
196	Dic₉₄	—	2	2	no	—
197	C₈×C₄₇	—	2	1	no	—
198	C₈×C₄₇	—	2	1	no	—
199	C₈×C₄₇	—	2	1	no	—
200	C₈×C₄₇	—	4	2	no	—
201	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
202	C₄₇⋊C₈	—	2	4	no	—
203	C₄₇⋊C₈	—	2	2	no	—
204	C₄₇⋊C₈	—	2	2	no	—
205	C₄₇⋊C₈	—	4	1	no	—
206	C₄₇⋊C₈	—	4	1	no	—
207	#17910	—	47	1	no	maximal, Sylow
208	C₂²×C₄₇	—	2	1	no	—
209	C₂²×C₄₇	—	2	1	no	—
210	C₂²×C₄₇	—	2	4	no	—
211	C₂²×C₄₇	—	4	8	no	—
212	C₂²×C₄₇	—	4	2	no	—
213	C₂²×C₄₇	—	4	2	no	—
214	C₂²×C₄₇	#443	1	2	yes	—
215	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
216	C₂×D₄₇	—	4	1	no	—
217	C₂×D₄₇	—	4	1	no	—
218	C₂×D₄₇	—	4	1	no	—
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	2	1	no	—
221	C₄×C₄₇	—	2	1	no	—
222	C₄×C₄₇	—	2	1	no	—
223	C₄×C₄₇	—	4	2	no	—
224	C₄×C₄₇	C₂×#131	1	2	yes	—
225	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
226	C₄×C₄₇	#575	1	1	yes	characteristic
227	Dic₄₇	—	4	1	no	—
228	Dic₄₇	—	4	1	no	—
229	Dic₄₇	—	4	1	no	—
230	#3105	—	47	1	no	—
231	#2966	—	47	1	no	—
232	C₂×C₈×D₄	D₄₇	1	1	yes	characteristic, complemented
233	#1586	—	47	2	no	—
234	#1585	—	47	2	no	—
235	C₈×SD₁₆	—	47	2	no	—
236	C₈×D₈	—	47	2	no	—
237	#1573	—	47	1	no	—
238	#1490	—	47	1	no	—
239	#1483	—	47	1	no	—
240	C₈×M₁₆	—	47	1	no	—
241	C₂×C₄₇	—	2	2	no	—
242	C₂×C₄₇	—	4	4	no	—
243	C₂×C₄₇	#2929	1	1	yes	characteristic
244	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
246	D₄₇	—	8	1	no	—
247	C₂³×C₈	—	2	1	no	—
248	#529	—	47	1	no	—
249	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
250	#484	—	47	1	no	—
251	#481	—	47	1	no	—
252	#478	—	47	2	no	—
253	#463	—	47	2	no	—
254	#450	—	47	1	no	—
255	#447	—	47	1	no	—
256	#446	—	47	1	no	—
257	C₈×Q₈	—	47	1	no	—
258	C₄×SD₁₆	—	47	2	no	—
259	C₄×D₈	—	47	2	no	—
260	#436	—	47	1	no	—
261	#435	—	94	1	no	—
262	C₈×D₄	—	2	1	no	—
263	C₈×D₄	—	2	1	no	—
264	C₈×D₄	—	47	1	no	—
265	C₈×D₄	—	94	1	no	—
266	C₈×D₄	C₂×D₄₇	1	2	yes	—
267	C₈×D₄	C₂×D₄₇	1	2	yes	—
268	#433	—	94	1	no	—
269	#432	—	47	1	no	—
270	#431	—	47	1	no	—
271	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	—	2	1	no	—
273	#405	—	94	1	no	—
274	C₄×M₁₆	—	47	1	no	—
275	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
276	#335	—	47	2	no	—
277	#334	—	47	2	no	—
278	Q₈⋊C₈	—	47	2	no	—
279	D₄⋊C₈	—	47	2	no	—
280	D₄⋊C₈	—	47	2	no	—
281	D₄⋊C₈	—	47	2	no	—
282	#322	—	47	2	no	—
283	C₈²	—	47	2	no	—
284	C₄₇	#17910	1	1	yes	characteristic, complemented, Sylow
285	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
286	C₂³×C₄	—	2	1	no	—
287	C₂×SD₁₆	—	47	2	no	—
288	C₂×D₈	—	47	2	no	—
289	C₂×M₁₆	—	94	1	no	—
290	C₂×M₁₆	—	94	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	4	4	no	—
295	C₂²×C₈	—	94	1	no	—
296	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
298	#126	—	94	1	no	—
299	#125	—	47	1	no	—
300	#124	—	47	1	no	—
301	#123	—	94	1	no	—
302	C₂²⋊Q₈	—	47	1	no	—
303	#121	—	47	1	no	—
304	C₄×Q₈	—	47	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	47	1	no	—
308	C₄×D₄	—	94	1	no	—
309	C₄×D₄	C₄×D₄₇	1	2	yes	—
310	C₄×D₄	C₂²×D₄₇	1	2	yes	—
311	#117	—	94	1	no	—
312	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
315	#107	—	47	2	no	—
316	#106	—	47	2	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	47	2	no	—
319	C₄⋊C₈	—	47	1	no	—
320	C₄⋊C₈	—	47	1	no	—
321	C₄⋊C₈	—	94	1	no	—
322	C₄⋊C₈	—	94	1	no	—
323	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
324	#103	—	47	2	no	—
325	#102	—	47	2	no	—
326	#102	—	47	2	no	—
327	#102	—	47	2	no	—
328	C₂²⋊C₈	—	2	2	no	—
329	C₂²⋊C₈	—	2	2	no	—
330	C₂²⋊C₈	—	47	1	no	—
331	C₂²⋊C₈	—	47	1	no	—
332	C₂²⋊C₈	—	94	1	no	—
333	C₂²⋊C₈	—	94	1	no	—
334	C₂²⋊C₈	—	94	1	no	—
335	#97	—	94	1	no	—
336	#97	—	94	1	no	—
337	#97	—	94	1	no	—
338	C₄×C₈	—	47	2	no	—
339	C₄×C₈	—	47	2	no	—
340	C₄×C₈	—	94	1	no	—
341	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
342	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
343	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
345	C₂⁴	—	2	1	no	—
346	C₂×Q₈	—	47	1	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	47	1	no	—
350	C₂×D₄	—	94	1	no	—
351	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	94	1	no	—
358	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
359	C₂²×C₄	#10625350	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
361	SD₁₆	—	94	4	no	—
362	D₈	—	94	4	no	—
363	M₁₆	—	94	4	no	—
364	M₁₆	—	188	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	4	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	4	4	no	—
371	C₂×C₈	—	47	2	no	—
372	C₂×C₈	—	47	2	no	—
373	C₂×C₈	—	94	2	no	—
374	C₂×C₈	—	94	1	no	—
375	C₂×C₈	—	94	1	no	—
376	C₂×C₈	—	188	2	no	—
377	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
378	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
379	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
380	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	47	1	no	—
383	C₄⋊C₄	—	47	1	no	—
384	C₄⋊C₄	—	94	1	no	—
385	C₄⋊C₄	—	94	1	no	—
386	C₄⋊C₄	—	94	1	no	—
387	C₄⋊C₄	—	94	1	no	—
388	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	94	1	no	—
392	C₂²⋊C₄	—	94	1	no	—
393	C₂²⋊C₄	—	94	1	no	—
394	C₂²⋊C₄	—	94	1	no	—
395	C₂²⋊C₄	—	94	1	no	—
396	C₄²	—	94	1	no	—
397	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
398	C₄²	#10625350	1	1	yes	characteristic
399	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
400	C₄²	C₂³×D₄₇	1	1	yes	characteristic
401	C₂³	—	2	4	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	94	1	no	—
406	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
407	Q₈	—	94	2	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	2	no	—
410	D₄	—	94	2	no	—
411	D₄	—	188	2	no	—
412	D₄	#13094030	1	4	yes	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	94	1	no	—
423	C₂×C₄	—	94	1	no	—
424	C₂×C₄	—	94	1	no	—
425	C₂×C₄	—	188	1	no	—
426	C₂×C₄	—	188	1	no	—
427	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
428	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
429	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
431	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	—	2	1	no	—
436	C₈	—	4	2	no	—
437	C₈	—	94	4	no	—
438	C₈	—	94	2	no	—
439	C₈	—	94	2	no	—
440	C₈	—	188	1	no	—
441	C₈	—	188	1	no	—
442	C₈	#13094050	1	2	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	4	8	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	188	1	no	—
450	C₂²	—	188	1	no	—
451	C₂²	—	188	1	no	—
452	C₂²	#15689238	1	2	yes	—
453	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	188	1	no	—
460	C₄	—	188	1	no	—
461	C₄	—	188	1	no	—
462	C₄	C₂×#13094030	1	2	yes	—
463	C₄	C₂×#13094050	1	1	yes	characteristic
464	C₄	#15689921	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	4	4	no	—
467	C₂	—	376	1	no	—
468	C₂	#20252082	1	1	yes	characteristic
469	C₂	C₄×#13094050	1	1	yes	characteristic
470	C₂	C₂×#15689238	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₈×D₄×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#15689257	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×C₈×D₄	D₄₇
hypocenter	C₄₇	#17910
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
2. #20252363	C₂	semidirect
3. #20242252	C₂	semidirect
4. #20242245	C₂	semidirect
5. C₈×#10625335	C₂	semidirect
6. C₈×#10625334	C₂	semidirect
7. #20242171	C₂	semidirect
8. #20241831	C₂	semidirect
9. #20241799	C₂	semidirect
10. C₈×#10625329	C₂	semidirect
11. C₂×C₈×D₄×C₄₇	C₂	semidirect
19. #15689253	C₂²	semidirect
20. C₈×Dic₉₄	C₂²	semidirect
23. #15689202	C₂²	semidirect
25. C₈×D₁₈₈	C₂²	semidirect
32. #15688875	C₂²	semidirect
33. #15688873	C₂²	semidirect
34. #15688853	C₂²	semidirect
37. #15688850	C₂²	semidirect
38. #15688845	C₂²	semidirect
39. C₈×C₄₇⋊C₈	C₂²	semidirect
232. C₂×C₈×D₄	D₄₇	semidirect
284. C₄₇	#17910	semidirect

Maximal subgroups

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

subgroup	index
#20253435	2
#20252363	2
#20242252	2
#20242245	2
C₈×#10625335	2
C₈×#10625334	2
#20242171	2
#20241831	2
#20241799	2
C₈×#10625329	2
C₂×C₈×D₄×C₄₇	2
#17910	47