Subgroups — #26186873

Order 12032.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253988	C₂	1	1	yes	maximal, characteristic
2	#20252363	C₂	1	1	yes	maximal, characteristic
3	#20242295	C₂	1	2	yes	maximal, complemented
4	#20242288	C₂	1	2	yes	maximal, complemented
5	C₈×#10625337	C₂	1	2	yes	maximal, complemented
6	C₈×#10625336	C₂	1	2	yes	maximal, complemented
7	#20242153	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241861	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241851	C₂	1	1	yes	maximal, characteristic
10	C₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689657	C₂²	1	1	yes	characteristic
13	#15689529	C₄	1	1	yes	characteristic
14	#15689515	C₄	1	1	yes	characteristic
15	#15689491	C₄	1	1	yes	characteristic
16	#15689485	C₄	1	1	yes	characteristic
17	#15689379	C₄	1	2	yes	—
18	#15689371	C₄	1	2	yes	—
19	#15689253	C₂²	1	1	yes	characteristic
20	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
21	C₄×#10625337	C₂²	1	2	yes	—
22	C₄×#10625336	C₂²	1	2	yes	—
23	#15689202	C₂²	1	1	yes	characteristic
24	#15689194	—	2	1	no	—
25	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
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	—
33	#15688873	C₂²	1	2	yes	—
34	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
35	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
36	#15688853	C₂²	1	2	yes	—
37	#15688850	C₂²	1	2	yes	—
38	#15688845	C₂²	1	2	yes	—
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
40	C₄₇×#533	C₂²	1	1	yes	characteristic
41	C₄₇×#446	—	2	1	no	—
42	C₄₇×#446	C₂²	1	2	yes	—
43	C₈×Q₈×C₄₇	—	2	1	no	—
44	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
45	C₄₇×#424	—	2	1	no	—
46	C₄₇×#423	C₂²	1	1	yes	characteristic
47	C₄₇×#405	—	2	1	no	—
48	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#10625337	C₂×C₄	1	2	yes	—
50	C₂×#10625336	C₂×C₄	1	2	yes	—
51	C₂×#10625329	C₂×C₄	1	2	yes	—
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)	—	2	1	no	—
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	#13093948	C₂×C₄	1	2	yes	—
72	#13093948	C₂×C₄	1	2	yes	—
73	#13093947	C₂×C₄	1	2	yes	—
74	#13093944	C₂×C₄	1	2	yes	—
75	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
76	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
77	(C₂×D₄₇)⋊C₈	—	2	1	no	—
78	(C₂×D₄₇)⋊C₈	—	2	1	no	—
79	#13093935	—	2	1	no	—
80	#13093935	C₂×C₄	1	1	yes	characteristic
81	#13093935	C₂×C₄	1	1	yes	characteristic
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	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
89	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
91	#125×C₄₇	—	2	1	no	—
92	C₂²⋊Q₈×C₄₇	—	2	1	no	—
93	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
94	C₄×Q₈×C₄₇	—	2	1	no	—
95	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
96	#117×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₇	—	2	2	no	—
99	C₄⋊C₈×C₄₇	—	2	2	no	—
100	C₄⋊C₈×C₄₇	—	2	1	no	—
101	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
102	#97×C₄₇	—	2	2	no	—
103	C₄×C₈×C₄₇	—	2	2	no	—
104	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
105	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₄₇	—	2	1	no	—
109	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₄₇	—	2	1	no	—
114	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₄₇	—	2	1	no	—
116	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
117	M₁₆×C₄₇	—	4	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	4	1	no	—
121	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂²⋊C₄×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	#41	1	1	yes	characteristic
136	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
137	C₂²⋊Dic₄₇	—	2	1	no	—
138	#10625337	—	2	4	no	—
139	#10625336	—	2	4	no	—
140	(C₂×D₄₇)⋊C₄	—	2	1	no	—
141	(C₂×D₄₇)⋊C₄	—	2	1	no	—
142	(C₂×D₄₇)⋊C₄	—	2	1	no	—
143	(C₂×D₄₇)⋊C₄	—	2	1	no	—
144	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
146	Dic₄₇⋊C₄	—	2	1	no	—
147	Dic₄₇⋊C₄	—	2	1	no	—
148	Dic₄₇⋊C₄	—	2	1	no	—
149	Dic₄₇⋊C₄	—	2	1	no	—
150	C₄×Dic₄₇	—	2	1	no	—
151	#10625329	—	2	4	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
156	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
157	#10625324	—	4	2	no	—
158	C₈×D₄₇	—	4	2	no	—
159	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₄₇	—	2	1	no	—
161	Q₈×C₄₇	—	2	2	no	—
162	Q₈×C₄₇	—	2	2	no	—
163	Q₈×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	D₁₈₈	—	2	2	no	—
181	C₄×D₄₇	—	4	1	no	—
182	C₄×D₄₇	—	4	1	no	—
183	Dic₉₄	—	2	2	no	—
184	C₈×C₄₇	—	2	1	no	—
185	C₈×C₄₇	—	2	1	no	—
186	C₈×C₄₇	—	2	1	no	—
187	C₈×C₄₇	—	4	2	no	—
188	C₈×C₄₇	#137	1	2	yes	—
189	C₄₇⋊C₈	—	2	2	no	—
190	C₄₇⋊C₈	—	4	2	no	—
191	C₄₇⋊C₈	—	4	1	no	—
192	C₄₇⋊C₈	—	4	1	no	—
193	C₄₇⋊C₈	#131	1	4	yes	—
194	#17965	—	47	1	no	maximal, Sylow
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂×D₄₇	—	4	1	no	—
200	C₂×D₄₇	—	4	1	no	—
201	C₂×D₄₇	—	4	1	no	—
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	—	2	1	no	—
204	C₄×C₄₇	—	2	1	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	4	2	no	—
207	C₄×C₄₇	—	4	2	no	—
208	C₄×C₄₇	C₂×#131	1	2	yes	—
209	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
210	C₄×C₄₇	#575	1	1	yes	characteristic
211	Dic₄₇	—	4	1	no	—
212	Dic₄₇	—	4	1	no	—
213	Dic₄₇	—	4	1	no	—
214	#3172	—	47	1	no	—
215	#2966	—	47	1	no	—
216	#2960	D₄₇	1	1	yes	characteristic, complemented
217	#1593	—	47	2	no	—
218	#1592	—	47	2	no	—
219	C₈×Q₁₆	—	47	2	no	—
220	C₈×SD₁₆	—	47	2	no	—
221	#1569	—	47	1	no	—
222	#1497	—	47	1	no	—
223	#1495	—	47	1	no	—
224	C₈×M₁₆	—	47	1	no	—
225	C₂×C₄₇	—	4	1	no	—
226	C₂×C₄₇	#2931	1	1	yes	characteristic
227	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
228	C₂×C₄₇	#2955	1	1	yes	characteristic
229	D₄₇	—	8	1	no	—
230	#533	C₂×D₄₇	1	1	yes	characteristic
231	#529	—	47	1	no	—
232	#501	—	47	1	no	—
233	#497	—	47	1	no	—
234	#491	—	47	1	no	—
235	#489	—	47	1	no	—
236	#470	—	47	2	no	—
237	#468	—	47	2	no	—
238	#446	—	2	1	no	—
239	#446	—	47	1	no	—
240	#446	C₂×D₄₇	1	2	yes	—
241	C₈×Q₈	—	2	1	no	—
242	C₈×Q₈	—	47	1	no	—
243	C₈×Q₈	C₂×D₄₇	1	2	yes	—
244	C₄×Q₁₆	—	47	2	no	—
245	C₄×SD₁₆	—	47	2	no	—
246	#436	—	47	1	no	—
247	#435	—	94	1	no	—
248	C₈×D₄	—	47	1	no	—
249	C₈×D₄	—	94	1	no	—
250	#433	—	94	1	no	—
251	#432	—	47	1	no	—
252	#431	—	47	1	no	—
253	#424	—	2	1	no	—
254	#423	C₂×D₄₇	1	1	yes	characteristic
255	#405	—	2	1	no	—
256	#405	—	94	1	no	—
257	C₄×M₁₆	—	47	1	no	—
258	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
259	#335	—	47	2	no	—
260	#334	—	47	2	no	—
261	Q₈⋊C₈	—	47	2	no	—
262	Q₈⋊C₈	—	47	2	no	—
263	Q₈⋊C₈	—	47	2	no	—
264	D₄⋊C₈	—	47	2	no	—
265	#322	—	47	2	no	—
266	C₈²	—	47	2	no	—
267	C₄₇	#17965	1	1	yes	characteristic, complemented, Sylow
268	C₂×Q₁₆	—	47	2	no	—
269	C₂×SD₁₆	—	47	2	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	47	2	no	—
272	C₂×M₁₆	—	94	1	no	—
273	C₂²×C₈	—	94	1	no	—
274	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
275	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
276	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
277	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
278	#126	—	94	1	no	—
279	#125	—	2	1	no	—
280	#125	—	47	1	no	—
281	#124	—	47	1	no	—
282	#123	—	94	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	—	47	1	no	—
285	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
286	#121	—	47	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	47	1	no	—
289	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
290	C₄×D₄	—	47	1	no	—
291	C₄×D₄	—	94	1	no	—
292	#117	—	2	1	no	—
293	#117	—	94	1	no	—
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	#107	—	47	2	no	—
296	#106	—	47	2	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	47	1	no	—
301	C₄⋊C₈	—	47	1	no	—
302	C₄⋊C₈	—	94	1	no	—
303	C₄⋊C₈	—	94	1	no	—
304	C₄⋊C₈	—	94	1	no	—
305	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
306	#103	—	47	2	no	—
307	#103	—	47	2	no	—
308	#103	—	47	2	no	—
309	#102	—	47	2	no	—
310	C₂²⋊C₈	—	94	1	no	—
311	C₂²⋊C₈	—	94	1	no	—
312	C₂²⋊C₈	—	94	1	no	—
313	C₂²⋊C₈	—	94	1	no	—
314	#97	—	2	2	no	—
315	#97	—	47	1	no	—
316	#97	—	47	1	no	—
317	#97	—	94	1	no	—
318	#97	—	94	1	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	47	2	no	—
321	C₄×C₈	—	47	2	no	—
322	C₄×C₈	—	94	1	no	—
323	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
324	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
325	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	47	1	no	—
329	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
330	C₂×D₄	—	47	1	no	—
331	C₂×D₄	—	94	1	no	—
332	C₂²×C₄	—	94	1	no	—
333	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	#10625350	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
336	Q₁₆	—	94	4	no	—
337	SD₁₆	—	94	4	no	—
338	M₁₆	—	4	2	no	—
339	M₁₆	—	94	4	no	—
340	M₁₆	—	188	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	47	2	no	—
345	C₂×C₈	—	47	2	no	—
346	C₂×C₈	—	94	1	no	—
347	C₂×C₈	—	94	1	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	188	2	no	—
350	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
352	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	47	1	no	—
360	C₄⋊C₄	—	47	1	no	—
361	C₄⋊C₄	—	94	1	no	—
362	C₄⋊C₄	—	94	1	no	—
363	C₄⋊C₄	—	94	1	no	—
364	C₄⋊C₄	—	94	1	no	—
365	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	94	1	no	—
368	C₂²⋊C₄	—	94	1	no	—
369	C₂²⋊C₄	—	94	1	no	—
370	C₂²⋊C₄	—	94	1	no	—
371	C₂²⋊C₄	—	94	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	94	1	no	—
374	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
375	C₄²	#10625350	1	1	yes	characteristic
376	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
377	C₄²	C₂³×D₄₇	1	1	yes	characteristic
378	C₂³	—	94	1	no	—
379	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	94	2	no	—
384	D₄	—	94	2	no	—
385	D₄	—	188	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	94	1	no	—
393	C₂×C₄	—	94	1	no	—
394	C₂×C₄	—	94	1	no	—
395	C₂×C₄	—	188	1	no	—
396	C₂×C₄	—	188	1	no	—
397	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
398	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
399	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	4	2	no	—
407	C₈	—	47	4	no	—
408	C₈	—	94	2	no	—
409	C₈	—	188	2	no	—
410	C₈	—	188	1	no	—
411	C₈	—	188	1	no	—
412	C₈	#13094055	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	188	1	no	—
417	C₂²	—	188	1	no	—
418	C₂²	—	188	1	no	—
419	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	188	1	no	—
427	C₄	—	188	1	no	—
428	C₄	—	188	1	no	—
429	C₄	#131×D₄₇	1	2	yes	—
430	C₄	C₂×#13094055	1	1	yes	characteristic
431	C₄	#15689921	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	376	1	no	—
434	C₂	#20252098	1	1	yes	characteristic
435	C₂	C₄×#13094055	1	1	yes	characteristic
436	C₂	#20252289	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#2960	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#13093998	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#2960	D₄₇
hypocenter	C₄₇	#17965
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #20242295	C₂	semidirect
4. #20242288	C₂	semidirect
5. C₈×#10625337	C₂	semidirect
6. C₈×#10625336	C₂	semidirect
7. #20242153	C₂	semidirect
8. #20241861	C₂	semidirect
10. C₈×#10625329	C₂	semidirect
11. C₄₇×#2960	C₂	semidirect
216. #2960	D₄₇	semidirect
267. C₄₇	#17965	semidirect

Maximal subgroups

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

subgroup	index
#20253988	2
#20252363	2
#20242295	2
#20242288	2
C₈×#10625337	2
C₈×#10625336	2
#20242153	2
#20241861	2
#20241851	2
C₈×#10625329	2
C₄₇×#2960	2
#17965	47