Subgroups — #26115261

Order 12032.

826 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15688857	C₂	1	4	yes	maximal, complemented
3	#20241618	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2856	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
6	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
8	C₂×C₄₇⋊#95	—	2	1	no	—
9	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
10	#15688878	—	2	1	no	—
11	#15688857	—	2	8	no	—
12	C₂×#127×C₄₇	C₄	1	1	yes	characteristic, complemented
13	C₂×#121×C₄₇	—	2	1	no	—
14	C₂×#121×C₄₇	—	2	1	no	—
15	C₂×#121×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#390	—	2	1	no	—
18	C₄₇×#390	—	2	1	no	—
19	C₄₇×#390	C₄	1	2	yes	complemented
20	C₄₇×#384	C₄	1	1	yes	characteristic, complemented
21	C₂³×Dic₄₇	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₂×C₄⋊Dic₄₇	—	2	4	no	—
24	C₂×C₄⋊Dic₄₇	—	4	2	no	—
25	C₂×C₄⋊Dic₄₇	—	4	2	no	—
26	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
27	C₂²⋊(C₄₇⋊C₈)	D₄	1	4	yes	complemented
28	C₄×C₄₇⋊C₈	—	4	2	no	—
29	C₄₇⋊#95	—	2	4	no	—
30	C₄₇⋊#95	—	4	2	no	—
31	C₂²×D₄×C₄₇	—	2	2	no	—
32	C₂²×D₄×C₄₇	—	2	1	no	—
33	C₂²×D₄×C₄₇	—	2	1	no	—
34	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	#127×C₄₇	—	4	2	no	—
39	#121×C₄₇	—	2	4	no	—
40	#121×C₄₇	—	2	4	no	—
41	#121×C₄₇	—	4	2	no	—
42	#121×C₄₇	—	4	2	no	—
43	#121×C₄₇	—	4	2	no	—
44	#121×C₄₇	—	4	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
47	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	—	4	2	no	—
52	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
56	C₂⁴×C₄₇	—	2	2	no	—
57	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₂×D₄×C₄₇	—	2	4	no	—
59	C₂×D₄×C₄₇	—	4	2	no	—
60	C₂×D₄×C₄₇	—	4	2	no	—
61	C₂×D₄×C₄₇	—	4	2	no	—
62	C₂×D₄×C₄₇	—	4	2	no	—
63	C₂×D₄×C₄₇	—	4	2	no	—
64	C₂×D₄×C₄₇	—	4	2	no	—
65	C₂×D₄×C₄₇	—	4	2	no	—
66	C₂×D₄×C₄₇	—	4	2	no	—
67	C₂×D₄×C₄₇	—	4	2	no	—
68	C₂×D₄×C₄₇	—	4	2	no	—
69	C₂×D₄×C₄₇	—	4	2	no	—
70	C₂×D₄×C₄₇	—	4	2	no	—
71	C₂×D₄×C₄₇	—	4	2	no	—
72	C₂×D₄×C₄₇	—	4	2	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	4	1	no	—
77	C₂²×C₄×C₄₇	—	4	1	no	—
78	C₂²×C₄×C₄₇	—	4	1	no	—
79	C₂²×C₄×C₄₇	—	4	1	no	—
80	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	D₈	1	2	yes	—
85	C₂²×C₄×C₄₇	D₈	1	2	yes	—
86	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂²×Dic₄₇	—	2	4	no	—
93	C₂²×Dic₄₇	—	4	2	no	—
94	C₂²×Dic₄₇	—	4	2	no	—
95	C₂²×Dic₄₇	—	4	2	no	—
96	C₂²×Dic₄₇	—	4	2	no	—
97	C₂²×Dic₄₇	—	4	2	no	—
98	C₂²×Dic₄₇	—	4	2	no	—
99	C₄⋊C₄×C₄₇	—	2	4	no	—
100	C₄⋊C₄×C₄₇	—	4	2	no	—
101	C₄⋊C₄×C₄₇	—	4	2	no	—
102	C₂²⋊C₄×C₄₇	—	4	4	no	—
103	C₂²⋊C₄×C₄₇	—	4	4	no	—
104	C₂²⋊C₄×C₄₇	—	4	4	no	—
105	C₄²×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	—	2	2	no	—
107	C₄²×C₄₇	—	4	1	no	—
108	C₄²×C₄₇	—	4	1	no	—
109	C₄⋊Dic₄₇	—	4	8	no	—
110	C₂×C₄₇⋊C₈	—	2	4	no	—
111	C₂×C₄₇⋊C₈	—	4	2	no	—
112	C₂×C₄₇⋊C₈	—	4	2	no	—
113	C₂³×C₄₇	—	2	1	no	—
114	C₂³×C₄₇	—	2	1	no	—
115	C₂³×C₄₇	—	2	1	no	—
116	C₂³×C₄₇	—	2	1	no	—
117	C₂³×C₄₇	—	4	2	no	—
118	C₂³×C₄₇	—	4	2	no	—
119	C₂³×C₄₇	—	4	2	no	—
120	C₂³×C₄₇	—	4	2	no	—
121	C₂³×C₄₇	—	4	2	no	—
122	C₂³×C₄₇	—	4	2	no	—
123	C₂³×C₄₇	—	4	2	no	—
124	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂³×C₄₇	#124	1	1	yes	characteristic
126	C₂³×C₄₇	#127	1	1	yes	characteristic
127	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
128	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
129	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
130	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
131	D₄×C₄₇	—	8	4	no	—
132	D₄×C₄₇	—	8	4	no	—
133	D₄×C₄₇	—	8	2	no	—
134	D₄×C₄₇	—	8	2	no	—
135	D₄×C₄₇	—	8	2	no	—
136	D₄×C₄₇	—	8	2	no	—
137	D₄×C₄₇	—	8	4	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	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	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	#99	1	2	yes	—
158	C₂×C₄×C₄₇	#102	1	2	yes	—
159	C₂×C₄×C₄₇	#102	1	2	yes	—
160	C₂×C₄×C₄₇	#102	1	2	yes	—
161	C₂×C₄×C₄₇	#102	1	2	yes	—
162	C₂×C₄×C₄₇	#104	1	2	yes	—
163	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₄₇	#121	1	2	yes	—
165	C₂×Dic₄₇	—	4	4	no	—
166	C₂×Dic₄₇	—	4	4	no	—
167	C₂×Dic₄₇	—	4	4	no	—
168	C₂×Dic₄₇	—	8	2	no	—
169	C₂×Dic₄₇	—	8	2	no	—
170	C₂×Dic₄₇	—	8	2	no	—
171	C₂×Dic₄₇	—	8	2	no	—
172	C₄₇⋊C₈	—	4	4	no	—
173	#9680	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	1	no	—
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	2	1	no	—
186	C₂²×C₄₇	—	8	2	no	—
187	C₂²×C₄₇	—	8	2	no	—
188	C₂²×C₄₇	—	8	2	no	—
189	C₂²×C₄₇	—	8	2	no	—
190	C₂²×C₄₇	—	8	2	no	—
191	C₂²×C₄₇	—	8	2	no	—
192	C₂²×C₄₇	—	8	2	no	—
193	C₂²×C₄₇	#390	1	1	yes	characteristic
194	C₂²×C₄₇	C₂×#99	1	1	yes	characteristic
195	C₂²×C₄₇	#410	1	1	yes	characteristic
196	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
199	C₂²×C₄₇	#421	1	1	yes	characteristic
200	C₂²×C₄₇	#486	1	1	yes	characteristic
201	C₂²×C₄₇	#486	1	1	yes	characteristic
202	C₂²×C₄₇	#492	1	1	yes	characteristic
203	C₂²×C₄₇	#493	1	1	yes	characteristic
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	8	2	no	—
210	C₄×C₄₇	#327	1	4	yes	complemented
211	Dic₄₇	—	8	4	no	—
212	#2856	D₄₇	1	1	yes	characteristic
213	C₄×C₂²⋊C₈	—	47	1	no	—
214	C₂×#327	—	47	4	no	—
215	C₄⋊#95	—	47	1	no	—
216	C₂×C₄₇	—	2	1	no	—
217	C₂×C₄₇	—	2	1	no	—
218	C₂×C₄₇	—	2	1	no	—
219	C₂×C₄₇	—	2	1	no	—
220	C₂×C₄₇	—	16	2	no	—
221	C₂×C₄₇	C₂×#327	1	1	yes	characteristic
222	C₂×C₄₇	#1502	1	1	yes	characteristic
223	C₂×C₄₇	#1517	1	1	yes	characteristic
224	C₂×C₄₇	#1519	1	1	yes	characteristic
225	C₂×C₄₇	#1957	1	1	yes	characteristic
226	C₂×C₄₇	#1964	1	1	yes	characteristic
227	C₂×C₄₇	#1980	1	1	yes	characteristic
228	C₂×#127	Dic₄₇	1	1	yes	characteristic, complemented
229	C₂×#121	—	2	1	no	—
230	C₂×#121	—	2	1	no	—
231	C₂×#121	C₂×D₄₇	1	2	yes	—
232	C₂²×C₄⋊C₄	—	94	1	no	—
233	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
234	C₂×C₂²⋊C₈	—	47	2	no	—
235	C₂×C₄×C₈	—	94	1	no	—
236	#390	—	2	1	no	—
237	#390	—	2	1	no	—
238	#390	Dic₄₇	1	2	yes	complemented
239	#384	Dic₄₇	1	1	yes	characteristic, complemented
240	C₂×#95	—	47	2	no	—
241	C₂×#95	—	94	1	no	—
242	#336	—	94	1	no	—
243	#327	—	94	8	no	—
244	C₄₇	#9680	1	1	yes	characteristic, complemented, Sylow
245	C₂²×D₄	—	2	2	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
249	C₂³×C₄	—	94	2	no	—
250	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
251	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
252	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
253	C₂²×C₈	—	94	2	no	—
254	#127	—	4	2	no	—
255	#121	—	2	4	no	—
256	#121	—	2	4	no	—
257	#121	—	4	2	no	—
258	#121	—	4	2	no	—
259	#121	—	4	2	no	—
260	#121	—	4	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	94	4	no	—
264	C₂×C₄⋊C₄	—	188	2	no	—
265	C₂×C₄⋊C₄	—	188	2	no	—
266	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²	—	4	2	no	—
271	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
272	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
273	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
274	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
275	C₂²⋊C₈	—	47	4	no	—
276	C₂²⋊C₈	—	94	2	no	—
277	C₄×C₈	—	188	2	no	—
278	#95	—	94	4	no	—
279	#95	—	188	2	no	—
280	C₂⁴	—	2	2	no	—
281	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	94	4	no	—
305	C₂²×C₄	—	188	2	no	—
306	C₂²×C₄	—	188	2	no	—
307	C₂²×C₄	—	188	2	no	—
308	C₂²×C₄	—	188	2	no	—
309	C₂²×C₄	—	188	2	no	—
310	C₂²×C₄	—	188	2	no	—
311	C₂²×C₄	#10625334	1	2	yes	—
312	C₂²×C₄	#10625334	1	2	yes	—
313	C₂²×C₄	#10625335	1	2	yes	—
314	C₂²×C₄	#10625335	1	2	yes	—
315	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
317	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
318	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₄₇	1	2	yes	—
320	C₂²×C₄	#10625352	1	2	yes	—
321	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂×C₈	—	94	4	no	—
324	C₂×C₈	—	188	2	no	—
325	C₂×C₈	—	188	2	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	188	8	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	—	4	4	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
349	C₂³	#13094011	1	1	yes	characteristic
350	C₂³	#13094020	1	1	yes	characteristic
351	C₂³	C₂×#10625334	1	1	yes	characteristic
352	C₂³	C₂×#10625334	1	1	yes	characteristic
353	C₂³	C₂×#10625335	1	1	yes	characteristic
354	C₂³	C₂×#10625335	1	1	yes	characteristic
355	D₄	—	8	4	no	—
356	D₄	—	8	4	no	—
357	D₄	—	8	2	no	—
358	D₄	—	8	2	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	4	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	376	2	no	—
382	C₂×C₄	—	376	2	no	—
383	C₂×C₄	—	376	2	no	—
384	C₂×C₄	—	376	2	no	—
385	C₂×C₄	—	188	4	no	—
386	C₂×C₄	—	188	4	no	—
387	C₂×C₄	—	188	4	no	—
388	C₂×C₄	#13093939	1	2	yes	—
389	C₂×C₄	#13093945	1	2	yes	—
390	C₂×C₄	#13093945	1	2	yes	—
391	C₂×C₄	#13093945	1	2	yes	—
392	C₂×C₄	#13093945	1	2	yes	—
393	C₂×C₄	#13093951	1	2	yes	—
394	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
395	C₂×C₄	#13093995	1	2	yes	—
396	C₈	—	188	4	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	#15689026	1	1	yes	characteristic
417	C₂²	C₂×#13093939	1	1	yes	characteristic
418	C₂²	#15689097	1	1	yes	characteristic
419	C₂²	C₂×#13093945	1	1	yes	characteristic
420	C₂²	C₂×#13093945	1	1	yes	characteristic
421	C₂²	C₂×#13093951	1	1	yes	characteristic
422	C₂²	#15689140	1	1	yes	characteristic
423	C₂²	#15689469	1	1	yes	characteristic
424	C₂²	#15689469	1	1	yes	characteristic
425	C₂²	#15689495	1	1	yes	characteristic
426	C₂²	#15689499	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	8	2	no	—
433	C₄	—	376	4	no	—
434	C₄	#15688857	1	4	yes	complemented
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	2	1	no	—
439	C₂	—	16	2	no	—
440	C₂	C₂×#15688857	1	1	yes	characteristic
441	C₂	#20241883	1	1	yes	characteristic
442	C₂	#20241948	1	1	yes	characteristic
443	C₂	#20241956	1	1	yes	characteristic
444	C₂	#20244195	1	1	yes	characteristic
445	C₂	#20244225	1	1	yes	characteristic
446	C₂	#20244308	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting, prime radical	C₄₇×#2856	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#2856	D₄₇
hypocenter	C₄₇	#9680
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2856

Complements

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

N	H ≅ G/N	type
1. C₄×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
2. C₂×#15688857	C₂	semidirect
3. #20241618	C₂	semidirect
12. C₂×#127×C₄₇	C₄	semidirect
19. C₄₇×#390	C₄	semidirect
20. C₄₇×#384	C₄	semidirect
27. C₂²⋊(C₄₇⋊C₈)	D₄	semidirect
210. C₄×C₄₇	#327	semidirect
228. C₂×#127	Dic₄₇	semidirect
238. #390	Dic₄₇	semidirect
239. #384	Dic₄₇	semidirect
244. C₄₇	#9680	semidirect
434. C₄	#15688857	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₂²⋊(C₄₇⋊C₈)	2
C₂×#15688857	2
#20241618	2
C₄₇×#2856	2
#9680	47