Subgroups — #26219252

Order 12032.

978 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	#20245866	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20244024	C₂	1	2	yes	maximal, complemented
4	#20243975	C₂	1	2	yes	maximal, complemented
5	#20243724	C₂	1	2	yes	maximal
6	#20243651	C₂	1	2	yes	maximal
7	C₄×#13093956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#13093948	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13093945	C₂	1	1	yes	maximal, characteristic
10	#20243133	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×SD₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
13	C₂²×C₄×Dic₄₇	—	2	1	no	—
14	C₂×#13093956	C₂²	1	2	yes	—
15	C₂×#13093948	C₂²	1	2	yes	—
16	C₂×#13093945	C₂²	1	2	yes	—
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	#15689030	C₂²	1	2	yes	—
19	#15689022	C₂²	1	2	yes	—
20	#15689009	—	2	2	no	—
21	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
22	C₄×C₄⋊Dic₄₇	—	2	1	no	—
23	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
26	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
27	#15688969	—	2	1	no	—
28	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
29	#15688886	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₄×SD₁₆×C₄₇	C₄	1	8	yes	complemented
38	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂³×Dic₄₇	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	D₄×Dic₄₇	—	2	4	no	—
45	D₄×Dic₄₇	—	2	4	no	—
46	C₂×C₄⋊Dic₄₇	—	2	2	no	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
50	C₂×C₄×Dic₄₇	—	2	1	no	—
51	C₂×C₄×Dic₄₇	—	2	1	no	—
52	C₂×C₄×Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	—	4	4	no	—
54	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
56	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
58	#13093956	—	2	4	no	—
59	#13093948	—	2	4	no	—
60	#13093945	—	2	4	no	—
61	C₄×C₄₇⋊C₈	—	2	2	no	—
62	C₄₇⋊#95	—	2	1	no	—
63	C₄₇⋊#95	—	2	1	no	—
64	C₄₇⋊#95	—	2	2	no	—
65	C₄₇⋊#95	—	2	2	no	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₇	—	2	1	no	—
71	C₂×SD₁₆×C₄₇	—	2	4	no	—
72	C₂×SD₁₆×C₄₇	C₂×C₄	1	4	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×Q₈×C₄₇	—	2	2	no	—
76	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
77	C₄×D₄×C₄₇	—	2	2	no	—
78	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄²×C₄₇	—	2	1	no	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	#106×C₄₇	C₂×C₄	1	4	yes	complemented
86	#103×C₄₇	C₂×C₄	1	4	yes	complemented
87	#102×C₄₇	C₂×C₄	1	4	yes	—
88	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
89	C₂⁴×C₄₇	—	2	1	no	—
90	C₂×Q₈×C₄₇	—	2	1	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₄₇	—	2	1	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₄₇	#41	1	4	yes	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	—	4	2	no	—
103	C₂²×C₄×C₄₇	—	4	2	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₂²×Dic₄₇	—	2	8	no	—
108	C₂²×Dic₄₇	—	2	2	no	—
109	C₂²×Dic₄₇	—	2	2	no	—
110	C₂²×Dic₄₇	—	4	4	no	—
111	C₂²×Dic₄₇	—	4	4	no	—
112	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
113	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
114	SD₁₆×C₄₇	—	2	8	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄⋊C₄×C₄₇	—	2	4	no	—
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
123	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂²⋊C₄×C₄₇	—	2	4	no	—
125	C₄²×C₄₇	—	2	4	no	—
126	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
127	C₄²×C₄₇	#41	1	2	yes	—
128	C₂²⋊Dic₄₇	—	2	8	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	—	4	4	no	—
133	C₄⋊Dic₄₇	#41	1	4	yes	—
134	C₄×Dic₄₇	—	2	2	no	—
135	C₄×Dic₄₇	—	2	2	no	—
136	C₄×Dic₄₇	—	2	2	no	—
137	C₄×Dic₄₇	—	4	2	no	—
138	C₄×Dic₄₇	—	4	2	no	—
139	C₄×Dic₄₇	—	4	2	no	—
140	C₄×Dic₄₇	—	4	4	no	—
141	C₄×Dic₄₇	SD₁₆	1	4	yes	complemented
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂³×C₄₇	—	2	2	no	—
146	C₂³×C₄₇	—	2	4	no	—
147	C₂³×C₄₇	—	4	1	no	—
148	C₂³×C₄₇	—	4	1	no	—
149	C₂³×C₄₇	—	4	2	no	—
150	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₄₇	—	2	2	no	—
152	Q₈×C₄₇	—	2	2	no	—
153	Q₈×C₄₇	—	4	2	no	—
154	D₄×C₄₇	—	2	2	no	—
155	D₄×C₄₇	—	2	4	no	—
156	D₄×C₄₇	#117	1	4	yes	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	8	no	—
166	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
169	C₂×C₄×C₄₇	#135	1	2	yes	—
170	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	4	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	4	16	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	4	2	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	C₂×Dic₄₇	C₂×SD₁₆	1	4	yes	—
187	C₈×C₄₇	—	2	2	no	—
188	C₈×C₄₇	—	2	2	no	—
189	C₄₇⋊C₈	—	4	2	no	—
190	#21117	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	—	2	4	no	—
192	C₂²×C₄₇	—	4	4	no	—
193	C₂²×C₄₇	—	4	4	no	—
194	C₂²×C₄₇	—	4	2	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₄₇	#525	1	2	yes	—
198	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
200	C₂²×C₄₇	#575	1	2	yes	—
201	C₄×C₄₇	—	2	2	no	—
202	C₄×C₄₇	—	4	2	no	—
203	C₄×C₄₇	—	4	2	no	—
204	C₄×C₄₇	—	4	2	no	—
205	C₄×C₄₇	C₄×SD₁₆	1	4	yes	—
206	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
207	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
208	C₄×C₄₇	#529	1	2	yes	—
209	Dic₄₇	—	2	4	no	—
210	Dic₄₇	—	4	4	no	—
211	Dic₄₇	—	4	2	no	—
212	Dic₄₇	—	8	2	no	—
213	C₂×C₄×SD₁₆	D₄₇	1	1	yes	characteristic
214	#2295	—	47	1	no	—
215	C₄²×D₄	—	47	1	no	—
216	#1927	—	47	2	no	—
217	#1920	—	47	2	no	—
218	#1877	—	47	2	no	—
219	#1864	—	47	2	no	—
220	C₄×#106	—	47	1	no	—
221	C₄×#103	—	47	1	no	—
222	C₄×#102	—	47	1	no	—
223	#1744	—	47	1	no	—
224	C₂×C₄₇	—	4	4	no	—
225	C₂×C₄₇	#2290	1	1	yes	characteristic
226	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
227	C₂×C₄₇	#2943	1	1	yes	characteristic
228	C₂×C₄₇	#3101	1	2	yes	—
229	C₂×C₄₇	#3102	1	2	yes	—
230	C₂²×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
232	C₂×C₄×D₄	—	47	2	no	—
233	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
234	C₂²×C₄²	—	94	1	no	—
235	C₄×SD₁₆	Dic₄₇	1	8	yes	complemented
236	C₂×#106	—	47	2	no	—
237	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
238	C₂×#103	—	47	2	no	—
239	C₂×#103	C₂×D₄₇	1	1	yes	characteristic
240	C₂×#102	—	47	2	no	—
241	C₂×#102	C₂×D₄₇	1	1	yes	characteristic
242	C₂×C₄×C₈	—	47	1	no	—
243	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
244	#391	—	47	2	no	—
245	#389	—	47	2	no	—
246	#387	—	94	2	no	—
247	C₄×C₄⋊C₄	—	47	2	no	—
248	C₄×C₄⋊C₄	—	47	1	no	—
249	C₄×C₄⋊C₄	—	47	1	no	—
250	C₄×C₄⋊C₄	—	94	1	no	—
251	C₄×C₂²⋊C₄	—	94	2	no	—
252	C₄×C₂²⋊C₄	—	94	1	no	—
253	#376	—	94	1	no	—
254	C₄³	—	47	1	no	—
255	#340	—	47	2	no	—
256	#340	—	47	2	no	—
257	#340	—	47	2	no	—
258	#336	—	47	2	no	—
259	#336	—	47	2	no	—
260	C₄₇	#21117	1	1	yes	characteristic, complemented, Sylow
261	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
262	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	—	94	2	no	—
265	C₂×SD₁₆	—	2	4	no	—
266	C₂×SD₁₆	C₂×Dic₄₇	1	4	yes	—
267	C₂²×C₈	—	47	2	no	—
268	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
269	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
270	C₄×Q₈	—	2	2	no	—
271	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	—	94	4	no	—
274	C₄×D₄	—	94	4	no	—
275	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	47	2	no	—
278	C₂×C₄⋊C₄	—	47	2	no	—
279	C₂×C₄⋊C₄	—	94	2	no	—
280	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	94	2	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	—	47	1	no	—
286	C₂×C₄²	—	47	1	no	—
287	C₂×C₄²	—	47	2	no	—
288	C₂×C₄²	—	47	2	no	—
289	C₂×C₄²	—	94	2	no	—
290	C₂×C₄²	—	94	1	no	—
291	C₂×C₄²	—	94	1	no	—
292	C₂×C₄²	—	188	4	no	—
293	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
294	#106	—	94	4	no	—
295	#106	C₂×Dic₄₇	1	4	yes	complemented
296	#103	—	94	4	no	—
297	#103	C₂×Dic₄₇	1	4	yes	complemented
298	#102	—	94	4	no	—
299	#102	C₂×Dic₄₇	1	4	yes	—
300	C₄×C₈	—	94	2	no	—
301	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
302	#95	—	94	2	no	—
303	#95	—	94	2	no	—
304	#95	—	94	2	no	—
305	#95	—	94	2	no	—
306	#95	—	94	1	no	—
307	#95	—	94	1	no	—
308	C₂⁴	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	#10625350	1	4	yes	—
316	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	47	2	no	—
324	C₂²×C₄	—	47	2	no	—
325	C₂²×C₄	—	94	8	no	—
326	C₂²×C₄	—	94	2	no	—
327	C₂²×C₄	—	94	2	no	—
328	C₂²×C₄	—	188	4	no	—
329	C₂²×C₄	—	188	4	no	—
330	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	SD₁₆	—	2	8	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	94	2	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
340	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	47	4	no	—
345	C₄⋊C₄	—	94	2	no	—
346	C₄⋊C₄	—	94	2	no	—
347	C₄⋊C₄	—	94	2	no	—
348	C₄⋊C₄	—	188	4	no	—
349	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
350	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	94	8	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	47	4	no	—
355	C₄²	—	94	2	no	—
356	C₄²	—	94	2	no	—
357	C₄²	—	94	2	no	—
358	C₄²	—	188	2	no	—
359	C₄²	—	188	4	no	—
360	C₄²	—	188	2	no	—
361	C₄²	—	188	2	no	—
362	C₄²	#10625352	1	2	yes	—
363	C₄²	C₂²×Dic₄₇	1	2	yes	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	2	no	—
369	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	4	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	4	no	—
375	D₄	#13093983	1	4	yes	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	8	no	—
385	C₂×C₄	—	47	4	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	2	no	—
388	C₂×C₄	—	94	2	no	—
389	C₂×C₄	—	94	4	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	94	2	no	—
392	C₂×C₄	—	188	16	no	—
393	C₂×C₄	—	188	2	no	—
394	C₂×C₄	—	188	2	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	—	188	2	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
399	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
400	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
401	C₂×C₄	#13094045	1	2	yes	—
402	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
403	C₂×C₄	#41×D₄₇	1	2	yes	—
404	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
405	C₂×C₄	C₂×#10625350	1	2	yes	—
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	188	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	4	2	no	—
414	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
415	C₂²	#15689632	1	2	yes	—
416	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
417	C₂²	C₂×#13094045	1	1	yes	characteristic
418	C₂²	#15689920	1	2	yes	—
419	C₄	—	2	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	94	4	no	—
424	C₄	—	376	2	no	—
425	C₄	—	188	4	no	—
426	C₄	—	188	2	no	—
427	C₄	SD₁₆×Dic₄₇	1	4	yes	—
428	C₄	C₂×#13093983	1	1	yes	characteristic
429	C₄	#41×Dic₄₇	1	1	yes	characteristic
430	C₄	#15689653	1	2	yes	—
431	C₂	—	4	4	no	—
432	C₂	#20245833	1	1	yes	characteristic
433	C₂	C₂×SD₁₆×Dic₄₇	1	1	yes	characteristic
434	C₂	#20252189	1	1	yes	characteristic
435	C₂	#20253394	1	2	yes	—
436	C₂	#20253410	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×SD₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₄×C₄₇	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×SD₁₆	D₄₇
hypocenter	C₄₇	#21117
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #20245866	C₂	semidirect
3. #20244024	C₂	semidirect
4. #20243975	C₂	semidirect
7. C₄×#13093956	C₂	semidirect
8. C₄×#13093948	C₂	semidirect
10. #20243133	C₂	semidirect
37. C₄×SD₁₆×C₄₇	C₄	semidirect
76. C₄×Q₈×C₄₇	C₂×C₄	semidirect
85. #106×C₄₇	C₂×C₄	semidirect
86. #103×C₄₇	C₂×C₄	semidirect
88. C₄×C₈×C₄₇	C₂×C₄	semidirect
141. C₄×Dic₄₇	SD₁₆	semidirect
235. C₄×SD₁₆	Dic₄₇	semidirect
260. C₄₇	#21117	semidirect
271. C₄×Q₈	C₂×Dic₄₇	semidirect
295. #106	C₂×Dic₄₇	semidirect
297. #103	C₂×Dic₄₇	semidirect
301. C₄×C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20245866	2
C₄×D₄×Dic₄₇	2
#20244024	2
#20243975	2
#20243724	2
#20243651	2
C₄×#13093956	2
C₄×#13093948	2
C₄×#13093945	2
#20243133	2
C₂×C₄×SD₁₆×C₄₇	2
#21117	47