Subgroups — #26220503

Order 12032.

822 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#20245863	C₂	1	2	yes	maximal
3	#20244250	C₂	1	1	yes	maximal, characteristic
4	#20244121	C₂	1	1	yes	maximal, characteristic
5	#20244119	C₂	1	1	yes	maximal, characteristic
6	#20244067	C₂	1	2	yes	maximal
7	#20244061	C₂	1	2	yes	maximal
8	#107×Dic₄₇	C₂	1	1	yes	maximal, characteristic
9	#103×Dic₄₇	C₂	1	2	yes	maximal
10	C₄×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1969	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
13	Q₁₆×Dic₄₇	C₄	1	8	yes	complemented
14	C₂×#13093958	C₂²	1	1	yes	characteristic
15	C₂×#13093958	C₂²	1	1	yes	characteristic
16	C₂×#13093948	C₂²	1	2	yes	—
17	C₂×#13093948	C₂²	1	2	yes	—
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
23	#15689030	C₂²	1	2	yes	—
24	#15689021	C₂²	1	2	yes	—
25	#15689019	C₂²	1	2	yes	—
26	#15689008	—	2	2	no	—
27	#15689006	—	2	2	no	—
28	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
29	#15688974	—	2	2	no	—
30	#15688968	—	2	2	no	—
31	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688886	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#103×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#391	C₂²	1	2	yes	—
40	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
41	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
42	Q₈×Dic₄₇	—	2	4	no	—
43	Q₈×Dic₄₇	C₂×C₄	1	8	yes	—
44	C₂×C₄⋊Dic₄₇	—	2	2	no	—
45	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
47	C₂×Dic₄₇⋊C₄	—	2	2	no	—
48	C₂×Dic₄₇⋊C₄	—	2	2	no	—
49	C₂×C₄×Dic₄₇	—	2	2	no	—
50	C₂×C₄×Dic₄₇	—	2	2	no	—
51	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
57	#13093958	—	2	2	no	—
58	#13093958	C₂×C₄	1	4	yes	—
59	#13093948	—	2	4	no	—
60	#13093948	C₂×C₄	1	8	yes	—
61	C₄×C₄₇⋊C₈	—	2	2	no	—
62	C₈×Dic₄₇	—	2	2	no	—
63	C₈×Dic₄₇	—	2	2	no	—
64	C₈×Dic₄₇	—	2	2	no	—
65	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
72	C₂×Q₁₆×C₄₇	—	2	2	no	—
73	C₂×Q₁₆×C₄₇	—	2	2	no	—
74	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	#107×C₄₇	—	2	2	no	—
80	#103×C₄₇	—	2	4	no	—
81	C₄×C₈×C₄₇	—	2	2	no	—
82	#95×C₄₇	—	2	2	no	—
83	#95×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	—	2	2	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	2	2	no	—
88	C₂×Q₈×C₄₇	—	2	2	no	—
89	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
101	Q₁₆×C₄₇	—	2	8	no	—
102	C₂×C₈×C₄₇	—	2	1	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₄₇	#41	1	2	yes	—
106	C₂×C₈×C₄₇	#41	1	2	yes	—
107	C₂×C₈×C₄₇	#41	1	2	yes	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	—	2	1	no	—
111	C₄²×C₄₇	—	2	1	no	—
112	C₄⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	—	2	8	no	—
114	C₄⋊Dic₄₇	—	2	2	no	—
115	C₄⋊Dic₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
117	Dic₄₇⋊C₄	—	4	4	no	—
118	Dic₄₇⋊C₄	—	4	4	no	—
119	C₄×Dic₄₇	—	2	2	no	—
120	C₄×Dic₄₇	—	2	1	no	—
121	C₄×Dic₄₇	—	2	1	no	—
122	C₄×Dic₄₇	—	2	8	no	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₄×Dic₄₇	—	4	4	no	—
126	C₄×Dic₄₇	Q₁₆	1	4	yes	complemented
127	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
128	C₄×Dic₄₇	#41	1	2	yes	—
129	C₂×C₄₇⋊C₈	—	2	1	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₄₇⋊C₈	#41	1	2	yes	—
135	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₄₇	—	2	4	no	—
137	Q₈×C₄₇	—	2	4	no	—
138	Q₈×C₄₇	—	4	2	no	—
139	Q₈×C₄₇	—	4	2	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	4	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
151	C₂×C₄×C₄₇	#135	1	2	yes	—
152	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×Dic₄₇	—	2	1	no	—
159	C₂×Dic₄₇	—	2	1	no	—
160	C₂×Dic₄₇	—	2	1	no	—
161	C₂×Dic₄₇	—	2	1	no	—
162	C₂×Dic₄₇	—	2	1	no	—
163	C₂×Dic₄₇	—	2	1	no	—
164	C₂×Dic₄₇	—	2	4	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
171	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
172	C₂×Dic₄₇	C₂×Q₁₆	1	2	yes	—
173	C₂×Dic₄₇	C₂×Q₁₆	1	2	yes	—
174	C₂×Dic₄₇	#135	1	2	yes	—
175	C₂×Dic₄₇	#135	1	2	yes	—
176	C₈×C₄₇	—	2	2	no	—
177	C₈×C₄₇	#117	1	4	yes	—
178	C₄₇⋊C₈	—	2	2	no	—
179	C₄₇⋊C₈	—	2	2	no	—
180	#21276	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
182	C₂²×C₄₇	#532	1	1	yes	characteristic
183	C₂²×C₄₇	#532	1	1	yes	characteristic
184	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	4	4	no	—
191	C₄×C₄₇	—	8	2	no	—
192	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
193	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
194	C₄×C₄₇	#529	1	1	yes	characteristic
195	C₄×C₄₇	#529	1	1	yes	characteristic
196	Dic₄₇	—	2	2	no	—
197	Dic₄₇	—	2	2	no	—
198	Dic₄₇	—	2	2	no	—
199	Dic₄₇	—	4	4	no	—
200	Dic₄₇	—	8	2	no	—
201	Dic₄₇	C₄×Q₁₆	1	4	yes	—
202	C₂×C₄×Q₁₆	—	47	1	no	—
203	#2295	—	47	2	no	—
204	#1969	—	47	1	no	—
205	#1969	D₄₇	1	1	yes	characteristic
206	#1942	—	47	1	no	—
207	#1942	—	47	1	no	—
208	#1933	—	47	2	no	—
209	#1933	—	47	2	no	—
210	C₄×#107	—	47	1	no	—
211	C₄×#103	—	47	2	no	—
212	C₄²×C₈	—	47	1	no	—
213	C₂×C₄₇	#2293	1	1	yes	characteristic
214	C₂×C₄₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
215	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
216	C₂×C₄₇	#3168	1	1	yes	characteristic
217	C₂×C₄₇	#3168	1	1	yes	characteristic
218	C₂×C₄₇	#3170	1	1	yes	characteristic
219	C₂×C₄₇	#3170	1	1	yes	characteristic
220	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
221	C₂×C₄×Q₈	—	47	2	no	—
222	C₄×Q₁₆	—	47	8	no	—
223	C₂×#107	—	47	1	no	—
224	C₂×#107	—	47	1	no	—
225	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
226	C₂×#103	—	47	2	no	—
227	C₂×#103	—	47	2	no	—
228	C₂×#103	C₂×D₄₇	1	2	yes	—
229	C₂×C₄×C₈	—	47	1	no	—
230	C₂×C₄×C₈	—	47	1	no	—
231	C₂×C₄×C₈	—	47	1	no	—
232	C₂×C₄×C₈	—	47	1	no	—
233	C₂×C₄×C₈	—	47	1	no	—
234	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
235	#391	—	47	2	no	—
236	#391	C₂×D₄₇	1	2	yes	—
237	#389	—	47	2	no	—
238	#389	—	47	2	no	—
239	#387	—	94	2	no	—
240	#387	—	94	2	no	—
241	C₄×C₄⋊C₄	—	47	2	no	—
242	C₄×C₄⋊C₄	—	94	2	no	—
243	#376	—	94	2	no	—
244	C₄³	—	47	1	no	—
245	#340	—	47	2	no	—
246	#340	—	47	2	no	—
247	#340	—	47	2	no	—
248	C₄₇	#21276	1	1	yes	characteristic, complemented, Sylow
249	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×Q₁₆	—	2	2	no	—
252	C₂×Q₁₆	C₄×D₄₇	1	4	yes	—
253	C₂²×C₈	—	47	1	no	—
254	C₂²×C₈	—	47	1	no	—
255	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
257	C₄×Q₈	—	47	8	no	—
258	C₄×Q₈	—	94	4	no	—
259	C₂×C₄⋊C₄	—	47	2	no	—
260	C₂×C₄⋊C₄	—	47	2	no	—
261	C₂×C₄⋊C₄	—	94	2	no	—
262	C₂×C₄⋊C₄	—	94	2	no	—
263	C₂×C₄⋊C₄	—	94	2	no	—
264	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
265	C₂×C₄²	—	47	1	no	—
266	C₂×C₄²	—	47	1	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	—	47	1	no	—
269	C₂×C₄²	—	47	1	no	—
270	C₂×C₄²	—	47	1	no	—
271	C₂×C₄²	—	94	2	no	—
272	C₂×C₄²	—	94	2	no	—
273	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
274	#107	—	2	2	no	—
275	#107	—	47	4	no	—
276	#107	—	94	2	no	—
277	#103	—	2	4	no	—
278	#103	—	47	8	no	—
279	#103	—	94	4	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	47	4	no	—
282	C₄×C₈	—	94	2	no	—
283	C₄×C₈	—	94	2	no	—
284	C₄×C₈	—	94	2	no	—
285	C₄×C₈	—	94	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	94	2	no	—
289	#95	—	94	2	no	—
290	#95	—	94	2	no	—
291	#95	—	94	2	no	—
292	#95	—	94	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	47	1	no	—
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	94	2	no	—
306	C₂²×C₄	—	94	2	no	—
307	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
310	Q₁₆	—	2	8	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	47	2	no	—
314	C₂×C₈	—	47	2	no	—
315	C₂×C₈	—	94	1	no	—
316	C₂×C₈	—	94	1	no	—
317	C₂×C₈	—	94	1	no	—
318	C₂×C₈	—	94	1	no	—
319	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
320	C₂×C₈	#10625352	1	2	yes	—
321	C₂×C₈	#10625352	1	2	yes	—
322	C₂×C₈	#10625352	1	2	yes	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	47	4	no	—
326	C₄⋊C₄	—	94	8	no	—
327	C₄⋊C₄	—	94	2	no	—
328	C₄⋊C₄	—	94	2	no	—
329	C₄⋊C₄	—	94	2	no	—
330	C₄⋊C₄	—	188	4	no	—
331	C₄⋊C₄	—	188	4	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	47	4	no	—
335	C₄²	—	47	2	no	—
336	C₄²	—	47	2	no	—
337	C₄²	—	94	2	no	—
338	C₄²	—	94	2	no	—
339	C₄²	—	94	8	no	—
340	C₄²	—	94	2	no	—
341	C₄²	—	94	1	no	—
342	C₄²	—	94	1	no	—
343	C₄²	—	188	4	no	—
344	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
345	Q₈	—	2	4	no	—
346	Q₈	—	2	4	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	4	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	47	2	no	—
360	C₂×C₄	—	47	2	no	—
361	C₂×C₄	—	47	2	no	—
362	C₂×C₄	—	47	2	no	—
363	C₂×C₄	—	47	2	no	—
364	C₂×C₄	—	47	2	no	—
365	C₂×C₄	—	94	1	no	—
366	C₂×C₄	—	94	1	no	—
367	C₂×C₄	—	94	1	no	—
368	C₂×C₄	—	94	1	no	—
369	C₂×C₄	—	94	1	no	—
370	C₂×C₄	—	94	1	no	—
371	C₂×C₄	—	94	4	no	—
372	C₂×C₄	—	188	2	no	—
373	C₂×C₄	—	188	2	no	—
374	C₂×C₄	—	188	2	no	—
375	C₂×C₄	—	188	2	no	—
376	C₂×C₄	—	188	2	no	—
377	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
378	C₂×C₄	#13094047	1	2	yes	—
379	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
380	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
381	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
383	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
384	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	94	2	no	—
387	C₈	—	94	2	no	—
388	C₈	#13093980	1	4	yes	—
389	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
390	C₂²	#15689668	1	1	yes	characteristic
391	C₂²	#15689671	1	1	yes	characteristic
392	C₂²	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
393	C₂²	#135×D₄₇	1	1	yes	characteristic
394	C₂²	#135×D₄₇	1	1	yes	characteristic
395	C₂²	C₂×#13094047	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	2	no	—
400	C₄	—	47	4	no	—
401	C₄	—	94	2	no	—
402	C₄	—	94	2	no	—
403	C₄	—	94	2	no	—
404	C₄	—	376	2	no	—
405	C₄	—	188	4	no	—
406	C₄	C₂×#13093980	1	1	yes	characteristic
407	C₄	C₄×#10625352	1	1	yes	characteristic
408	C₄	#15689652	1	1	yes	characteristic
409	C₄	#15689654	1	1	yes	characteristic
410	C₂	#20245850	1	1	yes	characteristic
411	C₂	C₄×Q₁₆×D₄₇	1	1	yes	characteristic
412	C₂	C₄×#13094047	1	1	yes	characteristic
413	C₂	#20253955	1	1	yes	characteristic
414	C₂	#20253959	1	1	yes	characteristic
415	C₂	#20253969	1	1	yes	characteristic
416	C₂	#20253972	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1969	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1969	D₄₇
hypocenter	C₄₇	#21276
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1969

Complements

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

N	H ≅ G/N	type
13. Q₁₆×Dic₄₇	C₄	semidirect
126. C₄×Dic₄₇	Q₁₆	semidirect
248. C₄₇	#21276	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×Dic₄₇	2
#20245863	2
#20244250	2
#20244121	2
#20244119	2
#20244067	2
#20244061	2
#107×Dic₄₇	2
#103×Dic₄₇	2
C₄×C₈×Dic₄₇	2
C₄₇×#1969	2
#21276	47