Subgroups — #26274379

Order 12032.

710 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246343	C₂	1	1	yes	maximal, characteristic
2	#20244766	C₂	1	2	yes	maximal
3	#20244526	C₂	1	2	yes	maximal
4	#20244341	C₂	1	2	yes	maximal
5	#20244151	C₂	1	1	yes	maximal, characteristic
6	#20244107	C₂	1	1	yes	maximal, characteristic
7	#20243963	C₂	1	2	yes	maximal
8	#20243515	C₂	1	1	yes	maximal, characteristic
9	#20243390	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093947	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#2551	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
13	C₂×#13093955	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	C₂×#13093947	C₂²	1	1	yes	characteristic
17	C₂×#13093947	C₂²	1	1	yes	characteristic
18	C₂×#13093947	C₂²	1	2	yes	—
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	#15689029	C₂²	1	2	yes	—
21	#15689010	—	2	2	no	—
22	#15688993	C₂²	1	1	yes	characteristic
23	#15688988	—	2	1	no	—
24	C₄⋊C₄×Dic₄₇	—	2	1	no	—
25	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
26	#15688885	C₂²	1	1	yes	characteristic
27	#15688885	C₂²	1	1	yes	characteristic
28	#15688885	C₂²	1	2	yes	—
29	#15688885	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688878	C₂²	1	2	yes	—
33	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
34	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
35	C₄₇×#395	—	2	2	no	—
36	C₄₇×#389	—	2	1	no	—
37	C₄₇×#389	C₂²	1	2	yes	—
38	C₄₇×#384	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₄×Dic₉₄	—	2	2	no	—
46	C₄×Dic₉₄	Q₈	1	4	yes	complemented
47	C₂×C₄⋊Dic₄₇	—	2	1	no	—
48	C₂×C₄⋊Dic₄₇	—	2	1	no	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
51	C₂×Dic₄₇⋊C₄	—	2	1	no	—
52	C₂×C₄×Dic₄₇	—	2	1	no	—
53	C₂×C₄×Dic₄₇	—	2	2	no	—
54	#13093955	—	2	4	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
57	#13093947	—	2	2	no	—
58	#13093947	—	2	2	no	—
59	#13093947	—	4	2	no	—
60	C₄×C₄₇⋊C₈	—	2	2	no	—
61	C₄₇⋊#95	—	2	2	no	—
62	C₄₇⋊#95	—	2	2	no	—
63	C₄₇⋊#95	—	2	2	no	—
64	C₂²×Q₈×C₄₇	—	2	2	no	—
65	C₄⋊Q₈×C₄₇	—	2	4	no	—
66	C₄⋊Q₈×C₄₇	—	4	2	no	—
67	C₄⋊Q₈×C₄₇	—	4	4	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	#95×C₄₇	—	2	1	no	—
81	#95×C₄₇	—	2	2	no	—
82	#95×C₄₇	D₄	1	2	yes	—
83	C₂×Q₈×C₄₇	—	4	4	no	—
84	C₂×Q₈×C₄₇	—	4	4	no	—
85	C₂×Q₈×C₄₇	—	8	2	no	—
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	1	no	—
95	C₂²×Dic₄₇	—	2	1	no	—
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₂×Dic₉₄	—	2	1	no	—
98	C₂×Dic₉₄	—	2	1	no	—
99	C₂×Dic₉₄	—	2	1	no	—
100	C₂×Dic₉₄	—	2	1	no	—
101	C₂×Dic₉₄	—	2	1	no	—
102	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	2	1	no	—
105	C₄⋊C₄×C₄₇	—	2	1	no	—
106	C₄⋊C₄×C₄₇	—	2	2	no	—
107	C₄⋊C₄×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	4	4	no	—
109	C₄⋊C₄×C₄₇	—	4	4	no	—
110	C₄⋊C₄×C₄₇	—	4	2	no	—
111	C₄⋊C₄×C₄₇	—	8	1	no	—
112	C₄⋊C₄×C₄₇	SD₁₆	1	4	yes	—
113	C₄⋊C₄×C₄₇	#41	1	2	yes	—
114	C₄⋊C₄×C₄₇	#41	1	2	yes	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	—	4	2	no	—
118	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
119	C₄²×C₄₇	#41	1	2	yes	—
120	C₄⋊Dic₄₇	—	2	1	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	4	2	no	—
124	C₄⋊Dic₄₇	—	8	1	no	—
125	C₄⋊Dic₄₇	C₂×Q₈	1	2	yes	—
126	Dic₄₇⋊C₄	—	2	4	no	—
127	C₄×Dic₄₇	—	2	4	no	—
128	C₄×Dic₄₇	—	8	2	no	—
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	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₄₇	—	8	8	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	4	1	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	—	4	1	no	—
152	C₂×C₄×C₄₇	—	4	1	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	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
159	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₄₇	#137	1	2	yes	—
161	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	4	1	no	—
170	C₂×Dic₄₇	—	4	1	no	—
171	C₂×Dic₄₇	—	4	1	no	—
172	C₂×Dic₄₇	—	4	1	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	—	4	2	no	—
176	Dic₉₄	—	2	2	no	—
177	Dic₉₄	—	2	2	no	—
178	Dic₉₄	—	4	1	no	—
179	Dic₉₄	—	4	1	no	—
180	C₄₇⋊C₈	—	4	1	no	—
181	C₄₇⋊C₈	—	4	2	no	—
182	C₄₇⋊C₈	—	4	1	no	—
183	#26022	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
185	C₂²×C₄₇	#546	1	1	yes	characteristic
186	C₂²×C₄₇	#548	1	1	yes	characteristic
187	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
189	C₂²×C₄₇	#576	1	1	yes	characteristic
190	C₂²×C₄₇	#578	1	1	yes	characteristic
191	C₄×C₄₇	—	2	2	no	—
192	C₄×C₄₇	—	2	4	no	—
193	C₄×C₄₇	—	4	2	no	—
194	C₄×C₄₇	—	4	2	no	—
195	C₄×C₄₇	—	4	2	no	—
196	C₄×C₄₇	—	8	2	no	—
197	C₄×C₄₇	#475	1	4	yes	—
198	C₄×C₄₇	#533	1	1	yes	characteristic
199	C₄×C₄₇	#544	1	1	yes	characteristic
200	C₄×C₄₇	#555	1	1	yes	characteristic
201	C₄×C₄₇	#556	1	1	yes	characteristic
202	Dic₄₇	—	4	2	no	—
203	Dic₄₇	—	4	2	no	—
204	Dic₄₇	—	8	2	no	—
205	#2551	D₄₇	1	1	yes	characteristic
206	#2355	—	47	1	no	—
207	#2066	—	47	2	no	—
208	#2024	—	47	2	no	—
209	#1988	—	47	2	no	—
210	#1948	—	47	1	no	—
211	#1939	—	47	1	no	—
212	#1919	—	47	2	no	—
213	#1834	—	47	1	no	—
214	#1803	—	47	1	no	—
215	C₄×#103	—	47	1	no	—
216	C₂×C₄₇	#2439	1	1	yes	characteristic
217	C₂×C₄₇	C₂×#475	1	1	yes	characteristic
218	C₂×C₄₇	#3083	1	1	yes	characteristic
219	C₂×C₄₇	#3295	1	1	yes	characteristic
220	C₂×C₄₇	#3328	1	1	yes	characteristic
221	C₂×C₄₇	#3359	1	1	yes	characteristic
222	C₂×C₄₇	#3375	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	—	2	1	no	—
224	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
225	C₂×C₄×Q₈	—	47	1	no	—
226	C₂×#106	—	47	2	no	—
227	C₂×C₄⋊C₈	—	47	1	no	—
228	C₂×C₄⋊C₈	—	47	2	no	—
229	C₂×#103	—	47	1	no	—
230	C₂×#103	—	47	1	no	—
231	C₂×#103	—	47	2	no	—
232	C₂×C₄×C₈	—	47	1	no	—
233	#395	—	2	2	no	—
234	#391	—	47	2	no	—
235	#389	—	2	1	no	—
236	#389	C₂×D₄₇	1	2	yes	—
237	#387	—	94	2	no	—
238	#384	—	47	1	no	—
239	#384	C₂×D₄₇	1	1	yes	characteristic
240	#382	—	94	1	no	—
241	C₄×C₄⋊C₄	—	47	2	no	—
242	C₄×C₄⋊C₄	—	94	1	no	—
243	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
244	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
245	#340	—	47	2	no	—
246	#340	—	47	2	no	—
247	#340	—	47	2	no	—
248	#340	—	47	1	no	—
249	#340	—	47	2	no	—
250	#340	—	47	1	no	—
251	#336	—	47	2	no	—
252	C₄₇	#26022	1	1	yes	characteristic, complemented, Sylow
253	C₂²×Q₈	—	2	2	no	—
254	C₂²×Q₈	—	47	1	no	—
255	C₂²×C₈	—	47	1	no	—
256	C₂²×C₈	—	47	2	no	—
257	C₂²×C₈	—	47	1	no	—
258	C₄⋊Q₈	—	2	4	no	—
259	C₄⋊Q₈	—	4	2	no	—
260	C₄⋊Q₈	—	4	4	no	—
261	C₄×Q₈	—	47	4	no	—
262	C₄×Q₈	—	94	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	47	1	no	—
268	C₂×C₄⋊C₄	—	47	2	no	—
269	C₂×C₄⋊C₄	—	94	1	no	—
270	C₂×C₄⋊C₄	—	94	1	no	—
271	C₂×C₄⋊C₄	—	94	1	no	—
272	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
275	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	94	1	no	—
279	C₂×C₄²	—	94	2	no	—
280	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
281	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
282	#106	—	94	4	no	—
283	C₄⋊C₈	—	94	2	no	—
284	C₄⋊C₈	—	188	2	no	—
285	#103	—	94	2	no	—
286	#103	—	94	2	no	—
287	#103	—	188	2	no	—
288	C₄×C₈	—	94	2	no	—
289	#95	—	2	1	no	—
290	#95	—	2	2	no	—
291	#95	—	94	2	no	—
292	#95	—	94	2	no	—
293	#95	—	94	2	no	—
294	#95	C₂²⋊D₄₇	1	2	yes	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	4	4	no	—
297	C₂×Q₈	—	8	2	no	—
298	C₂×Q₈	—	47	2	no	—
299	C₂×Q₈	—	94	1	no	—
300	C₂×Q₈	—	94	1	no	—
301	C₂×Q₈	—	94	1	no	—
302	C₂×Q₈	—	94	1	no	—
303	C₂×Q₈	—	94	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	94	1	no	—
308	C₂²×C₄	—	94	1	no	—
309	C₂²×C₄	—	94	2	no	—
310	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
311	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
313	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
314	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
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	—	94	2	no	—
320	C₂×C₈	—	94	2	no	—
321	C₂×C₈	—	94	2	no	—
322	C₂×C₈	—	94	1	no	—
323	C₂×C₈	—	94	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	8	1	no	—
333	C₄⋊C₄	—	47	2	no	—
334	C₄⋊C₄	—	94	4	no	—
335	C₄⋊C₄	—	94	1	no	—
336	C₄⋊C₄	—	94	2	no	—
337	C₄⋊C₄	—	94	2	no	—
338	C₄⋊C₄	—	376	1	no	—
339	C₄⋊C₄	—	188	2	no	—
340	C₄⋊C₄	#10625335	1	4	yes	—
341	C₄⋊C₄	#10625352	1	2	yes	—
342	C₄⋊C₄	#10625354	1	2	yes	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	4	2	no	—
346	C₄²	—	94	4	no	—
347	C₄²	—	376	2	no	—
348	C₄²	Q₈×D₄₇	1	2	yes	—
349	C₄²	#10625354	1	2	yes	—
350	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
351	Q₈	—	8	8	no	—
352	Q₈	—	94	2	no	—
353	Q₈	—	94	2	no	—
354	Q₈	—	188	1	no	—
355	Q₈	—	188	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	188	2	no	—
375	C₂×C₄	—	188	2	no	—
376	C₂×C₄	—	188	2	no	—
377	C₂×C₄	—	188	1	no	—
378	C₂×C₄	—	188	1	no	—
379	C₂×C₄	—	188	1	no	—
380	C₂×C₄	—	188	1	no	—
381	C₂×C₄	#13094000	1	2	yes	—
382	C₂×C₄	#13094000	1	2	yes	—
383	C₂×C₄	C₂×#10625335	1	4	yes	—
384	C₂×C₄	C₂×#10625335	1	2	yes	—
385	C₂×C₄	#13094055	1	2	yes	—
386	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
387	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
388	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
389	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
390	C₂×C₄	#13094069	1	1	yes	characteristic
391	C₂×C₄	#13094072	1	1	yes	characteristic
392	C₈	—	188	1	no	—
393	C₈	—	188	2	no	—
394	C₈	—	188	1	no	—
395	C₂²	C₂×#13094000	1	1	yes	characteristic
396	C₂²	#15689767	1	1	yes	characteristic
397	C₂²	#15689784	1	1	yes	characteristic
398	C₂²	C₂²×#10625335	1	1	yes	characteristic
399	C₂²	C₂×#13094055	1	1	yes	characteristic
400	C₂²	#15689926	1	1	yes	characteristic
401	C₂²	#15689938	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	4	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	8	2	no	—
408	C₄	—	376	2	no	—
409	C₄	—	188	2	no	—
410	C₄	—	188	2	no	—
411	C₄	#15689405	1	4	yes	—
412	C₄	#15689678	1	1	yes	characteristic
413	C₄	#15689750	1	1	yes	characteristic
414	C₄	#15689839	1	1	yes	characteristic
415	C₄	#15689847	1	1	yes	characteristic
416	C₂	#20247075	1	1	yes	characteristic
417	C₂	C₂×#15689405	1	1	yes	characteristic
418	C₂	#20253235	1	1	yes	characteristic
419	C₂	#20255212	1	1	yes	characteristic
420	C₂	#20255671	1	1	yes	characteristic
421	C₂	#20256030	1	1	yes	characteristic
422	C₂	#20256202	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2551	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
hypercenter	#2551	D₄₇
hypocenter	C₄₇	#26022
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2551

Complements

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

N	H ≅ G/N	type
46. C₄×Dic₉₄	Q₈	semidirect
252. C₄₇	#26022	semidirect

Maximal subgroups

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

subgroup	index
#20246343	2
#20244766	2
#20244526	2
#20244341	2
#20244151	2
#20244107	2
#20243963	2
#20243515	2
#20243390	2
C₄×#13093947	2
C₄₇×#2551	2
#26022	47