Subgroups — #26106472

Order 12032.

740 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252018	C₂	1	1	yes	maximal, characteristic
2	C₄×M₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20245727	C₂	1	1	yes	maximal, characteristic
4	#20241282	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241281	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241280	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1300	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₄₇	—	2	1	no	—
9	C₂×#13093981	—	2	1	no	—
10	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
11	#15689180	C₂²	1	1	yes	characteristic
12	#15689178	—	2	1	no	—
13	#15689175	C₄	1	2	yes	complemented
14	#15689173	—	2	1	no	—
15	#15689145	C₄	1	2	yes	complemented
16	#15689085	—	2	1	no	—
17	C₄×#10625329	C₂²	1	1	yes	characteristic
18	#15689075	—	2	1	no	—
19	#15689075	C₄	1	2	yes	complemented
20	M₁₆×Dic₄₇	—	2	1	no	—
21	C₄×#10625324	—	2	1	no	—
22	#97×D₄₇	C₄	1	2	yes	complemented
23	C₄×C₈×D₄₇	—	2	1	no	—
24	#15688974	—	2	1	no	—
25	#15688974	C₄	1	2	yes	—
26	#15688970	—	2	1	no	—
27	#15688970	C₄	1	2	yes	—
28	#15688969	C₂²	1	1	yes	characteristic
29	C₄²×Dic₄₇	—	2	1	no	—
30	C₄₇×#432	C₂²	1	1	yes	characteristic
31	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#376	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
36	C₂×#10625329	—	2	1	no	—
37	C₂×#10625324	—	2	2	no	—
38	C₂×#10625324	—	2	2	no	—
39	M₁₆×D₄₇	—	2	8	no	—
40	C₂×C₈×D₄₇	—	2	2	no	—
41	#13093981	—	2	8	no	—
42	C₂×Dic₄₇⋊C₄	—	2	2	no	—
43	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
44	C₂×C₄×Dic₄₇	—	2	1	no	—
45	C₂×C₄×Dic₄₇	—	2	2	no	—
46	C₂×C₄×Dic₄₇	—	2	2	no	—
47	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
50	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₄₇	D₄	1	1	yes	characteristic
55	C₄²×D₄₇	D₄	1	1	yes	characteristic
56	C₄²×D₄₇	Q₈	1	1	yes	characteristic
57	C₄²×D₄₇	Q₈	1	1	yes	characteristic
58	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
59	Dic₄₇⋊C₈	—	2	2	no	—
60	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
61	(C₂×D₄₇)⋊C₈	—	2	2	no	—
62	#13093935	—	2	1	no	—
63	#13093935	C₂×C₄	1	2	yes	—
64	#13093934	—	2	2	no	—
65	C₄×C₄₇⋊C₈	—	2	1	no	—
66	C₈×Dic₄₇	—	2	2	no	—
67	C₈×Dic₄₇	—	2	2	no	—
68	C₄₇⋊#95	—	2	1	no	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₂×M₁₆×C₄₇	—	2	1	no	—
71	C₂×C₄²×C₄₇	—	2	1	no	—
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
74	C₂²⋊C₈×C₄₇	—	2	1	no	—
75	#97×C₄₇	—	2	1	no	—
76	#97×C₄₇	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₄₇	—	2	1	no	—
78	#95×C₄₇	—	2	1	no	—
79	#95×C₄₇	C₂×C₄	1	2	yes	—
80	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×Dic₄₇	—	2	2	no	—
86	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₄₇	—	2	4	no	—
90	C₂×C₄×D₄₇	—	2	4	no	—
91	C₂×C₄×D₄₇	—	4	2	no	—
92	C₂×C₄×D₄₇	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₄₇	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
104	M₁₆×C₄₇	—	2	4	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₄²×C₄₇	—	2	4	no	—
108	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
112	(C₂×D₄₇)⋊C₄	—	2	8	no	—
113	Dic₄₇⋊C₄	—	2	8	no	—
114	C₄×Dic₄₇	—	2	4	no	—
115	C₄×Dic₄₇	—	4	4	no	—
116	C₄×Dic₄₇	—	4	4	no	—
117	C₄×Dic₄₇	C₄²	1	1	yes	characteristic
118	C₄×Dic₄₇	C₄²	1	1	yes	characteristic
119	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
129	#10625329	—	2	4	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	#10625324	—	2	8	no	—
133	#10625324	—	4	4	no	—
134	C₈×D₄₇	—	2	8	no	—
135	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×D₄₇	—	2	2	no	—
137	C₂²×D₄₇	—	2	2	no	—
138	C₂²×D₄₇	—	4	1	no	—
139	C₂²×D₄₇	#95	1	1	yes	characteristic
140	C₂²×D₄₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	4	1	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	2	2	no	—
155	C₂×Dic₄₇	—	2	4	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	#95	1	1	yes	characteristic
159	C₂×Dic₄₇	#95	1	1	yes	characteristic
160	C₂×Dic₄₇	#95	1	1	yes	characteristic
161	C₂×Dic₄₇	#95	1	1	yes	characteristic
162	C₂×Dic₄₇	#95	1	1	yes	characteristic
163	C₂×Dic₄₇	#95	1	1	yes	characteristic
164	C₂×Dic₄₇	#104	1	4	yes	—
165	C₄×D₄₇	—	2	2	no	—
166	C₄×D₄₇	—	2	2	no	—
167	C₄×D₄₇	—	2	2	no	—
168	C₄×D₄₇	—	2	2	no	—
169	C₄×D₄₇	—	2	2	no	—
170	C₄×D₄₇	—	2	2	no	—
171	C₄×D₄₇	—	2	2	no	—
172	C₄×D₄₇	—	2	2	no	—
173	C₄×D₄₇	—	2	2	no	—
174	C₄×D₄₇	—	4	1	no	—
175	C₄×D₄₇	—	4	1	no	—
176	C₄×D₄₇	#104	1	4	yes	—
177	C₈×C₄₇	—	2	4	no	—
178	C₈×C₄₇	—	4	2	no	—
179	C₄₇⋊C₈	—	2	4	no	—
180	C₄₇⋊C₈	—	4	2	no	—
181	#8068	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#104	1	2	yes	—
186	C₂×D₄₇	—	2	1	no	—
187	C₂×D₄₇	—	2	1	no	—
188	C₂×D₄₇	—	2	1	no	—
189	C₂×D₄₇	—	2	1	no	—
190	C₂×D₄₇	—	2	1	no	—
191	C₂×D₄₇	—	4	4	no	—
192	C₂×D₄₇	#339	1	2	yes	—
193	C₄×C₄₇	—	2	1	no	—
194	C₄×C₄₇	—	2	1	no	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	4	4	no	—
199	C₄×C₄₇	C₂×#104	1	2	yes	—
200	Dic₄₇	—	2	1	no	—
201	Dic₄₇	—	2	1	no	—
202	Dic₄₇	—	4	4	no	—
203	Dic₄₇	#339	1	2	yes	—
204	Dic₄₇	#339	1	2	yes	—
205	Dic₄₇	#339	1	2	yes	—
206	Dic₄₇	#344	1	2	yes	—
207	#2920	—	47	1	no	—
208	C₂×C₄×M₁₆	—	47	1	no	—
209	C₄×#117	—	47	1	no	—
210	#1300	—	47	1	no	—
211	#1300	—	47	1	no	—
212	#1300	—	47	1	no	—
213	#1300	D₄₇	1	1	yes	characteristic, complemented
214	C₂×C₄₇	—	2	2	no	—
215	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
216	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
217	C₂×C₄₇	C₂×#344	1	1	yes	characteristic
218	D₄₇	—	2	2	no	—
219	D₄₇	—	4	1	no	—
220	C₂²×M₁₆	—	94	1	no	—
221	C₂×#117	—	94	1	no	—
222	C₂²×C₄²	—	47	1	no	—
223	#432	—	47	1	no	—
224	#432	—	94	1	no	—
225	#432	C₂×D₄₇	1	1	yes	characteristic
226	#431	—	47	2	no	—
227	#431	—	94	1	no	—
228	#423	—	47	2	no	—
229	#407	—	94	1	no	—
230	C₄×M₁₆	—	47	1	no	—
231	C₄×M₁₆	—	47	2	no	—
232	C₄×M₁₆	—	94	1	no	—
233	C₄×M₁₆	—	94	1	no	—
234	C₄×M₁₆	—	94	1	no	—
235	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
236	C₂×#97	—	47	2	no	—
237	C₂×C₄×C₈	—	94	1	no	—
238	C₄×C₄⋊C₄	—	47	2	no	—
239	C₄×C₄⋊C₄	—	94	1	no	—
240	C₄×C₂²⋊C₄	—	47	2	no	—
241	C₄×C₂²⋊C₄	—	94	1	no	—
242	#376	—	47	1	no	—
243	#376	C₂×D₄₇	1	1	yes	characteristic
244	C₄³	—	94	1	no	—
245	C₄₇	#8068	1	1	yes	characteristic, complemented, Sylow
246	C₂³×C₄	—	47	1	no	—
247	C₂³×C₄	—	47	1	no	—
248	C₂³×C₄	—	47	1	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	94	2	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂×M₁₆	—	94	8	no	—
253	C₂×M₁₆	—	94	1	no	—
254	C₂²×C₈	—	94	2	no	—
255	#117	—	94	8	no	—
256	C₂×C₄⋊C₄	—	94	2	no	—
257	C₂×C₂²⋊C₄	—	94	2	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	—	47	1	no	—
260	C₂×C₄²	—	47	1	no	—
261	C₂×C₄²	—	47	1	no	—
262	C₂×C₄²	—	47	1	no	—
263	C₂×C₄²	—	47	1	no	—
264	C₂×C₄²	—	47	1	no	—
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	—	94	1	no	—
271	C₂×C₄²	—	94	2	no	—
272	C₂×C₄²	—	94	2	no	—
273	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
274	C₄⋊C₈	—	47	2	no	—
275	C₄⋊C₈	—	94	2	no	—
276	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
277	C₂²⋊C₈	—	2	1	no	—
278	C₂²⋊C₈	—	94	2	no	—
279	C₂²⋊C₈	—	94	1	no	—
280	#97	—	2	1	no	—
281	#97	—	47	2	no	—
282	#97	—	94	2	no	—
283	#97	—	94	1	no	—
284	#97	C₄×D₄₇	1	2	yes	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	94	2	no	—
287	C₄×C₈	—	94	2	no	—
288	C₄×C₈	—	94	1	no	—
289	#95	—	2	1	no	—
290	#95	—	47	2	no	—
291	#95	—	94	1	no	—
292	#95	C₄×D₄₇	1	2	yes	—
293	C₂⁴	—	47	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	47	1	no	—
296	C₂²×C₄	—	47	1	no	—
297	C₂²×C₄	—	47	1	no	—
298	C₂²×C₄	—	47	1	no	—
299	C₂²×C₄	—	47	1	no	—
300	C₂²×C₄	—	47	1	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	—	47	1	no	—
306	C₂²×C₄	—	47	1	no	—
307	C₂²×C₄	—	47	1	no	—
308	C₂²×C₄	—	47	1	no	—
309	C₂²×C₄	—	47	1	no	—
310	C₂²×C₄	—	94	4	no	—
311	C₂²×C₄	—	94	4	no	—
312	C₂²×C₄	—	94	2	no	—
313	C₂²×C₄	—	188	2	no	—
314	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
316	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
317	M₁₆	—	2	4	no	—
318	M₁₆	—	94	8	no	—
319	M₁₆	—	94	4	no	—
320	M₁₆	—	188	4	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	94	8	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	94	2	no	—
326	C₄⋊C₄	—	94	8	no	—
327	C₂²⋊C₄	—	94	8	no	—
328	C₄²	—	2	4	no	—
329	C₄²	—	47	1	no	—
330	C₄²	—	47	1	no	—
331	C₄²	—	47	1	no	—
332	C₄²	—	47	1	no	—
333	C₄²	—	47	1	no	—
334	C₄²	—	47	1	no	—
335	C₄²	—	47	1	no	—
336	C₄²	—	47	1	no	—
337	C₄²	—	47	1	no	—
338	C₄²	—	47	1	no	—
339	C₄²	—	47	1	no	—
340	C₄²	—	47	1	no	—
341	C₄²	—	94	4	no	—
342	C₄²	—	188	4	no	—
343	C₄²	—	188	4	no	—
344	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
345	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
346	C₄²	D₄×D₄₇	1	1	yes	characteristic
347	C₄²	Q₈×D₄₇	1	1	yes	characteristic
348	C₂³	—	47	1	no	—
349	C₂³	—	47	1	no	—
350	C₂³	—	94	2	no	—
351	C₂³	—	94	2	no	—
352	C₂³	—	188	1	no	—
353	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	47	1	no	—
361	C₂×C₄	—	47	1	no	—
362	C₂×C₄	—	47	1	no	—
363	C₂×C₄	—	47	1	no	—
364	C₂×C₄	—	47	4	no	—
365	C₂×C₄	—	47	4	no	—
366	C₂×C₄	—	47	1	no	—
367	C₂×C₄	—	47	1	no	—
368	C₂×C₄	—	94	2	no	—
369	C₂×C₄	—	94	2	no	—
370	C₂×C₄	—	94	2	no	—
371	C₂×C₄	—	94	2	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	—	94	2	no	—
376	C₂×C₄	—	94	2	no	—
377	C₂×C₄	—	94	2	no	—
378	C₂×C₄	—	94	2	no	—
379	C₂×C₄	—	94	4	no	—
380	C₂×C₄	—	188	1	no	—
381	C₂×C₄	—	188	1	no	—
382	C₂×C₄	—	188	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
385	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
386	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
387	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
388	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
390	C₈	—	2	4	no	—
391	C₈	—	4	2	no	—
392	C₈	—	94	4	no	—
393	C₈	—	188	2	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	47	2	no	—
397	C₂²	—	94	1	no	—
398	C₂²	—	94	1	no	—
399	C₂²	—	94	1	no	—
400	C₂²	—	94	1	no	—
401	C₂²	—	94	1	no	—
402	C₂²	—	188	4	no	—
403	C₂²	#95×D₄₇	1	1	yes	characteristic
404	C₂²	#104×D₄₇	1	2	yes	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	4	4	no	—
411	C₄	—	47	2	no	—
412	C₄	—	47	2	no	—
413	C₄	—	47	2	no	—
414	C₄	—	47	2	no	—
415	C₄	—	94	1	no	—
416	C₄	—	94	1	no	—
417	C₄	—	188	4	no	—
418	C₄	#104×D₄₇	1	2	yes	—
419	C₂	—	2	2	no	—
420	C₂	—	94	2	no	—
421	C₂	—	188	1	no	—
422	C₂	#339×D₄₇	1	1	yes	characteristic
423	C₂	#339×D₄₇	1	1	yes	characteristic
424	C₂	#344×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1300	C₂
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1300	D₄₇
hypocenter	C₄₇	#8068
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1300

Complements

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

N	H ≅ G/N	type
4. #20241282	C₂	semidirect
5. #20241281	C₂	semidirect
6. #20241280	C₂	semidirect
7. C₄₇×#1300	C₂	semidirect
13. #15689175	C₄	semidirect
15. #15689145	C₄	semidirect
19. #15689075	C₄	semidirect
22. #97×D₄₇	C₄	semidirect
213. #1300	D₄₇	semidirect
245. C₄₇	#8068	semidirect

Maximal subgroups

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

subgroup	index
#20252018	2
C₄×M₁₆×D₄₇	2
#20245727	2
#20241282	2
#20241281	2
#20241280	2
C₄₇×#1300	2
#8068	47