Subgroups — #26246197

Order 12032.

810 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	#20245872	C₂	1	1	yes	maximal, characteristic
2	#20245791	C₂	1	1	yes	maximal, characteristic
3	#20244961	C₂	1	2	yes	maximal, complemented
4	#20244959	C₂	1	2	yes	maximal, complemented
5	#20244954	C₂	1	2	yes	maximal, complemented
6	#20244949	C₂	1	2	yes	maximal, complemented
7	#20243105	C₂	1	1	yes	maximal, characteristic
8	#20243104	C₂	1	1	yes	maximal, characteristic
9	#20243104	C₂	1	1	yes	maximal, characteristic
10	C₂×#15688877	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1735	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×#13093983	C₂²	1	1	yes	characteristic
14	C₂×#13093983	C₂²	1	1	yes	characteristic
15	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
16	#15689022	C₂²	1	2	yes	—
17	#15689022	C₂²	1	2	yes	—
18	#15688998	—	2	2	no	—
19	#15688992	C₂²	1	1	yes	characteristic
20	#15688992	C₂²	1	1	yes	characteristic
21	#15688988	C₂²	1	1	yes	characteristic
22	#15688988	C₂²	1	1	yes	characteristic
23	#15688981	—	2	2	no	—
24	C₄×Dic₄₇⋊C₄	—	2	2	no	—
25	C₄×C₄⋊Dic₄₇	—	2	2	no	—
26	#15688886	C₂²	1	2	yes	—
27	#15688886	C₂²	1	2	yes	—
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	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#340	C₂²	1	2	yes	—
38	C₄₇×#340	C₂²	1	2	yes	—
39	C₂³×Dic₄₇	D₄	1	2	yes	—
40	C₂²×C₄₇⋊C₈	—	2	2	no	—
41	C₂²×C₄₇⋊C₈	—	2	2	no	—
42	C₂²×C₄₇⋊C₈	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	#13093983	—	2	2	no	—
45	#13093983	—	2	2	no	—
46	#13093983	—	2	2	no	—
47	#13093983	—	2	2	no	—
48	C₂×C₄⋊Dic₄₇	—	2	2	no	—
49	C₂×C₄⋊Dic₄₇	—	2	2	no	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
53	C₂×Dic₄₇⋊C₄	—	2	2	no	—
54	C₂×Dic₄₇⋊C₄	—	2	2	no	—
55	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
56	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
57	C₂×C₄×Dic₄₇	—	2	2	no	—
58	C₂×C₄×Dic₄₇	—	2	2	no	—
59	C₂×C₄×Dic₄₇	—	2	1	no	—
60	C₂×C₄×Dic₄₇	—	2	1	no	—
61	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₄₇	—	2	2	no	—
70	C₂²×C₈×C₄₇	—	2	2	no	—
71	C₂²×C₈×C₄₇	—	2	2	no	—
72	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
73	#117×C₄₇	—	2	2	no	—
74	#117×C₄₇	—	2	2	no	—
75	#117×C₄₇	—	2	2	no	—
76	#117×C₄₇	Q₈	1	4	yes	—
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₄²×C₄₇	—	2	1	no	—
83	C₂×C₄²×C₄₇	—	2	1	no	—
84	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₄₇	#41	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	#41	1	2	yes	—
94	C₂²×C₄×C₄₇	#41	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₇	—	2	4	no	—
97	C₂²×Dic₄₇	—	2	4	no	—
98	C₂²×Dic₄₇	—	2	1	no	—
99	C₂²×Dic₄₇	—	2	1	no	—
100	C₂²×Dic₄₇	—	2	2	no	—
101	C₂²×Dic₄₇	—	4	2	no	—
102	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
103	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	4	4	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	1	no	—
110	C₄⋊C₄×C₄₇	—	2	1	no	—
111	C₄⋊C₄×C₄₇	—	2	1	no	—
112	C₄⋊C₄×C₄₇	—	2	1	no	—
113	C₄⋊C₄×C₄₇	C₂×Q₈	1	4	yes	—
114	C₂²⋊C₄×C₄₇	—	2	4	no	—
115	C₂²⋊C₄×C₄₇	—	4	2	no	—
116	C₄²×C₄₇	—	2	4	no	—
117	C₄²×C₄₇	—	4	2	no	—
118	C₂²⋊Dic₄₇	—	4	2	no	—
119	C₂²⋊Dic₄₇	—	4	2	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	1	no	—
123	C₄⋊Dic₄₇	—	2	1	no	—
124	C₄⋊Dic₄₇	—	2	1	no	—
125	C₄⋊Dic₄₇	—	2	1	no	—
126	C₄⋊Dic₄₇	—	4	4	no	—
127	C₄⋊Dic₄₇	—	4	4	no	—
128	Dic₄₇⋊C₄	—	4	4	no	—
129	Dic₄₇⋊C₄	—	4	4	no	—
130	C₄×Dic₄₇	—	2	4	no	—
131	C₄×Dic₄₇	—	2	1	no	—
132	C₄×Dic₄₇	—	2	1	no	—
133	C₄×Dic₄₇	—	2	1	no	—
134	C₄×Dic₄₇	—	2	1	no	—
135	C₄×Dic₄₇	—	4	2	no	—
136	C₄×Dic₄₇	—	4	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	4	4	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
144	C₂³×C₄₇	#123	1	2	yes	—
145	C₂³×C₄₇	#124	1	2	yes	—
146	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	—	4	1	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	#123	1	2	yes	—
156	C₂×C₄×C₄₇	#124	1	2	yes	—
157	C₂×C₄×C₄₇	#125	1	4	yes	—
158	C₂×C₄×C₄₇	#125	1	4	yes	—
159	C₂×C₄×C₄₇	#126	1	4	yes	—
160	C₂×C₄×C₄₇	#126	1	4	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	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	4	8	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	4	1	no	—
175	C₂×Dic₄₇	—	4	1	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	C₂×Dic₄₇	—	4	2	no	—
180	C₂×Dic₄₇	#135	1	4	yes	—
181	C₈×C₄₇	—	4	2	no	—
182	C₄₇⋊C₈	—	4	2	no	—
183	#23744	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	#400	1	4	yes	—
189	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×#135	1	2	yes	—
193	C₂²×C₄₇	#575	1	2	yes	—
194	C₄×C₄₇	—	4	4	no	—
195	C₄×C₄₇	—	8	1	no	—
196	C₄×C₄₇	—	8	1	no	—
197	C₄×C₄₇	#400	1	4	yes	—
198	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
199	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
200	C₄×C₄₇	C₂×#126	1	1	yes	characteristic
201	C₄×C₄₇	C₂×#126	1	1	yes	characteristic
202	Dic₄₇	—	2	4	no	—
203	Dic₄₇	—	4	2	no	—
204	Dic₄₇	—	8	2	no	—
205	Dic₄₇	—	8	1	no	—
206	Dic₄₇	—	8	1	no	—
207	#2296	—	47	1	no	—
208	#2285	—	47	1	no	—
209	#2101	—	47	2	no	—
210	#2101	—	47	2	no	—
211	#2100	—	47	2	no	—
212	#2099	—	47	2	no	—
213	#1735	—	47	1	no	—
214	#1735	—	47	1	no	—
215	#1735	—	47	1	no	—
216	#1735	D₄₇	1	1	yes	characteristic
217	C₂×#336	—	47	1	no	—
218	C₂×C₄₇	—	2	4	no	—
219	C₂×C₄₇	C₂×#400	1	1	yes	characteristic
220	C₂×C₄₇	#3076	1	2	yes	—
221	C₂×C₄₇	#3091	1	2	yes	—
222	C₂×C₄₇	#3131	1	1	yes	characteristic
223	C₂×C₄₇	#3135	1	1	yes	characteristic
224	C₂³×C₈	—	47	1	no	—
225	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
226	C₂×#117	—	47	1	no	—
227	C₂×#117	—	47	1	no	—
228	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
229	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
230	C₂²×C₄²	—	47	1	no	—
231	#389	—	47	2	no	—
232	#389	—	47	2	no	—
233	#385	—	94	2	no	—
234	#384	—	47	1	no	—
235	#384	—	47	1	no	—
236	#382	—	47	1	no	—
237	#382	—	47	1	no	—
238	#380	—	94	2	no	—
239	C₄×C₄⋊C₄	—	94	2	no	—
240	C₄×C₄⋊C₄	—	94	2	no	—
241	#340	—	47	2	no	—
242	#340	—	47	2	no	—
243	#340	—	47	2	no	—
244	#340	—	47	2	no	—
245	#340	—	47	2	no	—
246	#340	—	47	2	no	—
247	#340	C₂×D₄₇	1	2	yes	—
248	#340	C₂×D₄₇	1	2	yes	—
249	#336	—	47	2	no	—
250	#336	—	47	2	no	—
251	C₄₇	#23744	1	1	yes	characteristic, complemented, Sylow
252	C₂³×C₄	—	47	2	no	—
253	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	47	2	no	—
258	C₂²×C₈	—	94	2	no	—
259	C₂²×C₈	—	94	2	no	—
260	C₂²×C₈	—	94	2	no	—
261	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
262	#117	—	2	2	no	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	#117	—	94	2	no	—
266	#117	—	94	2	no	—
267	#117	—	94	2	no	—
268	#117	—	94	2	no	—
269	#117	Dic₉₄	1	4	yes	—
270	C₂×C₄⋊C₄	—	47	1	no	—
271	C₂×C₄⋊C₄	—	47	1	no	—
272	C₂×C₄⋊C₄	—	47	2	no	—
273	C₂×C₄⋊C₄	—	94	2	no	—
274	C₂×C₄⋊C₄	—	94	2	no	—
275	C₂×C₄⋊C₄	—	94	2	no	—
276	C₂×C₄⋊C₄	—	94	2	no	—
277	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	94	1	no	—
283	C₂×C₂²⋊C₄	—	94	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	47	2	no	—
287	C₂×C₄²	—	47	1	no	—
288	C₂×C₄²	—	47	1	no	—
289	C₂×C₄²	—	94	2	no	—
290	C₂×C₄²	—	94	2	no	—
291	C₂×C₄²	—	94	1	no	—
292	C₂×C₄²	—	94	1	no	—
293	#95	—	94	2	no	—
294	#95	—	94	2	no	—
295	#95	—	94	2	no	—
296	#95	—	94	2	no	—
297	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	47	2	no	—
302	C₂²×C₄	—	47	2	no	—
303	C₂²×C₄	—	94	4	no	—
304	C₂²×C₄	—	94	4	no	—
305	C₂²×C₄	—	94	2	no	—
306	C₂²×C₄	—	94	1	no	—
307	C₂²×C₄	—	94	1	no	—
308	C₂²×C₄	—	188	2	no	—
309	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
310	C₂²×C₄	#10625350	1	2	yes	—
311	C₂²×C₄	#10625350	1	2	yes	—
312	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
313	C₂²×C₄	#10625352	1	2	yes	—
314	C₂²×C₄	#10625352	1	2	yes	—
315	C₂²×C₄	#10625354	1	2	yes	—
316	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	4	4	no	—
321	C₂×C₈	—	94	2	no	—
322	C₂×C₈	—	94	2	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	188	4	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	94	1	no	—
331	C₄⋊C₄	—	94	1	no	—
332	C₄⋊C₄	—	94	2	no	—
333	C₄⋊C₄	—	94	1	no	—
334	C₄⋊C₄	—	94	1	no	—
335	C₄⋊C₄	—	94	2	no	—
336	C₄⋊C₄	—	188	4	no	—
337	C₄⋊C₄	—	188	4	no	—
338	C₄⋊C₄	—	188	4	no	—
339	C₄⋊C₄	—	188	4	no	—
340	C₄⋊C₄	C₂×Dic₉₄	1	4	yes	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	188	2	no	—
344	C₂²⋊C₄	—	188	2	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	4	2	no	—
347	C₄²	—	94	4	no	—
348	C₄²	—	94	1	no	—
349	C₄²	—	94	1	no	—
350	C₄²	—	94	1	no	—
351	C₄²	—	94	1	no	—
352	C₄²	—	188	2	no	—
353	C₄²	—	188	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	#13094001	1	2	yes	—
357	C₂³	#13094009	1	2	yes	—
358	C₂³	#13094010	1	2	yes	—
359	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	47	4	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	—	188	8	no	—
374	C₂×C₄	—	188	2	no	—
375	C₂×C₄	—	188	1	no	—
376	C₂×C₄	—	188	1	no	—
377	C₂×C₄	—	188	2	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	#13094001	1	2	yes	—
382	C₂×C₄	#13094009	1	2	yes	—
383	C₂×C₄	#13094010	1	2	yes	—
384	C₂×C₄	#13094015	1	4	yes	—
385	C₂×C₄	#13094016	1	4	yes	—
386	C₂×C₄	#13094017	1	4	yes	—
387	C₂×C₄	#13094019	1	4	yes	—
388	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
389	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
390	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
391	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
392	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
393	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
394	C₈	—	4	2	no	—
395	C₈	—	188	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	2	4	no	—
400	C₂²	#15689065	1	4	yes	—
401	C₂²	C₂×#13094001	1	1	yes	characteristic
402	C₂²	C₂×#13094009	1	1	yes	characteristic
403	C₂²	C₂×#13094010	1	1	yes	characteristic
404	C₂²	#135×D₄₇	1	2	yes	—
405	C₂²	#15689920	1	2	yes	—
406	C₄	—	4	4	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	1	no	—
409	C₄	—	94	4	no	—
410	C₄	—	376	1	no	—
411	C₄	—	376	1	no	—
412	C₄	—	376	2	no	—
413	C₄	—	188	2	no	—
414	C₄	#15689065	1	4	yes	—
415	C₄	C₂×#13094015	1	1	yes	characteristic
416	C₄	C₂×#13094016	1	1	yes	characteristic
417	C₄	C₂×#13094017	1	1	yes	characteristic
418	C₄	C₂×#13094019	1	1	yes	characteristic
419	C₂	—	2	4	no	—
420	C₂	C₂×#15689065	1	1	yes	characteristic
421	C₂	#20253172	1	2	yes	—
422	C₂	#20253305	1	2	yes	—
423	C₂	#20253708	1	1	yes	characteristic
424	C₂	#20253731	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1735	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
hypercenter	#1735	D₄₇
hypocenter	C₄₇	#23744
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ #1735

Complements

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

N	H ≅ G/N	type
3. #20244961	C₂	semidirect
4. #20244959	C₂	semidirect
5. #20244954	C₂	semidirect
6. #20244949	C₂	semidirect
251. C₄₇	#23744	semidirect

Maximal subgroups

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

subgroup	index
#20245872	2
#20245791	2
#20244961	2
#20244959	2
#20244954	2
#20244949	2
#20243105	2
#20243104	2
C₂×#15688877	2
C₄₇×#1735	2
#23744	47