Subgroups — #26185628

Order 12032.

592 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252513	C₂	1	1	yes	maximal, characteristic
2	#20252355	C₂	1	1	yes	maximal, characteristic
3	#20242179	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242176	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242166	C₂	1	2	yes	maximal, complemented
6	#20242160	C₂	1	2	yes	maximal, complemented
7	#20242153	C₂	1	2	yes	maximal, complemented
8	#20242143	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242141	C₂	1	2	yes	maximal, complemented
10	#20242134	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2991	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	1	no	—
13	#15689254	C₄	1	1	yes	characteristic
14	#15689254	C₄	1	1	yes	characteristic
15	#15689201	C₄	1	1	yes	characteristic
16	#15689201	C₄	1	1	yes	characteristic
17	#15689195	—	2	2	no	—
18	#15689195	C₄	1	2	yes	—
19	#15689195	C₄	1	2	yes	—
20	D₄×C₄₇⋊C₈	—	2	1	no	—
21	#15689180	C₂²	1	2	yes	—
22	#15689176	C₂²	1	1	yes	characteristic
23	#15689176	C₂²	1	1	yes	characteristic
24	#15689176	C₂²	1	2	yes	—
25	#15689147	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
27	C₄×#10625329	C₂²	1	2	yes	—
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	#15688875	C₂²	1	2	yes	—
30	#15688875	C₂²	1	2	yes	—
31	#15688875	C₂²	1	1	yes	characteristic
32	#15688875	C₂²	1	1	yes	characteristic
33	#15688873	C₂²	1	2	yes	—
34	#15688873	C₂²	1	2	yes	—
35	#15688873	C₂²	1	1	yes	characteristic
36	#15688873	C₂²	1	1	yes	characteristic
37	#15688873	C₂²	1	2	yes	—
38	#15688873	C₂²	1	2	yes	—
39	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₄₇	—	2	1	no	—
41	C₄₇×#436	—	2	1	no	—
42	C₄₇×#436	—	2	2	no	—
43	C₄₇×#431	C₂²	1	1	yes	characteristic
44	C₄₇×#431	C₂²	1	2	yes	—
45	C₄₇×#423	C₂²	1	1	yes	characteristic
46	C₄₇×#423	C₂²	1	2	yes	—
47	C₂×#10625329	—	2	1	no	—
48	C₂×#10625329	C₂×C₄	1	2	yes	—
49	C₂×#10625329	C₂×C₄	1	2	yes	—
50	C₂²×C₄₇⋊C₈	—	2	2	no	—
51	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
57	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
58	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
59	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
60	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
62	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
65	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
66	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
67	#13093935	—	2	2	no	—
68	#13093935	C₂×C₄	1	2	yes	—
69	#13093935	C₂×C₄	1	2	yes	—
70	C₄×C₄₇⋊C₈	—	2	1	no	—
71	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
76	C₂×#41×C₄₇	Q₈	1	1	yes	characteristic
77	C₂×M₁₆×C₄₇	—	2	2	no	—
78	C₂×M₁₆×C₄₇	—	2	1	no	—
79	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
81	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
82	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
84	C₄×D₄×C₄₇	D₄	1	2	yes	—
85	#117×C₄₇	Q₈	1	1	yes	characteristic
86	#117×C₄₇	Q₈	1	2	yes	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
89	C₄⋊C₈×C₄₇	—	2	1	no	—
90	C₄⋊C₈×C₄₇	—	2	2	no	—
91	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
93	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²⋊C₈×C₄₇	—	2	2	no	—
95	C₂²⋊C₈×C₄₇	—	2	1	no	—
96	C₄×C₈×C₄₇	—	2	1	no	—
97	C₄×C₈×C₄₇	—	2	2	no	—
98	#41×C₄₇	—	4	2	no	—
99	C₂×Q₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
100	C₂×D₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
108	M₁₆×C₄₇	—	8	2	no	—
109	M₁₆×C₄₇	—	8	1	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
114	C₄⋊C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
115	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
116	C₄⋊C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
118	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
119	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
120	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
122	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₄₇	C₂×D₄	1	2	yes	—
124	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
125	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
126	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
127	#10625329	—	2	4	no	—
128	#10625329	—	4	2	no	—
129	#10625329	—	8	1	no	—
130	C₂×C₄₇⋊C₈	—	2	2	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	—	4	1	no	—
135	C₂×C₄₇⋊C₈	—	8	2	no	—
136	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
144	Q₈×C₄₇	—	2	2	no	—
145	D₄×C₄₇	—	2	2	no	—
146	D₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
166	C₈×C₄₇	—	4	1	no	—
167	C₈×C₄₇	—	4	2	no	—
168	C₈×C₄₇	—	4	1	no	—
169	C₄₇⋊C₈	—	2	1	no	—
170	C₄₇⋊C₈	—	2	2	no	—
171	C₄₇⋊C₈	—	2	1	no	—
172	C₄₇⋊C₈	—	2	1	no	—
173	C₄₇⋊C₈	—	2	2	no	—
174	C₄₇⋊C₈	—	4	1	no	—
175	C₄₇⋊C₈	—	4	1	no	—
176	C₄₇⋊C₈	—	4	2	no	—
177	C₄₇⋊C₈	#131	1	2	yes	—
178	#17841	—	47	1	no	maximal, Sylow
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	2	1	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	2	no	—
192	C₄×C₄₇	#430	1	2	yes	—
193	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
194	C₄×C₄₇	#568	1	1	yes	characteristic
195	C₄×C₄₇	#577	1	1	yes	characteristic
196	C₄×C₄₇	#577	1	1	yes	characteristic
197	#2991	D₄₇	1	1	yes	characteristic
198	#2990	—	47	1	no	—
199	#2965	—	47	1	no	—
200	#1574	—	47	1	no	—
201	#1574	—	47	1	no	—
202	#1572	—	47	2	no	—
203	#1570	—	47	2	no	—
204	#1569	—	47	2	no	—
205	#1566	—	47	1	no	—
206	#1565	—	47	2	no	—
207	#1564	—	47	1	no	—
208	C₂×C₄₇	—	4	1	no	—
209	C₂×C₄₇	—	4	2	no	—
210	C₂×C₄₇	#2906	1	1	yes	characteristic
211	C₂×C₄₇	#2912	1	1	yes	characteristic
212	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
213	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
214	#446	—	47	1	no	—
215	#446	—	47	1	no	—
216	#446	—	94	1	no	—
217	C₈×Q₈	—	2	1	no	—
218	#436	—	2	1	no	—
219	#436	—	2	2	no	—
220	#436	—	47	1	no	—
221	#436	—	47	1	no	—
222	#435	—	47	2	no	—
223	#435	—	47	2	no	—
224	#435	—	94	2	no	—
225	C₈×D₄	—	94	1	no	—
226	#432	—	47	2	no	—
227	#431	—	47	2	no	—
228	#431	—	47	1	no	—
229	#431	—	47	1	no	—
230	#431	C₂×D₄₇	1	1	yes	characteristic
231	#431	C₂×D₄₇	1	2	yes	—
232	#423	—	47	1	no	—
233	#423	C₂×D₄₇	1	1	yes	characteristic
234	#423	C₂×D₄₇	1	2	yes	—
235	C₂×C₄⋊C₈	—	47	2	no	—
236	C₄×M₁₆	—	47	2	no	—
237	C₂×C₄×C₈	—	47	1	no	—
238	#335	—	47	1	no	—
239	#335	—	47	1	no	—
240	#335	—	47	2	no	—
241	#335	—	47	2	no	—
242	#334	—	47	1	no	—
243	#334	—	47	1	no	—
244	#334	—	47	2	no	—
245	#334	—	47	2	no	—
246	#334	—	47	2	no	—
247	#334	—	47	2	no	—
248	C₄₇	#17841	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	Dic₉₄	1	1	yes	characteristic
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	47	2	no	—
253	C₂×M₁₆	—	47	2	no	—
254	C₂×M₁₆	—	94	1	no	—
255	C₂²×C₈	—	47	1	no	—
256	C₂²×C₈	—	47	1	no	—
257	C₂²×C₈	—	94	2	no	—
258	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
259	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
260	C₄×D₄	C₄×D₄₇	1	2	yes	—
261	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
262	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
263	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
264	#117	Dic₉₄	1	1	yes	characteristic
265	#117	Dic₉₄	1	2	yes	—
266	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	47	2	no	—
271	C₄⋊C₈	—	47	2	no	—
272	C₄⋊C₈	—	47	1	no	—
273	C₄⋊C₈	—	47	1	no	—
274	C₄⋊C₈	—	47	1	no	—
275	C₄⋊C₈	—	47	2	no	—
276	C₄⋊C₈	—	47	1	no	—
277	C₄⋊C₈	—	94	2	no	—
278	C₄⋊C₈	—	94	1	no	—
279	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
280	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
281	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
282	C₂²⋊C₈	—	2	2	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	47	2	no	—
285	C₂²⋊C₈	—	47	2	no	—
286	C₂²⋊C₈	—	47	2	no	—
287	C₂²⋊C₈	—	94	1	no	—
288	C₂²⋊C₈	—	94	2	no	—
289	#97	—	47	2	no	—
290	#97	—	47	2	no	—
291	#97	—	94	2	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	47	1	no	—
295	C₄×C₈	—	47	1	no	—
296	C₄×C₈	—	47	1	no	—
297	C₄×C₈	—	47	1	no	—
298	C₄×C₈	—	47	2	no	—
299	C₄×C₈	—	94	1	no	—
300	#41	—	4	2	no	—
301	C₂×Q₈	Dic₄₇⋊C₄	1	1	yes	characteristic
302	C₂×D₄	Dic₄₇⋊C₄	1	1	yes	characteristic
303	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
304	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
305	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
306	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
308	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
309	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
310	M₁₆	—	8	2	no	—
311	M₁₆	—	8	1	no	—
312	M₁₆	—	94	4	no	—
313	M₁₆	—	376	1	no	—
314	M₁₆	—	188	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	47	1	no	—
319	C₂×C₈	—	47	1	no	—
320	C₂×C₈	—	47	1	no	—
321	C₂×C₈	—	47	1	no	—
322	C₂×C₈	—	47	2	no	—
323	C₂×C₈	—	47	2	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	94	1	no	—
326	C₂×C₈	—	94	1	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	—	376	2	no	—
329	C₂×C₈	—	188	1	no	—
330	C₄⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
331	C₄⋊C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
332	C₄⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
333	C₄⋊C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
334	C₂²⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
335	C₂²⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
336	C₂²⋊C₄	Dic₄₇⋊C₄	1	2	yes	—
337	C₄²	C₂×Dic₉₄	1	1	yes	characteristic
338	C₄²	C₂×Dic₉₄	1	2	yes	—
339	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
340	C₄²	C₂×C₄×D₄₇	1	2	yes	—
341	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
342	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
343	C₄²	C₂³×D₄₇	1	1	yes	characteristic
344	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
345	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
346	Q₈	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
360	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
361	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
362	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
363	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
364	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
367	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
368	C₈	—	4	1	no	—
369	C₈	—	4	1	no	—
370	C₈	—	4	2	no	—
371	C₈	—	47	2	no	—
372	C₈	—	94	1	no	—
373	C₈	—	94	2	no	—
374	C₈	—	94	1	no	—
375	C₈	—	94	1	no	—
376	C₈	—	94	2	no	—
377	C₈	—	188	1	no	—
378	C₈	—	188	2	no	—
379	C₈	—	188	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	#15689171	1	2	yes	—
394	C₄	#131×D₄₇	1	1	yes	characteristic
395	C₄	#15689888	1	1	yes	characteristic
396	C₄	#15689931	1	1	yes	characteristic
397	C₄	#15689934	1	1	yes	characteristic
398	C₂	—	4	1	no	—
399	C₂	—	4	2	no	—
400	C₂	#20251954	1	1	yes	characteristic
401	C₂	#20251981	1	1	yes	characteristic
402	C₂	C₂×#15689171	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#2991	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₄₇	Q₈
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#2991	D₄₇
hypocenter	C₄₇	#17841
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2991

Complements

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

N	H ≅ G/N	type
3. #20242179	C₂	semidirect
4. #20242176	C₂	semidirect
5. #20242166	C₂	semidirect
6. #20242160	C₂	semidirect
7. #20242153	C₂	semidirect
8. #20242143	C₂	semidirect
9. #20242141	C₂	semidirect
10. #20242134	C₂	semidirect
248. C₄₇	#17841	semidirect

Maximal subgroups

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

subgroup	index
#20252513	2
#20252355	2
#20242179	2
#20242176	2
#20242166	2
#20242160	2
#20242153	2
#20242143	2
#20242141	2
#20242134	2
C₄₇×#2991	2
#17841	47