Subgroups — #26369495

Order 12032.

682 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689539	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252098	C₂	1	1	yes	maximal, characteristic
4	#20245217	C₂	1	2	yes	maximal, complemented
5	#20245216	C₂	1	2	yes	maximal, complemented
6	#20245210	C₂	1	2	yes	maximal, complemented
7	(C₂²⋊D₄₇)⋊C₁₆	C₂	1	2	yes	maximal, complemented
8	C₂×Dic₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#20245003	C₂	1	1	yes	maximal, characteristic, complemented
10	M₃₂×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094030	C₂²	1	1	yes	characteristic
13	#15689669	C₄	1	1	yes	characteristic
14	#15689540	—	2	4	no	—
15	#15689539	—	2	4	no	—
16	C₂×#13093964	C₂²	1	2	yes	—
17	C₂×#13093964	C₂²	1	1	yes	characteristic
18	C₂×#13093963	C₂²	1	2	yes	—
19	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	—
21	C₂×C₁₆×D₄₇	C₂²	1	2	yes	—
22	#15689199	C₄	1	2	yes	—
23	#15689199	C₄	1	2	yes	—
24	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
25	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
26	#15689146	C₄	1	1	yes	characteristic
27	#15689091	C₄	1	1	yes	characteristic
28	#15689090	C₄	1	1	yes	characteristic
29	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
30	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
31	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
32	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
33	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
34	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	—
35	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	—
36	#15688898	C₂²	1	2	yes	—
37	C₁₆×Dic₄₇	C₂²	1	2	yes	—
38	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
40	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×C₂²⋊C₁₆	C₂²	1	2	yes	—
42	C₄₇×C₂²⋊C₁₆	C₂²	1	2	yes	—
43	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
44	#13094030	—	2	2	no	—
45	#13094030	—	2	2	no	—
46	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
47	C₂×#10625324	C₂×C₄	1	2	yes	—
48	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₄₇	C₂³	1	2	yes	—
50	#13094022	C₈	1	1	yes	characteristic
51	#13094020	C₈	1	1	yes	characteristic
52	#13094013	C₈	1	1	yes	characteristic
53	#13094011	C₈	1	1	yes	characteristic
54	#13093996	C₈	1	2	yes	—
55	#13093996	C₈	1	2	yes	—
56	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
57	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	#13093964	—	2	4	no	—
60	#13093964	D₄	1	4	yes	complemented
61	#13093963	—	2	4	no	—
62	C₂×C₄₇⋊C₁₆	—	2	2	no	—
63	C₂×C₄₇⋊C₁₆	—	2	4	no	—
64	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
67	C₁₆×D₄₇	—	2	4	no	—
68	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
69	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
70	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
71	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
72	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
73	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
74	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
77	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
78	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
79	#131×C₄₇	—	2	2	no	—
80	#131×C₄₇	—	2	2	no	—
81	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	M₃₂×C₄₇	—	2	2	no	—
86	C₂×C₁₆×C₄₇	—	2	2	no	—
87	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
90	#41×C₄₇	—	2	2	no	—
91	#41×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	C₂×C₈	1	1	yes	characteristic
93	C₂×D₄×C₄₇	C₂×C₈	1	2	yes	—
94	C₂×D₄×C₄₇	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊D₄₇	C₂×C₈	1	2	yes	—
98	C₂×C₂²⋊D₄₇	C₂×C₈	1	2	yes	—
99	C₂×C₂²⋊D₄₇	C₂×C₈	1	2	yes	—
100	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
102	#10625350	—	2	2	no	—
103	#10625350	—	2	2	no	—
104	C₂×D₁₈₈	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
106	C₂×Dic₉₄	C₂×C₈	1	1	yes	characteristic
107	M₁₆×C₄₇	—	2	2	no	—
108	M₁₆×C₄₇	—	2	4	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₄₇	#41	1	2	yes	—
115	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
117	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
118	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
119	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
120	Dic₄₇⋊C₄	C₂×C₈	1	2	yes	—
121	Dic₄₇⋊C₄	C₂×C₈	1	2	yes	—
122	C₄×Dic₄₇	C₂×C₈	1	1	yes	characteristic
123	C₄×Dic₄₇	C₂×C₈	1	1	yes	characteristic
124	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
126	#10625329	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
131	#10625324	—	2	4	no	—
132	C₈×D₄₇	—	2	2	no	—
133	C₈×D₄₇	—	2	2	no	—
134	C₁₆×C₄₇	—	2	1	no	—
135	C₁₆×C₄₇	—	2	1	no	—
136	C₁₆×C₄₇	—	2	2	no	—
137	C₄₇⋊C₁₆	—	2	1	no	—
138	C₄₇⋊C₁₆	—	2	1	no	—
139	C₄₇⋊C₁₆	C₂×D₄	1	4	yes	—
140	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
141	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
142	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
143	Q₈×C₄₇	—	2	2	no	—
144	D₄×C₄₇	—	2	4	no	—
145	D₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
150	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#131	1	2	yes	—
152	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂²⋊D₄₇	—	2	4	no	—
154	C₂²⋊D₄₇	—	2	4	no	—
155	C₂²⋊D₄₇	—	4	2	no	—
156	C₂×Dic₄₇	—	2	2	no	—
157	C₂×Dic₄₇	—	4	1	no	—
158	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
159	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
160	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
161	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
162	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
163	D₁₈₈	—	2	2	no	—
164	C₄×D₄₇	—	2	2	no	—
165	C₄×D₄₇	—	2	2	no	—
166	Dic₉₄	—	2	2	no	—
167	C₈×C₄₇	—	2	2	no	—
168	C₈×C₄₇	C₄×D₄	1	2	yes	—
169	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₄₇⋊C₈	—	2	2	no	—
172	C₄₇⋊C₈	—	2	1	no	—
173	C₄₇⋊C₈	—	2	1	no	—
174	#33438	—	47	1	no	maximal, Sylow
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	2	no	—
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	C₈×D₄	1	2	yes	—
181	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
182	C₂×D₄₇	—	2	2	no	—
183	C₂×D₄₇	—	2	2	no	—
184	C₂×D₄₇	—	2	2	no	—
185	C₄×C₄₇	—	2	2	no	—
186	C₄×C₄₇	C₈×D₄	1	2	yes	—
187	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
188	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
189	Dic₄₇	—	2	1	no	—
190	Dic₄₇	—	2	1	no	—
191	Dic₄₇	—	2	1	no	—
192	Dic₄₇	—	2	2	no	—
193	Dic₄₇	#504	1	2	yes	complemented
194	C₂×#504	—	47	1	no	—
195	C₂×#504	—	47	1	no	—
196	#2931	—	47	1	no	—
197	#2169	—	47	2	no	—
198	#2168	—	47	2	no	—
199	#2168	—	47	2	no	—
200	D₄×C₁₆	—	47	2	no	—
201	C₂×C₄⋊C₁₆	—	47	1	no	—
202	#2113	—	47	1	no	—
203	#2113	D₄₇	1	1	yes	characteristic, complemented
204	C₄×M₃₂	—	47	1	no	—
205	C₂×C₄₇	—	2	2	no	—
206	C₂×C₄₇	—	4	2	no	—
207	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
208	C₂×C₄₇	C₂×#504	1	1	yes	characteristic
209	C₂×C₄₇	#3407	1	1	yes	characteristic
210	D₄₇	—	4	2	no	—
211	C₂×#131	—	47	1	no	—
212	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
213	#532	—	47	1	no	—
214	#504	—	94	4	no	—
215	#504	—	94	4	no	—
216	C₂×M₃₂	—	47	1	no	—
217	C₂×M₃₂	—	47	2	no	—
218	C₂×M₃₂	—	47	2	no	—
219	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
220	C₂²×C₁₆	—	47	1	no	—
221	C₂²×C₁₆	—	47	2	no	—
222	C₂²×C₁₆	—	47	2	no	—
223	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
224	#436	—	47	2	no	—
225	#436	—	47	2	no	—
226	C₈×D₄	—	47	2	no	—
227	C₈×D₄	—	47	2	no	—
228	#423	—	47	1	no	—
229	#408	—	47	1	no	—
230	#408	—	47	1	no	—
231	C₂×C₄×C₈	—	47	1	no	—
232	C₄⋊C₁₆	—	47	1	no	—
233	C₄⋊C₁₆	—	47	1	no	—
234	C₄⋊C₁₆	—	47	1	no	—
235	C₄⋊C₁₆	—	47	1	no	—
236	C₂²⋊C₁₆	—	47	2	no	—
237	C₂²⋊C₁₆	—	47	2	no	—
238	C₂²⋊C₁₆	C₂×D₄₇	1	2	yes	—
239	C₂²⋊C₁₆	C₂×D₄₇	1	2	yes	—
240	#346	—	47	2	no	—
241	C₄×C₁₆	—	47	2	no	—
242	C₄₇	#33438	1	1	yes	characteristic, complemented, Sylow
243	C₂×#41	—	47	1	no	—
244	C₂×#41	C₄×D₄₇	1	1	yes	characteristic
245	#131	—	2	2	no	—
246	#131	—	2	2	no	—
247	#131	—	94	2	no	—
248	#131	—	94	2	no	—
249	C₂×M₁₆	—	47	1	no	—
250	C₂×M₁₆	—	47	2	no	—
251	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
252	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
253	C₂²×C₈	—	47	1	no	—
254	C₂²×C₈	—	47	2	no	—
255	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
256	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
257	C₄⋊Q₈	—	47	1	no	—
258	#127	—	47	1	no	—
259	#124	—	47	1	no	—
260	#124	—	47	1	no	—
261	#121	—	47	2	no	—
262	#121	—	47	2	no	—
263	C₄×D₄	—	47	2	no	—
264	C₄×D₄	—	47	2	no	—
265	C₂×C₄²	—	47	1	no	—
266	M₃₂	—	2	2	no	—
267	M₃₂	—	47	4	no	—
268	M₃₂	—	94	4	no	—
269	M₃₂	—	94	4	no	—
270	C₂×C₁₆	—	2	2	no	—
271	C₂×C₁₆	—	47	2	no	—
272	C₂×C₁₆	—	47	1	no	—
273	C₂×C₁₆	—	47	1	no	—
274	C₂×C₁₆	—	94	4	no	—
275	C₂×C₁₆	—	94	4	no	—
276	C₂×C₁₆	—	94	2	no	—
277	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
278	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
279	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
280	C₄⋊C₈	—	47	2	no	—
281	C₄⋊C₈	—	47	2	no	—
282	C₂²⋊C₈	—	47	2	no	—
283	C₂²⋊C₈	—	47	2	no	—
284	C₂²⋊C₈	—	47	2	no	—
285	C₂²⋊C₈	—	47	2	no	—
286	C₄×C₈	—	47	1	no	—
287	C₄×C₈	—	47	1	no	—
288	C₄×C₈	—	47	1	no	—
289	C₄×C₈	—	47	1	no	—
290	#41	—	2	2	no	—
291	#41	—	2	2	no	—
292	#41	—	94	2	no	—
293	#41	—	94	2	no	—
294	C₂×Q₈	—	47	1	no	—
295	C₂×Q₈	C₈×D₄₇	1	1	yes	characteristic
296	C₂×D₄	—	47	2	no	—
297	C₂×D₄	—	47	2	no	—
298	C₂×D₄	—	47	2	no	—
299	C₂×D₄	—	47	1	no	—
300	C₂×D₄	C₈×D₄₇	1	2	yes	—
301	C₂×D₄	C₈×D₄₇	1	1	yes	characteristic
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	2	no	—
305	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
306	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	4	no	—
309	M₁₆	—	94	2	no	—
310	M₁₆	—	94	4	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	47	1	no	—
314	C₂×C₈	—	47	1	no	—
315	C₂×C₈	—	47	2	no	—
316	C₂×C₈	—	94	2	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	94	2	no	—
319	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
320	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
321	C₂×C₈	D₄×D₄₇	1	2	yes	—
322	C₂×C₈	#10625352	1	2	yes	—
323	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
324	C₄⋊C₄	—	47	2	no	—
325	C₄⋊C₄	—	47	2	no	—
326	C₂²⋊C₄	—	47	2	no	—
327	C₂²⋊C₄	—	47	2	no	—
328	C₂²⋊C₄	—	47	2	no	—
329	C₂²⋊C₄	—	47	2	no	—
330	C₄²	—	47	1	no	—
331	C₄²	—	47	1	no	—
332	C₄²	—	47	1	no	—
333	C₄²	—	47	1	no	—
334	C₁₆	—	2	1	no	—
335	C₁₆	—	2	1	no	—
336	C₁₆	—	2	2	no	—
337	C₁₆	—	47	4	no	—
338	C₁₆	—	94	1	no	—
339	C₁₆	—	94	1	no	—
340	C₂³	—	47	2	no	—
341	C₂³	C₂×C₈×D₄₇	1	2	yes	—
342	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	94	2	no	—
345	D₄	—	2	4	no	—
346	D₄	—	2	2	no	—
347	D₄	—	94	4	no	—
348	D₄	—	94	4	no	—
349	D₄	—	94	2	no	—
350	D₄	—	188	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	47	1	no	—
354	C₂×C₄	—	47	1	no	—
355	C₂×C₄	—	47	1	no	—
356	C₂×C₄	—	47	1	no	—
357	C₂×C₄	—	47	2	no	—
358	C₂×C₄	—	94	2	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	188	1	no	—
362	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
363	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
364	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
365	C₂×C₄	#13094032	1	2	yes	—
366	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
367	C₈	—	2	2	no	—
368	C₈	—	94	2	no	—
369	C₈	—	94	1	no	—
370	C₈	—	94	1	no	—
371	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
372	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
373	C₈	C₂×#10625352	1	1	yes	characteristic
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	94	2	no	—
380	C₂²	—	94	2	no	—
381	C₂²	—	94	2	no	—
382	C₂²	(C₂²⋊D₄₇)⋊C₈	1	2	yes	—
383	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	47	2	no	—
386	C₄	—	94	2	no	—
387	C₄	—	94	1	no	—
388	C₄	—	94	1	no	—
389	C₄	—	94	1	no	—
390	C₄	(C₂²⋊D₄₇)⋊C₈	1	2	yes	—
391	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
392	C₄	C₂×#13094032	1	1	yes	characteristic
393	C₂	—	2	2	no	—
394	C₂	—	4	2	no	—
395	C₂	—	188	2	no	—
396	C₂	C₂×(C₂²⋊D₄₇)⋊C₈	1	1	yes	characteristic
397	C₂	#504×D₄₇	1	1	yes	characteristic
398	C₂	#20256489	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#2113	C₂
prime radical	#15689669	C₄
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	#2113	D₄₇
hypocenter	C₄₇	#33438
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ #2113

Complements

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

N	H ≅ G/N	type
1. C₂×#15689540	C₂	semidirect
2. C₂×#15689539	C₂	semidirect
4. #20245217	C₂	semidirect
5. #20245216	C₂	semidirect
6. #20245210	C₂	semidirect
7. (C₂²⋊D₄₇)⋊C₁₆	C₂	semidirect
8. C₂×Dic₄₇⋊C₁₆	C₂	semidirect
9. #20245003	C₂	semidirect
10. M₃₂×Dic₄₇	C₂	semidirect
11. C₄₇×#2113	C₂	semidirect
60. #13093964	D₄	semidirect
193. Dic₄₇	#504	semidirect
203. #2113	D₄₇	semidirect
242. C₄₇	#33438	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689540	2
C₂×#15689539	2
#20252098	2
#20245217	2
#20245216	2
#20245210	2
(C₂²⋊D₄₇)⋊C₁₆	2
C₂×Dic₄₇⋊C₁₆	2
#20245003	2
M₃₂×Dic₄₇	2
C₄₇×#2113	2
#33438	47