Subgroups — #26115140

Order 12032.

606 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625334	C₂	1	1	yes	maximal, characteristic
2	#20244182	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15688875	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688850	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625334	C₄	1	1	yes	characteristic
9	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
10	C₄×#10625334	—	2	2	no	—
11	C₄×#10625334	—	2	2	no	—
12	C₂×#13093957	C₄	1	1	yes	characteristic
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#13093945	C₄	1	1	yes	characteristic
15	C₂×#13093944	C₄	1	1	yes	characteristic
16	C₂×(C₂×D₄₇)⋊C₈	—	2	2	no	—
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	#15688875	—	2	2	no	—
20	D₄⋊(C₄₇⋊C₈)	—	2	2	no	—
21	#15688850	—	2	2	no	—
22	C₈×C₄₇⋊C₈	—	2	2	no	—
23	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
26	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₄₇	—	2	1	no	—
29	C₂×#10625334	—	2	2	no	—
30	C₂×#10625334	—	2	2	no	—
31	C₂×#10625334	C₈	1	4	yes	complemented
32	C₂²×C₄₇⋊C₈	—	2	1	no	—
33	C₂²×C₄₇⋊C₈	—	2	1	no	—
34	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×D₁₈₈	—	2	1	no	—
37	C₄×D₁₈₈	—	2	1	no	—
38	C₄×D₁₈₈	—	2	1	no	—
39	C₄×D₁₈₈	—	2	1	no	—
40	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
42	#13093957	—	2	2	no	—
43	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
44	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
45	#13093945	—	2	2	no	—
46	#13093944	—	2	2	no	—
47	(C₂×D₄₇)⋊C₈	—	4	4	no	—
48	C₄×C₄₇⋊C₈	—	2	1	no	—
49	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
50	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
51	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
52	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	—	2	1	no	—
54	C₂²×C₈×C₄₇	—	2	1	no	—
55	C₂²×C₈×C₄₇	D₄	1	2	yes	—
56	C₄×D₄×C₄₇	—	2	1	no	—
57	C₄×D₄×C₄₇	—	2	1	no	—
58	C₄×D₄×C₄₇	—	2	1	no	—
59	C₄×D₄×C₄₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₄₇	—	2	1	no	—
64	C₄⋊C₈×C₄₇	—	2	1	no	—
65	C₂²⋊C₈×C₄₇	—	4	4	no	—
66	C₄×C₈×C₄₇	—	2	1	no	—
67	C₄×C₈×C₄₇	—	2	1	no	—
68	C₂⁴×C₄₇	—	2	1	no	—
69	C₂³×D₄₇	—	2	1	no	—
70	C₂×D₄×C₄₇	—	2	1	no	—
71	C₂×D₄×C₄₇	—	2	1	no	—
72	C₂×D₄×C₄₇	—	2	1	no	—
73	C₂×D₄×C₄₇	—	2	1	no	—
74	C₂×D₄×C₄₇	—	2	1	no	—
75	C₂×D₄×C₄₇	C₂×C₈	1	2	yes	—
76	C₂²×C₄×C₄₇	—	2	1	no	—
77	C₂²×C₄×C₄₇	—	4	1	no	—
78	C₂²×C₄×C₄₇	—	4	1	no	—
79	C₂²×C₄×C₄₇	—	4	2	no	—
80	C₂²×C₄×C₄₇	—	4	2	no	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
84	C₂²×Dic₄₇	—	2	1	no	—
85	C₂×D₁₈₈	—	2	1	no	—
86	C₂×D₁₈₈	—	2	1	no	—
87	C₂×D₁₈₈	—	2	1	no	—
88	C₂×D₁₈₈	—	2	1	no	—
89	C₂×D₁₈₈	—	2	1	no	—
90	C₂×D₁₈₈	C₂×C₈	1	2	yes	—
91	C₂×C₄×D₄₇	—	4	1	no	—
92	C₂×C₄×D₄₇	—	4	1	no	—
93	C₂×C₄×D₄₇	—	4	2	no	—
94	C₂×C₄×D₄₇	—	4	2	no	—
95	C₂×C₈×C₄₇	—	2	2	no	—
96	C₂×C₈×C₄₇	—	2	2	no	—
97	C₂×C₈×C₄₇	—	4	1	no	—
98	C₂×C₈×C₄₇	—	4	2	no	—
99	C₂×C₈×C₄₇	D₈	1	4	yes	complemented
100	C₄⋊C₄×C₄₇	—	2	1	no	—
101	C₄⋊C₄×C₄₇	—	2	1	no	—
102	C₂²⋊C₄×C₄₇	—	4	1	no	—
103	C₂²⋊C₄×C₄₇	—	4	1	no	—
104	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₄₇	#41	1	1	yes	characteristic
108	#10625334	—	2	8	no	—
109	(C₂×D₄₇)⋊C₄	—	4	1	no	—
110	(C₂×D₄₇)⋊C₄	—	4	1	no	—
111	C₄⋊Dic₄₇	—	2	1	no	—
112	C₄⋊Dic₄₇	—	2	1	no	—
113	C₂×C₄₇⋊C₈	—	2	4	no	—
114	C₂×C₄₇⋊C₈	—	2	2	no	—
115	C₂×C₄₇⋊C₈	—	2	1	no	—
116	C₂×C₄₇⋊C₈	—	2	1	no	—
117	C₂×C₄₇⋊C₈	—	4	1	no	—
118	C₂×C₄₇⋊C₈	—	4	2	no	—
119	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
120	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
121	C₂×C₄₇⋊C₈	C₂×C₈	1	2	yes	—
122	C₂×C₄₇⋊C₈	M₁₆	1	2	yes	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	4	1	no	—
125	C₂³×C₄₇	—	4	1	no	—
126	C₂³×C₄₇	—	4	2	no	—
127	C₂³×C₄₇	—	4	2	no	—
128	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
129	C₂²×D₄₇	—	2	2	no	—
130	C₂²×D₄₇	—	4	1	no	—
131	C₂²×D₄₇	—	4	1	no	—
132	C₂²×D₄₇	—	4	2	no	—
133	C₂²×D₄₇	—	4	2	no	—
134	D₄×C₄₇	—	2	2	no	—
135	D₄×C₄₇	—	2	2	no	—
136	D₄×C₄₇	—	4	1	no	—
137	D₄×C₄₇	—	4	1	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	4	1	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	8	2	no	—
142	C₂×C₄×C₄₇	—	8	1	no	—
143	C₂×C₄×C₄₇	—	8	1	no	—
144	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
152	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₄₇	#135	1	2	yes	—
156	C₂×Dic₄₇	—	4	1	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	D₁₈₈	—	2	2	no	—
159	D₁₈₈	—	2	2	no	—
160	D₁₈₈	—	4	1	no	—
161	D₁₈₈	—	4	1	no	—
162	C₄×D₄₇	—	8	2	no	—
163	C₄×D₄₇	—	8	1	no	—
164	C₄×D₄₇	—	8	1	no	—
165	C₈×C₄₇	—	2	4	no	—
166	C₈×C₄₇	—	8	1	no	—
167	C₄₇⋊C₈	—	2	4	no	—
168	C₄₇⋊C₈	—	2	2	no	—
169	C₄₇⋊C₈	—	8	1	no	—
170	C₄₇⋊C₈	C₂²⋊C₈	1	4	yes	complemented
171	#9657	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	—	4	4	no	—
173	C₂²×C₄₇	—	4	2	no	—
174	C₂²×C₄₇	—	8	2	no	—
175	C₂²×C₄₇	—	8	1	no	—
176	C₂²×C₄₇	—	8	1	no	—
177	C₂²×C₄₇	#390	1	1	yes	characteristic
178	C₂²×C₄₇	C₈×D₄	1	1	yes	characteristic
179	C₂²×C₄₇	#436	1	1	yes	characteristic
180	C₂²×C₄₇	C₄×D₈	1	2	yes	—
181	C₂²×C₄₇	#443	1	2	yes	—
182	C₂×D₄₇	—	4	4	no	—
183	C₂×D₄₇	—	4	2	no	—
184	C₂×D₄₇	—	8	2	no	—
185	C₂×D₄₇	—	8	1	no	—
186	C₂×D₄₇	—	8	1	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	8	1	no	—
190	C₄×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
191	C₄×C₄₇	#408	1	1	yes	characteristic
192	C₄×C₄₇	C₈×D₄	1	1	yes	characteristic
193	C₄×C₄₇	#436	1	1	yes	characteristic
194	C₄×C₄₇	#466	1	2	yes	—
195	C₄×C₄₇	#493	1	1	yes	characteristic
196	C₄×C₄₇	#495	1	1	yes	characteristic
197	Dic₄₇	—	8	1	no	—
198	C₂×C₄×D₈	—	47	1	no	—
199	#1954	—	47	1	no	—
200	#1954	D₄₇	1	1	yes	characteristic, complemented
201	C₂×#335	—	47	1	no	—
202	C₂×D₄⋊C₈	—	47	1	no	—
203	C₂×D₄⋊C₈	—	47	1	no	—
204	C₂×C₈²	—	47	1	no	—
205	C₂×C₄₇	—	8	2	no	—
206	C₂×C₄₇	C₈×D₈	1	2	yes	—
207	C₂×C₄₇	#1589	1	2	yes	—
208	C₂×C₄₇	#1954	1	1	yes	characteristic
209	C₂×C₄₇	#1970	1	1	yes	characteristic
210	C₂×C₄₇	#1974	1	1	yes	characteristic
211	D₄₇	—	8	2	no	—
212	C₂²×D₈	—	47	1	no	—
213	C₂×C₄×D₄	—	47	1	no	—
214	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
215	C₄×D₈	—	94	2	no	—
216	C₄×D₈	—	94	2	no	—
217	C₂×#107	—	47	1	no	—
218	C₂×C₄⋊C₈	—	47	1	no	—
219	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂×#102	—	47	1	no	—
221	C₂×#102	—	47	1	no	—
222	C₂×C₂²⋊C₈	—	2	2	no	—
223	C₂×C₂²⋊C₈	—	94	2	no	—
224	C₂×C₄×C₈	—	47	1	no	—
225	C₂×C₄×C₈	—	47	1	no	—
226	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
227	#335	—	94	2	no	—
228	D₄⋊C₈	—	94	2	no	—
229	D₄⋊C₈	—	94	2	no	—
230	C₈²	—	94	2	no	—
231	C₄₇	#9657	1	1	yes	characteristic, complemented, Sylow
232	C₂²×D₄	—	47	1	no	—
233	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
234	C₂³×C₄	—	2	1	no	—
235	C₂³×C₄	—	94	1	no	—
236	C₂×D₈	—	47	4	no	—
237	C₂×D₈	—	94	2	no	—
238	C₂×D₈	—	94	2	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	47	1	no	—
241	C₂²×C₈	—	47	1	no	—
242	C₂²×C₈	—	94	1	no	—
243	C₂²×C₈	—	94	1	no	—
244	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	94	1	no	—
250	C₄×D₄	—	94	1	no	—
251	C₄×D₄	—	94	1	no	—
252	C₄×D₄	—	94	1	no	—
253	C₂×C₄⋊C₄	—	47	1	no	—
254	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₂²⋊C₄	—	94	1	no	—
257	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
258	#107	—	94	2	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	94	1	no	—
262	C₄⋊C₈	—	94	1	no	—
263	#102	—	94	2	no	—
264	#102	—	94	2	no	—
265	C₂²⋊C₈	—	4	4	no	—
266	C₂²⋊C₈	—	188	4	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	—	47	2	no	—
270	C₄×C₈	—	47	2	no	—
271	C₄×C₈	—	47	2	no	—
272	C₄×C₈	—	94	1	no	—
273	C₂⁴	—	2	1	no	—
274	C₂⁴	—	94	1	no	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	47	2	no	—
281	C₂×D₄	—	94	1	no	—
282	C₂×D₄	—	94	1	no	—
283	C₂×D₄	—	94	1	no	—
284	C₂×D₄	—	94	1	no	—
285	C₂×D₄	—	94	1	no	—
286	C₂×D₄	C₈×D₄₇	1	2	yes	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	94	1	no	—
293	C₂²×C₄	—	188	1	no	—
294	C₂²×C₄	—	188	1	no	—
295	C₂²×C₄	—	188	2	no	—
296	C₂²×C₄	—	188	2	no	—
297	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	#10625350	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
300	D₈	—	94	8	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	—	47	2	no	—
306	C₂×C₈	—	47	2	no	—
307	C₂×C₈	—	47	2	no	—
308	C₂×C₈	—	47	2	no	—
309	C₂×C₈	—	94	4	no	—
310	C₂×C₈	—	94	2	no	—
311	C₂×C₈	—	94	1	no	—
312	C₂×C₈	—	94	1	no	—
313	C₂×C₈	—	188	1	no	—
314	C₂×C₈	—	188	2	no	—
315	C₂×C₈	#10625334	1	4	yes	complemented
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	94	1	no	—
319	C₄⋊C₄	—	94	1	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	188	1	no	—
323	C₂²⋊C₄	—	188	1	no	—
324	C₄²	D₄×D₄₇	1	1	yes	characteristic
325	C₄²	D₄×D₄₇	1	1	yes	characteristic
326	C₄²	D₄×D₄₇	1	1	yes	characteristic
327	C₄²	#10625352	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	94	2	no	—
334	C₂³	—	188	2	no	—
335	C₂³	—	188	1	no	—
336	C₂³	—	188	1	no	—
337	C₂³	—	188	2	no	—
338	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
339	D₄	—	2	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	4	1	no	—
342	D₄	—	4	1	no	—
343	D₄	—	94	2	no	—
344	D₄	—	94	2	no	—
345	D₄	—	188	1	no	—
346	D₄	—	188	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	—	8	1	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	—	376	1	no	—
354	C₂×C₄	—	376	1	no	—
355	C₂×C₄	—	376	2	no	—
356	C₂×C₄	—	188	1	no	—
357	C₂×C₄	—	188	2	no	—
358	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
359	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
360	C₂×C₄	#13093996	1	1	yes	characteristic
361	C₂×C₄	#13093997	1	1	yes	characteristic
362	C₂×C₄	#13094010	1	1	yes	characteristic
363	C₂×C₄	#13094020	1	1	yes	characteristic
364	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
365	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
366	C₂×C₄	#13094030	1	1	yes	characteristic
367	C₂×C₄	#13094032	1	1	yes	characteristic
368	C₂×C₄	C₂×#10625334	1	2	yes	—
369	C₂×C₄	#13094044	1	2	yes	—
370	C₈	—	2	4	no	—
371	C₈	—	8	1	no	—
372	C₈	—	47	4	no	—
373	C₈	—	94	4	no	—
374	C₈	—	94	2	no	—
375	C₈	—	376	1	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	376	1	no	—
382	C₂²	—	376	1	no	—
383	C₂²	—	376	2	no	—
384	C₂²	—	188	4	no	—
385	C₂²	—	188	2	no	—
386	C₂²	#15689023	1	1	yes	characteristic
387	C₂²	C₈×C₂²⋊D₄₇	1	1	yes	characteristic
388	C₂²	#15689199	1	1	yes	characteristic
389	C₂²	C₄×#10625334	1	2	yes	—
390	C₂²	#15689238	1	2	yes	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	8	1	no	—
394	C₄	—	376	1	no	—
395	C₄	C₂²⋊C₈×D₄₇	1	1	yes	characteristic
396	C₄	#15689088	1	1	yes	characteristic
397	C₄	(C₂²⋊D₄₇)⋊C₈	1	1	yes	characteristic
398	C₄	#15689198	1	1	yes	characteristic
399	C₄	#15689357	1	2	yes	—
400	C₄	#15689499	1	1	yes	characteristic
401	C₄	#15689505	1	1	yes	characteristic
402	C₂	—	8	2	no	—
403	C₂	—	376	2	no	—
404	C₂	C₈×#10625334	1	2	yes	—
405	C₂	#20242271	1	2	yes	—
406	C₂	#20244180	1	1	yes	characteristic
407	C₂	#20244253	1	1	yes	characteristic
408	C₂	#20244275	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1954	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×#10625334	C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1954	D₄₇
hypocenter	C₄₇	#9657
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1954

Complements

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

N	H ≅ G/N	type
2. #20244182	C₂	semidirect
3. C₂×#15688875	C₂	semidirect
4. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
5. C₂×#15688850	C₂	semidirect
6. C₂×C₈×C₄₇⋊C₈	C₂	semidirect
7. C₄₇×#1954	C₂	semidirect
31. C₂×#10625334	C₈	semidirect
99. C₂×C₈×C₄₇	D₈	semidirect
170. C₄₇⋊C₈	C₂²⋊C₈	semidirect
200. #1954	D₄₇	semidirect
231. C₄₇	#9657	semidirect
315. C₂×C₈	#10625334	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625334	2
#20244182	2
C₂×#15688875	2
C₂×D₄⋊(C₄₇⋊C₈)	2
C₂×#15688850	2
C₂×C₈×C₄₇⋊C₈	2
C₄₇×#1954	2
#9657	47