Subgroups — #26219703

Order 12032.

890 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689171	C₂	1	1	yes	maximal, characteristic
2	#20251977	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689149	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689078	C₂	1	1	yes	maximal, characteristic
5	#20244138	C₂	1	4	yes	maximal, complemented
6	#20244133	C₂	1	4	yes	maximal, complemented
7	#20243099	C₂	1	1	yes	maximal, characteristic
8	#20243097	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄₇×#424	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	C₂×#13093983	C₂²	1	1	yes	characteristic
13	C₂×#13093983	C₂²	1	1	yes	characteristic
14	#15689171	—	2	4	no	—
15	C₂×#13093959	C₂²	1	4	yes	—
16	#15689166	C₄	1	4	yes	complemented
17	#15689163	C₄	1	4	yes	complemented
18	#15689159	C₂²	1	4	yes	—
19	#15689149	—	2	2	no	—
20	#15689149	C₂²	1	2	yes	—
21	#15689149	C₂²	1	2	yes	—
22	C₂×Dic₄₇⋊C₈	—	2	2	no	—
23	#15689078	—	2	4	no	—
24	C₂×#13093934	C₂²	1	2	yes	—
25	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
26	#15688884	C₂²	1	4	yes	—
27	#15688882	C₂²	1	4	yes	—
28	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
29	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#424	—	2	2	no	—
32	C₄₇×#424	C₂²	1	2	yes	—
33	C₄₇×#424	C₂²	1	2	yes	—
34	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
35	C₂×#10625329	—	2	1	no	—
36	C₂×#10625329	—	2	2	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	C₂×C₄	1	2	yes	—
39	C₂×#10625329	C₂×C₄	1	2	yes	—
40	C₂×#10625329	D₄	1	4	yes	—
41	C₂×#10625329	Q₈	1	4	yes	—
42	C₂×#10625329	C₂³	1	2	yes	—
43	C₂²×C₄₇⋊C₈	—	2	1	no	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	#13093983	—	2	2	no	—
46	#13093983	—	2	1	no	—
47	#13093983	—	2	1	no	—
48	#13093983	C₂×C₄	1	2	yes	—
49	#13093983	Q₈	1	4	yes	—
50	#13093983	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₇	—	2	1	no	—
52	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
54	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
55	C₂×C₄×Dic₄₇	—	2	1	no	—
56	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
57	#13093959	—	2	8	no	—
58	#13093957	C₂×C₄	1	8	yes	—
59	#13093955	C₂×C₄	1	8	yes	—
60	Dic₄₇⋊C₈	—	2	4	no	—
61	Dic₄₇⋊C₈	—	2	4	no	—
62	#13093934	—	2	4	no	—
63	C₈×Dic₄₇	—	2	4	no	—
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₄₇	—	2	1	no	—
66	C₂×M₁₆×C₄₇	—	2	2	no	—
67	C₂×M₁₆×C₄₇	—	2	2	no	—
68	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
69	C₂²×C₈×C₄₇	—	2	2	no	—
70	C₂²×C₈×C₄₇	—	2	2	no	—
71	C₂²×C₈×C₄₇	—	2	1	no	—
72	C₂²×C₈×C₄₇	D₄	1	2	yes	—
73	C₂²×C₈×C₄₇	D₄	1	2	yes	—
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	#117×C₄₇	—	2	1	no	—
77	#117×C₄₇	—	2	1	no	—
78	#117×C₄₇	C₂×C₄	1	2	yes	—
79	#117×C₄₇	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₄²×C₄₇	—	2	1	no	—
83	C₄⋊C₈×C₄₇	—	2	4	no	—
84	C₄⋊C₈×C₄₇	—	2	4	no	—
85	C₂⁴×C₄₇	#41	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	#41	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	M₁₆×C₄₇	—	2	2	no	—
100	M₁₆×C₄₇	—	2	2	no	—
101	M₁₆×C₄₇	—	4	2	no	—
102	C₂×C₈×C₄₇	—	2	4	no	—
103	C₂×C₈×C₄₇	—	2	4	no	—
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	—	2	1	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	4	2	no	—
110	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
114	C₂²⋊C₄×C₄₇	—	2	2	no	—
115	C₂²⋊C₄×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	—	2	2	no	—
118	C₂²⋊Dic₄₇	—	2	2	no	—
119	C₂²⋊Dic₄₇	—	2	4	no	—
120	C₂²⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	4	no	—
123	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₄×Dic₄₇	—	2	2	no	—
126	C₄×Dic₄₇	—	2	2	no	—
127	C₄×Dic₄₇	C₂×Q₈	1	4	yes	—
128	#10625329	—	2	2	no	—
129	#10625329	—	2	2	no	—
130	#10625329	—	4	2	no	—
131	#10625329	C₄⋊C₄	1	8	yes	—
132	#10625329	C₄⋊C₄	1	8	yes	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	4	2	no	—
135	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
136	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
137	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
140	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
141	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
142	C₂³×C₄₇	#125	1	2	yes	—
143	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
151	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
152	C₂×C₄×C₄₇	#121	1	2	yes	—
153	C₂×C₄×C₄₇	#121	1	2	yes	—
154	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	#125	1	2	yes	—
156	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
157	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
158	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₄₇	—	2	4	no	—
165	C₂×Dic₄₇	—	2	4	no	—
166	C₂×Dic₄₇	—	4	4	no	—
167	C₂×Dic₄₇	—	4	4	no	—
168	C₈×C₄₇	—	2	2	no	—
169	C₈×C₄₇	—	2	2	no	—
170	C₈×C₄₇	—	4	2	no	—
171	C₄₇⋊C₈	—	4	2	no	—
172	C₄₇⋊C₈	C₂×C₄⋊C₄	1	8	yes	—
173	#21164	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	—	2	2	no	—
175	C₂²×C₄₇	—	2	2	no	—
176	C₂²×C₄₇	—	2	2	no	—
177	C₂²×C₄₇	—	4	2	no	—
178	C₂²×C₄₇	—	4	2	no	—
179	C₂²×C₄₇	#389	1	2	yes	—
180	C₂²×C₄₇	#389	1	2	yes	—
181	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×#125	1	1	yes	characteristic
184	C₄×C₄₇	—	4	4	no	—
185	C₄×C₄₇	#389	1	2	yes	—
186	C₄×C₄₇	#389	1	2	yes	—
187	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
188	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
189	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
190	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
191	Dic₄₇	—	4	4	no	—
192	Dic₄₇	—	4	4	no	—
193	C₂×#430	—	47	1	no	—
194	#2911	—	47	1	no	—
195	C₂×#424	—	47	1	no	—
196	C₂×#424	D₄₇	1	1	yes	characteristic
197	C₂×#405	—	47	1	no	—
198	#1946	—	47	4	no	—
199	#1945	—	47	4	no	—
200	#1733	—	47	1	no	—
201	#1733	—	47	1	no	—
202	C₂×C₄₇	—	2	1	no	—
203	C₂×C₄₇	—	2	1	no	—
204	C₂×C₄₇	—	2	2	no	—
205	C₂×C₄₇	—	2	2	no	—
206	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
207	C₂×C₄₇	#2955	1	2	yes	—
208	C₂²×M₁₆	—	47	1	no	—
209	C₂²×M₁₆	—	47	1	no	—
210	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
211	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
212	C₂×#117	—	47	1	no	—
213	C₂×#117	—	47	1	no	—
214	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
215	#430	—	94	4	no	—
216	C₂×#108	—	47	4	no	—
217	#428	—	47	4	no	—
218	#428	—	47	4	no	—
219	#427	—	47	4	no	—
220	#424	—	2	2	no	—
221	#424	—	47	2	no	—
222	#424	—	47	2	no	—
223	#424	—	94	2	no	—
224	#424	C₂×D₄₇	1	2	yes	—
225	#424	C₂×D₄₇	1	2	yes	—
226	C₂×C₄⋊C₈	—	2	2	no	—
227	C₂×C₄⋊C₈	—	94	2	no	—
228	#405	—	94	4	no	—
229	C₂×#97	—	47	2	no	—
230	C₂×C₄×C₈	—	47	2	no	—
231	#339	—	47	4	no	—
232	#339	—	47	4	no	—
233	C₄₇	#21164	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	47	2	no	—
239	C₂×M₁₆	—	47	2	no	—
240	C₂×M₁₆	—	47	4	no	—
241	C₂×M₁₆	—	47	4	no	—
242	C₂×M₁₆	—	47	2	no	—
243	C₂×M₁₆	—	94	1	no	—
244	C₂×M₁₆	—	94	2	no	—
245	C₂×M₁₆	—	94	2	no	—
246	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	47	2	no	—
251	C₂²×C₈	—	94	1	no	—
252	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
253	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
254	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
255	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
256	#117	—	2	1	no	—
257	#117	—	2	1	no	—
258	#117	—	47	4	no	—
259	#117	—	47	2	no	—
260	#117	—	47	2	no	—
261	#117	—	94	1	no	—
262	#117	—	94	2	no	—
263	#117	—	94	1	no	—
264	#117	C₄×D₄₇	1	2	yes	—
265	#117	C₂²×D₄₇	1	2	yes	—
266	C₂×C₄⋊C₄	—	47	2	no	—
267	C₂×C₄⋊C₄	—	94	1	no	—
268	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	94	1	no	—
271	C₂×C₂²⋊C₄	—	94	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	47	2	no	—
274	C₂×C₄²	—	94	1	no	—
275	#108	—	94	8	no	—
276	#107	—	47	8	no	—
277	#106	—	47	8	no	—
278	C₄⋊C₈	—	2	4	no	—
279	C₄⋊C₈	—	2	4	no	—
280	C₄⋊C₈	—	94	4	no	—
281	C₄⋊C₈	—	94	4	no	—
282	#97	—	94	4	no	—
283	C₄×C₈	—	94	4	no	—
284	C₂⁴	#10625350	1	1	yes	characteristic
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	94	2	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
290	C₂²×C₄	#10625350	1	1	yes	characteristic
291	C₂²×C₄	D₄×D₄₇	1	2	yes	—
292	C₂²×C₄	#10625352	1	2	yes	—
293	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
294	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
295	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
298	M₁₆	—	2	2	no	—
299	M₁₆	—	2	2	no	—
300	M₁₆	—	4	2	no	—
301	M₁₆	—	47	8	no	—
302	M₁₆	—	47	8	no	—
303	M₁₆	—	94	2	no	—
304	M₁₆	—	94	2	no	—
305	M₁₆	—	188	2	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	47	4	no	—
315	C₂×C₈	—	47	4	no	—
316	C₂×C₈	—	47	4	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	188	2	no	—
319	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
320	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	47	4	no	—
323	C₄⋊C₄	—	94	2	no	—
324	C₄⋊C₄	—	94	4	no	—
325	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	94	2	no	—
329	C₂²⋊C₄	—	94	4	no	—
330	C₂²⋊C₄	—	94	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	47	4	no	—
334	C₄²	—	94	2	no	—
335	C₄²	—	94	2	no	—
336	C₄²	—	94	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
339	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
340	C₂³	#13094002	1	2	yes	—
341	C₂³	#13094014	1	2	yes	—
342	C₂³	C₂×#10625350	1	1	yes	characteristic
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	94	4	no	—
346	C₂×C₄	—	94	4	no	—
347	C₂×C₄	—	188	4	no	—
348	C₂×C₄	—	188	4	no	—
349	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
350	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
351	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
352	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂×C₄	#13093989	1	2	yes	—
354	C₂×C₄	#13093989	1	2	yes	—
355	C₂×C₄	#13093996	1	2	yes	—
356	C₂×C₄	#13093996	1	2	yes	—
357	C₂×C₄	#13094002	1	2	yes	—
358	C₂×C₄	#13094014	1	2	yes	—
359	C₂×C₄	#13094022	1	2	yes	—
360	C₂×C₄	#13094022	1	2	yes	—
361	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
362	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
363	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
366	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
367	C₈	—	2	2	no	—
368	C₈	—	2	2	no	—
369	C₈	—	4	2	no	—
370	C₈	—	47	8	no	—
371	C₈	—	188	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	#15689018	1	2	yes	—
378	C₂²	#15689018	1	2	yes	—
379	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
380	C₂²	C₂×#13094002	1	1	yes	characteristic
381	C₂²	C₂×#13094014	1	1	yes	characteristic
382	C₄	—	4	4	no	—
383	C₄	—	188	4	no	—
384	C₄	—	188	4	no	—
385	C₄	#15689018	1	2	yes	—
386	C₄	#15689018	1	2	yes	—
387	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
388	C₄	C₂×#13093989	1	1	yes	characteristic
389	C₄	C₂×#13093996	1	1	yes	characteristic
390	C₄	C₂×#13094022	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	2	no	—
393	C₂	—	2	2	no	—
394	C₂	—	2	1	no	—
395	C₂	C₂×#15689018	1	1	yes	characteristic
396	C₂	#20252289	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#424	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂⁴×C₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#424	D₄₇
hypocenter	C₄₇	#21164
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ C₂×#424

Complements

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

N	H ≅ G/N	type
5. #20244138	C₂	semidirect
6. #20244133	C₂	semidirect
16. #15689166	C₄	semidirect
17. #15689163	C₄	semidirect
233. C₄₇	#21164	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689171	2
#20251977	2
C₂×#15689149	2
C₂×#15689078	2
#20244138	2
#20244133	2
#20243099	2
#20243097	2
C₂×C₄₇×#424	2
#21164	47