Subgroups — #26219529

Order 12032.

764 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13094044	C₂	1	1	yes	maximal, characteristic
2	#20251813	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244033	C₂	1	2	yes	maximal, complemented
4	#20243984	C₂	1	2	yes	maximal, complemented
5	#20243718	C₂	1	2	yes	maximal
6	#20243662	C₂	1	2	yes	maximal, complemented
7	C₄×#13093959	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243201	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243198	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094044	C₂²	1	1	yes	characteristic
13	C₂×#13094030	C₂²	1	2	yes	—
14	C₄×#10625350	C₂²	1	1	yes	characteristic
15	C₄×#10625337	C₄	1	2	yes	complemented
16	C₄×#10625336	C₄	1	2	yes	complemented
17	C₄×#10625335	C₄	1	2	yes	complemented
18	C₄×#10625334	C₄	1	2	yes	complemented
19	C₂×#13093959	C₂²	1	2	yes	—
20	#15689159	C₂²	1	1	yes	characteristic
21	C₂×#13093951	C₂²	1	2	yes	—
22	C₂×#13093950	C₂²	1	2	yes	—
23	#15689119	C₂²	1	1	yes	characteristic
24	#15689117	C₂²	1	1	yes	characteristic
25	#15689080	—	2	2	no	—
26	#15689078	C₂²	1	2	yes	—
27	C₄×#10625329	C₂²	1	1	yes	characteristic
28	#15689075	—	2	1	no	—
29	#97×D₄₇	—	2	1	no	—
30	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
31	#15688969	C₂²	1	1	yes	characteristic
32	#15688887	C₂²	1	2	yes	—
33	#15688884	C₂²	1	2	yes	—
34	#15688882	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#433	—	2	2	no	—
39	C₄₇×#432	—	2	1	no	—
40	C₄₇×#432	—	2	1	no	—
41	C₄₇×#424	C₂²	1	2	yes	—
42	C₄₇×#408	C₂²	1	2	yes	—
43	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#10625350	C₂³	1	1	yes	characteristic
46	#13094044	—	2	4	no	—
47	C₂×#10625337	C₂×C₄	1	1	yes	characteristic
48	C₂×#10625335	C₂×C₄	1	1	yes	characteristic
49	C₂×#10625336	C₂×C₄	1	1	yes	characteristic
50	C₂×#10625334	C₂×C₄	1	1	yes	characteristic
51	#13094030	—	2	4	no	—
52	#13094030	—	2	4	no	—
53	C₂×#10625329	C₂³	1	2	yes	—
54	C₂×#10625324	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₄₇	—	2	2	no	—
58	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
59	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
60	C₄×C₂²⋊D₄₇	—	2	2	no	—
61	#13093983	C₂³	1	1	yes	characteristic
62	#13093981	—	2	1	no	—
63	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
64	C₄²×D₄₇	—	2	1	no	—
65	#13093959	—	2	4	no	—
66	#13093957	C₂×C₄	1	2	yes	—
67	#13093955	C₂×C₄	1	2	yes	—
68	#13093951	—	2	4	no	—
69	#13093950	—	2	4	no	—
70	#13093948	C₂×C₄	1	2	yes	—
71	#13093947	C₂×C₄	1	2	yes	—
72	#13093945	C₂×C₄	1	2	yes	—
73	#13093944	C₂×C₄	1	2	yes	—
74	#13093935	—	2	1	no	—
75	#13093934	—	2	2	no	—
76	C₄×C₄₇⋊C₈	—	2	1	no	—
77	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
78	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
79	C₈×Dic₄₇	—	2	2	no	—
80	C₄₇⋊#95	—	2	2	no	—
81	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
84	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
85	C₄×D₄×C₄₇	—	2	2	no	—
86	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
87	#117×C₄₇	—	2	1	no	—
88	#117×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	—	2	1	no	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	—	2	2	no	—
92	C₄⋊C₈×C₄₇	—	2	2	no	—
93	C₂²⋊C₈×C₄₇	—	2	2	no	—
94	C₂²⋊C₈×C₄₇	—	2	2	no	—
95	#97×C₄₇	—	2	1	no	—
96	#97×C₄₇	D₄	1	1	yes	characteristic
97	#97×C₄₇	D₄	1	1	yes	characteristic
98	#97×C₄₇	D₄	1	2	yes	—
99	C₄×C₈×C₄₇	—	2	1	no	—
100	#41×C₄₇	—	2	2	no	—
101	#41×C₄₇	—	2	2	no	—
102	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×D₄×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	#41	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂×C₂²⋊D₄₇	—	2	1	no	—
110	C₂²×Dic₄₇	—	2	2	no	—
111	#10625350	—	2	2	no	—
112	#10625350	#41	1	4	yes	—
113	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₄₇	—	2	1	no	—
115	C₂×C₄×D₄₇	—	2	2	no	—
116	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
117	M₁₆×C₄₇	—	2	2	no	—
118	M₁₆×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂²⋊C₄×C₄₇	—	2	1	no	—
127	C₂²⋊C₄×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	1	no	—
130	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
131	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊Dic₄₇	—	2	1	no	—
134	#10625337	—	2	2	no	—
135	#10625336	—	2	2	no	—
136	#10625335	—	2	2	no	—
137	#10625334	—	2	2	no	—
138	(C₂×D₄₇)⋊C₄	—	2	2	no	—
139	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
140	Dic₄₇⋊C₄	—	2	2	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	#10625329	—	2	2	no	—
146	#10625329	#41	1	4	yes	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
153	#10625324	—	2	8	no	—
154	C₈×D₄₇	—	2	8	no	—
155	C₂³×C₄₇	—	2	1	no	—
156	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂²×D₄₇	—	2	1	no	—
158	Q₈×C₄₇	—	2	1	no	—
159	Q₈×C₄₇	—	2	1	no	—
160	D₄×C₄₇	—	2	1	no	—
161	D₄×C₄₇	—	2	1	no	—
162	D₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	8	2	no	—
168	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
174	C₂²⋊D₄₇	—	2	4	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	4	4	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	D₁₈₈	—	2	1	no	—
180	D₁₈₈	#117	1	2	yes	—
181	C₄×D₄₇	—	2	4	no	—
182	C₄×D₄₇	—	8	2	no	—
183	Dic₉₄	—	2	1	no	—
184	Dic₉₄	#117	1	2	yes	—
185	C₈×C₄₇	—	2	2	no	—
186	C₈×C₄₇	—	2	2	no	—
187	C₈×C₄₇	—	4	2	no	—
188	C₄₇⋊C₈	—	2	1	no	—
189	C₄₇⋊C₈	—	2	1	no	—
190	C₄₇⋊C₈	—	2	2	no	—
191	C₄₇⋊C₈	—	2	4	no	—
192	#21140	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	4	2	no	—
195	C₂²×C₄₇	—	4	1	no	—
196	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₄₇	#529	1	2	yes	—
198	C₂×D₄₇	—	2	2	no	—
199	C₂×D₄₇	—	4	2	no	—
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	2	2	no	—
202	C₄×C₄₇	—	4	2	no	—
203	C₄×C₄₇	—	4	1	no	—
204	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
205	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
206	C₄×C₄₇	#525	1	2	yes	—
207	Dic₄₇	—	2	2	no	—
208	Dic₄₇	—	4	2	no	—
209	Dic₄₇	—	8	2	no	—
210	C₄×#135	—	47	1	no	—
211	#2923	D₄₇	1	1	yes	characteristic, complemented
212	#2875	—	47	1	no	—
213	#1929	—	47	2	no	—
214	#1922	—	47	2	no	—
215	#1876	—	47	2	no	—
216	#1866	—	47	2	no	—
217	C₄×#108	—	47	1	no	—
218	#1759	—	47	1	no	—
219	#1759	—	47	1	no	—
220	#1746	—	47	1	no	—
221	C₂×C₄₇	—	2	2	no	—
222	C₂×C₄₇	—	8	1	no	—
223	C₂×C₄₇	#2290	1	1	yes	characteristic
224	C₂×C₄₇	#2957	1	2	yes	—
225	D₄₇	—	4	2	no	—
226	C₂×#135	—	47	1	no	—
227	C₂×#131	—	47	2	no	—
228	C₄×#41	—	47	1	no	—
229	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
230	C₄×Q₁₆	—	47	2	no	—
231	C₄×SD₁₆	—	47	2	no	—
232	C₄×SD₁₆	—	47	2	no	—
233	C₄×D₈	—	47	2	no	—
234	#433	—	2	2	no	—
235	#432	—	2	1	no	—
236	#432	—	2	1	no	—
237	C₂×#108	—	47	2	no	—
238	#427	—	47	1	no	—
239	#424	C₂×D₄₇	1	2	yes	—
240	C₂×#104	—	47	2	no	—
241	C₂×#104	—	47	2	no	—
242	#416	—	47	1	no	—
243	#416	—	47	1	no	—
244	#408	C₂×D₄₇	1	2	yes	—
245	#405	—	47	2	no	—
246	#405	—	94	2	no	—
247	C₄×M₁₆	—	47	1	no	—
248	C₄×M₁₆	—	94	1	no	—
249	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
250	C₂×#97	—	94	1	no	—
251	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
252	C₂×C₄×C₈	—	47	1	no	—
253	#376	—	47	1	no	—
254	#341	—	47	2	no	—
255	#339	—	47	2	no	—
256	#339	—	47	2	no	—
257	#336	—	47	2	no	—
258	#336	—	47	2	no	—
259	C₄₇	#21140	1	1	yes	characteristic, complemented, Sylow
260	C₂×#41	—	47	1	no	—
261	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
262	#135	—	94	4	no	—
263	C₂×Q₁₆	—	47	1	no	—
264	C₂×SD₁₆	—	47	1	no	—
265	C₂×SD₁₆	—	47	1	no	—
266	C₂×D₈	—	47	1	no	—
267	#131	—	94	4	no	—
268	#131	—	94	4	no	—
269	C₂×M₁₆	—	47	2	no	—
270	C₂×M₁₆	—	94	2	no	—
271	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
272	C₂²×C₈	—	47	1	no	—
273	C₂²×C₈	—	47	1	no	—
274	C₂²×C₈	—	94	2	no	—
275	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
276	C₄×Q₈	—	47	2	no	—
277	C₄×Q₈	C₄×D₄₇	1	2	yes	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	47	2	no	—
280	C₄×D₄	—	94	2	no	—
281	C₄×D₄	C₄×D₄₇	1	2	yes	—
282	#117	—	2	1	no	—
283	#117	—	47	1	no	—
284	#117	—	94	1	no	—
285	#117	C₂²×D₄₇	1	1	yes	characteristic
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	47	2	no	—
288	C₂×C₄²	—	94	1	no	—
289	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
290	#108	—	94	4	no	—
291	#107	—	47	2	no	—
292	#106	—	47	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	#104	—	94	4	no	—
296	#104	—	94	4	no	—
297	#103	—	47	2	no	—
298	#103	—	47	2	no	—
299	#102	—	47	2	no	—
300	#102	—	47	2	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂²⋊C₈	—	2	2	no	—
303	#97	—	2	1	no	—
304	#97	—	94	2	no	—
305	#97	—	94	1	no	—
306	#97	C₂²⋊D₄₇	1	1	yes	characteristic
307	#97	C₂²⋊D₄₇	1	1	yes	characteristic
308	#97	C₂²⋊D₄₇	1	2	yes	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	47	2	no	—
311	C₄×C₈	—	47	2	no	—
312	C₄×C₈	—	94	2	no	—
313	C₄×C₈	—	94	1	no	—
314	#95	—	94	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	47	4	no	—
318	#41	—	94	2	no	—
319	C₂×Q₈	—	47	1	no	—
320	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	47	1	no	—
323	C₂×D₄	—	94	1	no	—
324	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	94	1	no	—
328	C₂²×C₄	—	94	2	no	—
329	C₂²×C₄	—	94	2	no	—
330	C₂²×C₄	#10625350	1	2	yes	—
331	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
332	Q₁₆	—	94	2	no	—
333	SD₁₆	—	94	2	no	—
334	SD₁₆	—	94	2	no	—
335	D₈	—	94	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	47	4	no	—
339	M₁₆	—	94	8	no	—
340	M₁₆	—	94	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	47	2	no	—
345	C₂×C₈	—	47	1	no	—
346	C₂×C₈	—	47	1	no	—
347	C₂×C₈	—	94	8	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	94	2	no	—
350	C₂×C₈	—	94	2	no	—
351	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
352	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	47	2	no	—
355	C₄⋊C₄	—	94	2	no	—
356	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	94	1	no	—
360	C₂²⋊C₄	—	94	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	94	2	no	—
364	C₄²	—	94	1	no	—
365	C₄²	—	94	2	no	—
366	C₄²	—	94	2	no	—
367	C₄²	C₂×C₄×D₄₇	1	2	yes	—
368	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
369	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
370	C₂³	—	2	1	no	—
371	C₂³	—	94	1	no	—
372	C₂³	C₂×#10625350	1	1	yes	characteristic
373	Q₈	—	2	1	no	—
374	Q₈	—	2	1	no	—
375	Q₈	—	47	2	no	—
376	Q₈	—	94	1	no	—
377	D₄	—	2	1	no	—
378	D₄	—	2	1	no	—
379	D₄	—	4	2	no	—
380	D₄	—	47	2	no	—
381	D₄	—	94	4	no	—
382	D₄	—	94	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	—	94	1	no	—
389	C₂×C₄	—	94	4	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	376	2	no	—
392	C₂×C₄	—	188	4	no	—
393	C₂×C₄	—	188	2	no	—
394	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
395	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
396	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
398	C₂×C₄	#41×D₄₇	1	2	yes	—
399	C₂×C₄	#41×D₄₇	1	2	yes	—
400	C₈	—	2	2	no	—
401	C₈	—	2	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	94	1	no	—
404	C₈	—	94	1	no	—
405	C₈	—	94	2	no	—
406	C₈	—	94	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	94	2	no	—
411	C₂²	—	188	2	no	—
412	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
413	C₂²	#15689651	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	94	2	no	—
419	C₄	—	376	2	no	—
420	C₄	—	188	2	no	—
421	C₄	#117×D₄₇	1	1	yes	characteristic
422	C₄	#15689591	1	1	yes	characteristic
423	C₄	#15689630	1	2	yes	—
424	C₂	—	2	2	no	—
425	C₂	—	8	1	no	—
426	C₂	—	188	2	no	—
427	C₂	#20245825	1	1	yes	characteristic
428	C₂	#20252303	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2923	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094044	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2923	D₄₇
hypocenter	C₄₇	#21140
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #2923

Complements

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

N	H ≅ G/N	type
2. #20251813	C₂	semidirect
3. #20244033	C₂	semidirect
4. #20243984	C₂	semidirect
6. #20243662	C₂	semidirect
7. C₄×#13093959	C₂	semidirect
8. #20243201	C₂	semidirect
9. #20243198	C₂	semidirect
10. #20243141	C₂	semidirect
11. C₄₇×#2923	C₂	semidirect
15. C₄×#10625337	C₄	semidirect
16. C₄×#10625336	C₄	semidirect
17. C₄×#10625335	C₄	semidirect
18. C₄×#10625334	C₄	semidirect
211. #2923	D₄₇	semidirect
259. C₄₇	#21140	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13094044	2
#20251813	2
#20244033	2
#20243984	2
#20243718	2
#20243662	2
C₄×#13093959	2
#20243201	2
#20243198	2
#20243141	2
C₄₇×#2923	2
#21140	47