Subgroups — #26188301

Order 12032.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253947	C₂	1	1	yes	maximal, characteristic
2	#20252489	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252454	C₂	1	1	yes	maximal, characteristic
4	#20242292	C₂	1	2	yes	maximal, complemented
5	#20242233	C₂	1	2	yes	maximal, complemented
6	#20242226	C₂	1	2	yes	maximal, complemented
7	#20242202	C₂	1	2	yes	maximal, complemented
8	#20242136	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241810	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241806	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689680	C₂²	1	1	yes	characteristic
13	#15689673	C₂²	1	1	yes	characteristic
14	#15689521	C₄	1	1	yes	characteristic
15	#15689496	C₄	1	1	yes	characteristic
16	#15689474	C₄	1	1	yes	characteristic
17	#15689470	C₄	1	1	yes	characteristic
18	#15689352	C₄	1	2	yes	—
19	#15689352	C₄	1	2	yes	—
20	#15689253	C₂²	1	2	yes	—
21	#15689250	—	2	1	no	—
22	C₈×Dic₉₄	C₂²	1	2	yes	—
23	#15689247	—	2	1	no	—
24	C₄×#10625325	C₂²	1	2	yes	—
25	C₄×#10625325	C₂²	1	2	yes	—
26	#15689202	C₂²	1	2	yes	—
27	#15689200	—	2	1	no	—
28	C₈×D₁₈₈	C₂²	1	2	yes	—
29	#15689188	—	2	1	no	—
30	#15689181	—	2	2	no	—
31	#15689176	C₂²	1	1	yes	characteristic
32	#15689176	C₂²	1	1	yes	characteristic
33	#15689088	—	2	2	no	—
34	#15688876	C₂²	1	1	yes	characteristic
35	#15688876	C₂²	1	1	yes	characteristic
36	#15688874	C₂²	1	1	yes	characteristic
37	#15688874	C₂²	1	1	yes	characteristic
38	#15688855	C₂²	1	2	yes	—
39	#15688855	C₂²	1	2	yes	—
40	#15688852	C₂²	1	2	yes	—
41	#15688852	C₂²	1	2	yes	—
42	C₄₇×#431	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#322	C₂²	1	2	yes	—
46	C₄₇×#322	C₂²	1	2	yes	—
47	C₂×#10625350	—	2	1	no	—
48	C₂×#10625325	C₂×C₄	1	2	yes	—
49	C₂×#10625325	C₂×C₄	1	2	yes	—
50	C₂×#10625324	—	2	2	no	—
51	C₂×C₈×D₄₇	—	2	2	no	—
52	#13094024	C₂×C₄	1	1	yes	characteristic
53	#13094024	C₂×C₄	1	1	yes	characteristic
54	#13094024	C₂×C₄	1	1	yes	characteristic
55	#13094021	C₂×C₄	1	1	yes	characteristic
56	#13094016	—	2	1	no	—
57	#13094012	—	2	1	no	—
58	#13094003	—	2	1	no	—
59	#13094003	C₂×C₄	1	2	yes	—
60	#13093998	—	2	1	no	—
61	#13093998	C₂×C₄	1	2	yes	—
62	C₄×Dic₉₄	—	2	1	no	—
63	C₄×Dic₉₄	C₂³	1	2	yes	—
64	C₄×D₁₈₈	—	2	1	no	—
65	C₄×D₁₈₈	C₂³	1	2	yes	—
66	#13093983	—	2	1	no	—
67	#13093956	C₂×C₄	1	2	yes	—
68	#13093956	C₂×C₄	1	2	yes	—
69	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
70	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
71	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
72	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
73	Dic₄₇⋊C₈	—	2	2	no	—
74	Dic₄₇⋊C₈	—	2	2	no	—
75	#13093949	C₂×C₄	1	2	yes	—
76	#13093949	C₂×C₄	1	2	yes	—
77	#13093946	C₂×C₄	1	2	yes	—
78	#13093946	C₂×C₄	1	2	yes	—
79	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
80	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
81	(C₂×D₄₇)⋊C₈	—	2	2	no	—
82	(C₂×D₄₇)⋊C₈	—	2	2	no	—
83	#13093934	—	2	2	no	—
84	C₄×C₄₇⋊C₈	—	2	1	no	—
85	C₄×C₄₇⋊C₈	—	2	1	no	—
86	C₈×Dic₄₇	—	2	2	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
93	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
94	#97×C₄₇	—	2	1	no	—
95	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
97	C₄×C₈×C₄₇	C₂³	1	2	yes	—
98	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
104	C₂×C₂²⋊D₄₇	—	2	2	no	—
105	#10625350	—	8	1	no	—
106	#10625350	—	8	1	no	—
107	C₂×D₁₈₈	—	2	1	no	—
108	C₂×D₁₈₈	—	2	1	no	—
109	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₄₇	—	2	2	no	—
111	C₂×Dic₉₄	—	2	1	no	—
112	C₂×Dic₉₄	—	2	1	no	—
113	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
114	M₁₆×C₄₇	—	4	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	4	1	no	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
124	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₇	#41	1	1	yes	characteristic
127	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂²⋊Dic₄₇	—	2	2	no	—
129	(C₂×D₄₇)⋊C₄	—	2	2	no	—
130	(C₂×D₄₇)⋊C₄	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	1	no	—
132	C₄⋊Dic₄₇	—	2	1	no	—
133	C₄⋊Dic₄₇	—	2	1	no	—
134	C₄⋊Dic₄₇	—	2	1	no	—
135	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
136	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
137	Dic₄₇⋊C₄	—	2	2	no	—
138	Dic₄₇⋊C₄	—	2	2	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	#10625325	—	2	4	no	—
145	#10625325	—	4	2	no	—
146	#10625324	—	8	2	no	—
147	C₈×D₄₇	—	8	2	no	—
148	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
149	C₂²×D₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂²⋊D₄₇	—	8	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	D₁₈₈	—	2	2	no	—
166	D₁₈₈	—	2	2	no	—
167	D₁₈₈	—	4	2	no	—
168	D₁₈₈	—	8	1	no	—
169	C₄×D₄₇	—	4	2	no	—
170	C₄×D₄₇	—	4	2	no	—
171	Dic₉₄	—	2	2	no	—
172	Dic₉₄	—	2	2	no	—
173	Dic₉₄	—	4	2	no	—
174	Dic₉₄	—	8	1	no	—
175	C₈×C₄₇	—	2	1	no	—
176	C₈×C₄₇	—	2	1	no	—
177	C₈×C₄₇	—	2	1	no	—
178	C₈×C₄₇	—	2	2	no	—
179	C₈×C₄₇	—	2	2	no	—
180	C₈×C₄₇	—	4	2	no	—
181	C₈×C₄₇	#131	1	2	yes	—
182	C₄₇⋊C₈	—	4	1	no	—
183	C₄₇⋊C₈	—	4	1	no	—
184	C₄₇⋊C₈	—	4	1	no	—
185	C₄₇⋊C₈	—	4	1	no	—
186	#18089	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂×D₄₇	—	4	2	no	—
192	C₂×D₄₇	—	4	2	no	—
193	C₂×D₄₇	—	4	2	no	—
194	C₄×C₄₇	—	2	1	no	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	#444	1	2	yes	—
198	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
199	C₄×C₄₇	#568	1	1	yes	characteristic
200	C₄×C₄₇	#577	1	1	yes	characteristic
201	C₄×C₄₇	#577	1	1	yes	characteristic
202	Dic₄₇	—	4	2	no	—
203	Dic₄₇	—	4	2	no	—
204	Dic₄₇	—	4	2	no	—
205	#3167	—	47	1	no	—
206	#2986	—	47	1	no	—
207	#2979	—	47	1	no	—
208	#1592	—	47	2	no	—
209	#1583	—	47	2	no	—
210	#1582	—	47	2	no	—
211	SD₁₆⋊C₈	—	47	2	no	—
212	#1564	—	47	1	no	—
213	#1485	—	47	1	no	—
214	#1484	—	47	1	no	—
215	#1451	D₄₇	1	1	yes	characteristic, complemented
216	C₂×C₄₇	—	4	1	no	—
217	C₂×C₄₇	#2935	1	1	yes	characteristic
218	C₂×C₄₇	#2949	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
220	D₄₇	—	8	2	no	—
221	#533	—	47	1	no	—
222	#532	—	47	1	no	—
223	#498	—	47	1	no	—
224	#492	—	47	1	no	—
225	#487	—	47	1	no	—
226	#486	—	47	1	no	—
227	#465	—	47	2	no	—
228	#465	—	47	2	no	—
229	#446	—	47	2	no	—
230	#446	—	94	1	no	—
231	C₈×Q₈	—	47	2	no	—
232	C₈×Q₈	—	94	1	no	—
233	C₄×SD₁₆	—	47	2	no	—
234	C₄×SD₁₆	—	47	2	no	—
235	#436	—	47	2	no	—
236	#436	—	94	1	no	—
237	C₈×D₄	—	47	2	no	—
238	C₈×D₄	—	94	1	no	—
239	#433	—	94	2	no	—
240	#431	—	47	1	no	—
241	#431	—	47	1	no	—
242	#431	C₂×D₄₇	1	1	yes	characteristic
243	#408	—	94	2	no	—
244	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
246	#335	—	47	1	no	—
247	#335	—	47	1	no	—
248	#334	—	47	1	no	—
249	#334	—	47	1	no	—
250	Q₈⋊C₈	—	47	2	no	—
251	Q₈⋊C₈	—	47	2	no	—
252	D₄⋊C₈	—	47	2	no	—
253	D₄⋊C₈	—	47	2	no	—
254	#322	C₂×D₄₇	1	2	yes	—
255	#322	C₂×D₄₇	1	2	yes	—
256	C₄₇	#18089	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	94	1	no	—
258	C₂×SD₁₆	—	47	2	no	—
259	C₂×SD₁₆	—	47	2	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	94	2	no	—
262	C₂²×C₈	—	94	2	no	—
263	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
265	C₄⋊Q₈	—	47	1	no	—
266	C₄⋊Q₈	—	47	1	no	—
267	C₄⋊Q₈	—	47	1	no	—
268	#127	—	47	1	no	—
269	#125	—	94	1	no	—
270	#124	—	94	1	no	—
271	C₂²⋊Q₈	—	47	2	no	—
272	C₂²⋊Q₈	—	94	1	no	—
273	#121	—	47	2	no	—
274	#121	—	94	1	no	—
275	C₄×Q₈	—	47	2	no	—
276	C₄×Q₈	—	94	1	no	—
277	C₄×D₄	—	47	2	no	—
278	C₄×D₄	—	94	1	no	—
279	#117	—	94	1	no	—
280	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
281	#106	—	47	2	no	—
282	#106	—	47	2	no	—
283	C₄⋊C₈	—	47	1	no	—
284	C₄⋊C₈	—	47	1	no	—
285	C₄⋊C₈	—	47	1	no	—
286	C₄⋊C₈	—	47	1	no	—
287	C₄⋊C₈	—	94	2	no	—
288	C₄⋊C₈	—	94	2	no	—
289	C₄⋊C₈	D₁₈₈	1	1	yes	characteristic
290	C₄⋊C₈	D₁₈₈	1	1	yes	characteristic
291	#103	—	47	2	no	—
292	#103	—	47	2	no	—
293	#102	—	47	2	no	—
294	#102	—	47	2	no	—
295	C₂²⋊C₈	—	94	1	no	—
296	C₂²⋊C₈	—	94	1	no	—
297	C₂²⋊C₈	—	94	2	no	—
298	C₂²⋊C₈	—	94	2	no	—
299	C₂²⋊C₈	D₁₈₈	1	2	yes	—
300	#97	—	2	1	no	—
301	#97	—	94	2	no	—
302	C₄×C₈	—	94	2	no	—
303	C₄×C₈	—	94	1	no	—
304	C₄×C₈	—	94	1	no	—
305	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
306	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₄₇	1	2	yes	—
308	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₄₇	1	2	yes	—
311	#41	—	376	1	no	—
312	#41	—	376	1	no	—
313	C₂×Q₈	—	47	2	no	—
314	C₂×Q₈	—	94	1	no	—
315	C₂×Q₈	—	94	1	no	—
316	C₂×D₄	—	47	2	no	—
317	C₂×D₄	—	94	2	no	—
318	C₂×D₄	—	94	1	no	—
319	C₂×D₄	—	94	1	no	—
320	C₂²×C₄	—	94	2	no	—
321	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
323	C₂²×C₄	#10625350	1	1	yes	characteristic
324	SD₁₆	—	94	4	no	—
325	SD₁₆	—	188	2	no	—
326	M₁₆	—	4	2	no	—
327	M₁₆	—	376	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	94	1	no	—
332	C₂×C₈	—	94	1	no	—
333	C₂×C₈	—	94	1	no	—
334	C₂×C₈	—	94	1	no	—
335	C₂×C₈	—	376	2	no	—
336	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
337	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
338	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
339	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
340	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
341	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
342	C₄⋊C₄	—	47	2	no	—
343	C₄⋊C₄	—	47	2	no	—
344	C₄⋊C₄	—	94	2	no	—
345	C₄⋊C₄	—	94	1	no	—
346	C₄⋊C₄	—	94	1	no	—
347	C₄⋊C₄	—	94	1	no	—
348	C₄⋊C₄	—	94	1	no	—
349	C₄⋊C₄	—	94	2	no	—
350	C₂²⋊C₄	—	94	2	no	—
351	C₂²⋊C₄	—	94	2	no	—
352	C₂²⋊C₄	—	94	2	no	—
353	C₄²	—	94	2	no	—
354	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
355	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
356	C₄²	#10625350	1	1	yes	characteristic
357	C₄²	C₂³×D₄₇	1	1	yes	characteristic
358	C₂³	—	94	2	no	—
359	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
360	Q₈	—	94	2	no	—
361	Q₈	—	94	2	no	—
362	Q₈	—	376	1	no	—
363	Q₈	—	188	2	no	—
364	D₄	—	94	2	no	—
365	D₄	—	94	2	no	—
366	D₄	—	376	1	no	—
367	D₄	—	376	2	no	—
368	D₄	—	188	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	—	94	2	no	—
376	C₂×C₄	—	94	2	no	—
377	C₂×C₄	—	188	2	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
380	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
381	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
384	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	2	2	no	—
389	C₈	—	2	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	188	1	no	—
392	C₈	—	188	1	no	—
393	C₈	—	188	1	no	—
394	C₈	—	188	1	no	—
395	C₈	#13094032	1	2	yes	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	188	2	no	—
400	C₂²	—	188	2	no	—
401	C₂²	—	188	2	no	—
402	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	188	2	no	—
407	C₄	—	188	2	no	—
408	C₄	—	188	2	no	—
409	C₄	#15689246	1	2	yes	—
410	C₄	C₂×#13094032	1	1	yes	characteristic
411	C₄	#15689889	1	1	yes	characteristic
412	C₄	#15689935	1	1	yes	characteristic
413	C₄	#15689935	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	376	2	no	—
416	C₂	#20252134	1	1	yes	characteristic
417	C₂	#20252249	1	1	yes	characteristic
418	C₂	C₂×#15689246	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1451	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#15689673	C₂²
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1451	D₄₇
hypocenter	C₄₇	#18089
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1451

Complements

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

N	H ≅ G/N	type
2. #20252489	C₂	semidirect
4. #20242292	C₂	semidirect
5. #20242233	C₂	semidirect
6. #20242226	C₂	semidirect
7. #20242202	C₂	semidirect
8. #20242136	C₂	semidirect
9. #20241810	C₂	semidirect
11. C₄₇×#1451	C₂	semidirect
215. #1451	D₄₇	semidirect
256. C₄₇	#18089	semidirect

Maximal subgroups

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

subgroup	index
#20253947	2
#20252489	2
#20252454	2
#20242292	2
#20242233	2
#20242226	2
#20242202	2
#20242136	2
#20241810	2
#20241806	2
C₄₇×#1451	2
#18089	47