Subgroups — #26121769

Order 12032.

1178 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689132	C₂	1	2	yes	maximal
2	#20243127	C₂	1	1	yes	maximal, characteristic
3	#20243121	C₂	1	1	yes	maximal, characteristic
4	#20243097	C₂	1	2	yes	maximal
5	C₂×C₄₇×#519	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂×#13093983	C₂²	1	2	yes	—
8	#15689132	—	2	4	no	—
9	#15689132	C₄	1	8	yes	complemented
10	C₂×#13093948	—	2	4	no	—
11	#15688892	—	2	2	no	—
12	#15688890	—	2	2	no	—
13	#15688882	—	2	4	no	—
14	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₄₇×#519	—	2	4	no	—
16	C₄₇×#519	—	2	4	no	—
17	C₂×C₄×Q₈×C₄₇	—	2	2	no	—
18	C₂×C₄×Q₈×C₄₇	C₄	1	4	yes	complemented
19	C₂×#117×C₄₇	—	2	2	no	—
20	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#10625329	—	2	2	no	—
23	C₂×#10625329	—	2	2	no	—
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	C₂×C₄	1	4	yes	—
28	C₂²×C₄₇⋊C₈	—	2	2	no	—
29	#13093983	—	2	2	no	—
30	#13093983	—	2	2	no	—
31	#13093983	—	2	2	no	—
32	#13093983	C₂×C₄	1	4	yes	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	#13093948	—	2	16	no	—
37	C₂²×Q₈×C₄₇	—	2	1	no	—
38	C₂²×Q₈×C₄₇	—	2	2	no	—
39	C₂²×Q₈×C₄₇	—	2	2	no	—
40	C₂²×Q₈×C₄₇	—	2	1	no	—
41	C₂²×Q₈×C₄₇	—	2	1	no	—
42	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
43	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
44	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
45	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
46	C₂²×Q₈×C₄₇	Q₈	1	2	yes	—
47	C₂³×C₄×C₄₇	—	2	1	no	—
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₄×Q₈×C₄₇	—	2	16	no	—
50	C₄×Q₈×C₄₇	—	2	8	no	—
51	C₄×Q₈×C₄₇	—	2	8	no	—
52	#117×C₄₇	—	2	16	no	—
53	#117×C₄₇	—	2	2	no	—
54	#117×C₄₇	—	2	2	no	—
55	#117×C₄₇	—	2	2	no	—
56	#117×C₄₇	D₄	1	4	yes	—
57	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
62	C₂×C₄²×C₄₇	—	2	4	no	—
63	C₂×C₄²×C₄₇	—	2	1	no	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
65	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂×Q₈×C₄₇	—	2	2	no	—
67	C₂×Q₈×C₄₇	—	2	2	no	—
68	C₂×Q₈×C₄₇	—	2	2	no	—
69	C₂×Q₈×C₄₇	—	2	4	no	—
70	C₂×Q₈×C₄₇	—	2	4	no	—
71	C₂×Q₈×C₄₇	—	2	4	no	—
72	C₂×Q₈×C₄₇	—	2	4	no	—
73	C₂×Q₈×C₄₇	—	2	2	no	—
74	C₂×Q₈×C₄₇	—	2	4	no	—
75	C₂×Q₈×C₄₇	—	2	2	no	—
76	C₂×Q₈×C₄₇	—	2	4	no	—
77	C₂×Q₈×C₄₇	—	2	4	no	—
78	C₂×Q₈×C₄₇	—	2	4	no	—
79	C₂×Q₈×C₄₇	C₄²	1	4	yes	—
80	C₂×Q₈×C₄₇	C₂²⋊C₄	1	8	yes	—
81	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
82	C₂×Q₈×C₄₇	C₄⋊C₄	1	8	yes	—
83	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	#41	1	2	yes	—
101	C₂²×Dic₄₇	—	4	2	no	—
102	C₄⋊C₄×C₄₇	—	2	16	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	2	4	no	—
105	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
106	C₂²⋊C₄×C₄₇	—	2	4	no	—
107	C₂²⋊C₄×C₄₇	—	2	4	no	—
108	C₄²×C₄₇	—	2	16	no	—
109	C₄²×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	—	2	4	no	—
112	C₂²⋊Dic₄₇	—	2	4	no	—
113	C₂²⋊Dic₄₇	—	4	2	no	—
114	C₄⋊Dic₄₇	—	2	4	no	—
115	C₄⋊Dic₄₇	—	4	2	no	—
116	C₄×Dic₄₇	—	2	4	no	—
117	C₄×Dic₄₇	—	4	2	no	—
118	#10625329	—	2	4	no	—
119	#10625329	—	2	4	no	—
120	#10625329	—	4	2	no	—
121	#10625329	—	4	2	no	—
122	C₂×C₄₇⋊C₈	—	2	4	no	—
123	C₂×C₄₇⋊C₈	—	4	2	no	—
124	C₂×C₄₇⋊C₈	—	4	2	no	—
125	C₂³×C₄₇	—	4	2	no	—
126	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×C₄₇	C₄×D₄	1	2	yes	—
128	C₂³×C₄₇	#120	1	2	yes	—
129	C₂³×C₄₇	#121	1	1	yes	characteristic
130	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
131	Q₈×C₄₇	—	2	4	no	—
132	Q₈×C₄₇	—	2	4	no	—
133	Q₈×C₄₇	—	2	4	no	—
134	Q₈×C₄₇	—	2	8	no	—
135	Q₈×C₄₇	—	2	8	no	—
136	Q₈×C₄₇	#95	1	8	yes	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	8	no	—
141	C₂×C₄×C₄₇	—	2	8	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₄₇	#120	1	2	yes	—
158	C₂×C₄×C₄₇	#121	1	2	yes	—
159	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
161	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#123	1	2	yes	—
163	C₂×C₄×C₄₇	#123	1	2	yes	—
164	C₂×Dic₄₇	—	4	4	no	—
165	C₂×Dic₄₇	—	8	4	no	—
166	C₄₇⋊C₈	—	4	4	no	—
167	#10777	—	47	1	no	maximal, Sylow
168	C₂²×C₄₇	—	2	4	no	—
169	C₂²×C₄₇	—	2	2	no	—
170	C₂²×C₄₇	—	4	2	no	—
171	C₂²×C₄₇	—	4	1	no	—
172	C₂²×C₄₇	—	4	1	no	—
173	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₄₇	#379	1	1	yes	characteristic
175	C₂²×C₄₇	#380	1	1	yes	characteristic
176	C₂²×C₄₇	#385	1	2	yes	—
177	C₂²×C₄₇	#386	1	2	yes	—
178	C₄×C₄₇	—	2	8	no	—
179	C₄×C₄₇	—	4	4	no	—
180	C₄×C₄₇	—	4	4	no	—
181	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
182	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
183	C₄×C₄₇	#380	1	1	yes	characteristic
184	C₄×C₄₇	#381	1	1	yes	characteristic
185	C₄×C₄₇	#385	1	2	yes	—
186	C₄×C₄₇	#386	1	2	yes	—
187	Dic₄₇	—	8	4	no	—
188	C₂×#519	D₄₇	1	1	yes	characteristic
189	C₂×#419	—	47	2	no	—
190	#1742	—	47	1	no	—
191	#1740	—	47	1	no	—
192	#1733	—	47	2	no	—
193	C₂×C₄₇	—	2	2	no	—
194	C₂×C₄₇	—	2	1	no	—
195	C₂×C₄₇	—	2	1	no	—
196	C₂×C₄₇	—	2	2	no	—
197	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
198	C₂×C₄₇	#1796	1	2	yes	—
199	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
200	C₂²×M₁₆	—	47	2	no	—
201	#519	—	2	4	no	—
202	#519	—	2	4	no	—
203	C₂×C₄×Q₈	—	2	2	no	—
204	C₂×C₄×Q₈	Dic₄₇	1	4	yes	complemented
205	C₂×#117	—	2	2	no	—
206	C₂×#117	—	47	2	no	—
207	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
208	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
209	#419	—	47	8	no	—
210	#419	—	94	4	no	—
211	C₂×#103	—	94	4	no	—
212	#343	—	94	2	no	—
213	#342	—	94	2	no	—
214	#339	—	94	4	no	—
215	C₄₇	#10777	1	1	yes	characteristic, complemented, Sylow
216	C₂²×Q₈	—	2	2	no	—
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×Q₈	—	2	1	no	—
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	—	2	2	no	—
221	C₂²×Q₈	Dic₉₄	1	2	yes	—
222	C₂²×Q₈	C₄×D₄₇	1	4	yes	—
223	C₂²×Q₈	D₁₈₈	1	2	yes	—
224	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
225	C₂²×Q₈	C₂²⋊D₄₇	1	4	yes	—
226	C₂³×C₄	—	2	1	no	—
227	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
228	C₂×M₁₆	—	47	4	no	—
229	C₂×M₁₆	—	94	2	no	—
230	C₂×M₁₆	—	94	2	no	—
231	C₂×M₁₆	—	94	2	no	—
232	C₂×M₁₆	—	94	2	no	—
233	C₂×M₁₆	—	94	2	no	—
234	C₂²×C₈	—	94	2	no	—
235	C₄×Q₈	—	2	16	no	—
236	C₄×Q₈	—	2	8	no	—
237	C₄×Q₈	—	2	8	no	—
238	#117	—	2	16	no	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	47	4	no	—
243	#117	—	94	2	no	—
244	#117	—	94	2	no	—
245	#117	—	94	2	no	—
246	#117	C₂²⋊D₄₇	1	4	yes	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	94	2	no	—
249	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
250	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	94	2	no	—
253	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
254	C₂×C₄²	—	2	4	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	94	2	no	—
257	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
258	#103	—	94	16	no	—
259	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	C₄×Dic₄₇	1	4	yes	—
274	C₂×Q₈	Dic₄₇⋊C₄	1	8	yes	—
275	C₂×Q₈	C₄⋊Dic₄₇	1	4	yes	—
276	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	8	yes	—
277	C₂×Q₈	C₂²⋊Dic₄₇	1	4	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	188	2	no	—
285	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
286	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
288	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
289	C₂²×C₄	#10625350	1	1	yes	characteristic
290	C₂²×C₄	#10625350	1	1	yes	characteristic
291	C₂²×C₄	#10625350	1	2	yes	—
292	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
294	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
295	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
296	M₁₆	—	94	4	no	—
297	M₁₆	—	94	4	no	—
298	M₁₆	—	188	2	no	—
299	M₁₆	—	188	2	no	—
300	C₂×C₈	—	94	4	no	—
301	C₂×C₈	—	188	2	no	—
302	C₂×C₈	—	188	2	no	—
303	C₄⋊C₄	—	2	16	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	94	4	no	—
307	C₄⋊C₄	—	188	2	no	—
308	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
309	C₂²⋊C₄	—	2	4	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	94	4	no	—
312	C₂²⋊C₄	—	188	2	no	—
313	C₄²	—	2	16	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	94	4	no	—
318	C₄²	—	188	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
321	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
322	C₂³	#13093993	1	2	yes	—
323	C₂³	#13093998	1	1	yes	characteristic
324	C₂³	#13094003	1	1	yes	characteristic
325	Q₈	—	2	4	no	—
326	Q₈	—	2	4	no	—
327	Q₈	—	2	4	no	—
328	Q₈	—	2	8	no	—
329	Q₈	—	2	8	no	—
330	Q₈	C₄₇⋊#95	1	8	yes	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	376	4	no	—
341	C₂×C₄	—	188	4	no	—
342	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
343	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
344	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
345	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
346	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
347	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
348	C₂×C₄	#13093983	1	1	yes	characteristic
349	C₂×C₄	#13093983	1	1	yes	characteristic
350	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
351	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
352	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
353	C₂×C₄	#13093993	1	2	yes	—
354	C₂×C₄	#13093998	1	2	yes	—
355	C₂×C₄	#13093998	1	1	yes	characteristic
356	C₂×C₄	#13094003	1	2	yes	—
357	C₂×C₄	#13094003	1	1	yes	characteristic
358	C₂×C₄	#13094007	1	2	yes	—
359	C₂×C₄	#13094007	1	2	yes	—
360	C₈	—	188	4	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	4	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
367	C₂²	#15688979	1	1	yes	characteristic
368	C₂²	#15688983	1	1	yes	characteristic
369	C₂²	#15688996	1	2	yes	—
370	C₂²	#15689002	1	2	yes	—
371	C₄	—	2	8	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	4	no	—
374	C₄	—	376	4	no	—
375	C₄	C₂×C₄₇⋊#95	1	1	yes	characteristic
376	C₄	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
377	C₄	#15688983	1	1	yes	characteristic
378	C₄	#15688986	1	1	yes	characteristic
379	C₄	#15688996	1	2	yes	—
380	C₄	#15689002	1	2	yes	—
381	C₂	—	2	2	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	2	no	—
385	C₂	#20241611	1	1	yes	characteristic
386	C₂	#20243363	1	2	yes	—

	subgroup	G/H
center	C₂²	#15688979
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#519	C₂
socle	C₂²×C₄₇	#379
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#519	D₄₇
hypocenter	C₄₇	#10777
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#519

Complements

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

N	H ≅ G/N	type
9. #15689132	C₄	semidirect
18. C₂×C₄×Q₈×C₄₇	C₄	semidirect
204. C₂×C₄×Q₈	Dic₄₇	semidirect
215. C₄₇	#10777	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689132	2
#20243127	2
#20243121	2
#20243097	2
C₂×C₄₇×#519	2
#10777	47