Subgroups — C₄₇×#33842 #26073540

Order 12032.

664 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#510	C₂	1	2	yes	maximal, complemented
2	D₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3283	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2247	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2219	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#2189	C₂	1	2	yes	maximal, complemented
9	C₄₇×#2188	C₂	1	2	yes	maximal, complemented
10	C₄×SD₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₄₇	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
14	D₄×Q₈×C₄₇	—	2	1	no	—
15	C₄₇×#547	—	2	1	no	—
16	C₄₇×#510	—	2	8	no	—
17	C₂×Q₃₂×C₄₇	C₂²	1	2	yes	—
18	C₂×Q₃₂×C₄₇	C₂²	1	2	yes	—
19	C₂×Q₃₂×C₄₇	C₂²	1	2	yes	—
20	C₂×SD₃₂×C₄₇	C₂²	1	2	yes	—
21	C₂×SD₃₂×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
23	C₄₇×#494	C₂²	1	1	yes	characteristic
24	C₄₇×#494	C₂²	1	1	yes	characteristic
25	C₄₇×#467	C₂²	1	2	yes	—
26	C₄₇×#467	C₂²	1	2	yes	—
27	C₄₇×#462	—	2	1	no	—
28	C₄₇×#461	—	2	1	no	—
29	C₄₇×#452	—	2	2	no	—
30	C₄₇×#451	—	2	2	no	—
31	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#367	C₂²	1	1	yes	characteristic
35	C₄₇×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₄₇×#358	C₂²	1	1	yes	characteristic
37	C₄₇×#358	C₂²	1	2	yes	—
38	C₄₇×#358	C₂²	1	2	yes	—
39	C₄₇×#357	C₂²	1	1	yes	characteristic
40	C₄₇×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#41×C₄₇	—	2	2	no	—
43	C₂²×Q₈×C₄₇	—	2	2	no	—
44	#135×C₄₇	—	2	4	no	—
45	#135×C₄₇	—	4	2	no	—
46	C₂×Q₁₆×C₄₇	—	2	4	no	—
47	C₂×Q₁₆×C₄₇	—	2	2	no	—
48	C₂×Q₁₆×C₄₇	—	2	1	no	—
49	C₂×Q₁₆×C₄₇	—	2	1	no	—
50	C₂×Q₁₆×C₄₇	—	4	2	no	—
51	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
52	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
53	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
54	C₂×SD₁₆×C₄₇	—	2	2	no	—
55	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₄₇	—	2	1	no	—
58	C₄⋊Q₈×C₄₇	—	2	1	no	—
59	C₄⋊Q₈×C₄₇	—	4	1	no	—
60	#123×C₄₇	—	4	2	no	—
61	C₂²⋊Q₈×C₄₇	—	2	2	no	—
62	C₂²⋊Q₈×C₄₇	—	2	2	no	—
63	C₂²⋊Q₈×C₄₇	—	4	2	no	—
64	#121×C₄₇	—	4	1	no	—
65	C₄×Q₈×C₄₇	—	2	1	no	—
66	C₄×D₄×C₄₇	—	2	1	no	—
67	C₄×D₄×C₄₇	—	4	1	no	—
68	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₇	—	4	1	no	—
70	Q₃₂×C₄₇	—	2	4	no	—
71	Q₃₂×C₄₇	—	2	4	no	—
72	Q₃₂×C₄₇	—	4	2	no	—
73	SD₃₂×C₄₇	—	2	4	no	—
74	SD₃₂×C₄₇	D₄	1	4	yes	complemented
75	M₃₂×C₄₇	—	2	4	no	—
76	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
77	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
79	#107×C₄₇	C₂³	1	1	yes	characteristic
80	#107×C₄₇	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
82	#103×C₄₇	—	2	1	no	—
83	#103×C₄₇	—	2	2	no	—
84	#103×C₄₇	—	2	2	no	—
85	#102×C₄₇	—	2	1	no	—
86	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
87	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	#41×C₄₇	—	4	4	no	—
89	#41×C₄₇	—	8	2	no	—
90	C₂×Q₈×C₄₇	—	2	1	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	4	4	no	—
94	C₂×Q₈×C₄₇	—	4	2	no	—
95	C₂×Q₈×C₄₇	—	8	2	no	—
96	C₂×D₄×C₄₇	—	2	1	no	—
97	C₂×D₄×C₄₇	—	4	2	no	—
98	C₂×D₄×C₄₇	D₈	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	—	4	2	no	—
100	C₂²×C₄×C₄₇	—	4	1	no	—
101	C₂²×C₄×C₄₇	—	4	2	no	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	Q₁₆×C₄₇	—	2	2	no	—
104	Q₁₆×C₄₇	—	2	2	no	—
105	Q₁₆×C₄₇	—	2	1	no	—
106	Q₁₆×C₄₇	—	2	2	no	—
107	Q₁₆×C₄₇	—	2	2	no	—
108	Q₁₆×C₄₇	—	4	4	no	—
109	Q₁₆×C₄₇	—	8	1	no	—
110	Q₁₆×C₄₇	—	8	1	no	—
111	Q₁₆×C₄₇	C₂×D₄	1	2	yes	—
112	SD₁₆×C₄₇	—	4	4	no	—
113	D₈×C₄₇	—	2	1	no	—
114	D₈×C₄₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	4	1	no	—
123	C₄⋊C₄×C₄₇	—	4	2	no	—
124	C₄⋊C₄×C₄₇	—	4	1	no	—
125	C₄⋊C₄×C₄₇	—	4	1	no	—
126	C₄⋊C₄×C₄₇	—	4	2	no	—
127	C₄⋊C₄×C₄₇	—	4	1	no	—
128	C₄⋊C₄×C₄₇	—	4	1	no	—
129	C₄⋊C₄×C₄₇	D₈	1	1	yes	characteristic
130	C₂²⋊C₄×C₄₇	—	4	2	no	—
131	C₂²⋊C₄×C₄₇	—	4	2	no	—
132	C₂²⋊C₄×C₄₇	—	4	1	no	—
133	C₂²⋊C₄×C₄₇	D₈	1	2	yes	—
134	C₄²×C₄₇	—	4	1	no	—
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₁₆×C₄₇	—	2	2	no	—
137	C₁₆×C₄₇	—	2	1	no	—
138	C₁₆×C₄₇	C₂×D₄	1	2	yes	—
139	C₂³×C₄₇	—	4	1	no	—
140	C₂³×C₄₇	C₂×D₈	1	2	yes	—
141	Q₈×C₄₇	—	2	2	no	—
142	Q₈×C₄₇	—	4	1	no	—
143	Q₈×C₄₇	—	4	2	no	—
144	Q₈×C₄₇	—	4	2	no	—
145	Q₈×C₄₇	—	4	2	no	—
146	Q₈×C₄₇	—	4	2	no	—
147	Q₈×C₄₇	—	8	4	no	—
148	D₄×C₄₇	—	2	2	no	—
149	D₄×C₄₇	—	2	2	no	—
150	D₄×C₄₇	—	4	1	no	—
151	D₄×C₄₇	—	8	4	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	4	1	no	—
155	C₂×C₄×C₄₇	—	4	1	no	—
156	C₂×C₄×C₄₇	—	4	1	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	8	4	no	—
160	C₂×C₄×C₄₇	—	8	4	no	—
161	C₂×C₄×C₄₇	—	8	2	no	—
162	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₈×C₄₇	—	2	2	no	—
167	C₈×C₄₇	—	2	1	no	—
168	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
170	#33842	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₄₇	—	2	2	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	4	2	no	—
175	C₂²×C₄₇	—	8	1	no	—
176	C₂²×C₄₇	—	8	1	no	—
177	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
178	C₄×C₄₇	—	2	1	no	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	4	2	no	—
181	C₄×C₄₇	—	8	1	no	—
182	C₄×C₄₇	—	8	1	no	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	—	8	2	no	—
185	C₄×C₄₇	#510	1	2	yes	complemented
186	C₄×C₄₇	D₄²	1	1	yes	characteristic
187	C₄×C₄₇	#576	1	1	yes	characteristic
188	C₂×#510	C₂×C₄₇	1	2	yes	complemented
189	D₄×Q₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
190	#3283	C₂×C₄₇	1	1	yes	characteristic
191	#2247	C₂×C₄₇	1	1	yes	characteristic, complemented
192	#2219	C₂×C₄₇	1	2	yes	complemented
193	#2209	C₂×C₄₇	1	1	yes	characteristic, complemented
194	#2208	C₂×C₄₇	1	1	yes	characteristic, complemented
195	#2189	C₂×C₄₇	1	2	yes	complemented
196	#2188	C₂×C₄₇	1	2	yes	complemented
197	C₄×SD₃₂	C₂×C₄₇	1	1	yes	characteristic, complemented
198	#2169	C₂×C₄₇	1	1	yes	characteristic, complemented
199	C₂×C₄₇	—	4	2	no	—
200	C₂×C₄₇	—	8	2	no	—
201	C₂×C₄₇	D₄×D₈	1	1	yes	characteristic
202	C₂×C₄₇	C₂×#510	1	1	yes	characteristic
203	C₂×C₄₇	#3417	1	1	yes	characteristic
204	C₂×#135	C₂²×C₄₇	1	2	yes	—
205	C₂²×Q₁₆	C₂²×C₄₇	1	2	yes	—
206	D₄×Q₈	—	2	1	no	—
207	#547	—	2	1	no	—
208	#510	—	2	8	no	—
209	C₂×Q₃₂	C₂²×C₄₇	1	2	yes	—
210	C₂×Q₃₂	C₂²×C₄₇	1	2	yes	—
211	C₂×Q₃₂	C₂²×C₄₇	1	2	yes	—
212	C₂×SD₃₂	C₂²×C₄₇	1	2	yes	—
213	C₂×SD₃₂	C₂²×C₄₇	1	1	yes	characteristic
214	C₂×M₃₂	C₂²×C₄₇	1	2	yes	—
215	#494	C₂²×C₄₇	1	1	yes	characteristic
216	#494	C₂²×C₄₇	1	1	yes	characteristic
217	#467	C₂²×C₄₇	1	2	yes	—
218	#467	C₂²×C₄₇	1	2	yes	—
219	#462	—	2	1	no	—
220	#461	—	2	1	no	—
221	#452	—	2	2	no	—
222	#451	—	2	2	no	—
223	C₄×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
224	C₄×D₈	C₂²×C₄₇	1	1	yes	characteristic
225	C₈×D₄	C₂²×C₄₇	1	1	yes	characteristic
226	#367	C₂²×C₄₇	1	1	yes	characteristic
227	C₄⋊C₁₆	C₂²×C₄₇	1	1	yes	characteristic
228	#358	C₂²×C₄₇	1	1	yes	characteristic
229	#358	C₂²×C₄₇	1	2	yes	—
230	#358	C₂²×C₄₇	1	2	yes	—
231	#357	C₂²×C₄₇	1	1	yes	characteristic
232	C₂²⋊C₁₆	C₂²×C₄₇	1	2	yes	—
233	C₄×C₁₆	C₂²×C₄₇	1	1	yes	characteristic
234	C₄₇	#33842	1	1	yes	characteristic, direct product factor, Sylow
235	C₂×#41	—	2	2	no	—
236	C₂²×Q₈	—	2	2	no	—
237	#135	—	2	4	no	—
238	#135	—	4	2	no	—
239	C₂×Q₁₆	—	2	4	no	—
240	C₂×Q₁₆	—	2	2	no	—
241	C₂×Q₁₆	—	2	1	no	—
242	C₂×Q₁₆	—	2	1	no	—
243	C₂×Q₁₆	—	4	2	no	—
244	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
245	C₂×Q₁₆	C₂³×C₄₇	1	2	yes	—
246	C₂×Q₁₆	C₂³×C₄₇	1	1	yes	characteristic
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×D₈	C₂³×C₄₇	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	4	1	no	—
253	#123	—	4	2	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	C₂²⋊Q₈	—	2	2	no	—
256	C₂²⋊Q₈	—	4	2	no	—
257	#121	—	4	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	4	1	no	—
261	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
262	C₂×C₄⋊C₄	—	4	1	no	—
263	Q₃₂	—	2	4	no	—
264	Q₃₂	—	2	4	no	—
265	Q₃₂	—	4	2	no	—
266	SD₃₂	—	2	4	no	—
267	SD₃₂	D₄×C₄₇	1	4	yes	complemented
268	M₃₂	—	2	4	no	—
269	C₂×C₁₆	C₂³×C₄₇	1	1	yes	characteristic
270	C₂×C₁₆	C₂³×C₄₇	1	2	yes	—
271	C₂×C₁₆	C₂³×C₄₇	1	1	yes	characteristic
272	#107	C₂³×C₄₇	1	1	yes	characteristic
273	#107	C₂³×C₄₇	1	1	yes	characteristic
274	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
275	#103	—	2	1	no	—
276	#103	—	2	2	no	—
277	#103	—	2	2	no	—
278	#102	—	2	1	no	—
279	C₂²⋊C₈	D₄×C₄₇	1	2	yes	—
280	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
281	#41	—	4	4	no	—
282	#41	—	8	2	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	8	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	D₈×C₄₇	1	1	yes	characteristic
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	2	2	no	—
298	Q₁₆	—	2	1	no	—
299	Q₁₆	—	2	2	no	—
300	Q₁₆	—	2	2	no	—
301	Q₁₆	—	4	4	no	—
302	Q₁₆	—	8	1	no	—
303	Q₁₆	—	8	1	no	—
304	Q₁₆	C₂×D₄×C₄₇	1	2	yes	—
305	SD₁₆	—	4	4	no	—
306	D₈	—	2	1	no	—
307	D₈	C₂×D₄×C₄₇	1	2	yes	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
312	C₂×C₈	C₂⁴×C₄₇	1	1	yes	characteristic
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	D₈×C₄₇	1	1	yes	characteristic
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	D₈×C₄₇	1	2	yes	—
327	C₄²	—	4	1	no	—
328	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
329	C₁₆	—	2	2	no	—
330	C₁₆	—	2	1	no	—
331	C₁₆	C₂×D₄×C₄₇	1	2	yes	—
332	C₂³	—	4	1	no	—
333	C₂³	C₂×D₈×C₄₇	1	2	yes	—
334	Q₈	—	2	2	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	8	4	no	—
341	D₄	—	2	2	no	—
342	D₄	—	2	2	no	—
343	D₄	—	4	1	no	—
344	D₄	—	8	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	4	no	—
353	C₂×C₄	—	8	4	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	C₂×D₈×C₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
357	C₂×C₄	C₂×D₈×C₄₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
359	C₈	—	2	2	no	—
360	C₈	—	2	1	no	—
361	C₈	C₂²×D₄×C₄₇	1	1	yes	characteristic
362	C₈	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
370	C₄	—	2	1	no	—
371	C₄	—	2	2	no	—
372	C₄	—	4	2	no	—
373	C₄	—	8	1	no	—
374	C₄	—	8	1	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	2	no	—
377	C₄	C₄₇×#510	1	2	yes	complemented
378	C₄	D₄²×C₄₇	1	1	yes	characteristic
379	C₄	C₄₇×#576	1	1	yes	characteristic
380	C₂	—	4	2	no	—
381	C₂	—	8	2	no	—
382	C₂	D₄×D₈×C₄₇	1	1	yes	characteristic
383	C₂	C₂×C₄₇×#510	1	1	yes	characteristic
384	C₂	C₄₇×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₇
prime radical	C₄₇×#3283	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄×D₄×C₄₇ ◁ C₈×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#510	C₂	semidirect
2. D₄×Q₁₆×C₄₇	C₂	semidirect
4. C₄₇×#2247	C₂	semidirect
5. C₄₇×#2219	C₂	semidirect
6. C₄₇×#2209	C₂	semidirect
7. C₄₇×#2208	C₂	semidirect
8. C₄₇×#2189	C₂	semidirect
9. C₄₇×#2188	C₂	semidirect
10. C₄×SD₃₂×C₄₇	C₂	semidirect
11. C₄₇×#2169	C₂	semidirect
74. SD₃₂×C₄₇	D₄	semidirect
170. #33842	C₄₇	direct (N × H)
185. C₄×C₄₇	#510	semidirect
188. C₂×#510	C₂×C₄₇	semidirect
189. D₄×Q₁₆	C₂×C₄₇	semidirect
191. #2247	C₂×C₄₇	semidirect
192. #2219	C₂×C₄₇	semidirect
193. #2209	C₂×C₄₇	semidirect
194. #2208	C₂×C₄₇	semidirect
195. #2189	C₂×C₄₇	semidirect
196. #2188	C₂×C₄₇	semidirect
197. C₄×SD₃₂	C₂×C₄₇	semidirect
198. #2169	C₂×C₄₇	semidirect
234. C₄₇	#33842	direct (N × H)
267. SD₃₂	D₄×C₄₇	semidirect
377. C₄	C₄₇×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#510	2
D₄×Q₁₆×C₄₇	2
C₄₇×#3283	2
C₄₇×#2247	2
C₄₇×#2219	2
C₄₇×#2209	2
C₄₇×#2208	2
C₄₇×#2189	2
C₄₇×#2188	2
C₄×SD₃₂×C₄₇	2
C₄₇×#2169	2
#33842	47

Subgroups — C47×#33842 #26073540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#33842 #26073540