Subgroups — C₄₇×#15144 #26054842

Order 12032.

2214 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#393	C₂	1	4	yes	maximal, complemented
3	C₂×C₄₇×#390	C₂	1	2	yes	maximal
4	C₂×C₄₇×#390	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1439	C₂	1	4	yes	maximal, complemented
6	C₄₇×C₄⋊#95	C₂	1	2	yes	maximal, complemented
7	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
9	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₄₇	—	2	8	no	—
11	C₂×C₄⋊Q₈×C₄₇	—	2	4	no	—
12	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#393	—	2	16	no	—
21	C₄₇×#390	—	2	8	no	—
22	C₄₇×#390	—	2	4	no	—
23	C₂×#95×C₄₇	C₂²	1	8	yes	—
24	C₂×#95×C₄₇	C₂²	1	2	yes	—
25	C₂×#95×C₄₇	C₂²	1	2	yes	—
26	C₂⁵×C₄₇	C₂³	1	2	yes	—
27	C₂²×Q₈×C₄₇	—	2	8	no	—
28	C₂²×Q₈×C₄₇	—	2	4	no	—
29	C₂²×Q₈×C₄₇	—	2	8	no	—
30	C₂²×Q₈×C₄₇	—	4	4	no	—
31	C₂²×D₄×C₄₇	—	2	4	no	—
32	C₂²×D₄×C₄₇	—	2	2	no	—
33	C₂²×D₄×C₄₇	—	2	2	no	—
34	C₂²×D₄×C₄₇	—	2	4	no	—
35	C₂²×D₄×C₄₇	Q₈	1	4	yes	complemented
36	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₄⋊Q₈×C₄₇	—	2	32	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₇	D₄	1	8	yes	—
50	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
51	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
55	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
56	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
57	C₂×C₄²×C₄₇	—	2	4	no	—
58	C₂×C₄²×C₄₇	—	2	4	no	—
59	C₂×C₄²×C₄₇	—	2	4	no	—
60	C₂×C₄²×C₄₇	—	2	4	no	—
61	C₂×C₄²×C₄₇	D₄	1	4	yes	—
62	#95×C₄₇	—	2	16	no	—
63	#95×C₄₇	—	2	4	no	—
64	#95×C₄₇	D₄	1	8	yes	complemented
65	C₂⁴×C₄₇	—	2	4	no	—
66	C₂⁴×C₄₇	—	2	2	no	—
67	C₂⁴×C₄₇	—	2	4	no	—
68	C₂⁴×C₄₇	—	2	4	no	—
69	C₂⁴×C₄₇	—	2	4	no	—
70	C₂⁴×C₄₇	—	2	2	no	—
71	C₂⁴×C₄₇	—	2	4	no	—
72	C₂⁴×C₄₇	—	2	4	no	—
73	C₂⁴×C₄₇	C₂×Q₈	1	4	yes	—
74	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
75	C₂×Q₈×C₄₇	—	2	16	no	—
76	C₂×Q₈×C₄₇	—	4	32	no	—
77	C₂×Q₈×C₄₇	—	4	8	no	—
78	C₂×Q₈×C₄₇	—	4	8	no	—
79	C₂×D₄×C₄₇	—	2	8	no	—
80	C₂×D₄×C₄₇	—	2	16	no	—
81	C₂×D₄×C₄₇	—	4	4	no	—
82	C₂×D₄×C₄₇	—	4	8	no	—
83	C₂×D₄×C₄₇	—	4	4	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	8	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	8	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	4	no	—
100	C₂²×C₄×C₄₇	—	2	4	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₄₇	#41	1	4	yes	—
111	C₂²×C₄×C₄₇	#41	1	2	yes	—
112	C₂²×C₄×C₄₇	#41	1	4	yes	—
113	C₄⋊C₄×C₄₇	—	2	16	no	—
114	C₄⋊C₄×C₄₇	—	2	16	no	—
115	C₄⋊C₄×C₄₇	—	4	4	no	—
116	C₂²⋊C₄×C₄₇	—	4	32	no	—
117	C₂²⋊C₄×C₄₇	—	4	8	no	—
118	C₂²⋊C₄×C₄₇	—	4	8	no	—
119	C₄²×C₄₇	—	2	8	no	—
120	C₄²×C₄₇	—	4	8	no	—
121	C₂³×C₄₇	—	2	4	no	—
122	C₂³×C₄₇	—	2	8	no	—
123	C₂³×C₄₇	—	2	8	no	—
124	C₂³×C₄₇	—	2	8	no	—
125	C₂³×C₄₇	—	4	2	no	—
126	C₂³×C₄₇	—	4	2	no	—
127	C₂³×C₄₇	—	4	2	no	—
128	C₂³×C₄₇	—	4	4	no	—
129	C₂³×C₄₇	—	4	2	no	—
130	C₂³×C₄₇	—	4	8	no	—
131	C₂³×C₄₇	—	4	2	no	—
132	C₂³×C₄₇	—	4	2	no	—
133	C₂³×C₄₇	—	4	8	no	—
134	C₂³×C₄₇	—	4	8	no	—
135	C₂³×C₄₇	—	4	4	no	—
136	C₂³×C₄₇	—	4	8	no	—
137	C₂³×C₄₇	—	4	4	no	—
138	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
140	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
141	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
142	C₂³×C₄₇	C₂×#41	1	2	yes	—
143	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
144	C₂³×C₄₇	C₂×#41	1	2	yes	—
145	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
146	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
147	Q₈×C₄₇	—	4	32	no	—
148	D₄×C₄₇	—	4	16	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	8	no	—
154	C₂×C₄×C₄₇	—	2	8	no	—
155	C₂×C₄×C₄₇	—	2	8	no	—
156	C₂×C₄×C₄₇	—	2	8	no	—
157	C₂×C₄×C₄₇	—	2	8	no	—
158	C₂×C₄×C₄₇	—	2	16	no	—
159	C₂×C₄×C₄₇	—	2	8	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	—	4	4	no	—
162	C₂×C₄×C₄₇	—	4	4	no	—
163	C₂×C₄×C₄₇	—	4	4	no	—
164	C₂×C₄×C₄₇	—	4	8	no	—
165	C₂×C₄×C₄₇	—	4	4	no	—
166	C₂×C₄×C₄₇	—	4	4	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	8	no	—
171	C₂×C₄×C₄₇	#120	1	4	yes	—
172	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
173	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
174	C₂×C₄×C₄₇	#124	1	4	yes	—
175	C₂×C₄×C₄₇	#124	1	8	yes	—
176	C₂×C₄×C₄₇	#124	1	4	yes	—
177	C₂×C₄×C₄₇	#127	1	4	yes	—
178	#15144	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₇	—	4	4	no	—
180	C₂²×C₄₇	—	4	4	no	—
181	C₂²×C₄₇	—	4	16	no	—
182	C₂²×C₄₇	—	4	4	no	—
183	C₂²×C₄₇	—	8	2	no	—
184	C₂²×C₄₇	—	8	2	no	—
185	C₂²×C₄₇	—	8	2	no	—
186	C₂²×C₄₇	—	8	2	no	—
187	C₂²×C₄₇	—	8	8	no	—
188	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
191	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×#124	1	2	yes	—
194	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
195	C₂²×C₄₇	#532	1	4	yes	—
196	C₂²×C₄₇	#535	1	1	yes	characteristic
197	C₂²×C₄₇	#536	1	1	yes	characteristic
198	C₂²×C₄₇	#542	1	4	yes	—
199	C₂²×C₄₇	D₄²	1	4	yes	—
200	C₂²×C₄₇	#547	1	2	yes	—
201	C₂²×C₄₇	#548	1	4	yes	—
202	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
203	C₂²×C₄₇	#554	1	2	yes	—
204	C₂²×C₄₇	#555	1	2	yes	—
205	C₄×C₄₇	—	2	4	no	—
206	C₄×C₄₇	—	2	4	no	—
207	C₄×C₄₇	—	4	8	no	—
208	C₄×C₄₇	—	4	8	no	—
209	C₄×C₄₇	—	8	2	no	—
210	C₄×C₄₇	#393	1	8	yes	complemented
211	C₂²×C₄⋊Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
212	C₂×#393	C₂×C₄₇	1	4	yes	complemented
213	C₂×#390	C₂×C₄₇	1	1	yes	characteristic
214	C₂×#390	C₂×C₄₇	1	2	yes	—
215	#1439	C₂×C₄₇	1	4	yes	complemented
216	C₄⋊#95	C₂×C₄₇	1	2	yes	complemented
217	C₄×#95	C₂×C₄₇	1	1	yes	characteristic, complemented
218	C₂×C₄₇	—	8	4	no	—
219	C₂×C₄₇	C₂×#393	1	1	yes	characteristic
220	C₂×C₄₇	#2433	1	1	yes	characteristic
221	C₂×C₄₇	#2436	1	1	yes	characteristic
222	C₂×C₄₇	#2452	1	4	yes	—
223	C₂×C₄₇	#2491	1	4	yes	—
224	C₂×C₄₇	#2542	1	1	yes	characteristic
225	C₂×C₄₇	#2563	1	1	yes	characteristic
226	C₂×C₄₇	#2640	1	1	yes	characteristic
227	C₂×C₄₇	#2858	1	1	yes	characteristic
228	C₂³×Q₈	C₂²×C₄₇	1	2	yes	—
229	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	—	2	8	no	—
231	C₂×C₄⋊Q₈	—	2	4	no	—
232	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
233	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
235	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	—
238	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
239	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
240	#393	—	2	16	no	—
241	#390	—	2	8	no	—
242	#390	—	2	4	no	—
243	C₂×#95	C₂²×C₄₇	1	8	yes	—
244	C₂×#95	C₂²×C₄₇	1	2	yes	—
245	C₂×#95	C₂²×C₄₇	1	2	yes	—
246	C₄₇	#15144	1	1	yes	characteristic, direct product factor, Sylow
247	C₂⁵	C₂³×C₄₇	1	2	yes	—
248	C₂²×Q₈	—	2	8	no	—
249	C₂²×Q₈	—	2	4	no	—
250	C₂²×Q₈	—	2	8	no	—
251	C₂²×Q₈	—	4	4	no	—
252	C₂²×D₄	—	2	4	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	—	2	4	no	—
256	C₂²×D₄	Q₈×C₄₇	1	4	yes	complemented
257	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
258	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
259	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
260	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
261	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
263	C₄⋊Q₈	—	2	32	no	—
264	C₂×C₄⋊C₄	—	2	8	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	D₄×C₄₇	1	8	yes	—
271	C₂×C₂²⋊C₄	—	2	16	no	—
272	C₂×C₂²⋊C₄	—	2	4	no	—
273	C₂×C₂²⋊C₄	—	2	4	no	—
274	C₂×C₂²⋊C₄	—	2	16	no	—
275	C₂×C₂²⋊C₄	—	2	8	no	—
276	C₂×C₂²⋊C₄	—	2	8	no	—
277	C₂×C₂²⋊C₄	—	4	8	no	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	—	2	4	no	—
280	C₂×C₄²	—	2	4	no	—
281	C₂×C₄²	—	2	4	no	—
282	C₂×C₄²	D₄×C₄₇	1	4	yes	—
283	#95	—	2	16	no	—
284	#95	—	2	4	no	—
285	#95	D₄×C₄₇	1	8	yes	complemented
286	C₂⁴	—	2	4	no	—
287	C₂⁴	—	2	2	no	—
288	C₂⁴	—	2	4	no	—
289	C₂⁴	—	2	4	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	2	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	4	no	—
294	C₂⁴	C₂×Q₈×C₄₇	1	4	yes	—
295	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
296	C₂×Q₈	—	2	16	no	—
297	C₂×Q₈	—	4	32	no	—
298	C₂×Q₈	—	4	8	no	—
299	C₂×Q₈	—	4	8	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	16	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	8	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
324	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
325	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
327	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
329	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
330	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
331	C₂²×C₄	#41×C₄₇	1	4	yes	—
332	C₂²×C₄	#41×C₄₇	1	2	yes	—
333	C₂²×C₄	#41×C₄₇	1	4	yes	—
334	C₄⋊C₄	—	2	16	no	—
335	C₄⋊C₄	—	2	16	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	4	32	no	—
338	C₂²⋊C₄	—	4	8	no	—
339	C₂²⋊C₄	—	4	8	no	—
340	C₄²	—	2	8	no	—
341	C₄²	—	4	8	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	8	no	—
344	C₂³	—	2	8	no	—
345	C₂³	—	2	8	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	8	no	—
355	C₂³	—	4	8	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	8	no	—
358	C₂³	—	4	4	no	—
359	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
360	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
361	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
362	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
363	C₂³	C₂×#41×C₄₇	1	2	yes	—
364	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
365	C₂³	C₂×#41×C₄₇	1	2	yes	—
366	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
367	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
368	Q₈	—	4	32	no	—
369	D₄	—	4	16	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	16	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	#120×C₄₇	1	4	yes	—
393	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
394	C₂×C₄	C₂²⋊Q₈×C₄₇	1	8	yes	—
395	C₂×C₄	#124×C₄₇	1	4	yes	—
396	C₂×C₄	#124×C₄₇	1	8	yes	—
397	C₂×C₄	#124×C₄₇	1	4	yes	—
398	C₂×C₄	#127×C₄₇	1	4	yes	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	16	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	8	no	—
408	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
409	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
410	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
411	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
412	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
413	C₂²	C₂×#124×C₄₇	1	2	yes	—
414	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
415	C₂²	C₄₇×#532	1	4	yes	—
416	C₂²	C₄₇×#535	1	1	yes	characteristic
417	C₂²	C₄₇×#536	1	1	yes	characteristic
418	C₂²	C₄₇×#542	1	4	yes	—
419	C₂²	D₄²×C₄₇	1	4	yes	—
420	C₂²	C₄₇×#547	1	2	yes	—
421	C₂²	C₄₇×#548	1	4	yes	—
422	C₂²	D₄×Q₈×C₄₇	1	2	yes	—
423	C₂²	C₄₇×#554	1	2	yes	—
424	C₂²	C₄₇×#555	1	2	yes	—
425	C₄	—	2	4	no	—
426	C₄	—	2	4	no	—
427	C₄	—	4	8	no	—
428	C₄	—	4	8	no	—
429	C₄	—	8	2	no	—
430	C₄	C₄₇×#393	1	8	yes	complemented
431	C₂	—	8	4	no	—
432	C₂	C₂×C₄₇×#393	1	1	yes	characteristic
433	C₂	C₄₇×#2433	1	1	yes	characteristic
434	C₂	C₄₇×#2436	1	1	yes	characteristic
435	C₂	C₄₇×#2452	1	4	yes	—
436	C₂	C₄₇×#2491	1	4	yes	—
437	C₂	C₄₇×#2542	1	1	yes	characteristic
438	C₂	C₄₇×#2563	1	1	yes	characteristic
439	C₂	C₄₇×#2640	1	1	yes	characteristic
440	C₂	C₄₇×#2858	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊Q₈×C₄₇	C₂	semidirect
2. C₂×C₄₇×#393	C₂	semidirect
5. C₄₇×#1439	C₂	semidirect
6. C₄₇×C₄⋊#95	C₂	semidirect
7. C₄×#95×C₄₇	C₂	semidirect
35. C₂²×D₄×C₄₇	Q₈	semidirect
64. #95×C₄₇	D₄	semidirect
178. #15144	C₄₇	direct (N × H)
210. C₄×C₄₇	#393	semidirect
211. C₂²×C₄⋊Q₈	C₂×C₄₇	semidirect
212. C₂×#393	C₂×C₄₇	semidirect
215. #1439	C₂×C₄₇	semidirect
216. C₄⋊#95	C₂×C₄₇	semidirect
217. C₄×#95	C₂×C₄₇	semidirect
246. C₄₇	#15144	direct (N × H)
256. C₂²×D₄	Q₈×C₄₇	semidirect
285. #95	D₄×C₄₇	semidirect
430. C₄	C₄₇×#393	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₄₇	2
C₂×C₄₇×#393	2
C₂×C₄₇×#390	2
C₄₇×#1439	2
C₄₇×C₄⋊#95	2
C₄×#95×C₄₇	2
#15144	47

Subgroups — C47×#15144 #26054842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15144 #26054842