Subgroups — C₄₇×#15149 #26054847

Order 12032.

1410 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#398	C₂	1	2	yes	maximal
2	C₂×C₄₇×#389	C₂	1	2	yes	maximal
3	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1442	C₂	1	4	yes	maximal
6	C₄₇×#1441	C₂	1	2	yes	maximal
7	C₄₇×C₄⋊#95	C₂	1	2	yes	maximal
8	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#398	—	2	8	no	—
19	C₄₇×#389	—	2	8	no	—
20	C₄₇×#389	—	2	4	no	—
21	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
22	C₂×#95×C₄₇	C₂²	1	2	yes	—
23	C₂×#95×C₄₇	C₂²	1	4	yes	—
24	C₂×#95×C₄₇	C₂²	1	2	yes	—
25	C₂×#95×C₄₇	C₂²	1	2	yes	—
26	C₂×#95×C₄₇	C₂²	1	4	yes	—
27	C₂×#95×C₄₇	C₂²	1	4	yes	—
28	C₂×#95×C₄₇	C₂²	1	2	yes	—
29	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
30	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
31	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
33	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
34	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
53	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₄₇	Q₈	1	8	yes	—
56	C₂×C₄²×C₄₇	—	2	4	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	D₄	1	4	yes	—
61	#95×C₄₇	—	2	4	no	—
62	#95×C₄₇	—	2	8	no	—
63	#95×C₄₇	—	2	4	no	—
64	#95×C₄₇	—	2	4	no	—
65	#95×C₄₇	—	2	8	no	—
66	#95×C₄₇	—	2	8	no	—
67	#95×C₄₇	—	4	2	no	—
68	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	1	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	—	2	4	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×Q₈	1	8	yes	—
112	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
113	C₂²×C₄×C₄₇	#41	1	4	yes	—
114	C₂²×C₄×C₄₇	#41	1	2	yes	—
115	C₂²×C₄×C₄₇	#41	1	2	yes	—
116	C₂²×C₄×C₄₇	#41	1	4	yes	—
117	C₄⋊C₄×C₄₇	—	2	8	no	—
118	C₄⋊C₄×C₄₇	—	2	8	no	—
119	C₄⋊C₄×C₄₇	—	2	8	no	—
120	C₄⋊C₄×C₄₇	—	2	16	no	—
121	C₄⋊C₄×C₄₇	—	4	16	no	—
122	C₄⋊C₄×C₄₇	—	4	8	no	—
123	C₄⋊C₄×C₄₇	—	4	4	no	—
124	C₄²×C₄₇	—	2	8	no	—
125	C₄²×C₄₇	—	4	8	no	—
126	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
127	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
128	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
129	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
130	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
131	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
132	C₂³×C₄₇	C₂×#41	1	2	yes	—
133	C₂³×C₄₇	C₂×#41	1	2	yes	—
134	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
135	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
136	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	8	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	8	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	8	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	4	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	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	4	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	4	no	—
178	C₂×C₄×C₄₇	—	4	4	no	—
179	C₂×C₄×C₄₇	#121	1	4	yes	—
180	C₂×C₄×C₄₇	#121	1	4	yes	—
181	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
182	C₂×C₄×C₄₇	#123	1	4	yes	—
183	C₂×C₄×C₄₇	#125	1	8	yes	—
184	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
185	#15149	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
189	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
190	C₂²×C₄₇	#525	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#125	1	2	yes	—
192	C₂²×C₄₇	#529	1	2	yes	—
193	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
194	C₂²×C₄₇	#532	1	2	yes	—
195	C₂²×C₄₇	#536	1	1	yes	characteristic
196	C₂²×C₄₇	#537	1	1	yes	characteristic
197	C₂²×C₄₇	#541	1	2	yes	—
198	C₂²×C₄₇	#542	1	2	yes	—
199	C₂²×C₄₇	D₄²	1	1	yes	characteristic
200	C₂²×C₄₇	#547	1	1	yes	characteristic
201	C₂²×C₄₇	#547	1	1	yes	characteristic
202	C₂²×C₄₇	#548	1	2	yes	—
203	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
204	C₂²×C₄₇	#552	1	2	yes	—
205	C₂²×C₄₇	#554	1	2	yes	—
206	C₂²×C₄₇	#555	1	1	yes	characteristic
207	C₂²×C₄₇	#557	1	2	yes	—
208	C₂²×C₄₇	#557	1	2	yes	—
209	C₄×C₄₇	—	2	4	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	—	4	8	no	—
212	C₄×C₄₇	—	4	4	no	—
213	C₄×C₄₇	—	4	4	no	—
214	C₄×C₄₇	—	4	4	no	—
215	C₄×C₄₇	—	8	2	no	—
216	C₄×C₄₇	#398	1	8	yes	complemented
217	C₂×#398	C₂×C₄₇	1	2	yes	—
218	C₂×#389	C₂×C₄₇	1	1	yes	characteristic
219	C₂×#389	C₂×C₄₇	1	2	yes	—
220	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic
221	#1442	C₂×C₄₇	1	4	yes	—
222	#1441	C₂×C₄₇	1	2	yes	—
223	C₄⋊#95	C₂×C₄₇	1	2	yes	—
224	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic
225	C₂×C₄₇	C₂×#398	1	1	yes	characteristic
226	C₂×C₄₇	#2452	1	2	yes	—
227	C₂×C₄₇	#2453	1	2	yes	—
228	C₂×C₄₇	#2506	1	2	yes	—
229	C₂×C₄₇	#2508	1	2	yes	—
230	C₂×C₄₇	#2536	1	1	yes	characteristic
231	C₂×C₄₇	#2537	1	1	yes	characteristic
232	C₂×C₄₇	#2546	1	1	yes	characteristic
233	C₂×C₄₇	#2584	1	1	yes	characteristic
234	C₂×C₄₇	#2625	1	1	yes	characteristic
235	C₂×C₄₇	#2854	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
237	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
240	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
243	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
244	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
245	#398	—	2	8	no	—
246	#389	—	2	8	no	—
247	#389	—	2	4	no	—
248	C₄×C₄⋊C₄	—	2	4	no	—
249	C₂×#95	C₂²×C₄₇	1	2	yes	—
250	C₂×#95	C₂²×C₄₇	1	4	yes	—
251	C₂×#95	C₂²×C₄₇	1	4	yes	—
252	C₂×#95	C₂²×C₄₇	1	4	yes	—
253	C₂×#95	C₂²×C₄₇	1	2	yes	—
254	C₂×#95	C₂²×C₄₇	1	2	yes	—
255	C₂×#95	C₂²×C₄₇	1	2	yes	—
256	C₄₇	#15149	1	1	yes	characteristic, direct product factor, Sylow
257	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
258	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
259	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
260	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
261	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
262	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
263	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	4	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	8	no	—
274	C₂×C₄⋊C₄	—	2	4	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	8	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	—	2	4	no	—
280	C₂×C₄⋊C₄	—	4	4	no	—
281	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
282	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
283	C₂×C₄⋊C₄	Q₈×C₄₇	1	8	yes	—
284	C₂×C₄²	—	2	4	no	—
285	C₂×C₄²	—	2	4	no	—
286	C₂×C₄²	—	2	4	no	—
287	C₂×C₄²	—	2	4	no	—
288	C₂×C₄²	D₄×C₄₇	1	4	yes	—
289	#95	—	2	4	no	—
290	#95	—	2	8	no	—
291	#95	—	2	4	no	—
292	#95	—	2	4	no	—
293	#95	—	2	8	no	—
294	#95	—	2	8	no	—
295	#95	—	4	2	no	—
296	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
334	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
335	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
339	C₂²×C₄	C₂×Q₈×C₄₇	1	8	yes	—
340	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
341	C₂²×C₄	#41×C₄₇	1	4	yes	—
342	C₂²×C₄	#41×C₄₇	1	2	yes	—
343	C₂²×C₄	#41×C₄₇	1	2	yes	—
344	C₂²×C₄	#41×C₄₇	1	4	yes	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	16	no	—
349	C₄⋊C₄	—	4	16	no	—
350	C₄⋊C₄	—	4	8	no	—
351	C₄⋊C₄	—	4	4	no	—
352	C₄²	—	2	8	no	—
353	C₄²	—	4	8	no	—
354	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
355	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
356	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
357	C₂³	C₂²×Q₈×C₄₇	1	2	yes	—
358	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
359	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
360	C₂³	C₂×#41×C₄₇	1	2	yes	—
361	C₂³	C₂×#41×C₄₇	1	2	yes	—
362	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
363	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
364	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	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	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	#121×C₄₇	1	4	yes	—
408	C₂×C₄	#121×C₄₇	1	4	yes	—
409	C₂×C₄	C₂²⋊Q₈×C₄₇	1	8	yes	—
410	C₂×C₄	#123×C₄₇	1	4	yes	—
411	C₂×C₄	#125×C₄₇	1	8	yes	—
412	C₂×C₄	C₄⋊Q₈×C₄₇	1	4	yes	—
413	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
414	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
415	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
416	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
417	C₂²	C₄₇×#525	1	1	yes	characteristic
418	C₂²	C₂×#125×C₄₇	1	2	yes	—
419	C₂²	C₄₇×#529	1	2	yes	—
420	C₂²	C₂×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
421	C₂²	C₄₇×#532	1	2	yes	—
422	C₂²	C₄₇×#536	1	1	yes	characteristic
423	C₂²	C₄₇×#537	1	1	yes	characteristic
424	C₂²	C₄₇×#541	1	2	yes	—
425	C₂²	C₄₇×#542	1	2	yes	—
426	C₂²	D₄²×C₄₇	1	1	yes	characteristic
427	C₂²	C₄₇×#547	1	1	yes	characteristic
428	C₂²	C₄₇×#547	1	1	yes	characteristic
429	C₂²	C₄₇×#548	1	2	yes	—
430	C₂²	D₄×Q₈×C₄₇	1	2	yes	—
431	C₂²	C₄₇×#552	1	2	yes	—
432	C₂²	C₄₇×#554	1	2	yes	—
433	C₂²	C₄₇×#555	1	1	yes	characteristic
434	C₂²	C₄₇×#557	1	2	yes	—
435	C₂²	C₄₇×#557	1	2	yes	—
436	C₄	—	2	4	no	—
437	C₄	—	4	4	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	8	no	—
442	C₄	—	8	2	no	—
443	C₄	C₄₇×#398	1	8	yes	complemented
444	C₂	C₂×C₄₇×#398	1	1	yes	characteristic
445	C₂	C₄₇×#2452	1	2	yes	—
446	C₂	C₄₇×#2453	1	2	yes	—
447	C₂	C₄₇×#2506	1	2	yes	—
448	C₂	C₄₇×#2508	1	2	yes	—
449	C₂	C₄₇×#2536	1	1	yes	characteristic
450	C₂	C₄₇×#2537	1	1	yes	characteristic
451	C₂	C₄₇×#2546	1	1	yes	characteristic
452	C₂	C₄₇×#2584	1	1	yes	characteristic
453	C₂	C₄₇×#2625	1	1	yes	characteristic
454	C₂	C₄₇×#2854	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
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
185. #15149	C₄₇	direct (N × H)
216. C₄×C₄₇	#398	semidirect
256. C₄₇	#15149	direct (N × H)
443. C₄	C₄₇×#398	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#398	2
C₂×C₄₇×#389	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄₇×#1442	2
C₄₇×#1441	2
C₄₇×C₄⋊#95	2
#15149	47

Subgroups — C47×#15149 #26054847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15149 #26054847