Subgroups — C₄₇×#15134 #26054832

Order 12032.

2006 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#396	C₂	1	4	yes	maximal, complemented
2	C₂×C₄₇×#390	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#390	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#390	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₇×#384	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1439	C₂	1	4	yes	maximal, complemented
9	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
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	4	yes	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
19	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
20	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#396	—	2	16	no	—
25	C₄₇×#390	—	2	4	no	—
26	C₄₇×#390	—	2	4	no	—
27	C₄₇×#390	—	2	4	no	—
28	C₄₇×#389	—	2	4	no	—
29	C₄₇×#384	—	2	4	no	—
30	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
31	C₂×#95×C₄₇	C₂²	1	2	yes	—
32	C₂×#95×C₄₇	C₂²	1	2	yes	—
33	C₂×#95×C₄₇	C₂²	1	4	yes	—
34	C₂⁵×C₄₇	C₂³	1	2	yes	—
35	C₂²×D₄×C₄₇	—	2	2	no	—
36	C₂²×D₄×C₄₇	—	2	2	no	—
37	C₂²×D₄×C₄₇	—	2	2	no	—
38	C₂²×D₄×C₄₇	—	2	2	no	—
39	C₂²×D₄×C₄₇	—	2	2	no	—
40	C₂²×D₄×C₄₇	—	2	2	no	—
41	C₂²×D₄×C₄₇	Q₈	1	4	yes	—
42	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
49	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
65	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₄₇	D₄	1	8	yes	complemented
67	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
77	C₂×C₄²×C₄₇	—	2	2	no	—
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	—	2	2	no	—
80	C₂×C₄²×C₄₇	—	2	2	no	—
81	C₂×C₄²×C₄₇	—	2	2	no	—
82	C₂×C₄²×C₄₇	—	2	2	no	—
83	C₂×C₄²×C₄₇	—	2	2	no	—
84	C₂×C₄²×C₄₇	D₄	1	4	yes	—
85	C₂×C₄²×C₄₇	D₄	1	4	yes	—
86	#95×C₄₇	—	2	4	no	—
87	#95×C₄₇	—	2	4	no	—
88	#95×C₄₇	—	2	8	no	—
89	C₂⁴×C₄₇	—	2	4	no	—
90	C₂⁴×C₄₇	—	2	2	no	—
91	C₂⁴×C₄₇	—	2	2	no	—
92	C₂⁴×C₄₇	—	2	2	no	—
93	C₂⁴×C₄₇	—	2	4	no	—
94	C₂⁴×C₄₇	—	2	2	no	—
95	C₂⁴×C₄₇	—	2	2	no	—
96	C₂⁴×C₄₇	—	2	2	no	—
97	C₂⁴×C₄₇	—	2	4	no	—
98	C₂⁴×C₄₇	—	2	4	no	—
99	C₂⁴×C₄₇	C₂×Q₈	1	4	yes	—
100	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
101	C₂×D₄×C₄₇	—	2	8	no	—
102	C₂×D₄×C₄₇	—	2	8	no	—
103	C₂×D₄×C₄₇	—	2	8	no	—
104	C₂×D₄×C₄₇	—	4	4	no	—
105	C₂×D₄×C₄₇	—	4	4	no	—
106	C₂×D₄×C₄₇	—	4	4	no	—
107	C₂×D₄×C₄₇	—	4	4	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	4	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	2	2	no	—
126	C₂²×C₄×C₄₇	—	2	4	no	—
127	C₂²×C₄×C₄₇	—	2	2	no	—
128	C₂²×C₄×C₄₇	—	2	2	no	—
129	C₂²×C₄×C₄₇	—	2	2	no	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	4	no	—
132	C₂²×C₄×C₄₇	—	2	4	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	2	4	no	—
136	C₂²×C₄×C₄₇	—	2	2	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	4	no	—
139	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
150	C₂²×C₄×C₄₇	#41	1	4	yes	—
151	C₂²×C₄×C₄₇	#41	1	2	yes	—
152	C₂²×C₄×C₄₇	#41	1	2	yes	—
153	C₂²×C₄×C₄₇	#41	1	2	yes	—
154	C₄⋊C₄×C₄₇	—	2	8	no	—
155	C₄⋊C₄×C₄₇	—	2	16	no	—
156	C₄⋊C₄×C₄₇	—	4	16	no	—
157	C₄⋊C₄×C₄₇	—	4	4	no	—
158	C₄⋊C₄×C₄₇	—	4	4	no	—
159	C₄⋊C₄×C₄₇	—	4	8	no	—
160	C₂²⋊C₄×C₄₇	—	4	16	no	—
161	C₂²⋊C₄×C₄₇	—	4	8	no	—
162	C₂²⋊C₄×C₄₇	—	4	16	no	—
163	C₂²⋊C₄×C₄₇	—	4	8	no	—
164	C₄²×C₄₇	—	2	8	no	—
165	C₄²×C₄₇	—	2	8	no	—
166	C₄²×C₄₇	—	4	4	no	—
167	C₂³×C₄₇	—	2	4	no	—
168	C₂³×C₄₇	—	2	4	no	—
169	C₂³×C₄₇	—	2	4	no	—
170	C₂³×C₄₇	—	2	8	no	—
171	C₂³×C₄₇	—	2	8	no	—
172	C₂³×C₄₇	—	4	4	no	—
173	C₂³×C₄₇	—	4	2	no	—
174	C₂³×C₄₇	—	4	2	no	—
175	C₂³×C₄₇	—	4	2	no	—
176	C₂³×C₄₇	—	4	2	no	—
177	C₂³×C₄₇	—	4	2	no	—
178	C₂³×C₄₇	—	4	2	no	—
179	C₂³×C₄₇	—	4	4	no	—
180	C₂³×C₄₇	—	4	2	no	—
181	C₂³×C₄₇	—	4	2	no	—
182	C₂³×C₄₇	—	4	4	no	—
183	C₂³×C₄₇	—	4	4	no	—
184	C₂³×C₄₇	—	4	4	no	—
185	C₂³×C₄₇	—	4	4	no	—
186	C₂³×C₄₇	—	4	4	no	—
187	C₂³×C₄₇	—	4	4	no	—
188	C₂³×C₄₇	—	4	4	no	—
189	C₂³×C₄₇	—	4	4	no	—
190	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
191	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
192	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
194	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
195	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
196	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₂³×C₄₇	C₂×#41	1	2	yes	—
199	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
200	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
201	D₄×C₄₇	—	4	16	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	4	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	2	4	no	—
209	C₂×C₄×C₄₇	—	2	4	no	—
210	C₂×C₄×C₄₇	—	2	4	no	—
211	C₂×C₄×C₄₇	—	2	4	no	—
212	C₂×C₄×C₄₇	—	2	2	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	2	4	no	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	4	no	—
218	C₂×C₄×C₄₇	—	2	8	no	—
219	C₂×C₄×C₄₇	—	2	4	no	—
220	C₂×C₄×C₄₇	—	4	2	no	—
221	C₂×C₄×C₄₇	—	4	2	no	—
222	C₂×C₄×C₄₇	—	4	2	no	—
223	C₂×C₄×C₄₇	—	4	2	no	—
224	C₂×C₄×C₄₇	—	4	2	no	—
225	C₂×C₄×C₄₇	—	4	2	no	—
226	C₂×C₄×C₄₇	—	4	2	no	—
227	C₂×C₄×C₄₇	—	4	4	no	—
228	C₂×C₄×C₄₇	—	4	2	no	—
229	C₂×C₄×C₄₇	—	4	4	no	—
230	C₂×C₄×C₄₇	—	4	2	no	—
231	C₂×C₄×C₄₇	—	4	2	no	—
232	C₂×C₄×C₄₇	—	4	2	no	—
233	C₂×C₄×C₄₇	—	4	2	no	—
234	C₂×C₄×C₄₇	—	4	2	no	—
235	C₂×C₄×C₄₇	—	4	4	no	—
236	C₂×C₄×C₄₇	—	4	2	no	—
237	C₂×C₄×C₄₇	—	4	4	no	—
238	C₂×C₄×C₄₇	—	4	4	no	—
239	C₂×C₄×C₄₇	#121	1	8	yes	—
240	C₂×C₄×C₄₇	#121	1	4	yes	—
241	C₂×C₄×C₄₇	#121	1	4	yes	—
242	C₂×C₄×C₄₇	#121	1	4	yes	—
243	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
244	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
245	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
246	C₂×C₄×C₄₇	#126	1	4	yes	—
247	C₂×C₄×C₄₇	#127	1	4	yes	—
248	#15134	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₂²×C₄₇	—	4	4	no	—
250	C₂²×C₄₇	—	4	4	no	—
251	C₂²×C₄₇	—	4	8	no	—
252	C₂²×C₄₇	—	4	8	no	—
253	C₂²×C₄₇	—	4	4	no	—
254	C₂²×C₄₇	—	8	2	no	—
255	C₂²×C₄₇	—	8	2	no	—
256	C₂²×C₄₇	—	8	4	no	—
257	C₂²×C₄₇	—	8	4	no	—
258	C₂²×C₄₇	—	8	2	no	—
259	C₂²×C₄₇	—	8	2	no	—
260	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
261	C₂²×C₄₇	C₂×#121	1	2	yes	—
262	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
263	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
264	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
265	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
266	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
267	C₂²×C₄₇	C₂×#126	1	1	yes	characteristic
268	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
269	C₂²×C₄₇	#532	1	1	yes	characteristic
270	C₂²×C₄₇	#532	1	2	yes	—
271	C₂²×C₄₇	#535	1	1	yes	characteristic
272	C₂²×C₄₇	#536	1	1	yes	characteristic
273	C₂²×C₄₇	#537	1	2	yes	—
274	C₂²×C₄₇	#542	1	2	yes	—
275	C₂²×C₄₇	D₄²	1	2	yes	—
276	C₂²×C₄₇	#547	1	2	yes	—
277	C₂²×C₄₇	#548	1	2	yes	—
278	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
279	C₂²×C₄₇	#550	1	2	yes	—
280	C₂²×C₄₇	#553	1	2	yes	—
281	C₂²×C₄₇	#554	1	2	yes	—
282	C₂²×C₄₇	#556	1	2	yes	—
283	C₄×C₄₇	—	2	4	no	—
284	C₄×C₄₇	—	2	8	no	—
285	C₄×C₄₇	—	4	2	no	—
286	C₄×C₄₇	—	4	4	no	—
287	C₄×C₄₇	—	4	4	no	—
288	C₄×C₄₇	—	8	2	no	—
289	C₄×C₄₇	—	8	2	no	—
290	C₄×C₄₇	#396	1	8	yes	complemented
291	C₂×#396	C₂×C₄₇	1	4	yes	complemented
292	C₂×#390	C₂×C₄₇	1	1	yes	characteristic
293	C₂×#390	C₂×C₄₇	1	1	yes	characteristic
294	C₂×#390	C₂×C₄₇	1	1	yes	characteristic
295	C₂×#389	C₂×C₄₇	1	1	yes	characteristic, complemented
296	C₂×#384	C₂×C₄₇	1	1	yes	characteristic, complemented
297	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
298	#1439	C₂×C₄₇	1	4	yes	complemented
299	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic, complemented
300	C₂×C₄₇	—	8	4	no	—
301	C₂×C₄₇	C₂×#396	1	1	yes	characteristic
302	C₂×C₄₇	#2416	1	2	yes	—
303	C₂×C₄₇	#2452	1	2	yes	—
304	C₂×C₄₇	#2512	1	2	yes	—
305	C₂×C₄₇	#2538	1	2	yes	—
306	C₂×C₄₇	#2541	1	1	yes	characteristic
307	C₂×C₄₇	#2542	1	1	yes	characteristic
308	C₂×C₄₇	#2545	1	1	yes	characteristic
309	C₂×C₄₇	#2566	1	1	yes	characteristic
310	C₂×C₄₇	#2620	1	1	yes	characteristic
311	C₂×C₄₇	#2856	1	1	yes	characteristic
312	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
313	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
314	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
315	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
316	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
317	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
318	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
319	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
320	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
321	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
322	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
323	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
324	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
325	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
326	#396	—	2	16	no	—
327	#390	—	2	4	no	—
328	#390	—	2	4	no	—
329	#390	—	2	4	no	—
330	#389	—	2	4	no	—
331	#384	—	2	4	no	—
332	C₄×C₄⋊C₄	—	2	4	no	—
333	C₂×#95	C₂²×C₄₇	1	4	yes	—
334	C₂×#95	C₂²×C₄₇	1	2	yes	—
335	C₂×#95	C₂²×C₄₇	1	2	yes	—
336	C₄₇	#15134	1	1	yes	characteristic, direct product factor, Sylow
337	C₂⁵	C₂³×C₄₇	1	2	yes	—
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	—	2	2	no	—
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	Q₈×C₄₇	1	4	yes	—
345	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
346	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
347	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
348	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
349	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
352	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	4	no	—
357	C₂×C₄⋊C₄	—	2	8	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	4	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	—	2	8	no	—
364	C₂×C₄⋊C₄	—	2	8	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	4	4	no	—
368	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
369	C₂×C₄⋊C₄	D₄×C₄₇	1	8	yes	complemented
370	C₂×C₂²⋊C₄	—	2	8	no	—
371	C₂×C₂²⋊C₄	—	2	4	no	—
372	C₂×C₂²⋊C₄	—	2	8	no	—
373	C₂×C₂²⋊C₄	—	2	4	no	—
374	C₂×C₂²⋊C₄	—	2	8	no	—
375	C₂×C₂²⋊C₄	—	2	8	no	—
376	C₂×C₂²⋊C₄	—	2	8	no	—
377	C₂×C₂²⋊C₄	—	2	8	no	—
378	C₂×C₂²⋊C₄	—	4	4	no	—
379	C₂×C₂²⋊C₄	—	4	4	no	—
380	C₂×C₄²	—	2	2	no	—
381	C₂×C₄²	—	2	2	no	—
382	C₂×C₄²	—	2	2	no	—
383	C₂×C₄²	—	2	2	no	—
384	C₂×C₄²	—	2	2	no	—
385	C₂×C₄²	—	2	2	no	—
386	C₂×C₄²	—	2	2	no	—
387	C₂×C₄²	D₄×C₄₇	1	4	yes	—
388	C₂×C₄²	D₄×C₄₇	1	4	yes	—
389	#95	—	2	4	no	—
390	#95	—	2	4	no	—
391	#95	—	2	8	no	—
392	C₂⁴	—	2	4	no	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	—	2	4	no	—
402	C₂⁴	C₂×Q₈×C₄₇	1	4	yes	—
403	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	8	no	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
444	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
445	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
446	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
447	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
449	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
450	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
451	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
452	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
453	C₂²×C₄	#41×C₄₇	1	4	yes	—
454	C₂²×C₄	#41×C₄₇	1	2	yes	—
455	C₂²×C₄	#41×C₄₇	1	2	yes	—
456	C₂²×C₄	#41×C₄₇	1	2	yes	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	16	no	—
459	C₄⋊C₄	—	4	16	no	—
460	C₄⋊C₄	—	4	4	no	—
461	C₄⋊C₄	—	4	4	no	—
462	C₄⋊C₄	—	4	8	no	—
463	C₂²⋊C₄	—	4	16	no	—
464	C₂²⋊C₄	—	4	8	no	—
465	C₂²⋊C₄	—	4	16	no	—
466	C₂²⋊C₄	—	4	8	no	—
467	C₄²	—	2	8	no	—
468	C₄²	—	2	8	no	—
469	C₄²	—	4	4	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	8	no	—
474	C₂³	—	2	8	no	—
475	C₂³	—	4	4	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	4	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	4	4	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	4	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	4	4	no	—
493	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
494	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
495	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
496	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
497	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
498	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
499	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
500	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
501	C₂³	C₂×#41×C₄₇	1	2	yes	—
502	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
503	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
504	D₄	—	4	16	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	#121×C₄₇	1	8	yes	—
543	C₂×C₄	#121×C₄₇	1	4	yes	—
544	C₂×C₄	#121×C₄₇	1	4	yes	—
545	C₂×C₄	#121×C₄₇	1	4	yes	—
546	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
547	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
548	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
549	C₂×C₄	#126×C₄₇	1	4	yes	—
550	C₂×C₄	#127×C₄₇	1	4	yes	—
551	C₂²	—	4	8	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	8	no	—
556	C₂²	—	8	2	no	—
557	C₂²	—	8	2	no	—
558	C₂²	—	8	2	no	—
559	C₂²	—	8	2	no	—
560	C₂²	—	8	4	no	—
561	C₂²	—	8	4	no	—
562	C₂²	C₂×#121×C₄₇	1	2	yes	—
563	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
564	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
565	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
566	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
567	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
568	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
569	C₂²	C₂×#126×C₄₇	1	1	yes	characteristic
570	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
571	C₂²	C₄₇×#532	1	1	yes	characteristic
572	C₂²	C₄₇×#532	1	2	yes	—
573	C₂²	C₄₇×#535	1	1	yes	characteristic
574	C₂²	C₄₇×#536	1	1	yes	characteristic
575	C₂²	C₄₇×#537	1	2	yes	—
576	C₂²	C₄₇×#542	1	2	yes	—
577	C₂²	D₄²×C₄₇	1	2	yes	—
578	C₂²	C₄₇×#547	1	2	yes	—
579	C₂²	C₄₇×#548	1	2	yes	—
580	C₂²	D₄×Q₈×C₄₇	1	2	yes	—
581	C₂²	C₄₇×#550	1	2	yes	—
582	C₂²	C₄₇×#553	1	2	yes	—
583	C₂²	C₄₇×#554	1	2	yes	—
584	C₂²	C₄₇×#556	1	2	yes	—
585	C₄	—	2	4	no	—
586	C₄	—	2	8	no	—
587	C₄	—	4	4	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	4	no	—
590	C₄	—	8	2	no	—
591	C₄	—	8	2	no	—
592	C₄	C₄₇×#396	1	8	yes	complemented
593	C₂	—	8	4	no	—
594	C₂	C₂×C₄₇×#396	1	1	yes	characteristic
595	C₂	C₄₇×#2416	1	2	yes	—
596	C₂	C₄₇×#2452	1	2	yes	—
597	C₂	C₄₇×#2512	1	2	yes	—
598	C₂	C₄₇×#2538	1	2	yes	—
599	C₂	C₄₇×#2541	1	1	yes	characteristic
600	C₂	C₄₇×#2542	1	1	yes	characteristic
601	C₂	C₄₇×#2545	1	1	yes	characteristic
602	C₂	C₄₇×#2566	1	1	yes	characteristic
603	C₂	C₄₇×#2620	1	1	yes	characteristic
604	C₂	C₄₇×#2856	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. C₂×C₄₇×#396	C₂	semidirect
5. C₂×C₄₇×#389	C₂	semidirect
6. C₂×C₄₇×#384	C₂	semidirect
7. C₂×C₄×C₄⋊C₄×C₄₇	C₂	semidirect
8. C₄₇×#1439	C₂	semidirect
9. C₄₇×C₄⋊#95	C₂	semidirect
66. C₂×C₄⋊C₄×C₄₇	D₄	semidirect
248. #15134	C₄₇	direct (N × H)
290. C₄×C₄₇	#396	semidirect
291. C₂×#396	C₂×C₄₇	semidirect
295. C₂×#389	C₂×C₄₇	semidirect
296. C₂×#384	C₂×C₄₇	semidirect
297. C₂×C₄×C₄⋊C₄	C₂×C₄₇	semidirect
298. #1439	C₂×C₄₇	semidirect
299. C₄⋊#95	C₂×C₄₇	semidirect
336. C₄₇	#15134	direct (N × H)
369. C₂×C₄⋊C₄	D₄×C₄₇	semidirect
592. C₄	C₄₇×#396	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#396	2
C₂×C₄₇×#390	2
C₂×C₄₇×#389	2
C₂×C₄₇×#384	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄₇×#1439	2
C₄₇×C₄⋊#95	2
#15134	47

Subgroups — C47×#15134 #26054832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15134 #26054832