Subgroups — C₂×C₄₇×#2555 #26074520

Order 12032.

4110 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₄₇	C₂	1	2	yes	maximal, complemented
2	C₂²×#121×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2555	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₇×#395	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#394	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₇×#392	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₇×#390	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#388	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₇×#386	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	2	yes	maximal, complemented
11	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
13	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
14	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
17	C₂×#124×C₄₇	—	2	16	no	—
18	C₂×#124×C₄₇	C₂²	1	16	yes	complemented
19	C₂×#121×C₄₇	—	2	16	no	—
20	C₂×#121×C₄₇	C₂²	1	16	yes	complemented
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
30	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#395	C₂²	1	8	yes	complemented
33	C₄₇×#394	C₂²	1	8	yes	complemented
34	C₄₇×#392	C₂²	1	16	yes	complemented
35	C₄₇×#390	C₂²	1	8	yes	complemented
36	C₄₇×#388	C₂²	1	16	yes	complemented
37	C₄₇×#386	C₂²	1	16	yes	complemented
38	C₄×C₂²⋊C₄×C₄₇	C₂²	1	16	yes	complemented
39	C₂×#95×C₄₇	C₂²	1	2	yes	—
40	C₂×#95×C₄₇	C₂²	1	2	yes	—
41	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
43	C₂⁵×C₄₇	C₂³	1	2	yes	—
44	C₂⁵×C₄₇	C₂³	1	2	yes	—
45	C₂²×Q₈×C₄₇	—	2	8	no	—
46	C₂²×Q₈×C₄₇	—	4	2	no	—
47	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
48	C₂²×D₄×C₄₇	—	2	8	no	—
49	C₂²×D₄×C₄₇	—	2	8	no	—
50	C₂²×D₄×C₄₇	—	2	8	no	—
51	C₂²×D₄×C₄₇	—	2	8	no	—
52	C₂²×D₄×C₄₇	—	2	4	no	—
53	C₂²×D₄×C₄₇	—	2	8	no	—
54	C₂²×D₄×C₄₇	—	4	2	no	—
55	C₂²×D₄×C₄₇	—	4	2	no	—
56	C₂²×D₄×C₄₇	—	4	4	no	—
57	C₂²×D₄×C₄₇	—	4	4	no	—
58	C₂²×D₄×C₄₇	—	4	2	no	—
59	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
60	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
61	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
62	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
63	C₂³×C₄×C₄₇	—	2	8	no	—
64	C₂³×C₄×C₄₇	—	2	8	no	—
65	C₂³×C₄×C₄₇	—	4	4	no	—
66	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
70	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
71	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
72	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
74	#124×C₄₇	—	2	64	no	—
75	#121×C₄₇	—	2	64	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
77	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
82	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
84	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
85	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₄₇	D₄	1	16	yes	complemented
87	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
91	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
93	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
94	C₂×C₄²×C₄₇	—	2	8	no	—
95	C₂×C₄²×C₄₇	—	4	2	no	—
96	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
97	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
98	#95×C₄₇	C₂³	1	8	yes	—
99	#95×C₄₇	C₂³	1	8	yes	—
100	#95×C₄₇	C₂³	1	4	yes	—
101	#95×C₄₇	C₂³	1	4	yes	—
102	C₂⁴×C₄₇	—	2	4	no	—
103	C₂⁴×C₄₇	—	2	4	no	—
104	C₂⁴×C₄₇	—	2	4	no	—
105	C₂⁴×C₄₇	—	2	4	no	—
106	C₂⁴×C₄₇	—	2	4	no	—
107	C₂⁴×C₄₇	—	2	4	no	—
108	C₂⁴×C₄₇	—	2	4	no	—
109	C₂⁴×C₄₇	—	2	4	no	—
110	C₂⁴×C₄₇	—	2	4	no	—
111	C₂⁴×C₄₇	—	2	4	no	—
112	C₂⁴×C₄₇	—	2	4	no	—
113	C₂⁴×C₄₇	—	2	4	no	—
114	C₂⁴×C₄₇	—	2	4	no	—
115	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
116	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
117	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
118	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
119	C₂×Q₈×C₄₇	—	2	16	no	—
120	C₂×Q₈×C₄₇	—	4	4	no	—
121	C₂×Q₈×C₄₇	—	4	16	no	—
122	C₂×D₄×C₄₇	—	2	16	no	—
123	C₂×D₄×C₄₇	—	2	16	no	—
124	C₂×D₄×C₄₇	—	2	16	no	—
125	C₂×D₄×C₄₇	—	2	16	no	—
126	C₂×D₄×C₄₇	—	2	8	no	—
127	C₂×D₄×C₄₇	—	2	16	no	—
128	C₂×D₄×C₄₇	—	4	4	no	—
129	C₂×D₄×C₄₇	—	4	4	no	—
130	C₂×D₄×C₄₇	—	4	8	no	—
131	C₂×D₄×C₄₇	—	4	8	no	—
132	C₂×D₄×C₄₇	—	4	4	no	—
133	C₂×D₄×C₄₇	—	4	32	no	—
134	C₂×D₄×C₄₇	—	4	32	no	—
135	C₂×D₄×C₄₇	—	4	16	no	—
136	C₂×D₄×C₄₇	—	4	16	no	—
137	C₂²×C₄×C₄₇	—	2	4	no	—
138	C₂²×C₄×C₄₇	—	2	4	no	—
139	C₂²×C₄×C₄₇	—	2	4	no	—
140	C₂²×C₄×C₄₇	—	2	4	no	—
141	C₂²×C₄×C₄₇	—	2	2	no	—
142	C₂²×C₄×C₄₇	—	2	2	no	—
143	C₂²×C₄×C₄₇	—	2	4	no	—
144	C₂²×C₄×C₄₇	—	2	4	no	—
145	C₂²×C₄×C₄₇	—	2	4	no	—
146	C₂²×C₄×C₄₇	—	2	4	no	—
147	C₂²×C₄×C₄₇	—	2	4	no	—
148	C₂²×C₄×C₄₇	—	2	4	no	—
149	C₂²×C₄×C₄₇	—	2	4	no	—
150	C₂²×C₄×C₄₇	—	2	2	no	—
151	C₂²×C₄×C₄₇	—	2	2	no	—
152	C₂²×C₄×C₄₇	—	2	16	no	—
153	C₂²×C₄×C₄₇	—	2	16	no	—
154	C₂²×C₄×C₄₇	—	4	8	no	—
155	C₂²×C₄×C₄₇	—	4	32	no	—
156	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
157	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
158	C₂²×C₄×C₄₇	#41	1	4	yes	—
159	C₂²×C₄×C₄₇	#41	1	8	yes	—
160	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
167	C₄⋊C₄×C₄₇	—	2	16	no	—
168	C₄⋊C₄×C₄₇	—	4	4	no	—
169	C₂²⋊C₄×C₄₇	—	2	16	no	—
170	C₂²⋊C₄×C₄₇	—	2	16	no	—
171	C₂²⋊C₄×C₄₇	—	2	16	no	—
172	C₂²⋊C₄×C₄₇	—	2	16	no	—
173	C₂²⋊C₄×C₄₇	—	2	16	no	—
174	C₂²⋊C₄×C₄₇	—	2	16	no	—
175	C₂²⋊C₄×C₄₇	C₂×D₄	1	32	yes	complemented
176	C₄²×C₄₇	—	2	16	no	—
177	C₄²×C₄₇	—	4	4	no	—
178	C₂³×C₄₇	—	2	16	no	—
179	C₂³×C₄₇	—	2	16	no	—
180	C₂³×C₄₇	—	2	16	no	—
181	C₂³×C₄₇	—	2	4	no	—
182	C₂³×C₄₇	—	2	4	no	—
183	C₂³×C₄₇	—	2	4	no	—
184	C₂³×C₄₇	—	2	4	no	—
185	C₂³×C₄₇	—	2	4	no	—
186	C₂³×C₄₇	—	2	4	no	—
187	C₂³×C₄₇	—	2	4	no	—
188	C₂³×C₄₇	—	2	4	no	—
189	C₂³×C₄₇	—	2	4	no	—
190	C₂³×C₄₇	—	2	4	no	—
191	C₂³×C₄₇	—	2	4	no	—
192	C₂³×C₄₇	—	2	4	no	—
193	C₂³×C₄₇	—	2	4	no	—
194	C₂³×C₄₇	—	4	8	no	—
195	C₂³×C₄₇	—	4	8	no	—
196	C₂³×C₄₇	—	4	8	no	—
197	C₂³×C₄₇	—	4	8	no	—
198	C₂³×C₄₇	—	4	8	no	—
199	C₂³×C₄₇	—	4	8	no	—
200	C₂³×C₄₇	—	4	8	no	—
201	C₂³×C₄₇	—	4	8	no	—
202	C₂³×C₄₇	—	4	8	no	—
203	C₂³×C₄₇	—	4	8	no	—
204	C₂³×C₄₇	—	4	8	no	—
205	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
206	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
207	C₂³×C₄₇	C₂×#41	1	2	yes	—
208	C₂³×C₄₇	C₂×#41	1	4	yes	—
209	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
210	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
211	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
212	Q₈×C₄₇	—	4	16	no	—
213	D₄×C₄₇	—	4	32	no	—
214	D₄×C₄₇	—	4	32	no	—
215	D₄×C₄₇	—	4	16	no	—
216	D₄×C₄₇	—	4	16	no	—
217	C₂×C₄×C₄₇	—	2	8	no	—
218	C₂×C₄×C₄₇	—	2	16	no	—
219	C₂×C₄×C₄₇	—	2	16	no	—
220	C₂×C₄×C₄₇	—	2	16	no	—
221	C₂×C₄×C₄₇	—	2	4	no	—
222	C₂×C₄×C₄₇	—	2	4	no	—
223	C₂×C₄×C₄₇	—	2	4	no	—
224	C₂×C₄×C₄₇	—	2	4	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	4	no	—
228	C₂×C₄×C₄₇	—	2	4	no	—
229	C₂×C₄×C₄₇	—	2	4	no	—
230	C₂×C₄×C₄₇	—	2	4	no	—
231	C₂×C₄×C₄₇	—	2	4	no	—
232	C₂×C₄×C₄₇	—	2	4	no	—
233	C₂×C₄×C₄₇	—	2	4	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	4	32	no	—
237	C₂×C₄×C₄₇	—	4	8	no	—
238	C₂×C₄×C₄₇	—	4	4	no	—
239	C₂×C₄×C₄₇	—	4	4	no	—
240	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
241	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
242	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
243	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
244	C₂×#2555	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂²×C₄₇	—	2	8	no	—
246	C₂²×C₄₇	—	2	8	no	—
247	C₂²×C₄₇	—	2	8	no	—
248	C₂²×C₄₇	—	4	4	no	—
249	C₂²×C₄₇	—	4	4	no	—
250	C₂²×C₄₇	—	4	4	no	—
251	C₂²×C₄₇	—	4	4	no	—
252	C₂²×C₄₇	—	4	32	no	—
253	C₂²×C₄₇	—	4	4	no	—
254	C₂²×C₄₇	—	4	4	no	—
255	C₂²×C₄₇	—	4	4	no	—
256	C₂²×C₄₇	—	4	4	no	—
257	C₂²×C₄₇	—	4	4	no	—
258	C₂²×C₄₇	—	4	4	no	—
259	C₂²×C₄₇	—	4	4	no	—
260	C₂²×C₄₇	—	8	16	no	—
261	C₂²×C₄₇	#532	1	8	yes	—
262	C₂²×C₄₇	#538	1	4	yes	—
263	C₂²×C₄₇	D₄²	1	4	yes	—
264	C₂²×C₄₇	#546	1	8	yes	—
265	C₂²×C₄₇	#555	1	4	yes	—
266	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
267	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
268	C₂²×C₄₇	C₂²×#41	1	2	yes	—
269	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
270	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
271	C₄×C₄₇	—	2	4	no	—
272	C₄×C₄₇	—	2	8	no	—
273	C₄×C₄₇	—	2	8	no	—
274	C₄×C₄₇	—	2	8	no	—
275	C₄×C₄₇	—	4	4	no	—
276	C₄×C₄₇	—	4	2	no	—
277	C₄×C₄₇	—	4	2	no	—
278	C₂²×#124	C₂×C₄₇	1	2	yes	complemented
279	C₂²×#121	C₂×C₄₇	1	2	yes	complemented
280	#2555	C₂×C₄₇	1	16	yes	direct product factor
281	C₂×#395	C₂×C₄₇	1	1	yes	characteristic, complemented
282	C₂×#394	C₂×C₄₇	1	1	yes	characteristic, complemented
283	C₂×#392	C₂×C₄₇	1	2	yes	complemented
284	C₂×#390	C₂×C₄₇	1	1	yes	characteristic, complemented
285	C₂×#388	C₂×C₄₇	1	2	yes	complemented
286	C₂×#386	C₂×C₄₇	1	2	yes	complemented
287	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	2	yes	complemented
288	C₂×C₄₇	—	4	8	no	—
289	C₂×C₄₇	—	8	4	no	—
290	C₂×C₄₇	#2555	1	8	yes	direct product factor
291	C₂×C₄₇	C₂×#532	1	2	yes	—
292	C₂×C₄₇	C₂×#538	1	1	yes	characteristic
293	C₂×C₄₇	C₂×D₄²	1	1	yes	characteristic
294	C₂×C₄₇	C₂×#546	1	2	yes	—
295	C₂×C₄₇	C₂×#555	1	1	yes	characteristic
296	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
297	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
298	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
299	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
300	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
301	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
302	C₂×#124	—	2	16	no	—
303	C₂×#124	C₂²×C₄₇	1	16	yes	complemented
304	C₂×#121	—	2	16	no	—
305	C₂×#121	C₂²×C₄₇	1	16	yes	complemented
306	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
307	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
308	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
309	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
310	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
311	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
312	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
313	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
314	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
315	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
316	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
317	#395	C₂²×C₄₇	1	8	yes	complemented
318	#394	C₂²×C₄₇	1	8	yes	complemented
319	#392	C₂²×C₄₇	1	16	yes	complemented
320	#390	C₂²×C₄₇	1	8	yes	complemented
321	#388	C₂²×C₄₇	1	16	yes	complemented
322	#386	C₂²×C₄₇	1	16	yes	complemented
323	C₄×C₂²⋊C₄	C₂²×C₄₇	1	16	yes	complemented
324	C₂×#95	C₂²×C₄₇	1	2	yes	—
325	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
326	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
327	C₂×#95	C₂²×C₄₇	1	2	yes	—
328	C₄₇	C₂×#2555	1	1	yes	characteristic, direct product factor, Sylow
329	C₂⁵	C₂³×C₄₇	1	2	yes	—
330	C₂⁵	C₂³×C₄₇	1	2	yes	—
331	C₂²×Q₈	—	2	8	no	—
332	C₂²×Q₈	—	4	2	no	—
333	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
334	C₂²×D₄	—	2	8	no	—
335	C₂²×D₄	—	2	8	no	—
336	C₂²×D₄	—	2	8	no	—
337	C₂²×D₄	—	2	8	no	—
338	C₂²×D₄	—	2	4	no	—
339	C₂²×D₄	—	2	8	no	—
340	C₂²×D₄	—	4	2	no	—
341	C₂²×D₄	—	4	2	no	—
342	C₂²×D₄	—	4	4	no	—
343	C₂²×D₄	—	4	4	no	—
344	C₂²×D₄	—	4	2	no	—
345	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
346	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
347	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
348	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
349	C₂³×C₄	—	2	8	no	—
350	C₂³×C₄	—	2	8	no	—
351	C₂³×C₄	—	4	4	no	—
352	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
353	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
354	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₄₇	1	8	yes	—
356	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
357	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
358	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
360	#124	—	2	64	no	—
361	#121	—	2	64	no	—
362	C₂×C₄⋊C₄	—	2	8	no	—
363	C₂×C₄⋊C₄	—	4	2	no	—
364	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
365	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
366	C₂×C₂²⋊C₄	—	2	8	no	—
367	C₂×C₂²⋊C₄	—	2	8	no	—
368	C₂×C₂²⋊C₄	—	2	8	no	—
369	C₂×C₂²⋊C₄	—	2	8	no	—
370	C₂×C₂²⋊C₄	—	2	8	no	—
371	C₂×C₂²⋊C₄	—	2	8	no	—
372	C₂×C₂²⋊C₄	D₄×C₄₇	1	16	yes	complemented
373	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
380	C₂×C₄²	—	2	8	no	—
381	C₂×C₄²	—	4	2	no	—
382	C₂×C₄²	C₂³×C₄₇	1	8	yes	—
383	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
384	#95	C₂³×C₄₇	1	8	yes	—
385	#95	C₂³×C₄₇	1	8	yes	—
386	#95	C₂³×C₄₇	1	4	yes	—
387	#95	C₂³×C₄₇	1	4	yes	—
388	C₂⁴	—	2	4	no	—
389	C₂⁴	—	2	4	no	—
390	C₂⁴	—	2	4	no	—
391	C₂⁴	—	2	4	no	—
392	C₂⁴	—	2	4	no	—
393	C₂⁴	—	2	4	no	—
394	C₂⁴	—	2	4	no	—
395	C₂⁴	—	2	4	no	—
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	2	4	no	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
402	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
403	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
404	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
405	C₂×Q₈	—	2	16	no	—
406	C₂×Q₈	—	4	4	no	—
407	C₂×Q₈	—	4	16	no	—
408	C₂×D₄	—	2	16	no	—
409	C₂×D₄	—	2	16	no	—
410	C₂×D₄	—	2	16	no	—
411	C₂×D₄	—	2	16	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	16	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	—	4	8	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	32	no	—
420	C₂×D₄	—	4	32	no	—
421	C₂×D₄	—	4	16	no	—
422	C₂×D₄	—	4	16	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	16	no	—
439	C₂²×C₄	—	2	16	no	—
440	C₂²×C₄	—	4	8	no	—
441	C₂²×C₄	—	4	32	no	—
442	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
443	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
444	C₂²×C₄	#41×C₄₇	1	4	yes	—
445	C₂²×C₄	#41×C₄₇	1	8	yes	—
446	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
453	C₄⋊C₄	—	2	16	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₂²⋊C₄	—	2	16	no	—
456	C₂²⋊C₄	—	2	16	no	—
457	C₂²⋊C₄	—	2	16	no	—
458	C₂²⋊C₄	—	2	16	no	—
459	C₂²⋊C₄	—	2	16	no	—
460	C₂²⋊C₄	—	2	16	no	—
461	C₂²⋊C₄	C₂×D₄×C₄₇	1	32	yes	complemented
462	C₄²	—	2	16	no	—
463	C₄²	—	4	4	no	—
464	C₂³	—	2	16	no	—
465	C₂³	—	2	16	no	—
466	C₂³	—	2	16	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	4	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	8	no	—
483	C₂³	—	4	8	no	—
484	C₂³	—	4	8	no	—
485	C₂³	—	4	8	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	8	no	—
489	C₂³	—	4	8	no	—
490	C₂³	—	4	8	no	—
491	C₂³	C₂²×D₄×C₄₇	1	8	yes	—
492	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
493	C₂³	C₂×#41×C₄₇	1	2	yes	—
494	C₂³	C₂×#41×C₄₇	1	4	yes	—
495	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
496	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
497	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
498	Q₈	—	4	16	no	—
499	D₄	—	4	32	no	—
500	D₄	—	4	32	no	—
501	D₄	—	4	16	no	—
502	D₄	—	4	16	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	16	no	—
505	C₂×C₄	—	2	16	no	—
506	C₂×C₄	—	2	16	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	4	32	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
527	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
528	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
529	C₂×C₄	C₂×#41×C₄₇	1	8	yes	—
530	C₂²	—	2	8	no	—
531	C₂²	—	2	8	no	—
532	C₂²	—	2	8	no	—
533	C₂²	—	4	32	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	8	16	no	—
546	C₂²	C₄₇×#532	1	8	yes	—
547	C₂²	C₄₇×#538	1	4	yes	—
548	C₂²	D₄²×C₄₇	1	4	yes	—
549	C₂²	C₄₇×#546	1	8	yes	—
550	C₂²	C₄₇×#555	1	4	yes	—
551	C₂²	C₂³×D₄×C₄₇	1	2	yes	—
552	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
553	C₂²	C₂²×#41×C₄₇	1	2	yes	—
554	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
555	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
556	C₄	—	2	4	no	—
557	C₄	—	2	8	no	—
558	C₄	—	2	8	no	—
559	C₄	—	2	8	no	—
560	C₄	—	4	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₂	—	4	8	no	—
564	C₂	—	8	4	no	—
565	C₂	C₄₇×#2555	1	8	yes	direct product factor
566	C₂	C₂×C₄₇×#532	1	2	yes	—
567	C₂	C₂×C₄₇×#538	1	1	yes	characteristic
568	C₂	C₂×D₄²×C₄₇	1	1	yes	characteristic
569	C₂	C₂×C₄₇×#546	1	2	yes	—
570	C₂	C₂×C₄₇×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#124×C₄₇	C₂	semidirect
2. C₂²×#121×C₄₇	C₂	semidirect
3. C₄₇×#2555	C₂	direct (N × H)
4. C₂×C₄₇×#395	C₂	semidirect
5. C₂×C₄₇×#394	C₂	semidirect
6. C₂×C₄₇×#392	C₂	semidirect
7. C₂×C₄₇×#390	C₂	semidirect
8. C₂×C₄₇×#388	C₂	semidirect
9. C₂×C₄₇×#386	C₂	semidirect
10. C₂×C₄×C₂²⋊C₄×C₄₇	C₂	semidirect
18. C₂×#124×C₄₇	C₂²	semidirect
20. C₂×#121×C₄₇	C₂²	semidirect
32. C₄₇×#395	C₂²	semidirect
33. C₄₇×#394	C₂²	semidirect
34. C₄₇×#392	C₂²	semidirect
35. C₄₇×#390	C₂²	semidirect
36. C₄₇×#388	C₂²	semidirect
37. C₄₇×#386	C₂²	semidirect
38. C₄×C₂²⋊C₄×C₄₇	C₂²	semidirect
86. C₂×C₂²⋊C₄×C₄₇	D₄	semidirect
175. C₂²⋊C₄×C₄₇	C₂×D₄	semidirect
244. C₂×#2555	C₄₇	direct (N × H)
278. C₂²×#124	C₂×C₄₇	semidirect
279. C₂²×#121	C₂×C₄₇	semidirect
280. #2555	C₂×C₄₇	direct (N × H)
281. C₂×#395	C₂×C₄₇	semidirect
282. C₂×#394	C₂×C₄₇	semidirect
283. C₂×#392	C₂×C₄₇	semidirect
284. C₂×#390	C₂×C₄₇	semidirect
285. C₂×#388	C₂×C₄₇	semidirect
286. C₂×#386	C₂×C₄₇	semidirect
287. C₂×C₄×C₂²⋊C₄	C₂×C₄₇	semidirect
290. C₂×C₄₇	#2555	direct (N × H)
303. C₂×#124	C₂²×C₄₇	semidirect
305. C₂×#121	C₂²×C₄₇	semidirect
317. #395	C₂²×C₄₇	semidirect
318. #394	C₂²×C₄₇	semidirect
319. #392	C₂²×C₄₇	semidirect
320. #390	C₂²×C₄₇	semidirect
321. #388	C₂²×C₄₇	semidirect
322. #386	C₂²×C₄₇	semidirect
323. C₄×C₂²⋊C₄	C₂²×C₄₇	semidirect
328. C₄₇	C₂×#2555	direct (N × H)
372. C₂×C₂²⋊C₄	D₄×C₄₇	semidirect
461. C₂²⋊C₄	C₂×D₄×C₄₇	semidirect
565. C₂	C₄₇×#2555	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₄₇	2
C₂²×#121×C₄₇	2
C₄₇×#2555	2
C₂×C₄₇×#395	2
C₂×C₄₇×#394	2
C₂×C₄₇×#392	2
C₂×C₄₇×#390	2
C₂×C₄₇×#388	2
C₂×C₄₇×#386	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₂×#2555	47

Subgroups — C2×C47×#2555 #26074520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2555 #26074520