Subgroups — C₂×C₄₇×#2617 #26074252

Order 12032.

5222 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#120×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₂³×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2617	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₄₇×#397	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#394	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₇×#392	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₇×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
12	C₂³×D₄×C₄₇	C₂²	1	4	yes	—
13	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
14	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#121×C₄₇	—	2	8	no	—
17	C₂×#121×C₄₇	C₂²	1	8	yes	complemented
18	C₂×#120×C₄₇	—	2	16	no	—
19	C₂×#120×C₄₇	C₂²	1	16	yes	complemented
20	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊C₄×C₄₇	—	2	8	no	—
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	4	yes	—
27	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	complemented
28	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
29	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	complemented
30	C₄₇×#397	C₂²	1	16	yes	complemented
31	C₄₇×#394	C₂²	1	32	yes	complemented
32	C₄₇×#392	C₂²	1	16	yes	complemented
33	C₄₇×#386	C₂²	1	16	yes	complemented
34	C₄₇×#380	C₂²	1	8	yes	complemented
35	C₂×#95×C₄₇	C₂²	1	2	yes	complemented
36	C₂×#95×C₄₇	C₂²	1	4	yes	complemented
37	C₂⁵×C₄₇	—	2	4	no	—
38	C₂⁵×C₄₇	—	2	4	no	—
39	C₂⁵×C₄₇	—	4	4	no	—
40	C₂⁵×C₄₇	—	4	4	no	—
41	C₂⁵×C₄₇	D₄	1	8	yes	complemented
42	C₂⁵×C₄₇	C₂³	1	2	yes	—
43	C₂⁵×C₄₇	C₂³	1	2	yes	—
44	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
45	C₂⁵×C₄₇	C₂³	1	4	yes	—
46	C₂²×D₄×C₄₇	—	2	16	no	—
47	C₂²×D₄×C₄₇	—	2	8	no	—
48	C₂²×D₄×C₄₇	—	2	8	no	—
49	C₂²×D₄×C₄₇	—	2	8	no	—
50	C₂²×D₄×C₄₇	—	2	4	no	—
51	C₂²×D₄×C₄₇	—	4	8	no	—
52	C₂²×D₄×C₄₇	—	4	8	no	—
53	C₂²×D₄×C₄₇	—	4	4	no	—
54	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
55	C₂²×D₄×C₄₇	C₂³	1	16	yes	—
56	C₂²×D₄×C₄₇	C₂³	1	4	yes	complemented
57	C₂³×C₄×C₄₇	—	2	4	no	—
58	C₂³×C₄×C₄₇	—	4	4	no	—
59	C₂³×C₄×C₄₇	—	4	4	no	—
60	C₂³×C₄×C₄₇	D₄	1	8	yes	complemented
61	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
63	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
68	#121×C₄₇	—	2	32	no	—
69	#120×C₄₇	—	2	64	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
71	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	complemented
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	complemented
74	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	32	no	—
80	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
81	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
82	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
83	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
84	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
85	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	complemented
86	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	complemented
87	#95×C₄₇	C₂³	1	8	yes	complemented
88	#95×C₄₇	C₂³	1	16	yes	complemented
89	C₂⁴×C₄₇	—	2	4	no	—
90	C₂⁴×C₄₇	—	2	4	no	—
91	C₂⁴×C₄₇	—	2	32	no	—
92	C₂⁴×C₄₇	—	2	4	no	—
93	C₂⁴×C₄₇	—	2	8	no	—
94	C₂⁴×C₄₇	—	2	4	no	—
95	C₂⁴×C₄₇	—	2	8	no	—
96	C₂⁴×C₄₇	—	2	8	no	—
97	C₂⁴×C₄₇	—	2	8	no	—
98	C₂⁴×C₄₇	—	2	4	no	—
99	C₂⁴×C₄₇	—	2	4	no	—
100	C₂⁴×C₄₇	—	2	4	no	—
101	C₂⁴×C₄₇	—	2	8	no	—
102	C₂⁴×C₄₇	—	2	8	no	—
103	C₂⁴×C₄₇	—	4	32	no	—
104	C₂⁴×C₄₇	—	4	8	no	—
105	C₂⁴×C₄₇	—	4	8	no	—
106	C₂⁴×C₄₇	—	4	16	no	—
107	C₂⁴×C₄₇	—	4	16	no	—
108	C₂⁴×C₄₇	—	4	32	no	—
109	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
110	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
111	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
112	C₂⁴×C₄₇	C₂×D₄	1	16	yes	complemented
113	C₂⁴×C₄₇	#41	1	4	yes	—
114	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
115	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
116	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
117	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
118	C₂×D₄×C₄₇	—	2	32	no	—
119	C₂×D₄×C₄₇	—	2	16	no	—
120	C₂×D₄×C₄₇	—	2	16	no	—
121	C₂×D₄×C₄₇	—	2	16	no	—
122	C₂×D₄×C₄₇	—	2	8	no	—
123	C₂×D₄×C₄₇	—	4	16	no	—
124	C₂×D₄×C₄₇	—	4	16	no	—
125	C₂×D₄×C₄₇	—	4	8	no	—
126	C₂×D₄×C₄₇	—	4	16	no	—
127	C₂×D₄×C₄₇	—	4	64	no	—
128	C₂×D₄×C₄₇	—	4	32	no	—
129	C₂²×C₄×C₄₇	—	2	4	no	—
130	C₂²×C₄×C₄₇	—	2	4	no	—
131	C₂²×C₄×C₄₇	—	2	8	no	—
132	C₂²×C₄×C₄₇	—	2	4	no	—
133	C₂²×C₄×C₄₇	—	2	4	no	—
134	C₂²×C₄×C₄₇	—	2	8	no	—
135	C₂²×C₄×C₄₇	—	2	4	no	—
136	C₂²×C₄×C₄₇	—	2	4	no	—
137	C₂²×C₄×C₄₇	—	2	8	no	—
138	C₂²×C₄×C₄₇	—	2	8	no	—
139	C₂²×C₄×C₄₇	—	2	8	no	—
140	C₂²×C₄×C₄₇	—	4	16	no	—
141	C₂²×C₄×C₄₇	—	4	8	no	—
142	C₂²×C₄×C₄₇	—	4	8	no	—
143	C₂²×C₄×C₄₇	—	4	16	no	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₄₇	C₂×D₄	1	16	yes	complemented
147	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
150	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
152	C₄⋊C₄×C₄₇	—	2	8	no	—
153	C₄⋊C₄×C₄₇	—	4	8	no	—
154	C₂²⋊C₄×C₄₇	—	2	32	no	—
155	C₂²⋊C₄×C₄₇	—	2	16	no	—
156	C₂²⋊C₄×C₄₇	—	2	16	no	—
157	C₂²⋊C₄×C₄₇	—	2	16	no	—
158	C₂²⋊C₄×C₄₇	—	2	16	no	—
159	C₂²⋊C₄×C₄₇	—	4	16	no	—
160	C₂³×C₄₇	—	2	8	no	—
161	C₂³×C₄₇	—	2	16	no	—
162	C₂³×C₄₇	—	2	8	no	—
163	C₂³×C₄₇	—	2	16	no	—
164	C₂³×C₄₇	—	2	4	no	—
165	C₂³×C₄₇	—	2	4	no	—
166	C₂³×C₄₇	—	2	16	no	—
167	C₂³×C₄₇	—	2	32	no	—
168	C₂³×C₄₇	—	2	32	no	—
169	C₂³×C₄₇	—	2	4	no	—
170	C₂³×C₄₇	—	2	4	no	—
171	C₂³×C₄₇	—	2	8	no	—
172	C₂³×C₄₇	—	2	8	no	—
173	C₂³×C₄₇	—	2	4	no	—
174	C₂³×C₄₇	—	2	4	no	—
175	C₂³×C₄₇	—	2	4	no	—
176	C₂³×C₄₇	—	2	8	no	—
177	C₂³×C₄₇	—	2	8	no	—
178	C₂³×C₄₇	—	4	32	no	—
179	C₂³×C₄₇	—	4	128	no	—
180	C₂³×C₄₇	—	4	16	no	—
181	C₂³×C₄₇	—	4	16	no	—
182	C₂³×C₄₇	—	4	32	no	—
183	C₂³×C₄₇	—	4	8	no	—
184	C₂³×C₄₇	—	4	8	no	—
185	C₂³×C₄₇	—	4	16	no	—
186	C₂³×C₄₇	—	4	8	no	—
187	C₂³×C₄₇	—	4	8	no	—
188	C₂³×C₄₇	—	4	16	no	—
189	C₂³×C₄₇	—	4	8	no	—
190	C₂³×C₄₇	—	4	16	no	—
191	C₂³×C₄₇	#121	1	16	yes	—
192	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
193	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
194	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
195	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
196	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
197	C₂³×C₄₇	C₂×#41	1	4	yes	—
198	C₂³×C₄₇	C₂×#41	1	2	yes	—
199	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
200	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
201	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
202	D₄×C₄₇	—	4	16	no	—
203	D₄×C₄₇	—	4	64	no	—
204	D₄×C₄₇	—	4	32	no	—
205	C₂×C₄×C₄₇	—	2	8	no	—
206	C₂×C₄×C₄₇	—	2	8	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	8	no	—
212	C₂×C₄×C₄₇	—	2	4	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	2	8	no	—
215	C₂×C₄×C₄₇	—	2	8	no	—
216	C₂×C₄×C₄₇	—	2	8	no	—
217	C₂×C₄×C₄₇	—	4	16	no	—
218	C₂×C₄×C₄₇	—	4	16	no	—
219	C₂×C₄×C₄₇	—	4	8	no	—
220	C₂×C₄×C₄₇	—	4	16	no	—
221	C₂×C₄×C₄₇	—	4	8	no	—
222	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
224	C₂×#2617	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₄₇	—	2	32	no	—
226	C₂²×C₄₇	—	2	4	no	—
227	C₂²×C₄₇	—	2	8	no	—
228	C₂²×C₄₇	—	2	4	no	—
229	C₂²×C₄₇	—	2	8	no	—
230	C₂²×C₄₇	—	2	8	no	—
231	C₂²×C₄₇	—	2	16	no	—
232	C₂²×C₄₇	—	4	64	no	—
233	C₂²×C₄₇	—	4	32	no	—
234	C₂²×C₄₇	—	4	4	no	—
235	C₂²×C₄₇	—	4	4	no	—
236	C₂²×C₄₇	—	4	8	no	—
237	C₂²×C₄₇	—	4	4	no	—
238	C₂²×C₄₇	—	4	4	no	—
239	C₂²×C₄₇	—	4	8	no	—
240	C₂²×C₄₇	—	4	4	no	—
241	C₂²×C₄₇	—	4	8	no	—
242	C₂²×C₄₇	—	8	16	no	—
243	C₂²×C₄₇	C₂×#121	1	8	yes	—
244	C₂²×C₄₇	C₂×#121	1	4	yes	—
245	C₂²×C₄₇	#534	1	4	yes	—
246	C₂²×C₄₇	#534	1	8	yes	—
247	C₂²×C₄₇	#535	1	4	yes	—
248	C₂²×C₄₇	#538	1	8	yes	—
249	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
250	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
251	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
252	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
253	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
254	C₄×C₄₇	—	2	4	no	—
255	C₄×C₄₇	—	2	4	no	—
256	C₄×C₄₇	—	4	4	no	—
257	C₄×C₄₇	—	4	8	no	—
258	C₄×C₄₇	—	4	4	no	—
259	C₂²×#121	C₂×C₄₇	1	1	yes	characteristic, complemented
260	C₂²×#120	C₂×C₄₇	1	2	yes	complemented
261	C₂³×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
262	#2617	C₂×C₄₇	1	16	yes	direct product factor
263	C₂×#397	C₂×C₄₇	1	2	yes	complemented
264	C₂×#394	C₂×C₄₇	1	4	yes	complemented
265	C₂×#392	C₂×C₄₇	1	2	yes	complemented
266	C₂×#386	C₂×C₄₇	1	2	yes	complemented
267	C₂×#380	C₂×C₄₇	1	1	yes	characteristic, complemented
268	C₂×C₄₇	—	2	8	no	—
269	C₂×C₄₇	—	4	8	no	—
270	C₂×C₄₇	—	8	4	no	—
271	C₂×C₄₇	#2617	1	8	yes	direct product factor
272	C₂×C₄₇	C₂²×#121	1	1	yes	characteristic
273	C₂×C₄₇	C₂×#534	1	1	yes	characteristic
274	C₂×C₄₇	C₂×#534	1	2	yes	—
275	C₂×C₄₇	C₂×#535	1	1	yes	characteristic
276	C₂×C₄₇	C₂×#538	1	2	yes	—
277	C₂⁶	C₂²×C₄₇	1	1	yes	characteristic
278	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
279	C₂³×D₄	C₂²×C₄₇	1	4	yes	—
280	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic, complemented
281	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
282	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
283	C₂×#121	—	2	8	no	—
284	C₂×#121	C₂²×C₄₇	1	8	yes	complemented
285	C₂×#120	—	2	16	no	—
286	C₂×#120	C₂²×C₄₇	1	16	yes	complemented
287	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic, complemented
288	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
289	C₂²×C₂²⋊C₄	—	2	8	no	—
290	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
291	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
292	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
293	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
294	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	complemented
295	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	complemented
296	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	complemented
297	#397	C₂²×C₄₇	1	16	yes	complemented
298	#394	C₂²×C₄₇	1	32	yes	complemented
299	#392	C₂²×C₄₇	1	16	yes	complemented
300	#386	C₂²×C₄₇	1	16	yes	complemented
301	#380	C₂²×C₄₇	1	8	yes	complemented
302	C₂×#95	C₂²×C₄₇	1	2	yes	complemented
303	C₂×#95	C₂²×C₄₇	1	4	yes	complemented
304	C₄₇	C₂×#2617	1	1	yes	characteristic, direct product factor, Sylow
305	C₂⁵	—	2	4	no	—
306	C₂⁵	—	2	4	no	—
307	C₂⁵	—	4	4	no	—
308	C₂⁵	—	4	4	no	—
309	C₂⁵	D₄×C₄₇	1	8	yes	complemented
310	C₂⁵	C₂³×C₄₇	1	2	yes	—
311	C₂⁵	C₂³×C₄₇	1	2	yes	—
312	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
313	C₂⁵	C₂³×C₄₇	1	4	yes	—
314	C₂²×D₄	—	2	16	no	—
315	C₂²×D₄	—	2	8	no	—
316	C₂²×D₄	—	2	8	no	—
317	C₂²×D₄	—	2	8	no	—
318	C₂²×D₄	—	2	4	no	—
319	C₂²×D₄	—	4	8	no	—
320	C₂²×D₄	—	4	8	no	—
321	C₂²×D₄	—	4	4	no	—
322	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
323	C₂²×D₄	C₂³×C₄₇	1	16	yes	—
324	C₂²×D₄	C₂³×C₄₇	1	4	yes	complemented
325	C₂³×C₄	—	2	4	no	—
326	C₂³×C₄	—	4	4	no	—
327	C₂³×C₄	—	4	4	no	—
328	C₂³×C₄	D₄×C₄₇	1	8	yes	complemented
329	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
330	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
331	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
332	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
335	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
336	#121	—	2	32	no	—
337	#120	—	2	64	no	—
338	C₂×C₄⋊C₄	—	2	4	no	—
339	C₂×C₄⋊C₄	—	4	4	no	—
340	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	complemented
341	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	complemented
342	C₂×C₂²⋊C₄	—	2	16	no	—
343	C₂×C₂²⋊C₄	—	2	8	no	—
344	C₂×C₂²⋊C₄	—	2	8	no	—
345	C₂×C₂²⋊C₄	—	2	8	no	—
346	C₂×C₂²⋊C₄	—	2	8	no	—
347	C₂×C₂²⋊C₄	—	2	32	no	—
348	C₂×C₂²⋊C₄	—	4	8	no	—
349	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₄₇	1	16	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	complemented
354	C₂×C₂²⋊C₄	C₂³×C₄₇	1	16	yes	complemented
355	#95	C₂³×C₄₇	1	8	yes	complemented
356	#95	C₂³×C₄₇	1	16	yes	complemented
357	C₂⁴	—	2	4	no	—
358	C₂⁴	—	2	4	no	—
359	C₂⁴	—	2	32	no	—
360	C₂⁴	—	2	4	no	—
361	C₂⁴	—	2	8	no	—
362	C₂⁴	—	2	4	no	—
363	C₂⁴	—	2	8	no	—
364	C₂⁴	—	2	8	no	—
365	C₂⁴	—	2	8	no	—
366	C₂⁴	—	2	4	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	2	8	no	—
370	C₂⁴	—	2	8	no	—
371	C₂⁴	—	4	32	no	—
372	C₂⁴	—	4	8	no	—
373	C₂⁴	—	4	8	no	—
374	C₂⁴	—	4	16	no	—
375	C₂⁴	—	4	16	no	—
376	C₂⁴	—	4	32	no	—
377	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
378	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
379	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
380	C₂⁴	C₂×D₄×C₄₇	1	16	yes	complemented
381	C₂⁴	#41×C₄₇	1	4	yes	—
382	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
383	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
384	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
385	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
386	C₂×D₄	—	2	32	no	—
387	C₂×D₄	—	2	16	no	—
388	C₂×D₄	—	2	16	no	—
389	C₂×D₄	—	2	16	no	—
390	C₂×D₄	—	2	8	no	—
391	C₂×D₄	—	4	16	no	—
392	C₂×D₄	—	4	16	no	—
393	C₂×D₄	—	4	8	no	—
394	C₂×D₄	—	4	16	no	—
395	C₂×D₄	—	4	64	no	—
396	C₂×D₄	—	4	32	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	8	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	8	no	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	—	2	8	no	—
408	C₂²×C₄	—	4	16	no	—
409	C₂²×C₄	—	4	8	no	—
410	C₂²×C₄	—	4	8	no	—
411	C₂²×C₄	—	4	16	no	—
412	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
413	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
414	C₂²×C₄	C₂×D₄×C₄₇	1	16	yes	complemented
415	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
418	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	4	8	no	—
422	C₂²⋊C₄	—	2	32	no	—
423	C₂²⋊C₄	—	2	16	no	—
424	C₂²⋊C₄	—	2	16	no	—
425	C₂²⋊C₄	—	2	16	no	—
426	C₂²⋊C₄	—	2	16	no	—
427	C₂²⋊C₄	—	4	16	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	2	16	no	—
430	C₂³	—	2	8	no	—
431	C₂³	—	2	16	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	16	no	—
435	C₂³	—	2	32	no	—
436	C₂³	—	2	32	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	8	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	8	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	4	32	no	—
447	C₂³	—	4	128	no	—
448	C₂³	—	4	16	no	—
449	C₂³	—	4	16	no	—
450	C₂³	—	4	32	no	—
451	C₂³	—	4	8	no	—
452	C₂³	—	4	8	no	—
453	C₂³	—	4	16	no	—
454	C₂³	—	4	8	no	—
455	C₂³	—	4	8	no	—
456	C₂³	—	4	16	no	—
457	C₂³	—	4	8	no	—
458	C₂³	—	4	16	no	—
459	C₂³	#121×C₄₇	1	16	yes	—
460	C₂³	C₂²×D₄×C₄₇	1	8	yes	—
461	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
462	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
463	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
464	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
465	C₂³	C₂×#41×C₄₇	1	4	yes	—
466	C₂³	C₂×#41×C₄₇	1	2	yes	—
467	C₂³	H(5,𝔽₂)×C₄₇	1	4	yes	—
468	C₂³	H(5,𝔽₂)×C₄₇	1	4	yes	—
469	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
470	D₄	—	4	16	no	—
471	D₄	—	4	64	no	—
472	D₄	—	4	32	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	8	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	4	16	no	—
486	C₂×C₄	—	4	16	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	—	4	16	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
491	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
492	C₂²	—	2	32	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	8	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	8	no	—
497	C₂²	—	2	8	no	—
498	C₂²	—	2	16	no	—
499	C₂²	—	4	64	no	—
500	C₂²	—	4	32	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	8	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	8	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	8	no	—
509	C₂²	—	8	16	no	—
510	C₂²	C₂×#121×C₄₇	1	8	yes	—
511	C₂²	C₂×#121×C₄₇	1	4	yes	—
512	C₂²	C₄₇×#534	1	4	yes	—
513	C₂²	C₄₇×#534	1	8	yes	—
514	C₂²	C₄₇×#535	1	4	yes	—
515	C₂²	C₄₇×#538	1	8	yes	—
516	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
517	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
518	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
519	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	2	yes	—
520	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	2	yes	—
521	C₄	—	2	4	no	—
522	C₄	—	2	4	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	8	no	—
525	C₄	—	4	4	no	—
526	C₂	—	2	8	no	—
527	C₂	—	4	8	no	—
528	C₂	—	8	4	no	—
529	C₂	C₄₇×#2617	1	8	yes	direct product factor
530	C₂	C₂²×#121×C₄₇	1	1	yes	characteristic
531	C₂	C₂×C₄₇×#534	1	1	yes	characteristic
532	C₂	C₂×C₄₇×#534	1	2	yes	—
533	C₂	C₂×C₄₇×#535	1	1	yes	characteristic
534	C₂	C₂×C₄₇×#538	1	2	yes	—

	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×#121×C₄₇	C₂	semidirect
2. C₂²×#120×C₄₇	C₂	semidirect
3. C₂³×C₂²⋊C₄×C₄₇	C₂	semidirect
4. C₄₇×#2617	C₂	direct (N × H)
5. C₂×C₄₇×#397	C₂	semidirect
6. C₂×C₄₇×#394	C₂	semidirect
7. C₂×C₄₇×#392	C₂	semidirect
8. C₂×C₄₇×#386	C₂	semidirect
9. C₂×C₄₇×#380	C₂	semidirect
13. C₂³×D₄×C₄₇	C₂²	semidirect
17. C₂×#121×C₄₇	C₂²	semidirect
19. C₂×#120×C₄₇	C₂²	semidirect
20. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
21. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
27. C₂²×C₂²⋊C₄×C₄₇	C₂²	semidirect
28. C₂²×C₂²⋊C₄×C₄₇	C₂²	semidirect
29. C₂²×C₂²⋊C₄×C₄₇	C₂²	semidirect
30. C₄₇×#397	C₂²	semidirect
31. C₄₇×#394	C₂²	semidirect
32. C₄₇×#392	C₂²	semidirect
33. C₄₇×#386	C₂²	semidirect
34. C₄₇×#380	C₂²	semidirect
35. C₂×#95×C₄₇	C₂²	semidirect
36. C₂×#95×C₄₇	C₂²	semidirect
41. C₂⁵×C₄₇	D₄	semidirect
56. C₂²×D₄×C₄₇	C₂³	semidirect
60. C₂³×C₄×C₄₇	D₄	semidirect
72. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
73. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
85. C₂×C₂²⋊C₄×C₄₇	C₂³	semidirect
86. C₂×C₂²⋊C₄×C₄₇	C₂³	semidirect
87. #95×C₄₇	C₂³	semidirect
88. #95×C₄₇	C₂³	semidirect
112. C₂⁴×C₄₇	C₂×D₄	semidirect
146. C₂²×C₄×C₄₇	C₂×D₄	semidirect
224. C₂×#2617	C₄₇	direct (N × H)
259. C₂²×#121	C₂×C₄₇	semidirect
260. C₂²×#120	C₂×C₄₇	semidirect
261. C₂³×C₂²⋊C₄	C₂×C₄₇	semidirect
262. #2617	C₂×C₄₇	direct (N × H)
263. C₂×#397	C₂×C₄₇	semidirect
264. C₂×#394	C₂×C₄₇	semidirect
265. C₂×#392	C₂×C₄₇	semidirect
266. C₂×#386	C₂×C₄₇	semidirect
267. C₂×#380	C₂×C₄₇	semidirect
271. C₂×C₄₇	#2617	direct (N × H)
280. C₂³×D₄	C₂²×C₄₇	semidirect
284. C₂×#121	C₂²×C₄₇	semidirect
286. C₂×#120	C₂²×C₄₇	semidirect
287. C₂²×C₄⋊C₄	C₂²×C₄₇	semidirect
288. C₂²×C₄⋊C₄	C₂²×C₄₇	semidirect
294. C₂²×C₂²⋊C₄	C₂²×C₄₇	semidirect
295. C₂²×C₂²⋊C₄	C₂²×C₄₇	semidirect
296. C₂²×C₂²⋊C₄	C₂²×C₄₇	semidirect
297. #397	C₂²×C₄₇	semidirect
298. #394	C₂²×C₄₇	semidirect
299. #392	C₂²×C₄₇	semidirect
300. #386	C₂²×C₄₇	semidirect
301. #380	C₂²×C₄₇	semidirect
302. C₂×#95	C₂²×C₄₇	semidirect
303. C₂×#95	C₂²×C₄₇	semidirect
304. C₄₇	C₂×#2617	direct (N × H)
309. C₂⁵	D₄×C₄₇	semidirect
324. C₂²×D₄	C₂³×C₄₇	semidirect
328. C₂³×C₄	D₄×C₄₇	semidirect
340. C₂×C₄⋊C₄	C₂³×C₄₇	semidirect
341. C₂×C₄⋊C₄	C₂³×C₄₇	semidirect
353. C₂×C₂²⋊C₄	C₂³×C₄₇	semidirect
354. C₂×C₂²⋊C₄	C₂³×C₄₇	semidirect
355. #95	C₂³×C₄₇	semidirect
356. #95	C₂³×C₄₇	semidirect
380. C₂⁴	C₂×D₄×C₄₇	semidirect
414. C₂²×C₄	C₂×D₄×C₄₇	semidirect
529. C₂	C₄₇×#2617	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×#121×C₄₇	2
C₂²×#120×C₄₇	2
C₂³×C₂²⋊C₄×C₄₇	2
C₄₇×#2617	2
C₂×C₄₇×#397	2
C₂×C₄₇×#394	2
C₂×C₄₇×#392	2
C₂×C₄₇×#386	2
C₂×C₄₇×#380	2
C₂×#2617	47

Subgroups — C2×C47×#2617 #26074252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2617 #26074252