Subgroups — C₄₇×#35129 #26074827

Order 12032.

2826 conjugacy classes of subgroups.

The subgroup lattice has 628 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	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2850	C₂	1	4	yes	maximal, complemented
4	C₄₇×#2632	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2631	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2610	C₂	1	4	yes	maximal, complemented
7	C₄₇×#2592	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2540	C₂	1	2	yes	maximal, complemented
9	C₄₇×#2482	C₂	1	2	yes	maximal, complemented
10	C₄₇×#2409	C₂	1	2	yes	maximal, complemented
11	C₄₇×#2408	C₂	1	2	yes	maximal, complemented
12	C₄₇×#2404	C₂	1	2	yes	maximal, complemented
13	C₄₇×#2321	C₂	1	4	yes	maximal, complemented
14	C₄₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₇	—	2	8	no	—
19	C₂×#124×C₄₇	C₂²	1	2	yes	—
20	C₂×#124×C₄₇	C₂²	1	2	yes	—
21	C₂×#124×C₄₇	C₂²	1	2	yes	—
22	C₂×#124×C₄₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	complemented
24	C₂×#121×C₄₇	C₂²	1	4	yes	—
25	C₂×#120×C₄₇	C₂²	1	4	yes	—
26	C₄×#41×C₄₇	—	2	8	no	—
27	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#117×C₄₇	C₂²	1	2	yes	complemented
35	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
37	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₄₇	C₂²	1	2	yes	complemented
39	C₄₇×#399	C₂²	1	4	yes	complemented
40	C₄₇×#397	C₂²	1	4	yes	complemented
41	C₄₇×#395	C₂²	1	4	yes	complemented
42	C₄₇×#394	C₂²	1	4	yes	—
43	C₄₇×#393	C₂²	1	4	yes	complemented
44	C₄₇×#393	C₂²	1	4	yes	complemented
45	C₄₇×#392	C₂²	1	4	yes	—
46	C₄₇×#392	C₂²	1	4	yes	complemented
47	C₄₇×#391	C₂²	1	4	yes	complemented
48	C₄₇×#390	C₂²	1	4	yes	—
49	C₄₇×#390	C₂²	1	8	yes	complemented
50	C₄₇×#388	C₂²	1	8	yes	complemented
51	C₄₇×#388	C₂²	1	8	yes	complemented
52	C₄₇×#388	C₂²	1	8	yes	complemented
53	C₄₇×#386	C₂²	1	4	yes	—
54	C₄₇×#386	C₂²	1	8	yes	complemented
55	C₄₇×#386	C₂²	1	8	yes	complemented
56	C₄₇×#385	C₂²	1	4	yes	—
57	C₄₇×#383	C₂²	1	2	yes	complemented
58	C₄₇×#382	C₂²	1	2	yes	complemented
59	C₄₇×#381	C₂²	1	2	yes	—
60	C₄₇×#380	C₂²	1	2	yes	—
61	C₄₇×#379	C₂²	1	4	yes	—
62	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
64	C₄₇×#376	C₂²	1	2	yes	complemented
65	C₂⁵×C₄₇	C₂³	1	2	yes	—
66	C₂×#41×C₄₇	—	2	8	no	—
67	C₂×#41×C₄₇	—	2	4	no	—
68	C₂²×Q₈×C₄₇	—	2	4	no	—
69	C₂²×Q₈×C₄₇	—	4	4	no	—
70	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
72	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
73	C₂²×D₄×C₄₇	—	2	4	no	—
74	C₂²×D₄×C₄₇	—	4	4	no	—
75	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
77	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
78	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
79	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
80	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
81	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
82	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
85	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
86	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	#124×C₄₇	—	2	8	no	—
88	#124×C₄₇	—	2	8	no	—
89	#124×C₄₇	—	2	8	no	—
90	#124×C₄₇	—	2	8	no	—
91	C₂²⋊Q₈×C₄₇	—	4	8	no	—
92	#121×C₄₇	—	4	8	no	—
93	#120×C₄₇	—	2	16	no	—
94	C₄×Q₈×C₄₇	—	2	4	no	—
95	C₄×Q₈×C₄₇	—	2	4	no	—
96	C₄×D₄×C₄₇	—	2	8	no	—
97	C₄×D₄×C₄₇	—	2	8	no	—
98	C₄×D₄×C₄₇	—	2	4	no	—
99	C₄×D₄×C₄₇	—	2	4	no	—
100	#117×C₄₇	—	2	4	no	—
101	#117×C₄₇	—	2	8	no	—
102	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
108	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
109	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
110	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
119	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
120	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
122	C₂×C₄²×C₄₇	—	2	8	no	—
123	C₂×C₄²×C₄₇	D₄	1	8	yes	complemented
124	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
125	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
126	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
127	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
132	#95×C₄₇	C₂³	1	4	yes	—
133	#95×C₄₇	C₂³	1	4	yes	—
134	#95×C₄₇	C₂³	1	4	yes	—
135	#95×C₄₇	C₂³	1	4	yes	—
136	#95×C₄₇	C₂³	1	8	yes	—
137	#95×C₄₇	C₂³	1	8	yes	—
138	C₂⁴×C₄₇	—	2	4	no	—
139	C₂⁴×C₄₇	—	2	8	no	—
140	C₂⁴×C₄₇	—	4	4	no	—
141	C₂⁴×C₄₇	—	4	4	no	—
142	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
143	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
144	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
145	#41×C₄₇	—	2	32	no	—
146	C₂×Q₈×C₄₇	—	2	2	no	—
147	C₂×Q₈×C₄₇	—	2	4	no	—
148	C₂×Q₈×C₄₇	—	2	4	no	—
149	C₂×Q₈×C₄₇	—	2	4	no	—
150	C₂×Q₈×C₄₇	—	2	8	no	—
151	C₂×Q₈×C₄₇	—	4	4	no	—
152	C₂×Q₈×C₄₇	—	4	16	no	—
153	C₂×D₄×C₄₇	—	2	4	no	—
154	C₂×D₄×C₄₇	—	2	4	no	—
155	C₂×D₄×C₄₇	—	2	4	no	—
156	C₂×D₄×C₄₇	—	2	16	no	—
157	C₂×D₄×C₄₇	—	2	2	no	—
158	C₂×D₄×C₄₇	—	2	4	no	—
159	C₂×D₄×C₄₇	—	2	4	no	—
160	C₂×D₄×C₄₇	—	2	8	no	—
161	C₂×D₄×C₄₇	—	4	4	no	—
162	C₂×D₄×C₄₇	—	4	16	no	—
163	C₂×D₄×C₄₇	—	4	8	no	—
164	C₂×D₄×C₄₇	—	4	8	no	—
165	C₂×D₄×C₄₇	#41	1	8	yes	—
166	C₂²×C₄×C₄₇	—	2	4	no	—
167	C₂²×C₄×C₄₇	—	2	4	no	—
168	C₂²×C₄×C₄₇	—	2	4	no	—
169	C₂²×C₄×C₄₇	—	2	4	no	—
170	C₂²×C₄×C₄₇	—	2	4	no	—
171	C₂²×C₄×C₄₇	—	2	4	no	—
172	C₂²×C₄×C₄₇	—	2	4	no	—
173	C₂²×C₄×C₄₇	—	2	4	no	—
174	C₂²×C₄×C₄₇	—	2	8	no	—
175	C₂²×C₄×C₄₇	—	4	2	no	—
176	C₂²×C₄×C₄₇	—	4	4	no	—
177	C₂²×C₄×C₄₇	—	4	4	no	—
178	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
184	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
192	C₄⋊C₄×C₄₇	—	2	4	no	—
193	C₄⋊C₄×C₄₇	—	2	4	no	—
194	C₄⋊C₄×C₄₇	—	2	2	no	—
195	C₄⋊C₄×C₄₇	—	2	2	no	—
196	C₄⋊C₄×C₄₇	—	2	8	no	—
197	C₄⋊C₄×C₄₇	—	4	8	no	—
198	C₂²⋊C₄×C₄₇	—	2	4	no	—
199	C₂²⋊C₄×C₄₇	—	2	8	no	—
200	C₂²⋊C₄×C₄₇	—	2	8	no	—
201	C₂²⋊C₄×C₄₇	—	2	8	no	—
202	C₂²⋊C₄×C₄₇	—	2	8	no	—
203	C₂²⋊C₄×C₄₇	—	2	8	no	—
204	C₂²⋊C₄×C₄₇	—	2	4	no	—
205	C₂²⋊C₄×C₄₇	—	2	4	no	—
206	C₂²⋊C₄×C₄₇	—	2	16	no	—
207	C₂²⋊C₄×C₄₇	—	4	8	no	—
208	C₂²⋊C₄×C₄₇	—	4	8	no	—
209	C₂²⋊C₄×C₄₇	—	4	8	no	—
210	C₄²×C₄₇	—	2	4	no	—
211	C₄²×C₄₇	—	2	4	no	—
212	C₄²×C₄₇	—	2	4	no	—
213	C₄²×C₄₇	—	4	4	no	—
214	C₄²×C₄₇	C₂×D₄	1	4	yes	—
215	C₄²×C₄₇	C₂×D₄	1	4	yes	—
216	C₄²×C₄₇	C₂×D₄	1	4	yes	—
217	C₄²×C₄₇	C₂×D₄	1	4	yes	—
218	C₂³×C₄₇	—	2	2	no	—
219	C₂³×C₄₇	—	2	2	no	—
220	C₂³×C₄₇	—	2	2	no	—
221	C₂³×C₄₇	—	2	2	no	—
222	C₂³×C₄₇	—	2	4	no	—
223	C₂³×C₄₇	—	2	4	no	—
224	C₂³×C₄₇	—	2	4	no	—
225	C₂³×C₄₇	—	2	8	no	—
226	C₂³×C₄₇	—	2	8	no	—
227	C₂³×C₄₇	—	2	4	no	—
228	C₂³×C₄₇	—	2	4	no	—
229	C₂³×C₄₇	—	4	8	no	—
230	C₂³×C₄₇	—	4	8	no	—
231	C₂³×C₄₇	—	4	8	no	—
232	C₂³×C₄₇	—	8	16	no	—
233	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
234	C₂³×C₄₇	C₂×#41	1	4	yes	—
235	C₂³×C₄₇	C₂×#41	1	4	yes	—
236	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
237	Q₈×C₄₇	—	2	8	no	—
238	Q₈×C₄₇	—	4	8	no	—
239	Q₈×C₄₇	—	4	8	no	—
240	D₄×C₄₇	—	2	8	no	—
241	D₄×C₄₇	—	2	16	no	—
242	D₄×C₄₇	—	4	8	no	—
243	D₄×C₄₇	—	4	8	no	—
244	D₄×C₄₇	—	8	16	no	—
245	C₂×C₄×C₄₇	—	2	16	no	—
246	C₂×C₄×C₄₇	—	2	8	no	—
247	C₂×C₄×C₄₇	—	2	2	no	—
248	C₂×C₄×C₄₇	—	2	2	no	—
249	C₂×C₄×C₄₇	—	2	2	no	—
250	C₂×C₄×C₄₇	—	2	2	no	—
251	C₂×C₄×C₄₇	—	2	2	no	—
252	C₂×C₄×C₄₇	—	2	2	no	—
253	C₂×C₄×C₄₇	—	2	2	no	—
254	C₂×C₄×C₄₇	—	2	8	no	—
255	C₂×C₄×C₄₇	—	2	2	no	—
256	C₂×C₄×C₄₇	—	2	2	no	—
257	C₂×C₄×C₄₇	—	2	4	no	—
258	C₂×C₄×C₄₇	—	2	8	no	—
259	C₂×C₄×C₄₇	—	2	8	no	—
260	C₂×C₄×C₄₇	—	2	4	no	—
261	C₂×C₄×C₄₇	—	2	8	no	—
262	C₂×C₄×C₄₇	—	2	8	no	—
263	C₂×C₄×C₄₇	—	2	4	no	—
264	C₂×C₄×C₄₇	—	4	4	no	—
265	C₂×C₄×C₄₇	—	4	8	no	—
266	C₂×C₄×C₄₇	—	4	8	no	—
267	C₂×C₄×C₄₇	—	4	8	no	—
268	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
275	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
276	#35129	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂²×C₄₇	—	2	2	no	—
278	C₂²×C₄₇	—	2	2	no	—
279	C₂²×C₄₇	—	2	8	no	—
280	C₂²×C₄₇	—	2	4	no	—
281	C₂²×C₄₇	—	2	8	no	—
282	C₂²×C₄₇	—	4	2	no	—
283	C₂²×C₄₇	—	4	2	no	—
284	C₂²×C₄₇	—	4	4	no	—
285	C₂²×C₄₇	—	4	4	no	—
286	C₂²×C₄₇	—	4	4	no	—
287	C₂²×C₄₇	—	4	4	no	—
288	C₂²×C₄₇	—	4	8	no	—
289	C₂²×C₄₇	—	4	8	no	—
290	C₂²×C₄₇	—	8	16	no	—
291	C₂²×C₄₇	#525	1	4	yes	—
292	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
293	C₂²×C₄₇	C₂²×#41	1	2	yes	—
294	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
295	C₂²×C₄₇	#585	1	2	yes	—
296	C₄×C₄₇	—	2	2	no	—
297	C₄×C₄₇	—	2	2	no	—
298	C₄×C₄₇	—	2	4	no	—
299	C₄×C₄₇	—	2	2	no	—
300	C₄×C₄₇	—	2	2	no	—
301	C₄×C₄₇	—	2	2	no	—
302	C₄×C₄₇	—	4	2	no	—
303	C₄×C₄₇	—	4	4	no	—
304	C₄×C₄₇	—	4	2	no	—
305	C₄×C₄₇	—	4	8	no	—
306	C₄×C₄₇	#535	1	4	yes	—
307	C₂²×#124	C₂×C₄₇	1	1	yes	characteristic, complemented
308	C₂×C₄×#41	C₂×C₄₇	1	1	yes	characteristic, complemented
309	#2850	C₂×C₄₇	1	4	yes	complemented
310	#2632	C₂×C₄₇	1	2	yes	complemented
311	#2631	C₂×C₄₇	1	2	yes	complemented
312	#2610	C₂×C₄₇	1	4	yes	complemented
313	#2592	C₂×C₄₇	1	2	yes	complemented
314	#2540	C₂×C₄₇	1	2	yes	complemented
315	#2482	C₂×C₄₇	1	2	yes	complemented
316	#2409	C₂×C₄₇	1	2	yes	complemented
317	#2408	C₂×C₄₇	1	2	yes	complemented
318	#2404	C₂×C₄₇	1	2	yes	complemented
319	#2321	C₂×C₄₇	1	4	yes	complemented
320	#2283	C₂×C₄₇	1	1	yes	characteristic, complemented
321	C₂×C₄₇	—	2	4	no	—
322	C₂×C₄₇	—	4	4	no	—
323	C₂×C₄₇	—	8	4	no	—
324	C₂×C₄₇	C₂×#525	1	1	yes	characteristic
325	C₂×C₄₇	C₂×#535	1	1	yes	characteristic
326	C₂×C₄₇	#3449	1	1	yes	characteristic
327	C₂×C₄₇	#3514	1	4	yes	—
328	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
329	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
330	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
331	C₂×#124	—	2	8	no	—
332	C₂×#124	C₂²×C₄₇	1	2	yes	—
333	C₂×#124	C₂²×C₄₇	1	2	yes	—
334	C₂×#124	C₂²×C₄₇	1	2	yes	—
335	C₂×#124	C₂²×C₄₇	1	2	yes	—
336	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	4	yes	complemented
337	C₂×#121	C₂²×C₄₇	1	4	yes	—
338	C₂×#120	C₂²×C₄₇	1	4	yes	—
339	C₄×#41	—	2	8	no	—
340	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
341	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
342	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
343	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
344	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic, complemented
345	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic, complemented
346	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
347	C₂×#117	C₂²×C₄₇	1	2	yes	complemented
348	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
349	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
350	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
351	C₂²×C₄²	C₂²×C₄₇	1	2	yes	complemented
352	#399	C₂²×C₄₇	1	4	yes	complemented
353	#397	C₂²×C₄₇	1	4	yes	complemented
354	#395	C₂²×C₄₇	1	4	yes	complemented
355	#394	C₂²×C₄₇	1	4	yes	—
356	#393	C₂²×C₄₇	1	4	yes	complemented
357	#393	C₂²×C₄₇	1	4	yes	complemented
358	#392	C₂²×C₄₇	1	4	yes	—
359	#392	C₂²×C₄₇	1	4	yes	complemented
360	#391	C₂²×C₄₇	1	4	yes	complemented
361	#390	C₂²×C₄₇	1	4	yes	—
362	#390	C₂²×C₄₇	1	8	yes	complemented
363	#388	C₂²×C₄₇	1	8	yes	complemented
364	#388	C₂²×C₄₇	1	8	yes	complemented
365	#388	C₂²×C₄₇	1	8	yes	complemented
366	#386	C₂²×C₄₇	1	4	yes	—
367	#386	C₂²×C₄₇	1	8	yes	complemented
368	#386	C₂²×C₄₇	1	8	yes	complemented
369	#385	C₂²×C₄₇	1	4	yes	—
370	#383	C₂²×C₄₇	1	2	yes	complemented
371	#382	C₂²×C₄₇	1	2	yes	complemented
372	#381	C₂²×C₄₇	1	2	yes	—
373	#380	C₂²×C₄₇	1	2	yes	—
374	#379	C₂²×C₄₇	1	4	yes	—
375	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
376	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
377	#376	C₂²×C₄₇	1	2	yes	complemented
378	C₄₇	#35129	1	1	yes	characteristic, direct product factor, Sylow
379	C₂⁵	C₂³×C₄₇	1	2	yes	—
380	C₂×#41	—	2	8	no	—
381	C₂×#41	—	2	4	no	—
382	C₂²×Q₈	—	2	4	no	—
383	C₂²×Q₈	—	4	4	no	—
384	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
385	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
386	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
387	C₂²×D₄	—	2	4	no	—
388	C₂²×D₄	—	4	4	no	—
389	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
390	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
391	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
392	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
393	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
394	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
395	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
396	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
399	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
400	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
401	#124	—	2	8	no	—
402	#124	—	2	8	no	—
403	#124	—	2	8	no	—
404	#124	—	2	8	no	—
405	C₂²⋊Q₈	—	4	8	no	—
406	#121	—	4	8	no	—
407	#120	—	2	16	no	—
408	C₄×Q₈	—	2	4	no	—
409	C₄×Q₈	—	2	4	no	—
410	C₄×D₄	—	2	8	no	—
411	C₄×D₄	—	2	8	no	—
412	C₄×D₄	—	2	4	no	—
413	C₄×D₄	—	2	4	no	—
414	#117	—	2	4	no	—
415	#117	—	2	8	no	—
416	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
422	C₂×C₂²⋊C₄	—	2	8	no	—
423	C₂×C₂²⋊C₄	—	2	8	no	—
424	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
436	C₂×C₄²	—	2	8	no	—
437	C₂×C₄²	D₄×C₄₇	1	8	yes	complemented
438	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
439	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
440	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
441	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
442	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
446	#95	C₂³×C₄₇	1	4	yes	—
447	#95	C₂³×C₄₇	1	4	yes	—
448	#95	C₂³×C₄₇	1	4	yes	—
449	#95	C₂³×C₄₇	1	4	yes	—
450	#95	C₂³×C₄₇	1	8	yes	—
451	#95	C₂³×C₄₇	1	8	yes	—
452	C₂⁴	—	2	4	no	—
453	C₂⁴	—	2	8	no	—
454	C₂⁴	—	4	4	no	—
455	C₂⁴	—	4	4	no	—
456	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
457	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
458	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
459	#41	—	2	32	no	—
460	C₂×Q₈	—	2	2	no	—
461	C₂×Q₈	—	2	4	no	—
462	C₂×Q₈	—	2	4	no	—
463	C₂×Q₈	—	2	4	no	—
464	C₂×Q₈	—	2	8	no	—
465	C₂×Q₈	—	4	4	no	—
466	C₂×Q₈	—	4	16	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	16	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	2	8	no	—
475	C₂×D₄	—	4	4	no	—
476	C₂×D₄	—	4	16	no	—
477	C₂×D₄	—	4	8	no	—
478	C₂×D₄	—	4	8	no	—
479	C₂×D₄	#41×C₄₇	1	8	yes	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	8	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	—	4	4	no	—
492	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
493	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
494	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
496	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
501	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	8	no	—
511	C₄⋊C₄	—	4	8	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	8	no	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	—	2	8	no	—
516	C₂²⋊C₄	—	2	8	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	16	no	—
521	C₂²⋊C₄	—	4	8	no	—
522	C₂²⋊C₄	—	4	8	no	—
523	C₂²⋊C₄	—	4	8	no	—
524	C₄²	—	2	4	no	—
525	C₄²	—	2	4	no	—
526	C₄²	—	2	4	no	—
527	C₄²	—	4	4	no	—
528	C₄²	C₂×D₄×C₄₇	1	4	yes	—
529	C₄²	C₂×D₄×C₄₇	1	4	yes	—
530	C₄²	C₂×D₄×C₄₇	1	4	yes	—
531	C₄²	C₂×D₄×C₄₇	1	4	yes	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	8	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	4	8	no	—
544	C₂³	—	4	8	no	—
545	C₂³	—	4	8	no	—
546	C₂³	—	8	16	no	—
547	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
548	C₂³	C₂×#41×C₄₇	1	4	yes	—
549	C₂³	C₂×#41×C₄₇	1	4	yes	—
550	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
551	Q₈	—	2	8	no	—
552	Q₈	—	4	8	no	—
553	Q₈	—	4	8	no	—
554	D₄	—	2	8	no	—
555	D₄	—	2	16	no	—
556	D₄	—	4	8	no	—
557	D₄	—	4	8	no	—
558	D₄	—	8	16	no	—
559	C₂×C₄	—	2	16	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	8	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	8	no	—
576	C₂×C₄	—	2	8	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	8	no	—
580	C₂×C₄	—	4	8	no	—
581	C₂×C₄	—	4	8	no	—
582	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
583	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
584	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
585	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
586	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
587	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
588	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
589	C₂×C₄	H(5,𝔽₂)×C₄₇	1	4	yes	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	8	no	—
593	C₂²	—	2	4	no	—
594	C₂²	—	2	8	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	8	no	—
602	C₂²	—	4	8	no	—
603	C₂²	—	8	16	no	—
604	C₂²	C₄₇×#525	1	4	yes	—
605	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
606	C₂²	C₂²×#41×C₄₇	1	2	yes	—
607	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	2	yes	—
608	C₂²	C₄₇×#585	1	2	yes	—
609	C₄	—	2	2	no	—
610	C₄	—	2	2	no	—
611	C₄	—	2	4	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	4	4	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	8	no	—
619	C₄	C₄₇×#535	1	4	yes	—
620	C₂	—	2	4	no	—
621	C₂	—	4	4	no	—
622	C₂	—	8	4	no	—
623	C₂	C₂×C₄₇×#525	1	1	yes	characteristic
624	C₂	C₂×C₄₇×#535	1	1	yes	characteristic
625	C₂	C₄₇×#3449	1	1	yes	characteristic
626	C₂	C₄₇×#3514	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×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. C₂×C₄×#41×C₄₇	C₂	semidirect
3. C₄₇×#2850	C₂	semidirect
4. C₄₇×#2632	C₂	semidirect
5. C₄₇×#2631	C₂	semidirect
6. C₄₇×#2610	C₂	semidirect
7. C₄₇×#2592	C₂	semidirect
8. C₄₇×#2540	C₂	semidirect
9. C₄₇×#2482	C₂	semidirect
10. C₄₇×#2409	C₂	semidirect
11. C₄₇×#2408	C₂	semidirect
12. C₄₇×#2404	C₂	semidirect
13. C₄₇×#2321	C₂	semidirect
14. C₄₇×#2283	C₂	semidirect
23. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
27. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
28. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
31. C₂×C₄×D₄×C₄₇	C₂²	semidirect
32. C₂×C₄×D₄×C₄₇	C₂²	semidirect
34. C₂×#117×C₄₇	C₂²	semidirect
38. C₂²×C₄²×C₄₇	C₂²	semidirect
39. C₄₇×#399	C₂²	semidirect
40. C₄₇×#397	C₂²	semidirect
41. C₄₇×#395	C₂²	semidirect
43. C₄₇×#393	C₂²	semidirect
44. C₄₇×#393	C₂²	semidirect
46. C₄₇×#392	C₂²	semidirect
47. C₄₇×#391	C₂²	semidirect
49. C₄₇×#390	C₂²	semidirect
50. C₄₇×#388	C₂²	semidirect
51. C₄₇×#388	C₂²	semidirect
52. C₄₇×#388	C₂²	semidirect
54. C₄₇×#386	C₂²	semidirect
55. C₄₇×#386	C₂²	semidirect
57. C₄₇×#383	C₂²	semidirect
58. C₄₇×#382	C₂²	semidirect
62. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
64. C₄₇×#376	C₂²	semidirect
123. C₂×C₄²×C₄₇	D₄	semidirect
276. #35129	C₄₇	direct (N × H)
307. C₂²×#124	C₂×C₄₇	semidirect
308. C₂×C₄×#41	C₂×C₄₇	semidirect
309. #2850	C₂×C₄₇	semidirect
310. #2632	C₂×C₄₇	semidirect
311. #2631	C₂×C₄₇	semidirect
312. #2610	C₂×C₄₇	semidirect
313. #2592	C₂×C₄₇	semidirect
314. #2540	C₂×C₄₇	semidirect
315. #2482	C₂×C₄₇	semidirect
316. #2409	C₂×C₄₇	semidirect
317. #2408	C₂×C₄₇	semidirect
318. #2404	C₂×C₄₇	semidirect
319. #2321	C₂×C₄₇	semidirect
320. #2283	C₂×C₄₇	semidirect
336. C₂×C₂²⋊Q₈	C₂²×C₄₇	semidirect
340. C₂×C₄×Q₈	C₂²×C₄₇	semidirect
341. C₂×C₄×Q₈	C₂²×C₄₇	semidirect
344. C₂×C₄×D₄	C₂²×C₄₇	semidirect
345. C₂×C₄×D₄	C₂²×C₄₇	semidirect
347. C₂×#117	C₂²×C₄₇	semidirect
351. C₂²×C₄²	C₂²×C₄₇	semidirect
352. #399	C₂²×C₄₇	semidirect
353. #397	C₂²×C₄₇	semidirect
354. #395	C₂²×C₄₇	semidirect
356. #393	C₂²×C₄₇	semidirect
357. #393	C₂²×C₄₇	semidirect
359. #392	C₂²×C₄₇	semidirect
360. #391	C₂²×C₄₇	semidirect
362. #390	C₂²×C₄₇	semidirect
363. #388	C₂²×C₄₇	semidirect
364. #388	C₂²×C₄₇	semidirect
365. #388	C₂²×C₄₇	semidirect
367. #386	C₂²×C₄₇	semidirect
368. #386	C₂²×C₄₇	semidirect
370. #383	C₂²×C₄₇	semidirect
371. #382	C₂²×C₄₇	semidirect
375. C₄×C₄⋊C₄	C₂²×C₄₇	semidirect
377. #376	C₂²×C₄₇	semidirect
378. C₄₇	#35129	direct (N × H)
437. C₂×C₄²	D₄×C₄₇	semidirect

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
C₂×C₄×#41×C₄₇	2
C₄₇×#2850	2
C₄₇×#2632	2
C₄₇×#2631	2
C₄₇×#2610	2
C₄₇×#2592	2
C₄₇×#2540	2
C₄₇×#2482	2
C₄₇×#2409	2
C₄₇×#2408	2
C₄₇×#2404	2
C₄₇×#2321	2
C₄₇×#2283	2
#35129	47

Subgroups — C47×#35129 #26074827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#35129 #26074827