Subgroups — C₄₇×#13926 #26053624

Order 12032.

1854 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#391	C₂	1	2	yes	maximal
3	C₂×C₄₇×#384	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1441	C₂	1	4	yes	maximal
6	C₄₇×C₄⋊#95	C₂	1	2	yes	maximal
7	C₄₇×C₄⋊#95	C₂	1	4	yes	maximal
8	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₄₇	—	2	4	no	—
10	C₂×C₄×Q₈×C₄₇	—	2	4	no	—
11	C₂×C₄×Q₈×C₄₇	C₄	1	8	yes	complemented
12	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#391	—	2	8	no	—
22	C₄₇×#384	—	2	4	no	—
23	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
24	C₂×#95×C₄₇	C₂²	1	2	yes	—
25	C₂×#95×C₄₇	C₂²	1	8	yes	—
26	C₂×#95×C₄₇	C₂²	1	8	yes	—
27	C₂²×Q₈×C₄₇	—	2	2	no	—
28	C₂²×Q₈×C₄₇	—	2	2	no	—
29	C₂²×Q₈×C₄₇	—	2	2	no	—
30	C₂²×Q₈×C₄₇	—	2	2	no	—
31	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
32	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
33	C₂²×Q₈×C₄₇	Q₈	1	4	yes	—
34	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
35	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
36	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₄×Q₈×C₄₇	—	2	32	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	4	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	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
54	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
55	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
57	C₂×C₄⋊C₄×C₄₇	Q₈	1	8	yes	complemented
58	C₂×C₄²×C₄₇	—	2	4	no	—
59	C₂×C₄²×C₄₇	—	2	4	no	—
60	C₂×C₄²×C₄₇	—	2	4	no	—
61	C₂×C₄²×C₄₇	—	2	4	no	—
62	C₂×C₄²×C₄₇	—	2	4	no	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₄₇	D₄	1	4	yes	—
66	C₂×C₄²×C₄₇	D₄	1	4	yes	—
67	#95×C₄₇	—	2	4	no	—
68	#95×C₄₇	—	2	16	no	—
69	#95×C₄₇	—	4	8	no	—
70	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
71	C₂×Q₈×C₄₇	—	2	8	no	—
72	C₂×Q₈×C₄₇	—	2	8	no	—
73	C₂×Q₈×C₄₇	—	2	8	no	—
74	C₂×Q₈×C₄₇	—	2	8	no	—
75	C₂×Q₈×C₄₇	—	2	8	no	—
76	C₂×Q₈×C₄₇	—	2	8	no	—
77	C₂×Q₈×C₄₇	C₄⋊C₄	1	16	yes	complemented
78	C₂²×C₄×C₄₇	—	2	2	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	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	8	no	—
98	C₂²×C₄×C₄₇	—	2	8	no	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	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×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×Q₈	1	8	yes	—
113	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
114	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
116	C₂²×C₄×C₄₇	#41	1	2	yes	—
117	C₂²×C₄×C₄₇	#41	1	2	yes	—
118	C₂²×C₄×C₄₇	#41	1	4	yes	—
119	C₄⋊C₄×C₄₇	—	2	16	no	—
120	C₄⋊C₄×C₄₇	—	2	8	no	—
121	C₄⋊C₄×C₄₇	—	2	16	no	—
122	C₄⋊C₄×C₄₇	—	4	8	no	—
123	C₄⋊C₄×C₄₇	—	4	8	no	—
124	C₄⋊C₄×C₄₇	—	4	8	no	—
125	C₄²×C₄₇	—	2	16	no	—
126	C₄²×C₄₇	—	4	8	no	—
127	C₄²×C₄₇	C₂²⋊C₄	1	16	yes	—
128	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
129	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
130	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
131	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
132	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
133	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
134	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
135	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
136	C₂³×C₄₇	C₂×#41	1	2	yes	—
137	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
138	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
139	Q₈×C₄₇	—	2	32	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	4	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	8	no	—
152	C₂×C₄×C₄₇	—	2	8	no	—
153	C₂×C₄×C₄₇	—	2	8	no	—
154	C₂×C₄×C₄₇	—	2	8	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	4	no	—
159	C₂×C₄×C₄₇	—	4	4	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	—	4	4	no	—
162	C₂×C₄×C₄₇	—	4	4	no	—
163	C₂×C₄×C₄₇	—	4	4	no	—
164	C₂×C₄×C₄₇	—	4	4	no	—
165	C₂×C₄×C₄₇	—	4	8	no	—
166	C₂×C₄×C₄₇	—	4	8	no	—
167	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
168	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
169	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
170	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
171	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
172	C₂×C₄×C₄₇	#117	1	4	yes	—
173	C₂×C₄×C₄₇	C₄×Q₈	1	8	yes	—
174	C₂×C₄×C₄₇	#121	1	4	yes	—
175	C₂×C₄×C₄₇	#121	1	4	yes	—
176	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
177	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
178	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
179	C₂×C₄×C₄₇	#124	1	4	yes	—
180	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
181	#13926	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
186	C₂²×C₄₇	#520	1	2	yes	—
187	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
192	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
194	C₂²×C₄₇	#535	1	1	yes	characteristic
195	C₂²×C₄₇	#536	1	1	yes	characteristic
196	C₂²×C₄₇	#537	1	2	yes	—
197	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
198	C₂²×C₄₇	#550	1	2	yes	—
199	C₂²×C₄₇	#554	1	2	yes	—
200	C₂²×C₄₇	#556	1	2	yes	—
201	C₂²×C₄₇	#557	1	2	yes	—
202	C₂²×C₄₇	#557	1	2	yes	—
203	C₂²×C₄₇	Q₈²	1	2	yes	—
204	C₂²×C₄₇	#559	1	2	yes	—
205	C₄×C₄₇	—	2	4	no	—
206	C₄×C₄₇	—	2	8	no	—
207	C₄×C₄₇	—	4	4	no	—
208	C₄×C₄₇	—	4	8	no	—
209	C₄×C₄₇	—	8	4	no	—
210	C₄×C₄₇	#380	1	8	yes	—
211	C₄×C₄₇	#391	1	8	yes	complemented
212	C₂²×C₄×Q₈	C₂×C₄₇	1	1	yes	characteristic
213	C₂×#391	C₂×C₄₇	1	2	yes	—
214	C₂×#384	C₂×C₄₇	1	1	yes	characteristic
215	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic
216	#1441	C₂×C₄₇	1	4	yes	—
217	C₄⋊#95	C₂×C₄₇	1	4	yes	—
218	C₄⋊#95	C₂×C₄₇	1	2	yes	—
219	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
220	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
221	C₂×C₄₇	#2311	1	1	yes	characteristic
222	C₂×C₄₇	Q₈×C₄⋊C₄	1	2	yes	—
223	C₂×C₄₇	#2355	1	2	yes	—
224	C₂×C₄₇	#2538	1	2	yes	—
225	C₂×C₄₇	#2546	1	1	yes	characteristic
226	C₂×C₄₇	#2548	1	1	yes	characteristic
227	C₂×C₄₇	#2567	1	1	yes	characteristic
228	C₂×C₄₇	#2568	1	1	yes	characteristic
229	C₂×C₄₇	#2582	1	2	yes	—
230	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
231	C₂×C₄×Q₈	—	2	4	no	—
232	C₂×C₄×Q₈	—	2	4	no	—
233	C₂×C₄×Q₈	C₄×C₄₇	1	8	yes	complemented
234	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
236	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
238	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
239	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
240	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
241	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
242	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
243	#391	—	2	8	no	—
244	#384	—	2	4	no	—
245	C₄×C₄⋊C₄	—	2	4	no	—
246	C₂×#95	C₂²×C₄₇	1	8	yes	—
247	C₂×#95	C₂²×C₄₇	1	2	yes	—
248	C₂×#95	C₂²×C₄₇	1	8	yes	—
249	C₄₇	#13926	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×Q₈	—	2	2	no	—
251	C₂²×Q₈	—	2	2	no	—
252	C₂²×Q₈	—	2	2	no	—
253	C₂²×Q₈	—	2	2	no	—
254	C₂²×Q₈	C₂×C₄×C₄₇	1	4	yes	—
255	C₂²×Q₈	D₄×C₄₇	1	4	yes	—
256	C₂²×Q₈	Q₈×C₄₇	1	4	yes	—
257	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
258	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
259	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
260	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
261	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
262	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
264	C₄×Q₈	—	2	32	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	4	no	—
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	4	no	—
275	C₂×C₄⋊C₄	—	2	4	no	—
276	C₂×C₄⋊C₄	—	2	8	no	—
277	C₂×C₄⋊C₄	—	4	4	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
279	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
280	C₂×C₄⋊C₄	Q₈×C₄₇	1	8	yes	complemented
281	C₂×C₄²	—	2	4	no	—
282	C₂×C₄²	—	2	4	no	—
283	C₂×C₄²	—	2	4	no	—
284	C₂×C₄²	—	2	4	no	—
285	C₂×C₄²	—	2	4	no	—
286	C₂×C₄²	C₂×C₄×C₄₇	1	8	yes	—
287	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
288	C₂×C₄²	D₄×C₄₇	1	4	yes	—
289	C₂×C₄²	D₄×C₄₇	1	4	yes	—
290	#95	—	2	4	no	—
291	#95	—	2	16	no	—
292	#95	—	4	8	no	—
293	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
294	C₂×Q₈	—	2	8	no	—
295	C₂×Q₈	—	2	8	no	—
296	C₂×Q₈	—	2	8	no	—
297	C₂×Q₈	—	2	8	no	—
298	C₂×Q₈	—	2	8	no	—
299	C₂×Q₈	—	2	8	no	—
300	C₂×Q₈	C₄⋊C₄×C₄₇	1	16	yes	complemented
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
323	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
324	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
325	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
326	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
330	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
335	C₂²×C₄	C₂×Q₈×C₄₇	1	8	yes	—
336	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
337	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
338	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
339	C₂²×C₄	#41×C₄₇	1	2	yes	—
340	C₂²×C₄	#41×C₄₇	1	2	yes	—
341	C₂²×C₄	#41×C₄₇	1	4	yes	—
342	C₄⋊C₄	—	2	16	no	—
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	—	2	16	no	—
345	C₄⋊C₄	—	4	8	no	—
346	C₄⋊C₄	—	4	8	no	—
347	C₄⋊C₄	—	4	8	no	—
348	C₄²	—	2	16	no	—
349	C₄²	—	4	8	no	—
350	C₄²	C₂²⋊C₄×C₄₇	1	16	yes	—
351	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
352	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
353	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
354	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
355	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
356	C₂³	C₂²×Q₈×C₄₇	1	2	yes	—
357	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
358	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
359	C₂³	C₂×#41×C₄₇	1	2	yes	—
360	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
361	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
362	Q₈	—	2	32	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
392	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
393	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	8	yes	—
394	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
395	C₂×C₄	#117×C₄₇	1	4	yes	—
396	C₂×C₄	C₄×Q₈×C₄₇	1	8	yes	—
397	C₂×C₄	#121×C₄₇	1	4	yes	—
398	C₂×C₄	#121×C₄₇	1	4	yes	—
399	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
400	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
401	C₂×C₄	C₂²⋊Q₈×C₄₇	1	8	yes	—
402	C₂×C₄	#124×C₄₇	1	4	yes	—
403	C₂×C₄	C₄⋊Q₈×C₄₇	1	4	yes	—
404	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
405	C₂²	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
406	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
407	C₂²	C₂×C₄×Q₈×C₄₇	1	2	yes	—
408	C₂²	C₄₇×#520	1	2	yes	—
409	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
410	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
411	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
412	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
413	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
414	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
415	C₂²	C₂×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
416	C₂²	C₄₇×#535	1	1	yes	characteristic
417	C₂²	C₄₇×#536	1	1	yes	characteristic
418	C₂²	C₄₇×#537	1	2	yes	—
419	C₂²	D₄×Q₈×C₄₇	1	2	yes	—
420	C₂²	C₄₇×#550	1	2	yes	—
421	C₂²	C₄₇×#554	1	2	yes	—
422	C₂²	C₄₇×#556	1	2	yes	—
423	C₂²	C₄₇×#557	1	2	yes	—
424	C₂²	C₄₇×#557	1	2	yes	—
425	C₂²	Q₈²×C₄₇	1	2	yes	—
426	C₂²	C₄₇×#559	1	2	yes	—
427	C₄	—	2	8	no	—
428	C₄	—	2	4	no	—
429	C₄	—	4	8	no	—
430	C₄	—	4	4	no	—
431	C₄	—	8	4	no	—
432	C₄	C₄₇×#380	1	8	yes	—
433	C₄	C₄₇×#391	1	8	yes	complemented
434	C₂	C₂×C₄₇×#380	1	1	yes	characteristic
435	C₂	C₂×C₄₇×#391	1	1	yes	characteristic
436	C₂	C₄₇×#2311	1	1	yes	characteristic
437	C₂	Q₈×C₄⋊C₄×C₄₇	1	2	yes	—
438	C₂	C₄₇×#2355	1	2	yes	—
439	C₂	C₄₇×#2538	1	2	yes	—
440	C₂	C₄₇×#2546	1	1	yes	characteristic
441	C₂	C₄₇×#2548	1	1	yes	characteristic
442	C₂	C₄₇×#2567	1	1	yes	characteristic
443	C₂	C₄₇×#2568	1	1	yes	characteristic
444	C₂	C₄₇×#2582	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×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
11. C₂×C₄×Q₈×C₄₇	C₄	semidirect
57. C₂×C₄⋊C₄×C₄₇	Q₈	semidirect
77. C₂×Q₈×C₄₇	C₄⋊C₄	semidirect
181. #13926	C₄₇	direct (N × H)
211. C₄×C₄₇	#391	semidirect
233. C₂×C₄×Q₈	C₄×C₄₇	semidirect
249. C₄₇	#13926	direct (N × H)
280. C₂×C₄⋊C₄	Q₈×C₄₇	semidirect
300. C₂×Q₈	C₄⋊C₄×C₄₇	semidirect
433. C₄	C₄₇×#391	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₄₇	2
C₂×C₄₇×#391	2
C₂×C₄₇×#384	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄₇×#1441	2
C₄₇×C₄⋊#95	2
#13926	47

Subgroups — C47×#13926 #26053624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#13926 #26053624