Subgroups — C₄₇×#22483 #26062181

Order 12032.

1126 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#555	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₄₇×#1997	C₂	1	2	yes	maximal, complemented
4	C₄₇×#1900	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1822	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1800	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#100×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1742	C₂	1	2	yes	maximal, complemented
9	C₂²×M₁₆×C₄₇	C₂²	1	4	yes	—
10	C₄₇×#555	—	2	2	no	—
11	C₄₇×#555	—	2	4	no	—
12	C₄₇×#555	—	2	2	no	—
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₇	C₄	1	4	yes	—
15	C₂×#121×C₄₇	C₄	1	2	yes	—
16	C₂×#121×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₇	C₄	1	2	yes	—
20	C₂×#117×C₄₇	C₂²	1	2	yes	—
21	C₄₇×#436	—	2	2	no	—
22	C₄₇×#435	—	2	4	no	—
23	C₈×D₄×C₄₇	—	2	2	no	—
24	C₄₇×#423	C₂²	1	2	yes	—
25	C₂×#100×C₄₇	C₂²	1	2	yes	—
26	C₂×#100×C₄₇	C₂²	1	2	yes	—
27	C₄₇×#407	C₂²	1	4	yes	—
28	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
29	C₄₇×#343	C₂²	1	1	yes	characteristic
30	C₄₇×#343	C₂²	1	1	yes	characteristic
31	C₄₇×#343	C₂²	1	2	yes	—
32	C₄₇×#343	C₂²	1	4	yes	—
33	C₄₇×#343	C₂²	1	4	yes	—
34	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
35	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
36	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
40	C₂×M₁₆×C₄₇	—	2	4	no	—
41	C₂×M₁₆×C₄₇	—	2	8	no	—
42	C₂×M₁₆×C₄₇	—	4	4	no	—
43	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
44	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
45	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₇	—	2	4	no	—
47	C₄⋊Q₈×C₄₇	—	2	2	no	—
48	C₄⋊Q₈×C₄₇	—	2	2	no	—
49	#124×C₄₇	—	2	8	no	—
50	#124×C₄₇	—	2	8	no	—
51	#121×C₄₇	—	2	4	no	—
52	#121×C₄₇	—	2	4	no	—
53	#121×C₄₇	—	2	4	no	—
54	#121×C₄₇	—	2	4	no	—
55	C₄×D₄×C₄₇	—	2	2	no	—
56	C₄×D₄×C₄₇	—	2	2	no	—
57	C₄×D₄×C₄₇	D₄	1	2	yes	—
58	C₄×D₄×C₄₇	D₄	1	4	yes	—
59	C₄×D₄×C₄₇	D₄	1	2	yes	—
60	#117×C₄₇	—	2	4	no	—
61	#117×C₄₇	—	2	4	no	—
62	#117×C₄₇	—	2	4	no	—
63	#117×C₄₇	—	2	2	no	—
64	#117×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
71	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₄₇	—	2	2	no	—
76	C₄⋊C₈×C₄₇	—	2	2	no	—
77	#100×C₄₇	—	2	4	no	—
78	#100×C₄₇	—	4	2	no	—
79	C₂²⋊C₈×C₄₇	—	2	4	no	—
80	C₂²⋊C₈×C₄₇	—	2	4	no	—
81	#97×C₄₇	—	2	2	no	—
82	C₄×C₈×C₄₇	—	2	2	no	—
83	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
84	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
85	C₂×Q₈×C₄₇	—	2	4	no	—
86	C₂×Q₈×C₄₇	—	8	2	no	—
87	C₂×D₄×C₄₇	—	2	8	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	1	no	—
91	C₂×D₄×C₄₇	—	2	1	no	—
92	C₂×D₄×C₄₇	—	4	2	no	—
93	C₂×D₄×C₄₇	—	8	4	no	—
94	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
95	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	4	4	no	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₄₇	—	2	2	no	—
111	M₁₆×C₄₇	—	2	4	no	—
112	M₁₆×C₄₇	—	2	2	no	—
113	M₁₆×C₄₇	—	2	4	no	—
114	M₁₆×C₄₇	—	2	2	no	—
115	M₁₆×C₄₇	—	4	8	no	—
116	M₁₆×C₄₇	#41	1	4	yes	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	4	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	4	8	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	4	no	—
125	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
126	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
127	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₄₇	—	2	8	no	—
129	C₂²⋊C₄×C₄₇	—	2	4	no	—
130	C₂²⋊C₄×C₄₇	—	2	4	no	—
131	C₂²⋊C₄×C₄₇	—	2	4	no	—
132	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
133	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
134	C₄²×C₄₇	—	2	4	no	—
135	C₄²×C₄₇	—	2	4	no	—
136	C₄²×C₄₇	C₂×D₄	1	2	yes	—
137	C₄²×C₄₇	C₂×D₄	1	2	yes	—
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	—	2	2	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	—	4	2	no	—
145	C₂³×C₄₇	—	4	2	no	—
146	C₂³×C₄₇	—	4	2	no	—
147	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
148	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
149	Q₈×C₄₇	—	8	4	no	—
150	D₄×C₄₇	—	2	4	no	—
151	D₄×C₄₇	—	4	2	no	—
152	D₄×C₄₇	—	4	2	no	—
153	D₄×C₄₇	—	4	2	no	—
154	D₄×C₄₇	—	8	8	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	4	no	—
166	C₂×C₄×C₄₇	—	4	4	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	4	no	—
169	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
176	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
178	C₈×C₄₇	—	2	4	no	—
179	C₈×C₄₇	—	4	4	no	—
180	C₈×C₄₇	—	4	2	no	—
181	#22483	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	—	2	4	no	—
187	C₂²×C₄₇	—	4	2	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	—	8	2	no	—
191	C₂²×C₄₇	—	8	2	no	—
192	C₂²×C₄₇	—	8	2	no	—
193	C₂²×C₄₇	—	8	2	no	—
194	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
196	C₂²×C₄₇	#520	1	1	yes	characteristic
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	4	2	no	—
202	C₄×C₄₇	—	4	4	no	—
203	C₄×C₄₇	#413	1	2	yes	—
204	C₄×C₄₇	#546	1	2	yes	—
205	C₄×C₄₇	#547	1	2	yes	—
206	C₂×#555	C₂×C₄₇	1	1	yes	characteristic
207	D₄×M₁₆	C₂×C₄₇	1	2	yes	complemented
208	#1997	C₂×C₄₇	1	2	yes	complemented
209	#1900	C₂×C₄₇	1	4	yes	complemented
210	#1822	C₂×C₄₇	1	2	yes	complemented
211	#1800	C₂×C₄₇	1	1	yes	characteristic, complemented
212	C₄×#100	C₂×C₄₇	1	1	yes	characteristic, complemented
213	#1742	C₂×C₄₇	1	2	yes	complemented
214	C₂×C₄₇	—	2	1	no	—
215	C₂×C₄₇	—	2	1	no	—
216	C₂×C₄₇	—	4	4	no	—
217	C₂×C₄₇	—	8	2	no	—
218	C₂×C₄₇	#2339	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
220	C₂×C₄₇	#2888	1	1	yes	characteristic
221	C₂²×M₁₆	C₂²×C₄₇	1	4	yes	—
222	#555	—	2	2	no	—
223	#555	—	2	4	no	—
224	#555	—	2	2	no	—
225	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
226	C₂×#124	C₄×C₄₇	1	4	yes	—
227	C₂×#121	C₄×C₄₇	1	2	yes	—
228	C₂×#121	C₂²×C₄₇	1	2	yes	—
229	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
231	C₂×#117	C₄×C₄₇	1	2	yes	—
232	C₂×#117	C₂²×C₄₇	1	2	yes	—
233	#436	—	2	2	no	—
234	#435	—	2	4	no	—
235	C₈×D₄	—	2	2	no	—
236	#423	C₂²×C₄₇	1	2	yes	—
237	C₂×#100	C₂²×C₄₇	1	2	yes	—
238	C₂×#100	C₂²×C₄₇	1	2	yes	—
239	#407	C₂²×C₄₇	1	4	yes	—
240	C₄×M₁₆	C₂²×C₄₇	1	2	yes	—
241	#343	C₂²×C₄₇	1	2	yes	—
242	#343	C₂²×C₄₇	1	1	yes	characteristic
243	#343	C₂²×C₄₇	1	4	yes	—
244	#343	C₂²×C₄₇	1	4	yes	—
245	#343	C₂²×C₄₇	1	1	yes	characteristic
246	C₄₇	#22483	1	1	yes	characteristic, direct product factor, Sylow
247	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
248	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
249	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
250	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
251	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
252	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
253	C₂×M₁₆	—	2	4	no	—
254	C₂×M₁₆	—	2	8	no	—
255	C₂×M₁₆	—	4	4	no	—
256	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
257	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
258	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
259	C₂²×C₈	—	2	4	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	—	2	2	no	—
262	#124	—	2	8	no	—
263	#124	—	2	8	no	—
264	#121	—	2	4	no	—
265	#121	—	2	4	no	—
266	#121	—	2	4	no	—
267	#121	—	2	4	no	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	D₄×C₄₇	1	2	yes	—
271	C₄×D₄	D₄×C₄₇	1	4	yes	—
272	C₄×D₄	D₄×C₄₇	1	2	yes	—
273	#117	—	2	4	no	—
274	#117	—	2	4	no	—
275	#117	—	2	4	no	—
276	#117	—	2	2	no	—
277	#117	—	2	2	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
279	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
283	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
284	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
285	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
286	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
287	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	2	2	no	—
290	#100	—	2	4	no	—
291	#100	—	4	2	no	—
292	C₂²⋊C₈	—	2	4	no	—
293	C₂²⋊C₈	—	2	4	no	—
294	#97	—	2	2	no	—
295	C₄×C₈	—	2	2	no	—
296	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
297	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	8	2	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	8	4	no	—
307	C₂×D₄	C₂²⋊C₄×C₄₇	1	2	yes	—
308	C₂×D₄	C₂²⋊C₄×C₄₇	1	2	yes	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
316	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
318	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
319	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
321	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	—	2	4	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	4	8	no	—
329	M₁₆	#41×C₄₇	1	4	yes	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	4	8	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
339	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
340	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
346	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	4	no	—
349	C₄²	C₂×D₄×C₄₇	1	2	yes	—
350	C₄²	C₂×D₄×C₄₇	1	2	yes	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
361	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
362	Q₈	—	8	4	no	—
363	D₄	—	2	4	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	8	8	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
386	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
388	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
389	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
390	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₈	—	4	4	no	—
393	C₈	—	4	2	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
407	C₂²	C₄×#41×C₄₇	1	1	yes	characteristic
408	C₂²	C₄₇×#520	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	4	no	—
415	C₄	C₄₇×#413	1	2	yes	—
416	C₄	C₄₇×#546	1	2	yes	—
417	C₄	C₄₇×#547	1	2	yes	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	4	4	no	—
421	C₂	—	8	2	no	—
422	C₂	C₄₇×#2339	1	1	yes	characteristic
423	C₂	C₂×C₄₇×#413	1	1	yes	characteristic
424	C₂	C₄₇×#2888	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#555	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×M₁₆×C₄₇	C₂	semidirect
3. C₄₇×#1997	C₂	semidirect
4. C₄₇×#1900	C₂	semidirect
5. C₄₇×#1822	C₂	semidirect
6. C₄₇×#1800	C₂	semidirect
7. C₄×#100×C₄₇	C₂	semidirect
8. C₄₇×#1742	C₂	semidirect
181. #22483	C₄₇	direct (N × H)
207. D₄×M₁₆	C₂×C₄₇	semidirect
208. #1997	C₂×C₄₇	semidirect
209. #1900	C₂×C₄₇	semidirect
210. #1822	C₂×C₄₇	semidirect
211. #1800	C₂×C₄₇	semidirect
212. C₄×#100	C₂×C₄₇	semidirect
213. #1742	C₂×C₄₇	semidirect
246. C₄₇	#22483	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#555	2
D₄×M₁₆×C₄₇	2
C₄₇×#1997	2
C₄₇×#1900	2
C₄₇×#1822	2
C₄₇×#1800	2
C₄×#100×C₄₇	2
C₄₇×#1742	2
#22483	47

Subgroups — C47×#22483 #26062181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#22483 #26062181