Subgroups — C₂×C₄₇×#1800 #26060333

Order 12032.

1842 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#423	C₂	1	2	yes	maximal, complemented
3	C₂²×#100×C₄₇	C₂	1	2	yes	maximal
4	C₄₇×#1800	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₇×#343	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂⁴×C₄×C₄₇	C₄	1	2	yes	—
8	C₂²×M₁₆×C₄₇	C₂²	1	4	yes	—
9	C₂×C₄×D₄×C₄₇	—	2	2	no	—
10	C₂×C₄×D₄×C₄₇	—	2	2	no	—
11	C₂×C₄×D₄×C₄₇	—	2	4	no	—
12	C₂×C₄×D₄×C₄₇	C₄	1	4	yes	—
13	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#423	—	2	4	no	—
18	C₄₇×#423	C₂²	1	8	yes	complemented
19	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
20	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
21	C₂×#100×C₄₇	—	2	8	no	—
22	C₂×#100×C₄₇	C₂²	1	8	yes	—
23	C₄₇×#343	C₂²	1	8	yes	complemented
24	C₂⁵×C₄₇	C₂×C₄	1	2	yes	—
25	C₂²×D₄×C₄₇	—	2	2	no	—
26	C₂²×D₄×C₄₇	—	2	2	no	—
27	C₂²×D₄×C₄₇	—	2	4	no	—
28	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
29	C₂²×D₄×C₄₇	D₄	1	4	yes	—
30	C₂²×D₄×C₄₇	Q₈	1	4	yes	—
31	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
32	C₂³×C₄×C₄₇	—	2	4	no	—
33	C₂³×C₄×C₄₇	—	2	2	no	—
34	C₂³×C₄×C₄₇	—	2	2	no	—
35	C₂³×C₄×C₄₇	—	4	8	no	—
36	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
39	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₄₇	—	2	4	no	—
42	C₂×M₁₆×C₄₇	—	2	8	no	—
43	C₂×M₁₆×C₄₇	—	2	8	no	—
44	C₂×M₁₆×C₄₇	C₂³	1	8	yes	—
45	C₂²×C₈×C₄₇	—	2	4	no	—
46	C₄×D₄×C₄₇	—	2	8	no	—
47	C₄×D₄×C₄₇	—	2	8	no	—
48	C₄×D₄×C₄₇	—	2	8	no	—
49	C₄×D₄×C₄₇	—	2	8	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₄₇	D₄	1	2	yes	—
59	C₂×C₄²×C₄₇	D₄	1	2	yes	—
60	C₂×C₄²×C₄₇	D₄	1	4	yes	—
61	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
62	C₄⋊C₈×C₄₇	—	2	8	no	—
63	C₄⋊C₈×C₄₇	—	2	8	no	—
64	#100×C₄₇	—	2	16	no	—
65	C₂⁴×C₄₇	—	2	2	no	—
66	C₂⁴×C₄₇	—	2	2	no	—
67	C₂⁴×C₄₇	—	2	4	no	—
68	C₂⁴×C₄₇	—	4	4	no	—
69	C₂⁴×C₄₇	—	4	4	no	—
70	C₂⁴×C₄₇	C₄⋊C₄	1	8	yes	—
71	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
72	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
73	C₂×D₄×C₄₇	—	2	4	no	—
74	C₂×D₄×C₄₇	—	2	4	no	—
75	C₂×D₄×C₄₇	—	2	8	no	—
76	C₂×D₄×C₄₇	—	2	8	no	—
77	C₂×D₄×C₄₇	—	2	8	no	—
78	C₂×D₄×C₄₇	—	2	8	no	—
79	C₂×D₄×C₄₇	—	2	4	no	—
80	C₂×D₄×C₄₇	—	2	4	no	—
81	C₂×D₄×C₄₇	C₄⋊C₄	1	8	yes	—
82	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
83	C₂×D₄×C₄₇	C₂×Q₈	1	4	yes	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	8	no	—
88	C₂²×C₄×C₄₇	—	2	8	no	—
89	C₂²×C₄×C₄₇	—	4	2	no	—
90	C₂²×C₄×C₄₇	—	4	8	no	—
91	C₂²×C₄×C₄₇	—	4	16	no	—
92	C₂²×C₄×C₄₇	—	4	16	no	—
93	C₂²×C₄×C₄₇	—	4	8	no	—
94	C₂²×C₄×C₄₇	—	4	4	no	—
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
107	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₄₇	#41	1	4	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₄₇	—	2	8	no	—
111	M₁₆×C₄₇	—	2	8	no	—
112	M₁₆×C₄₇	—	4	8	no	—
113	C₂×C₈×C₄₇	—	2	8	no	—
114	C₂×C₈×C₄₇	—	4	8	no	—
115	C₄⋊C₄×C₄₇	—	2	4	no	—
116	C₄⋊C₄×C₄₇	—	2	4	no	—
117	C₂²⋊C₄×C₄₇	—	2	16	no	—
118	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
119	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
120	C₄²×C₄₇	C₂×D₄	1	4	yes	—
121	C₄²×C₄₇	C₂×D₄	1	4	yes	—
122	C₂³×C₄₇	—	2	2	no	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	4	no	—
125	C₂³×C₄₇	—	2	4	no	—
126	C₂³×C₄₇	—	2	8	no	—
127	C₂³×C₄₇	—	2	8	no	—
128	C₂³×C₄₇	—	4	4	no	—
129	C₂³×C₄₇	—	4	16	no	—
130	C₂³×C₄₇	—	4	4	no	—
131	C₂³×C₄₇	—	4	4	no	—
132	C₂³×C₄₇	—	4	16	no	—
133	C₂³×C₄₇	—	4	4	no	—
134	C₂³×C₄₇	—	4	4	no	—
135	C₂³×C₄₇	—	4	4	no	—
136	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
139	C₂³×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
140	C₂³×C₄₇	#117	1	2	yes	—
141	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
142	D₄×C₄₇	—	2	8	no	—
143	D₄×C₄₇	—	2	8	no	—
144	D₄×C₄₇	—	2	16	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	16	no	—
153	C₂×C₄×C₄₇	—	4	4	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	16	no	—
156	C₂×C₄×C₄₇	—	4	4	no	—
157	C₂×C₄×C₄₇	#100	1	4	yes	complemented
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
159	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₇	#117	1	2	yes	—
164	C₂×C₄×C₄₇	#121	1	4	yes	—
165	C₂×C₄×C₄₇	#121	1	4	yes	—
166	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
167	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
172	C₈×C₄₇	—	4	8	no	—
173	C₂×#1800	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₇	—	2	4	no	—
175	C₂²×C₄₇	—	2	4	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	1	no	—
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	8	no	—
181	C₂²×C₄₇	—	4	8	no	—
182	C₂²×C₄₇	—	4	8	no	—
183	C₂²×C₄₇	—	4	16	no	—
184	C₂²×C₄₇	—	4	16	no	—
185	C₂²×C₄₇	—	4	4	no	—
186	C₂²×C₄₇	—	4	4	no	—
187	C₂²×C₄₇	#380	1	2	yes	—
188	C₂²×C₄₇	#380	1	2	yes	—
189	C₂²×C₄₇	C₂×#100	1	2	yes	—
190	C₂²×C₄₇	#413	1	2	yes	—
191	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
194	C₄×C₄₇	—	2	2	no	—
195	C₄×C₄₇	—	2	4	no	—
196	C₄×C₄₇	—	4	4	no	—
197	C₄×C₄₇	#380	1	4	yes	—
198	C₄×C₄₇	C₂×#100	1	4	yes	complemented
199	C₄×C₄₇	C₂×#121	1	2	yes	—
200	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
201	C₂²×C₄×D₄	C₂×C₄₇	1	1	yes	characteristic
202	C₂×#423	C₂×C₄₇	1	2	yes	complemented
203	C₂²×#100	C₂×C₄₇	1	2	yes	—
204	#1800	C₂×C₄₇	1	8	yes	direct product factor
205	C₂×#343	C₂×C₄₇	1	2	yes	complemented
206	C₂×C₄₇	—	2	1	no	—
207	C₂×C₄₇	—	2	1	no	—
208	C₂×C₄₇	—	2	2	no	—
209	C₂×C₄₇	—	4	8	no	—
210	C₂×C₄₇	#1800	1	4	yes	direct product factor
211	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
212	C₂×C₄₇	C₂²×#100	1	1	yes	characteristic
213	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
214	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
215	C₂⁴×C₄	C₄×C₄₇	1	2	yes	—
216	C₂²×M₁₆	C₂²×C₄₇	1	4	yes	—
217	C₂×C₄×D₄	—	2	2	no	—
218	C₂×C₄×D₄	—	2	2	no	—
219	C₂×C₄×D₄	—	2	4	no	—
220	C₂×C₄×D₄	C₄×C₄₇	1	4	yes	—
221	C₂×C₄×D₄	C₂²×C₄₇	1	4	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
223	C₂²×C₂²⋊C₄	C₄×C₄₇	1	2	yes	—
224	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
225	#423	—	2	4	no	—
226	#423	C₂²×C₄₇	1	8	yes	complemented
227	C₂×C₄⋊C₈	—	2	2	no	—
228	C₂×C₄⋊C₈	—	2	2	no	—
229	C₂×#100	—	2	8	no	—
230	C₂×#100	C₂²×C₄₇	1	8	yes	—
231	#343	C₂²×C₄₇	1	8	yes	complemented
232	C₄₇	C₂×#1800	1	1	yes	characteristic, direct product factor, Sylow
233	C₂⁵	C₂×C₄×C₄₇	1	2	yes	—
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	—	2	4	no	—
237	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
238	C₂²×D₄	D₄×C₄₇	1	4	yes	—
239	C₂²×D₄	Q₈×C₄₇	1	4	yes	—
240	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
241	C₂³×C₄	—	2	4	no	—
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	—	2	2	no	—
244	C₂³×C₄	—	4	8	no	—
245	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
246	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
247	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	—
248	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
250	C₂×M₁₆	—	2	4	no	—
251	C₂×M₁₆	—	2	8	no	—
252	C₂×M₁₆	—	2	8	no	—
253	C₂×M₁₆	C₂³×C₄₇	1	8	yes	—
254	C₂²×C₈	—	2	4	no	—
255	C₄×D₄	—	2	8	no	—
256	C₄×D₄	—	2	8	no	—
257	C₄×D₄	—	2	8	no	—
258	C₄×D₄	—	2	8	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	4	no	—
264	C₂×C₂²⋊C₄	—	2	4	no	—
265	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
266	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
267	C₂×C₄²	D₄×C₄₇	1	2	yes	—
268	C₂×C₄²	D₄×C₄₇	1	2	yes	—
269	C₂×C₄²	D₄×C₄₇	1	4	yes	—
270	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
271	C₄⋊C₈	—	2	8	no	—
272	C₄⋊C₈	—	2	8	no	—
273	#100	—	2	16	no	—
274	C₂⁴	—	2	2	no	—
275	C₂⁴	—	2	2	no	—
276	C₂⁴	—	2	4	no	—
277	C₂⁴	—	4	4	no	—
278	C₂⁴	—	4	4	no	—
279	C₂⁴	C₄⋊C₄×C₄₇	1	8	yes	—
280	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
281	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	C₄⋊C₄×C₄₇	1	8	yes	—
291	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
292	C₂×D₄	C₂×Q₈×C₄₇	1	4	yes	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	8	no	—
300	C₂²×C₄	—	4	16	no	—
301	C₂²×C₄	—	4	16	no	—
302	C₂²×C₄	—	4	8	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
305	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
306	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
307	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
308	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
311	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
316	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
317	C₂²×C₄	#41×C₄₇	1	4	yes	—
318	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
319	M₁₆	—	2	8	no	—
320	M₁₆	—	2	8	no	—
321	M₁₆	—	4	8	no	—
322	C₂×C₈	—	2	8	no	—
323	C₂×C₈	—	4	8	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	16	no	—
327	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
328	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
329	C₄²	C₂×D₄×C₄₇	1	4	yes	—
330	C₄²	C₂×D₄×C₄₇	1	4	yes	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	8	no	—
336	C₂³	—	2	8	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	4	16	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	16	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	4	4	no	—
345	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
346	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
347	C₂³	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
348	C₂³	C₂×C₄⋊C₄×C₄₇	1	8	yes	—
349	C₂³	#117×C₄₇	1	2	yes	—
350	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
351	D₄	—	2	8	no	—
352	D₄	—	2	8	no	—
353	D₄	—	2	16	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	16	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	16	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	#100×C₄₇	1	4	yes	complemented
367	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
371	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
372	C₂×C₄	#117×C₄₇	1	2	yes	—
373	C₂×C₄	#121×C₄₇	1	4	yes	—
374	C₂×C₄	#121×C₄₇	1	4	yes	—
375	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
376	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
377	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
379	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
381	C₈	—	4	8	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	4	8	no	—
391	C₂²	—	4	16	no	—
392	C₂²	—	4	16	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	C₄₇×#380	1	2	yes	—
396	C₂²	C₄₇×#380	1	2	yes	—
397	C₂²	C₂×#100×C₄₇	1	2	yes	—
398	C₂²	C₄₇×#413	1	2	yes	—
399	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
400	C₂²	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
401	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	4	no	—
404	C₄	—	4	4	no	—
405	C₄	C₄₇×#380	1	4	yes	—
406	C₄	C₂×#100×C₄₇	1	4	yes	complemented
407	C₄	C₂×#121×C₄₇	1	2	yes	—
408	C₄	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	2	no	—
412	C₂	—	4	8	no	—
413	C₂	C₄₇×#1800	1	4	yes	direct product factor
414	C₂	C₂×C₄₇×#380	1	1	yes	characteristic
415	C₂	C₂²×#100×C₄₇	1	1	yes	characteristic
416	C₂	C₂×C₄₇×#413	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#423	C₂	semidirect
4. C₄₇×#1800	C₂	direct (N × H)
5. C₂×C₄₇×#343	C₂	semidirect
18. C₄₇×#423	C₂²	semidirect
23. C₄₇×#343	C₂²	semidirect
157. C₂×C₄×C₄₇	#100	semidirect
173. C₂×#1800	C₄₇	direct (N × H)
198. C₄×C₄₇	C₂×#100	semidirect
202. C₂×#423	C₂×C₄₇	semidirect
204. #1800	C₂×C₄₇	direct (N × H)
205. C₂×#343	C₂×C₄₇	semidirect
210. C₂×C₄₇	#1800	direct (N × H)
226. #423	C₂²×C₄₇	semidirect
231. #343	C₂²×C₄₇	semidirect
232. C₄₇	C₂×#1800	direct (N × H)
366. C₂×C₄	#100×C₄₇	semidirect
406. C₄	C₂×#100×C₄₇	semidirect
413. C₂	C₄₇×#1800	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×C₄×D₄×C₄₇	2
C₂×C₄₇×#423	2
C₂²×#100×C₄₇	2
C₄₇×#1800	2
C₂×C₄₇×#343	2
C₂×#1800	47

Subgroups — C2×C47×#1800 #26060333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1800 #26060333