Subgroups — C₂×C₄₇×#3203 #26100445

Order 12032.

2250 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#537	C₂	1	2	yes	maximal, complemented
2	C₄₇×#3203	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄₇×#484	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₇×#480	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#468	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#452	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₇×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₇×#408	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₄₇	C₂²	1	2	yes	—
12	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
15	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#537	—	2	8	no	—
19	C₄₇×#537	C₂²	1	16	yes	complemented
20	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
21	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
23	C₂×#121×C₄₇	—	2	2	no	—
24	C₂×#121×C₄₇	—	2	2	no	—
25	C₂×#121×C₄₇	—	2	2	no	—
26	C₂×#121×C₄₇	C₂²	1	2	yes	—
27	C₂×#121×C₄₇	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
29	C₄₇×#484	C₂²	1	16	yes	complemented
30	C₄₇×#480	C₂²	1	16	yes	complemented
31	C₄₇×#468	C₂²	1	16	yes	complemented
32	C₄₇×#467	C₂²	1	8	yes	complemented
33	C₄₇×#466	C₂²	1	8	yes	complemented
34	C₄₇×#452	C₂²	1	16	yes	complemented
35	C₄₇×#449	C₂²	1	16	yes	complemented
36	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#107×C₄₇	C₂²	1	2	yes	—
39	C₂×#103×C₄₇	C₂²	1	2	yes	—
40	C₂×#103×C₄₇	C₂²	1	2	yes	—
41	C₂×#102×C₄₇	C₂²	1	2	yes	—
42	C₂×#102×C₄₇	C₂²	1	2	yes	—
43	C₄₇×#408	C₂²	1	8	yes	complemented
44	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
45	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
46	C₂×#41×C₄₇	—	2	4	no	—
47	C₂×#41×C₄₇	—	4	2	no	—
48	C₂×#41×C₄₇	—	4	2	no	—
49	C₂×#41×C₄₇	—	4	4	no	—
50	C₂×#41×C₄₇	—	4	4	no	—
51	C₂×#41×C₄₇	D₄	1	4	yes	—
52	C₂×#41×C₄₇	C₂³	1	8	yes	—
53	C₂×#41×C₄₇	C₂³	1	4	yes	—
54	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
56	C₂²×D₄×C₄₇	—	2	2	no	—
57	C₂²×D₄×C₄₇	—	2	2	no	—
58	C₂²×D₄×C₄₇	—	2	2	no	—
59	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₄₇	D₄	1	2	yes	—
61	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₇	—	2	2	no	—
63	C₂³×C₄×C₄₇	—	2	2	no	—
64	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×Q₁₆×C₄₇	—	4	2	no	—
67	C₂×Q₁₆×C₄₇	C₂³	1	4	yes	—
68	C₂×SD₁₆×C₄₇	—	4	4	no	—
69	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
70	C₂×D₈×C₄₇	—	4	2	no	—
71	C₂×D₈×C₄₇	C₂³	1	4	yes	—
72	C₂×M₁₆×C₄₇	—	4	2	no	—
73	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
74	C₂²×C₈×C₄₇	—	4	2	no	—
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
78	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
79	C₂²⋊Q₈×C₄₇	—	2	16	no	—
80	C₂²⋊Q₈×C₄₇	—	2	4	no	—
81	C₂²⋊Q₈×C₄₇	—	2	4	no	—
82	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
83	C₂²⋊Q₈×C₄₇	C₂³	1	8	yes	—
84	#121×C₄₇	—	2	16	no	—
85	#121×C₄₇	—	2	16	no	—
86	#121×C₄₇	—	2	16	no	—
87	#121×C₄₇	—	2	4	no	—
88	#121×C₄₇	—	2	4	no	—
89	#121×C₄₇	C₂³	1	8	yes	—
90	#121×C₄₇	C₂³	1	8	yes	—
91	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
92	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
93	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
94	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
95	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
96	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
98	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
102	#107×C₄₇	C₂³	1	4	yes	—
103	#107×C₄₇	C₂³	1	4	yes	—
104	#107×C₄₇	C₂³	1	8	yes	—
105	#103×C₄₇	C₂³	1	8	yes	—
106	#103×C₄₇	C₂³	1	8	yes	—
107	#102×C₄₇	C₂³	1	8	yes	—
108	#102×C₄₇	C₂³	1	8	yes	—
109	C₂²⋊C₈×C₄₇	C₂³	1	8	yes	—
110	C₂²⋊C₈×C₄₇	C₂³	1	8	yes	—
111	C₂⁴×C₄₇	—	2	2	no	—
112	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
114	#41×C₄₇	—	4	8	no	—
115	#41×C₄₇	—	4	4	no	—
116	#41×C₄₇	—	4	4	no	—
117	#41×C₄₇	—	4	8	no	—
118	#41×C₄₇	—	4	8	no	—
119	#41×C₄₇	—	4	16	no	—
120	C₂×Q₈×C₄₇	—	2	2	no	—
121	C₂×Q₈×C₄₇	—	2	4	no	—
122	C₂×Q₈×C₄₇	—	2	4	no	—
123	C₂×Q₈×C₄₇	—	4	2	no	—
124	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
125	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
126	C₂×D₄×C₄₇	—	2	8	no	—
127	C₂×D₄×C₄₇	—	2	8	no	—
128	C₂×D₄×C₄₇	—	2	8	no	—
129	C₂×D₄×C₄₇	—	2	2	no	—
130	C₂×D₄×C₄₇	—	2	4	no	—
131	C₂×D₄×C₄₇	—	2	4	no	—
132	C₂×D₄×C₄₇	—	4	4	no	—
133	C₂×D₄×C₄₇	—	4	2	no	—
134	C₂×D₄×C₄₇	—	4	8	no	—
135	C₂×D₄×C₄₇	—	8	4	no	—
136	C₂×D₄×C₄₇	—	8	4	no	—
137	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
138	C₂×D₄×C₄₇	C₂×D₄	1	8	yes	—
139	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₄₇	—	2	2	no	—
141	C₂²×C₄×C₄₇	—	2	2	no	—
142	C₂²×C₄×C₄₇	—	2	4	no	—
143	C₂²×C₄×C₄₇	—	2	4	no	—
144	C₂²×C₄×C₄₇	—	2	2	no	—
145	C₂²×C₄×C₄₇	—	2	2	no	—
146	C₂²×C₄×C₄₇	—	2	2	no	—
147	C₂²×C₄×C₄₇	—	2	8	no	—
148	C₂²×C₄×C₄₇	—	2	8	no	—
149	C₂²×C₄×C₄₇	—	4	8	no	—
150	C₂²×C₄×C₄₇	—	8	4	no	—
151	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
158	Q₁₆×C₄₇	—	4	4	no	—
159	SD₁₆×C₄₇	—	4	8	no	—
160	D₈×C₄₇	—	4	4	no	—
161	M₁₆×C₄₇	—	4	4	no	—
162	C₂×C₈×C₄₇	—	2	2	no	—
163	C₂×C₈×C₄₇	—	2	2	no	—
164	C₂×C₈×C₄₇	—	2	4	no	—
165	C₂×C₈×C₄₇	—	4	4	no	—
166	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
167	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
168	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
169	C₄⋊C₄×C₄₇	—	2	8	no	—
170	C₄⋊C₄×C₄₇	—	2	2	no	—
171	C₄⋊C₄×C₄₇	—	2	2	no	—
172	C₄⋊C₄×C₄₇	—	2	8	no	—
173	C₄⋊C₄×C₄₇	—	2	8	no	—
174	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
175	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
176	C₂²⋊C₄×C₄₇	—	2	8	no	—
177	C₂²⋊C₄×C₄₇	—	2	8	no	—
178	C₂²⋊C₄×C₄₇	—	2	8	no	—
179	C₂²⋊C₄×C₄₇	—	2	8	no	—
180	C₂³×C₄₇	—	2	4	no	—
181	C₂³×C₄₇	—	2	2	no	—
182	C₂³×C₄₇	—	2	4	no	—
183	C₂³×C₄₇	—	2	2	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	2	4	no	—
186	C₂³×C₄₇	—	2	4	no	—
187	C₂³×C₄₇	—	4	4	no	—
188	C₂³×C₄₇	—	4	4	no	—
189	C₂³×C₄₇	—	4	4	no	—
190	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
191	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
192	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₄₇	—	2	4	no	—
194	Q₈×C₄₇	—	2	4	no	—
195	Q₈×C₄₇	—	4	4	no	—
196	Q₈×C₄₇	—	4	4	no	—
197	D₄×C₄₇	—	2	4	no	—
198	D₄×C₄₇	—	2	4	no	—
199	D₄×C₄₇	—	4	8	no	—
200	D₄×C₄₇	—	4	4	no	—
201	D₄×C₄₇	—	4	16	no	—
202	D₄×C₄₇	—	4	4	no	—
203	D₄×C₄₇	—	8	8	no	—
204	D₄×C₄₇	—	8	8	no	—
205	C₂×C₄×C₄₇	—	2	4	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	2	8	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	2	4	no	—
212	C₂×C₄×C₄₇	—	2	4	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	2	4	no	—
215	C₂×C₄×C₄₇	—	2	4	no	—
216	C₂×C₄×C₄₇	—	4	16	no	—
217	C₂×C₄×C₄₇	—	4	4	no	—
218	C₂×C₄×C₄₇	—	4	4	no	—
219	C₂×C₄×C₄₇	—	4	4	no	—
220	C₂×C₄×C₄₇	—	8	8	no	—
221	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
225	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
227	C₈×C₄₇	—	2	2	no	—
228	C₈×C₄₇	—	2	2	no	—
229	C₈×C₄₇	—	2	4	no	—
230	C₂×#3203	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂²×C₄₇	—	2	4	no	—
232	C₂²×C₄₇	—	2	2	no	—
233	C₂²×C₄₇	—	2	4	no	—
234	C₂²×C₄₇	—	2	2	no	—
235	C₂²×C₄₇	—	2	2	no	—
236	C₂²×C₄₇	—	2	4	no	—
237	C₂²×C₄₇	—	4	8	no	—
238	C₂²×C₄₇	—	4	4	no	—
239	C₂²×C₄₇	—	4	4	no	—
240	C₂²×C₄₇	—	4	4	no	—
241	C₂²×C₄₇	—	4	4	no	—
242	C₂²×C₄₇	—	8	8	no	—
243	C₂²×C₄₇	#534	1	2	yes	—
244	C₂²×C₄₇	#576	1	2	yes	—
245	C₂²×C₄₇	#578	1	2	yes	—
246	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
247	C₄×C₄₇	—	2	4	no	—
248	C₄×C₄₇	—	2	2	no	—
249	C₄×C₄₇	—	4	4	no	—
250	C₄×C₄₇	—	4	4	no	—
251	C₄×C₄₇	—	4	4	no	—
252	C₄×C₄₇	#534	1	2	yes	—
253	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
254	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
255	C₂×#537	C₂×C₄₇	1	2	yes	complemented
256	#3203	C₂×C₄₇	1	16	yes	direct product factor
257	C₂×#484	C₂×C₄₇	1	2	yes	complemented
258	C₂×#480	C₂×C₄₇	1	2	yes	complemented
259	C₂×#468	C₂×C₄₇	1	2	yes	complemented
260	C₂×#467	C₂×C₄₇	1	1	yes	characteristic, complemented
261	C₂×#466	C₂×C₄₇	1	1	yes	characteristic, complemented
262	C₂×#452	C₂×C₄₇	1	2	yes	complemented
263	C₂×#449	C₂×C₄₇	1	2	yes	complemented
264	C₂×#408	C₂×C₄₇	1	1	yes	characteristic, complemented
265	C₂×C₄₇	—	4	4	no	—
266	C₂×C₄₇	—	4	2	no	—
267	C₂×C₄₇	—	8	4	no	—
268	C₂×C₄₇	#3203	1	4	yes	direct product factor
269	C₂×C₄₇	C₂×#534	1	1	yes	characteristic
270	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
271	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
272	C₂²×#41	C₂²×C₄₇	1	2	yes	—
273	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
274	C₂²×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
275	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
276	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic
277	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
278	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
279	#537	—	2	8	no	—
280	#537	C₂²×C₄₇	1	16	yes	complemented
281	C₂×C₂²⋊Q₈	—	2	2	no	—
282	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
283	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
284	C₂×#121	—	2	2	no	—
285	C₂×#121	—	2	2	no	—
286	C₂×#121	—	2	2	no	—
287	C₂×#121	C₂²×C₄₇	1	2	yes	—
288	C₂×#121	C₂²×C₄₇	1	2	yes	—
289	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
290	#484	C₂²×C₄₇	1	16	yes	complemented
291	#480	C₂²×C₄₇	1	16	yes	complemented
292	#468	C₂²×C₄₇	1	16	yes	complemented
293	#467	C₂²×C₄₇	1	8	yes	complemented
294	#466	C₂²×C₄₇	1	8	yes	complemented
295	#452	C₂²×C₄₇	1	16	yes	complemented
296	#449	C₂²×C₄₇	1	16	yes	complemented
297	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
298	C₂×#107	C₂²×C₄₇	1	2	yes	—
299	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
300	C₂×#103	C₂²×C₄₇	1	2	yes	—
301	C₂×#103	C₂²×C₄₇	1	2	yes	—
302	C₂×#102	C₂²×C₄₇	1	2	yes	—
303	C₂×#102	C₂²×C₄₇	1	2	yes	—
304	#408	C₂²×C₄₇	1	8	yes	complemented
305	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
306	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
307	C₄₇	C₂×#3203	1	1	yes	characteristic, direct product factor, Sylow
308	C₂×#41	—	2	4	no	—
309	C₂×#41	—	4	2	no	—
310	C₂×#41	—	4	2	no	—
311	C₂×#41	—	4	4	no	—
312	C₂×#41	—	4	4	no	—
313	C₂×#41	D₄×C₄₇	1	4	yes	—
314	C₂×#41	C₂³×C₄₇	1	8	yes	—
315	C₂×#41	C₂³×C₄₇	1	4	yes	—
316	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
317	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
322	C₂²×D₄	D₄×C₄₇	1	2	yes	—
323	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
324	C₂³×C₄	—	2	2	no	—
325	C₂³×C₄	—	2	2	no	—
326	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
327	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
328	C₂×Q₁₆	—	4	2	no	—
329	C₂×Q₁₆	C₂³×C₄₇	1	4	yes	—
330	C₂×SD₁₆	—	4	4	no	—
331	C₂×SD₁₆	C₂³×C₄₇	1	8	yes	—
332	C₂×D₈	—	4	2	no	—
333	C₂×D₈	C₂³×C₄₇	1	4	yes	—
334	C₂×M₁₆	—	4	2	no	—
335	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
336	C₂²×C₈	—	4	2	no	—
337	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
340	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
341	C₂²⋊Q₈	—	2	16	no	—
342	C₂²⋊Q₈	—	2	4	no	—
343	C₂²⋊Q₈	—	2	4	no	—
344	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
345	C₂²⋊Q₈	C₂³×C₄₇	1	8	yes	—
346	#121	—	2	16	no	—
347	#121	—	2	16	no	—
348	#121	—	2	16	no	—
349	#121	—	2	4	no	—
350	#121	—	2	4	no	—
351	#121	C₂³×C₄₇	1	8	yes	—
352	#121	C₂³×C₄₇	1	8	yes	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	#107	C₂³×C₄₇	1	4	yes	—
365	#107	C₂³×C₄₇	1	4	yes	—
366	#107	C₂³×C₄₇	1	8	yes	—
367	#103	C₂³×C₄₇	1	8	yes	—
368	#103	C₂³×C₄₇	1	8	yes	—
369	#102	C₂³×C₄₇	1	8	yes	—
370	#102	C₂³×C₄₇	1	8	yes	—
371	C₂²⋊C₈	C₂³×C₄₇	1	8	yes	—
372	C₂²⋊C₈	C₂³×C₄₇	1	8	yes	—
373	C₂⁴	—	2	2	no	—
374	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
375	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
376	#41	—	4	8	no	—
377	#41	—	4	4	no	—
378	#41	—	4	4	no	—
379	#41	—	4	8	no	—
380	#41	—	4	8	no	—
381	#41	—	4	16	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	—	4	2	no	—
386	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
387	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	8	no	—
390	C₂×D₄	—	2	8	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	4	4	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	8	no	—
397	C₂×D₄	—	8	4	no	—
398	C₂×D₄	—	8	4	no	—
399	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
400	C₂×D₄	C₂×D₄×C₄₇	1	8	yes	—
401	C₂×D₄	C₂⁴×C₄₇	1	4	yes	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	2	8	no	—
411	C₂²×C₄	—	4	8	no	—
412	C₂²×C₄	—	8	4	no	—
413	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
416	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
417	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
420	Q₁₆	—	4	4	no	—
421	SD₁₆	—	4	8	no	—
422	D₈	—	4	4	no	—
423	M₁₆	—	4	4	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	4	no	—
427	C₂×C₈	—	4	4	no	—
428	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
429	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
430	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
437	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	4	no	—
451	C₂³	—	4	4	no	—
452	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
453	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
454	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
455	Q₈	—	2	4	no	—
456	Q₈	—	2	4	no	—
457	Q₈	—	4	4	no	—
458	Q₈	—	4	4	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	4	no	—
461	D₄	—	4	8	no	—
462	D₄	—	4	4	no	—
463	D₄	—	4	16	no	—
464	D₄	—	4	4	no	—
465	D₄	—	8	8	no	—
466	D₄	—	8	8	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	4	16	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	8	8	no	—
483	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
485	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
486	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
487	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
488	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	4	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	4	8	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	8	8	no	—
504	C₂²	C₄₇×#534	1	2	yes	—
505	C₂²	C₄₇×#576	1	2	yes	—
506	C₂²	C₄₇×#578	1	2	yes	—
507	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
508	C₄	—	2	4	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	4	no	—
513	C₄	C₄₇×#534	1	2	yes	—
514	C₄	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
515	C₄	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
516	C₂	—	4	4	no	—
517	C₂	—	4	2	no	—
518	C₂	—	8	4	no	—
519	C₂	C₄₇×#3203	1	4	yes	direct product factor
520	C₂	C₂×C₄₇×#534	1	1	yes	characteristic
521	C₂	C₂×C₄₇×#576	1	1	yes	characteristic
522	C₂	C₂×C₄₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×#41×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#537	C₂	semidirect
2. C₄₇×#3203	C₂	direct (N × H)
3. C₂×C₄₇×#484	C₂	semidirect
4. C₂×C₄₇×#480	C₂	semidirect
5. C₂×C₄₇×#468	C₂	semidirect
6. C₂×C₄₇×#467	C₂	semidirect
7. C₂×C₄₇×#466	C₂	semidirect
8. C₂×C₄₇×#452	C₂	semidirect
9. C₂×C₄₇×#449	C₂	semidirect
10. C₂×C₄₇×#408	C₂	semidirect
19. C₄₇×#537	C₂²	semidirect
29. C₄₇×#484	C₂²	semidirect
30. C₄₇×#480	C₂²	semidirect
31. C₄₇×#468	C₂²	semidirect
32. C₄₇×#467	C₂²	semidirect
33. C₄₇×#466	C₂²	semidirect
34. C₄₇×#452	C₂²	semidirect
35. C₄₇×#449	C₂²	semidirect
43. C₄₇×#408	C₂²	semidirect
230. C₂×#3203	C₄₇	direct (N × H)
255. C₂×#537	C₂×C₄₇	semidirect
256. #3203	C₂×C₄₇	direct (N × H)
257. C₂×#484	C₂×C₄₇	semidirect
258. C₂×#480	C₂×C₄₇	semidirect
259. C₂×#468	C₂×C₄₇	semidirect
260. C₂×#467	C₂×C₄₇	semidirect
261. C₂×#466	C₂×C₄₇	semidirect
262. C₂×#452	C₂×C₄₇	semidirect
263. C₂×#449	C₂×C₄₇	semidirect
264. C₂×#408	C₂×C₄₇	semidirect
268. C₂×C₄₇	#3203	direct (N × H)
280. #537	C₂²×C₄₇	semidirect
290. #484	C₂²×C₄₇	semidirect
291. #480	C₂²×C₄₇	semidirect
292. #468	C₂²×C₄₇	semidirect
293. #467	C₂²×C₄₇	semidirect
294. #466	C₂²×C₄₇	semidirect
295. #452	C₂²×C₄₇	semidirect
296. #449	C₂²×C₄₇	semidirect
304. #408	C₂²×C₄₇	semidirect
307. C₄₇	C₂×#3203	direct (N × H)
519. C₂	C₄₇×#3203	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×#537	2
C₄₇×#3203	2
C₂×C₄₇×#484	2
C₂×C₄₇×#480	2
C₂×C₄₇×#468	2
C₂×C₄₇×#467	2
C₂×C₄₇×#466	2
C₂×C₄₇×#452	2
C₂×C₄₇×#449	2
C₂×C₄₇×#408	2
C₂×#3203	47

Subgroups — C2×C47×#3203 #26100445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#3203 #26100445