Subgroups — C₂×#104×Dic₄₇ #26213990

Order 12032.

1878 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093951	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#104×Dic₄₇	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688884	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688883	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#104×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	#41×Dic₄₇	—	2	2	no	—
11	#41×Dic₄₇	—	2	2	no	—
12	#41×Dic₄₇	C₄	1	4	yes	complemented
13	#41×Dic₄₇	C₂²	1	4	yes	—
14	C₂×Q₈×Dic₄₇	C₄	1	2	yes	complemented
15	C₂×D₄×Dic₄₇	—	2	2	no	—
16	C₂×D₄×Dic₄₇	C₄	1	2	yes	complemented
17	C₂×#13093983	—	2	1	no	—
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	C₂²×C₄×Dic₄₇	—	2	2	no	—
20	C₂²×C₄×Dic₄₇	—	2	1	no	—
21	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂×#13093951	C₄	1	8	yes	complemented
24	C₂×#13093951	C₂²	1	4	yes	—
25	M₁₆×Dic₄₇	—	2	2	no	—
26	M₁₆×Dic₄₇	C₂²	1	4	yes	complemented
27	C₂×#13093934	—	2	1	no	—
28	C₂×C₈×Dic₄₇	—	2	1	no	—
29	C₄²×Dic₄₇	—	2	2	no	—
30	C₄²×Dic₄₇	C₂²	1	4	yes	complemented
31	#15688884	C₂²	1	4	yes	complemented
32	#15688883	C₂²	1	4	yes	complemented
33	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#104×C₄₇	C₄	1	8	yes	complemented
37	C₂×#104×C₄₇	C₂²	1	4	yes	—
38	C₂³×Dic₄₇	—	2	1	no	—
39	C₂³×Dic₄₇	—	2	2	no	—
40	C₂³×Dic₄₇	D₄	1	2	yes	—
41	C₂×#10625329	—	2	1	no	—
42	C₂×#10625329	—	2	2	no	—
43	C₂×#10625329	C₂×C₄	1	4	yes	complemented
44	C₂×#10625329	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	—	2	1	no	—
46	Q₈×Dic₄₇	—	2	4	no	—
47	Q₈×Dic₄₇	C₂×C₄	1	8	yes	complemented
48	D₄×Dic₄₇	—	2	8	no	—
49	D₄×Dic₄₇	—	2	8	no	—
50	D₄×Dic₄₇	—	2	4	no	—
51	D₄×Dic₄₇	C₂×C₄	1	8	yes	complemented
52	#13093983	—	2	1	no	—
53	#13093983	—	2	1	no	—
54	#13093983	—	2	4	no	—
55	#13093983	—	2	4	no	—
56	#13093983	C₂×C₄	1	2	yes	—
57	#13093983	C₂³	1	2	yes	—
58	C₂×C₄⋊Dic₄₇	—	2	2	no	—
59	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
61	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
62	C₂×C₄×Dic₄₇	—	2	16	no	—
63	C₂×C₄×Dic₄₇	—	2	1	no	—
64	C₂×C₄×Dic₄₇	—	2	1	no	—
65	C₂×C₄×Dic₄₇	—	2	2	no	—
66	C₂×C₄×Dic₄₇	—	2	2	no	—
67	C₂×C₄×Dic₄₇	—	2	8	no	—
68	C₂×C₄×Dic₄₇	—	2	4	no	—
69	C₂×C₄×Dic₄₇	—	2	4	no	—
70	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	complemented
73	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
74	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
75	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
76	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
77	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
78	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
79	#13093951	C₂×C₄	1	16	yes	complemented
80	#13093934	—	2	4	no	—
81	C₈×Dic₄₇	—	2	4	no	—
82	C₂×#41×C₄₇	—	2	1	no	—
83	C₂×#41×C₄₇	—	2	1	no	—
84	C₂×#41×C₄₇	—	2	2	no	—
85	C₂×#41×C₄₇	—	2	2	no	—
86	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
87	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
88	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
89	C₂×#41×C₄₇	C₂³	1	2	yes	—
90	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂²×D₄×C₄₇	—	2	1	no	—
92	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂³×C₄×C₄₇	—	2	1	no	—
94	C₂³×C₄×C₄₇	—	2	1	no	—
95	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₄₇	—	2	1	no	—
97	C₂×M₁₆×C₄₇	—	2	2	no	—
98	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
99	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
100	C₂²×C₈×C₄₇	—	2	1	no	—
101	C₂×C₄²×C₄₇	—	2	1	no	—
102	C₂×C₄²×C₄₇	—	2	2	no	—
103	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	complemented
104	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
105	#104×C₄₇	C₂×C₄	1	16	yes	complemented
106	C₂⁴×C₄₇	—	2	1	no	—
107	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
108	#41×C₄₇	—	2	4	no	—
109	#41×C₄₇	—	2	4	no	—
110	#41×C₄₇	—	2	4	no	—
111	#41×C₄₇	—	2	4	no	—
112	#41×C₄₇	—	2	4	no	—
113	#41×C₄₇	—	2	2	no	—
114	#41×C₄₇	—	2	2	no	—
115	#41×C₄₇	C₄²	1	8	yes	complemented
116	#41×C₄₇	C₂²×C₄	1	4	yes	—
117	#41×C₄₇	C₂²×C₄	1	4	yes	—
118	C₂×Q₈×C₄₇	—	2	1	no	—
119	C₂×Q₈×C₄₇	—	2	2	no	—
120	C₂×Q₈×C₄₇	C₄²	1	4	yes	complemented
121	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂×D₄×C₄₇	—	2	2	no	—
123	C₂×D₄×C₄₇	—	2	4	no	—
124	C₂×D₄×C₄₇	—	2	4	no	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	—	2	1	no	—
127	C₂×D₄×C₄₇	—	2	2	no	—
128	C₂×D₄×C₄₇	C₄²	1	4	yes	complemented
129	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₄₇	—	2	8	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	4	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	2	4	no	—
136	C₂²×C₄×C₄₇	—	2	4	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	#41	1	2	yes	—
146	C₂²×C₄×C₄₇	#41	1	2	yes	—
147	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
148	C₂²×Dic₄₇	—	2	8	no	—
149	C₂²×Dic₄₇	—	2	4	no	—
150	C₂²×Dic₄₇	—	2	2	no	—
151	C₂²×Dic₄₇	—	2	8	no	—
152	C₂²×Dic₄₇	—	2	2	no	—
153	C₂²×Dic₄₇	—	2	8	no	—
154	C₂²×Dic₄₇	—	4	8	no	—
155	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
156	C₂²×Dic₄₇	C₂²⋊C₄	1	4	yes	—
157	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
158	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
159	M₁₆×C₄₇	—	2	4	no	—
160	M₁₆×C₄₇	—	2	2	no	—
161	M₁₆×C₄₇	C₂²×C₄	1	4	yes	complemented
162	C₂×C₈×C₄₇	—	2	4	no	—
163	C₂×C₈×C₄₇	—	2	2	no	—
164	C₄²×C₄₇	—	2	4	no	—
165	C₄²×C₄₇	—	2	2	no	—
166	C₄²×C₄₇	C₂²×C₄	1	4	yes	complemented
167	C₂²⋊Dic₄₇	—	2	2	no	—
168	C₂²⋊Dic₄₇	—	2	2	no	—
169	C₂²⋊Dic₄₇	—	2	8	no	—
170	C₄⋊Dic₄₇	—	2	2	no	—
171	C₄⋊Dic₄₇	—	2	8	no	—
172	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
173	C₄×Dic₄₇	—	2	32	no	—
174	C₄×Dic₄₇	—	2	2	no	—
175	C₄×Dic₄₇	—	2	4	no	—
176	C₄×Dic₄₇	—	2	2	no	—
177	C₄×Dic₄₇	—	2	2	no	—
178	C₄×Dic₄₇	—	2	8	no	—
179	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
180	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
181	C₄×Dic₄₇	C₂²⋊C₄	1	4	yes	—
182	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
183	C₄×Dic₄₇	C₂²×C₄	1	4	yes	complemented
184	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
185	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
186	#10625329	—	2	4	no	—
187	#10625329	—	2	2	no	—
188	#10625329	C₂²×C₄	1	4	yes	complemented
189	C₂×C₄₇⋊C₈	—	2	4	no	—
190	C₂×C₄₇⋊C₈	—	2	2	no	—
191	C₂³×C₄₇	—	2	4	no	—
192	C₂³×C₄₇	—	2	2	no	—
193	C₂³×C₄₇	—	2	4	no	—
194	C₂³×C₄₇	—	4	4	no	—
195	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₄₇	C₄×D₄	1	2	yes	—
198	C₂³×C₄₇	C₄×D₄	1	2	yes	—
199	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₄₇	—	2	2	no	—
201	Q₈×C₄₇	—	2	4	no	—
202	Q₈×C₄₇	C₂×C₄²	1	4	yes	complemented
203	D₄×C₄₇	—	2	4	no	—
204	D₄×C₄₇	—	2	4	no	—
205	D₄×C₄₇	—	2	8	no	—
206	D₄×C₄₇	—	2	2	no	—
207	D₄×C₄₇	—	2	4	no	—
208	D₄×C₄₇	C₂×C₄²	1	4	yes	complemented
209	C₂×C₄×C₄₇	—	2	8	no	—
210	C₂×C₄×C₄₇	—	2	16	no	—
211	C₂×C₄×C₄₇	—	2	2	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	—	2	8	no	—
217	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
218	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
219	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	#117	1	2	yes	—
222	C₂×C₄×C₄₇	#117	1	2	yes	—
223	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
235	C₂×Dic₄₇	—	2	8	no	—
236	C₂×Dic₄₇	—	2	16	no	—
237	C₂×Dic₄₇	—	2	4	no	—
238	C₂×Dic₄₇	—	2	4	no	—
239	C₂×Dic₄₇	—	2	8	no	—
240	C₂×Dic₄₇	—	2	8	no	—
241	C₂×Dic₄₇	—	2	4	no	—
242	C₂×Dic₄₇	—	4	4	no	—
243	C₂×Dic₄₇	—	4	16	no	—
244	C₂×Dic₄₇	#104	1	8	yes	direct product factor
245	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	4	yes	—
246	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	4	yes	—
247	C₈×C₄₇	—	2	4	no	—
248	C₄₇⋊C₈	—	2	4	no	—
249	C₂×C₄×#104	—	47	1	no	maximal, Sylow
250	C₂²×C₄₇	—	2	2	no	—
251	C₂²×C₄₇	—	2	2	no	—
252	C₂²×C₄₇	—	2	4	no	—
253	C₂²×C₄₇	—	2	4	no	—
254	C₂²×C₄₇	—	2	4	no	—
255	C₂²×C₄₇	—	4	4	no	—
256	C₂²×C₄₇	—	4	8	no	—
257	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
258	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
259	C₂²×C₄₇	C₂×#104	1	4	yes	—
260	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
263	C₄×C₄₇	—	2	8	no	—
264	C₄×C₄₇	—	2	4	no	—
265	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
266	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
267	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
268	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
269	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
271	Dic₄₇	—	2	8	no	—
272	Dic₄₇	—	2	4	no	—
273	Dic₄₇	—	4	4	no	—
274	Dic₄₇	C₂×#104	1	8	yes	direct product factor
275	C₂×C₄×#41	—	47	1	no	—
276	C₂²×#104	—	47	1	no	—
277	C₂²×#104	D₄₇	1	1	yes	characteristic
278	C₂×C₄×M₁₆	—	47	1	no	—
279	C₂×C₄³	—	47	1	no	—
280	C₄×#104	—	47	8	no	—
281	C₂×#339	—	47	1	no	—
282	C₂×#339	—	47	1	no	—
283	C₂×C₄₇	—	2	1	no	—
284	C₂×C₄₇	—	2	1	no	—
285	C₂×C₄₇	—	2	2	no	—
286	C₂×C₄₇	—	4	4	no	—
287	C₂×C₄₇	C₄×#104	1	4	yes	complemented
288	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×C₄₇	C₂²×#104	1	2	yes	—
290	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
291	C₂²×M₁₆	—	47	1	no	—
292	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
293	C₄×#41	—	47	4	no	—
294	C₄×#41	—	47	4	no	—
295	C₄×#41	—	94	2	no	—
296	C₄×#41	—	94	2	no	—
297	C₂×C₄×Q₈	—	47	2	no	—
298	C₂×C₄×D₄	—	47	2	no	—
299	C₂×C₄×D₄	—	94	2	no	—
300	C₂×#117	—	47	1	no	—
301	C₂×#117	—	94	1	no	—
302	C₂²×C₄²	—	47	1	no	—
303	C₂²×C₄²	—	47	1	no	—
304	C₂²×C₄²	—	94	1	no	—
305	C₂²×C₄²	—	94	2	no	—
306	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
307	C₂×#104	—	47	8	no	—
308	C₂×#104	—	47	4	no	—
309	C₂×#104	Dic₄₇	1	8	yes	direct product factor
310	C₂×#104	C₂×D₄₇	1	4	yes	—
311	C₄×M₁₆	—	47	4	no	—
312	C₄×M₁₆	—	94	2	no	—
313	C₂×#97	—	94	1	no	—
314	C₂×C₄×C₈	—	94	1	no	—
315	C₄³	—	47	4	no	—
316	C₄³	—	94	2	no	—
317	#339	—	47	4	no	—
318	#339	—	47	4	no	—
319	C₄₇	C₂×C₄×#104	1	1	yes	characteristic, complemented, Sylow
320	C₂×#41	—	2	1	no	—
321	C₂×#41	—	2	1	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	C₄×D₄₇	1	4	yes	—
325	C₂×#41	C₄×D₄₇	1	2	yes	—
326	C₂×#41	C₂×Dic₄₇	1	4	yes	—
327	C₂×#41	C₂²×D₄₇	1	2	yes	—
328	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	—	47	2	no	—
334	C₂³×C₄	—	94	2	no	—
335	C₂³×C₄	—	94	1	no	—
336	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	2	2	no	—
339	C₂×M₁₆	—	47	4	no	—
340	C₂×M₁₆	—	47	2	no	—
341	C₂×M₁₆	—	94	1	no	—
342	C₂×M₁₆	—	94	2	no	—
343	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	complemented
344	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
345	C₂²×C₈	—	2	1	no	—
346	C₂²×C₈	—	94	1	no	—
347	C₄×Q₈	—	47	8	no	—
348	C₄×Q₈	—	94	4	no	—
349	C₄×D₄	—	47	8	no	—
350	C₄×D₄	—	94	4	no	—
351	C₄×D₄	—	94	8	no	—
352	C₄×D₄	—	94	8	no	—
353	#117	—	47	2	no	—
354	#117	—	47	2	no	—
355	#117	—	94	4	no	—
356	#117	—	94	4	no	—
357	#117	—	94	1	no	—
358	#117	—	94	1	no	—
359	C₂×C₄⋊C₄	—	47	2	no	—
360	C₂×C₄⋊C₄	—	94	2	no	—
361	C₂×C₂²⋊C₄	—	94	2	no	—
362	C₂×C₂²⋊C₄	—	94	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	—	47	2	no	—
366	C₂×C₄²	—	47	2	no	—
367	C₂×C₄²	—	47	2	no	—
368	C₂×C₄²	—	47	2	no	—
369	C₂×C₄²	—	47	1	no	—
370	C₂×C₄²	—	47	1	no	—
371	C₂×C₄²	—	47	2	no	—
372	C₂×C₄²	—	47	4	no	—
373	C₂×C₄²	—	47	2	no	—
374	C₂×C₄²	—	94	4	no	—
375	C₂×C₄²	—	94	4	no	—
376	C₂×C₄²	—	94	2	no	—
377	C₂×C₄²	—	94	8	no	—
378	C₂×C₄²	—	94	16	no	—
379	C₂×C₄²	—	94	1	no	—
380	C₂×C₄²	—	94	1	no	—
381	C₂×C₄²	—	94	2	no	—
382	C₂×C₄²	C₂×Dic₄₇	1	4	yes	complemented
383	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
384	#104	—	47	16	no	—
385	#104	C₂×Dic₄₇	1	16	yes	direct product factor
386	#97	—	94	4	no	—
387	C₄×C₈	—	94	4	no	—
388	C₂⁴	—	2	1	no	—
389	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
390	#41	—	2	4	no	—
391	#41	—	2	4	no	—
392	#41	—	2	4	no	—
393	#41	—	2	4	no	—
394	#41	—	2	4	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	C₄×Dic₄₇	1	8	yes	complemented
398	#41	C₂×C₄×D₄₇	1	4	yes	—
399	#41	C₂²×Dic₄₇	1	4	yes	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	C₄×Dic₄₇	1	4	yes	complemented
403	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	C₄×Dic₄₇	1	4	yes	complemented
411	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
412	C₂²×C₄	—	2	8	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	47	2	no	—
421	C₂²×C₄	—	47	2	no	—
422	C₂²×C₄	—	47	4	no	—
423	C₂²×C₄	—	47	4	no	—
424	C₂²×C₄	—	94	8	no	—
425	C₂²×C₄	—	94	8	no	—
426	C₂²×C₄	—	94	8	no	—
427	C₂²×C₄	—	94	4	no	—
428	C₂²×C₄	—	94	2	no	—
429	C₂²×C₄	—	94	2	no	—
430	C₂²×C₄	—	188	8	no	—
431	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
434	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
435	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
436	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
437	C₂²×C₄	#10625352	1	2	yes	—
438	C₂²×C₄	#10625352	1	2	yes	—
439	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
440	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
441	M₁₆	—	2	4	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	47	4	no	—
444	M₁₆	—	94	4	no	—
445	M₁₆	—	94	2	no	—
446	M₁₆	C₂²×Dic₄₇	1	4	yes	complemented
447	C₂×C₈	—	2	4	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	94	4	no	—
450	C₂×C₈	—	94	2	no	—
451	C₄⋊C₄	—	47	4	no	—
452	C₄⋊C₄	—	94	8	no	—
453	C₄⋊C₄	—	94	2	no	—
454	C₂²⋊C₄	—	94	8	no	—
455	C₂²⋊C₄	—	94	2	no	—
456	C₂²⋊C₄	—	94	2	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	47	2	no	—
460	C₄²	—	47	2	no	—
461	C₄²	—	47	4	no	—
462	C₄²	—	47	4	no	—
463	C₄²	—	47	2	no	—
464	C₄²	—	47	2	no	—
465	C₄²	—	47	4	no	—
466	C₄²	—	94	8	no	—
467	C₄²	—	94	32	no	—
468	C₄²	—	94	2	no	—
469	C₄²	—	94	4	no	—
470	C₄²	—	94	2	no	—
471	C₄²	—	94	2	no	—
472	C₄²	C₂²×Dic₄₇	1	4	yes	complemented
473	C₂³	—	2	4	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	4	4	no	—
477	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
478	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
479	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
480	C₂³	D₄×Dic₄₇	1	2	yes	—
481	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
482	Q₈	—	2	4	no	—
483	Q₈	—	2	2	no	—
484	Q₈	C₂×C₄×Dic₄₇	1	4	yes	complemented
485	D₄	—	2	8	no	—
486	D₄	—	2	4	no	—
487	D₄	—	2	4	no	—
488	D₄	—	2	4	no	—
489	D₄	—	2	2	no	—
490	D₄	C₂×C₄×Dic₄₇	1	4	yes	complemented
491	C₂×C₄	—	2	8	no	—
492	C₂×C₄	—	2	16	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	47	4	no	—
500	C₂×C₄	—	47	8	no	—
501	C₂×C₄	—	47	4	no	—
502	C₂×C₄	—	94	8	no	—
503	C₂×C₄	—	94	8	no	—
504	C₂×C₄	—	94	8	no	—
505	C₂×C₄	—	94	16	no	—
506	C₂×C₄	—	94	4	no	—
507	C₂×C₄	—	94	4	no	—
508	C₂×C₄	—	94	4	no	—
509	C₂×C₄	—	188	16	no	—
510	C₂×C₄	—	188	4	no	—
511	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
512	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
513	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
514	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
515	C₂×C₄	#13093980	1	2	yes	—
516	C₂×C₄	#13093980	1	2	yes	—
517	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
518	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
519	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
520	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
521	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
522	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
523	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
524	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
525	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
526	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
527	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
528	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
529	C₈	—	2	4	no	—
530	C₈	—	94	4	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	8	no	—
538	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
539	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
540	C₂²	#104×D₄₇	1	4	yes	—
541	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
542	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
543	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
544	C₄	—	2	8	no	—
545	C₄	—	2	4	no	—
546	C₄	—	47	8	no	—
547	C₄	—	94	8	no	—
548	C₄	—	94	4	no	—
549	C₄	—	188	4	no	—
550	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
551	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
552	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
553	C₄	C₂×#13093980	1	1	yes	characteristic
554	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
555	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
556	C₂	—	2	1	no	—
557	C₂	—	2	1	no	—
558	C₂	—	2	2	no	—
559	C₂	—	4	4	no	—
560	C₂	#104×Dic₄₇	1	4	yes	direct product factor
561	C₂	C₂×C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
562	C₂	C₂×#104×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#104×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#104	D₄₇
hypocenter	C₄₇	C₂×C₄×#104
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#104

Complements

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

N	H ≅ G/N	type
3. C₂×M₁₆×Dic₄₇	C₂	semidirect
4. C₂×C₄²×Dic₄₇	C₂	semidirect
5. #104×Dic₄₇	C₂	direct (N × H)
6. C₂×#15688884	C₂	semidirect
7. C₂×#15688883	C₂	semidirect
12. #41×Dic₄₇	C₄	semidirect
14. C₂×Q₈×Dic₄₇	C₄	semidirect
16. C₂×D₄×Dic₄₇	C₄	semidirect
23. C₂×#13093951	C₄	semidirect
26. M₁₆×Dic₄₇	C₂²	semidirect
30. C₄²×Dic₄₇	C₂²	semidirect
31. #15688884	C₂²	semidirect
32. #15688883	C₂²	semidirect
36. C₂×#104×C₄₇	C₄	semidirect
43. C₂×#10625329	C₂×C₄	semidirect
47. Q₈×Dic₄₇	C₂×C₄	semidirect
51. D₄×Dic₄₇	C₂×C₄	semidirect
72. C₂×C₄×Dic₄₇	C₂×C₄	semidirect
79. #13093951	C₂×C₄	semidirect
98. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
103. C₂×C₄²×C₄₇	C₂×C₄	semidirect
105. #104×C₄₇	C₂×C₄	semidirect
115. #41×C₄₇	C₄²	semidirect
120. C₂×Q₈×C₄₇	C₄²	semidirect
128. C₂×D₄×C₄₇	C₄²	semidirect
161. M₁₆×C₄₇	C₂²×C₄	semidirect
166. C₄²×C₄₇	C₂²×C₄	semidirect
183. C₄×Dic₄₇	C₂²×C₄	semidirect
188. #10625329	C₂²×C₄	semidirect
202. Q₈×C₄₇	C₂×C₄²	semidirect
208. D₄×C₄₇	C₂×C₄²	semidirect
244. C₂×Dic₄₇	#104	direct (N × H)
274. Dic₄₇	C₂×#104	direct (N × H)
287. C₂×C₄₇	C₄×#104	semidirect
309. C₂×#104	Dic₄₇	direct (N × H)
319. C₄₇	C₂×C₄×#104	semidirect
343. C₂×M₁₆	C₂×Dic₄₇	semidirect
382. C₂×C₄²	C₂×Dic₄₇	semidirect
385. #104	C₂×Dic₄₇	direct (N × H)
397. #41	C₄×Dic₄₇	semidirect
402. C₂×Q₈	C₄×Dic₄₇	semidirect
410. C₂×D₄	C₄×Dic₄₇	semidirect
446. M₁₆	C₂²×Dic₄₇	semidirect
472. C₄²	C₂²×Dic₄₇	semidirect
484. Q₈	C₂×C₄×Dic₄₇	semidirect
490. D₄	C₂×C₄×Dic₄₇	semidirect
560. C₂	#104×Dic₄₇	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×#41×Dic₄₇	2
C₂²×#13093951	2
C₂×M₁₆×Dic₄₇	2
C₂×C₄²×Dic₄₇	2
#104×Dic₄₇	2
C₂×#15688884	2
C₂×#15688883	2
C₂²×#104×C₄₇	2
C₂×C₄×#104	47

Subgroups — C2×#104×Dic47 #26213990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#104×Dic₄₇ #26213990