Subgroups — C₂×#20243772 #26217819

Order 12032.

1794 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689890	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689140	C₂	1	2	yes	maximal, complemented
3	C₂×#15689097	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243772	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688883	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
7	#15689890	—	2	4	no	—
8	#15689890	—	2	2	no	—
9	#15689890	C₂²	1	4	yes	complemented
10	C₂×#13094031	—	2	4	no	—
11	C₂²×#10625329	—	2	2	no	—
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂×#13093983	C₂²	1	2	yes	—
14	#15689140	—	2	4	no	—
15	#15689140	C₂²	1	8	yes	complemented
16	C₂×#13093951	—	2	4	no	—
17	#15689097	—	2	2	no	—
18	#15689097	C₂²	1	4	yes	complemented
19	C₂×#13093939	—	2	2	no	—
20	#15688883	C₂²	1	8	yes	complemented
21	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#532	—	2	2	no	—
24	C₄₇×#532	—	2	2	no	—
25	C₄₇×#532	C₄	1	4	yes	complemented
26	C₄₇×#532	C₂²	1	4	yes	—
27	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
28	C₂×#127×C₄₇	C₄	1	1	yes	characteristic, complemented
29	C₂×#124×C₄₇	C₄	1	1	yes	characteristic, complemented
30	C₂×#124×C₄₇	C₄	1	1	yes	characteristic, complemented
31	C₂×#121×C₄₇	—	2	2	no	—
32	C₂×C₄×D₄×C₄₇	—	2	2	no	—
33	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
34	#13094031	—	2	16	no	—
35	#13094031	—	2	16	no	—
36	C₂×#10625329	—	2	4	no	—
37	C₂×#10625329	—	2	8	no	—
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	—	2	8	no	—
40	C₂×#10625329	—	2	2	no	—
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	D₄	1	4	yes	complemented
43	C₂×#10625329	D₄	1	4	yes	complemented
44	C₂×#10625329	C₂³	1	4	yes	—
45	C₂²×C₄₇⋊C₈	—	2	4	no	—
46	C₂²×C₄₇⋊C₈	—	2	2	no	—
47	#13093983	—	2	2	no	—
48	#13093983	—	2	2	no	—
49	#13093983	—	2	2	no	—
50	#13093983	C₂³	1	4	yes	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	—	2	2	no	—
54	#13093951	—	2	16	no	—
55	#13093939	—	2	8	no	—
56	C₂×#41×C₄₇	—	2	2	no	—
57	C₂×#41×C₄₇	—	2	2	no	—
58	C₂×#41×C₄₇	—	2	1	no	—
59	C₂×#41×C₄₇	—	2	1	no	—
60	C₂×#41×C₄₇	—	2	2	no	—
61	C₂×#41×C₄₇	—	2	2	no	—
62	C₂×#41×C₄₇	—	2	2	no	—
63	C₂×#41×C₄₇	—	2	2	no	—
64	C₂×#41×C₄₇	—	2	2	no	—
65	C₂×#41×C₄₇	—	2	2	no	—
66	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×#41×C₄₇	D₄	1	2	yes	—
69	C₂×#41×C₄₇	D₄	1	2	yes	—
70	C₂×#41×C₄₇	C₂³	1	2	yes	—
71	C₂×#41×C₄₇	C₂³	1	2	yes	—
72	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂²×D₄×C₄₇	—	2	2	no	—
75	C₂²×D₄×C₄₇	—	2	1	no	—
76	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂²×D₄×C₄₇	D₄	1	2	yes	—
79	C₂³×C₄×C₄₇	—	2	1	no	—
80	C₂³×C₄×C₄₇	—	2	1	no	—
81	C₂³×C₄×C₄₇	D₄	1	2	yes	—
82	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₄₇	—	2	2	no	—
84	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
85	#127×C₄₇	—	2	2	no	—
86	#127×C₄₇	C₂×C₄	1	4	yes	complemented
87	#124×C₄₇	—	2	2	no	—
88	#124×C₄₇	—	2	2	no	—
89	#124×C₄₇	C₂×C₄	1	4	yes	complemented
90	#124×C₄₇	C₂×C₄	1	4	yes	complemented
91	#121×C₄₇	—	2	8	no	—
92	#121×C₄₇	—	2	8	no	—
93	C₄×D₄×C₄₇	—	2	8	no	—
94	C₄×D₄×C₄₇	—	2	8	no	—
95	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
98	C₂×C₄²×C₄₇	—	2	1	no	—
99	C₂×C₄²×C₄₇	—	2	1	no	—
100	C₂×C₄²×C₄₇	—	2	1	no	—
101	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
104	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
105	C₂⁴×C₄₇	—	2	1	no	—
106	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
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	4	no	—
114	#41×C₄₇	—	2	4	no	—
115	#41×C₄₇	—	2	4	no	—
116	#41×C₄₇	—	2	4	no	—
117	#41×C₄₇	—	2	4	no	—
118	#41×C₄₇	—	2	4	no	—
119	#41×C₄₇	—	2	4	no	—
120	#41×C₄₇	—	4	2	no	—
121	#41×C₄₇	—	4	2	no	—
122	#41×C₄₇	—	4	2	no	—
123	#41×C₄₇	—	4	2	no	—
124	C₂×Q₈×C₄₇	—	2	1	no	—
125	C₂×Q₈×C₄₇	—	2	2	no	—
126	C₂×Q₈×C₄₇	—	2	2	no	—
127	C₂×Q₈×C₄₇	—	2	2	no	—
128	C₂×Q₈×C₄₇	—	2	2	no	—
129	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
130	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
132	C₂×D₄×C₄₇	—	2	4	no	—
133	C₂×D₄×C₄₇	—	2	4	no	—
134	C₂×D₄×C₄₇	—	2	8	no	—
135	C₂×D₄×C₄₇	—	2	2	no	—
136	C₂×D₄×C₄₇	—	2	2	no	—
137	C₂×D₄×C₄₇	—	2	1	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	2	2	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	2	2	no	—
142	C₂×D₄×C₄₇	—	4	8	no	—
143	C₂×D₄×C₄₇	—	4	2	no	—
144	C₂×D₄×C₄₇	—	4	2	no	—
145	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
146	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
147	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
148	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂²×C₄×C₄₇	—	2	2	no	—
152	C₂²×C₄×C₄₇	—	2	2	no	—
153	C₂²×C₄×C₄₇	—	2	2	no	—
154	C₂²×C₄×C₄₇	—	2	2	no	—
155	C₂²×C₄×C₄₇	—	2	1	no	—
156	C₂²×C₄×C₄₇	—	2	2	no	—
157	C₂²×C₄×C₄₇	—	2	1	no	—
158	C₂²×C₄×C₄₇	—	2	2	no	—
159	C₂²×C₄×C₄₇	—	2	2	no	—
160	C₂²×C₄×C₄₇	—	2	2	no	—
161	C₂²×C₄×C₄₇	—	4	4	no	—
162	C₂²×C₄×C₄₇	—	4	1	no	—
163	C₂²×C₄×C₄₇	—	4	1	no	—
164	C₂²×C₄×C₄₇	—	4	1	no	—
165	C₂²×C₄×C₄₇	—	4	1	no	—
166	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
167	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
168	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₄₇	#41	1	2	yes	—
177	C₂²×C₄×C₄₇	#41	1	2	yes	—
178	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
179	C₂²×Dic₄₇	—	4	2	no	—
180	C₄⋊C₄×C₄₇	—	2	8	no	—
181	C₂²⋊C₄×C₄₇	—	2	8	no	—
182	C₂²⋊C₄×C₄₇	—	2	8	no	—
183	C₄²×C₄₇	—	2	2	no	—
184	C₄²×C₄₇	—	2	1	no	—
185	C₄²×C₄₇	—	2	1	no	—
186	C₄²×C₄₇	—	2	2	no	—
187	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
188	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
189	C₂²⋊Dic₄₇	—	2	4	no	—
190	C₂²⋊Dic₄₇	—	4	2	no	—
191	C₄⋊Dic₄₇	—	2	4	no	—
192	C₄⋊Dic₄₇	—	4	2	no	—
193	C₄×Dic₄₇	—	2	4	no	—
194	C₄×Dic₄₇	—	4	2	no	—
195	#10625329	—	2	16	no	—
196	#10625329	—	2	4	no	—
197	#10625329	—	2	4	no	—
198	#10625329	—	2	4	no	—
199	#10625329	C₂×D₄	1	8	yes	complemented
200	C₂×C₄₇⋊C₈	—	2	16	no	—
201	C₂×C₄₇⋊C₈	—	2	4	no	—
202	C₂×C₄₇⋊C₈	—	2	4	no	—
203	C₂×C₄₇⋊C₈	—	2	4	no	—
204	C₂³×C₄₇	—	2	2	no	—
205	C₂³×C₄₇	—	2	2	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	—	4	2	no	—
208	C₂³×C₄₇	—	4	4	no	—
209	C₂³×C₄₇	—	4	4	no	—
210	C₂³×C₄₇	—	4	1	no	—
211	C₂³×C₄₇	—	4	1	no	—
212	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
214	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×C₄₇	#121	1	2	yes	—
216	C₂³×C₄₇	#121	1	2	yes	—
217	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₄₇	—	2	4	no	—
219	Q₈×C₄₇	—	2	4	no	—
220	Q₈×C₄₇	—	2	4	no	—
221	Q₈×C₄₇	—	4	2	no	—
222	D₄×C₄₇	—	2	8	no	—
223	D₄×C₄₇	—	2	8	no	—
224	D₄×C₄₇	—	2	4	no	—
225	D₄×C₄₇	—	2	4	no	—
226	D₄×C₄₇	—	2	4	no	—
227	D₄×C₄₇	—	4	16	no	—
228	D₄×C₄₇	—	4	4	no	—
229	D₄×C₄₇	—	4	4	no	—
230	D₄×C₄₇	—	4	2	no	—
231	C₂×C₄×C₄₇	—	2	4	no	—
232	C₂×C₄×C₄₇	—	2	2	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	4	no	—
236	C₂×C₄×C₄₇	—	2	4	no	—
237	C₂×C₄×C₄₇	—	2	4	no	—
238	C₂×C₄×C₄₇	—	2	4	no	—
239	C₂×C₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	2	2	no	—
241	C₂×C₄×C₄₇	—	4	4	no	—
242	C₂×C₄×C₄₇	—	4	4	no	—
243	C₂×C₄×C₄₇	—	4	2	no	—
244	C₂×C₄×C₄₇	—	4	1	no	—
245	C₂×C₄×C₄₇	—	4	1	no	—
246	C₂×C₄×C₄₇	—	4	2	no	—
247	C₂×C₄×C₄₇	—	4	2	no	—
248	C₂×C₄×C₄₇	—	4	2	no	—
249	C₂×C₄×C₄₇	—	4	2	no	—
250	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
251	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
255	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
256	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₄₇	#120	1	2	yes	—
258	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
259	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
260	C₂×C₄×C₄₇	#121	1	2	yes	—
261	C₂×C₄×C₄₇	#121	1	2	yes	—
262	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
263	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
264	C₂×C₄×C₄₇	#123	1	2	yes	—
265	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
269	C₂×Dic₄₇	—	4	4	no	—
270	C₂×Dic₄₇	—	8	4	no	—
271	C₄₇⋊C₈	—	2	8	no	—
272	C₂×#1884	—	47	1	no	maximal, Sylow
273	C₂²×C₄₇	—	2	4	no	—
274	C₂²×C₄₇	—	2	2	no	—
275	C₂²×C₄₇	—	2	4	no	—
276	C₂²×C₄₇	—	4	1	no	—
277	C₂²×C₄₇	—	4	1	no	—
278	C₂²×C₄₇	—	4	2	no	—
279	C₂²×C₄₇	—	4	4	no	—
280	C₂²×C₄₇	—	4	4	no	—
281	C₂²×C₄₇	—	4	4	no	—
282	C₂²×C₄₇	—	4	2	no	—
283	C₂²×C₄₇	—	8	2	no	—
284	C₂²×C₄₇	—	8	2	no	—
285	C₂²×C₄₇	—	8	2	no	—
286	C₂²×C₄₇	#386	1	1	yes	characteristic
287	C₂²×C₄₇	#386	1	2	yes	—
288	C₂²×C₄₇	#386	1	1	yes	characteristic
289	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
290	C₂²×C₄₇	C₂×#121	1	2	yes	—
291	C₄×C₄₇	—	2	4	no	—
292	C₄×C₄₇	—	2	4	no	—
293	C₄×C₄₇	—	4	2	no	—
294	C₄×C₄₇	—	4	2	no	—
295	C₄×C₄₇	#386	1	1	yes	characteristic
296	C₄×C₄₇	#386	1	1	yes	characteristic
297	C₄×C₄₇	#386	1	2	yes	—
298	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
299	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
300	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
301	Dic₄₇	—	8	4	no	—
302	C₂×#568	—	47	1	no	—
303	C₂×#532	D₄₇	1	1	yes	characteristic
304	C₂×#421	—	47	2	no	—
305	C₂×#410	—	47	1	no	—
306	#1884	—	47	8	no	—
307	C₂×#339	—	47	2	no	—
308	C₂×C₄₇	—	2	2	no	—
309	C₂×C₄₇	—	2	1	no	—
310	C₂×C₄₇	—	2	1	no	—
311	C₂×C₄₇	—	2	2	no	—
312	C₂×C₄₇	—	4	4	no	—
313	C₂×C₄₇	—	8	2	no	—
314	C₂×C₄₇	#1884	1	2	yes	complemented
315	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
316	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
317	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
318	#568	—	47	4	no	—
319	#568	—	94	4	no	—
320	#568	—	94	2	no	—
321	C₂×#131	—	94	4	no	—
322	C₂²×M₁₆	—	47	2	no	—
323	C₂²×M₁₆	—	94	2	no	—
324	#532	—	2	2	no	—
325	#532	—	2	2	no	—
326	#532	Dic₄₇	1	4	yes	complemented
327	#532	C₂×D₄₇	1	4	yes	—
328	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
329	C₂×#127	Dic₄₇	1	1	yes	characteristic, complemented
330	C₂×#124	Dic₄₇	1	1	yes	characteristic, complemented
331	C₂×#124	Dic₄₇	1	1	yes	characteristic, complemented
332	C₂×#121	—	2	2	no	—
333	C₂×C₄×D₄	—	2	2	no	—
334	C₂×#117	—	47	2	no	—
335	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
336	#421	—	47	8	no	—
337	#421	—	94	4	no	—
338	C₂×#104	—	94	4	no	—
339	#410	—	47	4	no	—
340	#410	—	94	2	no	—
341	C₂×#99	—	94	2	no	—
342	#339	—	47	8	no	—
343	C₄₇	C₂×#1884	1	1	yes	characteristic, complemented, Sylow
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	—	2	2	no	—
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	2	no	—
351	C₂×#41	—	2	2	no	—
352	C₂×#41	—	2	2	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	C₂×Dic₄₇	1	2	yes	—
355	C₂×#41	C₂×Dic₄₇	1	2	yes	—
356	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
357	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
358	C₂×#41	C₂²×D₄₇	1	2	yes	—
359	C₂×#41	C₂²×D₄₇	1	2	yes	—
360	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
361	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
362	C₂²×D₄	—	2	2	no	—
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
365	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
366	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
367	C₂³×C₄	—	2	1	no	—
368	C₂³×C₄	—	2	1	no	—
369	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
370	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
371	#131	—	94	16	no	—
372	#131	—	94	16	no	—
373	C₂×M₁₆	—	47	4	no	—
374	C₂×M₁₆	—	47	4	no	—
375	C₂×M₁₆	—	47	4	no	—
376	C₂×M₁₆	—	94	4	no	—
377	C₂×M₁₆	—	94	8	no	—
378	C₂×M₁₆	—	94	2	no	—
379	C₂×M₁₆	—	94	2	no	—
380	C₂×M₁₆	—	94	2	no	—
381	C₂×M₁₆	—	94	8	no	—
382	C₂²×C₈	—	94	4	no	—
383	C₂²×C₈	—	94	2	no	—
384	C₄⋊Q₈	—	2	2	no	—
385	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
386	#127	—	2	2	no	—
387	#127	C₂×Dic₄₇	1	4	yes	complemented
388	#124	—	2	2	no	—
389	#124	—	2	2	no	—
390	#124	C₂×Dic₄₇	1	4	yes	complemented
391	#124	C₂×Dic₄₇	1	4	yes	complemented
392	#121	—	2	8	no	—
393	#121	—	2	8	no	—
394	C₄×D₄	—	2	8	no	—
395	C₄×D₄	—	2	8	no	—
396	#117	—	47	4	no	—
397	#117	—	94	2	no	—
398	#117	—	94	2	no	—
399	#117	—	94	2	no	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	—	94	2	no	—
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	C₂×C₂²⋊C₄	—	2	2	no	—
404	C₂×C₂²⋊C₄	—	94	2	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	94	2	no	—
409	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
410	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
411	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
412	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
413	#104	—	94	16	no	—
414	#99	—	94	8	no	—
415	C₂⁴	—	2	1	no	—
416	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
417	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
418	#41	—	2	4	no	—
419	#41	—	2	4	no	—
420	#41	—	2	4	no	—
421	#41	—	2	4	no	—
422	#41	—	2	4	no	—
423	#41	—	2	4	no	—
424	#41	—	2	4	no	—
425	#41	—	2	4	no	—
426	#41	—	2	4	no	—
427	#41	—	2	4	no	—
428	#41	—	2	4	no	—
429	#41	—	2	4	no	—
430	#41	—	4	2	no	—
431	#41	—	4	2	no	—
432	#41	—	4	2	no	—
433	#41	—	4	2	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
440	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
441	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	8	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	4	8	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
456	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
457	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
458	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
459	C₂×D₄	C₂×C₂²⋊D₄₇	1	4	yes	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	4	1	no	—
476	C₂²×C₄	—	188	2	no	—
477	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
478	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
479	C₂²×C₄	D₄×D₄₇	1	2	yes	—
480	C₂²×C₄	D₄×D₄₇	1	2	yes	—
481	C₂²×C₄	#10625352	1	2	yes	—
482	C₂²×C₄	#10625352	1	2	yes	—
483	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
484	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
486	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
487	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
489	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
490	M₁₆	—	47	8	no	—
491	M₁₆	—	94	16	no	—
492	M₁₆	—	94	4	no	—
493	M₁₆	—	94	4	no	—
494	M₁₆	—	94	4	no	—
495	C₂×C₈	—	94	16	no	—
496	C₂×C₈	—	94	4	no	—
497	C₂×C₈	—	94	4	no	—
498	C₂×C₈	—	94	4	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	94	4	no	—
501	C₄⋊C₄	—	188	2	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	—	94	4	no	—
505	C₂²⋊C₄	—	188	2	no	—
506	C₄²	—	2	2	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	94	4	no	—
511	C₄²	—	188	2	no	—
512	C₄²	C₂²×Dic₄₇	1	2	yes	—
513	C₄²	C₂²×Dic₄₇	1	2	yes	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	4	no	—
519	C₂³	—	4	4	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
523	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
524	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
525	C₂³	#13093996	1	2	yes	—
526	C₂³	#13093996	1	2	yes	—
527	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
528	Q₈	—	2	4	no	—
529	Q₈	—	2	4	no	—
530	Q₈	—	2	4	no	—
531	Q₈	—	4	2	no	—
532	D₄	—	2	8	no	—
533	D₄	—	2	8	no	—
534	D₄	—	2	4	no	—
535	D₄	—	2	4	no	—
536	D₄	—	2	4	no	—
537	D₄	—	4	16	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	4	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	376	4	no	—
561	C₂×C₄	—	188	4	no	—
562	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
563	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
564	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
565	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
566	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
567	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
568	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
569	C₂×C₄	#13093992	1	2	yes	—
570	C₂×C₄	#13093992	1	1	yes	characteristic
571	C₂×C₄	#13093992	1	1	yes	characteristic
572	C₂×C₄	#13093996	1	2	yes	—
573	C₂×C₄	#13093996	1	2	yes	—
574	C₂×C₄	#13094005	1	1	yes	characteristic
575	C₂×C₄	#13094005	1	1	yes	characteristic
576	C₂×C₄	#13094005	1	2	yes	—
577	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
578	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
579	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
580	C₂×C₄	C₂×#10625352	1	2	yes	—
581	C₈	—	94	8	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	4	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	8	2	no	—
593	C₂²	—	8	2	no	—
594	C₂²	—	8	2	no	—
595	C₂²	#15689003	1	1	yes	characteristic
596	C₂²	#15689003	1	2	yes	—
597	C₂²	#15689003	1	1	yes	characteristic
598	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
599	C₂²	C₂×#13093996	1	2	yes	—
600	C₄	—	2	4	no	—
601	C₄	—	2	4	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	—	376	4	no	—
605	C₄	#15689003	1	1	yes	characteristic
606	C₄	#15689003	1	1	yes	characteristic
607	C₄	#15689003	1	2	yes	—
608	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
609	C₄	C₂×#13093992	1	1	yes	characteristic
610	C₄	C₂×#13094005	1	1	yes	characteristic
611	C₂	—	2	1	no	—
612	C₂	—	2	2	no	—
613	C₂	—	2	1	no	—
614	C₂	—	2	2	no	—
615	C₂	—	4	4	no	—
616	C₂	—	8	2	no	—
617	C₂	#20243772	1	2	yes	direct product factor
618	C₂	C₂×#15689003	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093992
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#532	C₂
socle	C₂²×C₄₇	#386
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	C₂×#1884
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂×#15689890	C₂	semidirect
2. C₂×#15689140	C₂	semidirect
3. C₂×#15689097	C₂	semidirect
4. #20243772	C₂	direct (N × H)
5. C₂×#15688883	C₂	semidirect
9. #15689890	C₂²	semidirect
15. #15689140	C₂²	semidirect
18. #15689097	C₂²	semidirect
20. #15688883	C₂²	semidirect
25. C₄₇×#532	C₄	semidirect
27. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
28. C₂×#127×C₄₇	C₄	semidirect
29. C₂×#124×C₄₇	C₄	semidirect
30. C₂×#124×C₄₇	C₄	semidirect
42. C₂×#10625329	D₄	semidirect
43. C₂×#10625329	D₄	semidirect
84. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
86. #127×C₄₇	C₂×C₄	semidirect
89. #124×C₄₇	C₂×C₄	semidirect
90. #124×C₄₇	C₂×C₄	semidirect
199. #10625329	C₂×D₄	semidirect
314. C₂×C₄₇	#1884	semidirect
326. #532	Dic₄₇	semidirect
328. C₂×C₄⋊Q₈	Dic₄₇	semidirect
329. C₂×#127	Dic₄₇	semidirect
330. C₂×#124	Dic₄₇	semidirect
331. C₂×#124	Dic₄₇	semidirect
343. C₄₇	C₂×#1884	semidirect
385. C₄⋊Q₈	C₂×Dic₄₇	semidirect
387. #127	C₂×Dic₄₇	semidirect
390. #124	C₂×Dic₄₇	semidirect
391. #124	C₂×Dic₄₇	semidirect
617. C₂	#20243772	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×#15689890	2
C₂×#15689140	2
C₂×#15689097	2
#20243772	2
C₂×#15688883	2
C₂×C₄₇×#532	2
C₂×#1884	47

Subgroups — C2×#20243772 #26217819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243772 #26217819