Subgroups — C₂×#20244308 #26220310

Order 12032.

1746 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093951	C₂	1	4	yes	maximal, complemented
2	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244308	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
8	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
9	C₂×#13093951	—	2	16	no	—
10	C₂×#13093951	C₂²	1	16	yes	complemented
11	C₄×#10625329	—	2	2	no	—
12	C₄×#10625329	C₂²	1	4	yes	complemented
13	C₂×#13093935	—	2	1	no	—
14	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
15	C₄×C₄⋊Dic₄₇	—	2	2	no	—
16	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
17	C₂×C₄₇⋊#95	—	2	1	no	—
18	C₂²×#41×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#532	—	2	2	no	—
20	C₄₇×#532	—	2	2	no	—
21	C₄₇×#532	C₄	1	4	yes	complemented
22	C₄₇×#532	C₂²	1	4	yes	—
23	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
24	C₂×#127×C₄₇	C₄	1	1	yes	characteristic, complemented
25	C₂×#124×C₄₇	C₄	1	2	yes	complemented
26	C₂×#121×C₄₇	—	2	1	no	—
27	C₂×#121×C₄₇	—	2	1	no	—
28	C₂×C₄×D₄×C₄₇	—	2	1	no	—
29	C₂×C₄×D₄×C₄₇	—	2	1	no	—
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₂³×Dic₄₇	—	2	2	no	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	4	no	—
34	C₂×#10625329	D₄	1	8	yes	complemented
35	C₂×#10625329	C₂³	1	4	yes	—
36	C₂²×C₄₇⋊C₈	—	2	2	no	—
37	C₂×C₄⋊Dic₄₇	—	2	8	no	—
38	C₂×C₄⋊Dic₄₇	—	2	4	no	—
39	C₂×C₄×Dic₄₇	—	2	8	no	—
40	C₂×C₄×Dic₄₇	—	2	2	no	—
41	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
42	#13093951	—	2	32	no	—
43	#13093935	—	2	4	no	—
44	C₄×C₄₇⋊C₈	—	2	4	no	—
45	C₄₇⋊#95	—	2	4	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	—	2	8	no	—
49	C₂×#41×C₄₇	—	2	8	no	—
50	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
51	C₂×#41×C₄₇	C₂³	1	4	yes	—
52	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
53	C₂²×D₄×C₄₇	—	2	2	no	—
54	C₂²×D₄×C₄₇	—	2	1	no	—
55	C₂²×D₄×C₄₇	—	2	1	no	—
56	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
57	C₂³×C₄×C₄₇	—	2	2	no	—
58	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₄₇	—	2	2	no	—
62	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
63	#127×C₄₇	—	2	2	no	—
64	#127×C₄₇	C₂×C₄	1	4	yes	complemented
65	#124×C₄₇	—	2	4	no	—
66	#124×C₄₇	C₂×C₄	1	8	yes	complemented
67	#121×C₄₇	—	2	4	no	—
68	#121×C₄₇	—	2	4	no	—
69	#121×C₄₇	—	2	4	no	—
70	#121×C₄₇	—	2	4	no	—
71	C₄×D₄×C₄₇	—	2	4	no	—
72	C₄×D₄×C₄₇	—	2	4	no	—
73	C₄×D₄×C₄₇	—	2	4	no	—
74	C₄×D₄×C₄₇	—	2	4	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₄₇	D₄	1	2	yes	—
83	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	D₄	1	2	yes	—
86	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
87	C₂⁴×C₄₇	—	2	2	no	—
88	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
89	#41×C₄₇	—	2	16	no	—
90	#41×C₄₇	—	2	8	no	—
91	#41×C₄₇	—	2	8	no	—
92	#41×C₄₇	—	4	8	no	—
93	#41×C₄₇	—	4	4	no	—
94	#41×C₄₇	—	4	4	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	8	no	—
97	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
98	C₂×D₄×C₄₇	—	2	4	no	—
99	C₂×D₄×C₄₇	—	2	4	no	—
100	C₂×D₄×C₄₇	—	2	4	no	—
101	C₂×D₄×C₄₇	—	2	4	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	8	no	—
104	C₂×D₄×C₄₇	—	4	4	no	—
105	C₂×D₄×C₄₇	—	4	4	no	—
106	C₂×D₄×C₄₇	—	4	4	no	—
107	C₂×D₄×C₄₇	—	4	4	no	—
108	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	4	2	no	—
114	C₂²×C₄×C₄₇	—	4	8	no	—
115	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₄₇	#41	1	4	yes	—
130	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
131	C₂²×Dic₄₇	—	2	8	no	—
132	C₂²×Dic₄₇	—	2	4	no	—
133	C₂²×Dic₄₇	—	4	4	no	—
134	C₂²×Dic₄₇	—	4	4	no	—
135	C₄⋊C₄×C₄₇	—	2	4	no	—
136	C₄⋊C₄×C₄₇	—	2	4	no	—
137	C₂²⋊C₄×C₄₇	—	2	8	no	—
138	C₂²⋊C₄×C₄₇	—	2	8	no	—
139	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
140	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
141	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
142	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
143	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
144	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
145	C₄²×C₄₇	C₂×D₄	1	2	yes	—
146	C₄²×C₄₇	C₂×D₄	1	2	yes	—
147	C₄⋊Dic₄₇	—	2	16	no	—
148	C₄×Dic₄₇	—	2	8	no	—
149	C₄×Dic₄₇	—	4	4	no	—
150	#10625329	—	2	8	no	—
151	#10625329	—	2	4	no	—
152	#10625329	C₂×D₄	1	8	yes	complemented
153	C₂×C₄₇⋊C₈	—	2	8	no	—
154	C₂×C₄₇⋊C₈	—	2	4	no	—
155	C₂³×C₄₇	—	2	2	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	—	2	4	no	—
158	C₂³×C₄₇	—	4	4	no	—
159	C₂³×C₄₇	—	4	4	no	—
160	C₂³×C₄₇	—	4	4	no	—
161	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂³×C₄₇	#124	1	2	yes	—
164	C₂³×C₄₇	#127	1	2	yes	—
165	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₄₇	—	2	8	no	—
167	Q₈×C₄₇	—	4	4	no	—
168	D₄×C₄₇	—	2	8	no	—
169	D₄×C₄₇	—	4	8	no	—
170	D₄×C₄₇	—	4	4	no	—
171	D₄×C₄₇	—	4	4	no	—
172	D₄×C₄₇	—	4	8	no	—
173	D₄×C₄₇	—	4	4	no	—
174	D₄×C₄₇	—	4	8	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	2	4	no	—
180	C₂×C₄×C₄₇	—	2	4	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	4	no	—
184	C₂×C₄×C₄₇	—	4	8	no	—
185	C₂×C₄×C₄₇	—	4	8	no	—
186	C₂×C₄×C₄₇	#104	1	4	yes	complemented
187	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
194	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
195	C₂×C₄×C₄₇	#121	1	4	yes	—
196	C₂×C₄×C₄₇	#121	1	4	yes	—
197	C₂×C₄×C₄₇	#124	1	2	yes	—
198	C₂×C₄×C₄₇	#127	1	2	yes	—
199	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
203	C₂×Dic₄₇	—	2	8	no	—
204	C₂×Dic₄₇	—	4	4	no	—
205	C₂×Dic₄₇	—	4	16	no	—
206	C₂×Dic₄₇	—	4	4	no	—
207	C₄₇⋊C₈	—	2	8	no	—
208	C₂×#1980	—	47	1	no	maximal, Sylow
209	C₂²×C₄₇	—	2	1	no	—
210	C₂²×C₄₇	—	2	1	no	—
211	C₂²×C₄₇	—	2	1	no	—
212	C₂²×C₄₇	—	2	1	no	—
213	C₂²×C₄₇	—	2	4	no	—
214	C₂²×C₄₇	—	2	4	no	—
215	C₂²×C₄₇	—	4	4	no	—
216	C₂²×C₄₇	—	4	4	no	—
217	C₂²×C₄₇	—	4	4	no	—
218	C₂²×C₄₇	—	8	8	no	—
219	C₂²×C₄₇	#390	1	2	yes	—
220	C₂²×C₄₇	#390	1	2	yes	—
221	C₂²×C₄₇	C₂×#104	1	2	yes	—
222	C₂²×C₄₇	#421	1	2	yes	—
223	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
224	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
225	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
226	C₄×C₄₇	—	2	2	no	—
227	C₄×C₄₇	—	2	2	no	—
228	C₄×C₄₇	—	2	2	no	—
229	C₄×C₄₇	—	4	4	no	—
230	C₄×C₄₇	#390	1	2	yes	—
231	C₄×C₄₇	#390	1	2	yes	—
232	C₄×C₄₇	C₂×#104	1	4	yes	complemented
233	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
234	C₄×C₄₇	C₂×#121	1	2	yes	—
235	Dic₄₇	—	4	8	no	—
236	C₂×#532	D₄₇	1	1	yes	characteristic
237	C₂²×#104	—	47	4	no	—
238	C₂×C₄×M₁₆	—	47	1	no	—
239	C₂×C₄×C₄⋊C₄	—	47	1	no	—
240	#1980	—	47	8	no	—
241	C₂×C₄₇	—	2	1	no	—
242	C₂×C₄₇	—	2	1	no	—
243	C₂×C₄₇	—	2	2	no	—
244	C₂×C₄₇	—	8	4	no	—
245	C₂×C₄₇	#1980	1	4	yes	complemented
246	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
247	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
248	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
249	C₂²×#41	C₂×D₄₇	1	2	yes	—
250	C₂²×M₁₆	—	47	2	no	—
251	#532	—	2	2	no	—
252	#532	—	2	2	no	—
253	#532	Dic₄₇	1	4	yes	complemented
254	#532	C₂×D₄₇	1	4	yes	—
255	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
256	C₂×#127	Dic₄₇	1	1	yes	characteristic, complemented
257	C₂×#124	Dic₄₇	1	2	yes	complemented
258	C₂×#121	—	2	1	no	—
259	C₂×#121	—	2	1	no	—
260	C₂×C₄×D₄	—	2	1	no	—
261	C₂×C₄×D₄	—	2	1	no	—
262	C₂²×C₄⋊C₄	—	94	1	no	—
263	C₂²×C₄²	—	47	2	no	—
264	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
265	C₂×#104	—	47	16	no	—
266	C₂×#104	—	94	16	no	—
267	C₄×M₁₆	—	47	4	no	—
268	C₄×M₁₆	—	94	2	no	—
269	C₂×#97	—	94	1	no	—
270	C₂×C₄×C₈	—	94	1	no	—
271	C₄×C₄⋊C₄	—	47	4	no	—
272	C₄×C₄⋊C₄	—	94	2	no	—
273	C₂×#95	—	94	1	no	—
274	C₄₇	C₂×#1980	1	1	yes	characteristic, complemented, Sylow
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	8	no	—
278	C₂×#41	—	2	8	no	—
279	C₂×#41	C₂×Dic₄₇	1	4	yes	—
280	C₂×#41	C₂²×D₄₇	1	4	yes	—
281	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	—	94	2	no	—
288	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
289	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
290	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
291	C₂×M₁₆	—	47	8	no	—
292	C₂×M₁₆	—	47	4	no	—
293	C₂×M₁₆	—	94	4	no	—
294	C₂×M₁₆	—	94	2	no	—
295	C₂²×C₈	—	94	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
298	#127	—	2	2	no	—
299	#127	C₂×Dic₄₇	1	4	yes	complemented
300	#124	—	2	4	no	—
301	#124	C₂×Dic₄₇	1	8	yes	complemented
302	#121	—	2	4	no	—
303	#121	—	2	4	no	—
304	#121	—	2	4	no	—
305	#121	—	2	4	no	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	—	2	4	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	94	8	no	—
313	C₂×C₄⋊C₄	—	94	4	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₄²	—	47	4	no	—
317	C₂×C₄²	—	94	8	no	—
318	C₂×C₄²	—	94	2	no	—
319	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
320	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
321	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
322	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
323	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
324	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
325	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
326	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
327	#104	—	94	32	no	—
328	#97	—	94	4	no	—
329	C₄×C₈	—	94	4	no	—
330	#95	—	94	4	no	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
333	#41	—	2	16	no	—
334	#41	—	2	8	no	—
335	#41	—	2	8	no	—
336	#41	—	4	8	no	—
337	#41	—	4	4	no	—
338	#41	—	4	4	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	8	no	—
341	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	4	4	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	8	no	—
359	C₂²×C₄	—	94	8	no	—
360	C₂²×C₄	—	94	4	no	—
361	C₂²×C₄	—	188	4	no	—
362	C₂²×C₄	—	188	4	no	—
363	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
364	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
367	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
368	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
369	C₂²×C₄	D₄×D₄₇	1	4	yes	—
370	C₂²×C₄	#10625352	1	4	yes	—
371	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
372	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
374	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
375	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
378	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
379	M₁₆	—	47	8	no	—
380	M₁₆	—	94	8	no	—
381	M₁₆	—	94	4	no	—
382	C₂×C₈	—	94	8	no	—
383	C₂×C₈	—	94	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	94	16	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₄²	—	94	8	no	—
390	C₄²	—	188	4	no	—
391	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
392	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
393	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
394	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
395	C₄²	C₂²×Dic₄₇	1	2	yes	—
396	C₄²	C₂²×Dic₄₇	1	2	yes	—
397	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
398	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	4	no	—
403	C₂³	—	4	4	no	—
404	C₂³	—	4	4	no	—
405	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
406	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
407	C₂³	#13094011	1	2	yes	—
408	C₂³	#13094020	1	2	yes	—
409	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
410	Q₈	—	2	8	no	—
411	Q₈	—	4	4	no	—
412	D₄	—	2	8	no	—
413	D₄	—	4	8	no	—
414	D₄	—	4	8	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	4	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	8	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	8	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	94	8	no	—
431	C₂×C₄	—	188	4	no	—
432	C₂×C₄	—	188	16	no	—
433	C₂×C₄	—	188	4	no	—
434	C₂×C₄	#13093951	1	4	yes	complemented
435	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
436	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
437	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
438	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
439	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
440	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
441	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
442	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
443	C₂×C₄	#13093995	1	4	yes	—
444	C₂×C₄	#13093995	1	4	yes	—
445	C₂×C₄	#13094011	1	2	yes	—
446	C₂×C₄	#13094020	1	2	yes	—
447	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
448	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
449	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂×#10625352	1	2	yes	—
451	C₈	—	94	8	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	8	no	—
462	C₂²	#15689026	1	2	yes	—
463	C₂²	#15689026	1	2	yes	—
464	C₂²	C₂×#13093951	1	2	yes	—
465	C₂²	#15689140	1	2	yes	—
466	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
467	C₂²	C₂×#13094011	1	1	yes	characteristic
468	C₂²	C₂×#13094020	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	4	no	—
473	C₄	—	188	8	no	—
474	C₄	#15689026	1	2	yes	—
475	C₄	#15689026	1	2	yes	—
476	C₄	C₂×#13093951	1	4	yes	complemented
477	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
478	C₄	C₂×#13093995	1	2	yes	—
479	C₂	—	2	1	no	—
480	C₂	—	2	2	no	—
481	C₂	—	2	1	no	—
482	C₂	—	8	4	no	—
483	C₂	#20244308	1	4	yes	direct product factor
484	C₂	C₂×#15689026	1	1	yes	characteristic
485	C₂	C₂²×#13093951	1	1	yes	characteristic
486	C₂	C₂×#15689140	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#532	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	C₂×#1980
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂²×#13093951	C₂	semidirect
2. C₂×C₄×#10625329	C₂	semidirect
3. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
4. #20244308	C₂	direct (N × H)
10. C₂×#13093951	C₂²	semidirect
12. C₄×#10625329	C₂²	semidirect
16. C₄×C₄⋊Dic₄₇	C₂²	semidirect
21. C₄₇×#532	C₄	semidirect
23. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
24. C₂×#127×C₄₇	C₄	semidirect
25. C₂×#124×C₄₇	C₄	semidirect
34. C₂×#10625329	D₄	semidirect
62. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
64. #127×C₄₇	C₂×C₄	semidirect
66. #124×C₄₇	C₂×C₄	semidirect
152. #10625329	C₂×D₄	semidirect
186. C₂×C₄×C₄₇	#104	semidirect
232. C₄×C₄₇	C₂×#104	semidirect
245. C₂×C₄₇	#1980	semidirect
253. #532	Dic₄₇	semidirect
255. C₂×C₄⋊Q₈	Dic₄₇	semidirect
256. C₂×#127	Dic₄₇	semidirect
257. C₂×#124	Dic₄₇	semidirect
274. C₄₇	C₂×#1980	semidirect
297. C₄⋊Q₈	C₂×Dic₄₇	semidirect
299. #127	C₂×Dic₄₇	semidirect
301. #124	C₂×Dic₄₇	semidirect
434. C₂×C₄	#13093951	semidirect
476. C₄	C₂×#13093951	semidirect
483. C₂	#20244308	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×#13093951	2
C₂×C₄×#10625329	2
C₂×C₄×C₄⋊Dic₄₇	2
#20244308	2
C₂×C₄₇×#532	2
C₂×#1980	47

Subgroups — C2×#20244308 #26220310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244308 #26220310