Subgroups — #26183249

Order 12032.

1096 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252513	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13094031	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241848	C₂	1	2	yes	maximal, complemented
4	#20241839	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241831	C₂	1	2	yes	maximal, complemented
6	#20241827	C₂	1	1	yes	maximal, characteristic, complemented
7	#20241805	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241801	C₂	1	2	yes	maximal, complemented
9	#20241770	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3481	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	—	2	1	no	—
13	#15689254	—	2	1	no	—
14	#15689195	—	2	2	no	—
15	D₄×C₄₇⋊C₈	—	2	1	no	—
16	#15689180	C₂²	1	2	yes	complemented
17	#15689176	C₂²	1	1	yes	characteristic, complemented
18	#15689147	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
20	#15689079	—	2	2	no	—
21	#15689079	—	2	1	no	—
22	C₄×#10625329	C₂²	1	2	yes	complemented
23	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
26	Q₈⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
27	Q₈⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
28	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
29	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
30	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
31	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
32	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
33	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
34	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
35	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
36	C₄₇×#559	C₄	1	1	yes	characteristic
37	C₄₇×#554	C₄	1	1	yes	characteristic
38	C₄₇×#554	C₄	1	1	yes	characteristic
39	C₄₇×#553	—	2	1	no	—
40	C₄₇×#553	C₄	1	2	yes	—
41	C₄₇×#551	—	2	2	no	—
42	C₄₇×#546	—	2	1	no	—
43	C₄₇×#546	C₄	1	2	yes	—
44	D₄²×C₄₇	C₄	1	1	yes	characteristic
45	C₄₇×#532	C₂²	1	1	yes	characteristic
46	C₄₇×#529	—	2	1	no	—
47	C₄₇×#529	C₂²	1	2	yes	—
48	C₄₇×#525	—	2	2	no	—
49	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
50	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₄₇	—	2	1	no	—
52	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
53	#13094031	—	2	8	no	—
54	C₂×#10625329	—	2	2	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂×#10625329	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	2	no	—
58	C₂²×C₄₇⋊C₈	—	2	1	no	—
59	C₂²×C₄₇⋊C₈	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
62	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
63	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
64	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
65	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
67	#13093935	—	2	2	no	—
68	#13093935	—	2	1	no	—
69	#13093935	—	2	2	no	—
70	C₄×C₄₇⋊C₈	—	2	1	no	—
71	C₄×C₄₇⋊C₈	—	2	1	no	—
72	C₄×C₄₇⋊C₈	—	2	2	no	—
73	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
75	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
76	C₂×#41×C₄₇	—	2	1	no	—
77	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
79	C₂²×D₄×C₄₇	—	2	1	no	—
80	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
81	C₂³×C₄×C₄₇	—	2	2	no	—
82	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
83	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
84	#126×C₄₇	—	2	2	no	—
85	#126×C₄₇	—	2	2	no	—
86	#125×C₄₇	—	2	1	no	—
87	#125×C₄₇	C₂×C₄	1	2	yes	—
88	#124×C₄₇	—	2	1	no	—
89	#124×C₄₇	—	2	1	no	—
90	#124×C₄₇	C₂×C₄	1	2	yes	—
91	#123×C₄₇	—	2	2	no	—
92	#123×C₄₇	—	2	2	no	—
93	#123×C₄₇	—	2	2	no	—
94	#123×C₄₇	—	2	2	no	—
95	C₂²⋊Q₈×C₄₇	—	2	1	no	—
96	C₂²⋊Q₈×C₄₇	—	2	2	no	—
97	C₂²⋊Q₈×C₄₇	—	2	2	no	—
98	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
99	#121×C₄₇	—	2	2	no	—
100	#121×C₄₇	—	2	1	no	—
101	#121×C₄₇	—	2	1	no	—
102	#121×C₄₇	—	2	2	no	—
103	#121×C₄₇	C₂×C₄	1	2	yes	—
104	#121×C₄₇	C₂×C₄	1	2	yes	—
105	#120×C₄₇	—	2	2	no	—
106	#120×C₄₇	—	2	2	no	—
107	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
108	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
109	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
110	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
111	C₄×D₄×C₄₇	—	2	1	no	—
112	C₄×D₄×C₄₇	—	2	2	no	—
113	C₄×D₄×C₄₇	—	2	1	no	—
114	C₄×D₄×C₄₇	—	2	1	no	—
115	C₄×D₄×C₄₇	—	2	1	no	—
116	C₄×D₄×C₄₇	—	2	2	no	—
117	C₄×D₄×C₄₇	—	2	1	no	—
118	C₄×D₄×C₄₇	—	2	2	no	—
119	C₄×D₄×C₄₇	—	2	2	no	—
120	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
121	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
122	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
123	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
124	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
125	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
126	C₄×D₄×C₄₇	D₄	1	2	yes	—
127	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₄₇	C₂³	1	2	yes	—
129	#117×C₄₇	—	2	1	no	—
130	#117×C₄₇	—	2	2	no	—
131	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
132	#117×C₄₇	D₄	1	2	yes	—
133	#117×C₄₇	D₄	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
136	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
137	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
138	C₂×C₄²×C₄₇	—	2	1	no	—
139	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
141	C₂⁴×C₄₇	—	2	2	no	—
142	#41×C₄₇	—	2	4	no	—
143	#41×C₄₇	—	2	2	no	—
144	#41×C₄₇	—	4	1	no	—
145	#41×C₄₇	—	8	1	no	—
146	#41×C₄₇	—	8	1	no	—
147	C₂×Q₈×C₄₇	—	2	1	no	—
148	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₄×C₄₇	—	2	4	no	—
151	C₂×D₄×C₄₇	—	2	1	no	—
152	C₂×D₄×C₄₇	—	2	2	no	—
153	C₂×D₄×C₄₇	—	2	2	no	—
154	C₂×D₄×C₄₇	—	2	2	no	—
155	C₂×D₄×C₄₇	—	2	1	no	—
156	C₂×D₄×C₄₇	—	2	1	no	—
157	C₂×D₄×C₄₇	—	4	2	no	—
158	C₂×D₄×C₄₇	—	4	4	no	—
159	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
160	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
162	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	2	1	no	—
165	C₂²×C₄×C₄₇	—	2	1	no	—
166	C₂²×C₄×C₄₇	—	2	1	no	—
167	C₂²×C₄×C₄₇	—	2	2	no	—
168	C₂²×C₄×C₄₇	—	2	2	no	—
169	C₂²×C₄×C₄₇	—	2	2	no	—
170	C₂²×C₄×C₄₇	—	8	2	no	—
171	C₂²×C₄×C₄₇	—	8	2	no	—
172	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
178	C₄⋊C₄×C₄₇	—	2	1	no	—
179	C₄⋊C₄×C₄₇	—	2	2	no	—
180	C₄⋊C₄×C₄₇	—	2	2	no	—
181	C₄⋊C₄×C₄₇	—	2	1	no	—
182	C₄⋊C₄×C₄₇	—	2	2	no	—
183	C₄⋊C₄×C₄₇	—	2	2	no	—
184	C₄⋊C₄×C₄₇	—	2	1	no	—
185	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
186	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
187	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
188	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
189	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
190	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
191	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²⋊C₄×C₄₇	—	2	2	no	—
193	C₂²⋊C₄×C₄₇	—	2	1	no	—
194	C₂²⋊C₄×C₄₇	—	2	2	no	—
195	C₂²⋊C₄×C₄₇	—	2	2	no	—
196	C₂²⋊C₄×C₄₇	—	2	2	no	—
197	C₂²⋊C₄×C₄₇	—	2	2	no	—
198	C₂²⋊C₄×C₄₇	—	2	1	no	—
199	C₂²⋊C₄×C₄₇	—	2	2	no	—
200	C₂²⋊C₄×C₄₇	—	2	2	no	—
201	C₂²⋊C₄×C₄₇	—	2	1	no	—
202	C₂²⋊C₄×C₄₇	—	2	2	no	—
203	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
204	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
205	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
206	C₄²×C₄₇	—	2	1	no	—
207	C₄²×C₄₇	—	2	1	no	—
208	C₄²×C₄₇	—	2	1	no	—
209	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
210	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₄₇	C₂×D₄	1	2	yes	—
214	C₄²×C₄₇	C₂×D₄	1	2	yes	—
215	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
216	#10625329	—	2	8	no	—
217	#10625329	—	2	4	no	—
218	#10625329	—	8	1	no	—
219	C₂×C₄₇⋊C₈	—	2	8	no	—
220	C₂×C₄₇⋊C₈	—	2	4	no	—
221	C₂×C₄₇⋊C₈	—	2	1	no	—
222	C₂×C₄₇⋊C₈	—	2	1	no	—
223	C₂×C₄₇⋊C₈	—	2	2	no	—
224	C₂×C₄₇⋊C₈	—	2	1	no	—
225	C₂×C₄₇⋊C₈	—	2	1	no	—
226	C₂×C₄₇⋊C₈	—	2	2	no	—
227	C₂×C₄₇⋊C₈	—	8	2	no	—
228	C₂³×C₄₇	—	2	1	no	—
229	C₂³×C₄₇	—	2	2	no	—
230	C₂³×C₄₇	—	4	4	no	—
231	C₂³×C₄₇	—	4	4	no	—
232	C₂³×C₄₇	—	8	2	no	—
233	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
235	Q₈×C₄₇	—	2	2	no	—
236	Q₈×C₄₇	—	2	1	no	—
237	Q₈×C₄₇	—	2	1	no	—
238	Q₈×C₄₇	—	8	1	no	—
239	D₄×C₄₇	—	2	4	no	—
240	D₄×C₄₇	—	2	2	no	—
241	D₄×C₄₇	—	2	1	no	—
242	D₄×C₄₇	—	2	2	no	—
243	D₄×C₄₇	—	4	4	no	—
244	D₄×C₄₇	—	4	2	no	—
245	D₄×C₄₇	—	4	4	no	—
246	D₄×C₄₇	—	4	2	no	—
247	D₄×C₄₇	—	8	1	no	—
248	D₄×C₄₇	—	8	2	no	—
249	D₄×C₄₇	#104	1	4	yes	—
250	D₄×C₄₇	#131	1	2	yes	complemented
251	C₂×C₄×C₄₇	—	2	4	no	—
252	C₂×C₄×C₄₇	—	2	2	no	—
253	C₂×C₄×C₄₇	—	2	1	no	—
254	C₂×C₄×C₄₇	—	2	2	no	—
255	C₂×C₄×C₄₇	—	2	1	no	—
256	C₂×C₄×C₄₇	—	2	2	no	—
257	C₂×C₄×C₄₇	—	2	1	no	—
258	C₂×C₄×C₄₇	—	2	2	no	—
259	C₂×C₄×C₄₇	—	2	1	no	—
260	C₂×C₄×C₄₇	—	2	2	no	—
261	C₂×C₄×C₄₇	—	2	1	no	—
262	C₂×C₄×C₄₇	—	2	1	no	—
263	C₂×C₄×C₄₇	—	2	1	no	—
264	C₂×C₄×C₄₇	—	2	2	no	—
265	C₂×C₄×C₄₇	—	4	2	no	—
266	C₂×C₄×C₄₇	—	4	1	no	—
267	C₂×C₄×C₄₇	—	4	2	no	—
268	C₂×C₄×C₄₇	—	4	1	no	—
269	C₂×C₄×C₄₇	—	4	2	no	—
270	C₂×C₄×C₄₇	—	4	2	no	—
271	C₂×C₄×C₄₇	—	8	2	no	—
272	C₂×C₄×C₄₇	—	8	2	no	—
273	C₂×C₄×C₄₇	—	8	2	no	—
274	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
276	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
277	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
281	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
283	C₄₇⋊C₈	—	2	2	no	—
284	C₄₇⋊C₈	—	2	4	no	—
285	C₄₇⋊C₈	—	2	2	no	—
286	C₄₇⋊C₈	—	4	1	no	—
287	C₄₇⋊C₈	—	4	2	no	—
288	C₄₇⋊C₈	—	4	1	no	—
289	#17517	—	47	1	no	maximal, Sylow
290	C₂²×C₄₇	—	2	2	no	—
291	C₂²×C₄₇	—	2	2	no	—
292	C₂²×C₄₇	—	2	1	no	—
293	C₂²×C₄₇	—	2	2	no	—
294	C₂²×C₄₇	—	2	1	no	—
295	C₂²×C₄₇	—	2	1	no	—
296	C₂²×C₄₇	—	4	1	no	—
297	C₂²×C₄₇	—	4	1	no	—
298	C₂²×C₄₇	—	4	2	no	—
299	C₂²×C₄₇	—	4	2	no	—
300	C₂²×C₄₇	—	4	2	no	—
301	C₂²×C₄₇	—	8	8	no	—
302	C₂²×C₄₇	C₂×#104	1	4	yes	—
303	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
304	C₄×C₄₇	—	2	1	no	—
305	C₄×C₄₇	—	2	2	no	—
306	C₄×C₄₇	—	2	2	no	—
307	C₄×C₄₇	—	2	1	no	—
308	C₄×C₄₇	—	2	1	no	—
309	C₄×C₄₇	—	2	2	no	—
310	C₄×C₄₇	—	4	1	no	—
311	C₄×C₄₇	—	4	1	no	—
312	C₄×C₄₇	—	4	2	no	—
313	C₄×C₄₇	—	4	1	no	—
314	C₄×C₄₇	C₂×#104	1	2	yes	—
315	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
316	C₄×C₄₇	#568	1	1	yes	characteristic
317	C₄×C₄₇	#576	1	1	yes	characteristic
318	C₄×C₄₇	#577	1	1	yes	characteristic
319	#3481	D₄₇	1	1	yes	characteristic
320	#2990	—	47	1	no	—
321	C₄×#131	—	47	1	no	—
322	#1494	—	47	2	no	—
323	#1492	—	47	1	no	—
324	#1490	—	47	2	no	—
325	#1489	—	47	1	no	—
326	#1484	—	47	1	no	—
327	#1483	—	47	2	no	—
328	#1476	—	47	1	no	—
329	C₂×D₄⋊C₈	—	47	2	no	—
330	C₂×C₄₇	—	2	4	no	—
331	C₂×C₄₇	—	4	1	no	—
332	C₂×C₄₇	—	4	2	no	—
333	C₂×C₄₇	—	8	2	no	—
334	C₂×C₄₇	#2880	1	1	yes	characteristic
335	C₂×C₄₇	#2897	1	1	yes	characteristic
336	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
337	C₂×#131	—	94	1	no	—
338	#559	Dic₄₇	1	1	yes	characteristic
339	#554	Dic₄₇	1	1	yes	characteristic
340	#554	Dic₄₇	1	1	yes	characteristic
341	#553	—	2	1	no	—
342	#553	Dic₄₇	1	2	yes	—
343	#551	—	2	2	no	—
344	#546	—	2	1	no	—
345	#546	Dic₄₇	1	2	yes	—
346	D₄²	Dic₄₇	1	1	yes	characteristic
347	#532	C₂×D₄₇	1	1	yes	characteristic
348	#529	—	2	1	no	—
349	#529	C₂×D₄₇	1	2	yes	—
350	#525	—	2	2	no	—
351	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
352	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
353	C₂×C₄×D₄	—	2	1	no	—
354	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
355	#446	—	94	1	no	—
356	#435	—	94	2	no	—
357	C₈×D₄	—	94	1	no	—
358	#432	—	47	2	no	—
359	#431	—	47	1	no	—
360	#423	—	47	1	no	—
361	C₂×C₄⋊C₈	—	47	2	no	—
362	#405	—	94	2	no	—
363	#405	—	94	1	no	—
364	C₄×M₁₆	—	47	2	no	—
365	C₄×M₁₆	—	47	1	no	—
366	C₂×C₄×C₈	—	47	2	no	—
367	C₂×C₄×C₈	—	47	1	no	—
368	Q₈⋊C₈	—	47	1	no	—
369	Q₈⋊C₈	—	47	1	no	—
370	Q₈⋊C₈	—	47	2	no	—
371	D₄⋊C₈	—	47	1	no	—
372	D₄⋊C₈	—	47	2	no	—
373	D₄⋊C₈	—	47	1	no	—
374	D₄⋊C₈	—	47	2	no	—
375	D₄⋊C₈	—	47	2	no	—
376	D₄⋊C₈	—	47	2	no	—
377	D₄⋊C₈	—	47	2	no	—
378	C₄₇	#17517	1	1	yes	characteristic, complemented, Sylow
379	C₂×#41	—	2	1	no	—
380	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
381	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
382	C₂²×D₄	—	2	1	no	—
383	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
384	C₂³×C₄	—	2	2	no	—
385	#131	—	94	8	no	—
386	C₂×M₁₆	—	94	2	no	—
387	C₂×M₁₆	—	94	1	no	—
388	C₂×M₁₆	—	94	1	no	—
389	C₂²×C₈	—	94	2	no	—
390	C₂²×C₈	—	94	1	no	—
391	C₂²×C₈	—	94	2	no	—
392	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
393	#127	C₂×Dic₄₇	1	1	yes	characteristic
394	#126	—	2	2	no	—
395	#126	—	2	2	no	—
396	#125	—	2	1	no	—
397	#125	C₂×Dic₄₇	1	2	yes	—
398	#124	—	2	1	no	—
399	#124	—	2	1	no	—
400	#124	C₂×Dic₄₇	1	2	yes	—
401	#123	—	2	2	no	—
402	#123	—	2	2	no	—
403	#123	—	2	2	no	—
404	#123	—	2	2	no	—
405	C₂²⋊Q₈	—	2	1	no	—
406	C₂²⋊Q₈	—	2	2	no	—
407	C₂²⋊Q₈	—	2	2	no	—
408	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
409	#121	—	2	2	no	—
410	#121	—	2	1	no	—
411	#121	—	2	1	no	—
412	#121	—	2	2	no	—
413	#121	C₂×Dic₄₇	1	2	yes	—
414	#121	C₂×Dic₄₇	1	2	yes	—
415	#120	—	2	2	no	—
416	#120	—	2	2	no	—
417	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
418	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
419	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
420	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	—	2	1	no	—
425	C₄×D₄	—	2	1	no	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	1	no	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
431	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
432	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
433	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
434	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
435	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
436	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
437	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
438	C₄×D₄	C₂²×D₄₇	1	2	yes	—
439	#117	—	2	1	no	—
440	#117	—	2	2	no	—
441	#117	C₂×Dic₄₇	1	1	yes	characteristic
442	#117	C₂²⋊D₄₇	1	2	yes	—
443	#117	C₂²⋊D₄₇	1	1	yes	characteristic
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
446	C₂×C₂²⋊C₄	—	2	2	no	—
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₄²	—	2	1	no	—
449	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
450	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
451	C₄⋊C₈	—	47	1	no	—
452	C₄⋊C₈	—	47	2	no	—
453	C₄⋊C₈	—	47	1	no	—
454	C₄⋊C₈	—	94	2	no	—
455	C₄⋊C₈	—	94	1	no	—
456	C₂²⋊C₈	—	94	1	no	—
457	C₂²⋊C₈	—	94	2	no	—
458	#97	—	94	1	no	—
459	#97	—	94	2	no	—
460	#97	—	94	2	no	—
461	C₄×C₈	—	47	1	no	—
462	C₄×C₈	—	47	2	no	—
463	C₄×C₈	—	47	1	no	—
464	C₄×C₈	—	94	1	no	—
465	C₄×C₈	—	94	2	no	—
466	C₄×C₈	—	94	1	no	—
467	C₂⁴	—	2	2	no	—
468	#41	—	2	4	no	—
469	#41	—	2	2	no	—
470	#41	—	4	1	no	—
471	#41	—	8	1	no	—
472	#41	—	8	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
475	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	4	2	no	—
484	C₂×D₄	—	4	4	no	—
485	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
486	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
487	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
488	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	8	2	no	—
497	C₂²×C₄	—	8	2	no	—
498	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
499	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
500	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
501	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
502	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
503	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
504	M₁₆	—	94	8	no	—
505	M₁₆	—	94	4	no	—
506	M₁₆	—	376	1	no	—
507	C₂×C₈	—	94	8	no	—
508	C₂×C₈	—	94	4	no	—
509	C₂×C₈	—	94	1	no	—
510	C₂×C₈	—	94	2	no	—
511	C₂×C₈	—	94	1	no	—
512	C₂×C₈	—	94	1	no	—
513	C₂×C₈	—	94	1	no	—
514	C₂×C₈	—	94	2	no	—
515	C₂×C₈	—	376	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
524	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
525	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
526	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
527	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
529	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
542	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
543	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	C₂²×Dic₄₇	1	2	yes	—
548	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
549	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
550	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
551	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
552	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
553	C₄²	C₂³×D₄₇	1	1	yes	characteristic
554	C₂³	—	2	1	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	4	4	no	—
557	C₂³	—	4	4	no	—
558	C₂³	—	8	2	no	—
559	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
560	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
561	Q₈	—	2	2	no	—
562	Q₈	—	2	1	no	—
563	Q₈	—	2	1	no	—
564	Q₈	—	8	1	no	—
565	D₄	—	2	4	no	—
566	D₄	—	2	2	no	—
567	D₄	—	2	1	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	4	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	4	no	—
572	D₄	—	4	2	no	—
573	D₄	—	8	1	no	—
574	D₄	—	8	2	no	—
575	D₄	#13093951	1	4	yes	—
576	D₄	#13094031	1	2	yes	complemented
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	8	2	no	—
598	C₂×C₄	—	8	2	no	—
599	C₂×C₄	—	8	2	no	—
600	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
601	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
602	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
603	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
604	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
605	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
606	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
607	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
608	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
609	C₈	—	94	2	no	—
610	C₈	—	94	4	no	—
611	C₈	—	94	2	no	—
612	C₈	—	188	1	no	—
613	C₈	—	188	2	no	—
614	C₈	—	188	1	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	8	8	no	—
627	C₂²	C₂×#13093951	1	4	yes	—
628	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
629	C₄	—	2	2	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	C₂×#13093951	1	2	yes	—
640	C₄	C₂×#13094031	1	1	yes	characteristic
641	C₄	#15689890	1	1	yes	characteristic
642	C₄	#15689926	1	1	yes	characteristic
643	C₄	#15689934	1	1	yes	characteristic
644	C₂	—	2	4	no	—
645	C₂	—	4	1	no	—
646	C₂	—	4	2	no	—
647	C₂	—	8	2	no	—
648	C₂	#20251837	1	1	yes	characteristic
649	C₂	#20251914	1	1	yes	characteristic
650	C₂	C₂²×#13093951	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3481	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3481	D₄₇
hypocenter	C₄₇	#17517
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3481

Complements

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

N	H ≅ G/N	type
1. #20252513	C₂	semidirect
2. C₄×#13094031	C₂	semidirect
3. #20241848	C₂	semidirect
4. #20241839	C₂	semidirect
5. #20241831	C₂	semidirect
6. #20241827	C₂	semidirect
7. #20241805	C₂	semidirect
8. #20241801	C₂	semidirect
9. #20241770	C₂	semidirect
10. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
16. #15689180	C₂²	semidirect
17. #15689176	C₂²	semidirect
18. #15689147	C₂²	semidirect
19. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
22. C₄×#10625329	C₂²	semidirect
23. C₄×#10625329	C₂²	semidirect
24. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
25. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
26. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
27. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
28. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
32. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
33. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
34. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
35. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
250. D₄×C₄₇	#131	semidirect
378. C₄₇	#17517	semidirect
576. D₄	#13094031	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20252513	2
C₄×#13094031	2
#20241848	2
#20241839	2
#20241831	2
#20241827	2
#20241805	2
#20241801	2
#20241770	2
C₂×D₄⋊(C₄₇⋊C₈)	2
C₄₇×#3481	2
#17517	47