Subgroups — #26183311

Order 12032.

936 conjugacy classes of subgroups.

The subgroup lattice has 612 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	#20252032	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241861	C₂	1	2	yes	maximal, complemented
4	#20241843	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241827	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241822	C₂	1	2	yes	maximal, complemented
7	#20241809	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241791	C₂	1	2	yes	maximal, complemented
9	#20241775	C₂	1	2	yes	maximal, complemented
10	#20241770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3482	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	1	no	—
13	#15689195	—	2	2	no	—
14	D₄×C₄₇⋊C₈	—	2	1	no	—
15	#15689184	—	2	2	no	—
16	#15689180	C₂²	1	2	yes	—
17	#15689176	C₂²	1	1	yes	characteristic
18	#15689176	C₂²	1	2	yes	—
19	#15689176	C₂²	1	2	yes	—
20	#15689150	—	2	1	no	—
21	#15689147	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
23	#15689090	—	2	1	no	—
24	C₄×#10625329	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	Q₈⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	Q₈⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
28	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
29	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
30	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
31	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
32	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
33	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
35	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
36	C₄₇×#557	C₄	1	1	yes	characteristic
37	C₄₇×#556	C₄	1	2	yes	—
38	C₄₇×#556	C₄	1	1	yes	characteristic
39	C₄₇×#552	—	2	1	no	—
40	C₄₇×#552	—	2	2	no	—
41	D₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
42	C₄₇×#548	—	2	1	no	—
43	C₄₇×#547	C₄	1	1	yes	characteristic
44	C₄₇×#547	C₄	1	2	yes	—
45	C₄₇×#533	C₂²	1	2	yes	—
46	C₄₇×#533	C₂²	1	1	yes	characteristic
47	C₄₇×#529	—	2	1	no	—
48	C₄₇×#529	—	2	2	no	—
49	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
50	C₄×#41×C₄₇	C₂²	1	2	yes	—
51	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	C₂²×C₄₇⋊C₈	—	2	2	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
59	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
62	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
63	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
64	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
68	#13093935	—	2	2	no	—
69	#13093935	—	2	1	no	—
70	C₄×C₄₇⋊C₈	—	2	1	no	—
71	C₄×C₄₇⋊C₈	—	2	1	no	—
72	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
73	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
75	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
78	C₂²×Q₈×C₄₇	—	2	1	no	—
79	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
80	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
82	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
83	#126×C₄₇	—	2	2	no	—
84	#126×C₄₇	—	2	2	no	—
85	#126×C₄₇	—	2	2	no	—
86	#125×C₄₇	—	2	2	no	—
87	#125×C₄₇	—	2	1	no	—
88	#125×C₄₇	—	2	1	no	—
89	#125×C₄₇	—	2	2	no	—
90	#124×C₄₇	—	2	1	no	—
91	#124×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	—	2	1	no	—
99	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
100	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
101	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
102	#121×C₄₇	—	2	1	no	—
103	#121×C₄₇	—	2	2	no	—
104	C₄×Q₈×C₄₇	—	2	1	no	—
105	C₄×Q₈×C₄₇	—	2	2	no	—
106	C₄×Q₈×C₄₇	—	2	1	no	—
107	C₄×Q₈×C₄₇	—	2	1	no	—
108	C₄×Q₈×C₄₇	—	2	2	no	—
109	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
110	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
111	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
112	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
113	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
115	C₄×D₄×C₄₇	—	2	2	no	—
116	C₄×D₄×C₄₇	—	2	1	no	—
117	C₄×D₄×C₄₇	—	2	1	no	—
118	C₄×D₄×C₄₇	—	2	2	no	—
119	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
121	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
122	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
123	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
124	C₄×D₄×C₄₇	D₄	1	2	yes	—
125	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
126	#117×C₄₇	—	2	2	no	—
127	#117×C₄₇	—	2	1	no	—
128	#117×C₄₇	—	2	1	no	—
129	#117×C₄₇	—	2	2	no	—
130	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
131	#117×C₄₇	C₂×C₄	1	2	yes	—
132	#117×C₄₇	D₄	1	1	yes	characteristic
133	#117×C₄₇	D₄	1	2	yes	—
134	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
135	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₂×C₄²×C₄₇	—	2	1	no	—
137	C₂×C₄²×C₄₇	—	2	2	no	—
138	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
140	#41×C₄₇	—	2	2	no	—
141	#41×C₄₇	—	2	4	no	—
142	#41×C₄₇	—	4	1	no	—
143	#41×C₄₇	—	4	2	no	—
144	#41×C₄₇	—	4	2	no	—
145	C₂×Q₈×C₄₇	—	2	2	no	—
146	C₂×Q₈×C₄₇	—	2	1	no	—
147	C₂×Q₈×C₄₇	—	4	4	no	—
148	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
151	C₂×D₄×C₄₇	—	2	1	no	—
152	C₂×D₄×C₄₇	—	2	2	no	—
153	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
155	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	—	2	1	no	—
157	C₂²×C₄×C₄₇	—	2	2	no	—
158	C₂²×C₄×C₄₇	—	2	2	no	—
159	C₂²×C₄×C₄₇	—	2	1	no	—
160	C₂²×C₄×C₄₇	—	2	1	no	—
161	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
163	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	—	2	1	no	—
169	C₄⋊C₄×C₄₇	—	2	2	no	—
170	C₄⋊C₄×C₄₇	—	2	2	no	—
171	C₄⋊C₄×C₄₇	—	2	2	no	—
172	C₄⋊C₄×C₄₇	—	2	1	no	—
173	C₄⋊C₄×C₄₇	—	2	2	no	—
174	C₄⋊C₄×C₄₇	—	2	1	no	—
175	C₄⋊C₄×C₄₇	—	2	2	no	—
176	C₄⋊C₄×C₄₇	—	2	1	no	—
177	C₄⋊C₄×C₄₇	—	2	2	no	—
178	C₄⋊C₄×C₄₇	—	2	1	no	—
179	C₄⋊C₄×C₄₇	—	2	2	no	—
180	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
181	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
182	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
183	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
184	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
185	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
186	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₂²⋊C₄×C₄₇	—	2	2	no	—
189	C₂²⋊C₄×C₄₇	—	2	2	no	—
190	C₂²⋊C₄×C₄₇	—	2	1	no	—
191	C₂²⋊C₄×C₄₇	—	2	2	no	—
192	C₂²⋊C₄×C₄₇	—	2	1	no	—
193	C₂²⋊C₄×C₄₇	—	2	2	no	—
194	C₂²⋊C₄×C₄₇	—	2	1	no	—
195	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
196	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
197	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
198	C₄²×C₄₇	—	2	1	no	—
199	C₄²×C₄₇	—	2	2	no	—
200	C₄²×C₄₇	—	2	2	no	—
201	C₄²×C₄₇	—	2	1	no	—
202	C₄²×C₄₇	—	2	1	no	—
203	C₄²×C₄₇	—	2	2	no	—
204	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
205	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₄₇	C₂×D₄	1	2	yes	—
208	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₄₇	C₂×D₄	1	2	yes	—
210	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
211	#10625329	—	4	2	no	—
212	#10625329	—	8	1	no	—
213	C₂×C₄₇⋊C₈	—	2	1	no	—
214	C₂×C₄₇⋊C₈	—	2	1	no	—
215	C₂×C₄₇⋊C₈	—	2	1	no	—
216	C₂×C₄₇⋊C₈	—	2	1	no	—
217	C₂×C₄₇⋊C₈	—	2	2	no	—
218	C₂×C₄₇⋊C₈	—	2	2	no	—
219	C₂×C₄₇⋊C₈	—	4	2	no	—
220	C₂×C₄₇⋊C₈	—	8	2	no	—
221	C₂³×C₄₇	—	2	1	no	—
222	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
224	Q₈×C₄₇	—	2	2	no	—
225	Q₈×C₄₇	—	2	1	no	—
226	Q₈×C₄₇	—	2	2	no	—
227	Q₈×C₄₇	—	2	1	no	—
228	Q₈×C₄₇	—	2	2	no	—
229	Q₈×C₄₇	—	4	4	no	—
230	Q₈×C₄₇	—	4	2	no	—
231	D₄×C₄₇	—	2	1	no	—
232	D₄×C₄₇	—	2	2	no	—
233	D₄×C₄₇	—	4	2	no	—
234	D₄×C₄₇	—	4	2	no	—
235	D₄×C₄₇	—	4	4	no	—
236	D₄×C₄₇	#131	1	2	yes	—
237	C₂×C₄×C₄₇	—	2	1	no	—
238	C₂×C₄×C₄₇	—	2	2	no	—
239	C₂×C₄×C₄₇	—	2	1	no	—
240	C₂×C₄×C₄₇	—	2	2	no	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	2	no	—
244	C₂×C₄×C₄₇	—	2	1	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	2	1	no	—
247	C₂×C₄×C₄₇	—	2	2	no	—
248	C₂×C₄×C₄₇	—	2	1	no	—
249	C₂×C₄×C₄₇	—	2	2	no	—
250	C₂×C₄×C₄₇	—	2	1	no	—
251	C₂×C₄×C₄₇	—	4	2	no	—
252	C₂×C₄×C₄₇	—	4	2	no	—
253	C₂×C₄×C₄₇	—	4	4	no	—
254	C₂×C₄×C₄₇	—	4	4	no	—
255	C₂×C₄×C₄₇	—	4	1	no	—
256	C₂×C₄×C₄₇	—	4	1	no	—
257	C₂×C₄×C₄₇	—	4	2	no	—
258	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
259	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
261	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
265	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
267	C₄₇⋊C₈	—	4	1	no	—
268	C₄₇⋊C₈	—	4	1	no	—
269	C₄₇⋊C₈	—	4	2	no	—
270	C₄₇⋊C₈	—	4	1	no	—
271	C₄₇⋊C₈	—	4	2	no	—
272	C₄₇⋊C₈	—	4	1	no	—
273	#17523	—	47	1	no	maximal, Sylow
274	C₂²×C₄₇	—	2	1	no	—
275	C₂²×C₄₇	—	2	2	no	—
276	C₂²×C₄₇	—	2	2	no	—
277	C₂²×C₄₇	—	2	2	no	—
278	C₂²×C₄₇	—	2	1	no	—
279	C₂²×C₄₇	—	2	1	no	—
280	C₂²×C₄₇	—	2	2	no	—
281	C₂²×C₄₇	—	4	1	no	—
282	C₂²×C₄₇	—	4	1	no	—
283	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
284	C₄×C₄₇	—	2	1	no	—
285	C₄×C₄₇	—	2	2	no	—
286	C₄×C₄₇	—	2	2	no	—
287	C₄×C₄₇	—	2	1	no	—
288	C₄×C₄₇	—	2	1	no	—
289	C₄×C₄₇	—	2	2	no	—
290	C₄×C₄₇	—	4	2	no	—
291	C₄×C₄₇	—	4	1	no	—
292	C₄×C₄₇	—	4	1	no	—
293	C₄×C₄₇	—	4	2	no	—
294	C₄×C₄₇	—	4	1	no	—
295	C₄×C₄₇	#421	1	2	yes	—
296	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
297	C₄×C₄₇	#568	1	1	yes	characteristic
298	C₄×C₄₇	#577	1	1	yes	characteristic
299	C₄×C₄₇	#578	1	1	yes	characteristic
300	#3482	D₄₇	1	1	yes	characteristic
301	#2990	—	47	1	no	—
302	#2922	—	47	1	no	—
303	#1497	—	47	2	no	—
304	#1493	—	47	1	no	—
305	#1489	—	47	1	no	—
306	#1488	—	47	2	no	—
307	#1485	—	47	1	no	—
308	#1481	—	47	2	no	—
309	#1477	—	47	2	no	—
310	#1476	—	47	1	no	—
311	C₂×C₄₇	—	4	1	no	—
312	C₂×C₄₇	—	4	2	no	—
313	C₂×C₄₇	—	4	2	no	—
314	C₂×C₄₇	#2880	1	1	yes	characteristic
315	C₂×C₄₇	#2898	1	1	yes	characteristic
316	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
317	#557	Dic₄₇	1	1	yes	characteristic
318	#556	Dic₄₇	1	2	yes	—
319	#556	Dic₄₇	1	1	yes	characteristic
320	#552	—	2	1	no	—
321	#552	—	2	2	no	—
322	D₄×Q₈	Dic₄₇	1	1	yes	characteristic
323	#548	—	2	1	no	—
324	#547	Dic₄₇	1	1	yes	characteristic
325	#547	Dic₄₇	1	2	yes	—
326	#533	C₂×D₄₇	1	2	yes	—
327	#533	C₂×D₄₇	1	1	yes	characteristic
328	#529	—	2	1	no	—
329	#529	—	2	2	no	—
330	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
331	C₄×#41	C₂×D₄₇	1	2	yes	—
332	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
333	C₂×C₄×Q₈	—	2	1	no	—
334	#446	—	94	1	no	—
335	#435	—	94	2	no	—
336	C₈×D₄	—	94	1	no	—
337	#433	—	94	2	no	—
338	#432	—	47	2	no	—
339	#431	—	47	2	no	—
340	#431	—	47	2	no	—
341	#431	—	47	1	no	—
342	#424	—	94	1	no	—
343	#423	—	47	1	no	—
344	C₂×C₄⋊C₈	—	47	2	no	—
345	#408	—	94	1	no	—
346	C₄×M₁₆	—	47	1	no	—
347	C₂×C₄×C₈	—	47	1	no	—
348	Q₈⋊C₈	—	47	1	no	—
349	Q₈⋊C₈	—	47	1	no	—
350	Q₈⋊C₈	—	47	2	no	—
351	Q₈⋊C₈	—	47	2	no	—
352	Q₈⋊C₈	—	47	2	no	—
353	Q₈⋊C₈	—	47	2	no	—
354	Q₈⋊C₈	—	47	2	no	—
355	D₄⋊C₈	—	47	1	no	—
356	D₄⋊C₈	—	47	1	no	—
357	D₄⋊C₈	—	47	2	no	—
358	C₄₇	#17523	1	1	yes	characteristic, complemented, Sylow
359	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
360	C₂×#41	C₂×Dic₄₇	1	2	yes	—
361	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
362	C₂²×Q₈	—	2	1	no	—
363	C₂×M₁₆	—	94	1	no	—
364	C₂×M₁₆	—	94	1	no	—
365	C₂²×C₈	—	94	2	no	—
366	C₂²×C₈	—	94	1	no	—
367	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
368	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
369	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
370	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
371	#126	—	2	2	no	—
372	#126	—	2	2	no	—
373	#126	—	2	2	no	—
374	#125	—	2	2	no	—
375	#125	—	2	1	no	—
376	#125	—	2	1	no	—
377	#125	—	2	2	no	—
378	#124	—	2	1	no	—
379	#124	—	2	2	no	—
380	#123	—	2	2	no	—
381	#123	—	2	2	no	—
382	#123	—	2	2	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
388	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
389	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
390	#121	—	2	1	no	—
391	#121	—	2	2	no	—
392	C₄×Q₈	—	2	1	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
398	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
399	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
400	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
401	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
402	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
408	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
409	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
410	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
411	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
412	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
413	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
414	#117	—	2	2	no	—
415	#117	—	2	1	no	—
416	#117	—	2	1	no	—
417	#117	—	2	2	no	—
418	#117	C₂×Dic₄₇	1	1	yes	characteristic
419	#117	C₂×Dic₄₇	1	2	yes	—
420	#117	C₂²⋊D₄₇	1	1	yes	characteristic
421	#117	C₂²⋊D₄₇	1	2	yes	—
422	C₂×C₄⋊C₄	—	2	2	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	—	2	2	no	—
426	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
427	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
428	C₄⋊C₈	—	47	1	no	—
429	C₄⋊C₈	—	47	2	no	—
430	C₄⋊C₈	—	47	1	no	—
431	C₄⋊C₈	—	94	2	no	—
432	C₄⋊C₈	—	94	1	no	—
433	C₄⋊C₈	—	94	2	no	—
434	C₄⋊C₈	—	94	2	no	—
435	C₂²⋊C₈	—	94	2	no	—
436	C₂²⋊C₈	—	94	2	no	—
437	C₂²⋊C₈	—	94	1	no	—
438	C₂²⋊C₈	—	94	2	no	—
439	#97	—	94	1	no	—
440	#97	—	94	2	no	—
441	C₄×C₈	—	47	1	no	—
442	C₄×C₈	—	47	1	no	—
443	C₄×C₈	—	47	2	no	—
444	C₄×C₈	—	94	1	no	—
445	C₄×C₈	—	94	1	no	—
446	#41	—	2	2	no	—
447	#41	—	2	4	no	—
448	#41	—	4	1	no	—
449	#41	—	4	2	no	—
450	#41	—	4	2	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	4	4	no	—
454	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
455	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
456	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
460	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
461	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
468	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
469	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
471	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
473	M₁₆	—	376	1	no	—
474	M₁₆	—	188	2	no	—
475	C₂×C₈	—	94	1	no	—
476	C₂×C₈	—	94	1	no	—
477	C₂×C₈	—	94	2	no	—
478	C₂×C₈	—	94	1	no	—
479	C₂×C₈	—	94	1	no	—
480	C₂×C₈	—	94	2	no	—
481	C₂×C₈	—	376	2	no	—
482	C₂×C₈	—	188	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
497	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
499	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
512	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
513	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	2	no	—
520	C₄²	C₂²×Dic₄₇	1	2	yes	—
521	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
522	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
523	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
524	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
525	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
526	C₄²	C₂³×D₄₇	1	1	yes	characteristic
527	C₂³	—	2	1	no	—
528	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
529	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	1	no	—
532	Q₈	—	2	2	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	2	2	no	—
535	Q₈	—	4	4	no	—
536	Q₈	—	4	2	no	—
537	D₄	—	2	1	no	—
538	D₄	—	2	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	4	no	—
542	D₄	#13094031	1	2	yes	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
565	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
566	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
567	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
568	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
569	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
570	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
571	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
572	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
573	C₈	—	188	1	no	—
574	C₈	—	188	1	no	—
575	C₈	—	188	2	no	—
576	C₈	—	188	1	no	—
577	C₈	—	188	2	no	—
578	C₈	—	188	1	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
589	C₄	—	2	2	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	2	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	1	no	—
600	C₄	#15689140	1	2	yes	—
601	C₄	C₂×#13094031	1	1	yes	characteristic
602	C₄	#15689890	1	1	yes	characteristic
603	C₄	#15689931	1	1	yes	characteristic
604	C₄	#15689938	1	1	yes	characteristic
605	C₂	—	4	1	no	—
606	C₂	—	4	2	no	—
607	C₂	—	4	2	no	—
608	C₂	#20251837	1	1	yes	characteristic
609	C₂	#20251921	1	1	yes	characteristic
610	C₂	C₂×#15689140	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×#3482	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3482	D₄₇
hypocenter	C₄₇	#17523
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3482

Complements

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

N	H ≅ G/N	type
1. #20252513	C₂	semidirect
2. #20252032	C₂	semidirect
3. #20241861	C₂	semidirect
4. #20241843	C₂	semidirect
5. #20241827	C₂	semidirect
6. #20241822	C₂	semidirect
7. #20241809	C₂	semidirect
8. #20241791	C₂	semidirect
9. #20241775	C₂	semidirect
10. #20241770	C₂	semidirect
358. C₄₇	#17523	semidirect

Maximal subgroups

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

subgroup	index
#20252513	2
#20252032	2
#20241861	2
#20241843	2
#20241827	2
#20241822	2
#20241809	2
#20241791	2
#20241775	2
#20241770	2
C₄₇×#3482	2
#17523	47