Subgroups — #26183223

Order 12032.

994 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252355	C₂	1	1	yes	maximal, characteristic, complemented
2	#20251956	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241853	C₂	1	2	yes	maximal, complemented
4	#20241839	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241827	C₂	1	2	yes	maximal, complemented
6	#20241817	C₂	1	1	yes	maximal, characteristic, complemented
7	#20241801	C₂	1	2	yes	maximal, complemented
8	#20241787	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241775	C₂	1	2	yes	maximal, complemented
10	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3480	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	—	2	1	no	—
13	#15689254	—	2	1	no	—
14	#15689201	—	2	1	no	—
15	#15689195	—	2	2	no	—
16	#15689176	C₂²	1	2	yes	—
17	#15689176	C₂²	1	1	yes	characteristic
18	#15689150	—	2	1	no	—
19	#15689150	—	2	2	no	—
20	#15689147	C₂²	1	1	yes	characteristic
21	#15689147	C₂²	1	2	yes	—
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
24	C₄×#10625329	C₂²	1	2	yes	—
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	1	yes	characteristic
29	Q₈⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
30	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
31	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
32	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
33	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
34	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
35	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
36	C₄₇×#559	—	2	1	no	—
37	C₄₇×#559	C₄	1	1	yes	characteristic
38	C₄₇×#557	C₄	1	1	yes	characteristic
39	C₄₇×#556	—	2	1	no	—
40	C₄₇×#556	C₄	1	1	yes	characteristic
41	C₄₇×#553	—	2	2	no	—
42	C₄₇×#553	C₄	1	2	yes	—
43	C₄₇×#550	C₄	1	1	yes	characteristic
44	C₄₇×#548	C₄	1	2	yes	—
45	C₄₇×#532	—	2	1	no	—
46	C₄₇×#532	C₂²	1	1	yes	characteristic
47	C₄₇×#529	—	2	2	no	—
48	C₄₇×#529	C₂²	1	2	yes	—
49	C₄×#41×C₄₇	—	2	1	no	—
50	C₄×#41×C₄₇	C₂²	1	2	yes	—
51	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
53	#13094031	—	4	4	no	—
54	C₂×#10625329	—	2	2	no	—
55	C₂×#10625329	—	2	2	no	—
56	C₂×#10625329	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	—	2	2	no	—
59	C₂²×C₄₇⋊C₈	—	2	1	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
62	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
63	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
64	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
69	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
70	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
71	#13093935	—	2	2	no	—
72	C₄×C₄₇⋊C₈	—	2	1	no	—
73	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
76	C₂×#41×C₄₇	—	2	1	no	—
77	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₄⋊Q₈×C₄₇	—	2	1	no	—
81	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	#127×C₄₇	—	2	1	no	—
83	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
84	#126×C₄₇	—	2	2	no	—
85	#126×C₄₇	—	2	2	no	—
86	#126×C₄₇	—	2	2	no	—
87	#125×C₄₇	—	2	2	no	—
88	#125×C₄₇	C₂×C₄	1	2	yes	—
89	#124×C₄₇	—	2	1	no	—
90	#124×C₄₇	—	2	1	no	—
91	#124×C₄₇	—	2	2	no	—
92	#124×C₄₇	—	2	1	no	—
93	#124×C₄₇	C₂×C₄	1	2	yes	—
94	#123×C₄₇	—	2	2	no	—
95	#123×C₄₇	—	2	2	no	—
96	#123×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	2	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	C₄×Q₈×C₄₇	—	2	1	no	—
106	C₄×Q₈×C₄₇	—	2	1	no	—
107	C₄×Q₈×C₄₇	—	2	1	no	—
108	C₄×Q₈×C₄₇	—	2	1	no	—
109	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
110	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
111	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
112	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
113	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
114	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
115	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
116	C₄×D₄×C₄₇	—	2	2	no	—
117	C₄×D₄×C₄₇	—	2	2	no	—
118	C₄×D₄×C₄₇	—	2	2	no	—
119	C₄×D₄×C₄₇	—	2	1	no	—
120	C₄×D₄×C₄₇	—	2	1	no	—
121	C₄×D₄×C₄₇	—	2	2	no	—
122	C₄×D₄×C₄₇	—	2	2	no	—
123	C₄×D₄×C₄₇	—	2	1	no	—
124	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
125	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
126	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
127	C₄×D₄×C₄₇	D₄	1	2	yes	—
128	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
129	C₄×D₄×C₄₇	C₂³	1	2	yes	—
130	#117×C₄₇	—	2	2	no	—
131	#117×C₄₇	—	2	2	no	—
132	#117×C₄₇	C₂×C₄	1	2	yes	—
133	#117×C₄₇	D₄	1	1	yes	characteristic
134	#117×C₄₇	D₄	1	2	yes	—
135	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄²×C₄₇	—	2	1	no	—
138	C₂×C₄²×C₄₇	—	2	2	no	—
139	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
141	#41×C₄₇	—	2	2	no	—
142	#41×C₄₇	—	2	2	no	—
143	#41×C₄₇	—	2	4	no	—
144	#41×C₄₇	—	4	2	no	—
145	#41×C₄₇	—	4	2	no	—
146	#41×C₄₇	—	4	2	no	—
147	C₂×Q₈×C₄₇	—	2	1	no	—
148	C₂×Q₈×C₄₇	—	2	1	no	—
149	C₂×Q₈×C₄₇	—	2	2	no	—
150	C₂×Q₈×C₄₇	—	4	1	no	—
151	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₂×D₄×C₄₇	—	2	2	no	—
155	C₂×D₄×C₄₇	—	2	2	no	—
156	C₂×D₄×C₄₇	—	2	2	no	—
157	C₂×D₄×C₄₇	—	2	1	no	—
158	C₂×D₄×C₄₇	—	2	1	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	C₂²×C₄×C₄₇	—	2	1	no	—
163	C₂²×C₄×C₄₇	—	2	1	no	—
164	C₂²×C₄×C₄₇	—	2	2	no	—
165	C₂²×C₄×C₄₇	—	2	2	no	—
166	C₂²×C₄×C₄₇	—	2	2	no	—
167	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
173	C₄⋊C₄×C₄₇	—	2	1	no	—
174	C₄⋊C₄×C₄₇	—	2	1	no	—
175	C₄⋊C₄×C₄₇	—	2	1	no	—
176	C₄⋊C₄×C₄₇	—	2	2	no	—
177	C₄⋊C₄×C₄₇	—	2	2	no	—
178	C₄⋊C₄×C₄₇	—	2	2	no	—
179	C₄⋊C₄×C₄₇	—	2	1	no	—
180	C₄⋊C₄×C₄₇	—	2	2	no	—
181	C₄⋊C₄×C₄₇	—	2	1	no	—
182	C₄⋊C₄×C₄₇	—	2	1	no	—
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	2	yes	—
186	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
187	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
188	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
189	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
190	C₂²⋊C₄×C₄₇	—	2	2	no	—
191	C₂²⋊C₄×C₄₇	—	2	2	no	—
192	C₂²⋊C₄×C₄₇	—	2	2	no	—
193	C₂²⋊C₄×C₄₇	—	2	2	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	C₂²⋊C₄	1	2	yes	—
199	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
200	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
201	C₄²×C₄₇	—	2	2	no	—
202	C₄²×C₄₇	—	2	2	no	—
203	C₄²×C₄₇	—	2	1	no	—
204	C₄²×C₄₇	—	2	1	no	—
205	C₄²×C₄₇	—	2	1	no	—
206	C₄²×C₄₇	—	2	1	no	—
207	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
208	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₄₇	C₂×D₄	1	2	yes	—
210	C₄²×C₄₇	C₂×D₄	1	2	yes	—
211	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
214	#10625329	—	4	4	no	—
215	#10625329	—	4	4	no	—
216	#10625329	—	4	2	no	—
217	C₂×C₄₇⋊C₈	—	2	1	no	—
218	C₂×C₄₇⋊C₈	—	2	1	no	—
219	C₂×C₄₇⋊C₈	—	2	2	no	—
220	C₂×C₄₇⋊C₈	—	2	1	no	—
221	C₂×C₄₇⋊C₈	—	2	2	no	—
222	C₂×C₄₇⋊C₈	—	2	1	no	—
223	C₂×C₄₇⋊C₈	—	4	2	no	—
224	C₂×C₄₇⋊C₈	—	4	4	no	—
225	C₂×C₄₇⋊C₈	—	4	2	no	—
226	C₂³×C₄₇	—	2	2	no	—
227	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
228	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	Q₈×C₄₇	—	2	1	no	—
230	Q₈×C₄₇	—	2	2	no	—
231	Q₈×C₄₇	—	2	1	no	—
232	Q₈×C₄₇	—	2	1	no	—
233	Q₈×C₄₇	—	4	2	no	—
234	Q₈×C₄₇	—	4	2	no	—
235	Q₈×C₄₇	#131	1	2	yes	complemented
236	D₄×C₄₇	—	2	4	no	—
237	D₄×C₄₇	—	2	2	no	—
238	D₄×C₄₇	—	2	2	no	—
239	D₄×C₄₇	—	2	2	no	—
240	D₄×C₄₇	—	4	4	no	—
241	D₄×C₄₇	—	4	4	no	—
242	D₄×C₄₇	—	4	2	no	—
243	D₄×C₄₇	—	8	1	no	—
244	D₄×C₄₇	—	8	2	no	—
245	C₂×C₄×C₄₇	—	2	1	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	2	no	—
251	C₂×C₄×C₄₇	—	2	2	no	—
252	C₂×C₄×C₄₇	—	2	1	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	—	4	1	no	—
257	C₂×C₄×C₄₇	—	4	2	no	—
258	C₂×C₄×C₄₇	—	4	4	no	—
259	C₂×C₄×C₄₇	—	4	2	no	—
260	C₂×C₄×C₄₇	—	4	2	no	—
261	C₂×C₄×C₄₇	—	4	2	no	—
262	C₂×C₄×C₄₇	—	8	2	no	—
263	C₂×C₄×C₄₇	—	8	1	no	—
264	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
265	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
266	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
267	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
271	C₂×C₄×C₄₇	#137	1	2	yes	—
272	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
273	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
275	C₄₇⋊C₈	—	2	2	no	—
276	C₄₇⋊C₈	—	4	1	no	—
277	C₄₇⋊C₈	—	4	2	no	—
278	C₄₇⋊C₈	—	4	1	no	—
279	C₄₇⋊C₈	—	4	2	no	—
280	C₄₇⋊C₈	—	4	1	no	—
281	#17515	—	47	1	no	maximal, Sylow
282	C₂²×C₄₇	—	2	1	no	—
283	C₂²×C₄₇	—	2	1	no	—
284	C₂²×C₄₇	—	2	2	no	—
285	C₂²×C₄₇	—	2	2	no	—
286	C₂²×C₄₇	—	2	2	no	—
287	C₂²×C₄₇	—	4	2	no	—
288	C₂²×C₄₇	—	4	2	no	—
289	C₂²×C₄₇	—	4	2	no	—
290	C₂²×C₄₇	#417	1	2	yes	—
291	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
292	C₄×C₄₇	—	2	2	no	—
293	C₄×C₄₇	—	2	1	no	—
294	C₄×C₄₇	—	2	2	no	—
295	C₄×C₄₇	—	2	2	no	—
296	C₄×C₄₇	—	2	1	no	—
297	C₄×C₄₇	—	2	2	no	—
298	C₄×C₄₇	—	2	1	no	—
299	C₄×C₄₇	—	4	1	no	—
300	C₄×C₄₇	—	4	2	no	—
301	C₄×C₄₇	—	4	1	no	—
302	C₄×C₄₇	—	4	1	no	—
303	C₄×C₄₇	#417	1	2	yes	—
304	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
305	C₄×C₄₇	#568	1	1	yes	characteristic
306	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
307	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
308	#3480	D₄₇	1	1	yes	characteristic
309	#2965	—	47	1	no	—
310	#2906	—	47	1	no	—
311	#1495	—	47	2	no	—
312	#1492	—	47	1	no	—
313	#1489	—	47	2	no	—
314	#1487	—	47	1	no	—
315	#1483	—	47	2	no	—
316	#1480	—	47	1	no	—
317	#1477	—	47	2	no	—
318	C₂×Q₈⋊C₈	—	47	1	no	—
319	C₂×C₄₇	—	2	2	no	—
320	C₂×C₄₇	—	4	2	no	—
321	C₂×C₄₇	—	8	2	no	—
322	C₂×C₄₇	#2880	1	1	yes	characteristic
323	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
324	C₂×C₄₇	#2901	1	1	yes	characteristic
325	C₂×#131	—	94	1	no	—
326	#559	—	2	1	no	—
327	#559	Dic₄₇	1	1	yes	characteristic
328	#557	Dic₄₇	1	1	yes	characteristic
329	#556	—	2	1	no	—
330	#556	Dic₄₇	1	1	yes	characteristic
331	#553	—	2	2	no	—
332	#553	Dic₄₇	1	2	yes	—
333	#550	Dic₄₇	1	1	yes	characteristic
334	#548	Dic₄₇	1	2	yes	—
335	#532	—	2	1	no	—
336	#532	C₂×D₄₇	1	1	yes	characteristic
337	#529	—	2	2	no	—
338	#529	C₂×D₄₇	1	2	yes	—
339	C₄×#41	—	2	1	no	—
340	C₄×#41	C₂×D₄₇	1	2	yes	—
341	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
342	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
343	#446	—	94	1	no	—
344	#436	—	94	1	no	—
345	#435	—	94	2	no	—
346	#431	—	47	2	no	—
347	#431	—	47	1	no	—
348	#424	—	94	1	no	—
349	#424	—	94	2	no	—
350	#423	—	47	1	no	—
351	#423	—	47	2	no	—
352	C₂×C₄⋊C₈	—	47	1	no	—
353	C₂×C₄⋊C₈	—	47	2	no	—
354	C₄×M₁₆	—	47	2	no	—
355	C₂×C₄×C₈	—	47	1	no	—
356	Q₈⋊C₈	—	47	1	no	—
357	Q₈⋊C₈	—	47	1	no	—
358	Q₈⋊C₈	—	47	1	no	—
359	Q₈⋊C₈	—	47	1	no	—
360	Q₈⋊C₈	—	47	2	no	—
361	Q₈⋊C₈	—	47	2	no	—
362	D₄⋊C₈	—	47	2	no	—
363	D₄⋊C₈	—	47	2	no	—
364	D₄⋊C₈	—	47	2	no	—
365	D₄⋊C₈	—	47	2	no	—
366	C₄₇	#17515	1	1	yes	characteristic, complemented, Sylow
367	C₂×#41	—	2	1	no	—
368	C₂×#41	C₂×Dic₄₇	1	2	yes	—
369	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
370	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
371	#131	—	188	4	no	—
372	C₂×M₁₆	—	94	2	no	—
373	C₂×M₁₆	—	94	1	no	—
374	C₂×M₁₆	—	94	2	no	—
375	C₂²×C₈	—	94	2	no	—
376	C₂²×C₈	—	94	1	no	—
377	C₂²×C₈	—	94	1	no	—
378	C₄⋊Q₈	—	2	1	no	—
379	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
380	#127	—	2	1	no	—
381	#127	C₂×Dic₄₇	1	1	yes	characteristic
382	#126	—	2	2	no	—
383	#126	—	2	2	no	—
384	#126	—	2	2	no	—
385	#125	—	2	2	no	—
386	#125	C₂×Dic₄₇	1	2	yes	—
387	#124	—	2	1	no	—
388	#124	—	2	1	no	—
389	#124	—	2	2	no	—
390	#124	—	2	1	no	—
391	#124	C₂×Dic₄₇	1	2	yes	—
392	#123	—	2	2	no	—
393	#123	—	2	2	no	—
394	#123	—	2	2	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
397	#121	—	2	2	no	—
398	#121	—	2	2	no	—
399	#121	—	2	1	no	—
400	#121	—	2	2	no	—
401	#121	C₂×Dic₄₇	1	2	yes	—
402	#121	C₂×Dic₄₇	1	2	yes	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	—	2	1	no	—
406	C₄×Q₈	—	2	1	no	—
407	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
408	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
409	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
410	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
411	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
412	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
413	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
423	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
424	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
425	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
426	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
427	C₄×D₄	C₂²×D₄₇	1	2	yes	—
428	#117	—	2	2	no	—
429	#117	—	2	2	no	—
430	#117	C₂×Dic₄₇	1	2	yes	—
431	#117	C₂²⋊D₄₇	1	1	yes	characteristic
432	#117	C₂²⋊D₄₇	1	2	yes	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	2	no	—
437	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
438	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
439	C₄⋊C₈	—	47	1	no	—
440	C₄⋊C₈	—	47	2	no	—
441	C₄⋊C₈	—	47	1	no	—
442	C₄⋊C₈	—	94	2	no	—
443	C₄⋊C₈	—	94	1	no	—
444	C₄⋊C₈	—	94	2	no	—
445	C₄⋊C₈	—	94	1	no	—
446	C₄⋊C₈	—	94	2	no	—
447	C₄⋊C₈	—	94	1	no	—
448	C₂²⋊C₈	—	94	1	no	—
449	C₂²⋊C₈	—	94	2	no	—
450	#97	—	94	2	no	—
451	C₄×C₈	—	47	1	no	—
452	C₄×C₈	—	47	1	no	—
453	C₄×C₈	—	47	2	no	—
454	C₄×C₈	—	94	1	no	—
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	2	4	no	—
458	#41	—	4	2	no	—
459	#41	—	4	2	no	—
460	#41	—	4	2	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×Q₈	—	4	1	no	—
465	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
466	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
467	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
474	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
475	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
482	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
483	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
484	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
486	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
487	M₁₆	—	188	4	no	—
488	M₁₆	—	188	4	no	—
489	M₁₆	—	188	2	no	—
490	C₂×C₈	—	94	1	no	—
491	C₂×C₈	—	94	1	no	—
492	C₂×C₈	—	94	2	no	—
493	C₂×C₈	—	94	1	no	—
494	C₂×C₈	—	94	2	no	—
495	C₂×C₈	—	94	1	no	—
496	C₂×C₈	—	188	2	no	—
497	C₂×C₈	—	188	4	no	—
498	C₂×C₈	—	188	2	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
510	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
511	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
512	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
513	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
525	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
526	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	C₂²×Dic₄₇	1	2	yes	—
534	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
535	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
536	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
537	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
538	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
539	C₄²	C₂³×D₄₇	1	1	yes	characteristic
540	C₂³	—	2	2	no	—
541	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
542	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
543	Q₈	—	2	1	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	2	1	no	—
546	Q₈	—	2	1	no	—
547	Q₈	—	4	2	no	—
548	Q₈	—	4	2	no	—
549	Q₈	#13094031	1	2	yes	complemented
550	D₄	—	2	4	no	—
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	2	2	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	4	no	—
556	D₄	—	4	2	no	—
557	D₄	—	8	1	no	—
558	D₄	—	8	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	8	2	no	—
577	C₂×C₄	—	8	1	no	—
578	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
579	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
580	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
581	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
582	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
583	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
584	C₂×C₄	#13094049	1	2	yes	—
585	C₂×C₄	#13094054	1	2	yes	—
586	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
587	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
588	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
589	C₈	—	94	2	no	—
590	C₈	—	188	1	no	—
591	C₈	—	188	2	no	—
592	C₈	—	188	1	no	—
593	C₈	—	188	2	no	—
594	C₈	—	188	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	#15689124	1	2	yes	—
604	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	2	no	—
611	C₄	—	2	2	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	#15689124	1	2	yes	—
617	C₄	C₂×#13094031	1	1	yes	characteristic
618	C₄	#15689890	1	1	yes	characteristic
619	C₄	C₂×#13094049	1	1	yes	characteristic
620	C₄	C₂×#13094054	1	1	yes	characteristic
621	C₂	—	2	2	no	—
622	C₂	—	4	2	no	—
623	C₂	—	8	2	no	—
624	C₂	#20251837	1	1	yes	characteristic
625	C₂	C₂×#15689124	1	1	yes	characteristic
626	C₂	#20251935	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×#3480	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3480	D₄₇
hypocenter	C₄₇	#17515
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3480

Complements

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

N	H ≅ G/N	type
1. #20252355	C₂	semidirect
2. #20251956	C₂	semidirect
3. #20241853	C₂	semidirect
4. #20241839	C₂	semidirect
5. #20241827	C₂	semidirect
6. #20241817	C₂	semidirect
7. #20241801	C₂	semidirect
8. #20241787	C₂	semidirect
9. #20241775	C₂	semidirect
10. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
235. Q₈×C₄₇	#131	semidirect
366. C₄₇	#17515	semidirect
549. Q₈	#13094031	semidirect

Maximal subgroups

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

subgroup	index
#20252355	2
#20251956	2
#20241853	2
#20241839	2
#20241827	2
#20241817	2
#20241801	2
#20241787	2
#20241775	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₄₇×#3480	2
#17515	47