Subgroups — #26182766

Order 12032.

1138 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252505	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252355	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241835	C₂	1	2	yes	maximal, complemented
4	#20241827	C₂	1	2	yes	maximal, complemented
5	#20241822	C₂	1	2	yes	maximal, complemented
6	#20241817	C₂	1	2	yes	maximal, complemented
7	#20241783	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241775	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241770	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×2₋¹⁺⁴×C₄₇	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	1	no	—
13	#15689254	—	2	1	no	—
14	#15689201	—	2	1	no	—
15	#15689201	—	2	1	no	—
16	#15689195	—	2	2	no	—
17	#15689195	—	2	2	no	—
18	#15689180	C₂²	1	2	yes	—
19	#15689176	C₂²	1	1	yes	characteristic
20	#15689176	C₂²	1	1	yes	characteristic
21	#15689176	C₂²	1	2	yes	—
22	#15689147	C₂²	1	2	yes	—
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₄×#10625329	C₂²	1	2	yes	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
27	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
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	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	C₂×2₋¹⁺⁴×C₄₇	C₄	1	1	yes	characteristic
37	C₄₇×#520	—	2	2	no	—
38	C₄₇×#520	—	2	1	no	—
39	C₄₇×#520	C₄	1	2	yes	—
40	C₄₇×#520	C₄	1	1	yes	characteristic
41	C₄₇×#520	C₄	1	1	yes	characteristic
42	C₄₇×#519	—	2	1	no	—
43	C₄₇×#519	C₄	1	2	yes	—
44	C₄₇×#519	C₄	1	1	yes	characteristic
45	C₄×#41×C₄₇	—	2	2	no	—
46	C₄×#41×C₄₇	—	2	1	no	—
47	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
48	C₄×#41×C₄₇	C₂²	1	2	yes	—
49	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
51	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
53	C₂×#10625329	—	2	2	no	—
54	C₂×#10625329	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	C₂²×C₄₇⋊C₈	—	2	1	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
62	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
63	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
64	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
68	#13093935	—	2	2	no	—
69	#13093935	—	2	2	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	2₋¹⁺⁴×C₄₇	—	2	4	no	—
76	2₋¹⁺⁴×C₄₇	—	2	4	no	—
77	C₂×#41×C₄₇	—	2	1	no	—
78	C₂×#41×C₄₇	—	2	2	no	—
79	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
80	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂²×Q₈×C₄₇	—	2	1	no	—
83	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
84	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₄₇	—	2	1	no	—
86	C₄×Q₈×C₄₇	—	2	2	no	—
87	C₄×Q₈×C₄₇	—	2	1	no	—
88	C₄×Q₈×C₄₇	—	2	2	no	—
89	C₄×Q₈×C₄₇	—	2	1	no	—
90	C₄×Q₈×C₄₇	—	2	1	no	—
91	C₄×Q₈×C₄₇	—	2	2	no	—
92	C₄×Q₈×C₄₇	—	2	1	no	—
93	C₄×Q₈×C₄₇	—	2	2	no	—
94	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
95	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
96	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
99	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
101	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
102	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₄₇	—	2	2	no	—
104	C₄×D₄×C₄₇	—	2	1	no	—
105	C₄×D₄×C₄₇	—	2	1	no	—
106	C₄×D₄×C₄₇	—	2	2	no	—
107	C₄×D₄×C₄₇	—	2	1	no	—
108	C₄×D₄×C₄₇	—	2	2	no	—
109	C₄×D₄×C₄₇	—	2	2	no	—
110	C₄×D₄×C₄₇	—	2	2	no	—
111	C₄×D₄×C₄₇	—	2	2	no	—
112	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
113	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
114	C₄×D₄×C₄₇	D₄	1	2	yes	—
115	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
116	C₄×D₄×C₄₇	D₄	1	2	yes	—
117	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
118	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
119	#117×C₄₇	—	2	2	no	—
120	#117×C₄₇	—	2	1	no	—
121	#117×C₄₇	—	2	2	no	—
122	#117×C₄₇	—	2	2	no	—
123	#117×C₄₇	—	2	2	no	—
124	#117×C₄₇	—	2	1	no	—
125	#117×C₄₇	—	2	2	no	—
126	#117×C₄₇	C₂×C₄	1	2	yes	—
127	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
128	#117×C₄₇	C₂×C₄	1	2	yes	—
129	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
131	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
135	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄²×C₄₇	—	2	1	no	—
137	C₂×C₄²×C₄₇	—	2	2	no	—
138	C₂×C₄²×C₄₇	—	2	1	no	—
139	C₂×C₄²×C₄₇	—	2	2	no	—
140	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
142	#41×C₄₇	—	2	16	no	—
143	#41×C₄₇	—	2	8	no	—
144	#41×C₄₇	—	2	4	no	—
145	#41×C₄₇	—	2	4	no	—
146	#41×C₄₇	—	2	2	no	—
147	#41×C₄₇	—	2	2	no	—
148	#41×C₄₇	—	2	2	no	—
149	#41×C₄₇	M₁₆	1	4	yes	complemented
150	C₂×Q₈×C₄₇	—	2	8	no	—
151	C₂×Q₈×C₄₇	—	2	4	no	—
152	C₂×Q₈×C₄₇	—	2	4	no	—
153	C₂×Q₈×C₄₇	—	2	2	no	—
154	C₂×Q₈×C₄₇	—	2	1	no	—
155	C₂×Q₈×C₄₇	—	2	2	no	—
156	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×Q₈×C₄₇	M₁₆	1	4	yes	complemented
158	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
159	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
160	C₂×D₄×C₄₇	—	2	2	no	—
161	C₂×D₄×C₄₇	—	2	1	no	—
162	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
163	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₇	—	2	2	no	—
166	C₂²×C₄×C₄₇	—	2	1	no	—
167	C₂²×C₄×C₄₇	—	2	2	no	—
168	C₂²×C₄×C₄₇	—	2	1	no	—
169	C₂²×C₄×C₄₇	—	2	2	no	—
170	C₂²×C₄×C₄₇	—	2	1	no	—
171	C₂²×C₄×C₄₇	—	2	1	no	—
172	C₂²×C₄×C₄₇	—	2	1	no	—
173	C₂²×C₄×C₄₇	—	2	2	no	—
174	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
175	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₄₇	—	2	2	no	—
181	C₄⋊C₄×C₄₇	—	2	2	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	—	2	1	no	—
186	C₄⋊C₄×C₄₇	—	2	2	no	—
187	C₄⋊C₄×C₄₇	—	2	2	no	—
188	C₄⋊C₄×C₄₇	—	2	1	no	—
189	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
190	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
192	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
194	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
195	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²⋊C₄×C₄₇	—	2	2	no	—
197	C₂²⋊C₄×C₄₇	—	2	1	no	—
198	C₂²⋊C₄×C₄₇	—	2	1	no	—
199	C₂²⋊C₄×C₄₇	—	2	2	no	—
200	C₂²⋊C₄×C₄₇	—	2	1	no	—
201	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
202	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
203	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
204	C₄²×C₄₇	—	2	1	no	—
205	C₄²×C₄₇	—	2	2	no	—
206	C₄²×C₄₇	—	2	2	no	—
207	C₄²×C₄₇	—	2	2	no	—
208	C₄²×C₄₇	—	2	2	no	—
209	C₄²×C₄₇	—	2	2	no	—
210	C₄²×C₄₇	—	2	1	no	—
211	C₄²×C₄₇	—	2	2	no	—
212	C₄²×C₄₇	—	2	1	no	—
213	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
215	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₄₇	C₂×D₄	1	2	yes	—
217	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₄₇	C₂×D₄	1	2	yes	—
219	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
220	#10625329	—	4	4	no	—
221	#10625329	—	8	2	no	—
222	C₂×C₄₇⋊C₈	—	2	1	no	—
223	C₂×C₄₇⋊C₈	—	2	1	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	—	2	2	no	—
228	C₂×C₄₇⋊C₈	—	4	2	no	—
229	C₂×C₄₇⋊C₈	—	8	1	no	—
230	C₂³×C₄₇	—	2	1	no	—
231	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
232	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	Q₈×C₄₇	—	2	8	no	—
234	Q₈×C₄₇	—	2	1	no	—
235	Q₈×C₄₇	—	2	2	no	—
236	Q₈×C₄₇	—	2	2	no	—
237	Q₈×C₄₇	—	2	4	no	—
238	Q₈×C₄₇	C₂×M₁₆	1	2	yes	—
239	Q₈×C₄₇	C₂×M₁₆	1	4	yes	—
240	D₄×C₄₇	—	2	8	no	—
241	D₄×C₄₇	—	2	4	no	—
242	D₄×C₄₇	—	2	4	no	—
243	D₄×C₄₇	—	2	1	no	—
244	D₄×C₄₇	—	2	2	no	—
245	D₄×C₄₇	C₂×M₁₆	1	2	yes	—
246	C₂×C₄×C₄₇	—	2	8	no	—
247	C₂×C₄×C₄₇	—	2	8	no	—
248	C₂×C₄×C₄₇	—	2	2	no	—
249	C₂×C₄×C₄₇	—	2	1	no	—
250	C₂×C₄×C₄₇	—	2	4	no	—
251	C₂×C₄×C₄₇	—	2	2	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	4	no	—
258	C₂×C₄×C₄₇	—	2	1	no	—
259	C₂×C₄×C₄₇	—	2	2	no	—
260	C₂×C₄×C₄₇	—	2	1	no	—
261	C₂×C₄×C₄₇	—	4	1	no	—
262	C₂×C₄×C₄₇	—	4	2	no	—
263	C₂×C₄×C₄₇	—	4	1	no	—
264	C₂×C₄×C₄₇	—	4	1	no	—
265	C₂×C₄×C₄₇	—	8	1	no	—
266	C₂×C₄×C₄₇	—	8	2	no	—
267	C₂×C₄×C₄₇	—	8	1	no	—
268	C₂×C₄×C₄₇	—	8	2	no	—
269	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
271	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
273	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
274	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
276	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
277	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
278	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
280	C₄₇⋊C₈	—	2	2	no	—
281	C₄₇⋊C₈	—	4	1	no	—
282	C₄₇⋊C₈	—	4	2	no	—
283	C₄₇⋊C₈	—	4	2	no	—
284	C₄₇⋊C₈	—	4	1	no	—
285	C₄₇⋊C₈	—	4	1	no	—
286	#17454	—	47	1	no	maximal, Sylow
287	C₂²×C₄₇	—	2	1	no	—
288	C₂²×C₄₇	—	2	1	no	—
289	C₂²×C₄₇	—	2	2	no	—
290	C₂²×C₄₇	—	2	2	no	—
291	C₂²×C₄₇	—	2	2	no	—
292	C₂²×C₄₇	—	2	2	no	—
293	C₂²×C₄₇	—	4	1	no	—
294	C₂²×C₄₇	—	4	1	no	—
295	C₂²×C₄₇	#407	1	2	yes	—
296	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
297	C₄×C₄₇	—	2	4	no	—
298	C₄×C₄₇	—	2	2	no	—
299	C₄×C₄₇	—	2	2	no	—
300	C₄×C₄₇	—	2	1	no	—
301	C₄×C₄₇	—	2	2	no	—
302	C₄×C₄₇	—	2	1	no	—
303	C₄×C₄₇	—	2	1	no	—
304	C₄×C₄₇	—	2	2	no	—
305	C₄×C₄₇	—	4	1	no	—
306	C₄×C₄₇	—	4	2	no	—
307	C₄×C₄₇	—	4	1	no	—
308	C₄×C₄₇	#407	1	2	yes	—
309	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
310	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
311	C₄×C₄₇	#577	1	1	yes	characteristic
312	C₄×C₄₇	#578	1	1	yes	characteristic
313	C₄×2₋¹⁺⁴	D₄₇	1	1	yes	characteristic
314	#2989	—	47	1	no	—
315	#2965	—	47	1	no	—
316	#1491	—	47	2	no	—
317	#1489	—	47	2	no	—
318	#1488	—	47	2	no	—
319	#1487	—	47	2	no	—
320	#1479	—	47	1	no	—
321	#1477	—	47	1	no	—
322	#1476	—	47	1	no	—
323	C₂×Q₈⋊C₈	—	47	1	no	—
324	C₂×C₄₇	—	2	2	no	—
325	C₂×C₄₇	—	4	2	no	—
326	C₂×C₄₇	—	4	2	no	—
327	C₂×C₄₇	C₂×#407	1	1	yes	characteristic
328	C₂×C₄₇	#2898	1	1	yes	characteristic
329	C₂×C₄₇	#2901	1	1	yes	characteristic
330	C₂×2₋¹⁺⁴	Dic₄₇	1	1	yes	characteristic
331	#520	—	2	2	no	—
332	#520	—	2	1	no	—
333	#520	Dic₄₇	1	2	yes	—
334	#520	Dic₄₇	1	1	yes	characteristic
335	#520	Dic₄₇	1	1	yes	characteristic
336	#519	—	2	1	no	—
337	#519	Dic₄₇	1	2	yes	—
338	#519	Dic₄₇	1	1	yes	characteristic
339	C₄×#41	—	2	2	no	—
340	C₄×#41	—	2	1	no	—
341	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
342	C₄×#41	C₂×D₄₇	1	2	yes	—
343	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
344	C₂×C₄×Q₈	—	2	1	no	—
345	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
346	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
347	#446	—	94	1	no	—
348	#446	—	94	1	no	—
349	#436	—	94	1	no	—
350	#436	—	94	1	no	—
351	#435	—	94	2	no	—
352	#435	—	94	2	no	—
353	#432	—	47	2	no	—
354	#431	—	47	1	no	—
355	#431	—	47	2	no	—
356	#431	—	47	1	no	—
357	#423	—	47	2	no	—
358	C₂×C₄⋊C₈	—	47	1	no	—
359	C₄×M₁₆	—	47	2	no	—
360	C₂×C₄×C₈	—	47	1	no	—
361	Q₈⋊C₈	—	47	2	no	—
362	Q₈⋊C₈	—	47	2	no	—
363	Q₈⋊C₈	—	47	1	no	—
364	Q₈⋊C₈	—	47	1	no	—
365	Q₈⋊C₈	—	47	2	no	—
366	Q₈⋊C₈	—	47	2	no	—
367	Q₈⋊C₈	—	47	2	no	—
368	D₄⋊C₈	—	47	1	no	—
369	D₄⋊C₈	—	47	1	no	—
370	D₄⋊C₈	—	47	2	no	—
371	C₄₇	#17454	1	1	yes	characteristic, complemented, Sylow
372	2₋¹⁺⁴	—	2	4	no	—
373	2₋¹⁺⁴	—	2	4	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	2	no	—
376	C₂×#41	C₂×Dic₄₇	1	2	yes	—
377	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
378	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
379	C₂²×Q₈	—	2	1	no	—
380	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
381	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
382	C₂×M₁₆	—	94	2	no	—
383	C₂×M₁₆	—	94	2	no	—
384	C₂²×C₈	—	94	1	no	—
385	C₂²×C₈	—	94	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
396	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
397	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
398	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
399	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
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×Q₈	C₂²×D₄₇	1	1	yes	characteristic
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
414	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
415	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
416	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
417	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
418	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
419	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
420	#117	—	2	2	no	—
421	#117	—	2	1	no	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	#117	—	2	2	no	—
425	#117	—	2	1	no	—
426	#117	—	2	2	no	—
427	#117	C₂×Dic₄₇	1	2	yes	—
428	#117	C₂×Dic₄₇	1	1	yes	characteristic
429	#117	C₂×Dic₄₇	1	2	yes	—
430	#117	C₂×Dic₄₇	1	1	yes	characteristic
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	2	no	—
433	C₂×C₄⋊C₄	—	2	2	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
436	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	2	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	—	2	2	no	—
441	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
442	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
443	C₄⋊C₈	—	47	2	no	—
444	C₄⋊C₈	—	47	1	no	—
445	C₄⋊C₈	—	47	1	no	—
446	C₄⋊C₈	—	94	1	no	—
447	C₄⋊C₈	—	94	2	no	—
448	C₄⋊C₈	—	94	2	no	—
449	C₄⋊C₈	—	94	1	no	—
450	C₂²⋊C₈	—	94	1	no	—
451	C₂²⋊C₈	—	94	1	no	—
452	C₂²⋊C₈	—	94	2	no	—
453	C₂²⋊C₈	—	94	2	no	—
454	#97	—	94	2	no	—
455	#97	—	94	2	no	—
456	C₄×C₈	—	47	1	no	—
457	C₄×C₈	—	47	1	no	—
458	C₄×C₈	—	47	2	no	—
459	C₄×C₈	—	94	1	no	—
460	C₄×C₈	—	94	1	no	—
461	#41	—	2	16	no	—
462	#41	—	2	8	no	—
463	#41	—	2	4	no	—
464	#41	—	2	4	no	—
465	#41	—	2	2	no	—
466	#41	—	2	2	no	—
467	#41	—	2	2	no	—
468	#41	#10625329	1	4	yes	complemented
469	C₂×Q₈	—	2	8	no	—
470	C₂×Q₈	—	2	4	no	—
471	C₂×Q₈	—	2	4	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	#10625329	1	4	yes	complemented
476	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
477	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
478	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
482	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
483	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
494	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
495	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
496	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
497	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
499	M₁₆	—	376	2	no	—
500	M₁₆	—	188	4	no	—
501	C₂×C₈	—	94	1	no	—
502	C₂×C₈	—	94	1	no	—
503	C₂×C₈	—	94	2	no	—
504	C₂×C₈	—	94	1	no	—
505	C₂×C₈	—	94	1	no	—
506	C₂×C₈	—	94	2	no	—
507	C₂×C₈	—	376	1	no	—
508	C₂×C₈	—	188	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
519	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
520	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
521	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
524	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
531	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
532	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	2	no	—
541	C₄²	—	2	1	no	—
542	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
543	C₄²	C₂²×Dic₄₇	1	2	yes	—
544	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
545	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
546	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
547	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
548	C₄²	C₂³×D₄₇	1	1	yes	characteristic
549	C₂³	—	2	1	no	—
550	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
551	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
552	Q₈	—	2	8	no	—
553	Q₈	—	2	4	no	—
554	Q₈	—	2	2	no	—
555	Q₈	—	2	1	no	—
556	Q₈	—	2	2	no	—
557	Q₈	C₂×#10625329	1	2	yes	—
558	Q₈	C₂×#10625329	1	4	yes	—
559	D₄	—	2	8	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	2	no	—
563	D₄	—	2	1	no	—
564	D₄	C₂×#10625329	1	2	yes	—
565	C₂×C₄	—	2	8	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	8	1	no	—
585	C₂×C₄	—	8	2	no	—
586	C₂×C₄	—	8	1	no	—
587	C₂×C₄	—	8	2	no	—
588	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
589	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
590	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
591	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
592	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
593	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
594	C₂×C₄	C₂×#10625329	1	2	yes	—
595	C₂×C₄	C₂×#10625329	1	2	yes	—
596	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
597	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
598	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
599	C₈	—	94	2	no	—
600	C₈	—	188	1	no	—
601	C₈	—	188	2	no	—
602	C₈	—	188	2	no	—
603	C₈	—	188	1	no	—
604	C₈	—	188	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	#15689087	1	2	yes	—
614	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
615	C₄	—	2	1	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	4	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	1	no	—
626	C₄	#15689087	1	2	yes	—
627	C₄	C₂²×#10625329	1	1	yes	characteristic
628	C₄	C₂²×#10625329	1	1	yes	characteristic
629	C₄	#15689931	1	1	yes	characteristic
630	C₄	#15689938	1	1	yes	characteristic
631	C₂	—	2	2	no	—
632	C₂	—	4	2	no	—
633	C₂	—	4	2	no	—
634	C₂	C₂×#15689087	1	1	yes	characteristic
635	C₂	#20251921	1	1	yes	characteristic
636	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	C₄×2₋¹⁺⁴×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂×2₋¹⁺⁴×C₄₇	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₄×2₋¹⁺⁴	D₄₇
hypocenter	C₄₇	#17454
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ C₄×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. #20252505	C₂	semidirect
2. #20252355	C₂	semidirect
3. #20241835	C₂	semidirect
4. #20241827	C₂	semidirect
5. #20241822	C₂	semidirect
6. #20241817	C₂	semidirect
7. #20241783	C₂	semidirect
8. #20241775	C₂	semidirect
9. #20241770	C₂	semidirect
10. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
149. #41×C₄₇	M₁₆	semidirect
157. C₂×Q₈×C₄₇	M₁₆	semidirect
371. C₄₇	#17454	semidirect
468. #41	#10625329	semidirect
475. C₂×Q₈	#10625329	semidirect

Maximal subgroups

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

subgroup	index
#20252505	2
#20252355	2
#20241835	2
#20241827	2
#20241822	2
#20241817	2
#20241783	2
#20241775	2
#20241770	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₄×2₋¹⁺⁴×C₄₇	2
#17454	47