Subgroups — #26183267

Order 12032.

1022 conjugacy classes of subgroups.

The subgroup lattice has 618 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	#20241843	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241835	C₂	1	2	yes	maximal, complemented
6	#20241827	C₂	1	1	yes	maximal, characteristic, complemented
7	#20241809	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×Q₈⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3482	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	—
17	#15689176	C₂²	1	1	yes	characteristic
18	#15689147	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
20	#15689079	—	2	2	no	—
21	#15689079	—	2	1	no	—
22	C₄×#10625329	C₂²	1	2	yes	—
23	C₄×#10625329	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₇⋊C₈	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	2	yes	—
28	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
29	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
30	Q₈⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
38	C₄₇×#556	C₄	1	1	yes	characteristic
39	C₄₇×#552	—	2	2	no	—
40	C₄₇×#552	C₄	1	2	yes	—
41	D₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
42	C₄₇×#548	C₄	1	2	yes	—
43	C₄₇×#547	—	2	1	no	—
44	C₄₇×#547	C₄	1	1	yes	characteristic
45	C₄₇×#533	—	2	1	no	—
46	C₄₇×#533	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	1	yes	characteristic
51	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×C₄×Q₈×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×Q₈×C₄₇	C₂×C₄	1	2	yes	—
80	C₄⋊Q₈×C₄₇	—	2	1	no	—
81	C₄⋊Q₈×C₄₇	—	2	1	no	—
82	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₄⋊Q₈×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	—	2	2	no	—
89	#125×C₄₇	—	2	1	no	—
90	#125×C₄₇	C₂×C₄	1	2	yes	—
91	#124×C₄₇	—	2	2	no	—
92	#124×C₄₇	C₂×C₄	1	2	yes	—
93	#123×C₄₇	—	2	2	no	—
94	#123×C₄₇	—	2	2	no	—
95	#123×C₄₇	—	2	2	no	—
96	C₂²⋊Q₈×C₄₇	—	2	1	no	—
97	C₂²⋊Q₈×C₄₇	—	2	1	no	—
98	C₂²⋊Q₈×C₄₇	—	2	1	no	—
99	C₂²⋊Q₈×C₄₇	—	2	2	no	—
100	C₂²⋊Q₈×C₄₇	—	2	2	no	—
101	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
102	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
103	#121×C₄₇	—	2	2	no	—
104	#121×C₄₇	C₂×C₄	1	2	yes	—
105	C₄×Q₈×C₄₇	—	2	1	no	—
106	C₄×Q₈×C₄₇	—	2	2	no	—
107	C₄×Q₈×C₄₇	—	2	2	no	—
108	C₄×Q₈×C₄₇	—	2	1	no	—
109	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
110	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
111	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
116	C₄×D₄×C₄₇	—	2	1	no	—
117	C₄×D₄×C₄₇	—	2	2	no	—
118	C₄×D₄×C₄₇	—	2	1	no	—
119	C₄×D₄×C₄₇	—	2	1	no	—
120	C₄×D₄×C₄₇	—	2	2	no	—
121	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
122	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
123	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
124	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
125	C₄×D₄×C₄₇	D₄	1	2	yes	—
126	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
127	#117×C₄₇	—	2	1	no	—
128	#117×C₄₇	—	2	1	no	—
129	#117×C₄₇	—	2	2	no	—
130	#117×C₄₇	—	2	1	no	—
131	#117×C₄₇	—	2	2	no	—
132	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
133	#117×C₄₇	D₄	1	2	yes	—
134	#117×C₄₇	D₄	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
137	C₂×C₄²×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	#41×C₄₇	—	2	4	no	—
142	#41×C₄₇	—	2	2	no	—
143	#41×C₄₇	—	4	1	no	—
144	#41×C₄₇	—	4	4	no	—
145	C₂×Q₈×C₄₇	—	2	2	no	—
146	C₂×Q₈×C₄₇	—	2	1	no	—
147	C₂×Q₈×C₄₇	—	2	4	no	—
148	C₂×Q₈×C₄₇	—	4	2	no	—
149	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
151	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₄₇	—	2	1	no	—
153	C₂×D₄×C₄₇	—	2	2	no	—
154	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
155	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
162	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
163	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
168	C₄⋊C₄×C₄₇	—	2	2	no	—
169	C₄⋊C₄×C₄₇	—	2	2	no	—
170	C₄⋊C₄×C₄₇	—	2	2	no	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	—	2	2	no	—
173	C₄⋊C₄×C₄₇	—	2	2	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	1	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	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	2	yes	—
185	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
186	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
187	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	2	no	—
195	C₂²⋊C₄×C₄₇	—	2	1	no	—
196	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
197	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
198	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
199	C₄²×C₄₇	—	2	1	no	—
200	C₄²×C₄₇	—	2	2	no	—
201	C₄²×C₄₇	—	2	1	no	—
202	C₄²×C₄₇	—	2	2	no	—
203	C₄²×C₄₇	—	2	1	no	—
204	C₄²×C₄₇	—	2	2	no	—
205	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
207	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₄₇	C₂×D₄	1	2	yes	—
210	C₄²×C₄₇	C₂×D₄	1	2	yes	—
211	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
212	#10625329	—	2	8	no	—
213	#10625329	—	2	4	no	—
214	#10625329	—	8	1	no	—
215	C₂×C₄₇⋊C₈	—	2	8	no	—
216	C₂×C₄₇⋊C₈	—	2	4	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	1	no	—
222	C₂×C₄₇⋊C₈	—	2	2	no	—
223	C₂×C₄₇⋊C₈	—	8	2	no	—
224	C₂³×C₄₇	—	2	1	no	—
225	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
227	Q₈×C₄₇	—	2	1	no	—
228	Q₈×C₄₇	—	2	2	no	—
229	Q₈×C₄₇	—	2	2	no	—
230	Q₈×C₄₇	—	2	2	no	—
231	Q₈×C₄₇	—	4	4	no	—
232	Q₈×C₄₇	—	4	2	no	—
233	Q₈×C₄₇	#131	1	2	yes	complemented
234	D₄×C₄₇	—	2	4	no	—
235	D₄×C₄₇	—	2	1	no	—
236	D₄×C₄₇	—	2	1	no	—
237	D₄×C₄₇	—	4	2	no	—
238	D₄×C₄₇	—	4	4	no	—
239	D₄×C₄₇	#104	1	4	yes	—
240	C₂×C₄×C₄₇	—	2	1	no	—
241	C₂×C₄×C₄₇	—	2	4	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	2	1	no	—
244	C₂×C₄×C₄₇	—	2	2	no	—
245	C₂×C₄×C₄₇	—	2	1	no	—
246	C₂×C₄×C₄₇	—	2	2	no	—
247	C₂×C₄×C₄₇	—	2	1	no	—
248	C₂×C₄×C₄₇	—	2	2	no	—
249	C₂×C₄×C₄₇	—	2	1	no	—
250	C₂×C₄×C₄₇	—	2	2	no	—
251	C₂×C₄×C₄₇	—	2	1	no	—
252	C₂×C₄×C₄₇	—	2	1	no	—
253	C₂×C₄×C₄₇	—	2	2	no	—
254	C₂×C₄×C₄₇	—	2	2	no	—
255	C₂×C₄×C₄₇	—	4	2	no	—
256	C₂×C₄×C₄₇	—	4	4	no	—
257	C₂×C₄×C₄₇	—	4	4	no	—
258	C₂×C₄×C₄₇	—	4	1	no	—
259	C₂×C₄×C₄₇	—	4	1	no	—
260	C₂×C₄×C₄₇	—	4	2	no	—
261	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
267	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
270	C₄₇⋊C₈	—	2	2	no	—
271	C₄₇⋊C₈	—	2	4	no	—
272	C₄₇⋊C₈	—	2	2	no	—
273	C₄₇⋊C₈	—	4	1	no	—
274	C₄₇⋊C₈	—	4	2	no	—
275	C₄₇⋊C₈	—	4	1	no	—
276	#17519	—	47	1	no	maximal, Sylow
277	C₂²×C₄₇	—	2	2	no	—
278	C₂²×C₄₇	—	2	2	no	—
279	C₂²×C₄₇	—	2	1	no	—
280	C₂²×C₄₇	—	2	1	no	—
281	C₂²×C₄₇	—	2	1	no	—
282	C₂²×C₄₇	—	4	1	no	—
283	C₂²×C₄₇	—	4	1	no	—
284	C₂²×C₄₇	—	4	1	no	—
285	C₂²×C₄₇	C₂×#104	1	4	yes	—
286	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
287	C₄×C₄₇	—	2	1	no	—
288	C₄×C₄₇	—	2	2	no	—
289	C₄×C₄₇	—	2	2	no	—
290	C₄×C₄₇	—	2	2	no	—
291	C₄×C₄₇	—	2	1	no	—
292	C₄×C₄₇	—	2	1	no	—
293	C₄×C₄₇	—	2	2	no	—
294	C₄×C₄₇	—	4	2	no	—
295	C₄×C₄₇	—	4	1	no	—
296	C₄×C₄₇	—	4	1	no	—
297	C₄×C₄₇	—	4	2	no	—
298	C₄×C₄₇	C₂×#104	1	2	yes	—
299	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
300	C₄×C₄₇	#568	1	1	yes	characteristic
301	C₄×C₄₇	#577	1	1	yes	characteristic
302	C₄×C₄₇	#578	1	1	yes	characteristic
303	#3482	D₄₇	1	1	yes	characteristic
304	#2990	—	47	1	no	—
305	C₄×#131	—	47	1	no	—
306	#1494	—	47	2	no	—
307	#1493	—	47	1	no	—
308	#1491	—	47	2	no	—
309	#1489	—	47	1	no	—
310	#1485	—	47	1	no	—
311	#1483	—	47	2	no	—
312	#1476	—	47	1	no	—
313	C₂×Q₈⋊C₈	—	47	2	no	—
314	C₂×C₄₇	—	2	4	no	—
315	C₂×C₄₇	—	4	1	no	—
316	C₂×C₄₇	—	8	1	no	—
317	C₂×C₄₇	#2880	1	1	yes	characteristic
318	C₂×C₄₇	#2898	1	1	yes	characteristic
319	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
320	C₂×#131	—	94	1	no	—
321	#557	Dic₄₇	1	1	yes	characteristic
322	#556	—	2	1	no	—
323	#556	Dic₄₇	1	1	yes	characteristic
324	#552	—	2	2	no	—
325	#552	Dic₄₇	1	2	yes	—
326	D₄×Q₈	Dic₄₇	1	1	yes	characteristic
327	#548	Dic₄₇	1	2	yes	—
328	#547	—	2	1	no	—
329	#547	Dic₄₇	1	1	yes	characteristic
330	#533	—	2	1	no	—
331	#533	C₂×D₄₇	1	1	yes	characteristic
332	#529	—	2	2	no	—
333	#529	C₂×D₄₇	1	2	yes	—
334	C₄×#41	—	2	1	no	—
335	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
336	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
337	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
338	#446	—	94	1	no	—
339	#435	—	94	2	no	—
340	C₈×D₄	—	94	1	no	—
341	#432	—	47	2	no	—
342	#431	—	47	1	no	—
343	#423	—	47	1	no	—
344	C₂×C₄⋊C₈	—	47	2	no	—
345	#405	—	94	2	no	—
346	#405	—	94	1	no	—
347	C₄×M₁₆	—	47	2	no	—
348	C₄×M₁₆	—	47	1	no	—
349	C₂×C₄×C₈	—	47	2	no	—
350	C₂×C₄×C₈	—	47	1	no	—
351	Q₈⋊C₈	—	47	1	no	—
352	Q₈⋊C₈	—	47	2	no	—
353	Q₈⋊C₈	—	47	2	no	—
354	Q₈⋊C₈	—	47	2	no	—
355	Q₈⋊C₈	—	47	1	no	—
356	Q₈⋊C₈	—	47	2	no	—
357	Q₈⋊C₈	—	47	2	no	—
358	D₄⋊C₈	—	47	1	no	—
359	D₄⋊C₈	—	47	1	no	—
360	D₄⋊C₈	—	47	2	no	—
361	C₄₇	#17519	1	1	yes	characteristic, complemented, Sylow
362	C₂×#41	—	2	1	no	—
363	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
364	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
365	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
366	#131	—	94	8	no	—
367	C₂×M₁₆	—	94	2	no	—
368	C₂×M₁₆	—	94	1	no	—
369	C₂×M₁₆	—	94	1	no	—
370	C₂²×C₈	—	94	2	no	—
371	C₂²×C₈	—	94	1	no	—
372	C₂²×C₈	—	94	2	no	—
373	C₄⋊Q₈	—	2	1	no	—
374	C₄⋊Q₈	—	2	1	no	—
375	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
376	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
377	#126	—	2	2	no	—
378	#126	—	2	2	no	—
379	#126	—	2	2	no	—
380	#125	—	2	2	no	—
381	#125	—	2	2	no	—
382	#125	—	2	1	no	—
383	#125	C₂×Dic₄₇	1	2	yes	—
384	#124	—	2	2	no	—
385	#124	C₂×Dic₄₇	1	2	yes	—
386	#123	—	2	2	no	—
387	#123	—	2	2	no	—
388	#123	—	2	2	no	—
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	—	2	1	no	—
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
395	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
396	#121	—	2	2	no	—
397	#121	C₂×Dic₄₇	1	2	yes	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	—	2	2	no	—
400	C₄×Q₈	—	2	2	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
403	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
404	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
405	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
406	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
407	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
408	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
415	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
416	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
417	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
418	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
419	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
420	#117	—	2	1	no	—
421	#117	—	2	1	no	—
422	#117	—	2	2	no	—
423	#117	—	2	1	no	—
424	#117	—	2	2	no	—
425	#117	C₂×Dic₄₇	1	1	yes	characteristic
426	#117	C₂²⋊D₄₇	1	2	yes	—
427	#117	C₂²⋊D₄₇	1	1	yes	characteristic
428	C₂×C₄⋊C₄	—	2	2	no	—
429	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
430	C₂×C₄²	—	2	2	no	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
433	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
434	C₄⋊C₈	—	47	1	no	—
435	C₄⋊C₈	—	47	2	no	—
436	C₄⋊C₈	—	47	1	no	—
437	C₄⋊C₈	—	94	2	no	—
438	C₄⋊C₈	—	94	1	no	—
439	C₂²⋊C₈	—	94	1	no	—
440	C₂²⋊C₈	—	94	2	no	—
441	#97	—	94	1	no	—
442	#97	—	94	2	no	—
443	#97	—	94	2	no	—
444	C₄×C₈	—	47	1	no	—
445	C₄×C₈	—	47	1	no	—
446	C₄×C₈	—	47	2	no	—
447	C₄×C₈	—	94	1	no	—
448	C₄×C₈	—	94	2	no	—
449	C₄×C₈	—	94	1	no	—
450	#41	—	2	4	no	—
451	#41	—	2	2	no	—
452	#41	—	4	1	no	—
453	#41	—	4	4	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	4	no	—
457	C₂×Q₈	—	4	2	no	—
458	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
459	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
460	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
464	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
465	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
472	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
474	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
476	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
477	M₁₆	—	94	8	no	—
478	M₁₆	—	94	4	no	—
479	M₁₆	—	376	1	no	—
480	C₂×C₈	—	94	8	no	—
481	C₂×C₈	—	94	4	no	—
482	C₂×C₈	—	94	1	no	—
483	C₂×C₈	—	94	1	no	—
484	C₂×C₈	—	94	2	no	—
485	C₂×C₈	—	94	1	no	—
486	C₂×C₈	—	94	1	no	—
487	C₂×C₈	—	94	2	no	—
488	C₂×C₈	—	376	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
503	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
504	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
505	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
506	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
508	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
518	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
519	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	2	no	—
526	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
527	C₄²	C₂²×Dic₄₇	1	2	yes	—
528	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
529	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
530	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
531	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
532	C₄²	C₂³×D₄₇	1	1	yes	characteristic
533	C₂³	—	2	1	no	—
534	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
535	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
536	Q₈	—	2	1	no	—
537	Q₈	—	2	2	no	—
538	Q₈	—	2	2	no	—
539	Q₈	—	2	2	no	—
540	Q₈	—	4	4	no	—
541	Q₈	—	4	2	no	—
542	Q₈	#13094031	1	2	yes	complemented
543	D₄	—	2	4	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	4	no	—
548	D₄	#13093951	1	4	yes	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	2	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	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
571	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
572	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
573	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
574	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
575	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
576	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
577	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
578	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
579	C₈	—	94	2	no	—
580	C₈	—	94	4	no	—
581	C₈	—	94	2	no	—
582	C₈	—	188	1	no	—
583	C₈	—	188	2	no	—
584	C₈	—	188	1	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	C₂×#13093951	1	4	yes	—
594	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
595	C₄	—	2	2	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	2	no	—
606	C₄	C₂×#13093951	1	2	yes	—
607	C₄	C₂×#13094031	1	1	yes	characteristic
608	C₄	#15689890	1	1	yes	characteristic
609	C₄	#15689931	1	1	yes	characteristic
610	C₄	#15689938	1	1	yes	characteristic
611	C₂	—	2	4	no	—
612	C₂	—	4	1	no	—
613	C₂	—	8	1	no	—
614	C₂	#20251837	1	1	yes	characteristic
615	C₂	#20251921	1	1	yes	characteristic
616	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×#3482	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3482	D₄₇
hypocenter	C₄₇	#17519
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. C₄×#13094031	C₂	semidirect
3. #20241848	C₂	semidirect
4. #20241843	C₂	semidirect
5. #20241835	C₂	semidirect
6. #20241827	C₂	semidirect
7. #20241809	C₂	semidirect
8. #20241801	C₂	semidirect
9. #20241770	C₂	semidirect
10. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
233. Q₈×C₄₇	#131	semidirect
361. C₄₇	#17519	semidirect
542. Q₈	#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
#20241843	2
#20241835	2
#20241827	2
#20241809	2
#20241801	2
#20241770	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₄₇×#3482	2
#17519	47