Subgroups — #26183186

Order 12032.

1004 conjugacy classes of subgroups.

The subgroup lattice has 642 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	#20241843	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241827	C₂	1	2	yes	maximal, complemented
6	#20241813	C₂	1	1	yes	maximal, characteristic, complemented
7	#20241801	C₂	1	2	yes	maximal, complemented
8	#20241791	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241775	C₂	1	2	yes	maximal, complemented
10	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3475	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	1	yes	characteristic
17	#15689176	C₂²	1	2	yes	complemented
18	#15689150	—	2	1	no	—
19	#15689150	—	2	2	no	—
20	#15689147	C₂²	1	1	yes	characteristic
21	#15689147	C₂²	1	2	yes	complemented
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
24	C₄×#10625329	C₂²	1	2	yes	complemented
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
27	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
28	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
29	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
30	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
31	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
32	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
33	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
35	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
36	C₄₇×#556	C₄	1	1	yes	characteristic
37	C₄₇×#555	C₄	1	1	yes	characteristic
38	C₄₇×#554	C₄	1	1	yes	characteristic
39	C₄₇×#553	—	2	1	no	—
40	C₄₇×#552	—	2	1	no	—
41	C₄₇×#552	C₄	1	2	yes	—
42	C₄₇×#551	—	2	2	no	—
43	C₄₇×#547	C₄	1	1	yes	characteristic
44	C₄₇×#546	C₄	1	2	yes	—
45	C₄₇×#533	C₂²	1	1	yes	characteristic
46	C₄₇×#529	—	2	2	no	—
47	C₄₇×#529	C₂²	1	2	yes	—
48	C₄₇×#525	—	2	1	no	—
49	C₄×#41×C₄₇	C₂²	1	2	yes	—
50	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×#117×C₄₇	—	2	1	no	—
53	#13094031	—	4	4	no	—
54	C₂×#10625329	—	2	2	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂×#10625329	—	2	2	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	—	2	1	no	—
59	C₂²×C₄₇⋊C₈	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
62	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
63	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
64	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
66	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
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	C₂×C₄	1	2	yes	—
77	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
78	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₄₇	—	2	1	no	—
80	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	#126×C₄₇	—	2	2	no	—
83	#126×C₄₇	—	2	2	no	—
84	#126×C₄₇	—	2	2	no	—
85	#125×C₄₇	—	2	2	no	—
86	#125×C₄₇	—	2	1	no	—
87	#125×C₄₇	C₂×C₄	1	2	yes	—
88	#124×C₄₇	—	2	2	no	—
89	#124×C₄₇	C₂×C₄	1	2	yes	—
90	#123×C₄₇	—	2	2	no	—
91	#123×C₄₇	—	2	2	no	—
92	#123×C₄₇	—	2	2	no	—
93	#123×C₄₇	—	2	2	no	—
94	C₂²⋊Q₈×C₄₇	—	2	1	no	—
95	C₂²⋊Q₈×C₄₇	—	2	1	no	—
96	C₂²⋊Q₈×C₄₇	—	2	1	no	—
97	C₂²⋊Q₈×C₄₇	—	2	2	no	—
98	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
99	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
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	#120×C₄₇	—	2	2	no	—
105	C₄×Q₈×C₄₇	—	2	1	no	—
106	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
107	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
108	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
109	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
110	C₄×D₄×C₄₇	—	2	2	no	—
111	C₄×D₄×C₄₇	—	2	2	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	C₂×C₄	1	1	yes	characteristic
116	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
117	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
118	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
119	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₄×D₄×C₄₇	D₄	1	2	yes	—
121	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
122	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
123	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
124	#117×C₄₇	—	2	1	no	—
125	#117×C₄₇	—	2	1	no	—
126	#117×C₄₇	—	2	1	no	—
127	#117×C₄₇	—	2	2	no	—
128	#117×C₄₇	—	2	2	no	—
129	#117×C₄₇	—	2	2	no	—
130	#117×C₄₇	C₂×C₄	1	2	yes	—
131	#117×C₄₇	D₄	1	1	yes	characteristic
132	#117×C₄₇	D₄	1	2	yes	—
133	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₄₇	—	2	2	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	C₂⁴×C₄₇	—	2	1	no	—
142	#41×C₄₇	—	2	2	no	—
143	#41×C₄₇	—	2	2	no	—
144	#41×C₄₇	—	2	4	no	—
145	#41×C₄₇	—	4	2	no	—
146	C₂×Q₈×C₄₇	—	2	1	no	—
147	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₄₇	—	2	2	no	—
150	C₂×D₄×C₄₇	—	2	2	no	—
151	C₂×D₄×C₄₇	—	2	2	no	—
152	C₂×D₄×C₄₇	—	2	1	no	—
153	C₂×D₄×C₄₇	—	4	1	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	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	—	2	1	no	—
159	C₂²×C₄×C₄₇	—	2	2	no	—
160	C₂²×C₄×C₄₇	—	2	1	no	—
161	C₂²×C₄×C₄₇	—	2	1	no	—
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	—	4	2	no	—
166	C₂²×C₄×C₄₇	—	4	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	2	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	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	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	1	no	—
196	C₂²⋊C₄×C₄₇	—	2	1	no	—
197	C₂²⋊C₄×C₄₇	—	2	2	no	—
198	C₂²⋊C₄×C₄₇	—	2	2	no	—
199	C₂²⋊C₄×C₄₇	—	2	1	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	2	no	—
205	C₄²×C₄₇	—	2	2	no	—
206	C₄²×C₄₇	—	2	2	no	—
207	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
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	1	no	—
222	C₂×C₄₇⋊C₈	—	2	2	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	1	no	—
227	C₂³×C₄₇	—	2	1	no	—
228	C₂³×C₄₇	—	4	2	no	—
229	C₂³×C₄₇	—	4	2	no	—
230	C₂³×C₄₇	—	8	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	2	no	—
234	Q₈×C₄₇	—	2	2	no	—
235	Q₈×C₄₇	—	2	2	no	—
236	Q₈×C₄₇	—	8	1	no	—
237	D₄×C₄₇	—	2	4	no	—
238	D₄×C₄₇	—	2	1	no	—
239	D₄×C₄₇	—	2	1	no	—
240	D₄×C₄₇	—	2	1	no	—
241	D₄×C₄₇	—	2	2	no	—
242	D₄×C₄₇	—	4	2	no	—
243	D₄×C₄₇	—	4	4	no	—
244	D₄×C₄₇	—	8	2	no	—
245	D₄×C₄₇	#131	1	2	yes	complemented
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	2	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	1	no	—
261	C₂×C₄×C₄₇	—	4	1	no	—
262	C₂×C₄×C₄₇	—	4	1	no	—
263	C₂×C₄×C₄₇	—	4	1	no	—
264	C₂×C₄×C₄₇	—	4	2	no	—
265	C₂×C₄×C₄₇	—	4	2	no	—
266	C₂×C₄×C₄₇	—	8	2	no	—
267	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
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	1	yes	characteristic
273	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
274	C₂×C₄×C₄₇	#137	1	2	yes	—
275	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
276	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
278	C₄₇⋊C₈	—	2	2	no	—
279	C₄₇⋊C₈	—	4	1	no	—
280	C₄₇⋊C₈	—	4	2	no	—
281	C₄₇⋊C₈	—	4	1	no	—
282	C₄₇⋊C₈	—	4	2	no	—
283	C₄₇⋊C₈	—	4	1	no	—
284	#17512	—	47	1	no	maximal, Sylow
285	C₂²×C₄₇	—	2	1	no	—
286	C₂²×C₄₇	—	2	1	no	—
287	C₂²×C₄₇	—	2	2	no	—
288	C₂²×C₄₇	—	2	2	no	—
289	C₂²×C₄₇	—	2	2	no	—
290	C₂²×C₄₇	—	2	2	no	—
291	C₂²×C₄₇	—	4	1	no	—
292	C₂²×C₄₇	—	4	1	no	—
293	C₂²×C₄₇	—	4	1	no	—
294	C₂²×C₄₇	—	4	1	no	—
295	C₂²×C₄₇	—	4	1	no	—
296	C₂²×C₄₇	—	8	4	no	—
297	C₂²×C₄₇	#417	1	2	yes	—
298	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
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	2	no	—
304	C₄×C₄₇	—	2	1	no	—
305	C₄×C₄₇	—	4	2	no	—
306	C₄×C₄₇	—	4	1	no	—
307	C₄×C₄₇	—	4	1	no	—
308	C₄×C₄₇	—	4	2	no	—
309	C₄×C₄₇	#417	1	2	yes	—
310	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
311	C₄×C₄₇	#568	1	1	yes	characteristic
312	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
313	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
314	#3475	D₄₇	1	1	yes	characteristic
315	#2965	—	47	1	no	—
316	#2906	—	47	1	no	—
317	#1495	—	47	2	no	—
318	#1493	—	47	1	no	—
319	#1489	—	47	2	no	—
320	#1486	—	47	1	no	—
321	#1483	—	47	2	no	—
322	#1481	—	47	1	no	—
323	#1477	—	47	2	no	—
324	C₂×D₄⋊C₈	—	47	1	no	—
325	C₂×C₄₇	—	2	2	no	—
326	C₂×C₄₇	—	4	2	no	—
327	C₂×C₄₇	—	4	2	no	—
328	C₂×C₄₇	—	8	1	no	—
329	C₂×C₄₇	#2880	1	1	yes	characteristic
330	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
331	C₂×C₄₇	#2901	1	1	yes	characteristic
332	C₂×#131	—	94	1	no	—
333	#556	Dic₄₇	1	1	yes	characteristic
334	#555	Dic₄₇	1	1	yes	characteristic
335	#554	Dic₄₇	1	1	yes	characteristic
336	#553	—	2	1	no	—
337	#552	—	2	1	no	—
338	#552	Dic₄₇	1	2	yes	—
339	#551	—	2	2	no	—
340	#547	Dic₄₇	1	1	yes	characteristic
341	#546	Dic₄₇	1	2	yes	—
342	#533	C₂×D₄₇	1	1	yes	characteristic
343	#529	—	2	2	no	—
344	#529	C₂×D₄₇	1	2	yes	—
345	#525	—	2	1	no	—
346	C₄×#41	C₂×D₄₇	1	2	yes	—
347	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
348	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
349	C₂×#117	—	2	1	no	—
350	#446	—	94	1	no	—
351	#436	—	94	1	no	—
352	#435	—	94	2	no	—
353	#431	—	47	2	no	—
354	#431	—	47	1	no	—
355	#424	—	94	1	no	—
356	#424	—	94	2	no	—
357	#423	—	47	1	no	—
358	#423	—	47	2	no	—
359	C₂×C₄⋊C₈	—	47	1	no	—
360	C₂×C₄⋊C₈	—	47	2	no	—
361	C₄×M₁₆	—	47	2	no	—
362	C₂×C₄×C₈	—	47	1	no	—
363	Q₈⋊C₈	—	47	2	no	—
364	Q₈⋊C₈	—	47	2	no	—
365	Q₈⋊C₈	—	47	2	no	—
366	Q₈⋊C₈	—	47	2	no	—
367	D₄⋊C₈	—	47	1	no	—
368	D₄⋊C₈	—	47	1	no	—
369	D₄⋊C₈	—	47	1	no	—
370	D₄⋊C₈	—	47	1	no	—
371	D₄⋊C₈	—	47	2	no	—
372	D₄⋊C₈	—	47	2	no	—
373	C₄₇	#17512	1	1	yes	characteristic, complemented, Sylow
374	C₂×#41	C₂×Dic₄₇	1	2	yes	—
375	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
376	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
377	C₂³×C₄	—	2	1	no	—
378	#131	—	188	4	no	—
379	C₂×M₁₆	—	94	2	no	—
380	C₂×M₁₆	—	94	1	no	—
381	C₂×M₁₆	—	94	2	no	—
382	C₂²×C₈	—	94	2	no	—
383	C₂²×C₈	—	94	1	no	—
384	C₂²×C₈	—	94	1	no	—
385	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
386	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
387	#126	—	2	2	no	—
388	#126	—	2	2	no	—
389	#126	—	2	2	no	—
390	#125	—	2	2	no	—
391	#125	—	2	1	no	—
392	#125	C₂×Dic₄₇	1	2	yes	—
393	#124	—	2	2	no	—
394	#124	C₂×Dic₄₇	1	2	yes	—
395	#123	—	2	2	no	—
396	#123	—	2	2	no	—
397	#123	—	2	2	no	—
398	#123	—	2	2	no	—
399	C₂²⋊Q₈	—	2	1	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	2	1	no	—
402	C₂²⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
404	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
405	#121	—	2	1	no	—
406	#121	—	2	1	no	—
407	#121	—	2	2	no	—
408	#121	C₂×Dic₄₇	1	2	yes	—
409	#120	—	2	2	no	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
412	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
413	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
414	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
421	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
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	1	yes	characteristic
428	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
429	#117	—	2	1	no	—
430	#117	—	2	1	no	—
431	#117	—	2	1	no	—
432	#117	—	2	2	no	—
433	#117	—	2	2	no	—
434	#117	—	2	2	no	—
435	#117	C₂×Dic₄₇	1	2	yes	—
436	#117	C₂²⋊D₄₇	1	1	yes	characteristic
437	#117	C₂²⋊D₄₇	1	2	yes	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	2	no	—
443	C₂×C₄²	—	2	2	no	—
444	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
445	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
446	C₄⋊C₈	—	47	1	no	—
447	C₄⋊C₈	—	47	1	no	—
448	C₄⋊C₈	—	47	2	no	—
449	C₄⋊C₈	—	94	2	no	—
450	C₄⋊C₈	—	94	1	no	—
451	C₄⋊C₈	—	94	2	no	—
452	C₄⋊C₈	—	94	1	no	—
453	C₄⋊C₈	—	94	2	no	—
454	C₄⋊C₈	—	94	1	no	—
455	C₂²⋊C₈	—	94	1	no	—
456	C₂²⋊C₈	—	94	2	no	—
457	#97	—	94	2	no	—
458	C₄×C₈	—	47	1	no	—
459	C₄×C₈	—	47	1	no	—
460	C₄×C₈	—	47	2	no	—
461	C₄×C₈	—	94	1	no	—
462	C₂⁴	—	2	1	no	—
463	#41	—	2	2	no	—
464	#41	—	2	2	no	—
465	#41	—	2	4	no	—
466	#41	—	4	2	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
469	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
476	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
477	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
478	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
490	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
491	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
492	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
493	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
494	M₁₆	—	188	4	no	—
495	M₁₆	—	188	4	no	—
496	M₁₆	—	188	2	no	—
497	C₂×C₈	—	94	1	no	—
498	C₂×C₈	—	94	1	no	—
499	C₂×C₈	—	94	2	no	—
500	C₂×C₈	—	94	1	no	—
501	C₂×C₈	—	94	2	no	—
502	C₂×C₈	—	94	1	no	—
503	C₂×C₈	—	188	2	no	—
504	C₂×C₈	—	188	4	no	—
505	C₂×C₈	—	188	2	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
517	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
518	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
519	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
520	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
535	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
536	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	2	no	—
540	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
541	C₄²	C₂²×Dic₄₇	1	2	yes	—
542	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
543	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
544	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
545	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
546	C₄²	C₂³×D₄₇	1	1	yes	characteristic
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	8	1	no	—
552	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
553	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
554	Q₈	—	2	2	no	—
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	—	8	1	no	—
558	D₄	—	2	4	no	—
559	D₄	—	2	1	no	—
560	D₄	—	2	1	no	—
561	D₄	—	2	1	no	—
562	D₄	—	2	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	4	no	—
565	D₄	—	8	2	no	—
566	D₄	#13094031	1	2	yes	complemented
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	2	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	2	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	4	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	8	2	no	—
588	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
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	1	yes	characteristic
593	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
594	C₂×C₄	#13094049	1	2	yes	—
595	C₂×C₄	#13094054	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	1	no	—
603	C₈	—	188	2	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	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	8	4	no	—
617	C₂²	#15689124	1	2	yes	—
618	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	#15689124	1	2	yes	—
630	C₄	C₂×#13094031	1	1	yes	characteristic
631	C₄	#15689890	1	1	yes	characteristic
632	C₄	C₂×#13094049	1	1	yes	characteristic
633	C₄	C₂×#13094054	1	1	yes	characteristic
634	C₂	—	2	2	no	—
635	C₂	—	4	2	no	—
636	C₂	—	4	2	no	—
637	C₂	—	8	1	no	—
638	C₂	#20251837	1	1	yes	characteristic
639	C₂	C₂×#15689124	1	1	yes	characteristic
640	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×#3475	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3475	D₄₇
hypocenter	C₄₇	#17512
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3475

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. #20241843	C₂	semidirect
5. #20241827	C₂	semidirect
6. #20241813	C₂	semidirect
7. #20241801	C₂	semidirect
8. #20241791	C₂	semidirect
9. #20241775	C₂	semidirect
10. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
17. #15689176	C₂²	semidirect
21. #15689147	C₂²	semidirect
23. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
24. C₄×#10625329	C₂²	semidirect
26. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
27. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
28. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
29. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
245. D₄×C₄₇	#131	semidirect
373. C₄₇	#17512	semidirect
566. D₄	#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
#20241843	2
#20241827	2
#20241813	2
#20241801	2
#20241791	2
#20241775	2
C₂×D₄⋊(C₄₇⋊C₈)	2
C₄₇×#3475	2
#17512	47