Subgroups — #26183475

Order 12032.

1166 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252423	C₂	1	1	yes	maximal, characteristic, complemented
2	#20245749	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241913	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241904	C₂	1	2	yes	maximal, complemented
5	#20241896	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241892	C₂	1	2	yes	maximal, complemented
7	#20241883	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241879	C₂	1	2	yes	maximal, complemented
9	#20241874	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688857	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3519	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₄₇	—	2	1	no	—
13	#15689201	—	2	1	no	—
14	#15689195	—	2	2	no	—
15	D₄×C₄₇⋊C₈	—	2	1	no	—
16	#15689180	C₂²	1	1	yes	characteristic, complemented
17	#15689176	C₂²	1	1	yes	characteristic, complemented
18	#15689087	C₂²	1	2	yes	complemented
19	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
20	C₄⋊C₄×Dic₄₇	—	2	1	no	—
21	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
22	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
23	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
24	#15688969	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄₇⋊#95	C₂²	1	2	yes	complemented
26	#15688860	C₂²	1	1	yes	characteristic, complemented
27	#15688860	C₂²	1	1	yes	characteristic, complemented
28	#15688860	C₂²	1	2	yes	complemented
29	#15688857	C₂²	1	1	yes	characteristic
30	#15688857	C₂²	1	2	yes	—
31	#15688857	C₂²	1	1	yes	characteristic
32	#15688857	C₂²	1	2	yes	complemented
33	#15688857	C₂²	1	2	yes	complemented
34	#15688857	C₂²	1	2	yes	complemented
35	#15688857	C₂²	1	2	yes	complemented
36	C₄₇×#555	C₄	1	1	yes	characteristic, complemented
37	C₄₇×#554	C₄	1	1	yes	characteristic, complemented
38	C₄₇×#553	—	2	1	no	—
39	C₄₇×#553	C₄	1	2	yes	complemented
40	C₄₇×#550	C₄	1	1	yes	characteristic, complemented
41	C₄₇×#546	—	2	2	no	—
42	C₄₇×#546	C₄	1	2	yes	complemented
43	D₄²×C₄₇	—	2	1	no	—
44	D₄²×C₄₇	C₄	1	1	yes	characteristic, complemented
45	C₄₇×#540	—	2	1	no	—
46	C₄₇×#538	—	2	2	no	—
47	C₄₇×#532	C₂²	1	1	yes	characteristic
48	C₄₇×#529	C₂²	1	1	yes	characteristic
49	C₄₇×#525	C₂²	1	2	yes	—
50	C₂×#121×C₄₇	C₂²	1	2	yes	—
51	C₄₇×#518	—	2	1	no	—
52	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
53	C₂³×Dic₄₇	—	2	2	no	—
54	C₂×#10625329	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	—	2	2	no	—
56	D₄×Dic₄₇	—	2	8	no	—
57	C₂×C₄⋊Dic₄₇	—	2	1	no	—
58	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
59	C₂×C₄×Dic₄₇	—	2	1	no	—
60	C₂×C₄×Dic₄₇	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
63	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
66	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
67	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
68	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
69	#13093935	—	2	1	no	—
70	C₄×C₄₇⋊C₈	—	2	1	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₄₇⋊#95	—	2	1	no	—
73	C₄₇⋊#95	C₂³	1	1	yes	characteristic
74	C₄₇⋊#95	C₂³	1	2	yes	—
75	C₄₇⋊#95	C₂³	1	1	yes	characteristic
76	C₂×#41×C₄₇	—	2	1	no	—
77	C₂×#41×C₄₇	C₂×C₄	1	2	yes	complemented
78	C₂²×D₄×C₄₇	—	2	2	no	—
79	C₂²×D₄×C₄₇	—	2	1	no	—
80	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	complemented
81	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
83	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
84	#127×C₄₇	—	2	1	no	—
85	#127×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
86	#126×C₄₇	—	2	2	no	—
87	#126×C₄₇	—	2	1	no	—
88	#125×C₄₇	—	2	1	no	—
89	#125×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
90	#124×C₄₇	—	2	2	no	—
91	#124×C₄₇	—	2	1	no	—
92	#124×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
93	#123×C₄₇	—	2	2	no	—
94	#123×C₄₇	—	2	1	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	complemented
99	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
100	#121×C₄₇	—	2	2	no	—
101	#121×C₄₇	—	2	1	no	—
102	#121×C₄₇	—	2	2	no	—
103	#121×C₄₇	—	2	2	no	—
104	#121×C₄₇	—	2	1	no	—
105	#121×C₄₇	—	2	1	no	—
106	#121×C₄₇	—	2	2	no	—
107	#121×C₄₇	—	2	2	no	—
108	#121×C₄₇	C₂×C₄	1	2	yes	complemented
109	#121×C₄₇	C₂×C₄	1	2	yes	complemented
110	#121×C₄₇	C₂×C₄	1	2	yes	complemented
111	#121×C₄₇	C₂³	1	1	yes	characteristic
112	#121×C₄₇	C₂³	1	2	yes	—
113	#120×C₄₇	—	2	2	no	—
114	#120×C₄₇	—	2	2	no	—
115	#120×C₄₇	—	2	2	no	—
116	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
117	C₄×D₄×C₄₇	—	2	1	no	—
118	C₄×D₄×C₄₇	—	2	2	no	—
119	C₄×D₄×C₄₇	—	2	2	no	—
120	C₄×D₄×C₄₇	—	2	1	no	—
121	C₄×D₄×C₄₇	—	2	1	no	—
122	C₄×D₄×C₄₇	—	2	2	no	—
123	C₄×D₄×C₄₇	—	2	1	no	—
124	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
125	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
126	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
127	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
128	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	complemented
129	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
130	C₄×D₄×C₄₇	D₄	1	2	yes	—
131	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
132	#117×C₄₇	—	2	1	no	—
133	#117×C₄₇	—	2	1	no	—
134	#117×C₄₇	C₂×C₄	1	2	yes	complemented
135	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	complemented
136	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
138	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
139	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
140	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
141	C₂⁴×C₄₇	—	2	2	no	—
142	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
143	#41×C₄₇	—	8	1	no	—
144	#41×C₄₇	—	8	1	no	—
145	#41×C₄₇	—	8	2	no	—
146	C₂×Q₈×C₄₇	—	2	1	no	—
147	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₄₇	—	2	4	no	—
149	C₂×D₄×C₄₇	—	2	2	no	—
150	C₂×D₄×C₄₇	—	2	2	no	—
151	C₂×D₄×C₄₇	—	2	1	no	—
152	C₂×D₄×C₄₇	—	2	2	no	—
153	C₂×D₄×C₄₇	—	2	2	no	—
154	C₂×D₄×C₄₇	—	2	2	no	—
155	C₂×D₄×C₄₇	—	2	1	no	—
156	C₂×D₄×C₄₇	—	2	1	no	—
157	C₂×D₄×C₄₇	—	2	2	no	—
158	C₂×D₄×C₄₇	—	4	4	no	—
159	C₂×D₄×C₄₇	—	8	2	no	—
160	C₂×D₄×C₄₇	—	8	2	no	—
161	C₂×D₄×C₄₇	—	8	2	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	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
166	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
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	2	no	—
171	C₂²×C₄×C₄₇	—	8	2	no	—
172	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
180	C₂²×Dic₄₇	—	2	1	no	—
181	C₂²×Dic₄₇	—	2	1	no	—
182	C₂²×Dic₄₇	—	2	2	no	—
183	C₂²×Dic₄₇	—	2	8	no	—
184	C₂²×Dic₄₇	—	8	2	no	—
185	C₂²×Dic₄₇	—	8	2	no	—
186	C₄⋊C₄×C₄₇	—	2	2	no	—
187	C₄⋊C₄×C₄₇	—	2	1	no	—
188	C₄⋊C₄×C₄₇	—	2	1	no	—
189	C₄⋊C₄×C₄₇	—	2	1	no	—
190	C₄⋊C₄×C₄₇	—	2	2	no	—
191	C₄⋊C₄×C₄₇	—	2	1	no	—
192	C₄⋊C₄×C₄₇	—	2	1	no	—
193	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
194	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
195	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
196	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
198	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
199	C₂²⋊C₄×C₄₇	—	2	2	no	—
200	C₂²⋊C₄×C₄₇	—	2	2	no	—
201	C₂²⋊C₄×C₄₇	—	2	1	no	—
202	C₂²⋊C₄×C₄₇	—	2	1	no	—
203	C₂²⋊C₄×C₄₇	—	2	2	no	—
204	C₂²⋊C₄×C₄₇	—	2	2	no	—
205	C₂²⋊C₄×C₄₇	—	2	1	no	—
206	C₂²⋊C₄×C₄₇	—	2	2	no	—
207	C₂²⋊C₄×C₄₇	—	2	1	no	—
208	C₂²⋊C₄×C₄₇	—	2	2	no	—
209	C₂²⋊C₄×C₄₇	—	2	1	no	—
210	C₂²⋊C₄×C₄₇	—	2	2	no	—
211	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
212	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
213	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
214	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
215	C₄²×C₄₇	—	2	2	no	—
216	C₄²×C₄₇	—	2	1	no	—
217	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
218	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
219	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
221	C₂²⋊Dic₄₇	—	2	8	no	—
222	C₄⋊Dic₄₇	—	2	4	no	—
223	C₄×Dic₄₇	—	2	4	no	—
224	C₄×Dic₄₇	—	8	1	no	—
225	C₄×Dic₄₇	—	8	2	no	—
226	#10625329	—	8	2	no	—
227	C₂×C₄₇⋊C₈	—	2	1	no	—
228	C₂×C₄₇⋊C₈	—	2	1	no	—
229	C₂×C₄₇⋊C₈	—	2	2	no	—
230	C₂×C₄₇⋊C₈	—	8	2	no	—
231	C₂³×C₄₇	—	2	2	no	—
232	C₂³×C₄₇	—	2	2	no	—
233	C₂³×C₄₇	—	2	4	no	—
234	C₂³×C₄₇	—	2	1	no	—
235	C₂³×C₄₇	—	2	2	no	—
236	C₂³×C₄₇	—	4	2	no	—
237	C₂³×C₄₇	—	4	4	no	—
238	C₂³×C₄₇	—	8	2	no	—
239	C₂³×C₄₇	—	8	2	no	—
240	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
241	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
242	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
243	Q₈×C₄₇	—	4	1	no	—
244	Q₈×C₄₇	—	8	1	no	—
245	D₄×C₄₇	—	2	4	no	—
246	D₄×C₄₇	—	2	2	no	—
247	D₄×C₄₇	—	4	1	no	—
248	D₄×C₄₇	—	4	2	no	—
249	D₄×C₄₇	—	4	1	no	—
250	D₄×C₄₇	—	4	2	no	—
251	D₄×C₄₇	—	4	1	no	—
252	D₄×C₄₇	—	4	2	no	—
253	D₄×C₄₇	—	4	4	no	—
254	D₄×C₄₇	—	4	2	no	—
255	D₄×C₄₇	—	8	2	no	—
256	D₄×C₄₇	—	8	1	no	—
257	D₄×C₄₇	—	8	2	no	—
258	D₄×C₄₇	—	8	2	no	—
259	D₄×C₄₇	—	8	2	no	—
260	D₄×C₄₇	#104	1	4	yes	—
261	C₂×C₄×C₄₇	—	2	1	no	—
262	C₂×C₄×C₄₇	—	2	1	no	—
263	C₂×C₄×C₄₇	—	2	2	no	—
264	C₂×C₄×C₄₇	—	2	1	no	—
265	C₂×C₄×C₄₇	—	2	1	no	—
266	C₂×C₄×C₄₇	—	2	2	no	—
267	C₂×C₄×C₄₇	—	2	1	no	—
268	C₂×C₄×C₄₇	—	4	2	no	—
269	C₂×C₄×C₄₇	—	4	2	no	—
270	C₂×C₄×C₄₇	—	4	2	no	—
271	C₂×C₄×C₄₇	—	4	1	no	—
272	C₂×C₄×C₄₇	—	4	2	no	—
273	C₂×C₄×C₄₇	—	4	2	no	—
274	C₂×C₄×C₄₇	—	4	2	no	—
275	C₂×C₄×C₄₇	—	8	2	no	—
276	C₂×C₄×C₄₇	—	8	2	no	—
277	C₂×C₄×C₄₇	—	8	2	no	—
278	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
283	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
285	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
286	C₂×Dic₄₇	—	2	2	no	—
287	C₂×Dic₄₇	—	2	2	no	—
288	C₂×Dic₄₇	—	2	4	no	—
289	C₂×Dic₄₇	—	4	1	no	—
290	C₂×Dic₄₇	—	4	2	no	—
291	C₂×Dic₄₇	—	4	1	no	—
292	C₂×Dic₄₇	—	4	2	no	—
293	C₂×Dic₄₇	—	4	1	no	—
294	C₂×Dic₄₇	—	4	1	no	—
295	C₂×Dic₄₇	—	8	8	no	—
296	C₄₇⋊C₈	—	4	1	no	—
297	C₄₇⋊C₈	—	4	2	no	—
298	C₄₇⋊C₈	—	4	1	no	—
299	#17547	—	47	1	no	maximal, Sylow
300	C₂²×C₄₇	—	2	1	no	—
301	C₂²×C₄₇	—	2	2	no	—
302	C₂²×C₄₇	—	2	2	no	—
303	C₂²×C₄₇	—	2	1	no	—
304	C₂²×C₄₇	—	2	2	no	—
305	C₂²×C₄₇	—	2	2	no	—
306	C₂²×C₄₇	—	2	2	no	—
307	C₂²×C₄₇	—	4	4	no	—
308	C₂²×C₄₇	—	4	4	no	—
309	C₂²×C₄₇	—	4	2	no	—
310	C₂²×C₄₇	—	4	1	no	—
311	C₂²×C₄₇	—	4	2	no	—
312	C₂²×C₄₇	—	4	1	no	—
313	C₂²×C₄₇	—	4	1	no	—
314	C₂²×C₄₇	—	4	2	no	—
315	C₂²×C₄₇	—	16	4	no	—
316	C₂²×C₄₇	C₂×#104	1	4	yes	—
317	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×C₄₇	#576	1	1	yes	characteristic
319	C₂²×C₄₇	#577	1	1	yes	characteristic
320	C₄×C₄₇	—	2	1	no	—
321	C₄×C₄₇	—	2	1	no	—
322	C₄×C₄₇	—	2	2	no	—
323	C₄×C₄₇	—	2	2	no	—
324	C₄×C₄₇	—	2	1	no	—
325	C₄×C₄₇	—	2	1	no	—
326	C₄×C₄₇	—	2	1	no	—
327	C₄×C₄₇	—	4	1	no	—
328	C₄×C₄₇	—	4	1	no	—
329	C₄×C₄₇	—	4	2	no	—
330	C₄×C₄₇	—	4	1	no	—
331	C₄×C₄₇	C₂×#104	1	2	yes	—
332	Dic₄₇	—	4	2	no	—
333	Dic₄₇	—	4	4	no	—
334	Dic₄₇	—	4	2	no	—
335	#3519	D₄₇	1	1	yes	characteristic
336	#2974	—	47	1	no	—
337	#2275	—	47	1	no	—
338	#1509	—	47	1	no	—
339	#1507	—	47	2	no	—
340	#1505	—	47	1	no	—
341	#1504	—	47	2	no	—
342	#1502	—	47	1	no	—
343	#1501	—	47	2	no	—
344	#1500	—	47	1	no	—
345	C₂×#327	—	47	2	no	—
346	C₂×C₄₇	—	2	1	no	—
347	C₂×C₄₇	—	2	1	no	—
348	C₂×C₄₇	—	2	4	no	—
349	C₂×C₄₇	—	4	2	no	—
350	C₂×C₄₇	—	8	2	no	—
351	C₂×C₄₇	—	8	1	no	—
352	C₂×C₄₇	#2883	1	1	yes	characteristic
353	C₂×C₄₇	#2897	1	1	yes	characteristic
354	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
355	#555	Dic₄₇	1	1	yes	characteristic, complemented
356	#554	Dic₄₇	1	1	yes	characteristic, complemented
357	#553	—	2	1	no	—
358	#553	Dic₄₇	1	2	yes	complemented
359	#550	Dic₄₇	1	1	yes	characteristic, complemented
360	#546	—	2	2	no	—
361	#546	Dic₄₇	1	2	yes	complemented
362	D₄²	—	2	1	no	—
363	D₄²	Dic₄₇	1	1	yes	characteristic, complemented
364	#540	—	2	1	no	—
365	#538	—	2	2	no	—
366	#532	C₂×D₄₇	1	1	yes	characteristic
367	#529	C₂×D₄₇	1	1	yes	characteristic
368	#525	C₂×D₄₇	1	2	yes	—
369	C₂×#121	C₂×D₄₇	1	2	yes	—
370	#518	—	2	1	no	—
371	C₂×C₄×D₄	—	94	1	no	—
372	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
373	#436	—	94	1	no	—
374	#435	—	94	2	no	—
375	C₈×D₄	—	94	1	no	—
376	#432	—	47	1	no	—
377	#431	—	47	1	no	—
378	#407	—	47	2	no	—
379	C₂×C₂²⋊C₈	—	47	2	no	—
380	C₄×C₄⋊C₄	—	47	1	no	—
381	C₄×C₄⋊C₄	—	94	1	no	—
382	C₄×C₂²⋊C₄	—	47	2	no	—
383	C₄×C₂²⋊C₄	—	94	2	no	—
384	#376	—	47	1	no	—
385	C₂×#95	—	47	2	no	—
386	#328	—	47	1	no	—
387	#328	—	47	1	no	—
388	#328	—	47	2	no	—
389	#327	—	47	1	no	—
390	#327	—	47	2	no	—
391	#327	—	47	1	no	—
392	#327	—	47	2	no	—
393	#327	—	47	2	no	—
394	#327	—	47	2	no	—
395	#327	—	47	2	no	—
396	C₄₇	#17547	1	1	yes	characteristic, complemented, Sylow
397	C₂×#41	—	2	1	no	—
398	C₂×#41	C₂×Dic₄₇	1	2	yes	complemented
399	C₂²×D₄	—	2	2	no	—
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	C₂×Dic₄₇	1	2	yes	complemented
402	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
403	C₂³×C₄	—	94	2	no	—
404	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
405	C₂×M₁₆	—	94	2	no	—
406	C₂²×C₈	—	94	2	no	—
407	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
408	#127	—	2	1	no	—
409	#127	C₂×Dic₄₇	1	1	yes	characteristic, complemented
410	#126	—	2	2	no	—
411	#126	—	2	1	no	—
412	#125	—	2	1	no	—
413	#125	C₂×Dic₄₇	1	1	yes	characteristic, complemented
414	#124	—	2	2	no	—
415	#124	—	2	1	no	—
416	#124	C₂×Dic₄₇	1	1	yes	characteristic, complemented
417	#123	—	2	2	no	—
418	#123	—	2	1	no	—
419	#123	—	2	2	no	—
420	#123	—	2	2	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
423	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
424	#121	—	2	2	no	—
425	#121	—	2	1	no	—
426	#121	—	2	2	no	—
427	#121	—	2	2	no	—
428	#121	—	2	1	no	—
429	#121	—	2	1	no	—
430	#121	—	2	2	no	—
431	#121	—	2	2	no	—
432	#121	C₂×Dic₄₇	1	2	yes	complemented
433	#121	C₂×Dic₄₇	1	2	yes	complemented
434	#121	C₂×Dic₄₇	1	2	yes	complemented
435	#121	C₂²×D₄₇	1	1	yes	characteristic
436	#121	C₂²×D₄₇	1	2	yes	—
437	#120	—	2	2	no	—
438	#120	—	2	2	no	—
439	#120	—	2	2	no	—
440	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
441	C₄×D₄	—	2	1	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	—	2	1	no	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	—	2	1	no	—
448	C₄×D₄	—	94	8	no	—
449	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
450	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
451	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
452	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic, complemented
453	C₄×D₄	C₂×Dic₄₇	1	2	yes	complemented
454	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
455	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
456	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
457	#117	—	2	1	no	—
458	#117	—	2	1	no	—
459	#117	C₂×Dic₄₇	1	2	yes	complemented
460	C₂×C₄⋊C₄	—	94	1	no	—
461	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	complemented
462	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	—	2	2	no	—
464	C₂×C₂²⋊C₄	—	2	2	no	—
465	C₂×C₂²⋊C₄	—	94	2	no	—
466	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
467	C₂×C₄²	—	94	1	no	—
468	C₂×C₄²	—	94	2	no	—
469	C₂×C₄²	—	94	1	no	—
470	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
471	C₄⋊C₈	—	94	1	no	—
472	C₄⋊C₈	—	94	1	no	—
473	C₂²⋊C₈	—	47	1	no	—
474	C₂²⋊C₈	—	47	2	no	—
475	C₂²⋊C₈	—	47	1	no	—
476	C₂²⋊C₈	—	94	2	no	—
477	C₂²⋊C₈	—	94	2	no	—
478	#97	—	94	1	no	—
479	C₄×C₈	—	94	1	no	—
480	#95	—	47	1	no	—
481	#95	—	47	2	no	—
482	#95	—	47	1	no	—
483	#95	—	94	2	no	—
484	#95	—	94	1	no	—
485	C₂⁴	—	2	2	no	—
486	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
487	#41	—	8	1	no	—
488	#41	—	8	1	no	—
489	#41	—	8	2	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	2	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	4	4	no	—
503	C₂×D₄	—	8	2	no	—
504	C₂×D₄	—	8	2	no	—
505	C₂×D₄	—	8	2	no	—
506	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
507	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
508	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
509	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
510	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	8	2	no	—
516	C₂²×C₄	—	94	8	no	—
517	C₂²×C₄	—	94	1	no	—
518	C₂²×C₄	—	94	1	no	—
519	C₂²×C₄	—	94	2	no	—
520	C₂²×C₄	—	376	2	no	—
521	C₂²×C₄	—	376	2	no	—
522	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
523	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
524	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
526	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
527	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
528	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
529	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
530	M₁₆	—	376	2	no	—
531	C₂×C₈	—	94	1	no	—
532	C₂×C₈	—	94	1	no	—
533	C₂×C₈	—	94	2	no	—
534	C₂×C₈	—	376	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	94	4	no	—
543	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
544	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
545	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
546	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
548	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	1	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	1	no	—
556	C₂²⋊C₄	—	2	2	no	—
557	C₂²⋊C₄	—	2	1	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	1	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	94	8	no	—
562	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
563	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
564	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
565	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	94	4	no	—
569	C₄²	—	376	1	no	—
570	C₄²	—	376	2	no	—
571	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
572	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
573	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
574	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
575	C₂³	—	2	4	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	4	2	no	—
581	C₂³	—	4	4	no	—
582	C₂³	—	8	2	no	—
583	C₂³	—	8	2	no	—
584	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
585	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
586	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
587	Q₈	—	4	1	no	—
588	Q₈	—	8	1	no	—
589	D₄	—	2	4	no	—
590	D₄	—	2	2	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	4	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	2	no	—
599	D₄	—	8	2	no	—
600	D₄	—	8	1	no	—
601	D₄	—	8	2	no	—
602	D₄	—	8	2	no	—
603	D₄	—	8	2	no	—
604	D₄	#13093951	1	4	yes	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	4	2	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	8	2	no	—
620	C₂×C₄	—	8	2	no	—
621	C₂×C₄	—	8	2	no	—
622	C₂×C₄	—	94	2	no	—
623	C₂×C₄	—	94	2	no	—
624	C₂×C₄	—	94	4	no	—
625	C₂×C₄	—	376	8	no	—
626	C₂×C₄	—	188	1	no	—
627	C₂×C₄	—	188	2	no	—
628	C₂×C₄	—	188	1	no	—
629	C₂×C₄	—	188	2	no	—
630	C₂×C₄	—	188	1	no	—
631	C₂×C₄	—	188	1	no	—
632	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
633	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
634	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
635	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
636	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
637	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
638	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
639	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
640	C₈	—	188	1	no	—
641	C₈	—	188	2	no	—
642	C₈	—	188	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	4	4	no	—
651	C₂²	—	4	4	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	16	4	no	—
659	C₂²	C₂×#13093951	1	4	yes	—
660	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
661	C₂²	#15689926	1	1	yes	characteristic
662	C₂²	#15689934	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	—	188	2	no	—
675	C₄	—	188	4	no	—
676	C₄	—	188	2	no	—
677	C₄	C₂×#13093951	1	2	yes	—
678	C₂	—	2	1	no	—
679	C₂	—	2	1	no	—
680	C₂	—	2	4	no	—
681	C₂	—	4	2	no	—
682	C₂	—	8	1	no	—
683	C₂	—	8	2	no	—
684	C₂	#20251849	1	1	yes	characteristic
685	C₂	#20251914	1	1	yes	characteristic
686	C₂	C₂²×#13093951	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3519	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3519	D₄₇
hypocenter	C₄₇	#17547
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ #3519

Complements

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

N	H ≅ G/N	type
1. #20252423	C₂	semidirect
2. #20245749	C₂	semidirect
3. #20241913	C₂	semidirect
4. #20241904	C₂	semidirect
5. #20241896	C₂	semidirect
6. #20241892	C₂	semidirect
7. #20241883	C₂	semidirect
8. #20241879	C₂	semidirect
9. #20241874	C₂	semidirect
10. C₂×#15688857	C₂	semidirect
16. #15689180	C₂²	semidirect
17. #15689176	C₂²	semidirect
18. #15689087	C₂²	semidirect
19. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
21. C₄×C₄⋊Dic₄₇	C₂²	semidirect
23. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
24. #15688969	C₂²	semidirect
25. C₂×C₄₇⋊#95	C₂²	semidirect
26. #15688860	C₂²	semidirect
27. #15688860	C₂²	semidirect
28. #15688860	C₂²	semidirect
32. #15688857	C₂²	semidirect
33. #15688857	C₂²	semidirect
34. #15688857	C₂²	semidirect
35. #15688857	C₂²	semidirect
36. C₄₇×#555	C₄	semidirect
37. C₄₇×#554	C₄	semidirect
39. C₄₇×#553	C₄	semidirect
40. C₄₇×#550	C₄	semidirect
42. C₄₇×#546	C₄	semidirect
44. D₄²×C₄₇	C₄	semidirect
77. C₂×#41×C₄₇	C₂×C₄	semidirect
80. C₂²×D₄×C₄₇	C₂×C₄	semidirect
83. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
85. #127×C₄₇	C₂×C₄	semidirect
89. #125×C₄₇	C₂×C₄	semidirect
92. #124×C₄₇	C₂×C₄	semidirect
98. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
108. #121×C₄₇	C₂×C₄	semidirect
109. #121×C₄₇	C₂×C₄	semidirect
110. #121×C₄₇	C₂×C₄	semidirect
116. C₄×Q₈×C₄₇	C₂×C₄	semidirect
127. C₄×D₄×C₄₇	C₂×C₄	semidirect
128. C₄×D₄×C₄₇	C₂×C₄	semidirect
134. #117×C₄₇	C₂×C₄	semidirect
135. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
355. #555	Dic₄₇	semidirect
356. #554	Dic₄₇	semidirect
358. #553	Dic₄₇	semidirect
359. #550	Dic₄₇	semidirect
361. #546	Dic₄₇	semidirect
363. D₄²	Dic₄₇	semidirect
396. C₄₇	#17547	semidirect
398. C₂×#41	C₂×Dic₄₇	semidirect
401. C₂²×D₄	C₂×Dic₄₇	semidirect
407. C₄⋊Q₈	C₂×Dic₄₇	semidirect
409. #127	C₂×Dic₄₇	semidirect
413. #125	C₂×Dic₄₇	semidirect
416. #124	C₂×Dic₄₇	semidirect
422. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
432. #121	C₂×Dic₄₇	semidirect
433. #121	C₂×Dic₄₇	semidirect
434. #121	C₂×Dic₄₇	semidirect
440. C₄×Q₈	C₂×Dic₄₇	semidirect
452. C₄×D₄	C₂×Dic₄₇	semidirect
453. C₄×D₄	C₂×Dic₄₇	semidirect
459. #117	C₂×Dic₄₇	semidirect
461. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252423	2
#20245749	2
#20241913	2
#20241904	2
#20241896	2
#20241892	2
#20241883	2
#20241879	2
#20241874	2
C₂×#15688857	2
C₄₇×#3519	2
#17547	47