Subgroups — #26233184

Order 12032.

1058 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
2	#20245866	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244308	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244308	C₂	1	2	yes	maximal, complemented
5	#20244221	C₂	1	2	yes	maximal, complemented
6	#20244217	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243408	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243408	C₂	1	2	yes	maximal, complemented
9	#20243198	C₂	1	2	yes	maximal, complemented
10	C₄×#13093951	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3480	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	1	no	—
13	#15689254	—	2	2	no	—
14	Q₈×C₄₇⋊C₈	—	2	1	no	—
15	#15689147	C₂²	1	1	yes	characteristic
16	#15689147	C₂²	1	2	yes	—
17	C₂×#13093951	C₂²	1	1	yes	characteristic
18	C₂×#13093951	C₂²	1	2	yes	—
19	C₂×#13093951	C₂²	1	1	yes	characteristic
20	C₂×#13093951	C₂²	1	2	yes	—
21	C₂×#13093951	C₂²	1	2	yes	—
22	C₂×#13093951	C₂²	1	2	yes	—
23	C₂×#13093951	C₂²	1	2	yes	—
24	C₄×#10625329	C₂²	1	1	yes	characteristic
25	C₄×#10625329	C₂²	1	2	yes	—
26	#15689030	—	2	1	no	—
27	#15689022	—	2	1	no	—
28	#15689009	—	2	2	no	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
31	#15688969	C₂²	1	2	yes	—
32	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
33	#15688882	C₂²	1	1	yes	characteristic
34	#15688882	C₂²	1	2	yes	—
35	#15688882	C₂²	1	1	yes	characteristic
36	C₄₇×#559	C₄	1	2	yes	complemented
37	C₄₇×#559	C₄	1	1	yes	characteristic, complemented
38	C₄₇×#557	C₄	1	1	yes	characteristic, complemented
39	C₄₇×#556	C₄	1	1	yes	characteristic, complemented
40	C₄₇×#556	C₄	1	2	yes	complemented
41	C₄₇×#553	—	2	2	no	—
42	C₄₇×#553	—	2	1	no	—
43	C₄₇×#550	C₄	1	1	yes	characteristic, complemented
44	C₄₇×#548	—	2	1	no	—
45	C₄₇×#532	C₂²	1	1	yes	characteristic
46	C₄₇×#532	C₂²	1	2	yes	—
47	C₄₇×#529	—	2	1	no	—
48	C₄₇×#529	—	2	2	no	—
49	C₄×#41×C₄₇	—	2	1	no	—
50	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
51	C₄×#41×C₄₇	C₂²	1	2	yes	—
52	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×#10625329	C₂³	1	1	yes	characteristic
54	C₂×#10625329	C₂³	1	2	yes	—
55	C₂×#10625329	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊Dic₄₇	—	2	2	no	—
57	C₂×C₄⋊Dic₄₇	—	2	1	no	—
58	C₂×C₄×Dic₄₇	—	2	1	no	—
59	C₂×C₄×Dic₄₇	—	2	1	no	—
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
64	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
66	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
67	#13093951	—	2	2	no	—
68	#13093951	—	2	4	no	—
69	#13093951	—	2	2	no	—
70	#13093951	—	2	4	no	—
71	#13093951	—	4	2	no	—
72	#13093951	—	4	2	no	—
73	#13093951	—	4	2	no	—
74	#13093935	—	2	2	no	—
75	#13093935	—	2	1	no	—
76	C₄×C₄₇⋊C₈	—	2	1	no	—
77	C₄×C₄₇⋊C₈	—	2	2	no	—
78	C₄₇⋊#95	—	2	2	no	—
79	C₄₇⋊#95	—	2	2	no	—
80	C₄₇⋊#95	—	2	1	no	—
81	C₄₇⋊#95	—	2	2	no	—
82	C₂×#41×C₄₇	—	2	1	no	—
83	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×#41×C₄₇	C₂³	1	2	yes	—
85	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
86	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
88	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
89	#127×C₄₇	C₂×C₄	1	2	yes	—
90	#126×C₄₇	—	2	2	no	—
91	#126×C₄₇	—	2	2	no	—
92	#126×C₄₇	—	2	2	no	—
93	#125×C₄₇	—	2	2	no	—
94	#125×C₄₇	—	2	1	no	—
95	#124×C₄₇	—	2	1	no	—
96	#124×C₄₇	—	2	2	no	—
97	#124×C₄₇	C₂×C₄	1	2	yes	—
98	#124×C₄₇	C₂×C₄	1	2	yes	—
99	#124×C₄₇	C₂×C₄	1	2	yes	—
100	#123×C₄₇	—	2	2	no	—
101	#123×C₄₇	—	2	2	no	—
102	#123×C₄₇	—	2	2	no	—
103	C₂²⋊Q₈×C₄₇	—	2	1	no	—
104	C₂²⋊Q₈×C₄₇	—	2	2	no	—
105	#121×C₄₇	—	2	1	no	—
106	#121×C₄₇	—	2	2	no	—
107	#121×C₄₇	—	2	1	no	—
108	#121×C₄₇	—	2	2	no	—
109	#121×C₄₇	—	2	2	no	—
110	#121×C₄₇	—	2	1	no	—
111	C₄×Q₈×C₄₇	—	2	1	no	—
112	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
113	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
114	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
115	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
116	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
117	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
118	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
119	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
120	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
121	C₄×Q₈×C₄₇	D₄	1	2	yes	—
122	C₄×D₄×C₄₇	—	2	1	no	—
123	C₄×D₄×C₄₇	—	2	2	no	—
124	C₄×D₄×C₄₇	—	2	1	no	—
125	C₄×D₄×C₄₇	—	2	2	no	—
126	C₄×D₄×C₄₇	—	2	2	no	—
127	C₄×D₄×C₄₇	—	2	1	no	—
128	C₄×D₄×C₄₇	—	2	1	no	—
129	C₄×D₄×C₄₇	—	2	2	no	—
130	C₄×D₄×C₄₇	—	2	2	no	—
131	C₄×D₄×C₄₇	—	2	1	no	—
132	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
133	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
134	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
135	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
136	#117×C₄₇	—	2	2	no	—
137	#117×C₄₇	—	2	1	no	—
138	#117×C₄₇	—	2	2	no	—
139	#117×C₄₇	—	2	1	no	—
140	#117×C₄₇	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
142	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
143	C₂×C₄²×C₄₇	—	2	1	no	—
144	C₂×C₄²×C₄₇	—	2	2	no	—
145	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
147	#41×C₄₇	—	2	1	no	—
148	#41×C₄₇	—	2	2	no	—
149	#41×C₄₇	—	2	1	no	—
150	#41×C₄₇	—	2	2	no	—
151	#41×C₄₇	—	2	1	no	—
152	#41×C₄₇	—	2	2	no	—
153	#41×C₄₇	—	2	1	no	—
154	#41×C₄₇	—	2	2	no	—
155	#41×C₄₇	—	4	4	no	—
156	C₂×Q₈×C₄₇	—	4	2	no	—
157	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
160	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
161	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
162	C₂×D₄×C₄₇	—	2	1	no	—
163	C₂×D₄×C₄₇	—	2	2	no	—
164	C₂×D₄×C₄₇	—	2	2	no	—
165	C₂×D₄×C₄₇	—	2	1	no	—
166	C₂×D₄×C₄₇	—	2	2	no	—
167	C₂×D₄×C₄₇	—	2	1	no	—
168	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
169	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
170	C₂²×C₄×C₄₇	—	2	2	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	—	2	1	no	—
175	C₂²×C₄×C₄₇	—	2	2	no	—
176	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
181	C₂²×Dic₄₇	—	2	1	no	—
182	C₂²×Dic₄₇	—	2	1	no	—
183	C₂²×Dic₄₇	—	2	2	no	—
184	C₄⋊C₄×C₄₇	—	2	2	no	—
185	C₄⋊C₄×C₄₇	—	2	1	no	—
186	C₄⋊C₄×C₄₇	—	2	1	no	—
187	C₄⋊C₄×C₄₇	—	2	2	no	—
188	C₄⋊C₄×C₄₇	—	2	2	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	C₂²⋊C₄	1	2	yes	—
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	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
197	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
198	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
199	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
201	C₂²⋊C₄×C₄₇	—	2	1	no	—
202	C₂²⋊C₄×C₄₇	—	2	2	no	—
203	C₂²⋊C₄×C₄₇	—	2	2	no	—
204	C₂²⋊C₄×C₄₇	—	2	2	no	—
205	C₂²⋊C₄×C₄₇	—	2	2	no	—
206	C₂²⋊C₄×C₄₇	—	2	1	no	—
207	C₂²⋊C₄×C₄₇	—	2	1	no	—
208	C₂²⋊C₄×C₄₇	—	2	2	no	—
209	C₂²⋊C₄×C₄₇	—	2	2	no	—
210	C₂²⋊C₄×C₄₇	—	2	2	no	—
211	C₂²⋊C₄×C₄₇	—	2	2	no	—
212	C₄²×C₄₇	—	2	1	no	—
213	C₄²×C₄₇	—	2	2	no	—
214	C₄²×C₄₇	—	2	2	no	—
215	C₄²×C₄₇	—	2	1	no	—
216	C₄²×C₄₇	—	2	1	no	—
217	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
218	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
219	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
220	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
221	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₄₇	C₂×D₄	1	2	yes	—
223	C₄²×C₄₇	C₂×D₄	1	2	yes	—
224	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
225	C₄⋊Dic₄₇	—	4	4	no	—
226	C₄⋊Dic₄₇	—	4	2	no	—
227	C₄×Dic₄₇	—	2	1	no	—
228	C₄×Dic₄₇	—	2	1	no	—
229	C₄×Dic₄₇	—	2	2	no	—
230	C₄×Dic₄₇	—	2	1	no	—
231	C₄×Dic₄₇	—	2	2	no	—
232	C₄×Dic₄₇	—	4	2	no	—
233	C₄×Dic₄₇	—	4	2	no	—
234	C₄×Dic₄₇	#41	1	2	yes	complemented
235	#10625329	—	2	1	no	—
236	#10625329	—	2	1	no	—
237	#10625329	—	2	2	no	—
238	#10625329	—	2	2	no	—
239	#10625329	—	2	1	no	—
240	#10625329	#41	1	2	yes	complemented
241	C₂×C₄₇⋊C₈	—	2	1	no	—
242	C₂×C₄₇⋊C₈	—	2	1	no	—
243	C₂×C₄₇⋊C₈	—	2	2	no	—
244	C₂³×C₄₇	—	2	2	no	—
245	C₂³×C₄₇	—	2	1	no	—
246	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
247	Q₈×C₄₇	—	2	2	no	—
248	Q₈×C₄₇	—	2	2	no	—
249	Q₈×C₄₇	—	2	1	no	—
250	Q₈×C₄₇	—	2	2	no	—
251	Q₈×C₄₇	—	2	1	no	—
252	Q₈×C₄₇	—	2	2	no	—
253	Q₈×C₄₇	—	4	2	no	—
254	D₄×C₄₇	—	2	1	no	—
255	D₄×C₄₇	—	2	2	no	—
256	D₄×C₄₇	—	2	1	no	—
257	D₄×C₄₇	—	2	2	no	—
258	D₄×C₄₇	—	4	4	no	—
259	D₄×C₄₇	—	4	1	no	—
260	D₄×C₄₇	—	4	2	no	—
261	D₄×C₄₇	—	4	1	no	—
262	D₄×C₄₇	—	4	2	no	—
263	D₄×C₄₇	—	4	2	no	—
264	D₄×C₄₇	—	8	1	no	—
265	D₄×C₄₇	—	8	2	no	—
266	C₂×C₄×C₄₇	—	2	2	no	—
267	C₂×C₄×C₄₇	—	2	1	no	—
268	C₂×C₄×C₄₇	—	2	1	no	—
269	C₂×C₄×C₄₇	—	2	2	no	—
270	C₂×C₄×C₄₇	—	2	1	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	4	no	—
275	C₂×C₄×C₄₇	—	4	1	no	—
276	C₂×C₄×C₄₇	—	4	2	no	—
277	C₂×C₄×C₄₇	—	4	1	no	—
278	C₂×C₄×C₄₇	—	4	2	no	—
279	C₂×C₄×C₄₇	—	4	2	no	—
280	C₂×C₄×C₄₇	—	8	1	no	—
281	C₂×C₄×C₄₇	—	8	2	no	—
282	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
284	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
285	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
287	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
288	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
291	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
295	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
296	C₂×Dic₄₇	—	2	2	no	—
297	C₂×Dic₄₇	—	2	2	no	—
298	C₂×Dic₄₇	—	4	1	no	—
299	C₂×Dic₄₇	—	4	1	no	—
300	C₂×Dic₄₇	—	4	1	no	—
301	C₂×Dic₄₇	—	4	1	no	—
302	C₂×Dic₄₇	—	4	2	no	—
303	C₂×Dic₄₇	—	4	2	no	—
304	C₂×Dic₄₇	—	4	2	no	—
305	C₄₇⋊C₈	—	2	2	no	—
306	C₄₇⋊C₈	—	4	1	no	—
307	C₄₇⋊C₈	—	4	2	no	—
308	#22551	—	47	1	no	maximal, Sylow
309	C₂²×C₄₇	—	2	1	no	—
310	C₂²×C₄₇	—	2	1	no	—
311	C₂²×C₄₇	—	4	2	no	—
312	C₂²×C₄₇	—	4	1	no	—
313	C₂²×C₄₇	—	4	2	no	—
314	C₂²×C₄₇	—	4	1	no	—
315	C₂²×C₄₇	—	4	2	no	—
316	C₂²×C₄₇	—	4	1	no	—
317	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×C₄₇	#548	1	1	yes	characteristic
319	C₂²×C₄₇	#550	1	1	yes	characteristic
320	C₄×C₄₇	—	2	1	no	—
321	C₄×C₄₇	—	2	2	no	—
322	C₄×C₄₇	—	2	2	no	—
323	C₄×C₄₇	—	2	1	no	—
324	C₄×C₄₇	—	2	2	no	—
325	C₄×C₄₇	—	2	1	no	—
326	C₄×C₄₇	—	2	2	no	—
327	C₄×C₄₇	—	4	2	no	—
328	C₄×C₄₇	—	4	1	no	—
329	C₄×C₄₇	—	4	1	no	—
330	C₄×C₄₇	—	4	1	no	—
331	C₄×C₄₇	#421	1	2	yes	—
332	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
333	C₄×C₄₇	#520	1	1	yes	characteristic
334	C₄×C₄₇	#548	1	1	yes	characteristic
335	C₄×C₄₇	#550	1	1	yes	characteristic
336	Dic₄₇	—	4	2	no	—
337	Dic₄₇	—	4	2	no	—
338	Dic₄₇	—	8	2	no	—
339	#3480	D₄₇	1	1	yes	characteristic
340	Q₈×M₁₆	—	47	1	no	—
341	#2295	—	47	1	no	—
342	#1980	—	47	1	no	—
343	#1980	—	47	2	no	—
344	#1963	—	47	2	no	—
345	#1962	—	47	1	no	—
346	#1806	—	47	1	no	—
347	#1806	—	47	2	no	—
348	#1759	—	47	2	no	—
349	C₄×#104	—	47	1	no	—
350	C₂×C₄₇	—	2	1	no	—
351	C₂×C₄₇	—	2	1	no	—
352	C₂×C₄₇	—	8	2	no	—
353	C₂×C₄₇	—	8	1	no	—
354	C₂×C₄₇	#2341	1	1	yes	characteristic
355	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
356	C₂×C₄₇	#2901	1	1	yes	characteristic
357	#559	Dic₄₇	1	2	yes	complemented
358	#559	Dic₄₇	1	1	yes	characteristic, complemented
359	#557	Dic₄₇	1	1	yes	characteristic, complemented
360	#556	Dic₄₇	1	1	yes	characteristic, complemented
361	#556	Dic₄₇	1	2	yes	complemented
362	#553	—	2	2	no	—
363	#553	—	2	1	no	—
364	#550	Dic₄₇	1	1	yes	characteristic, complemented
365	#548	—	2	1	no	—
366	#532	C₂×D₄₇	1	1	yes	characteristic
367	#532	C₂×D₄₇	1	2	yes	—
368	#529	—	2	1	no	—
369	#529	—	2	2	no	—
370	C₄×#41	—	2	1	no	—
371	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
372	C₄×#41	C₂×D₄₇	1	2	yes	—
373	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
374	#446	—	94	1	no	—
375	#446	—	94	2	no	—
376	C₈×Q₈	—	94	1	no	—
377	#423	—	47	1	no	—
378	#423	—	47	2	no	—
379	C₂×#104	—	47	2	no	—
380	C₂×#104	—	47	1	no	—
381	C₂×#104	—	47	1	no	—
382	C₂×#104	—	47	2	no	—
383	C₂×#104	—	47	2	no	—
384	C₂×#104	—	47	2	no	—
385	C₂×#104	—	47	2	no	—
386	C₄×M₁₆	—	47	1	no	—
387	C₄×M₁₆	—	47	2	no	—
388	#391	—	94	1	no	—
389	#389	—	94	1	no	—
390	#387	—	94	2	no	—
391	C₄×C₄⋊C₄	—	47	1	no	—
392	C₄×C₄⋊C₄	—	47	2	no	—
393	#376	—	47	2	no	—
394	C₄³	—	47	1	no	—
395	#339	—	47	1	no	—
396	#339	—	47	2	no	—
397	#339	—	47	1	no	—
398	C₄₇	#22551	1	1	yes	characteristic, complemented, Sylow
399	C₂×#41	—	2	1	no	—
400	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
401	C₂×#41	C₂²×D₄₇	1	2	yes	—
402	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
403	C₂×M₁₆	—	47	1	no	—
404	C₂×M₁₆	—	47	1	no	—
405	C₂×M₁₆	—	47	2	no	—
406	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
407	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
408	#127	C₂×Dic₄₇	1	1	yes	characteristic
409	#127	C₂×Dic₄₇	1	2	yes	—
410	#126	—	2	2	no	—
411	#126	—	2	2	no	—
412	#126	—	2	2	no	—
413	#125	—	2	2	no	—
414	#125	—	2	1	no	—
415	#124	—	2	1	no	—
416	#124	—	2	2	no	—
417	#124	C₂×Dic₄₇	1	2	yes	—
418	#124	C₂×Dic₄₇	1	2	yes	—
419	#124	C₂×Dic₄₇	1	2	yes	—
420	#123	—	2	2	no	—
421	#123	—	2	2	no	—
422	#123	—	2	2	no	—
423	C₂²⋊Q₈	—	2	1	no	—
424	C₂²⋊Q₈	—	2	2	no	—
425	#121	—	2	1	no	—
426	#121	—	2	2	no	—
427	#121	—	2	1	no	—
428	#121	—	2	2	no	—
429	#121	—	2	2	no	—
430	#121	—	2	1	no	—
431	C₄×Q₈	—	2	1	no	—
432	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
433	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
434	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
435	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
436	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
437	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
438	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
439	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
440	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
441	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
442	C₄×D₄	—	2	1	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	—	2	1	no	—
448	C₄×D₄	—	2	1	no	—
449	C₄×D₄	—	2	2	no	—
450	C₄×D₄	—	2	2	no	—
451	C₄×D₄	—	2	1	no	—
452	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
453	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
454	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
455	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
456	#117	—	2	2	no	—
457	#117	—	2	1	no	—
458	#117	—	2	2	no	—
459	#117	—	2	1	no	—
460	#117	C₂²×D₄₇	1	1	yes	characteristic
461	C₂×C₄⋊C₄	—	94	2	no	—
462	C₂×C₄⋊C₄	—	94	1	no	—
463	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
464	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
465	C₂×C₄²	—	2	1	no	—
466	C₂×C₄²	—	2	2	no	—
467	C₂×C₄²	—	47	1	no	—
468	C₂×C₄²	—	47	1	no	—
469	C₂×C₄²	—	47	2	no	—
470	C₂×C₄²	—	94	1	no	—
471	C₂×C₄²	—	94	1	no	—
472	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
473	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
474	C₄⋊C₈	—	94	1	no	—
475	C₄⋊C₈	—	94	2	no	—
476	C₄⋊C₈	—	94	2	no	—
477	C₄⋊C₈	—	94	1	no	—
478	#104	—	94	4	no	—
479	#104	—	94	2	no	—
480	#104	—	94	2	no	—
481	#104	—	94	4	no	—
482	#104	—	188	2	no	—
483	#104	—	188	2	no	—
484	#104	—	188	2	no	—
485	#97	—	94	2	no	—
486	#97	—	94	1	no	—
487	C₄×C₈	—	94	1	no	—
488	C₄×C₈	—	94	2	no	—
489	#95	—	94	2	no	—
490	#95	—	94	2	no	—
491	#95	—	94	1	no	—
492	#95	—	94	2	no	—
493	#41	—	2	1	no	—
494	#41	—	2	2	no	—
495	#41	—	2	2	no	—
496	#41	—	2	1	no	—
497	#41	—	2	2	no	—
498	#41	—	2	1	no	—
499	#41	—	2	1	no	—
500	#41	—	2	2	no	—
501	#41	—	4	4	no	—
502	C₂×Q₈	—	4	2	no	—
503	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
504	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
505	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
506	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
507	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
515	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	94	1	no	—
523	C₂²×C₄	—	94	1	no	—
524	C₂²×C₄	—	94	2	no	—
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	1	yes	characteristic
528	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
529	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
530	M₁₆	—	47	2	no	—
531	M₁₆	—	94	1	no	—
532	M₁₆	—	94	2	no	—
533	M₁₆	—	94	1	no	—
534	M₁₆	—	94	2	no	—
535	M₁₆	—	94	1	no	—
536	C₂×C₈	—	94	1	no	—
537	C₂×C₈	—	94	1	no	—
538	C₂×C₈	—	94	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	188	2	no	—
548	C₄⋊C₄	—	188	4	no	—
549	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
550	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
551	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
552	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
553	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
554	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
555	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
556	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
557	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₂²⋊C₄	—	2	1	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	—	2	2	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	2	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	47	2	no	—
575	C₄²	—	94	1	no	—
576	C₄²	—	94	2	no	—
577	C₄²	—	94	1	no	—
578	C₄²	—	94	2	no	—
579	C₄²	—	94	1	no	—
580	C₄²	—	188	2	no	—
581	C₄²	—	188	2	no	—
582	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
583	C₄²	C₂²×Dic₄₇	1	2	yes	—
584	C₄²	C₂²×Dic₄₇	1	2	yes	—
585	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
586	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
587	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
588	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
589	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
590	C₂³	—	2	2	no	—
591	C₂³	—	2	1	no	—
592	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
593	Q₈	—	2	2	no	—
594	Q₈	—	2	2	no	—
595	Q₈	—	2	1	no	—
596	Q₈	—	2	2	no	—
597	Q₈	—	2	1	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	4	2	no	—
600	D₄	—	2	1	no	—
601	D₄	—	2	2	no	—
602	D₄	—	2	1	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	4	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	8	1	no	—
611	D₄	—	8	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	4	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	8	1	no	—
627	C₂×C₄	—	8	2	no	—
628	C₂×C₄	—	94	2	no	—
629	C₂×C₄	—	94	2	no	—
630	C₂×C₄	—	188	2	no	—
631	C₂×C₄	—	188	2	no	—
632	C₂×C₄	—	188	2	no	—
633	C₂×C₄	—	188	1	no	—
634	C₂×C₄	—	188	1	no	—
635	C₂×C₄	—	188	1	no	—
636	C₂×C₄	—	188	1	no	—
637	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
638	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
639	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
640	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
641	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
642	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
643	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
644	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
645	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
646	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
647	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
648	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
649	C₂×C₄	#13094070	1	1	yes	characteristic
650	C₂×C₄	#13094071	1	1	yes	characteristic
651	C₈	—	94	2	no	—
652	C₈	—	188	1	no	—
653	C₈	—	188	2	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	1	no	—
662	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
663	C₂²	#15689780	1	1	yes	characteristic
664	C₂²	#15689792	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	1	no	—
676	C₄	—	376	2	no	—
677	C₄	—	188	2	no	—
678	C₄	—	188	2	no	—
679	C₄	#15689140	1	2	yes	—
680	C₄	#41×Dic₄₇	1	1	yes	characteristic
681	C₄	#15689606	1	1	yes	characteristic
682	C₄	#15689780	1	1	yes	characteristic
683	C₄	#15689792	1	1	yes	characteristic
684	C₂	—	2	1	no	—
685	C₂	—	2	1	no	—
686	C₂	—	8	2	no	—
687	C₂	—	8	1	no	—
688	C₂	#20246229	1	1	yes	characteristic
689	C₂	C₂×#15689140	1	1	yes	characteristic
690	C₂	#20251935	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3480	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3480	D₄₇
hypocenter	C₄₇	#22551
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×Q₈ ◁ #3480

Complements

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

N	H ≅ G/N	type
1. Q₈×#10625329	C₂	semidirect
2. #20245866	C₂	semidirect
3. #20244308	C₂	semidirect
4. #20244308	C₂	semidirect
5. #20244221	C₂	semidirect
6. #20244217	C₂	semidirect
7. #20243408	C₂	semidirect
8. #20243408	C₂	semidirect
9. #20243198	C₂	semidirect
10. C₄×#13093951	C₂	semidirect
36. C₄₇×#559	C₄	semidirect
37. C₄₇×#559	C₄	semidirect
38. C₄₇×#557	C₄	semidirect
39. C₄₇×#556	C₄	semidirect
40. C₄₇×#556	C₄	semidirect
43. C₄₇×#550	C₄	semidirect
234. C₄×Dic₄₇	#41	semidirect
240. #10625329	#41	semidirect
357. #559	Dic₄₇	semidirect
358. #559	Dic₄₇	semidirect
359. #557	Dic₄₇	semidirect
360. #556	Dic₄₇	semidirect
361. #556	Dic₄₇	semidirect
364. #550	Dic₄₇	semidirect
398. C₄₇	#22551	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#10625329	2
#20245866	2
#20244308	2
#20244221	2
#20244217	2
#20243408	2
#20243198	2
C₄×#13093951	2
C₄₇×#3480	2
#22551	47