Subgroups — M₁₆×#10625334 #26187698

Order 12032.

794 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625334	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242271	C₂	1	2	yes	maximal, complemented
4	#20242217	C₂	1	2	yes	maximal, complemented
5	#20242215	C₂	1	2	yes	maximal, complemented
6	C₈×#10625334	C₂	1	2	yes	maximal, complemented
7	#20242146	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241813	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241812	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625334	C₄	1	1	yes	characteristic
13	C₂×M₁₆×D₄₇	—	2	1	no	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₄×#10625334	C₄	1	1	yes	characteristic
16	C₄×#10625334	C₄	1	1	yes	characteristic
17	C₄×#10625334	C₄	1	1	yes	characteristic
18	C₄×#10625334	C₄	1	1	yes	characteristic
19	C₄×#10625334	C₂²	1	1	yes	characteristic
20	C₄×#10625334	C₂²	1	1	yes	characteristic
21	C₄×#10625334	C₂²	1	1	yes	characteristic
22	C₄×#10625334	C₂²	1	1	yes	characteristic
23	#15689202	C₂²	1	2	yes	complemented
24	#15689196	—	2	2	no	—
25	C₈×D₁₈₈	C₂²	1	2	yes	complemented
26	#15689176	C₂²	1	1	yes	characteristic
27	C₂×#13093957	C₄	1	1	yes	characteristic
28	#15689147	C₂²	1	1	yes	characteristic
29	C₂×#13093945	C₄	1	1	yes	characteristic
30	C₂×#13093944	C₄	1	1	yes	characteristic
31	#15689086	—	2	1	no	—
32	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
33	#15688875	C₂²	1	2	yes	complemented
34	#15688875	C₂²	1	2	yes	complemented
35	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
36	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
37	#15688850	C₂²	1	2	yes	complemented
38	#15688850	C₂²	1	2	yes	complemented
39	#15688844	C₂²	1	2	yes	complemented
40	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
41	C₂²×M₁₆×C₄₇	—	2	1	no	—
42	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#436	C₂²	1	2	yes	complemented
44	C₄₇×#435	—	2	2	no	—
45	C₈×D₄×C₄₇	C₂²	1	2	yes	complemented
46	C₄₇×#423	C₂²	1	1	yes	characteristic
47	C₄₇×#407	—	2	1	no	—
48	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
49	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₄₇	—	2	1	no	—
51	C₂×#10625334	—	2	4	no	—
52	C₂×#10625334	C₂×C₄	1	1	yes	characteristic
53	C₂×#10625334	C₂×C₄	1	1	yes	characteristic
54	C₂×#10625334	C₂×C₄	1	1	yes	characteristic
55	C₂×#10625334	C₂×C₄	1	1	yes	characteristic
56	C₂×#10625329	—	2	1	no	—
57	C₂×#10625324	—	2	2	no	—
58	M₁₆×D₄₇	—	4	4	no	—
59	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₄₇	—	2	2	no	—
62	C₄×D₁₈₈	—	2	1	no	—
63	C₄×D₁₈₈	—	2	1	no	—
64	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
65	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
66	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
67	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
70	#13093957	C₂×C₄	1	1	yes	characteristic
71	#13093957	C₂×C₄	1	1	yes	characteristic
72	#13093957	C₂×C₄	1	1	yes	characteristic
73	#13093957	C₂×C₄	1	1	yes	characteristic
74	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
75	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
76	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
77	#13093945	C₂×C₄	1	1	yes	characteristic
78	#13093945	C₂×C₄	1	1	yes	characteristic
79	#13093945	C₂×C₄	1	1	yes	characteristic
80	#13093945	C₂×C₄	1	1	yes	characteristic
81	#13093944	C₂×C₄	1	1	yes	characteristic
82	#13093944	C₂×C₄	1	1	yes	characteristic
83	#13093944	C₂×C₄	1	1	yes	characteristic
84	#13093944	C₂×C₄	1	1	yes	characteristic
85	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
86	(C₂×D₄₇)⋊C₈	—	2	2	no	—
87	(C₂×D₄₇)⋊C₈	—	2	2	no	—
88	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
91	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
92	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂³×C₄×C₄₇	—	2	1	no	—
95	C₂×M₁₆×C₄₇	—	2	1	no	—
96	C₂×M₁₆×C₄₇	—	2	2	no	—
97	C₂×M₁₆×C₄₇	—	4	4	no	—
98	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
99	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
100	C₂²×C₈×C₄₇	—	2	2	no	—
101	C₄×D₄×C₄₇	—	2	1	no	—
102	C₄×D₄×C₄₇	—	2	1	no	—
103	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
109	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₄₇	—	2	1	no	—
111	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
112	C₂²⋊C₈×C₄₇	—	2	2	no	—
113	C₂²⋊C₈×C₄₇	—	2	2	no	—
114	#97×C₄₇	D₄	1	2	yes	—
115	C₄×C₈×C₄₇	C₂³	1	2	yes	—
116	C₂⁴×C₄₇	—	2	1	no	—
117	C₂³×D₄₇	—	2	1	no	—
118	C₂×D₄×C₄₇	—	2	2	no	—
119	C₂×D₄×C₄₇	—	2	1	no	—
120	C₂×D₄×C₄₇	—	4	1	no	—
121	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	2	1	no	—
126	C₂²×C₄×C₄₇	—	2	1	no	—
127	C₂²×C₄×C₄₇	—	2	1	no	—
128	C₂²×C₄×C₄₇	—	4	2	no	—
129	C₂²×C₄×C₄₇	—	4	2	no	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
133	C₂²×Dic₄₇	—	2	1	no	—
134	C₂×D₁₈₈	—	2	2	no	—
135	C₂×D₁₈₈	—	2	1	no	—
136	C₂×D₁₈₈	—	4	1	no	—
137	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₄₇	—	2	1	no	—
140	C₂×C₄×D₄₇	—	2	1	no	—
141	C₂×C₄×D₄₇	—	2	1	no	—
142	C₂×C₄×D₄₇	—	2	1	no	—
143	C₂×C₄×D₄₇	—	4	2	no	—
144	C₂×C₄×D₄₇	—	4	2	no	—
145	M₁₆×C₄₇	—	2	2	no	—
146	M₁₆×C₄₇	—	4	2	no	—
147	M₁₆×C₄₇	—	4	4	no	—
148	M₁₆×C₄₇	D₈	1	4	yes	complemented
149	C₂×C₈×C₄₇	—	2	2	no	—
150	C₂×C₈×C₄₇	—	4	4	no	—
151	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₄₇	—	2	1	no	—
154	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²⋊C₄×C₄₇	—	2	1	no	—
157	C₂²⋊C₄×C₄₇	—	2	1	no	—
158	C₂²⋊C₄×C₄₇	—	2	1	no	—
159	C₂²⋊C₄×C₄₇	—	2	1	no	—
160	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₄₇	#41	1	1	yes	characteristic
163	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
164	#10625334	—	2	2	no	—
165	#10625334	—	2	2	no	—
166	#10625334	—	2	2	no	—
167	#10625334	M₁₆	1	4	yes	direct product factor
168	(C₂×D₄₇)⋊C₄	—	2	1	no	—
169	(C₂×D₄₇)⋊C₄	—	2	1	no	—
170	(C₂×D₄₇)⋊C₄	—	2	1	no	—
171	(C₂×D₄₇)⋊C₄	—	2	1	no	—
172	C₄⋊Dic₄₇	—	2	1	no	—
173	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
175	#10625329	—	4	2	no	—
176	C₂×C₄₇⋊C₈	—	2	2	no	—
177	C₂×C₄₇⋊C₈	—	2	2	no	—
178	C₂×C₄₇⋊C₈	—	2	2	no	—
179	C₂×C₄₇⋊C₈	—	4	1	no	—
180	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
184	#10625324	—	4	4	no	—
185	C₈×D₄₇	—	4	4	no	—
186	C₂³×C₄₇	—	2	1	no	—
187	C₂³×C₄₇	—	2	1	no	—
188	C₂³×C₄₇	—	4	2	no	—
189	C₂³×C₄₇	—	4	2	no	—
190	C₂³×C₄₇	—	8	1	no	—
191	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
192	C₂²×D₄₇	—	2	1	no	—
193	C₂²×D₄₇	—	2	1	no	—
194	C₂²×D₄₇	—	4	2	no	—
195	C₂²×D₄₇	—	4	2	no	—
196	C₂²×D₄₇	—	8	1	no	—
197	D₄×C₄₇	—	2	1	no	—
198	D₄×C₄₇	—	2	1	no	—
199	D₄×C₄₇	—	2	1	no	—
200	D₄×C₄₇	—	4	2	no	—
201	D₄×C₄₇	C₂×M₁₆	1	2	yes	complemented
202	C₂×C₄×C₄₇	—	2	1	no	—
203	C₂×C₄×C₄₇	—	2	1	no	—
204	C₂×C₄×C₄₇	—	2	1	no	—
205	C₂×C₄×C₄₇	—	2	1	no	—
206	C₂×C₄×C₄₇	—	4	1	no	—
207	C₂×C₄×C₄₇	—	4	2	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	—	4	1	no	—
210	C₂×C₄×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	1	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	2	no	—
214	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
218	C₂×C₄×C₄₇	#135	1	2	yes	—
219	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
222	C₂×Dic₄₇	—	2	1	no	—
223	C₂×Dic₄₇	—	2	1	no	—
224	C₂×Dic₄₇	—	4	2	no	—
225	D₁₈₈	—	2	1	no	—
226	D₁₈₈	—	2	1	no	—
227	D₁₈₈	—	2	1	no	—
228	D₁₈₈	—	4	2	no	—
229	D₁₈₈	C₂×M₁₆	1	2	yes	complemented
230	C₄×D₄₇	—	4	1	no	—
231	C₄×D₄₇	—	4	1	no	—
232	C₄×D₄₇	—	4	1	no	—
233	C₄×D₄₇	—	4	1	no	—
234	C₄×D₄₇	—	4	2	no	—
235	C₄×D₄₇	—	4	2	no	—
236	C₈×C₄₇	—	2	2	no	—
237	C₈×C₄₇	—	4	2	no	—
238	C₈×C₄₇	C₂×D₈	1	4	yes	complemented
239	C₄₇⋊C₈	—	2	1	no	—
240	C₄₇⋊C₈	—	2	1	no	—
241	C₄₇⋊C₈	—	2	1	no	—
242	C₄₇⋊C₈	—	4	2	no	—
243	C₄₇⋊C₈	—	4	2	no	—
244	C₄₇⋊C₈	C₂×M₁₆	1	2	yes	complemented
245	M₁₆×D₈	—	47	1	no	maximal, Sylow
246	C₂²×C₄₇	—	2	1	no	—
247	C₂²×C₄₇	—	2	1	no	—
248	C₂²×C₄₇	—	2	2	no	—
249	C₂²×C₄₇	—	4	1	no	—
250	C₂²×C₄₇	—	4	1	no	—
251	C₂²×C₄₇	—	4	1	no	—
252	C₂²×C₄₇	—	4	1	no	—
253	C₂²×C₄₇	—	4	1	no	—
254	C₂²×C₄₇	—	8	4	no	—
255	C₂²×C₄₇	C₄×D₈	1	2	yes	—
256	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂×D₄₇	—	2	2	no	—
258	C₂×D₄₇	—	4	1	no	—
259	C₂×D₄₇	—	4	1	no	—
260	C₂×D₄₇	—	4	1	no	—
261	C₂×D₄₇	—	4	1	no	—
262	C₂×D₄₇	—	4	1	no	—
263	C₂×D₄₇	—	8	4	no	—
264	C₄×C₄₇	—	2	1	no	—
265	C₄×C₄₇	—	2	1	no	—
266	C₄×C₄₇	—	2	1	no	—
267	C₄×C₄₇	—	4	1	no	—
268	C₄×C₄₇	—	4	1	no	—
269	C₄×C₄₇	C₄×D₈	1	2	yes	—
270	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
271	C₄×C₄₇	#568	1	1	yes	characteristic
272	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
273	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
274	Dic₄₇	—	4	1	no	—
275	Dic₄₇	—	4	1	no	—
276	C₂×C₄×D₈	—	47	1	no	—
277	D₄×M₁₆	—	47	1	no	—
278	D₄×M₁₆	D₄₇	1	1	yes	characteristic, complemented
279	#1589	—	47	2	no	—
280	#1581	—	47	2	no	—
281	#1581	—	47	2	no	—
282	C₈×D₈	—	47	2	no	—
283	#1567	—	47	1	no	—
284	#1486	—	47	1	no	—
285	#1486	—	47	1	no	—
286	C₈×M₁₆	—	47	1	no	—
287	C₂×C₄₇	—	2	2	no	—
288	C₂×C₄₇	—	4	2	no	—
289	C₂×C₄₇	—	8	1	no	—
290	C₂×C₄₇	D₄×M₁₆	1	1	yes	characteristic
291	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
292	C₂×C₄₇	#2957	1	1	yes	characteristic
293	D₄₇	—	4	2	no	—
294	D₄₇	—	8	1	no	—
295	C₂²×D₈	—	47	1	no	—
296	C₂²×M₁₆	—	2	1	no	—
297	C₂²×M₁₆	—	94	1	no	—
298	C₂×C₄×D₄	—	47	1	no	—
299	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
300	C₄×D₈	—	47	1	no	—
301	C₄×D₈	—	47	1	no	—
302	C₄×D₈	—	47	1	no	—
303	C₄×D₈	—	47	1	no	—
304	C₄×D₈	—	47	1	no	—
305	C₄×D₈	—	47	1	no	—
306	C₄×D₈	—	47	1	no	—
307	C₄×D₈	—	47	1	no	—
308	#436	—	47	2	no	—
309	#436	C₂×D₄₇	1	2	yes	complemented
310	#435	—	2	2	no	—
311	#435	—	94	2	no	—
312	C₈×D₄	—	47	2	no	—
313	C₈×D₄	C₂×D₄₇	1	2	yes	complemented
314	#431	—	47	1	no	—
315	C₂×#107	—	47	1	no	—
316	#423	—	47	1	no	—
317	#423	C₂×D₄₇	1	1	yes	characteristic
318	C₂×#102	—	47	1	no	—
319	C₂×#102	—	47	1	no	—
320	#407	—	2	1	no	—
321	#407	—	94	1	no	—
322	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
323	C₂×C₄×C₈	—	47	1	no	—
324	#335	—	47	2	no	—
325	#335	—	47	2	no	—
326	D₄⋊C₈	—	47	2	no	—
327	D₄⋊C₈	—	47	2	no	—
328	D₄⋊C₈	—	47	2	no	—
329	D₄⋊C₈	—	47	2	no	—
330	#322	—	47	2	no	—
331	C₈²	—	47	2	no	—
332	C₄₇	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
333	C₂²×D₄	—	47	1	no	—
334	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	—	94	1	no	—
337	C₂×D₈	—	47	1	no	—
338	C₂×D₈	—	47	1	no	—
339	C₂×D₈	—	47	1	no	—
340	C₂×D₈	—	47	1	no	—
341	C₂×D₈	—	94	4	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	2	no	—
344	C₂×M₁₆	—	4	4	no	—
345	C₂×M₁₆	—	94	1	no	—
346	C₂×M₁₆	—	94	2	no	—
347	C₂×M₁₆	—	188	4	no	—
348	C₂×M₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
349	C₂×M₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
350	C₂²×C₈	—	2	2	no	—
351	C₂²×C₈	—	47	1	no	—
352	C₂²×C₈	—	47	1	no	—
353	C₂²×C₈	—	94	2	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	47	1	no	—
357	C₄×D₄	—	47	1	no	—
358	C₄×D₄	—	47	1	no	—
359	C₄×D₄	—	47	1	no	—
360	C₄×D₄	—	94	1	no	—
361	C₄×D₄	—	94	1	no	—
362	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
363	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
364	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
365	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
366	C₂×C₄⋊C₄	—	47	1	no	—
367	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	94	1	no	—
370	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
371	#107	—	47	1	no	—
372	#107	—	47	1	no	—
373	#107	—	47	1	no	—
374	#107	—	47	1	no	—
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	—	47	2	no	—
377	C₄⋊C₈	—	94	1	no	—
378	C₄⋊C₈	—	94	1	no	—
379	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
380	#102	—	47	1	no	—
381	#102	—	47	1	no	—
382	#102	—	47	1	no	—
383	#102	—	47	1	no	—
384	#102	—	47	1	no	—
385	#102	—	47	1	no	—
386	#102	—	47	1	no	—
387	#102	—	47	1	no	—
388	C₂²⋊C₈	—	2	2	no	—
389	C₂²⋊C₈	—	2	2	no	—
390	C₂²⋊C₈	—	94	1	no	—
391	C₂²⋊C₈	—	94	2	no	—
392	C₂²⋊C₈	—	94	2	no	—
393	#97	C₂²⋊D₄₇	1	2	yes	—
394	C₄×C₈	—	47	1	no	—
395	C₄×C₈	—	47	1	no	—
396	C₄×C₈	—	47	1	no	—
397	C₄×C₈	—	47	1	no	—
398	C₄×C₈	—	47	2	no	—
399	C₄×C₈	C₂²×D₄₇	1	2	yes	—
400	C₂⁴	—	2	1	no	—
401	C₂⁴	—	94	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	4	1	no	—
405	C₂×D₄	—	47	1	no	—
406	C₂×D₄	—	47	1	no	—
407	C₂×D₄	—	94	2	no	—
408	C₂×D₄	—	94	1	no	—
409	C₂×D₄	—	188	1	no	—
410	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
411	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	94	1	no	—
420	C₂²×C₄	—	94	1	no	—
421	C₂²×C₄	—	94	1	no	—
422	C₂²×C₄	—	94	1	no	—
423	C₂²×C₄	—	94	1	no	—
424	C₂²×C₄	—	188	2	no	—
425	C₂²×C₄	—	188	2	no	—
426	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
427	C₂²×C₄	#10625350	1	1	yes	characteristic
428	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
429	D₈	—	47	4	no	—
430	D₈	—	94	2	no	—
431	D₈	—	94	2	no	—
432	D₈	—	94	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	4	2	no	—
435	M₁₆	—	4	4	no	—
436	M₁₆	—	188	2	no	—
437	M₁₆	—	188	4	no	—
438	M₁₆	#10625334	1	4	yes	direct product factor
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	4	4	no	—
441	C₂×C₈	—	47	1	no	—
442	C₂×C₈	—	47	1	no	—
443	C₂×C₈	—	47	1	no	—
444	C₂×C₈	—	47	1	no	—
445	C₂×C₈	—	94	2	no	—
446	C₂×C₈	—	94	2	no	—
447	C₂×C₈	—	94	2	no	—
448	C₂×C₈	—	188	1	no	—
449	C₂×C₈	—	188	4	no	—
450	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
451	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	47	1	no	—
454	C₄⋊C₄	—	47	1	no	—
455	C₄⋊C₄	—	94	1	no	—
456	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
457	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	94	1	no	—
463	C₂²⋊C₄	—	94	1	no	—
464	C₂²⋊C₄	—	94	1	no	—
465	C₂²⋊C₄	—	94	1	no	—
466	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
467	C₄²	#10625350	1	1	yes	characteristic
468	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
469	C₄²	C₂³×D₄₇	1	1	yes	characteristic
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	8	1	no	—
475	C₂³	—	94	1	no	—
476	C₂³	—	94	1	no	—
477	C₂³	—	376	1	no	—
478	C₂³	—	188	2	no	—
479	C₂³	—	188	2	no	—
480	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
481	D₄	—	2	1	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	1	no	—
484	D₄	—	4	2	no	—
485	D₄	—	47	2	no	—
486	D₄	—	94	1	no	—
487	D₄	—	94	1	no	—
488	D₄	—	94	1	no	—
489	D₄	—	188	2	no	—
490	D₄	M₁₆×D₄₇	1	2	yes	complemented
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	94	1	no	—
504	C₂×C₄	—	94	1	no	—
505	C₂×C₄	—	188	2	no	—
506	C₂×C₄	—	188	1	no	—
507	C₂×C₄	—	188	1	no	—
508	C₂×C₄	—	188	1	no	—
509	C₂×C₄	—	188	1	no	—
510	C₂×C₄	—	188	2	no	—
511	C₂×C₄	—	188	2	no	—
512	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
513	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
514	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
515	C₂×C₄	C₂×#10625334	1	2	yes	—
516	C₂×C₄	#13094044	1	2	yes	—
517	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
518	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
519	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	4	2	no	—
522	C₈	—	47	2	no	—
523	C₈	—	94	1	no	—
524	C₈	—	94	1	no	—
525	C₈	—	94	1	no	—
526	C₈	—	188	2	no	—
527	C₈	—	188	2	no	—
528	C₈	C₂×#10625334	1	4	yes	complemented
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	8	4	no	—
538	C₂²	—	94	2	no	—
539	C₂²	—	376	4	no	—
540	C₂²	—	188	1	no	—
541	C₂²	—	188	1	no	—
542	C₂²	—	188	1	no	—
543	C₂²	—	188	1	no	—
544	C₂²	—	188	1	no	—
545	C₂²	C₄×#10625334	1	2	yes	—
546	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	188	1	no	—
553	C₄	—	188	1	no	—
554	C₄	C₄×#10625334	1	2	yes	—
555	C₄	C₂×M₁₆×D₄₇	1	1	yes	characteristic
556	C₄	#15689889	1	1	yes	characteristic
557	C₄	C₂²×#10625334	1	1	yes	characteristic
558	C₄	C₂×#13094044	1	1	yes	characteristic
559	C₂	—	2	2	no	—
560	C₂	—	4	2	no	—
561	C₂	—	8	1	no	—
562	C₂	—	376	1	no	—
563	C₂	—	188	2	no	—
564	C₂	M₁₆×C₂²⋊D₄₇	1	1	yes	characteristic
565	C₂	C₂×C₄×#10625334	1	1	yes	characteristic
566	C₂	#20252303	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	D₄×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂²×#10625334	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	D₄×M₁₆	D₄₇
hypocenter	C₄₇	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. M₁₆×D₁₈₈	C₂	semidirect
3. #20242271	C₂	semidirect
4. #20242217	C₂	semidirect
5. #20242215	C₂	semidirect
6. C₈×#10625334	C₂	semidirect
7. #20242146	C₂	semidirect
8. #20241813	C₂	semidirect
9. #20241812	C₂	semidirect
10. M₁₆×C₄₇⋊C₈	C₂	semidirect
11. D₄×M₁₆×C₄₇	C₂	semidirect
23. #15689202	C₂²	semidirect
25. C₈×D₁₈₈	C₂²	semidirect
33. #15688875	C₂²	semidirect
34. #15688875	C₂²	semidirect
35. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
36. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
37. #15688850	C₂²	semidirect
38. #15688850	C₂²	semidirect
39. #15688844	C₂²	semidirect
40. C₈×C₄₇⋊C₈	C₂²	semidirect
43. C₄₇×#436	C₂²	semidirect
45. C₈×D₄×C₄₇	C₂²	semidirect
148. M₁₆×C₄₇	D₈	semidirect
167. #10625334	M₁₆	direct (N × H)
201. D₄×C₄₇	C₂×M₁₆	semidirect
229. D₁₈₈	C₂×M₁₆	semidirect
238. C₈×C₄₇	C₂×D₈	semidirect
244. C₄₇⋊C₈	C₂×M₁₆	semidirect
278. D₄×M₁₆	D₄₇	semidirect
309. #436	C₂×D₄₇	semidirect
313. C₈×D₄	C₂×D₄₇	semidirect
332. C₄₇	M₁₆×D₈	semidirect
438. M₁₆	#10625334	direct (N × H)
490. D₄	M₁₆×D₄₇	semidirect
528. C₈	C₂×#10625334	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625334	2
M₁₆×D₁₈₈	2
#20242271	2
#20242217	2
#20242215	2
C₈×#10625334	2
#20242146	2
#20241813	2
#20241812	2
M₁₆×C₄₇⋊C₈	2
D₄×M₁₆×C₄₇	2
M₁₆×D₈	47

Subgroups — M16×#10625334 #26187698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×#10625334 #26187698