Subgroups — C₄×#15689925 #27080492

Order 12032.

2826 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689925	C₂	1	1	yes	maximal, characteristic
2	C₄×#13094070	C₂	1	2	yes	maximal, complemented
3	#20252264	C₂	1	1	yes	maximal, characteristic, complemented
4	#20252263	C₂	1	2	yes	maximal, complemented
5	#20252239	C₂	1	1	yes	maximal, characteristic, complemented
6	#20252235	C₂	1	2	yes	maximal, complemented
7	#20252223	C₂	1	2	yes	maximal, complemented
8	#20252215	C₂	1	4	yes	maximal, complemented
9	C₄×#13094051	C₂	1	4	yes	maximal, complemented
10	C₄×#13094049	C₂	1	2	yes	maximal, complemented
11	C₄×#13094047	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×D₈×D₄₇	C₂	1	2	yes	maximal, complemented
14	#20251985	C₂	1	1	yes	maximal, characteristic, complemented
15	#20251910	C₂	1	2	yes	maximal, complemented
16	C₄×#13094030	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#135×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13094070	C₂²	1	2	yes	—
19	#15689925	C₄	1	16	yes	direct product factor
20	C₂×#13094051	C₂²	1	4	yes	—
21	C₂×#13094049	C₂²	1	2	yes	—
22	C₂×#13094047	C₂²	1	2	yes	—
23	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
24	C₂×D₈×D₄₇	C₂²	1	2	yes	—
25	C₂×#13094030	C₂²	1	1	yes	characteristic
26	C₂×#13094030	C₂²	1	1	yes	characteristic
27	#15689606	C₂²	1	2	yes	complemented
28	#15689605	C₂²	1	4	yes	complemented
29	#15689603	—	2	2	no	—
30	#15689603	C₂²	1	2	yes	—
31	#15689597	—	2	2	no	—
32	#15689597	C₂²	1	2	yes	complemented
33	#15689595	—	2	4	no	—
34	#15689595	C₂²	1	4	yes	complemented
35	C₄×#10625354	C₂²	1	4	yes	complemented
36	C₄×#10625350	—	2	2	no	—
37	C₄×#10625350	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₁₈₈	—	2	2	no	—
39	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
40	C₄×D₄×D₄₇	—	2	4	no	—
41	C₄×D₄×D₄₇	C₂²	1	4	yes	complemented
42	#15689234	C₂²	1	4	yes	complemented
43	#15689233	C₂²	1	4	yes	complemented
44	#15689232	C₂²	1	4	yes	complemented
45	#15689226	C₂²	1	4	yes	complemented
46	#15689224	C₂²	1	4	yes	complemented
47	#15689221	C₂²	1	4	yes	complemented
48	Q₁₆×Dic₄₇	C₂²	1	2	yes	complemented
49	C₄×#10625336	C₂²	1	4	yes	complemented
50	#15689208	C₂²	1	4	yes	complemented
51	C₄×D₃₇₆	C₂²	1	2	yes	complemented
52	C₄×D₃₇₆	C₂²	1	2	yes	complemented
53	C₄×D₃₇₆	C₂²	1	2	yes	complemented
54	C₄×D₃₇₆	C₂²	1	2	yes	complemented
55	D₈×Dic₄₇	C₂²	1	2	yes	complemented
56	#15689205	C₂²	1	2	yes	complemented
57	#15689205	C₂²	1	2	yes	complemented
58	C₄×#10625334	C₂²	1	4	yes	complemented
59	#15689203	C₂²	1	4	yes	complemented
60	#15689166	C₂²	1	2	yes	complemented
61	#15689162	C₂²	1	4	yes	complemented
62	#15689160	C₂²	1	2	yes	complemented
63	C₂×#13093958	C₂²	1	1	yes	characteristic, complemented
64	#107×D₄₇	C₂²	1	2	yes	complemented
65	#15689127	C₂²	1	2	yes	complemented
66	#15689126	C₂²	1	4	yes	complemented
67	#15689124	C₂²	1	2	yes	complemented
68	#15689123	C₂²	1	4	yes	complemented
69	#15689118	C₂²	1	4	yes	complemented
70	C₂×#13093946	C₂²	1	2	yes	complemented
71	#102×D₄₇	C₂²	1	4	yes	complemented
72	#15689078	C₂²	1	1	yes	characteristic, complemented
73	#15689078	C₂²	1	1	yes	characteristic, complemented
74	#15689077	C₂²	1	2	yes	complemented
75	#15689077	C₂²	1	2	yes	complemented
76	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
77	C₄×#10625324	C₂²	1	2	yes	complemented
78	C₄×C₈×D₄₇	C₂²	1	2	yes	complemented
79	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
80	C₄×#41×C₄₇	C₂²	1	2	yes	complemented
81	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
82	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
83	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
85	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
86	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
87	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
88	C₄₇×#416	C₂²	1	2	yes	complemented
89	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
90	#13094070	—	2	8	no	—
91	#13094070	C₂×C₄	1	16	yes	complemented
92	C₂×#10625354	C₂³	1	4	yes	—
93	C₂×#10625350	—	2	2	no	—
94	C₂×#10625350	C₂³	1	1	yes	characteristic
95	C₂²×D₁₈₈	—	2	2	no	—
96	C₂²×D₁₈₈	C₂³	1	2	yes	—
97	C₂×D₄×D₄₇	—	2	4	no	—
98	C₂×D₄×D₄₇	C₂³	1	4	yes	—
99	C₂²×C₄×D₄₇	—	2	2	no	—
100	C₂²×C₄×D₄₇	—	2	4	no	—
101	#13094051	C₂×C₄	1	32	yes	complemented
102	#13094049	C₂×C₄	1	16	yes	complemented
103	#13094047	C₂×C₄	1	16	yes	complemented
104	C₂×#10625336	C₂³	1	4	yes	—
105	C₂×D₃₇₆	C₂×C₄	1	8	yes	complemented
106	C₂×D₃₇₆	C₂³	1	2	yes	—
107	C₂×D₃₇₆	C₂³	1	2	yes	—
108	C₂×#10625334	C₂³	1	4	yes	—
109	D₈×D₄₇	C₂×C₄	1	16	yes	complemented
110	#13094030	—	2	4	no	—
111	#13094030	C₂×C₄	1	8	yes	complemented
112	C₂×#10625329	C₂³	1	1	yes	characteristic
113	C₂×#10625329	C₂³	1	1	yes	characteristic
114	C₂×#10625324	C₂³	1	2	yes	—
115	C₂×#10625324	C₂³	1	2	yes	—
116	C₂×C₈×D₄₇	C₂³	1	2	yes	—
117	C₂×C₈×D₄₇	C₂³	1	2	yes	—
118	Q₈×Dic₄₇	C₂³	1	4	yes	—
119	C₄×Dic₉₄	—	2	2	no	—
120	C₄×Dic₉₄	D₄	1	1	yes	characteristic
121	C₄×Dic₉₄	D₄	1	1	yes	characteristic
122	C₄×D₁₈₈	—	2	2	no	—
123	C₄×D₁₈₈	—	2	4	no	—
124	C₄×D₁₈₈	—	2	2	no	—
125	C₄×D₁₈₈	—	2	2	no	—
126	C₄×D₁₈₈	—	2	4	no	—
127	C₄×D₁₈₈	—	2	2	no	—
128	C₄×D₁₈₈	—	2	2	no	—
129	C₄×D₁₈₈	D₄	1	1	yes	characteristic
130	C₄×D₁₈₈	D₄	1	1	yes	characteristic
131	C₄×D₁₈₈	C₂³	1	4	yes	—
132	C₄×D₁₈₈	C₂³	1	4	yes	—
133	D₄×Dic₄₇	—	2	4	no	—
134	D₄×Dic₄₇	C₂³	1	4	yes	—
135	#13093986	—	2	4	no	—
136	#13093986	—	2	4	no	—
137	#13093986	C₂³	1	4	yes	—
138	#13093986	C₂³	1	4	yes	—
139	C₄×C₂²⋊D₄₇	—	2	4	no	—
140	C₄×C₂²⋊D₄₇	—	2	4	no	—
141	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
142	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
143	(C₂²⋊D₄₇)⋊C₄	—	2	4	no	—
144	(C₂²⋊D₄₇)⋊C₄	—	2	4	no	—
145	(C₂²⋊D₄₇)⋊C₄	—	2	4	no	—
146	#13093983	—	2	2	no	—
147	#13093983	C₂³	1	1	yes	characteristic
148	#13093982	—	2	4	no	—
149	#13093982	C₂³	1	4	yes	—
150	#13093981	—	2	4	no	—
151	#13093981	C₂³	1	2	yes	—
152	C₂×C₄⋊Dic₄₇	—	2	2	no	—
153	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
154	C₄⋊C₄×D₄₇	—	2	4	no	—
155	C₄⋊C₄×D₄₇	C₂³	1	4	yes	—
156	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
157	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
158	C₂²⋊C₄×D₄₇	—	2	4	no	—
159	C₂²⋊C₄×D₄₇	—	2	4	no	—
160	C₂²⋊C₄×D₄₇	—	2	4	no	—
161	C₄²×D₄₇	—	2	4	no	—
162	C₄²×D₄₇	C₂³	1	2	yes	—
163	#13093958	C₂³	1	2	yes	—
164	#13093958	C₂³	1	2	yes	—
165	#13093957	C₂³	1	4	yes	—
166	#13093955	C₂³	1	4	yes	—
167	#13093948	C₂³	1	4	yes	—
168	#13093946	C₂³	1	4	yes	—
169	#13093946	C₂³	1	4	yes	—
170	#13093945	C₂³	1	4	yes	—
171	#13093944	C₂³	1	4	yes	—
172	#13093944	C₂³	1	4	yes	—
173	#13093935	C₂³	1	2	yes	—
174	#13093934	C₂³	1	2	yes	—
175	#13093934	C₂³	1	2	yes	—
176	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
177	C₈×Dic₄₇	C₂³	1	2	yes	—
178	C₈×Dic₄₇	C₂³	1	2	yes	—
179	C₂×#41×C₄₇	C₂³	1	2	yes	—
180	#135×C₄₇	C₂×C₄	1	8	yes	complemented
181	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
182	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
183	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
184	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
185	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
186	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
187	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
188	C₄×D₄×C₄₇	—	2	2	no	—
189	C₄×D₄×C₄₇	—	2	2	no	—
190	C₄×D₄×C₄₇	C₂³	1	2	yes	—
191	C₄×D₄×C₄₇	C₂³	1	2	yes	—
192	#117×C₄₇	—	2	2	no	—
193	#117×C₄₇	C₂³	1	2	yes	—
194	C₂×C₄²×C₄₇	—	2	2	no	—
195	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
196	#107×C₄₇	C₂³	1	1	yes	characteristic
197	#107×C₄₇	C₂³	1	1	yes	characteristic
198	#106×C₄₇	C₂³	1	2	yes	—
199	#103×C₄₇	C₂³	1	2	yes	—
200	#103×C₄₇	C₂³	1	2	yes	—
201	#102×C₄₇	C₂³	1	2	yes	—
202	#102×C₄₇	C₂³	1	2	yes	—
203	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
205	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
206	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
207	C₂³×D₄₇	—	2	2	no	—
208	C₂³×D₄₇	—	2	4	no	—
209	#41×C₄₇	—	2	4	no	—
210	#41×C₄₇	C₂²×C₄	1	8	yes	complemented
211	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
212	C₂×D₄×C₄₇	—	2	2	no	—
213	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₄₇	—	2	2	no	—
215	C₂²×C₄×C₄₇	—	2	2	no	—
216	C₂²×C₄×C₄₇	—	2	2	no	—
217	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
220	C₂×C₂²⋊D₄₇	—	2	4	no	—
221	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
222	C₂²×Dic₄₇	—	2	2	no	—
223	C₂²×Dic₄₇	—	2	4	no	—
224	#10625354	—	2	8	no	—
225	#10625354	C₂²×C₄	1	16	yes	complemented
226	D₄×D₄₇	—	2	32	no	—
227	D₄×D₄₇	—	2	8	no	—
228	D₄×D₄₇	C₂²×C₄	1	16	yes	complemented
229	#10625350	—	2	16	no	—
230	#10625350	C₂²×C₄	1	4	yes	—
231	#10625350	#41	1	4	yes	—
232	C₂×D₁₈₈	—	2	4	no	—
233	C₂×D₁₈₈	—	2	2	no	—
234	C₂×D₁₈₈	—	2	4	no	—
235	C₂×D₁₈₈	—	2	16	no	—
236	C₂×D₁₈₈	C₂²×C₄	1	8	yes	complemented
237	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
238	C₂×D₁₈₈	C₂⁴	1	4	yes	—
239	C₂×C₄×D₄₇	—	2	4	no	—
240	C₂×C₄×D₄₇	—	2	4	no	—
241	C₂×C₄×D₄₇	—	2	4	no	—
242	C₂×C₄×D₄₇	—	2	4	no	—
243	C₂×C₄×D₄₇	—	2	4	no	—
244	C₂×C₄×D₄₇	—	2	4	no	—
245	C₂×C₄×D₄₇	—	8	8	no	—
246	C₂×C₄×D₄₇	—	8	4	no	—
247	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
248	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
249	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
250	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
251	Q₁₆×C₄₇	C₂²×C₄	1	4	yes	complemented
252	SD₁₆×C₄₇	C₂²×C₄	1	8	yes	complemented
253	D₈×C₄₇	C₂²×C₄	1	4	yes	complemented
254	C₂×C₈×C₄₇	—	2	2	no	—
255	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	complemented
256	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
258	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
259	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
260	C₄⋊C₄×C₄₇	—	2	2	no	—
261	C₄⋊C₄×C₄₇	—	2	2	no	—
262	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₄₇	—	2	2	no	—
265	C₂²⋊C₄×C₄₇	—	2	2	no	—
266	C₂²⋊C₄×C₄₇	—	2	2	no	—
267	C₄²×C₄₇	—	2	2	no	—
268	C₄²×C₄₇	—	2	2	no	—
269	C₄²×C₄₇	—	2	2	no	—
270	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
273	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
274	C₂²⋊Dic₄₇	—	2	4	no	—
275	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
276	#10625336	C₂²×C₄	1	16	yes	complemented
277	#10625334	C₂²×C₄	1	16	yes	complemented
278	(C₂×D₄₇)⋊C₄	—	2	4	no	—
279	(C₂×D₄₇)⋊C₄	—	2	4	no	—
280	(C₂×D₄₇)⋊C₄	—	2	4	no	—
281	(C₂×D₄₇)⋊C₄	—	2	4	no	—
282	(C₂×D₄₇)⋊C₄	—	2	4	no	—
283	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
284	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
285	C₄⋊Dic₄₇	—	2	2	no	—
286	C₄⋊Dic₄₇	—	2	4	no	—
287	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
288	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
289	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
290	Dic₄₇⋊C₄	—	2	4	no	—
291	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
292	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
293	C₄×Dic₄₇	—	2	4	no	—
294	C₄×Dic₄₇	—	2	4	no	—
295	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
296	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
297	C₄×Dic₄₇	C₂⁴	1	2	yes	—
298	#10625329	—	2	2	no	—
299	#10625329	C₂²×C₄	1	4	yes	complemented
300	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
301	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
302	D₃₇₆	C₂²×C₄	1	8	yes	complemented
303	D₃₇₆	C₂²×C₄	1	8	yes	complemented
304	#10625324	—	2	4	no	—
305	#10625324	C₂²×C₄	1	8	yes	complemented
306	C₈×D₄₇	—	2	4	no	—
307	C₈×D₄₇	C₂²×C₄	1	8	yes	complemented
308	C₂³×C₄₇	—	2	2	no	—
309	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
310	C₂²×D₄₇	—	2	4	no	—
311	C₂²×D₄₇	—	2	8	no	—
312	C₂²×D₄₇	—	2	16	no	—
313	C₂²×D₄₇	—	8	4	no	—
314	C₂²×D₄₇	—	8	4	no	—
315	C₂²×D₄₇	—	8	2	no	—
316	C₂²×D₄₇	—	8	2	no	—
317	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
318	Q₈×C₄₇	—	2	2	no	—
319	Q₈×C₄₇	C₂³×C₄	1	4	yes	—
320	D₄×C₄₇	—	2	8	no	—
321	D₄×C₄₇	—	2	2	no	—
322	D₄×C₄₇	C₂³×C₄	1	4	yes	—
323	C₂×C₄×C₄₇	—	2	2	no	—
324	C₂×C₄×C₄₇	—	2	8	no	—
325	C₂×C₄×C₄₇	—	2	2	no	—
326	C₂×C₄×C₄₇	—	2	2	no	—
327	C₂×C₄×C₄₇	—	2	2	no	—
328	C₂×C₄×C₄₇	—	4	1	no	—
329	C₂×C₄×C₄₇	—	4	4	no	—
330	C₂×C₄×C₄₇	—	8	2	no	—
331	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
332	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
338	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
339	C₂²⋊D₄₇	—	2	16	no	—
340	C₂²⋊D₄₇	C₄×D₄	1	8	yes	—
341	C₂×Dic₄₇	—	2	4	no	—
342	C₂×Dic₄₇	—	8	4	no	—
343	C₂×Dic₄₇	—	8	2	no	—
344	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
345	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
346	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
347	D₁₈₈	—	2	16	no	—
348	D₁₈₈	—	2	8	no	—
349	D₁₈₈	—	2	4	no	—
350	D₁₈₈	C₄×D₄	1	4	yes	—
351	D₁₈₈	C₂³×C₄	1	8	yes	—
352	C₄×D₄₇	—	2	4	no	—
353	C₄×D₄₇	—	2	16	no	—
354	C₄×D₄₇	—	4	2	no	—
355	C₄×D₄₇	—	4	8	no	—
356	C₄×D₄₇	—	8	4	no	—
357	C₄×D₄₇	—	8	4	no	—
358	C₄×D₄₇	—	8	4	no	—
359	C₄×D₄₇	—	8	4	no	—
360	C₄×D₄₇	C₂³×C₄	1	4	yes	—
361	C₄×D₄₇	C₂×#41	1	4	yes	—
362	Dic₉₄	C₄×D₄	1	4	yes	—
363	C₈×C₄₇	—	2	1	no	—
364	C₈×C₄₇	—	2	1	no	—
365	C₈×C₄₇	C₂³×C₄	1	2	yes	—
366	C₈×C₄₇	C₂³×C₄	1	2	yes	—
367	C₄₇⋊C₈	—	2	2	no	—
368	C₄₇⋊C₈	C₂³×C₄	1	4	yes	—
369	C₄×#576	—	47	1	no	maximal, Sylow
370	C₂²×C₄₇	—	2	1	no	—
371	C₂²×C₄₇	—	2	1	no	—
372	C₂²×C₄₇	—	2	4	no	—
373	C₂²×C₄₇	—	4	2	no	—
374	C₂²×C₄₇	—	4	2	no	—
375	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
376	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
377	C₂×D₄₇	—	2	2	no	—
378	C₂×D₄₇	—	2	2	no	—
379	C₂×D₄₇	—	2	8	no	—
380	C₂×D₄₇	—	4	4	no	—
381	C₂×D₄₇	—	4	4	no	—
382	C₂×D₄₇	—	8	16	no	—
383	C₂×D₄₇	—	8	8	no	—
384	C₂×D₄₇	C₂×C₄×D₄	1	4	yes	—
385	C₄×C₄₇	—	2	1	no	—
386	C₄×C₄₇	—	2	1	no	—
387	C₄×C₄₇	—	2	4	no	—
388	C₄×C₄₇	—	2	1	no	—
389	C₄×C₄₇	—	4	2	no	—
390	C₄×C₄₇	—	4	2	no	—
391	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
392	C₄×C₄₇	#576	1	2	yes	complemented
393	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
394	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
395	Dic₄₇	—	2	2	no	—
396	Dic₄₇	—	2	2	no	—
397	Dic₄₇	—	4	4	no	—
398	Dic₄₇	C₂×C₄×D₄	1	4	yes	—
399	C₂×#576	—	47	1	no	—
400	C₄×H(5,𝔽₂)	—	47	2	no	—
401	#2951	—	47	2	no	—
402	#2951	—	47	1	no	—
403	#2948	—	47	2	no	—
404	#2948	—	47	1	no	—
405	#2946	—	47	4	no	—
406	#2946	—	47	2	no	—
407	C₄×AGL(1,ℤ/8)	—	47	4	no	—
408	C₄×AGL(1,ℤ/8)	—	47	2	no	—
409	C₄×#135	—	47	2	no	—
410	C₄×#135	D₄₇	1	1	yes	characteristic, complemented
411	C₂×C₄×D₈	—	47	2	no	—
412	C₂×C₄×D₈	—	47	1	no	—
413	#2913	—	47	1	no	—
414	#2897	—	47	2	no	—
415	C₄×#131	—	47	1	no	—
416	C₂×C₄₇	—	2	2	no	—
417	C₂×C₄₇	—	4	4	no	—
418	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
419	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
420	C₂×C₄₇	#3584	1	1	yes	characteristic
421	D₄₇	—	2	4	no	—
422	D₄₇	—	4	8	no	—
423	C₂×H(5,𝔽₂)	—	47	2	no	—
424	#576	—	47	16	no	—
425	C₂×AGL(1,ℤ/8)	—	47	2	no	—
426	C₂×AGL(1,ℤ/8)	—	47	4	no	—
427	C₂×#135	—	47	2	no	—
428	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
429	C₂²×D₈	—	47	2	no	—
430	C₂²×D₈	—	47	1	no	—
431	C₂×#131	—	47	1	no	—
432	C₂×#131	—	47	1	no	—
433	#520	—	47	2	no	—
434	#520	—	47	2	no	—
435	#520	—	47	4	no	—
436	#520	—	94	2	no	—
437	#518	—	47	4	no	—
438	#518	—	47	2	no	—
439	#518	—	94	2	no	—
440	#518	—	94	4	no	—
441	C₄×#41	—	47	1	no	—
442	C₄×#41	—	47	4	no	—
443	C₄×#41	—	94	2	no	—
444	C₄×#41	C₂×D₄₇	1	2	yes	complemented
445	C₂×C₄×D₄	—	47	4	no	—
446	C₂×C₄×D₄	—	47	2	no	—
447	C₂×C₄×D₄	—	94	2	no	—
448	C₂×C₄×D₄	—	94	4	no	—
449	#442	—	47	4	no	—
450	#442	—	47	4	no	—
451	#442	—	47	4	no	—
452	#440	—	47	4	no	—
453	#440	—	47	4	no	—
454	#440	—	47	4	no	—
455	C₄×Q₁₆	—	47	2	no	—
456	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
457	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
458	C₄×SD₁₆	—	47	4	no	—
459	C₄×SD₁₆	—	47	4	no	—
460	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
461	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
462	C₄×D₈	—	47	2	no	—
463	C₄×D₈	—	47	4	no	—
464	C₄×D₈	—	47	2	no	—
465	C₄×D₈	—	47	2	no	—
466	C₄×D₈	—	47	4	no	—
467	C₄×D₈	—	47	2	no	—
468	C₄×D₈	—	47	2	no	—
469	C₄×D₈	—	47	2	no	—
470	C₄×D₈	—	47	2	no	—
471	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
472	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
473	#428	—	47	2	no	—
474	#428	—	47	4	no	—
475	#427	—	47	2	no	—
476	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
477	C₂×#107	—	47	1	no	—
478	C₂×#107	—	47	2	no	—
479	#418	—	47	2	no	—
480	#418	—	47	4	no	—
481	#417	—	47	2	no	—
482	#417	—	47	4	no	—
483	#416	—	47	4	no	—
484	#416	C₂×D₄₇	1	2	yes	complemented
485	C₂×#102	—	47	2	no	—
486	C₂×#102	—	47	4	no	—
487	#405	—	47	1	no	—
488	#405	—	47	1	no	—
489	#405	—	47	2	no	—
490	#405	—	47	2	no	—
491	C₄×M₁₆	—	47	1	no	—
492	C₄×M₁₆	—	47	2	no	—
493	C₂×C₄×C₈	—	47	2	no	—
494	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
495	C₄₇	C₄×#576	1	1	yes	characteristic, complemented, Sylow
496	H(5,𝔽₂)	—	47	16	no	—
497	H(5,𝔽₂)	—	94	8	no	—
498	C₂×#41	—	47	1	no	—
499	C₂×#41	—	47	4	no	—
500	C₂×#41	—	94	2	no	—
501	C₂×#41	C₂²×D₄₇	1	2	yes	—
502	C₂²×D₄	—	47	4	no	—
503	C₂²×D₄	—	47	2	no	—
504	C₂²×D₄	—	94	2	no	—
505	C₂²×D₄	—	94	4	no	—
506	C₂³×C₄	—	94	4	no	—
507	C₂³×C₄	—	94	2	no	—
508	AGL(1,ℤ/8)	—	47	16	no	—
509	AGL(1,ℤ/8)	—	47	32	no	—
510	#135	—	47	16	no	—
511	#135	C₄×D₄₇	1	8	yes	complemented
512	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
513	C₂×SD₁₆	—	47	4	no	—
514	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
515	C₂×D₈	—	47	4	no	—
516	C₂×D₈	—	47	16	no	—
517	C₂×D₈	—	47	8	no	—
518	C₂×D₈	—	47	2	no	—
519	C₂×D₈	—	47	2	no	—
520	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
521	#131	—	47	8	no	—
522	#131	—	94	4	no	—
523	C₂×M₁₆	—	47	1	no	—
524	C₂×M₁₆	—	47	1	no	—
525	C₂×M₁₆	—	47	2	no	—
526	C₂×M₁₆	—	47	2	no	—
527	C₂²×C₈	—	47	2	no	—
528	C₂²×C₈	—	47	2	no	—
529	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
530	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
531	C₄×Q₈	—	47	1	no	—
532	C₄×Q₈	—	47	1	no	—
533	C₄×Q₈	—	47	4	no	—
534	C₄×Q₈	—	94	2	no	—
535	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
536	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	47	2	no	—
540	C₄×D₄	—	47	2	no	—
541	C₄×D₄	—	47	4	no	—
542	C₄×D₄	—	47	4	no	—
543	C₄×D₄	—	47	4	no	—
544	C₄×D₄	—	47	1	no	—
545	C₄×D₄	—	47	1	no	—
546	C₄×D₄	—	47	4	no	—
547	C₄×D₄	—	47	4	no	—
548	C₄×D₄	—	94	4	no	—
549	C₄×D₄	—	94	2	no	—
550	C₄×D₄	—	94	2	no	—
551	C₄×D₄	—	94	4	no	—
552	C₄×D₄	—	94	2	no	—
553	C₄×D₄	—	94	4	no	—
554	C₄×D₄	—	94	4	no	—
555	C₄×D₄	—	94	4	no	—
556	C₄×D₄	—	94	4	no	—
557	C₄×D₄	—	94	4	no	—
558	C₄×D₄	—	94	4	no	—
559	C₄×D₄	—	94	4	no	—
560	C₄×D₄	—	94	4	no	—
561	C₄×D₄	—	94	2	no	—
562	C₄×D₄	—	94	2	no	—
563	C₄×D₄	C₂²×D₄₇	1	2	yes	—
564	C₄×D₄	C₂²×D₄₇	1	2	yes	—
565	#117	—	2	2	no	—
566	#117	—	47	1	no	—
567	#117	—	47	2	no	—
568	#117	—	47	4	no	—
569	#117	—	94	4	no	—
570	#117	—	94	4	no	—
571	#117	—	94	2	no	—
572	#117	C₂²×D₄₇	1	2	yes	—
573	C₂×C₄⋊C₄	—	47	2	no	—
574	C₂×C₄⋊C₄	—	47	4	no	—
575	C₂×C₄⋊C₄	—	94	4	no	—
576	C₂×C₄⋊C₄	—	94	2	no	—
577	C₂×C₂²⋊C₄	—	94	4	no	—
578	C₂×C₂²⋊C₄	—	94	4	no	—
579	C₂×C₂²⋊C₄	—	94	4	no	—
580	C₂×C₂²⋊C₄	—	94	4	no	—
581	C₂×C₂²⋊C₄	—	94	2	no	—
582	C₂×C₄²	—	2	2	no	—
583	C₂×C₄²	—	47	2	no	—
584	C₂×C₄²	—	94	4	no	—
585	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
586	#107	—	47	2	no	—
587	#107	—	47	2	no	—
588	#107	—	47	4	no	—
589	#107	C₂²×D₄₇	1	1	yes	characteristic
590	#107	C₂²×D₄₇	1	1	yes	characteristic
591	#106	—	47	4	no	—
592	#106	C₂²×D₄₇	1	2	yes	—
593	#103	—	47	4	no	—
594	#103	C₂²×D₄₇	1	2	yes	—
595	#103	C₂²×D₄₇	1	2	yes	—
596	#102	—	47	4	no	—
597	#102	—	47	4	no	—
598	#102	—	47	4	no	—
599	#102	—	47	4	no	—
600	#102	—	47	4	no	—
601	#102	C₂²×D₄₇	1	2	yes	—
602	#102	C₂²×D₄₇	1	2	yes	—
603	#97	—	47	2	no	—
604	#97	—	47	2	no	—
605	#97	—	47	2	no	—
606	C₄×C₈	—	47	2	no	—
607	C₄×C₈	—	47	2	no	—
608	C₄×C₈	—	47	2	no	—
609	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
610	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
611	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
612	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
613	C₂⁴	—	94	4	no	—
614	C₂⁴	—	94	2	no	—
615	#41	—	2	4	no	—
616	#41	—	47	4	no	—
617	#41	—	47	4	no	—
618	#41	—	47	16	no	—
619	#41	—	94	16	no	—
620	#41	—	94	8	no	—
621	#41	C₂×C₄×D₄₇	1	8	yes	complemented
622	C₂×Q₈	—	47	1	no	—
623	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	47	2	no	—
626	C₂×D₄	—	47	16	no	—
627	C₂×D₄	—	47	8	no	—
628	C₂×D₄	—	47	1	no	—
629	C₂×D₄	—	47	4	no	—
630	C₂×D₄	—	94	16	no	—
631	C₂×D₄	—	94	4	no	—
632	C₂×D₄	—	94	8	no	—
633	C₂×D₄	—	94	4	no	—
634	C₂×D₄	—	94	32	no	—
635	C₂×D₄	—	94	2	no	—
636	C₂×D₄	—	94	4	no	—
637	C₂×D₄	C₂³×D₄₇	1	2	yes	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	47	2	no	—
642	C₂²×C₄	—	47	2	no	—
643	C₂²×C₄	—	47	2	no	—
644	C₂²×C₄	—	94	4	no	—
645	C₂²×C₄	—	94	4	no	—
646	C₂²×C₄	—	94	4	no	—
647	C₂²×C₄	—	94	4	no	—
648	C₂²×C₄	—	94	4	no	—
649	C₂²×C₄	—	94	2	no	—
650	C₂²×C₄	—	94	4	no	—
651	C₂²×C₄	—	94	4	no	—
652	C₂²×C₄	—	376	4	no	—
653	C₂²×C₄	—	376	8	no	—
654	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
655	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
656	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
657	Q₁₆	C₂×C₄×D₄₇	1	4	yes	complemented
658	SD₁₆	—	47	16	no	—
659	SD₁₆	C₂×C₄×D₄₇	1	8	yes	complemented
660	D₈	—	47	16	no	—
661	D₈	—	47	8	no	—
662	D₈	—	47	8	no	—
663	D₈	C₂×C₄×D₄₇	1	4	yes	complemented
664	M₁₆	—	47	4	no	—
665	M₁₆	—	47	8	no	—
666	M₁₆	—	94	4	no	—
667	M₁₆	—	94	2	no	—
668	C₂×C₈	—	2	2	no	—
669	C₂×C₈	—	47	2	no	—
670	C₂×C₈	—	47	8	no	—
671	C₂×C₈	—	47	2	no	—
672	C₂×C₈	—	94	4	no	—
673	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	complemented
674	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
675	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
676	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
677	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	47	2	no	—
681	C₄⋊C₄	—	47	2	no	—
682	C₄⋊C₄	—	47	1	no	—
683	C₄⋊C₄	—	47	1	no	—
684	C₄⋊C₄	—	47	4	no	—
685	C₄⋊C₄	—	94	4	no	—
686	C₄⋊C₄	—	94	4	no	—
687	C₄⋊C₄	—	94	2	no	—
688	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
689	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	47	2	no	—
694	C₂²⋊C₄	—	47	2	no	—
695	C₂²⋊C₄	—	47	2	no	—
696	C₂²⋊C₄	—	94	4	no	—
697	C₂²⋊C₄	—	94	4	no	—
698	C₂²⋊C₄	—	94	4	no	—
699	C₂²⋊C₄	—	94	4	no	—
700	C₂²⋊C₄	—	94	4	no	—
701	C₂²⋊C₄	—	94	4	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	47	2	no	—
706	C₄²	—	47	2	no	—
707	C₄²	—	47	2	no	—
708	C₄²	—	94	4	no	—
709	C₄²	—	94	4	no	—
710	C₄²	D₄×D₄₇	1	1	yes	characteristic
711	C₄²	D₄×D₄₇	1	1	yes	characteristic
712	C₄²	C₂³×D₄₇	1	1	yes	characteristic
713	C₄²	C₂³×D₄₇	1	1	yes	characteristic
714	C₂³	—	2	2	no	—
715	C₂³	—	47	2	no	—
716	C₂³	—	94	16	no	—
717	C₂³	—	94	8	no	—
718	C₂³	—	94	4	no	—
719	C₂³	—	376	2	no	—
720	C₂³	—	376	2	no	—
721	C₂³	—	376	4	no	—
722	C₂³	—	376	4	no	—
723	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
724	Q₈	—	2	2	no	—
725	Q₈	—	47	4	no	—
726	Q₈	C₂²×C₄×D₄₇	1	4	yes	—
727	D₄	—	2	8	no	—
728	D₄	—	2	2	no	—
729	D₄	—	47	8	no	—
730	D₄	—	47	4	no	—
731	D₄	—	47	8	no	—
732	D₄	—	94	16	no	—
733	D₄	—	94	16	no	—
734	D₄	—	94	8	no	—
735	D₄	—	94	4	no	—
736	D₄	C₂²×C₄×D₄₇	1	4	yes	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	8	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	4	no	—
744	C₂×C₄	—	8	2	no	—
745	C₂×C₄	—	47	2	no	—
746	C₂×C₄	—	47	4	no	—
747	C₂×C₄	—	47	4	no	—
748	C₂×C₄	—	47	2	no	—
749	C₂×C₄	—	47	2	no	—
750	C₂×C₄	—	94	16	no	—
751	C₂×C₄	—	94	4	no	—
752	C₂×C₄	—	94	4	no	—
753	C₂×C₄	—	376	4	no	—
754	C₂×C₄	—	376	4	no	—
755	C₂×C₄	—	376	4	no	—
756	C₂×C₄	—	376	4	no	—
757	C₂×C₄	—	376	4	no	—
758	C₂×C₄	—	376	2	no	—
759	C₂×C₄	—	188	2	no	—
760	C₂×C₄	—	188	8	no	—
761	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
762	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
763	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
764	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
765	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
766	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
767	C₂×C₄	#41×D₄₇	1	2	yes	—
768	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
769	C₈	—	2	1	no	—
770	C₈	—	2	1	no	—
771	C₈	—	47	4	no	—
772	C₈	—	94	2	no	—
773	C₈	C₂²×C₄×D₄₇	1	2	yes	—
774	C₈	C₂²×C₄×D₄₇	1	2	yes	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	47	4	no	—
781	C₂²	—	94	2	no	—
782	C₂²	—	94	2	no	—
783	C₂²	—	94	8	no	—
784	C₂²	—	376	8	no	—
785	C₂²	—	376	16	no	—
786	C₂²	—	188	4	no	—
787	C₂²	—	188	4	no	—
788	C₂²	C₄×D₄×D₄₇	1	2	yes	—
789	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
790	C₄	—	2	4	no	—
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	47	4	no	—
797	C₄	—	94	2	no	—
798	C₄	—	94	2	no	—
799	C₄	—	188	4	no	—
800	C₄	C₄×D₄×D₄₇	1	2	yes	—
801	C₄	#15689925	1	2	yes	direct product factor
802	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
803	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
804	C₂	—	2	2	no	—
805	C₂	—	4	4	no	—
806	C₂	—	94	4	no	—
807	C₂	—	188	8	no	—
808	C₂	C₂×C₄×D₄×D₄₇	1	1	yes	characteristic
809	C₂	C₂×#15689925	1	1	yes	characteristic
810	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄×#135×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂×#15689925	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₄×#135	D₄₇
hypocenter	C₄₇	C₄×#576
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
2. C₄×#13094070	C₂	semidirect
3. #20252264	C₂	semidirect
4. #20252263	C₂	semidirect
5. #20252239	C₂	semidirect
6. #20252235	C₂	semidirect
7. #20252223	C₂	semidirect
8. #20252215	C₂	semidirect
9. C₄×#13094051	C₂	semidirect
10. C₄×#13094049	C₂	semidirect
11. C₄×#13094047	C₂	semidirect
12. C₂×C₄×D₃₇₆	C₂	semidirect
13. C₄×D₈×D₄₇	C₂	semidirect
14. #20251985	C₂	semidirect
15. #20251910	C₂	semidirect
16. C₄×#13094030	C₂	semidirect
17. C₄×#135×C₄₇	C₂	semidirect
19. #15689925	C₄	direct (N × H)
27. #15689606	C₂²	semidirect
28. #15689605	C₂²	semidirect
32. #15689597	C₂²	semidirect
34. #15689595	C₂²	semidirect
35. C₄×#10625354	C₂²	semidirect
39. C₂×C₄×D₁₈₈	C₂²	semidirect
41. C₄×D₄×D₄₇	C₂²	semidirect
42. #15689234	C₂²	semidirect
43. #15689233	C₂²	semidirect
44. #15689232	C₂²	semidirect
45. #15689226	C₂²	semidirect
46. #15689224	C₂²	semidirect
47. #15689221	C₂²	semidirect
48. Q₁₆×Dic₄₇	C₂²	semidirect
49. C₄×#10625336	C₂²	semidirect
50. #15689208	C₂²	semidirect
51. C₄×D₃₇₆	C₂²	semidirect
52. C₄×D₃₇₆	C₂²	semidirect
53. C₄×D₃₇₆	C₂²	semidirect
54. C₄×D₃₇₆	C₂²	semidirect
55. D₈×Dic₄₇	C₂²	semidirect
56. #15689205	C₂²	semidirect
57. #15689205	C₂²	semidirect
58. C₄×#10625334	C₂²	semidirect
59. #15689203	C₂²	semidirect
60. #15689166	C₂²	semidirect
61. #15689162	C₂²	semidirect
62. #15689160	C₂²	semidirect
63. C₂×#13093958	C₂²	semidirect
64. #107×D₄₇	C₂²	semidirect
65. #15689127	C₂²	semidirect
66. #15689126	C₂²	semidirect
67. #15689124	C₂²	semidirect
68. #15689123	C₂²	semidirect
69. #15689118	C₂²	semidirect
70. C₂×#13093946	C₂²	semidirect
71. #102×D₄₇	C₂²	semidirect
72. #15689078	C₂²	semidirect
73. #15689078	C₂²	semidirect
74. #15689077	C₂²	semidirect
75. #15689077	C₂²	semidirect
76. C₄×#10625329	C₂²	semidirect
77. C₄×#10625324	C₂²	semidirect
78. C₄×C₈×D₄₇	C₂²	semidirect
80. C₄×#41×C₄₇	C₂²	semidirect
81. C₄×Q₁₆×C₄₇	C₂²	semidirect
82. C₄×Q₁₆×C₄₇	C₂²	semidirect
83. C₄×SD₁₆×C₄₇	C₂²	semidirect
84. C₄×SD₁₆×C₄₇	C₂²	semidirect
85. C₄×D₈×C₄₇	C₂²	semidirect
86. C₄×D₈×C₄₇	C₂²	semidirect
87. C₄₇×#427	C₂²	semidirect
88. C₄₇×#416	C₂²	semidirect
89. C₂×C₄×C₈×C₄₇	C₂²	semidirect
91. #13094070	C₂×C₄	semidirect
101. #13094051	C₂×C₄	semidirect
102. #13094049	C₂×C₄	semidirect
103. #13094047	C₂×C₄	semidirect
105. C₂×D₃₇₆	C₂×C₄	semidirect
109. D₈×D₄₇	C₂×C₄	semidirect
111. #13094030	C₂×C₄	semidirect
180. #135×C₄₇	C₂×C₄	semidirect
210. #41×C₄₇	C₂²×C₄	semidirect
225. #10625354	C₂²×C₄	semidirect
228. D₄×D₄₇	C₂²×C₄	semidirect
236. C₂×D₁₈₈	C₂²×C₄	semidirect
251. Q₁₆×C₄₇	C₂²×C₄	semidirect
252. SD₁₆×C₄₇	C₂²×C₄	semidirect
253. D₈×C₄₇	C₂²×C₄	semidirect
255. C₂×C₈×C₄₇	C₂²×C₄	semidirect
276. #10625336	C₂²×C₄	semidirect
277. #10625334	C₂²×C₄	semidirect
299. #10625329	C₂²×C₄	semidirect
302. D₃₇₆	C₂²×C₄	semidirect
303. D₃₇₆	C₂²×C₄	semidirect
305. #10625324	C₂²×C₄	semidirect
307. C₈×D₄₇	C₂²×C₄	semidirect
392. C₄×C₄₇	#576	semidirect
410. C₄×#135	D₄₇	semidirect
444. C₄×#41	C₂×D₄₇	semidirect
456. C₄×Q₁₆	C₂×D₄₇	semidirect
457. C₄×Q₁₆	C₂×D₄₇	semidirect
460. C₄×SD₁₆	C₂×D₄₇	semidirect
461. C₄×SD₁₆	C₂×D₄₇	semidirect
471. C₄×D₈	C₂×D₄₇	semidirect
472. C₄×D₈	C₂×D₄₇	semidirect
476. #427	C₂×D₄₇	semidirect
484. #416	C₂×D₄₇	semidirect
494. C₂×C₄×C₈	C₂×D₄₇	semidirect
495. C₄₇	C₄×#576	semidirect
511. #135	C₄×D₄₇	semidirect
621. #41	C₂×C₄×D₄₇	semidirect
657. Q₁₆	C₂×C₄×D₄₇	semidirect
659. SD₁₆	C₂×C₄×D₄₇	semidirect
663. D₈	C₂×C₄×D₄₇	semidirect
673. C₂×C₈	C₂×C₄×D₄₇	semidirect
801. C₄	#15689925	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689925	2
C₄×#13094070	2
#20252264	2
#20252263	2
#20252239	2
#20252235	2
#20252223	2
#20252215	2
C₄×#13094051	2
C₄×#13094049	2
C₄×#13094047	2
C₂×C₄×D₃₇₆	2
C₄×D₈×D₄₇	2
#20251985	2
#20251910	2
C₄×#13094030	2
C₄×#135×C₄₇	2
C₄×#576	47

Subgroups — C4×#15689925 #27080492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689925 #27080492