Subgroups — #26121679

Order 12032.

1168 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689889	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689096	C₂	1	1	yes	maximal, characteristic
3	#20251832	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688893	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243126	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625350	C₂²	1	1	yes	characteristic
9	#15689889	—	2	2	no	—
10	#15689889	—	2	2	no	—
11	#15689889	—	2	2	no	—
12	#15689889	C₄	1	4	yes	complemented
13	C₂×#13094032	—	2	2	no	—
14	C₂×#13094030	—	2	2	no	—
15	C₂²×#10625329	C₂²	1	1	yes	characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×D₄₇	—	2	2	no	—
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	#15689096	—	2	2	no	—
20	#15689096	—	2	2	no	—
21	C₂×#13093938	C₄	1	4	yes	—
22	#15689091	C₄	1	4	yes	complemented
23	#15689089	—	2	2	no	—
24	#15689086	—	2	2	no	—
25	#15688895	—	2	2	no	—
26	#15688893	—	2	2	no	—
27	#15688891	—	2	2	no	—
28	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#343	—	2	2	no	—
32	C₂×#10625350	—	2	1	no	—
33	C₂×#10625350	—	2	1	no	—
34	C₂×#10625350	—	2	1	no	—
35	C₂×#10625350	—	2	1	no	—
36	C₂×#10625350	—	2	1	no	—
37	C₂×#10625350	—	2	1	no	—
38	C₂×#10625350	—	2	1	no	—
39	C₂×#10625350	—	2	1	no	—
40	C₂×#10625350	C₂×C₄	1	2	yes	—
41	C₂×#10625350	C₂×C₄	1	2	yes	—
42	C₂×#10625350	D₄	1	2	yes	—
43	C₂×#10625350	D₄	1	2	yes	—
44	C₂²×Dic₉₄	Q₈	1	1	yes	characteristic
45	C₂²×D₁₈₈	Q₈	1	1	yes	characteristic
46	C₂²×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
47	C₂²×C₄×D₄₇	D₄	1	2	yes	—
48	#13094032	—	2	8	no	—
49	#13094032	—	2	8	no	—
50	#13094030	—	2	8	no	—
51	#13094030	—	2	8	no	—
52	C₂×#10625329	—	2	1	no	—
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂×#10625329	—	2	1	no	—
57	C₂×#10625329	—	2	1	no	—
58	C₂×#10625329	—	2	1	no	—
59	C₂×#10625329	—	2	1	no	—
60	C₂×#10625329	—	2	1	no	—
61	C₂×#10625329	C₂×C₄	1	2	yes	—
62	C₂×#10625329	D₄	1	2	yes	—
63	C₂×#10625329	D₄	1	2	yes	—
64	C₂×#10625324	—	2	4	no	—
65	M₁₆×D₄₇	—	2	8	no	—
66	M₁₆×D₄₇	—	2	8	no	—
67	C₂²×C₄₇⋊C₈	—	2	1	no	—
68	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
69	C₂×C₈×D₄₇	—	2	4	no	—
70	#13093983	—	2	1	no	—
71	#13093983	—	2	1	no	—
72	#13093983	—	2	1	no	—
73	#13093983	—	2	1	no	—
74	C₂×C₄⋊Dic₄₇	—	2	1	no	—
75	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₄×Dic₄₇	—	2	1	no	—
77	#13093938	—	2	8	no	—
78	(C₂×D₄₇)⋊C₈	—	2	8	no	—
79	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₄₇	—	2	1	no	—
81	C₂×M₁₆×C₄₇	—	2	1	no	—
82	C₂×M₁₆×C₄₇	—	2	1	no	—
83	C₂×M₁₆×C₄₇	—	2	1	no	—
84	C₂×M₁₆×C₄₇	—	2	1	no	—
85	C₂×M₁₆×C₄₇	—	2	1	no	—
86	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
89	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
90	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
91	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
92	C₂²×C₈×C₄₇	—	2	1	no	—
93	C₂²×C₈×C₄₇	—	2	1	no	—
94	#117×C₄₇	—	2	1	no	—
95	#117×C₄₇	—	2	1	no	—
96	#117×C₄₇	—	2	1	no	—
97	#117×C₄₇	—	2	1	no	—
98	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
100	C₂×C₄²×C₄₇	—	2	1	no	—
101	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂³×D₄₇	C₄⋊C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
118	C₂×C₂²⋊D₄₇	—	2	2	no	—
119	C₂×C₂²⋊D₄₇	—	2	2	no	—
120	C₂×C₂²⋊D₄₇	—	2	2	no	—
121	C₂×C₂²⋊D₄₇	—	2	2	no	—
122	C₂×C₂²⋊D₄₇	C₄²	1	4	yes	—
123	C₂×C₂²⋊D₄₇	C₂²⋊C₄	1	4	yes	—
124	C₂²×Dic₄₇	—	2	2	no	—
125	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
126	#10625350	—	2	2	no	—
127	#10625350	—	2	2	no	—
128	#10625350	—	2	2	no	—
129	#10625350	—	2	2	no	—
130	#10625350	—	2	2	no	—
131	#10625350	—	2	2	no	—
132	#10625350	—	2	2	no	—
133	#10625350	—	2	2	no	—
134	#10625350	—	2	2	no	—
135	#10625350	—	2	2	no	—
136	#10625350	—	2	2	no	—
137	#10625350	—	2	2	no	—
138	#10625350	—	2	2	no	—
139	#10625350	—	2	2	no	—
140	#10625350	—	2	2	no	—
141	#10625350	—	2	2	no	—
142	C₂×D₁₈₈	—	2	1	no	—
143	C₂×D₁₈₈	—	2	1	no	—
144	C₂×D₁₈₈	—	2	1	no	—
145	C₂×D₁₈₈	—	2	1	no	—
146	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
147	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
148	C₂×C₄×D₄₇	—	2	2	no	—
149	C₂×C₄×D₄₇	—	2	2	no	—
150	C₂×C₄×D₄₇	—	2	2	no	—
151	C₂×C₄×D₄₇	—	2	2	no	—
152	C₂×C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
153	C₂×C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
154	C₂×Dic₉₄	—	2	1	no	—
155	C₂×Dic₉₄	—	2	1	no	—
156	C₂×Dic₉₄	—	2	1	no	—
157	C₂×Dic₉₄	—	2	1	no	—
158	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
159	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
160	M₁₆×C₄₇	—	2	2	no	—
161	M₁₆×C₄₇	—	2	2	no	—
162	M₁₆×C₄₇	—	2	2	no	—
163	M₁₆×C₄₇	—	2	2	no	—
164	M₁₆×C₄₇	—	2	2	no	—
165	M₁₆×C₄₇	—	4	1	no	—
166	M₁₆×C₄₇	—	4	1	no	—
167	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
168	C₂×C₈×C₄₇	—	2	2	no	—
169	C₂×C₈×C₄₇	—	2	2	no	—
170	C₂×C₈×C₄₇	—	2	2	no	—
171	C₂×C₈×C₄₇	—	2	2	no	—
172	C₂×C₈×C₄₇	—	4	1	no	—
173	C₂×C₈×C₄₇	—	4	1	no	—
174	C₄⋊C₄×C₄₇	—	4	1	no	—
175	C₄⋊C₄×C₄₇	—	4	1	no	—
176	C₂²⋊C₄×C₄₇	—	2	2	no	—
177	C₂²⋊C₄×C₄₇	—	2	2	no	—
178	C₄²×C₄₇	—	4	1	no	—
179	C₄²×C₄₇	—	4	1	no	—
180	C₂²⋊Dic₄₇	—	2	2	no	—
181	C₂²⋊Dic₄₇	—	2	2	no	—
182	C₄⋊Dic₄₇	—	4	1	no	—
183	C₄⋊Dic₄₇	—	4	1	no	—
184	C₄×Dic₄₇	—	4	1	no	—
185	C₄×Dic₄₇	—	4	1	no	—
186	#10625329	—	2	2	no	—
187	#10625329	—	2	2	no	—
188	#10625329	—	2	2	no	—
189	#10625329	—	4	1	no	—
190	#10625329	—	4	1	no	—
191	#10625329	—	4	1	no	—
192	#10625329	—	4	1	no	—
193	#10625329	C₂²⋊C₄	1	4	yes	—
194	C₂×C₄₇⋊C₈	—	2	2	no	—
195	C₂×C₄₇⋊C₈	—	2	2	no	—
196	C₂×C₄₇⋊C₈	—	2	2	no	—
197	C₂×C₄₇⋊C₈	—	2	2	no	—
198	C₂×C₄₇⋊C₈	—	2	2	no	—
199	C₂×C₄₇⋊C₈	—	2	2	no	—
200	#10625324	—	2	16	no	—
201	C₈×D₄₇	—	2	16	no	—
202	C₂³×C₄₇	—	8	1	no	—
203	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
204	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
207	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
208	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
209	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
210	C₂²×D₄₇	—	2	2	no	—
211	C₂²×D₄₇	—	2	2	no	—
212	C₂²×D₄₇	—	8	2	no	—
213	C₂²×D₄₇	#95	1	4	yes	—
214	C₂×C₄×C₄₇	—	4	2	no	—
215	C₂×C₄×C₄₇	—	8	2	no	—
216	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
223	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
229	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
230	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
232	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
243	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
244	C₂²⋊D₄₇	—	2	4	no	—
245	C₂²⋊D₄₇	—	2	4	no	—
246	C₂²⋊D₄₇	—	2	4	no	—
247	C₂²⋊D₄₇	—	2	4	no	—
248	C₂×Dic₄₇	—	2	2	no	—
249	C₂×Dic₄₇	—	2	2	no	—
250	C₂×Dic₄₇	—	4	2	no	—
251	C₂×Dic₄₇	—	8	2	no	—
252	C₂×Dic₄₇	#95	1	4	yes	—
253	D₁₈₈	—	2	2	no	—
254	D₁₈₈	—	2	2	no	—
255	D₁₈₈	—	2	2	no	—
256	D₁₈₈	—	2	2	no	—
257	C₄×D₄₇	—	2	4	no	—
258	C₄×D₄₇	—	2	4	no	—
259	C₄×D₄₇	—	2	4	no	—
260	C₄×D₄₇	—	2	4	no	—
261	Dic₉₄	—	2	2	no	—
262	Dic₉₄	—	2	2	no	—
263	Dic₉₄	—	2	2	no	—
264	Dic₉₄	—	2	2	no	—
265	C₈×C₄₇	—	2	4	no	—
266	C₈×C₄₇	—	4	2	no	—
267	C₄₇⋊C₈	—	2	4	no	—
268	C₄₇⋊C₈	—	4	2	no	—
269	#10757	—	47	1	no	maximal, Sylow
270	C₂²×C₄₇	—	4	1	no	—
271	C₂²×C₄₇	—	4	1	no	—
272	C₂²×C₄₇	—	4	1	no	—
273	C₂²×C₄₇	—	4	1	no	—
274	C₂²×C₄₇	—	4	1	no	—
275	C₂²×C₄₇	—	4	1	no	—
276	C₂²×C₄₇	—	4	1	no	—
277	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
278	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
279	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
280	C₂²×C₄₇	#385	1	1	yes	characteristic
281	C₂²×C₄₇	#385	1	1	yes	characteristic
282	C₂²×C₄₇	#386	1	1	yes	characteristic
283	C₂²×C₄₇	#386	1	1	yes	characteristic
284	C₂×D₄₇	—	2	4	no	—
285	C₂×D₄₇	—	4	4	no	—
286	C₂×D₄₇	—	4	4	no	—
287	C₂×D₄₇	—	8	2	no	—
288	C₄×C₄₇	—	8	2	no	—
289	C₄×C₄₇	#379	1	1	yes	characteristic
290	C₄×C₄₇	#380	1	1	yes	characteristic
291	C₄×C₄₇	#380	1	1	yes	characteristic
292	C₄×C₄₇	#381	1	1	yes	characteristic
293	C₄×C₄₇	#385	1	1	yes	characteristic
294	C₄×C₄₇	#385	1	1	yes	characteristic
295	C₄×C₄₇	#386	1	1	yes	characteristic
296	C₄×C₄₇	#386	1	1	yes	characteristic
297	Dic₄₇	—	2	4	no	—
298	Dic₄₇	—	8	2	no	—
299	C₂×#568	—	47	1	no	—
300	C₂×#410	—	47	1	no	—
301	#2879	—	47	1	no	—
302	C₂×#344	—	47	1	no	—
303	C₂×#344	—	47	1	no	—
304	#1742	—	47	1	no	—
305	#1742	D₄₇	1	1	yes	characteristic, complemented
306	C₂×C₄₇	—	2	1	no	—
307	C₂×C₄₇	—	2	1	no	—
308	C₂×C₄₇	—	2	1	no	—
309	C₂×C₄₇	—	2	1	no	—
310	C₂×C₄₇	—	2	1	no	—
311	C₂×C₄₇	—	2	1	no	—
312	C₂×C₄₇	—	2	1	no	—
313	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
314	D₄₇	—	4	4	no	—
315	C₂²×#41	—	47	1	no	—
316	#568	—	47	4	no	—
317	#568	—	94	2	no	—
318	#568	—	94	2	no	—
319	#568	—	94	2	no	—
320	C₂×#131	—	94	2	no	—
321	C₂×#131	—	94	2	no	—
322	C₂²×M₁₆	—	47	1	no	—
323	C₂²×M₁₆	—	47	1	no	—
324	C₂²×M₁₆	—	94	2	no	—
325	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
326	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
327	C₂×#117	—	47	1	no	—
328	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
329	#410	—	94	2	no	—
330	#410	—	94	2	no	—
331	C₂×#99	—	47	4	no	—
332	#408	—	47	4	no	—
333	#408	—	94	2	no	—
334	#407	—	94	2	no	—
335	#344	—	94	2	no	—
336	#344	—	94	2	no	—
337	#343	—	2	2	no	—
338	#343	—	94	2	no	—
339	C₄₇	#10757	1	1	yes	characteristic, complemented, Sylow
340	C₂×#41	—	47	2	no	—
341	C₂×#41	—	47	2	no	—
342	C₂×#41	—	47	2	no	—
343	C₂×#41	—	47	2	no	—
344	C₂×#41	—	94	1	no	—
345	C₂×#41	—	94	1	no	—
346	C₂×#41	—	94	1	no	—
347	C₂×#41	—	94	1	no	—
348	C₂×#41	—	94	1	no	—
349	C₂×#41	—	94	1	no	—
350	C₂×#41	—	94	1	no	—
351	C₂×#41	—	94	1	no	—
352	C₂²×Q₈	—	47	1	no	—
353	C₂²×D₄	—	47	2	no	—
354	C₂²×D₄	—	47	1	no	—
355	C₂³×C₄	—	47	2	no	—
356	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
357	#131	—	94	8	no	—
358	#131	—	94	8	no	—
359	#131	—	94	8	no	—
360	#131	—	94	8	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	47	2	no	—
370	C₂×M₁₆	—	47	2	no	—
371	C₂×M₁₆	—	47	2	no	—
372	C₂×M₁₆	—	94	4	no	—
373	C₂×M₁₆	—	94	8	no	—
374	C₂×M₁₆	—	94	8	no	—
375	C₂×M₁₆	—	94	1	no	—
376	C₂×M₁₆	—	94	1	no	—
377	C₂×M₁₆	—	94	1	no	—
378	C₂×M₁₆	—	94	1	no	—
379	C₂×M₁₆	—	94	1	no	—
380	C₂×M₁₆	—	94	1	no	—
381	C₂×M₁₆	—	94	1	no	—
382	C₂×M₁₆	—	94	1	no	—
383	C₂×M₁₆	—	94	1	no	—
384	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
385	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
386	C₂×M₁₆	D₁₈₈	1	2	yes	—
387	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	47	2	no	—
391	C₂²×C₈	—	94	4	no	—
392	C₂²×C₈	—	94	1	no	—
393	#117	—	2	1	no	—
394	#117	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	94	1	no	—
398	#117	—	94	1	no	—
399	#117	—	94	1	no	—
400	#117	—	94	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	94	1	no	—
403	C₂×C₂²⋊C₄	—	47	2	no	—
404	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	—	94	1	no	—
407	#99	—	94	8	no	—
408	C₂²⋊C₈	—	94	8	no	—
409	C₂⁴	—	47	2	no	—
410	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
411	#41	—	94	2	no	—
412	#41	—	94	2	no	—
413	#41	—	94	2	no	—
414	#41	—	94	2	no	—
415	#41	—	94	2	no	—
416	#41	—	94	2	no	—
417	#41	—	94	2	no	—
418	#41	—	94	2	no	—
419	#41	—	94	2	no	—
420	#41	—	94	2	no	—
421	#41	—	94	2	no	—
422	#41	—	94	2	no	—
423	#41	—	94	2	no	—
424	#41	—	94	2	no	—
425	#41	—	94	2	no	—
426	#41	—	94	2	no	—
427	C₂×Q₈	—	47	2	no	—
428	C₂×Q₈	—	47	2	no	—
429	C₂×Q₈	—	94	1	no	—
430	C₂×Q₈	—	94	1	no	—
431	C₂×Q₈	—	94	1	no	—
432	C₂×Q₈	—	94	1	no	—
433	C₂×D₄	—	47	4	no	—
434	C₂×D₄	—	47	4	no	—
435	C₂×D₄	—	47	2	no	—
436	C₂×D₄	—	47	2	no	—
437	C₂×D₄	—	94	2	no	—
438	C₂×D₄	—	94	2	no	—
439	C₂×D₄	—	94	2	no	—
440	C₂×D₄	—	94	2	no	—
441	C₂×D₄	—	94	1	no	—
442	C₂×D₄	—	94	1	no	—
443	C₂×D₄	—	94	1	no	—
444	C₂×D₄	—	94	1	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	47	2	no	—
447	C₂²×C₄	—	47	4	no	—
448	C₂²×C₄	—	47	4	no	—
449	C₂²×C₄	—	94	2	no	—
450	C₂²×C₄	—	94	2	no	—
451	C₂²×C₄	—	94	2	no	—
452	C₂²×C₄	—	94	2	no	—
453	C₂²×C₄	—	94	2	no	—
454	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
457	C₂²×C₄	#10625350	1	1	yes	characteristic
458	C₂²×C₄	#10625350	1	1	yes	characteristic
459	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
460	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
461	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
462	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
463	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
464	C₂²×C₄	#10625352	1	1	yes	characteristic
465	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
466	C₂²×C₄	#10625354	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	2	2	no	—
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	4	1	no	—
474	M₁₆	—	4	1	no	—
475	M₁₆	—	47	4	no	—
476	M₁₆	—	94	16	no	—
477	M₁₆	—	94	2	no	—
478	M₁₆	—	94	2	no	—
479	M₁₆	—	94	2	no	—
480	M₁₆	—	188	1	no	—
481	M₁₆	—	188	1	no	—
482	M₁₆	—	188	1	no	—
483	M₁₆	—	188	1	no	—
484	M₁₆	(C₂×D₄₇)⋊C₄	1	4	yes	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	4	1	no	—
490	C₂×C₈	—	4	1	no	—
491	C₂×C₈	—	94	16	no	—
492	C₂×C₈	—	94	2	no	—
493	C₂×C₈	—	94	2	no	—
494	C₂×C₈	—	94	2	no	—
495	C₂×C₈	—	94	2	no	—
496	C₂×C₈	—	94	2	no	—
497	C₂×C₈	—	94	2	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	188	1	no	—
501	C₄⋊C₄	—	188	1	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	94	2	no	—
505	C₂²⋊C₄	—	94	2	no	—
506	C₄²	—	4	1	no	—
507	C₄²	—	4	1	no	—
508	C₄²	—	188	1	no	—
509	C₄²	—	188	1	no	—
510	C₂³	—	8	1	no	—
511	C₂³	—	47	4	no	—
512	C₂³	—	94	2	no	—
513	C₂³	—	94	2	no	—
514	C₂³	—	376	2	no	—
515	C₂³	C₄²×D₄₇	1	1	yes	characteristic
516	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
517	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
518	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
519	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
520	C₂³	#13093986	1	1	yes	characteristic
521	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
522	Q₈	—	94	2	no	—
523	Q₈	—	94	2	no	—
524	Q₈	—	94	2	no	—
525	Q₈	—	94	2	no	—
526	D₄	—	94	4	no	—
527	D₄	—	94	4	no	—
528	D₄	—	94	4	no	—
529	D₄	—	94	4	no	—
530	D₄	—	94	2	no	—
531	D₄	—	94	2	no	—
532	D₄	—	94	2	no	—
533	D₄	—	94	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	—	47	4	no	—
537	C₂×C₄	—	94	2	no	—
538	C₂×C₄	—	94	2	no	—
539	C₂×C₄	—	94	4	no	—
540	C₂×C₄	—	94	4	no	—
541	C₂×C₄	—	94	4	no	—
542	C₂×C₄	—	94	4	no	—
543	C₂×C₄	—	376	2	no	—
544	C₂×C₄	—	188	2	no	—
545	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
546	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
547	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
548	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
549	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
550	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
551	C₂×C₄	#13093981	1	1	yes	characteristic
552	C₂×C₄	#13093982	1	1	yes	characteristic
553	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
554	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
555	C₂×C₄	#13093986	1	1	yes	characteristic
556	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
557	C₂×C₄	#13093992	1	1	yes	characteristic
558	C₂×C₄	#13093992	1	1	yes	characteristic
559	C₂×C₄	#13093994	1	1	yes	characteristic
560	C₂×C₄	#13093994	1	1	yes	characteristic
561	C₂×C₄	#13093995	1	1	yes	characteristic
562	C₂×C₄	#13093997	1	1	yes	characteristic
563	C₂×C₄	#13093997	1	1	yes	characteristic
564	C₂×C₄	#13093999	1	1	yes	characteristic
565	C₂×C₄	#13094000	1	1	yes	characteristic
566	C₂×C₄	#13094002	1	1	yes	characteristic
567	C₂×C₄	#13094002	1	1	yes	characteristic
568	C₂×C₄	#13094004	1	1	yes	characteristic
569	C₂×C₄	#13094006	1	1	yes	characteristic
570	C₂×C₄	#13094006	1	1	yes	characteristic
571	C₂×C₄	#13094009	1	1	yes	characteristic
572	C₂×C₄	#13094009	1	1	yes	characteristic
573	C₈	—	2	4	no	—
574	C₈	—	4	2	no	—
575	C₈	—	94	4	no	—
576	C₈	—	188	2	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	94	4	no	—
585	C₂²	—	376	2	no	—
586	C₂²	—	188	4	no	—
587	C₂²	—	188	4	no	—
588	C₂²	#95×D₄₇	1	1	yes	characteristic
589	C₂²	#15688970	1	1	yes	characteristic
590	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
591	C₂²	#15688994	1	1	yes	characteristic
592	C₂²	#15688997	1	1	yes	characteristic
593	C₂²	#15688999	1	1	yes	characteristic
594	C₂²	#15689001	1	1	yes	characteristic
595	C₄	—	8	2	no	—
596	C₄	—	94	4	no	—
597	C₄	—	376	2	no	—
598	C₄	#15688978	1	1	yes	characteristic
599	C₄	#15688980	1	1	yes	characteristic
600	C₄	#15688982	1	1	yes	characteristic
601	C₄	#15688985	1	1	yes	characteristic
602	C₄	#15688994	1	1	yes	characteristic
603	C₄	#15688997	1	1	yes	characteristic
604	C₄	#15688999	1	1	yes	characteristic
605	C₄	#15689001	1	1	yes	characteristic
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	188	4	no	—
614	C₂	(C₂×D₄₇)⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15689001
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#1742	C₂
socle	C₂×C₄₇	C₂²⋊#95
prime radical	C₂²×#10625350	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#1742	D₄₇
hypocenter	C₄₇	#10757
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1742

Complements

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

N	H ≅ G/N	type
4. C₂×#15688895	C₂	semidirect
5. C₂×#15688893	C₂	semidirect
6. #20243126	C₂	semidirect
7. C₄₇×#1742	C₂	semidirect
12. #15689889	C₄	semidirect
22. #15689091	C₄	semidirect
305. #1742	D₄₇	semidirect
339. C₄₇	#10757	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689889	2
C₂×#15689096	2
#20251832	2
C₂×#15688895	2
C₂×#15688893	2
#20243126	2
C₄₇×#1742	2
#10757	47