Subgroups — #20257824

Order 6016.

1004 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689874	C₂	1	2	yes	maximal, complemented
2	#15689873	C₂	1	2	yes	maximal, complemented
3	#15689849	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689844	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689833	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689831	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689823	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689820	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689786	C₂	1	2	yes	maximal, complemented
11	#15689781	C₂	1	2	yes	maximal, complemented
12	#15689773	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689751	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689750	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689742	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689730	C₂	1	2	yes	maximal, complemented
17	#15689716	C₂	1	2	yes	maximal, complemented
18	#15689714	C₂	1	2	yes	maximal, complemented
19	#15689695	C₂	1	2	yes	maximal, complemented
20	C₄⋊Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
21	#15689652	C₂	1	1	yes	maximal, characteristic, complemented
22	#15689651	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#542	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10625352	C₂²	1	2	yes	—
25	C₂²×Dic₉₄	C₂²	1	2	yes	—
26	C₂×Q₈×D₄₇	C₂²	1	2	yes	—
27	#13094024	C₂²	1	1	yes	characteristic
28	#13094024	C₂²	1	1	yes	characteristic
29	#13094023	C₂²	1	2	yes	—
30	#13094023	C₂²	1	1	yes	characteristic
31	#13094023	C₂²	1	2	yes	—
32	#13094023	C₂²	1	1	yes	characteristic
33	#13094023	C₂²	1	2	yes	—
34	#13094023	C₂²	1	1	yes	characteristic
35	#13094022	C₂²	1	2	yes	—
36	#13094022	C₂²	1	2	yes	—
37	#13094019	C₂²	1	2	yes	—
38	#13094019	C₂²	1	1	yes	characteristic
39	#13094017	C₂²	1	2	yes	—
40	#13094017	C₂²	1	2	yes	—
41	#13094017	C₂²	1	2	yes	—
42	#13094017	C₂²	1	2	yes	—
43	#13094017	C₂²	1	1	yes	characteristic
44	#13094017	C₂²	1	2	yes	—
45	#13094016	C₂²	1	2	yes	—
46	#13094016	C₂²	1	1	yes	characteristic
47	#13094016	C₂²	1	1	yes	characteristic
48	#13094016	C₂²	1	2	yes	—
49	#13094015	C₂²	1	2	yes	—
50	#13094015	C₂²	1	1	yes	characteristic
51	#13094015	C₂²	1	2	yes	—
52	#13094014	C₂²	1	1	yes	characteristic
53	#13094014	C₂²	1	2	yes	—
54	#13094014	C₂²	1	2	yes	—
55	#13094010	C₂²	1	2	yes	—
56	#13094010	C₂²	1	2	yes	—
57	#13094010	C₂²	1	1	yes	characteristic
58	#13094009	C₂²	1	1	yes	characteristic
59	#13094008	C₂²	1	2	yes	—
60	#13094007	C₂²	1	2	yes	—
61	#13094006	C₂²	1	2	yes	—
62	#13094006	C₂²	1	1	yes	characteristic
63	#13094006	C₂²	1	2	yes	—
64	#13094005	C₂²	1	2	yes	—
65	#13094005	C₂²	1	2	yes	—
66	#13094004	C₂²	1	2	yes	—
67	#13094003	C₂²	1	2	yes	—
68	#13094002	C₂²	1	2	yes	—
69	#13094002	C₂²	1	1	yes	characteristic
70	#13094002	C₂²	1	2	yes	—
71	#13094002	C₂²	1	2	yes	—
72	#13094001	C₂²	1	2	yes	—
73	#13094001	C₂²	1	2	yes	—
74	#13094001	C₂²	1	2	yes	—
75	#13094001	C₂²	1	2	yes	—
76	#13094001	C₂²	1	2	yes	—
77	#13094001	C₂²	1	2	yes	—
78	#13094001	C₂²	1	2	yes	—
79	#13094000	C₂²	1	1	yes	characteristic
80	#13094000	C₂²	1	2	yes	—
81	#13094000	C₂²	1	1	yes	characteristic
82	#13093997	C₂²	1	1	yes	characteristic
83	#13093997	C₂²	1	2	yes	—
84	#13093995	C₂²	1	1	yes	characteristic
85	#13093995	C₂²	1	2	yes	—
86	#13093995	C₂²	1	1	yes	characteristic
87	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
88	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
89	C₄×Dic₉₄	C₂²	1	2	yes	—
90	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
91	#13093989	C₂²	1	2	yes	—
92	C₄×D₁₈₈	C₂²	1	2	yes	—
93	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
94	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
95	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
98	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
99	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
100	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
101	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
102	#13093983	C₂²	1	1	yes	characteristic
103	#13093982	C₂²	1	1	yes	characteristic
104	#13093981	C₂²	1	1	yes	characteristic
105	#13093980	C₂²	1	2	yes	—
106	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
111	C₄²×D₄₇	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
113	#126×C₄₇	C₂²	1	2	yes	—
114	#124×C₄₇	C₂²	1	1	yes	characteristic
115	#124×C₄₇	C₂²	1	2	yes	—
116	#123×C₄₇	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
118	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
119	#121×C₄₇	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
122	#117×C₄₇	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
125	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₄₇	C₂³	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
133	C₂²×Dic₄₇	C₂³	1	2	yes	—
134	C₂²×Dic₄₇	C₂³	1	2	yes	—
135	C₂²×Dic₄₇	C₂³	1	2	yes	—
136	Q₈×D₄₇	—	4	4	no	—
137	#10625352	—	4	4	no	—
138	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₄₇	C₂³	1	2	yes	—
144	C₂×C₄×D₄₇	C₂³	1	2	yes	—
145	C₂×C₄×D₄₇	C₂³	1	2	yes	—
146	C₂×Dic₉₄	—	4	4	no	—
147	C₂×Dic₉₄	C₂³	1	2	yes	—
148	C₂×Dic₉₄	C₂³	1	2	yes	—
149	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
150	C₂×Dic₉₄	C₂³	1	2	yes	—
151	C₂×Dic₉₄	C₂³	1	2	yes	—
152	C₂×Dic₉₄	C₂³	1	2	yes	—
153	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
154	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
158	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
159	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
161	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
162	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
167	C₄²×C₄₇	C₂³	1	1	yes	characteristic
168	C₄²×C₄₇	C₂³	1	1	yes	characteristic
169	C₄²×C₄₇	C₂³	1	2	yes	—
170	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
171	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
172	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
176	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
177	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
186	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₄₇	C₂³	1	2	yes	—
190	C₄⋊Dic₄₇	C₂³	1	2	yes	—
191	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₄₇	C₂³	1	2	yes	—
193	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₄₇	C₂³	1	2	yes	—
195	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₄₇	C₂³	1	2	yes	—
197	C₄⋊Dic₄₇	C₂³	1	2	yes	—
198	Dic₄₇⋊C₄	C₂³	1	2	yes	—
199	Dic₄₇⋊C₄	C₂³	1	2	yes	—
200	Dic₄₇⋊C₄	C₂³	1	2	yes	—
201	Dic₄₇⋊C₄	C₂³	1	2	yes	—
202	Dic₄₇⋊C₄	C₂³	1	2	yes	—
203	Dic₄₇⋊C₄	C₂³	1	2	yes	—
204	Dic₄₇⋊C₄	C₂³	1	2	yes	—
205	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₄₇⋊C₄	C₂³	1	2	yes	—
208	Dic₄₇⋊C₄	C₂³	1	2	yes	—
209	Dic₄₇⋊C₄	C₂³	1	2	yes	—
210	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₄₇⋊C₄	C₂³	1	2	yes	—
212	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₄₇⋊C₄	C₂³	1	2	yes	—
214	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₄₇⋊C₄	C₂³	1	2	yes	—
216	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
217	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
218	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
219	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
220	C₄×Dic₄₇	C₂³	1	2	yes	—
221	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₄₇	C₂³	1	2	yes	—
223	C₄×Dic₄₇	C₂³	1	2	yes	—
224	C₄×Dic₄₇	C₂³	1	2	yes	—
225	C₂³×C₄₇	C₂⁴	1	2	yes	—
226	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
227	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
228	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
229	Q₈×C₄₇	—	2	2	no	—
230	Q₈×C₄₇	—	4	2	no	—
231	D₄×C₄₇	—	2	2	no	—
232	D₄×C₄₇	—	4	2	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	4	2	no	—
235	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
236	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
240	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
242	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂²⋊D₄₇	—	2	4	no	—
245	C₂²⋊D₄₇	—	2	2	no	—
246	C₂²⋊D₄₇	—	2	2	no	—
247	C₂²⋊D₄₇	—	4	2	no	—
248	C₂×Dic₄₇	—	2	4	no	—
249	C₂×Dic₄₇	—	4	2	no	—
250	C₂×Dic₄₇	—	4	2	no	—
251	C₂×Dic₄₇	C₂⁴	1	2	yes	—
252	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₄₇	C₂⁴	1	2	yes	—
257	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₄₇	C₂⁴	1	2	yes	—
259	C₂×Dic₄₇	C₂⁴	1	2	yes	—
260	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
261	D₁₈₈	—	2	2	no	—
262	C₄×D₄₇	—	2	2	no	—
263	C₄×D₄₇	—	2	2	no	—
264	C₄×D₄₇	—	2	2	no	—
265	C₄×D₄₇	—	2	2	no	—
266	C₄×D₄₇	—	4	2	no	—
267	C₄×D₄₇	—	4	2	no	—
268	C₄×D₄₇	—	4	2	no	—
269	Dic₉₄	—	2	2	no	—
270	Dic₉₄	—	2	4	no	—
271	Dic₉₄	—	2	4	no	—
272	Dic₉₄	—	4	2	no	—
273	Dic₉₄	—	4	2	no	—
274	Dic₉₄	—	4	2	no	—
275	C₂²×C₄₇	—	2	2	no	—
276	C₂²×C₄₇	—	2	1	no	—
277	C₂²×C₄₇	—	2	2	no	—
278	C₂²×C₄₇	—	2	1	no	—
279	C₂²×C₄₇	—	2	1	no	—
280	C₂²×C₄₇	—	2	2	no	—
281	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
282	C₂×D₄₇	—	2	1	no	—
283	C₂×D₄₇	—	2	1	no	—
284	C₂×D₄₇	—	2	1	no	—
285	C₂×D₄₇	—	2	1	no	—
286	C₂×D₄₇	—	2	1	no	—
287	C₂×D₄₇	2₋¹⁺⁴	1	2	yes	—
288	C₄×C₄₇	—	2	1	no	—
289	C₄×C₄₇	—	2	2	no	—
290	C₄×C₄₇	—	2	2	no	—
291	C₄×C₄₇	—	2	1	no	—
292	C₄×C₄₇	—	2	1	no	—
293	C₄×C₄₇	—	2	1	no	—
294	C₄×C₄₇	—	2	1	no	—
295	C₄×C₄₇	—	2	2	no	—
296	C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
297	Dic₄₇	—	2	2	no	—
298	Dic₄₇	—	2	1	no	—
299	Dic₄₇	—	2	2	no	—
300	Dic₄₇	—	2	2	no	—
301	Dic₄₇	—	2	1	no	—
302	Dic₄₇	—	2	1	no	—
303	Dic₄₇	—	2	1	no	—
304	Dic₄₇	—	2	2	no	—
305	Dic₄₇	—	2	1	no	—
306	Dic₄₇	H(5,𝔽₂)	1	2	yes	—
307	#3552	—	47	1	no	maximal, Sylow
308	C₂×C₄₇	—	4	2	no	—
309	C₂×C₄₇	—	4	1	no	—
310	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
312	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
313	D₄₇	—	2	2	no	—
314	D₄₇	—	4	1	no	—
315	#563	—	47	2	no	—
316	#563	—	47	2	no	—
317	#557	—	47	1	no	—
318	#556	—	47	1	no	—
319	#554	—	47	1	no	—
320	#554	—	47	1	no	—
321	#553	—	47	1	no	—
322	#553	—	47	1	no	—
323	D₄×Q₈	—	47	2	no	—
324	D₄×Q₈	—	47	1	no	—
325	#548	—	47	2	no	—
326	#547	—	47	1	no	—
327	#544	—	47	1	no	—
328	#544	—	47	1	no	—
329	#542	—	47	1	no	—
330	#542	D₄₇	1	1	yes	characteristic, complemented
331	#541	—	47	2	no	—
332	#539	—	47	2	no	—
333	#539	—	47	2	no	—
334	#536	—	47	2	no	—
335	C₂×C₄⋊Q₈	—	47	1	no	—
336	#529	—	47	1	no	—
337	#529	—	47	1	no	—
338	C₄₇	#3552	1	1	yes	characteristic, complemented, Sylow
339	C₂×#41	—	47	2	no	—
340	C₂²×Q₈	—	47	2	no	—
341	C₂²×Q₈	—	47	2	no	—
342	C₄⋊Q₈	—	47	2	no	—
343	C₄⋊Q₈	—	47	2	no	—
344	C₄⋊Q₈	—	47	2	no	—
345	C₄⋊Q₈	—	47	1	no	—
346	C₄⋊Q₈	—	47	1	no	—
347	C₄⋊Q₈	—	47	2	no	—
348	C₄⋊Q₈	—	47	1	no	—
349	C₄⋊Q₈	—	47	2	no	—
350	C₄⋊Q₈	—	47	1	no	—
351	C₄⋊Q₈	—	47	1	no	—
352	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
353	#126	—	47	1	no	—
354	#126	—	47	2	no	—
355	#126	—	47	2	no	—
356	#126	—	47	1	no	—
357	#126	—	47	2	no	—
358	#126	—	47	2	no	—
359	#126	—	47	2	no	—
360	#126	—	47	2	no	—
361	#126	C₂×D₄₇	1	2	yes	—
362	#125	—	47	1	no	—
363	#125	—	47	2	no	—
364	#125	—	47	2	no	—
365	#125	—	47	2	no	—
366	#125	—	47	2	no	—
367	#125	—	47	1	no	—
368	#125	—	47	1	no	—
369	#125	—	47	2	no	—
370	#125	—	47	2	no	—
371	#125	—	47	1	no	—
372	#124	—	47	1	no	—
373	#124	—	47	2	no	—
374	#124	—	47	2	no	—
375	#124	C₂×D₄₇	1	1	yes	characteristic
376	#124	C₂×D₄₇	1	2	yes	—
377	#123	—	47	2	no	—
378	#123	—	47	2	no	—
379	#123	—	47	2	no	—
380	#123	—	47	1	no	—
381	#123	—	47	2	no	—
382	#123	—	47	1	no	—
383	#123	—	47	2	no	—
384	#123	—	47	2	no	—
385	#123	C₂×D₄₇	1	2	yes	—
386	C₂²⋊Q₈	—	47	1	no	—
387	C₂²⋊Q₈	—	47	1	no	—
388	C₂²⋊Q₈	—	47	2	no	—
389	C₂²⋊Q₈	—	47	2	no	—
390	C₂²⋊Q₈	—	47	1	no	—
391	C₂²⋊Q₈	—	47	2	no	—
392	C₂²⋊Q₈	—	47	2	no	—
393	C₂²⋊Q₈	—	47	2	no	—
394	C₂²⋊Q₈	—	47	2	no	—
395	C₂²⋊Q₈	—	47	2	no	—
396	C₂²⋊Q₈	—	47	2	no	—
397	C₂²⋊Q₈	—	47	2	no	—
398	C₂²⋊Q₈	—	47	2	no	—
399	C₂²⋊Q₈	—	47	2	no	—
400	C₂²⋊Q₈	—	47	2	no	—
401	C₂²⋊Q₈	—	47	2	no	—
402	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
403	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
404	#121	—	47	1	no	—
405	#121	—	47	2	no	—
406	#121	—	47	1	no	—
407	#121	—	47	1	no	—
408	#121	—	47	2	no	—
409	#121	C₂×D₄₇	1	1	yes	characteristic
410	C₄×Q₈	—	47	1	no	—
411	C₄×Q₈	—	47	1	no	—
412	C₄×Q₈	—	47	2	no	—
413	C₄×Q₈	—	47	1	no	—
414	C₄×Q₈	—	47	2	no	—
415	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
416	C₄×D₄	—	47	1	no	—
417	C₄×D₄	—	47	1	no	—
418	C₄×D₄	—	47	1	no	—
419	C₄×D₄	—	47	1	no	—
420	C₄×D₄	—	47	2	no	—
421	C₄×D₄	—	47	2	no	—
422	C₄×D₄	—	47	2	no	—
423	C₄×D₄	—	47	2	no	—
424	C₄×D₄	—	47	1	no	—
425	C₄×D₄	—	47	2	no	—
426	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
427	#117	—	47	1	no	—
428	#117	—	47	1	no	—
429	#117	—	47	2	no	—
430	#117	—	47	1	no	—
431	#117	C₂×D₄₇	1	1	yes	characteristic
432	C₂×C₄⋊C₄	—	47	1	no	—
433	C₂×C₄⋊C₄	—	47	2	no	—
434	C₂×C₄⋊C₄	—	47	1	no	—
435	C₂×C₄⋊C₄	—	47	1	no	—
436	C₂×C₄⋊C₄	—	47	1	no	—
437	C₂×C₄²	—	47	1	no	—
438	#41	—	188	4	no	—
439	C₂×Q₈	—	47	2	no	—
440	C₂×Q₈	—	47	1	no	—
441	C₂×Q₈	—	47	2	no	—
442	C₂×Q₈	—	47	2	no	—
443	C₂×Q₈	—	47	2	no	—
444	C₂×Q₈	—	47	2	no	—
445	C₂×Q₈	—	188	4	no	—
446	C₂×Q₈	—	188	4	no	—
447	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
448	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
449	C₂×D₄	—	47	1	no	—
450	C₂×D₄	—	47	2	no	—
451	C₂×D₄	—	47	1	no	—
452	C₂×D₄	—	47	2	no	—
453	C₂×D₄	—	47	1	no	—
454	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
455	C₂×D₄	C₂²×D₄₇	1	2	yes	—
456	C₂²×C₄	—	47	2	no	—
457	C₂²×C₄	—	47	2	no	—
458	C₂²×C₄	—	47	2	no	—
459	C₂²×C₄	—	47	1	no	—
460	C₂²×C₄	—	47	1	no	—
461	C₂²×C₄	—	47	1	no	—
462	C₂²×C₄	—	47	1	no	—
463	C₂²×C₄	—	47	2	no	—
464	C₂²×C₄	—	47	2	no	—
465	C₂²×C₄	—	47	2	no	—
466	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
468	C₄⋊C₄	—	47	2	no	—
469	C₄⋊C₄	—	47	2	no	—
470	C₄⋊C₄	—	47	2	no	—
471	C₄⋊C₄	—	47	2	no	—
472	C₄⋊C₄	—	47	2	no	—
473	C₄⋊C₄	—	47	2	no	—
474	C₄⋊C₄	—	47	1	no	—
475	C₄⋊C₄	—	47	2	no	—
476	C₄⋊C₄	—	47	1	no	—
477	C₄⋊C₄	—	47	1	no	—
478	C₄⋊C₄	—	47	2	no	—
479	C₄⋊C₄	—	47	2	no	—
480	C₄⋊C₄	—	47	2	no	—
481	C₄⋊C₄	—	47	2	no	—
482	C₄⋊C₄	—	47	1	no	—
483	C₄⋊C₄	—	47	1	no	—
484	C₄⋊C₄	—	47	2	no	—
485	C₄⋊C₄	—	47	2	no	—
486	C₄⋊C₄	—	47	1	no	—
487	C₄⋊C₄	—	47	1	no	—
488	C₄⋊C₄	—	47	1	no	—
489	C₄⋊C₄	—	47	1	no	—
490	C₄⋊C₄	—	47	2	no	—
491	C₄⋊C₄	—	47	2	no	—
492	C₄⋊C₄	—	47	1	no	—
493	C₄⋊C₄	—	47	2	no	—
494	C₄⋊C₄	—	47	1	no	—
495	C₄⋊C₄	—	47	2	no	—
496	C₄⋊C₄	—	47	2	no	—
497	C₄⋊C₄	—	47	1	no	—
498	C₄⋊C₄	—	47	2	no	—
499	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
502	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
505	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
506	C₂²⋊C₄	—	47	2	no	—
507	C₂²⋊C₄	—	47	2	no	—
508	C₂²⋊C₄	—	47	2	no	—
509	C₂²⋊C₄	—	47	2	no	—
510	C₂²⋊C₄	—	47	2	no	—
511	C₂²⋊C₄	—	47	1	no	—
512	C₂²⋊C₄	—	47	1	no	—
513	C₂²⋊C₄	—	47	2	no	—
514	C₂²⋊C₄	—	47	1	no	—
515	C₂²⋊C₄	—	47	1	no	—
516	C₂²⋊C₄	—	47	1	no	—
517	C₂²⋊C₄	—	47	1	no	—
518	C₂²⋊C₄	—	47	2	no	—
519	C₂²⋊C₄	—	47	1	no	—
520	C₂²⋊C₄	—	47	2	no	—
521	C₂²⋊C₄	—	47	1	no	—
522	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
524	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
525	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
529	C₄²	—	47	1	no	—
530	C₄²	—	47	1	no	—
531	C₄²	—	47	1	no	—
532	C₄²	—	47	1	no	—
533	C₄²	—	47	2	no	—
534	C₄²	—	47	2	no	—
535	C₄²	—	47	2	no	—
536	C₄²	—	47	2	no	—
537	C₄²	C₂²×D₄₇	1	1	yes	characteristic
538	C₄²	C₂²×D₄₇	1	1	yes	characteristic
539	C₄²	C₂²×D₄₇	1	2	yes	—
540	C₂³	—	47	1	no	—
541	C₂³	—	47	1	no	—
542	C₂³	C₂³×D₄₇	1	2	yes	—
543	C₂³	C₂³×D₄₇	1	1	yes	characteristic
544	Q₈	—	2	2	no	—
545	Q₈	—	4	2	no	—
546	Q₈	—	94	2	no	—
547	Q₈	—	94	4	no	—
548	Q₈	—	94	4	no	—
549	Q₈	—	188	2	no	—
550	Q₈	—	188	2	no	—
551	Q₈	—	188	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	94	2	no	—
555	D₄	—	94	2	no	—
556	D₄	—	94	2	no	—
557	D₄	—	94	4	no	—
558	D₄	—	188	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	47	1	no	—
562	C₂×C₄	—	47	1	no	—
563	C₂×C₄	—	47	2	no	—
564	C₂×C₄	—	47	1	no	—
565	C₂×C₄	—	47	1	no	—
566	C₂×C₄	—	47	1	no	—
567	C₂×C₄	—	47	1	no	—
568	C₂×C₄	—	47	2	no	—
569	C₂×C₄	—	47	2	no	—
570	C₂×C₄	—	47	2	no	—
571	C₂×C₄	—	94	2	no	—
572	C₂×C₄	—	94	2	no	—
573	C₂×C₄	—	94	4	no	—
574	C₂×C₄	—	94	2	no	—
575	C₂×C₄	—	94	2	no	—
576	C₂×C₄	—	188	2	no	—
577	C₂×C₄	—	188	2	no	—
578	C₂×C₄	—	188	2	no	—
579	C₂×C₄	—	188	2	no	—
580	C₂×C₄	—	188	2	no	—
581	C₂×C₄	C₂³×D₄₇	1	2	yes	—
582	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₄₇	1	2	yes	—
586	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₄₇	1	2	yes	—
589	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
590	C₂²	—	2	2	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	47	2	no	—
597	C₂²	—	94	1	no	—
598	C₂²	—	94	1	no	—
599	C₂²	—	94	1	no	—
600	C₂²	—	94	1	no	—
601	C₂²	—	94	1	no	—
602	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
603	C₄	—	2	1	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	2	no	—
611	C₄	—	47	2	no	—
612	C₄	—	94	2	no	—
613	C₄	—	94	2	no	—
614	C₄	—	94	2	no	—
615	C₄	—	94	1	no	—
616	C₄	—	94	1	no	—
617	C₄	—	94	1	no	—
618	C₄	—	94	2	no	—
619	C₄	—	94	1	no	—
620	C₄	—	94	1	no	—
621	C₄	#13094071	1	2	yes	—
622	C₂	—	4	2	no	—
623	C₂	—	4	1	no	—
624	C₂	—	94	2	no	—
625	C₂	—	188	1	no	—
626	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
627	C₂	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
628	C₂	C₂×#13094071	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#542	C₂
hypercenter	#542	D₄₇
hypocenter	C₄₇	#3552
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #15689874	C₂	semidirect
2. #15689873	C₂	semidirect
3. #15689849	C₂	semidirect
4. #15689844	C₂	semidirect
5. #15689833	C₂	semidirect
6. #15689831	C₂	semidirect
7. #15689823	C₂	semidirect
8. #15689820	C₂	semidirect
9. D₄×Dic₉₄	C₂	semidirect
10. #15689786	C₂	semidirect
11. #15689781	C₂	semidirect
12. #15689773	C₂	semidirect
13. #15689751	C₂	semidirect
14. #15689750	C₂	semidirect
15. #15689742	C₂	semidirect
16. #15689730	C₂	semidirect
17. #15689716	C₂	semidirect
18. #15689714	C₂	semidirect
19. #15689695	C₂	semidirect
20. C₄⋊Q₈×D₄₇	C₂	semidirect
21. #15689652	C₂	semidirect
22. #15689651	C₂	semidirect
23. C₄₇×#542	C₂	semidirect
330. #542	D₄₇	semidirect
338. C₄₇	#3552	semidirect