Subgroups — #20257145

Order 6016.

1660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094069	C₂	1	2	yes	maximal, complemented
2	#15689774	C₂	1	2	yes	maximal, complemented
3	#15689773	C₂	1	2	yes	maximal, complemented
4	#15689763	C₂	1	4	yes	maximal, complemented
5	#15689762	C₂	1	4	yes	maximal, complemented
6	#15689757	C₂	1	2	yes	maximal, complemented
7	D₄×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
8	#15689700	C₂	1	2	yes	maximal, complemented
9	#15689682	C₂	1	2	yes	maximal, complemented
10	#15689681	C₂	1	2	yes	maximal, complemented
11	#15689668	C₂	1	2	yes	maximal, complemented
12	C₂×#13093998	C₂	1	1	yes	maximal, characteristic, complemented
13	#121×D₄₇	C₂	1	2	yes	maximal, complemented
14	C₂×C₄×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#121×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#13094069	—	2	16	no	—
17	C₂×#10625350	C₂²	1	4	yes	complemented
18	C₂×#10625352	C₂²	1	4	yes	complemented
19	C₂×#10625352	C₂²	1	4	yes	complemented
20	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
23	C₂²×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
24	C₂×D₄×D₄₇	C₂²	1	4	yes	complemented
25	C₂×D₄×D₄₇	C₂²	1	4	yes	complemented
26	C₂×D₄×D₄₇	C₂²	1	2	yes	complemented
27	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
28	#13094023	C₂²	1	2	yes	complemented
29	#13094020	C₂²	1	2	yes	complemented
30	#13094010	C₂²	1	4	yes	complemented
31	#13094009	C₂²	1	4	yes	complemented
32	#13094007	C₂²	1	4	yes	complemented
33	#13094006	C₂²	1	4	yes	complemented
34	#13094005	C₂²	1	4	yes	complemented
35	#13094002	C₂²	1	4	yes	complemented
36	#13094001	C₂²	1	4	yes	complemented
37	#13093999	C₂²	1	2	yes	complemented
38	#13093998	C₂²	1	2	yes	complemented
39	#13093998	C₂²	1	2	yes	complemented
40	#13093998	C₂²	1	2	yes	complemented
41	#13093998	C₂²	1	2	yes	complemented
42	#13093997	C₂²	1	4	yes	complemented
43	#13093997	C₂²	1	4	yes	complemented
44	#13093996	C₂²	1	4	yes	complemented
45	#13093996	C₂²	1	4	yes	complemented
46	#13093996	C₂²	1	4	yes	complemented
47	#13093995	C₂²	1	2	yes	complemented
48	#13093994	C₂²	1	4	yes	complemented
49	#13093993	C₂²	1	4	yes	complemented
50	#13093992	C₂²	1	4	yes	complemented
51	#13093992	C₂²	1	4	yes	complemented
52	D₄×Dic₄₇	C₂²	1	2	yes	complemented
53	#13093986	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
58	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
59	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
60	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
61	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
62	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
63	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
64	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
65	C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
66	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₄₇	C₂²	1	2	yes	complemented
68	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
69	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
70	#121×C₄₇	C₂²	1	2	yes	complemented
71	#121×C₄₇	C₂²	1	2	yes	complemented
72	#121×C₄₇	C₂²	1	2	yes	complemented
73	#121×C₄₇	C₂²	1	2	yes	complemented
74	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
76	C₂⁴×C₄₇	C₂³	1	2	yes	—
77	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
78	C₂³×D₄₇	C₂³	1	4	yes	—
79	C₂³×D₄₇	C₂³	1	2	yes	—
80	C₂³×D₄₇	C₂³	1	1	yes	characteristic
81	C₂×D₄×C₄₇	—	2	8	no	—
82	C₂×D₄×C₄₇	—	4	2	no	—
83	C₂×D₄×C₄₇	C₂³	1	2	yes	—
84	C₂×D₄×C₄₇	C₂³	1	4	yes	—
85	C₂×D₄×C₄₇	C₂³	1	4	yes	—
86	C₂×D₄×C₄₇	C₂³	1	2	yes	—
87	C₂²×C₄×C₄₇	—	4	2	no	—
88	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊D₄₇	—	2	8	no	—
96	C₂×C₂²⋊D₄₇	—	2	16	no	—
97	C₂×C₂²⋊D₄₇	D₄	1	8	yes	complemented
98	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
104	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
105	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
106	C₂²×Dic₄₇	C₂³	1	2	yes	—
107	C₂²×Dic₄₇	C₂³	1	4	yes	—
108	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
109	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
110	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
111	#10625352	—	2	16	no	—
112	#10625352	—	2	16	no	—
113	D₄×D₄₇	—	2	16	no	—
114	D₄×D₄₇	—	2	16	no	—
115	D₄×D₄₇	—	4	4	no	—
116	#10625350	—	2	16	no	—
117	C₂×D₁₈₈	—	4	2	no	—
118	C₂×D₁₈₈	C₂³	1	2	yes	—
119	C₂×D₁₈₈	C₂³	1	4	yes	—
120	C₂×D₁₈₈	C₂³	1	2	yes	—
121	C₂×C₄×D₄₇	—	4	2	no	—
122	C₂×C₄×D₄₇	C₂³	1	4	yes	—
123	C₂×C₄×D₄₇	C₂³	1	2	yes	—
124	C₂×C₄×D₄₇	C₂³	1	4	yes	—
125	C₂×C₄×D₄₇	C₂³	1	2	yes	—
126	C₂×Dic₉₄	C₂³	1	4	yes	—
127	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
128	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
129	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
130	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
131	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
132	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
133	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
134	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
135	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
136	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
137	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
138	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
139	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
140	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
141	C₄⋊Dic₄₇	C₂³	1	2	yes	—
142	C₄⋊Dic₄₇	C₂³	1	2	yes	—
143	Dic₄₇⋊C₄	C₂³	1	4	yes	—
144	Dic₄₇⋊C₄	C₂³	1	2	yes	—
145	Dic₄₇⋊C₄	C₂³	1	2	yes	—
146	Dic₄₇⋊C₄	C₂³	1	4	yes	—
147	C₄×Dic₄₇	C₂³	1	2	yes	—
148	C₄×Dic₄₇	C₂³	1	2	yes	—
149	C₂³×C₄₇	—	2	4	no	—
150	C₂³×C₄₇	—	4	1	no	—
151	C₂³×C₄₇	—	4	1	no	—
152	C₂³×C₄₇	—	4	2	no	—
153	C₂³×C₄₇	—	4	2	no	—
154	C₂³×C₄₇	C₂×D₄	1	4	yes	complemented
155	C₂³×C₄₇	C₂⁴	1	4	yes	—
156	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
157	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
158	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
159	C₂²×D₄₇	—	2	4	no	—
160	C₂²×D₄₇	—	2	8	no	—
161	C₂²×D₄₇	—	4	1	no	—
162	C₂²×D₄₇	—	4	1	no	—
163	C₂²×D₄₇	—	4	2	no	—
164	C₂²×D₄₇	—	4	4	no	—
165	C₂²×D₄₇	—	4	4	no	—
166	C₂²×D₄₇	—	4	2	no	—
167	C₂²×D₄₇	C₂×D₄	1	4	yes	complemented
168	C₂²×D₄₇	C₂⁴	1	4	yes	—
169	C₂²×D₄₇	C₂⁴	1	2	yes	—
170	D₄×C₄₇	—	2	8	no	—
171	D₄×C₄₇	—	2	8	no	—
172	D₄×C₄₇	—	2	4	no	—
173	D₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
185	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
186	C₂²⋊D₄₇	—	2	8	no	—
187	C₂²⋊D₄₇	—	2	8	no	—
188	C₂²⋊D₄₇	—	2	8	no	—
189	C₂²⋊D₄₇	—	2	8	no	—
190	C₂²⋊D₄₇	—	4	4	no	—
191	C₂²⋊D₄₇	—	4	4	no	—
192	C₂²⋊D₄₇	C₂×D₄	1	8	yes	complemented
193	C₂²⋊D₄₇	C₂×D₄	1	8	yes	complemented
194	C₂×Dic₄₇	—	2	4	no	—
195	C₂×Dic₄₇	—	2	8	no	—
196	C₂×Dic₄₇	—	4	1	no	—
197	C₂×Dic₄₇	—	4	1	no	—
198	C₂×Dic₄₇	C₂×D₄	1	4	yes	complemented
199	C₂×Dic₄₇	C₂⁴	1	2	yes	—
200	C₂×Dic₄₇	C₂⁴	1	2	yes	—
201	C₂×Dic₄₇	C₂⁴	1	4	yes	—
202	C₂×Dic₄₇	C₂⁴	1	2	yes	—
203	D₁₈₈	—	2	8	no	—
204	D₁₈₈	—	2	4	no	—
205	D₁₈₈	—	4	2	no	—
206	C₄×D₄₇	—	2	8	no	—
207	C₄×D₄₇	—	2	4	no	—
208	C₄×D₄₇	—	2	8	no	—
209	C₄×D₄₇	—	4	2	no	—
210	Dic₉₄	—	2	8	no	—
211	C₂²×C₄₇	—	2	1	no	—
212	C₂²×C₄₇	—	2	1	no	—
213	C₂²×C₄₇	—	2	1	no	—
214	C₂²×C₄₇	—	2	1	no	—
215	C₂²×C₄₇	—	2	1	no	—
216	C₂²×C₄₇	—	2	1	no	—
217	C₂²×C₄₇	—	2	4	no	—
218	C₂²×C₄₇	—	2	4	no	—
219	C₂²×C₄₇	—	2	4	no	—
220	C₂²×C₄₇	—	4	4	no	—
221	C₂²×C₄₇	—	8	4	no	—
222	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
223	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
224	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
225	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
226	C₂×D₄₇	—	2	2	no	—
227	C₂×D₄₇	—	2	2	no	—
228	C₂×D₄₇	—	2	4	no	—
229	C₂×D₄₇	—	2	4	no	—
230	C₂×D₄₇	—	2	4	no	—
231	C₂×D₄₇	—	4	4	no	—
232	C₂×D₄₇	—	8	8	no	—
233	C₂×D₄₇	—	8	4	no	—
234	C₂×D₄₇	C₂²×D₄	1	4	yes	—
235	C₄×C₄₇	—	2	4	no	—
236	C₄×C₄₇	—	2	1	no	—
237	C₄×C₄₇	—	2	1	no	—
238	C₄×C₄₇	—	2	1	no	—
239	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	complemented
240	Dic₄₇	—	2	4	no	—
241	Dic₄₇	—	2	2	no	—
242	Dic₄₇	—	2	2	no	—
243	Dic₄₇	C₂²×D₄	1	4	yes	—
244	#3496	—	47	1	no	maximal, Sylow
245	C₂×C₄₇	—	2	2	no	—
246	C₂×C₄₇	—	2	2	no	—
247	C₂×C₄₇	—	2	2	no	—
248	C₂×C₄₇	—	4	4	no	—
249	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
250	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
251	C₂×C₄₇	#585	1	1	yes	characteristic
252	D₄₇	—	2	4	no	—
253	D₄₇	—	4	4	no	—
254	C₂×H(5,𝔽₂)	—	47	2	no	—
255	#547	—	47	2	no	—
256	#547	—	47	2	no	—
257	#546	—	47	4	no	—
258	#546	—	47	4	no	—
259	D₄²	—	47	2	no	—
260	D₄²	—	47	2	no	—
261	#537	—	47	2	no	—
262	#534	—	47	2	no	—
263	#534	—	47	2	no	—
264	#532	—	47	2	no	—
265	C₂×#121	—	47	1	no	—
266	C₂×#121	—	47	2	no	—
267	C₂×#121	D₄₇	1	1	yes	characteristic, complemented
268	C₂×C₄×D₄	—	47	1	no	—
269	C₄₇	#3496	1	1	yes	characteristic, complemented, Sylow
270	H(5,𝔽₂)	—	94	16	no	—
271	C₂×#41	—	47	4	no	—
272	C₂×#41	—	47	4	no	—
273	C₂×#41	—	47	4	no	—
274	C₂²×D₄	—	47	1	no	—
275	C₂²×D₄	—	47	2	no	—
276	C₂²×D₄	—	47	4	no	—
277	C₂²×D₄	—	47	4	no	—
278	C₂²×D₄	—	47	4	no	—
279	C₂²×D₄	—	47	2	no	—
280	C₂²×D₄	—	47	1	no	—
281	C₂²×D₄	C₂×D₄₇	1	2	yes	complemented
282	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
283	C₂³×C₄	—	47	1	no	—
284	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
285	C₄⋊Q₈	—	47	2	no	—
286	#127	—	47	2	no	—
287	#124	—	47	4	no	—
288	#123	—	47	4	no	—
289	#123	—	47	4	no	—
290	#123	—	47	4	no	—
291	#123	—	47	4	no	—
292	C₂²⋊Q₈	—	47	4	no	—
293	C₂²⋊Q₈	—	47	4	no	—
294	#121	—	47	4	no	—
295	#121	—	47	2	no	—
296	#121	—	47	4	no	—
297	#121	—	47	4	no	—
298	#121	—	47	2	no	—
299	#121	—	47	2	no	—
300	#121	—	47	2	no	—
301	#121	—	47	2	no	—
302	#121	—	47	2	no	—
303	#121	—	47	4	no	—
304	#121	—	47	4	no	—
305	#121	C₂×D₄₇	1	2	yes	complemented
306	#121	C₂×D₄₇	1	2	yes	complemented
307	#121	C₂×D₄₇	1	2	yes	complemented
308	#121	C₂×D₄₇	1	2	yes	complemented
309	#120	—	47	4	no	—
310	#120	—	47	4	no	—
311	#120	—	47	4	no	—
312	#120	—	47	4	no	—
313	C₄×D₄	—	47	2	no	—
314	C₄×D₄	—	47	2	no	—
315	C₄×D₄	—	47	2	no	—
316	C₄×D₄	—	47	2	no	—
317	C₄×D₄	—	47	2	no	—
318	C₄×D₄	—	47	2	no	—
319	C₄×D₄	—	47	4	no	—
320	C₂×C₄⋊C₄	—	47	1	no	—
321	C₂×C₄⋊C₄	—	47	1	no	—
322	C₂×C₄⋊C₄	—	47	2	no	—
323	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
324	C₂×C₂²⋊C₄	—	47	1	no	—
325	C₂×C₂²⋊C₄	—	47	1	no	—
326	C₂×C₂²⋊C₄	—	47	2	no	—
327	C₂×C₂²⋊C₄	—	47	4	no	—
328	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	complemented
329	C₂×C₄²	—	47	1	no	—
330	C₂⁴	—	47	1	no	—
331	C₂⁴	—	47	4	no	—
332	C₂⁴	—	47	2	no	—
333	C₂⁴	C₂²×D₄₇	1	2	yes	—
334	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
335	#41	—	94	16	no	—
336	#41	—	94	16	no	—
337	#41	—	94	16	no	—
338	C₂×Q₈	—	47	4	no	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	47	8	no	—
342	C₂×D₄	—	47	2	no	—
343	C₂×D₄	—	47	2	no	—
344	C₂×D₄	—	47	4	no	—
345	C₂×D₄	—	47	4	no	—
346	C₂×D₄	—	47	4	no	—
347	C₂×D₄	—	47	4	no	—
348	C₂×D₄	—	47	4	no	—
349	C₂×D₄	—	47	4	no	—
350	C₂×D₄	—	47	2	no	—
351	C₂×D₄	—	47	4	no	—
352	C₂×D₄	—	47	2	no	—
353	C₂×D₄	—	94	16	no	—
354	C₂×D₄	—	94	16	no	—
355	C₂×D₄	—	94	16	no	—
356	C₂×D₄	—	94	8	no	—
357	C₂×D₄	—	188	2	no	—
358	C₂×D₄	—	188	4	no	—
359	C₂×D₄	C₂²×D₄₇	1	2	yes	—
360	C₂×D₄	C₂²×D₄₇	1	4	yes	—
361	C₂×D₄	C₂²×D₄₇	1	4	yes	—
362	C₂×D₄	C₂²×D₄₇	1	2	yes	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	47	1	no	—
365	C₂²×C₄	—	47	2	no	—
366	C₂²×C₄	—	47	4	no	—
367	C₂²×C₄	—	47	1	no	—
368	C₂²×C₄	—	47	1	no	—
369	C₂²×C₄	—	47	4	no	—
370	C₂²×C₄	—	47	2	no	—
371	C₂²×C₄	—	47	4	no	—
372	C₂²×C₄	—	47	2	no	—
373	C₂²×C₄	—	188	2	no	—
374	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
375	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
376	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
377	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
378	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
379	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
380	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
381	C₄⋊C₄	—	47	2	no	—
382	C₄⋊C₄	—	47	2	no	—
383	C₄⋊C₄	—	47	4	no	—
384	C₄⋊C₄	—	47	4	no	—
385	C₄⋊C₄	—	47	2	no	—
386	C₄⋊C₄	—	47	2	no	—
387	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
388	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
389	C₂²⋊C₄	—	47	2	no	—
390	C₂²⋊C₄	—	47	2	no	—
391	C₂²⋊C₄	—	47	4	no	—
392	C₂²⋊C₄	—	47	4	no	—
393	C₂²⋊C₄	—	47	4	no	—
394	C₂²⋊C₄	—	47	2	no	—
395	C₂²⋊C₄	—	47	2	no	—
396	C₂²⋊C₄	—	47	4	no	—
397	C₂²⋊C₄	—	47	4	no	—
398	C₂²⋊C₄	—	47	4	no	—
399	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
400	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
401	C₄²	—	47	2	no	—
402	C₄²	—	47	2	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	47	2	no	—
409	C₂³	—	47	4	no	—
410	C₂³	—	47	4	no	—
411	C₂³	—	94	8	no	—
412	C₂³	—	94	4	no	—
413	C₂³	—	188	2	no	—
414	C₂³	—	188	4	no	—
415	C₂³	—	188	2	no	—
416	C₂³	—	188	4	no	—
417	C₂³	—	188	1	no	—
418	C₂³	—	188	1	no	—
419	C₂³	D₄×D₄₇	1	4	yes	complemented
420	C₂³	C₂³×D₄₇	1	4	yes	—
421	C₂³	C₂³×D₄₇	1	1	yes	characteristic
422	C₂³	C₂³×D₄₇	1	1	yes	characteristic
423	C₂³	C₂³×D₄₇	1	1	yes	characteristic
424	Q₈	—	94	8	no	—
425	D₄	—	2	8	no	—
426	D₄	—	2	8	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	2	no	—
429	D₄	—	47	8	no	—
430	D₄	—	47	8	no	—
431	D₄	—	94	8	no	—
432	D₄	—	94	8	no	—
433	D₄	—	94	8	no	—
434	D₄	—	94	8	no	—
435	D₄	—	94	8	no	—
436	D₄	—	94	4	no	—
437	D₄	—	188	2	no	—
438	D₄	—	188	4	no	—
439	D₄	—	188	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	47	4	no	—
448	C₂×C₄	—	47	2	no	—
449	C₂×C₄	—	47	2	no	—
450	C₂×C₄	—	47	2	no	—
451	C₂×C₄	—	47	4	no	—
452	C₂×C₄	—	94	8	no	—
453	C₂×C₄	—	94	8	no	—
454	C₂×C₄	—	94	8	no	—
455	C₂×C₄	—	94	4	no	—
456	C₂×C₄	—	94	4	no	—
457	C₂×C₄	—	188	2	no	—
458	C₂×C₄	—	188	1	no	—
459	C₂×C₄	—	188	1	no	—
460	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
461	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
462	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
463	C₂×C₄	C₂³×D₄₇	1	4	yes	—
464	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	8	4	no	—
476	C₂²	—	47	4	no	—
477	C₂²	—	94	2	no	—
478	C₂²	—	94	2	no	—
479	C₂²	—	94	4	no	—
480	C₂²	—	94	4	no	—
481	C₂²	—	94	4	no	—
482	C₂²	—	376	4	no	—
483	C₂²	—	376	8	no	—
484	C₂²	—	188	4	no	—
485	C₂²	C₂×D₄×D₄₇	1	2	yes	—
486	C₂²	C₂×D₄×D₄₇	1	2	yes	—
487	C₂²	C₂×D₄×D₄₇	1	2	yes	—
488	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
489	C₄	—	2	4	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	47	4	no	—
494	C₄	—	94	4	no	—
495	C₄	—	94	2	no	—
496	C₄	—	94	2	no	—
497	C₄	#13094069	1	2	yes	complemented
498	C₂	—	2	2	no	—
499	C₂	—	2	2	no	—
500	C₂	—	2	2	no	—
501	C₂	—	4	4	no	—
502	C₂	—	94	4	no	—
503	C₂	—	188	4	no	—
504	C₂	C₂²×D₄×D₄₇	1	1	yes	characteristic
505	C₂	C₂×#13094069	1	1	yes	characteristic
506	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₂×#121×C₄₇	C₂
hypercenter	C₂×#121	D₄₇
hypocenter	C₄₇	#3496
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂×#13094069	C₂	semidirect
2. #15689774	C₂	semidirect
3. #15689773	C₂	semidirect
4. #15689763	C₂	semidirect
5. #15689762	C₂	semidirect
6. #15689757	C₂	semidirect
7. D₄×C₂²⋊D₄₇	C₂	semidirect
8. #15689700	C₂	semidirect
9. #15689682	C₂	semidirect
10. #15689681	C₂	semidirect
11. #15689668	C₂	semidirect
12. C₂×#13093998	C₂	semidirect
13. #121×D₄₇	C₂	semidirect
14. C₂×C₄×C₂²⋊D₄₇	C₂	semidirect
15. C₂×#121×C₄₇	C₂	semidirect
17. C₂×#10625350	C₂²	semidirect
18. C₂×#10625352	C₂²	semidirect
19. C₂×#10625352	C₂²	semidirect
20. C₂²×D₁₈₈	C₂²	semidirect
22. C₂²×C₂²⋊D₄₇	C₂²	semidirect
23. C₂²×C₂²⋊D₄₇	C₂²	semidirect
24. C₂×D₄×D₄₇	C₂²	semidirect
25. C₂×D₄×D₄₇	C₂²	semidirect
26. C₂×D₄×D₄₇	C₂²	semidirect
27. C₂²×C₄×D₄₇	C₂²	semidirect
28. #13094023	C₂²	semidirect
29. #13094020	C₂²	semidirect
30. #13094010	C₂²	semidirect
31. #13094009	C₂²	semidirect
32. #13094007	C₂²	semidirect
33. #13094006	C₂²	semidirect
34. #13094005	C₂²	semidirect
35. #13094002	C₂²	semidirect
36. #13094001	C₂²	semidirect
37. #13093999	C₂²	semidirect
38. #13093998	C₂²	semidirect
39. #13093998	C₂²	semidirect
40. #13093998	C₂²	semidirect
41. #13093998	C₂²	semidirect
42. #13093997	C₂²	semidirect
43. #13093997	C₂²	semidirect
44. #13093996	C₂²	semidirect
45. #13093996	C₂²	semidirect
46. #13093996	C₂²	semidirect
47. #13093995	C₂²	semidirect
48. #13093994	C₂²	semidirect
49. #13093993	C₂²	semidirect
50. #13093992	C₂²	semidirect
51. #13093992	C₂²	semidirect
52. D₄×Dic₄₇	C₂²	semidirect
53. #13093986	C₂²	semidirect
54. C₄×C₂²⋊D₄₇	C₂²	semidirect
55. C₄×C₂²⋊D₄₇	C₂²	semidirect
56. C₄×C₂²⋊D₄₇	C₂²	semidirect
57. C₄×C₂²⋊D₄₇	C₂²	semidirect
58. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
59. C₂×C₄⋊Dic₄₇	C₂²	semidirect
60. C₂×Dic₄₇⋊C₄	C₂²	semidirect
61. C₄⋊C₄×D₄₇	C₂²	semidirect
62. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
63. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
64. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
65. C₂²⋊C₄×D₄₇	C₂²	semidirect
66. C₂×C₄×Dic₄₇	C₂²	semidirect
67. C₂²×D₄×C₄₇	C₂²	semidirect
68. C₂²×D₄×C₄₇	C₂²	semidirect
69. C₂³×C₄×C₄₇	C₂²	semidirect
70. #121×C₄₇	C₂²	semidirect
71. #121×C₄₇	C₂²	semidirect
72. #121×C₄₇	C₂²	semidirect
73. #121×C₄₇	C₂²	semidirect
74. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
75. C₂×C₂²⋊C₄×C₄₇	C₂²	semidirect
97. C₂×C₂²⋊D₄₇	D₄	semidirect
154. C₂³×C₄₇	C₂×D₄	semidirect
167. C₂²×D₄₇	C₂×D₄	semidirect
192. C₂²⋊D₄₇	C₂×D₄	semidirect
193. C₂²⋊D₄₇	C₂×D₄	semidirect
198. C₂×Dic₄₇	C₂×D₄	semidirect
239. C₄×C₄₇	H(5,𝔽₂)	semidirect
267. C₂×#121	D₄₇	semidirect
269. C₄₇	#3496	semidirect
281. C₂²×D₄	C₂×D₄₇	semidirect
282. C₂²×D₄	C₂×D₄₇	semidirect
284. C₂³×C₄	C₂×D₄₇	semidirect
305. #121	C₂×D₄₇	semidirect
306. #121	C₂×D₄₇	semidirect
307. #121	C₂×D₄₇	semidirect
308. #121	C₂×D₄₇	semidirect
323. C₂×C₄⋊C₄	C₂×D₄₇	semidirect
328. C₂×C₂²⋊C₄	C₂×D₄₇	semidirect
419. C₂³	D₄×D₄₇	semidirect
497. C₄	#13094069	semidirect