Subgroups — #26225486

Order 12032.

1278 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	#20251867	C₂	1	1	yes	maximal, characteristic, complemented
2	#20251849	C₂	1	1	yes	maximal, characteristic, complemented
3	#20243921	C₂	1	2	yes	maximal, complemented
4	#20243911	C₂	1	2	yes	maximal, complemented
5	#20243777	C₂	1	2	yes	maximal, complemented
6	#20243772	C₂	1	2	yes	maximal, complemented
7	#20243492	C₂	1	2	yes	maximal, complemented
8	#20243363	C₂	1	2	yes	maximal, complemented
9	C₄₇×#3500	C₂	1	1	yes	maximal, characteristic
10	#15689890	C₂²	1	2	yes	—
11	#15689598	C₂²	1	2	yes	—
12	#15689140	C₂²	1	4	yes	complemented
13	#15689132	C₂²	1	4	yes	complemented
14	#15689107	—	2	2	no	—
15	#15689107	C₂²	1	2	yes	—
16	C₂×#13093941	—	2	2	no	—
17	C₂×#13093941	C₂²	1	2	yes	—
18	#15689097	C₂²	1	2	yes	—
19	#15689097	C₂²	1	2	yes	—
20	C₂×#13093939	—	2	4	no	—
21	#15688883	C₂²	1	4	yes	complemented
22	#15688879	C₂²	1	4	yes	complemented
23	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#548	—	2	2	no	—
26	C₄₇×#546	—	2	2	no	—
27	C₄₇×#546	—	2	4	no	—
28	C₄₇×#536	C₄	1	2	yes	complemented
29	C₄₇×#536	C₂²	1	1	yes	characteristic
30	C₄₇×#535	C₄	1	2	yes	complemented
31	C₄₇×#535	C₂²	1	1	yes	characteristic
32	C₄₇×#532	C₄	1	2	yes	complemented
33	C₄₇×#532	C₂²	1	1	yes	characteristic
34	C₂×#124×C₄₇	C₄	1	2	yes	complemented
35	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
36	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
37	#13094031	—	4	4	no	—
38	C₂×#10625329	—	2	4	no	—
39	C₂×#10625329	C₂³	1	4	yes	—
40	D₄×Dic₄₇	—	4	4	no	—
41	#13093983	C₂³	1	4	yes	—
42	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
43	#13093951	—	4	4	no	—
44	#13093948	—	4	4	no	—
45	#13093943	—	2	2	no	—
46	#13093941	—	2	2	no	—
47	#13093941	—	2	4	no	—
48	#13093939	—	2	4	no	—
49	#13093939	—	2	4	no	—
50	2₋¹⁺⁴×C₄₇	—	4	4	no	—
51	H(5,𝔽₂)×C₄₇	—	4	4	no	—
52	C₂×#41×C₄₇	—	2	1	no	—
53	C₂×#41×C₄₇	—	2	2	no	—
54	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×#41×C₄₇	C₂×C₄	1	2	yes	complemented
56	C₂×#41×C₄₇	D₄	1	2	yes	—
57	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
58	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
59	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₄₇	—	2	1	no	—
61	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
62	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
64	C₂²×D₄×C₄₇	D₄	1	4	yes	—
65	C₂²×D₄×C₄₇	D₄	1	2	yes	—
66	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
68	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
69	#127×C₄₇	C₂×C₄	1	2	yes	—
70	#127×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
71	#124×C₄₇	—	2	4	no	—
72	#124×C₄₇	—	2	2	no	—
73	#124×C₄₇	C₂×C₄	1	2	yes	—
74	#124×C₄₇	C₂×C₄	1	2	yes	—
75	#124×C₄₇	C₂×C₄	1	2	yes	—
76	#124×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
77	#124×C₄₇	C₂×C₄	1	2	yes	complemented
78	#124×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
79	#123×C₄₇	—	2	4	no	—
80	#123×C₄₇	—	2	2	no	—
81	C₂²⋊Q₈×C₄₇	—	2	4	no	—
82	C₂²⋊Q₈×C₄₇	—	2	2	no	—
83	#121×C₄₇	—	2	4	no	—
84	#121×C₄₇	—	2	4	no	—
85	#121×C₄₇	—	2	2	no	—
86	#121×C₄₇	—	2	2	no	—
87	#120×C₄₇	—	2	4	no	—
88	#120×C₄₇	—	2	2	no	—
89	C₄×Q₈×C₄₇	—	2	1	no	—
90	C₄×D₄×C₄₇	—	2	2	no	—
91	C₄×D₄×C₄₇	—	2	1	no	—
92	C₄×D₄×C₄₇	—	2	4	no	—
93	C₄×D₄×C₄₇	—	2	2	no	—
94	#117×C₄₇	C₂×C₄	1	2	yes	complemented
95	#117×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
97	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
98	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	complemented
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
101	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
102	#41×C₄₇	—	2	4	no	—
103	#41×C₄₇	—	2	4	no	—
104	#41×C₄₇	—	2	4	no	—
105	#41×C₄₇	—	4	4	no	—
106	#41×C₄₇	—	4	4	no	—
107	#41×C₄₇	—	4	4	no	—
108	#41×C₄₇	—	4	8	no	—
109	#41×C₄₇	—	4	4	no	—
110	C₂×Q₈×C₄₇	—	2	2	no	—
111	C₂×Q₈×C₄₇	—	2	1	no	—
112	C₂×Q₈×C₄₇	—	2	4	no	—
113	C₂×Q₈×C₄₇	—	4	4	no	—
114	C₂×Q₈×C₄₇	—	4	4	no	—
115	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₄₇	—	2	2	no	—
120	C₂×D₄×C₄₇	—	2	1	no	—
121	C₂×D₄×C₄₇	—	2	4	no	—
122	C₂×D₄×C₄₇	—	2	2	no	—
123	C₂×D₄×C₄₇	—	2	4	no	—
124	C₂×D₄×C₄₇	—	4	4	no	—
125	C₂×D₄×C₄₇	—	4	4	no	—
126	C₂×D₄×C₄₇	—	4	8	no	—
127	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
128	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
129	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₄₇	—	2	2	no	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	2	1	no	—
140	C₂²×C₄×C₄₇	—	2	2	no	—
141	C₂²×C₄×C₄₇	—	2	1	no	—
142	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
143	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂²×Dic₄₇	—	4	4	no	—
147	C₄⋊C₄×C₄₇	—	2	2	no	—
148	C₄⋊C₄×C₄₇	—	2	4	no	—
149	C₄⋊C₄×C₄₇	—	2	2	no	—
150	C₄⋊C₄×C₄₇	—	2	1	no	—
151	C₂²⋊C₄×C₄₇	—	2	4	no	—
152	C₂²⋊C₄×C₄₇	—	2	2	no	—
153	C₂²⋊C₄×C₄₇	—	2	4	no	—
154	C₂²⋊C₄×C₄₇	—	2	4	no	—
155	C₂²⋊C₄×C₄₇	—	2	4	no	—
156	C₂²⋊C₄×C₄₇	—	2	2	no	—
157	C₂²⋊C₄×C₄₇	—	2	1	no	—
158	C₂²⋊C₄×C₄₇	—	2	2	no	—
159	C₄²×C₄₇	—	2	2	no	—
160	C₄²×C₄₇	—	2	1	no	—
161	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
163	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²⋊Dic₄₇	—	2	4	no	—
165	C₂²⋊Dic₄₇	—	4	4	no	—
166	C₄⋊Dic₄₇	—	2	4	no	—
167	C₄×Dic₄₇	—	2	4	no	—
168	#10625329	—	2	4	no	—
169	#10625329	—	2	4	no	—
170	#10625329	—	4	4	no	—
171	C₂×C₄₇⋊C₈	—	2	4	no	—
172	C₂×C₄₇⋊C₈	—	4	4	no	—
173	C₂³×C₄₇	—	2	4	no	—
174	C₂³×C₄₇	—	2	1	no	—
175	C₂³×C₄₇	—	4	4	no	—
176	C₂³×C₄₇	—	8	2	no	—
177	C₂³×C₄₇	—	8	4	no	—
178	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
179	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₄₇	—	2	2	no	—
183	Q₈×C₄₇	—	2	2	no	—
184	Q₈×C₄₇	—	2	4	no	—
185	Q₈×C₄₇	—	2	2	no	—
186	Q₈×C₄₇	—	4	4	no	—
187	Q₈×C₄₇	—	4	2	no	—
188	D₄×C₄₇	—	2	4	no	—
189	D₄×C₄₇	—	2	4	no	—
190	D₄×C₄₇	—	2	4	no	—
191	D₄×C₄₇	—	2	2	no	—
192	D₄×C₄₇	—	2	2	no	—
193	D₄×C₄₇	—	2	4	no	—
194	D₄×C₄₇	—	2	2	no	—
195	D₄×C₄₇	—	4	4	no	—
196	D₄×C₄₇	—	4	4	no	—
197	D₄×C₄₇	—	4	4	no	—
198	D₄×C₄₇	—	4	2	no	—
199	D₄×C₄₇	—	8	4	no	—
200	D₄×C₄₇	—	8	2	no	—
201	C₂×C₄×C₄₇	—	2	4	no	—
202	C₂×C₄×C₄₇	—	2	4	no	—
203	C₂×C₄×C₄₇	—	2	1	no	—
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	—	2	1	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	1	no	—
208	C₂×C₄×C₄₇	—	4	4	no	—
209	C₂×C₄×C₄₇	—	4	4	no	—
210	C₂×C₄×C₄₇	—	4	4	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	8	1	no	—
214	C₂×C₄×C₄₇	—	8	2	no	—
215	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
216	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
220	C₂×Dic₄₇	—	4	4	no	—
221	C₂×Dic₄₇	—	16	4	no	—
222	C₄₇⋊C₈	—	4	4	no	—
223	#21784	—	47	1	no	maximal, Sylow
224	C₂²×C₄₇	—	2	2	no	—
225	C₂²×C₄₇	—	2	2	no	—
226	C₂²×C₄₇	—	2	4	no	—
227	C₂²×C₄₇	—	4	1	no	—
228	C₂²×C₄₇	—	4	2	no	—
229	C₂²×C₄₇	—	4	4	no	—
230	C₂²×C₄₇	—	4	2	no	—
231	C₂²×C₄₇	—	4	2	no	—
232	C₂²×C₄₇	—	4	1	no	—
233	C₂²×C₄₇	—	8	4	no	—
234	C₂²×C₄₇	—	16	4	no	—
235	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₄₇	#534	1	2	yes	—
237	C₄×C₄₇	—	2	2	no	—
238	C₄×C₄₇	—	2	2	no	—
239	C₄×C₄₇	—	4	1	no	—
240	C₄×C₄₇	—	4	2	no	—
241	C₄×C₄₇	—	4	1	no	—
242	C₄×C₄₇	—	4	2	no	—
243	C₄×C₄₇	—	4	1	no	—
244	C₄×C₄₇	#518	1	2	yes	—
245	C₄×C₄₇	#534	1	2	yes	—
246	Dic₄₇	—	8	4	no	—
247	#3500	D₄₇	1	1	yes	characteristic
248	#2888	—	47	1	no	—
249	#2883	—	47	1	no	—
250	#1911	—	47	2	no	—
251	#1909	—	47	2	no	—
252	#1885	—	47	2	no	—
253	#1884	—	47	2	no	—
254	#1827	—	47	2	no	—
255	#1796	—	47	2	no	—
256	C₂×C₄₇	—	2	2	no	—
257	C₂×C₄₇	—	2	1	no	—
258	C₂×C₄₇	—	4	4	no	—
259	C₂×C₄₇	—	4	2	no	—
260	C₂×C₄₇	—	4	2	no	—
261	C₂×C₄₇	—	8	1	no	—
262	C₂×C₄₇	#2308	1	1	yes	characteristic
263	C₂×2₋¹⁺⁴	C₂×D₄₇	1	1	yes	characteristic
264	C₂×H(5,𝔽₂)	C₂×D₄₇	1	1	yes	characteristic
265	#568	—	47	2	no	—
266	#548	—	2	2	no	—
267	#546	—	2	2	no	—
268	#546	—	2	4	no	—
269	#536	Dic₄₇	1	2	yes	complemented
270	#536	C₂×D₄₇	1	1	yes	characteristic
271	#535	Dic₄₇	1	2	yes	complemented
272	#535	C₂×D₄₇	1	1	yes	characteristic
273	#532	Dic₄₇	1	2	yes	complemented
274	#532	C₂×D₄₇	1	1	yes	characteristic
275	C₂×#124	Dic₄₇	1	2	yes	complemented
276	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
277	#518	—	47	2	no	—
278	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
279	#421	—	47	4	no	—
280	#419	—	47	4	no	—
281	#413	—	47	2	no	—
282	#413	—	94	2	no	—
283	C₂×#100	—	47	2	no	—
284	C₂×#100	—	94	2	no	—
285	#410	—	47	2	no	—
286	#410	—	47	2	no	—
287	C₂×#99	—	94	4	no	—
288	#339	—	47	4	no	—
289	H(3,ℤ/4)	—	47	4	no	—
290	C₄₇	#21784	1	1	yes	characteristic, complemented, Sylow
291	2₋¹⁺⁴	—	4	4	no	—
292	H(5,𝔽₂)	—	4	4	no	—
293	C₂×#41	—	2	1	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	C₂×Dic₄₇	1	2	yes	—
296	C₂×#41	C₂×Dic₄₇	1	2	yes	complemented
297	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
298	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
299	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
300	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
301	C₂²×Q₈	—	2	1	no	—
302	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	complemented
303	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
304	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
305	C₂²×D₄	C₂²⋊D₄₇	1	4	yes	—
306	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
307	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
308	#131	—	188	4	no	—
309	C₂×M₁₆	—	47	4	no	—
310	C₂×M₁₆	—	94	4	no	—
311	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
312	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
313	#127	C₂×Dic₄₇	1	2	yes	—
314	#127	C₂×Dic₄₇	1	1	yes	characteristic, complemented
315	#124	—	2	4	no	—
316	#124	—	2	2	no	—
317	#124	C₂×Dic₄₇	1	2	yes	—
318	#124	C₂×Dic₄₇	1	2	yes	—
319	#124	C₂×Dic₄₇	1	2	yes	—
320	#124	C₂×Dic₄₇	1	1	yes	characteristic, complemented
321	#124	C₂×Dic₄₇	1	2	yes	complemented
322	#124	C₂×Dic₄₇	1	1	yes	characteristic, complemented
323	#123	—	2	4	no	—
324	#123	—	2	2	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	#121	—	2	4	no	—
328	#121	—	2	4	no	—
329	#121	—	2	2	no	—
330	#121	—	2	2	no	—
331	#120	—	2	4	no	—
332	#120	—	2	2	no	—
333	C₄×Q₈	—	2	1	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	188	4	no	—
339	#117	—	47	4	no	—
340	#117	C₂×Dic₄₇	1	2	yes	complemented
341	#117	C₂²×D₄₇	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	94	4	no	—
345	C₂×C₄²	C₂×Dic₄₇	1	2	yes	complemented
346	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
347	#104	—	188	4	no	—
348	#103	—	188	4	no	—
349	#101	—	94	2	no	—
350	#100	—	94	4	no	—
351	#100	—	94	2	no	—
352	#99	—	94	4	no	—
353	#99	—	94	4	no	—
354	C₂⁴	C₂²⋊Dic₄₇	1	4	yes	—
355	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
356	#41	—	2	4	no	—
357	#41	—	2	4	no	—
358	#41	—	2	4	no	—
359	#41	—	4	4	no	—
360	#41	—	4	4	no	—
361	#41	—	4	4	no	—
362	#41	—	4	8	no	—
363	#41	—	4	4	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	4	4	no	—
368	C₂×Q₈	—	4	4	no	—
369	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
370	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
371	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
372	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	8	no	—
381	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
382	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
383	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
384	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
385	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
386	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
387	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
388	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	188	4	no	—
397	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
398	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
399	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
400	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
401	M₁₆	—	94	4	no	—
402	M₁₆	—	94	4	no	—
403	M₁₆	—	188	4	no	—
404	C₂×C₈	—	94	4	no	—
405	C₂×C₈	—	188	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	94	4	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	94	4	no	—
420	C₂²⋊C₄	—	188	4	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	94	4	no	—
424	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
425	C₄²	C₂²×Dic₄₇	1	2	yes	—
426	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
427	C₂³	—	2	4	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	8	2	no	—
431	C₂³	—	8	4	no	—
432	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
433	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
434	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
435	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	4	no	—
439	Q₈	—	2	2	no	—
440	Q₈	—	4	4	no	—
441	Q₈	—	4	2	no	—
442	D₄	—	2	4	no	—
443	D₄	—	2	4	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	4	no	—
448	D₄	—	2	2	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	4	no	—
451	D₄	—	4	4	no	—
452	D₄	—	4	2	no	—
453	D₄	—	8	4	no	—
454	D₄	—	8	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	8	1	no	—
468	C₂×C₄	—	8	2	no	—
469	C₂×C₄	—	188	4	no	—
470	C₂×C₄	—	752	4	no	—
471	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
472	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
473	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
474	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
475	C₂×C₄	#13094069	1	4	yes	—
476	C₈	—	188	4	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	8	4	no	—
487	C₂²	—	16	4	no	—
488	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
489	C₂²	#15689682	1	2	yes	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	376	4	no	—
498	C₄	#15689598	1	2	yes	—
499	C₄	#15689682	1	2	yes	—
500	C₂	—	2	1	no	—
501	C₂	—	2	2	no	—
502	C₂	—	4	4	no	—
503	C₂	—	4	2	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	1	no	—
506	C₂	#20245966	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20245966
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3500	C₂
socle	C₂×C₄₇	#2308
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3500	D₄₇
hypocenter	C₄₇	#21784
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3500

Complements

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

N	H ≅ G/N	type
1. #20251867	C₂	semidirect
2. #20251849	C₂	semidirect
3. #20243921	C₂	semidirect
4. #20243911	C₂	semidirect
5. #20243777	C₂	semidirect
6. #20243772	C₂	semidirect
7. #20243492	C₂	semidirect
8. #20243363	C₂	semidirect
12. #15689140	C₂²	semidirect
13. #15689132	C₂²	semidirect
21. #15688883	C₂²	semidirect
22. #15688879	C₂²	semidirect
28. C₄₇×#536	C₄	semidirect
30. C₄₇×#535	C₄	semidirect
32. C₄₇×#532	C₄	semidirect
34. C₂×#124×C₄₇	C₄	semidirect
55. C₂×#41×C₄₇	C₂×C₄	semidirect
61. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
67. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
68. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
70. #127×C₄₇	C₂×C₄	semidirect
76. #124×C₄₇	C₂×C₄	semidirect
77. #124×C₄₇	C₂×C₄	semidirect
78. #124×C₄₇	C₂×C₄	semidirect
94. #117×C₄₇	C₂×C₄	semidirect
98. C₂×C₄²×C₄₇	C₂×C₄	semidirect
269. #536	Dic₄₇	semidirect
271. #535	Dic₄₇	semidirect
273. #532	Dic₄₇	semidirect
275. C₂×#124	Dic₄₇	semidirect
290. C₄₇	#21784	semidirect
296. C₂×#41	C₂×Dic₄₇	semidirect
302. C₂²×Q₈	C₂×Dic₄₇	semidirect
311. C₄⋊Q₈	C₂×Dic₄₇	semidirect
312. C₄⋊Q₈	C₂×Dic₄₇	semidirect
314. #127	C₂×Dic₄₇	semidirect
320. #124	C₂×Dic₄₇	semidirect
321. #124	C₂×Dic₄₇	semidirect
322. #124	C₂×Dic₄₇	semidirect
340. #117	C₂×Dic₄₇	semidirect
345. C₂×C₄²	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20251867	2
#20251849	2
#20243921	2
#20243911	2
#20243777	2
#20243772	2
#20243492	2
#20243363	2
C₄₇×#3500	2
#21784	47