Subgroups — #26225468

Order 12032.

1382 conjugacy classes of subgroups.

The subgroup lattice has 530 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	#20243916	C₂	1	2	yes	maximal, complemented
5	#20243787	C₂	1	2	yes	maximal, complemented
6	#20243772	C₂	1	2	yes	maximal, complemented
7	#20243492	C₂	1	2	yes	maximal, complemented
8	#20243358	C₂	1	2	yes	maximal, complemented
9	C₄₇×#3498	C₂	1	1	yes	maximal, characteristic
10	#15689890	C₂²	1	2	yes	complemented
11	#15689598	C₂²	1	2	yes	complemented
12	#15689140	C₂²	1	4	yes	complemented
13	#15689128	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	complemented
18	#15689097	C₂²	1	2	yes	—
19	#15689097	C₂²	1	2	yes	complemented
20	C₂×#13093939	—	2	4	no	—
21	#15688883	C₂²	1	4	yes	complemented
22	#15688879	C₂²	1	4	yes	complemented
23	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#550	—	2	2	no	—
26	D₄²×C₄₇	—	2	4	no	—
27	D₄²×C₄₇	—	2	2	no	—
28	C₄₇×#535	C₄	1	2	yes	complemented
29	C₄₇×#535	C₄	1	2	yes	complemented
30	C₄₇×#535	C₂²	1	1	yes	characteristic
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×#127×C₄₇	C₄	1	2	yes	complemented
35	C₂×#127×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	#13093945	—	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	H(5,𝔽₂)×C₄₇	—	4	4	no	—
51	H(5,𝔽₂)×C₄₇	—	4	4	no	—
52	C₂×#41×C₄₇	—	2	1	no	—
53	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
54	C₂×#41×C₄₇	C₂×C₄	1	2	yes	complemented
55	C₂×#41×C₄₇	D₄	1	2	yes	—
56	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
57	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
58	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₄₇	—	2	4	no	—
60	C₂²×D₄×C₄₇	—	2	2	no	—
61	C₂²×D₄×C₄₇	—	2	2	no	—
62	C₂²×D₄×C₄₇	—	2	1	no	—
63	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
64	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	complemented
65	C₂²×D₄×C₄₇	D₄	1	4	yes	—
66	C₂²×D₄×C₄₇	D₄	1	2	yes	—
67	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
70	#127×C₄₇	—	2	4	no	—
71	#127×C₄₇	—	2	2	no	—
72	#127×C₄₇	C₂×C₄	1	2	yes	—
73	#127×C₄₇	C₂×C₄	1	2	yes	—
74	#127×C₄₇	C₂×C₄	1	2	yes	—
75	#127×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
76	#127×C₄₇	C₂×C₄	1	2	yes	complemented
77	#124×C₄₇	C₂×C₄	1	2	yes	—
78	#124×C₄₇	C₂×C₄	1	2	yes	complemented
79	#124×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
80	#124×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
81	#121×C₄₇	—	2	4	no	—
82	#121×C₄₇	—	2	4	no	—
83	#121×C₄₇	—	2	2	no	—
84	#121×C₄₇	—	2	2	no	—
85	#121×C₄₇	—	2	4	no	—
86	#121×C₄₇	—	2	2	no	—
87	#120×C₄₇	—	2	4	no	—
88	#120×C₄₇	—	2	2	no	—
89	#120×C₄₇	—	2	4	no	—
90	#120×C₄₇	—	2	2	no	—
91	C₄×Q₈×C₄₇	—	2	1	no	—
92	C₄×D₄×C₄₇	—	2	2	no	—
93	C₄×D₄×C₄₇	—	2	1	no	—
94	C₄×D₄×C₄₇	—	2	4	no	—
95	C₄×D₄×C₄₇	—	2	2	no	—
96	#117×C₄₇	C₂×C₄	1	2	yes	complemented
97	#117×C₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	complemented
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	C₂⁴×C₄₇	—	2	2	no	—
101	C₂⁴×C₄₇	—	2	1	no	—
102	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
103	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
104	#41×C₄₇	—	2	4	no	—
105	#41×C₄₇	—	2	4	no	—
106	#41×C₄₇	—	2	4	no	—
107	#41×C₄₇	—	4	4	no	—
108	#41×C₄₇	—	4	4	no	—
109	#41×C₄₇	—	4	4	no	—
110	#41×C₄₇	—	4	4	no	—
111	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂×D₄×C₄₇	—	2	4	no	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	2	2	no	—
117	C₂×D₄×C₄₇	—	2	1	no	—
118	C₂×D₄×C₄₇	—	2	4	no	—
119	C₂×D₄×C₄₇	—	2	4	no	—
120	C₂×D₄×C₄₇	—	2	4	no	—
121	C₂×D₄×C₄₇	—	2	2	no	—
122	C₂×D₄×C₄₇	—	2	1	no	—
123	C₂×D₄×C₄₇	—	2	4	no	—
124	C₂×D₄×C₄₇	—	2	4	no	—
125	C₂×D₄×C₄₇	—	4	4	no	—
126	C₂×D₄×C₄₇	—	4	4	no	—
127	C₂×D₄×C₄₇	—	4	4	no	—
128	C₂×D₄×C₄₇	—	4	8	no	—
129	C₂×D₄×C₄₇	—	4	8	no	—
130	C₂×D₄×C₄₇	—	4	4	no	—
131	C₂×D₄×C₄₇	—	8	4	no	—
132	C₂×D₄×C₄₇	—	8	8	no	—
133	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
134	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
135	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
138	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
140	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
142	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₇	—	2	2	no	—
144	C₂²×C₄×C₄₇	—	2	1	no	—
145	C₂²×C₄×C₄₇	—	2	2	no	—
146	C₂²×C₄×C₄₇	—	2	1	no	—
147	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
148	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
151	C₂²×Dic₄₇	—	4	4	no	—
152	C₄⋊C₄×C₄₇	—	2	2	no	—
153	C₄⋊C₄×C₄₇	—	2	2	no	—
154	C₄⋊C₄×C₄₇	—	2	1	no	—
155	C₂²⋊C₄×C₄₇	—	2	2	no	—
156	C₂²⋊C₄×C₄₇	—	2	4	no	—
157	C₂²⋊C₄×C₄₇	—	2	2	no	—
158	C₂²⋊C₄×C₄₇	—	2	1	no	—
159	C₂²⋊C₄×C₄₇	—	2	4	no	—
160	C₂²⋊C₄×C₄₇	—	2	2	no	—
161	C₄²×C₄₇	—	2	2	no	—
162	C₄²×C₄₇	—	2	1	no	—
163	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
165	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²⋊Dic₄₇	—	2	4	no	—
167	C₂²⋊Dic₄₇	—	4	4	no	—
168	C₄⋊Dic₄₇	—	2	4	no	—
169	C₄×Dic₄₇	—	2	4	no	—
170	#10625329	—	2	4	no	—
171	#10625329	—	2	4	no	—
172	#10625329	—	4	4	no	—
173	C₂×C₄₇⋊C₈	—	2	4	no	—
174	C₂×C₄₇⋊C₈	—	4	4	no	—
175	C₂³×C₄₇	—	2	4	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	1	no	—
178	C₂³×C₄₇	—	4	4	no	—
179	C₂³×C₄₇	—	4	4	no	—
180	C₂³×C₄₇	—	4	2	no	—
181	C₂³×C₄₇	—	8	2	no	—
182	C₂³×C₄₇	—	8	4	no	—
183	C₂³×C₄₇	—	8	2	no	—
184	C₂³×C₄₇	—	8	4	no	—
185	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
187	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₄₇	—	2	2	no	—
190	Q₈×C₄₇	—	2	2	no	—
191	Q₈×C₄₇	—	2	2	no	—
192	D₄×C₄₇	—	2	4	no	—
193	D₄×C₄₇	—	2	4	no	—
194	D₄×C₄₇	—	2	4	no	—
195	D₄×C₄₇	—	2	2	no	—
196	D₄×C₄₇	—	2	4	no	—
197	D₄×C₄₇	—	2	2	no	—
198	D₄×C₄₇	—	2	4	no	—
199	D₄×C₄₇	—	2	2	no	—
200	D₄×C₄₇	—	4	4	no	—
201	D₄×C₄₇	—	4	4	no	—
202	D₄×C₄₇	—	4	4	no	—
203	D₄×C₄₇	—	4	8	no	—
204	D₄×C₄₇	—	4	4	no	—
205	D₄×C₄₇	—	4	4	no	—
206	D₄×C₄₇	—	4	2	no	—
207	D₄×C₄₇	—	4	2	no	—
208	D₄×C₄₇	—	8	4	no	—
209	D₄×C₄₇	—	8	4	no	—
210	D₄×C₄₇	—	8	4	no	—
211	C₂×C₄×C₄₇	—	2	1	no	—
212	C₂×C₄×C₄₇	—	2	4	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	2	1	no	—
216	C₂×C₄×C₄₇	—	2	1	no	—
217	C₂×C₄×C₄₇	—	4	4	no	—
218	C₂×C₄×C₄₇	—	4	4	no	—
219	C₂×C₄×C₄₇	—	4	2	no	—
220	C₂×C₄×C₄₇	—	4	4	no	—
221	C₂×C₄×C₄₇	—	4	2	no	—
222	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
224	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
227	C₂×Dic₄₇	—	4	4	no	—
228	C₂×Dic₄₇	—	16	4	no	—
229	C₄₇⋊C₈	—	4	4	no	—
230	#21782	—	47	1	no	maximal, Sylow
231	C₂²×C₄₇	—	2	2	no	—
232	C₂²×C₄₇	—	2	2	no	—
233	C₂²×C₄₇	—	2	4	no	—
234	C₂²×C₄₇	—	4	1	no	—
235	C₂²×C₄₇	—	4	2	no	—
236	C₂²×C₄₇	—	4	4	no	—
237	C₂²×C₄₇	—	4	2	no	—
238	C₂²×C₄₇	—	4	4	no	—
239	C₂²×C₄₇	—	4	2	no	—
240	C₂²×C₄₇	—	4	2	no	—
241	C₂²×C₄₇	—	4	1	no	—
242	C₂²×C₄₇	—	8	4	no	—
243	C₂²×C₄₇	—	16	2	no	—
244	C₂²×C₄₇	—	16	4	no	—
245	C₂²×C₄₇	—	16	4	no	—
246	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₄₇	#534	1	2	yes	—
248	C₄×C₄₇	—	2	2	no	—
249	C₄×C₄₇	—	2	2	no	—
250	C₄×C₄₇	—	2	2	no	—
251	C₄×C₄₇	—	4	2	no	—
252	C₄×C₄₇	—	4	1	no	—
253	C₄×C₄₇	—	4	1	no	—
254	C₄×C₄₇	#518	1	2	yes	—
255	C₄×C₄₇	#534	1	2	yes	—
256	Dic₄₇	—	8	4	no	—
257	#3498	D₄₇	1	1	yes	characteristic
258	#2888	—	47	1	no	—
259	#2883	—	47	1	no	—
260	#1911	—	47	2	no	—
261	#1910	—	47	2	no	—
262	#1887	—	47	2	no	—
263	#1884	—	47	2	no	—
264	#1827	—	47	2	no	—
265	#1795	—	47	2	no	—
266	C₂×C₄₇	—	2	2	no	—
267	C₂×C₄₇	—	2	1	no	—
268	C₂×C₄₇	—	4	4	no	—
269	C₂×C₄₇	—	4	2	no	—
270	C₂×C₄₇	—	4	2	no	—
271	C₂×C₄₇	—	8	2	no	—
272	C₂×C₄₇	—	8	1	no	—
273	C₂×C₄₇	#2308	1	1	yes	characteristic
274	C₂×H(5,𝔽₂)	C₂×D₄₇	1	1	yes	characteristic
275	C₂×H(5,𝔽₂)	C₂×D₄₇	1	1	yes	characteristic
276	#568	—	47	2	no	—
277	#550	—	2	2	no	—
278	D₄²	—	2	4	no	—
279	D₄²	—	2	2	no	—
280	#535	Dic₄₇	1	2	yes	complemented
281	#535	Dic₄₇	1	2	yes	complemented
282	#535	C₂×D₄₇	1	1	yes	characteristic
283	#535	C₂×D₄₇	1	1	yes	characteristic
284	#532	Dic₄₇	1	2	yes	complemented
285	#532	C₂×D₄₇	1	1	yes	characteristic
286	C₂×#127	Dic₄₇	1	2	yes	complemented
287	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
288	#518	—	47	2	no	—
289	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
290	#421	—	47	4	no	—
291	#418	—	47	4	no	—
292	#413	—	47	2	no	—
293	#413	—	94	2	no	—
294	C₂×#100	—	47	2	no	—
295	C₂×#100	—	94	2	no	—
296	#410	—	47	2	no	—
297	#410	—	47	2	no	—
298	C₂×#99	—	94	4	no	—
299	#339	—	47	4	no	—
300	H(3,ℤ/4)	—	47	4	no	—
301	C₄₇	#21782	1	1	yes	characteristic, complemented, Sylow
302	H(5,𝔽₂)	—	4	4	no	—
303	H(5,𝔽₂)	—	4	4	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	C₂×Dic₄₇	1	2	yes	—
306	C₂×#41	C₂×Dic₄₇	1	2	yes	complemented
307	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
308	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
309	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
310	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
311	C₂²×D₄	—	2	4	no	—
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	—	2	2	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
316	C₂²×D₄	C₂×Dic₄₇	1	2	yes	complemented
317	C₂²×D₄	C₂²⋊D₄₇	1	4	yes	—
318	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
319	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
321	#131	—	188	4	no	—
322	C₂×M₁₆	—	47	4	no	—
323	C₂×M₁₆	—	94	4	no	—
324	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
325	#127	—	2	4	no	—
326	#127	—	2	2	no	—
327	#127	C₂×Dic₄₇	1	2	yes	—
328	#127	C₂×Dic₄₇	1	2	yes	—
329	#127	C₂×Dic₄₇	1	2	yes	—
330	#127	C₂×Dic₄₇	1	1	yes	characteristic, complemented
331	#127	C₂×Dic₄₇	1	2	yes	complemented
332	#124	C₂×Dic₄₇	1	2	yes	—
333	#124	C₂×Dic₄₇	1	2	yes	complemented
334	#124	C₂×Dic₄₇	1	1	yes	characteristic, complemented
335	#124	C₂×Dic₄₇	1	1	yes	characteristic, complemented
336	#121	—	2	4	no	—
337	#121	—	2	4	no	—
338	#121	—	2	2	no	—
339	#121	—	2	2	no	—
340	#121	—	2	4	no	—
341	#121	—	2	2	no	—
342	#120	—	2	4	no	—
343	#120	—	2	2	no	—
344	#120	—	2	4	no	—
345	#120	—	2	2	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	—	2	4	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	188	4	no	—
352	#117	—	47	4	no	—
353	#117	C₂×Dic₄₇	1	2	yes	complemented
354	#117	C₂²×D₄₇	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	—	94	4	no	—
356	C₂×C₄²	C₂×Dic₄₇	1	2	yes	complemented
357	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
358	#104	—	188	4	no	—
359	#102	—	188	4	no	—
360	#101	—	94	2	no	—
361	#100	—	94	4	no	—
362	#100	—	94	2	no	—
363	#99	—	94	4	no	—
364	#99	—	94	4	no	—
365	C₂⁴	—	2	2	no	—
366	C₂⁴	—	2	1	no	—
367	C₂⁴	C₂²⋊Dic₄₇	1	4	yes	—
368	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
369	#41	—	2	4	no	—
370	#41	—	2	4	no	—
371	#41	—	2	4	no	—
372	#41	—	4	4	no	—
373	#41	—	4	4	no	—
374	#41	—	4	4	no	—
375	#41	—	4	4	no	—
376	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
377	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
378	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	—	4	8	no	—
394	C₂×D₄	—	4	8	no	—
395	C₂×D₄	—	4	4	no	—
396	C₂×D₄	—	8	4	no	—
397	C₂×D₄	—	8	8	no	—
398	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
399	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
400	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
401	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
402	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
403	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
404	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
405	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
406	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
407	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	188	4	no	—
413	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
414	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
415	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
416	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
417	M₁₆	—	94	4	no	—
418	M₁₆	—	94	4	no	—
419	M₁₆	—	188	4	no	—
420	C₂×C₈	—	94	4	no	—
421	C₂×C₈	—	188	4	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	94	4	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	94	4	no	—
433	C₂²⋊C₄	—	188	4	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	94	4	no	—
437	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
438	C₄²	C₂²×Dic₄₇	1	2	yes	—
439	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
440	C₂³	—	2	4	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	8	2	no	—
447	C₂³	—	8	4	no	—
448	C₂³	—	8	2	no	—
449	C₂³	—	8	4	no	—
450	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
451	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
452	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
453	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
454	Q₈	—	2	2	no	—
455	Q₈	—	2	2	no	—
456	Q₈	—	2	2	no	—
457	D₄	—	2	4	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	4	no	—
462	D₄	—	2	2	no	—
463	D₄	—	2	4	no	—
464	D₄	—	2	2	no	—
465	D₄	—	4	4	no	—
466	D₄	—	4	4	no	—
467	D₄	—	4	4	no	—
468	D₄	—	4	8	no	—
469	D₄	—	4	4	no	—
470	D₄	—	4	4	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	8	4	no	—
474	D₄	—	8	4	no	—
475	D₄	—	8	4	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	188	4	no	—
488	C₂×C₄	—	752	4	no	—
489	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
490	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
491	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
492	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
493	C₂×C₄	#13094069	1	4	yes	—
494	C₈	—	188	4	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	8	4	no	—
507	C₂²	—	16	2	no	—
508	C₂²	—	16	4	no	—
509	C₂²	—	16	4	no	—
510	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
511	C₂²	#15689682	1	2	yes	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	376	4	no	—
519	C₄	#15689598	1	2	yes	—
520	C₄	#15689682	1	2	yes	—
521	C₂	—	2	1	no	—
522	C₂	—	2	2	no	—
523	C₂	—	4	4	no	—
524	C₂	—	4	2	no	—
525	C₂	—	4	2	no	—
526	C₂	—	8	2	no	—
527	C₂	—	8	1	no	—
528	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×#3498	C₂
socle	C₂×C₄₇	#2308
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3498	D₄₇
hypocenter	C₄₇	#21782
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3498

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. #20243916	C₂	semidirect
5. #20243787	C₂	semidirect
6. #20243772	C₂	semidirect
7. #20243492	C₂	semidirect
8. #20243358	C₂	semidirect
10. #15689890	C₂²	semidirect
11. #15689598	C₂²	semidirect
12. #15689140	C₂²	semidirect
13. #15689128	C₂²	semidirect
17. C₂×#13093941	C₂²	semidirect
19. #15689097	C₂²	semidirect
21. #15688883	C₂²	semidirect
22. #15688879	C₂²	semidirect
28. C₄₇×#535	C₄	semidirect
29. C₄₇×#535	C₄	semidirect
32. C₄₇×#532	C₄	semidirect
34. C₂×#127×C₄₇	C₄	semidirect
54. C₂×#41×C₄₇	C₂×C₄	semidirect
64. C₂²×D₄×C₄₇	C₂×C₄	semidirect
69. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
75. #127×C₄₇	C₂×C₄	semidirect
76. #127×C₄₇	C₂×C₄	semidirect
78. #124×C₄₇	C₂×C₄	semidirect
79. #124×C₄₇	C₂×C₄	semidirect
80. #124×C₄₇	C₂×C₄	semidirect
96. #117×C₄₇	C₂×C₄	semidirect
98. C₂×C₄²×C₄₇	C₂×C₄	semidirect
280. #535	Dic₄₇	semidirect
281. #535	Dic₄₇	semidirect
284. #532	Dic₄₇	semidirect
286. C₂×#127	Dic₄₇	semidirect
301. C₄₇	#21782	semidirect
306. C₂×#41	C₂×Dic₄₇	semidirect
316. C₂²×D₄	C₂×Dic₄₇	semidirect
324. C₄⋊Q₈	C₂×Dic₄₇	semidirect
330. #127	C₂×Dic₄₇	semidirect
331. #127	C₂×Dic₄₇	semidirect
333. #124	C₂×Dic₄₇	semidirect
334. #124	C₂×Dic₄₇	semidirect
335. #124	C₂×Dic₄₇	semidirect
353. #117	C₂×Dic₄₇	semidirect
356. 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
#20243916	2
#20243787	2
#20243772	2
#20243492	2
#20243358	2
C₄₇×#3498	2
#21782	47