Subgroups — #26225436

Order 12032.

1318 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20251849	C₂	1	2	yes	maximal, complemented
2	#20243931	C₂	1	4	yes	maximal, complemented
3	#20243802	C₂	1	4	yes	maximal, complemented
4	#20243496	C₂	1	2	yes	maximal, complemented
5	#20243306	C₂	1	2	yes	maximal, complemented
6	C₄₇×#3485	C₂	1	1	yes	maximal, characteristic
7	#15689598	C₂²	1	4	yes	—
8	#15689097	—	2	4	no	—
9	C₂×#13093939	—	2	4	no	—
10	C₂×#13093939	C₂²	1	4	yes	—
11	C₂×#13093939	C₂²	1	4	yes	—
12	C₂×#13093939	C₂²	1	4	yes	complemented
13	#15688986	C₂²	1	4	yes	complemented
14	#15688889	C₂²	1	8	yes	complemented
15	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#547	—	2	4	no	—
18	C₄₇×#546	—	2	4	no	—
19	C₄₇×#536	C₄	1	2	yes	complemented
20	C₄₇×#534	C₄	1	2	yes	complemented
21	C₄₇×#534	C₂²	1	2	yes	—
22	C₄₇×#525	C₄	1	2	yes	complemented
23	C₂×#123×C₄₇	C₄	1	2	yes	complemented
24	C₂×#123×C₄₇	C₂²	1	2	yes	—
25	C₄₇×#518	C₂²	1	1	yes	characteristic
26	D₄×Dic₄₇	—	4	8	no	—
27	#13093983	—	2	4	no	—
28	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
29	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
30	#13093939	—	2	8	no	—
31	#13093939	—	2	8	no	—
32	#13093939	—	4	4	no	—
33	C₄₇⋊#95	—	4	4	no	—
34	H(5,𝔽₂)×C₄₇	—	4	4	no	—
35	C₂×#41×C₄₇	—	2	4	no	—
36	C₂×#41×C₄₇	—	4	4	no	—
37	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
38	C₂×#41×C₄₇	D₄	1	4	yes	—
39	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
40	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
41	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
42	C₂²×D₄×C₄₇	D₄	1	4	yes	—
43	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
47	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₄₇	—	2	2	no	—
50	#124×C₄₇	—	2	2	no	—
51	#123×C₄₇	—	2	4	no	—
52	#123×C₄₇	—	2	4	no	—
53	#123×C₄₇	—	2	2	no	—
54	#123×C₄₇	—	2	2	no	—
55	#123×C₄₇	C₂×C₄	1	4	yes	complemented
56	#123×C₄₇	C₂×C₄	1	4	yes	complemented
57	#123×C₄₇	C₂×C₄	1	4	yes	complemented
58	C₂²⋊Q₈×C₄₇	—	2	2	no	—
59	C₂²⋊Q₈×C₄₇	—	2	4	no	—
60	#121×C₄₇	—	2	2	no	—
61	#121×C₄₇	—	2	4	no	—
62	#121×C₄₇	—	2	4	no	—
63	#120×C₄₇	—	2	2	no	—
64	#120×C₄₇	—	2	2	no	—
65	#120×C₄₇	C₂×C₄	1	4	yes	complemented
66	C₄×D₄×C₄₇	—	2	4	no	—
67	C₄×D₄×C₄₇	—	2	4	no	—
68	#117×C₄₇	C₂×C₄	1	2	yes	complemented
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	complemented
74	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
75	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
76	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
79	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
80	#41×C₄₇	—	4	4	no	—
81	#41×C₄₇	—	4	8	no	—
82	#41×C₄₇	—	4	16	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	4	2	no	—
85	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	8	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	4	no	—
91	C₂×D₄×C₄₇	—	2	4	no	—
92	C₂×D₄×C₄₇	—	4	2	no	—
93	C₂×D₄×C₄₇	—	4	4	no	—
94	C₂×D₄×C₄₇	—	4	8	no	—
95	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
96	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
97	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
98	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
99	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	4	2	no	—
107	C₂²×C₄×C₄₇	—	4	2	no	—
108	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
115	C₂²×Dic₄₇	—	2	8	no	—
116	C₂²×Dic₄₇	—	4	4	no	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	4	no	—
119	C₄⋊C₄×C₄₇	—	2	4	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₂²⋊C₄×C₄₇	—	2	4	no	—
122	C₂²⋊C₄×C₄₇	—	2	4	no	—
123	C₂²⋊C₄×C₄₇	—	2	4	no	—
124	C₂²⋊C₄×C₄₇	—	2	2	no	—
125	C₂²⋊C₄×C₄₇	—	2	2	no	—
126	C₂²⋊C₄×C₄₇	—	2	4	no	—
127	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₂²⋊Dic₄₇	—	2	8	no	—
130	C₂²⋊Dic₄₇	—	2	8	no	—
131	C₂²⋊Dic₄₇	—	4	4	no	—
132	C₄⋊Dic₄₇	—	4	4	no	—
133	C₄×Dic₄₇	—	4	4	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	4	no	—
136	C₂³×C₄₇	—	2	1	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	8	1	no	—
140	C₂³×C₄₇	—	8	1	no	—
141	C₂³×C₄₇	—	8	1	no	—
142	C₂³×C₄₇	—	8	2	no	—
143	C₂³×C₄₇	—	8	2	no	—
144	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
145	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
148	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
149	Q₈×C₄₇	—	4	2	no	—
150	Q₈×C₄₇	—	4	4	no	—
151	D₄×C₄₇	—	2	8	no	—
152	D₄×C₄₇	—	2	8	no	—
153	D₄×C₄₇	—	2	8	no	—
154	D₄×C₄₇	—	4	2	no	—
155	D₄×C₄₇	—	4	4	no	—
156	D₄×C₄₇	—	4	4	no	—
157	D₄×C₄₇	—	4	4	no	—
158	D₄×C₄₇	—	8	4	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	4	4	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	4	no	—
171	C₂×C₄×C₄₇	—	4	4	no	—
172	C₂×C₄×C₄₇	—	4	4	no	—
173	C₂×C₄×C₄₇	—	8	2	no	—
174	C₂×C₄×C₄₇	—	8	2	no	—
175	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
177	C₂×Dic₄₇	—	4	8	no	—
178	C₂×Dic₄₇	—	8	8	no	—
179	C₂×Dic₄₇	—	16	4	no	—
180	#21777	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	4	no	—
183	C₂²×C₄₇	—	4	4	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	4	1	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	4	4	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	4	1	no	—
190	C₂²×C₄₇	—	8	4	no	—
191	C₂²×C₄₇	—	8	2	no	—
192	C₂²×C₄₇	—	8	2	no	—
193	C₂²×C₄₇	—	16	2	no	—
194	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄₇	#518	1	2	yes	—
196	C₂²×C₄₇	#534	1	4	yes	—
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	—	2	4	no	—
199	C₄×C₄₇	—	4	4	no	—
200	C₄×C₄₇	—	4	1	no	—
201	C₄×C₄₇	—	4	1	no	—
202	C₄×C₄₇	—	4	1	no	—
203	Dic₄₇	—	8	8	no	—
204	#3485	D₄₇	1	1	yes	characteristic
205	#2883	—	47	2	no	—
206	#1913	—	47	4	no	—
207	#1890	—	47	4	no	—
208	#1828	—	47	2	no	—
209	#1782	—	47	2	no	—
210	C₂×C₄₇	—	2	4	no	—
211	C₂×C₄₇	—	2	1	no	—
212	C₂×C₄₇	—	2	2	no	—
213	C₂×C₄₇	—	4	2	no	—
214	C₂×C₄₇	—	4	4	no	—
215	C₂×C₄₇	—	8	1	no	—
216	C₂×C₄₇	#2308	1	1	yes	characteristic
217	C₂×H(5,𝔽₂)	C₂×D₄₇	1	1	yes	characteristic
218	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
219	#547	—	2	4	no	—
220	#546	—	2	4	no	—
221	#536	Dic₄₇	1	2	yes	complemented
222	#534	Dic₄₇	1	2	yes	complemented
223	#534	C₂×D₄₇	1	2	yes	—
224	#525	Dic₄₇	1	2	yes	complemented
225	C₂×#123	Dic₄₇	1	2	yes	complemented
226	C₂×#123	C₂×D₄₇	1	2	yes	—
227	#518	—	47	4	no	—
228	#518	C₂×D₄₇	1	1	yes	characteristic
229	#410	—	94	4	no	—
230	C₂×#99	—	47	4	no	—
231	C₂×#99	—	47	4	no	—
232	C₂×#99	—	47	4	no	—
233	C₂×#99	—	94	4	no	—
234	#381	—	47	4	no	—
235	#342	—	47	8	no	—
236	C₄₇	#21777	1	1	yes	characteristic, complemented, Sylow
237	H(5,𝔽₂)	—	4	4	no	—
238	C₂×#41	—	2	4	no	—
239	C₂×#41	—	4	4	no	—
240	C₂×#41	C₂×Dic₄₇	1	2	yes	—
241	C₂×#41	C₂²⋊D₄₇	1	4	yes	—
242	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
243	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
244	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic, complemented
245	C₂²×D₄	C₂²⋊D₄₇	1	4	yes	—
246	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
247	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
248	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
249	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic, complemented
250	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic, complemented
251	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
252	C₄⋊Q₈	—	2	2	no	—
253	#124	—	2	2	no	—
254	#123	—	2	4	no	—
255	#123	—	2	4	no	—
256	#123	—	2	2	no	—
257	#123	—	2	2	no	—
258	#123	C₂×Dic₄₇	1	4	yes	complemented
259	#123	C₂×Dic₄₇	1	4	yes	complemented
260	#123	C₂×Dic₄₇	1	4	yes	complemented
261	C₂²⋊Q₈	—	2	2	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	#121	—	2	2	no	—
264	#121	—	2	4	no	—
265	#121	—	2	4	no	—
266	#120	—	2	2	no	—
267	#120	—	2	2	no	—
268	#120	C₂×Dic₄₇	1	4	yes	complemented
269	C₄×D₄	—	2	4	no	—
270	C₄×D₄	—	2	4	no	—
271	C₄×D₄	—	188	8	no	—
272	#117	—	94	4	no	—
273	#117	C₂×Dic₄₇	1	2	yes	complemented
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	47	8	no	—
279	C₂×C₂²⋊C₄	—	94	4	no	—
280	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	complemented
281	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
282	#99	—	94	8	no	—
283	#99	—	94	8	no	—
284	#99	—	188	4	no	—
285	#95	—	188	4	no	—
286	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
287	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
288	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
289	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
290	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
291	#41	—	4	4	no	—
292	#41	—	4	8	no	—
293	#41	—	4	16	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	8	no	—
306	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
307	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
308	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
309	C₂×D₄	C₂×C₂²⋊D₄₇	1	4	yes	—
310	C₂×D₄	C₂×C₂²⋊D₄₇	1	4	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	94	8	no	—
320	C₂²×C₄	—	188	4	no	—
321	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
322	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
323	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	188	4	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	94	8	no	—
340	C₂²⋊C₄	—	94	8	no	—
341	C₂²⋊C₄	—	188	4	no	—
342	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
343	C₄²	—	2	2	no	—
344	C₄²	—	188	4	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	8	1	no	—
352	C₂³	—	8	1	no	—
353	C₂³	—	8	2	no	—
354	C₂³	—	8	2	no	—
355	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
356	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
357	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
358	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
359	C₂³	#13094069	1	4	yes	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	4	no	—
362	D₄	—	2	8	no	—
363	D₄	—	2	8	no	—
364	D₄	—	2	8	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	4	no	—
367	D₄	—	4	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	8	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	376	8	no	—
387	C₂×C₄	—	188	8	no	—
388	C₂×C₄	—	752	4	no	—
389	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
390	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	8	4	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	16	2	no	—
404	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
405	C₂²	#15689598	1	2	yes	—
406	C₂²	#15689682	1	4	yes	—
407	C₄	—	2	2	no	—
408	C₄	—	2	4	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	376	8	no	—
414	C₂	—	2	1	no	—
415	C₂	—	2	4	no	—
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	—	4	4	no	—
419	C₂	—	8	1	no	—
420	C₂	#20245966	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20245966
commutator	C₂³×C₄₇	C₂³×C₄
Frattini	C₂⁴	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3485	C₂
socle	C₂×C₄₇	#2308
cosocle	C₂⁴×C₄₇	C₂⁴
hypercenter	#3485	D₄₇
hypocenter	C₄₇	#21777
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #3485

Complements

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

N	H ≅ G/N	type
1. #20251849	C₂	semidirect
2. #20243931	C₂	semidirect
3. #20243802	C₂	semidirect
4. #20243496	C₂	semidirect
5. #20243306	C₂	semidirect
12. C₂×#13093939	C₂²	semidirect
13. #15688986	C₂²	semidirect
14. #15688889	C₂²	semidirect
19. C₄₇×#536	C₄	semidirect
20. C₄₇×#534	C₄	semidirect
22. C₄₇×#525	C₄	semidirect
23. C₂×#123×C₄₇	C₄	semidirect
39. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
41. C₂²×D₄×C₄₇	C₂×C₄	semidirect
46. C₂³×C₄×C₄₇	C₂×C₄	semidirect
47. C₂³×C₄×C₄₇	C₂×C₄	semidirect
55. #123×C₄₇	C₂×C₄	semidirect
56. #123×C₄₇	C₂×C₄	semidirect
57. #123×C₄₇	C₂×C₄	semidirect
65. #120×C₄₇	C₂×C₄	semidirect
68. #117×C₄₇	C₂×C₄	semidirect
73. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
221. #536	Dic₄₇	semidirect
222. #534	Dic₄₇	semidirect
224. #525	Dic₄₇	semidirect
225. C₂×#123	Dic₄₇	semidirect
236. C₄₇	#21777	semidirect
242. C₂²×Q₈	C₂×Dic₄₇	semidirect
244. C₂²×D₄	C₂×Dic₄₇	semidirect
249. C₂³×C₄	C₂×Dic₄₇	semidirect
250. C₂³×C₄	C₂×Dic₄₇	semidirect
258. #123	C₂×Dic₄₇	semidirect
259. #123	C₂×Dic₄₇	semidirect
260. #123	C₂×Dic₄₇	semidirect
268. #120	C₂×Dic₄₇	semidirect
273. #117	C₂×Dic₄₇	semidirect
280. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20251849	2
#20243931	2
#20243802	2
#20243496	2
#20243306	2
C₄₇×#3485	2
#21777	47