Subgroups — #26224792

Order 12032.

1110 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689224	C₂	1	2	yes	maximal, complemented
2	C₂×Q₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20246101	C₂	1	2	yes	maximal, complemented
5	#20244271	C₂	1	2	yes	maximal, complemented
6	#20244255	C₂	1	1	yes	maximal, characteristic
7	#20244250	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244205	C₂	1	2	yes	maximal, complemented
9	#20243548	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243074	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#495	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
14	#15689224	—	2	8	no	—
15	Q₁₆×Dic₄₇	—	2	4	no	—
16	D₈×Dic₄₇	—	2	4	no	—
17	C₂×#13093958	C₂²	1	2	yes	—
18	C₂×#13093958	C₂²	1	1	yes	characteristic
19	C₂×#13093958	C₂²	1	1	yes	characteristic
20	C₂×#13093948	C₂²	1	2	yes	—
21	C₂×#13093948	C₂²	1	2	yes	—
22	C₂×#13093945	C₂²	1	2	yes	—
23	C₂×#13093945	C₂²	1	2	yes	—
24	C₂×#13093935	C₂²	1	1	yes	characteristic
25	C₂×#13093934	C₂²	1	1	yes	characteristic
26	C₂×#13093934	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
29	#15689030	C₂²	1	2	yes	—
30	#15689026	C₂²	1	2	yes	—
31	#15689016	—	2	4	no	—
32	#15688998	—	2	4	no	—
33	#15688993	C₂²	1	2	yes	—
34	#15688969	C₂²	1	1	yes	characteristic
35	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
37	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#124×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#495	C₄	1	8	yes	complemented
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂³×Dic₄₇	—	2	2	no	—
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	Q₈×Dic₄₇	—	2	4	no	—
45	Q₈×Dic₄₇	—	2	4	no	—
46	D₄×Dic₄₇	—	2	4	no	—
47	D₄×Dic₄₇	—	2	4	no	—
48	C₂×C₄⋊Dic₄₇	—	2	2	no	—
49	C₂×C₄⋊Dic₄₇	—	2	4	no	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
53	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
57	#13093958	—	2	2	no	—
58	#13093958	—	2	4	no	—
59	#13093958	—	2	2	no	—
60	#13093948	—	2	4	no	—
61	#13093948	—	2	4	no	—
62	#13093945	—	2	4	no	—
63	#13093945	—	2	4	no	—
64	#13093935	—	2	2	no	—
65	#13093934	—	2	2	no	—
66	#13093934	D₄	1	4	yes	—
67	C₈×Dic₄₇	—	2	2	no	—
68	C₈×Dic₄₇	D₄	1	4	yes	—
69	C₄₇⋊#95	—	2	4	no	—
70	C₄₇⋊#95	D₄	1	2	yes	—
71	C₄₇⋊#95	D₄	1	2	yes	—
72	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
73	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
74	C₂×Q₁₆×C₄₇	—	2	2	no	—
75	C₂×Q₁₆×C₄₇	—	2	2	no	—
76	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
77	C₂×SD₁₆×C₄₇	—	2	4	no	—
78	C₂×SD₁₆×C₄₇	—	2	4	no	—
79	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
80	C₂×D₈×C₄₇	—	2	2	no	—
81	C₂×D₈×C₄₇	—	2	2	no	—
82	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	#124×C₄₇	—	2	4	no	—
86	#124×C₄₇	C₂×C₄	1	8	yes	complemented
87	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
90	C₂⁴×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₄₇	—	2	2	no	—
107	C₂²×Dic₄₇	—	2	2	no	—
108	C₂²×Dic₄₇	—	4	4	no	—
109	C₂²×Dic₄₇	—	8	4	no	—
110	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
111	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
113	Q₁₆×C₄₇	—	2	8	no	—
114	SD₁₆×C₄₇	—	2	16	no	—
115	D₈×C₄₇	—	2	8	no	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₄₇	#41	1	2	yes	—
121	C₂×C₈×C₄₇	#41	1	2	yes	—
122	C₂²⋊C₄×C₄₇	—	2	16	no	—
123	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
124	C₄²×C₄₇	#41	1	2	yes	—
125	C₂²⋊Dic₄₇	—	4	4	no	—
126	C₂²⋊Dic₄₇	—	8	4	no	—
127	C₄⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	4	4	no	—
132	C₄⋊Dic₄₇	—	8	4	no	—
133	C₄×Dic₄₇	—	2	1	no	—
134	C₄×Dic₄₇	—	2	1	no	—
135	C₄×Dic₄₇	—	4	4	no	—
136	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
137	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
143	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
144	C₂³×C₄₇	—	2	4	no	—
145	C₂³×C₄₇	—	4	2	no	—
146	C₂³×C₄₇	—	4	2	no	—
147	C₂³×C₄₇	—	4	4	no	—
148	C₂³×C₄₇	—	4	4	no	—
149	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₄₇	—	2	4	no	—
151	Q₈×C₄₇	—	2	4	no	—
152	Q₈×C₄₇	—	4	2	no	—
153	Q₈×C₄₇	—	4	2	no	—
154	D₄×C₄₇	—	2	4	no	—
155	D₄×C₄₇	—	2	4	no	—
156	D₄×C₄₇	—	4	2	no	—
157	D₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	4	no	—
178	C₂×Dic₄₇	—	4	4	no	—
179	C₂×Dic₄₇	—	8	8	no	—
180	C₂×Dic₄₇	#127	1	2	yes	—
181	C₂×Dic₄₇	#127	1	2	yes	—
182	C₈×C₄₇	C₄×D₄	1	4	yes	—
183	C₈×C₄₇	C₄×D₄	1	4	yes	—
184	C₄₇⋊C₈	—	2	2	no	—
185	C₄₇⋊C₈	—	2	2	no	—
186	#21696	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	4	4	no	—
188	C₂²×C₄₇	—	4	8	no	—
189	C₂²×C₄₇	—	8	2	no	—
190	C₂²×C₄₇	—	8	2	no	—
191	C₂²×C₄₇	—	8	4	no	—
192	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
194	C₂²×C₄₇	#532	1	1	yes	characteristic
195	C₂²×C₄₇	#576	1	2	yes	—
196	C₂²×C₄₇	#578	1	2	yes	—
197	C₄×C₄₇	—	2	4	no	—
198	C₄×C₄₇	—	4	4	no	—
199	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
200	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
201	C₄×C₄₇	#532	1	1	yes	characteristic
202	C₄×C₄₇	#532	1	1	yes	characteristic
203	Dic₄₇	—	2	2	no	—
204	Dic₄₇	—	2	2	no	—
205	Dic₄₇	—	4	2	no	—
206	Dic₄₇	—	8	2	no	—
207	Dic₄₇	—	8	2	no	—
208	C₂×#495	D₄₇	1	1	yes	characteristic
209	C₂×#440	—	47	2	no	—
210	C₂×C₄×Q₁₆	—	47	1	no	—
211	C₂×C₄×D₈	—	47	1	no	—
212	#2326	—	47	2	no	—
213	#1973	—	47	2	no	—
214	#1970	—	47	1	no	—
215	#1969	—	47	1	no	—
216	#1959	—	47	2	no	—
217	#1845	—	47	1	no	—
218	#1726	—	47	1	no	—
219	C₂×C₄₇	—	8	4	no	—
220	C₂×C₄₇	C₄×#127	1	1	yes	characteristic
221	C₂×C₄₇	#2951	1	2	yes	—
222	C₂×C₄₇	#3155	1	1	yes	characteristic
223	C₂×C₄₇	#3156	1	1	yes	characteristic
224	C₂×C₄₇	#3175	1	2	yes	—
225	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
226	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
227	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
228	C₂×#124	C₂×D₄₇	1	2	yes	—
229	C₂×C₄×Q₈	—	47	2	no	—
230	C₂×C₄×D₄	—	47	2	no	—
231	#495	Dic₄₇	1	8	yes	complemented
232	#440	—	94	8	no	—
233	C₄×Q₁₆	—	94	4	no	—
234	C₄×D₈	—	94	4	no	—
235	C₂×#107	—	47	1	no	—
236	C₂×#107	—	47	1	no	—
237	C₂×#107	—	47	2	no	—
238	C₂×#103	—	47	2	no	—
239	C₂×#103	—	47	2	no	—
240	C₂×#102	—	47	2	no	—
241	C₂×#102	—	47	2	no	—
242	C₂×#97	—	47	1	no	—
243	C₂×#97	—	47	1	no	—
244	C₂×#97	—	47	1	no	—
245	C₂×C₄×C₈	—	47	1	no	—
246	C₂×C₄×C₈	—	47	1	no	—
247	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
248	#391	—	47	2	no	—
249	#390	—	47	2	no	—
250	#388	—	94	4	no	—
251	#385	—	94	4	no	—
252	#384	—	47	2	no	—
253	#376	—	47	1	no	—
254	C₄₇	#21696	1	1	yes	characteristic, complemented, Sylow
255	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
256	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
257	C₂³×C₄	—	94	2	no	—
258	C₂×Q₁₆	—	2	2	no	—
259	C₂×Q₁₆	—	2	2	no	—
260	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	complemented
261	C₂×SD₁₆	—	2	4	no	—
262	C₂×SD₁₆	—	2	4	no	—
263	C₂×SD₁₆	C₂×Dic₄₇	1	8	yes	complemented
264	C₂×D₈	—	2	2	no	—
265	C₂×D₈	—	2	2	no	—
266	C₂×D₈	C₂×Dic₄₇	1	4	yes	—
267	C₂²×C₈	—	47	1	no	—
268	C₂²×C₈	—	47	1	no	—
269	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
271	#124	—	2	4	no	—
272	#124	C₂×Dic₄₇	1	8	yes	complemented
273	C₄×Q₈	—	94	4	no	—
274	C₄×Q₈	—	94	4	no	—
275	C₄×D₄	—	94	4	no	—
276	C₄×D₄	—	94	4	no	—
277	C₂×C₄⋊C₄	—	47	2	no	—
278	C₂×C₄⋊C₄	—	47	2	no	—
279	C₂×C₄⋊C₄	—	94	4	no	—
280	C₂×C₄⋊C₄	—	94	2	no	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	94	4	no	—
283	C₂×C₂²⋊C₄	—	94	2	no	—
284	C₂×C₄²	—	47	1	no	—
285	C₂×C₄²	—	47	1	no	—
286	C₂×C₄²	—	94	2	no	—
287	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
288	#107	—	94	2	no	—
289	#107	—	94	2	no	—
290	#107	—	94	4	no	—
291	#103	—	94	4	no	—
292	#103	—	94	4	no	—
293	#102	—	94	4	no	—
294	#102	—	94	4	no	—
295	#97	—	47	4	no	—
296	#97	—	94	2	no	—
297	#97	—	94	2	no	—
298	C₄×C₈	—	47	4	no	—
299	C₄×C₈	—	94	2	no	—
300	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
301	#95	—	47	2	no	—
302	#95	—	47	2	no	—
303	#95	—	94	4	no	—
304	C₂⁴	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	47	1	no	—
319	C₂²×C₄	—	47	1	no	—
320	C₂²×C₄	—	47	2	no	—
321	C₂²×C₄	—	94	2	no	—
322	C₂²×C₄	—	94	2	no	—
323	C₂²×C₄	—	376	4	no	—
324	C₂²×C₄	—	188	4	no	—
325	C₂²×C₄	D₄×D₄₇	1	2	yes	—
326	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
327	Q₁₆	—	2	8	no	—
328	SD₁₆	—	2	16	no	—
329	D₈	—	2	8	no	—
330	C₂×C₈	—	47	2	no	—
331	C₂×C₈	—	47	2	no	—
332	C₂×C₈	—	94	1	no	—
333	C₂×C₈	—	94	1	no	—
334	C₂×C₈	—	94	1	no	—
335	C₂×C₈	—	94	1	no	—
336	C₂×C₈	D₄×D₄₇	1	2	yes	—
337	C₂×C₈	D₄×D₄₇	1	2	yes	—
338	C₂×C₈	#10625352	1	2	yes	—
339	C₂×C₈	#10625352	1	2	yes	—
340	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
341	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
342	C₄⋊C₄	—	94	2	no	—
343	C₄⋊C₄	—	94	2	no	—
344	C₄⋊C₄	—	94	2	no	—
345	C₄⋊C₄	—	94	2	no	—
346	C₄⋊C₄	—	376	4	no	—
347	C₄⋊C₄	—	188	4	no	—
348	C₂²⋊C₄	—	2	16	no	—
349	C₂²⋊C₄	—	376	4	no	—
350	C₂²⋊C₄	—	188	4	no	—
351	C₄²	—	47	2	no	—
352	C₄²	—	47	2	no	—
353	C₄²	—	94	1	no	—
354	C₄²	—	94	1	no	—
355	C₄²	—	188	4	no	—
356	C₄²	#10625352	1	2	yes	—
357	C₄²	C₂²×Dic₄₇	1	2	yes	—
358	C₂³	—	2	4	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
364	Q₈	—	2	4	no	—
365	Q₈	—	2	4	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	D₄	—	2	4	no	—
369	D₄	—	2	4	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	47	2	no	—
378	C₂×C₄	—	47	2	no	—
379	C₂×C₄	—	94	2	no	—
380	C₂×C₄	—	94	2	no	—
381	C₂×C₄	—	94	2	no	—
382	C₂×C₄	—	94	2	no	—
383	C₂×C₄	—	94	2	no	—
384	C₂×C₄	—	376	8	no	—
385	C₂×C₄	—	188	2	no	—
386	C₂×C₄	—	188	2	no	—
387	C₂×C₄	—	188	4	no	—
388	C₂×C₄	—	188	4	no	—
389	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
390	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
394	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
395	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
396	C₈	—	94	2	no	—
397	C₈	—	94	2	no	—
398	C₈	D₄×Dic₄₇	1	4	yes	—
399	C₈	D₄×Dic₄₇	1	4	yes	—
400	C₂²	—	4	8	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	8	4	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
406	C₂²	#127×D₄₇	1	1	yes	characteristic
407	C₂²	#15689671	1	1	yes	characteristic
408	C₂²	#15689925	1	2	yes	—
409	C₂²	#15689937	1	2	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	4	4	no	—
412	C₄	—	94	2	no	—
413	C₄	—	94	2	no	—
414	C₄	—	376	2	no	—
415	C₄	—	376	2	no	—
416	C₄	—	188	2	no	—
417	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
418	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
419	C₄	#15689671	1	1	yes	characteristic
420	C₄	#15689671	1	1	yes	characteristic
421	C₂	—	8	4	no	—
422	C₂	#127×Dic₄₇	1	1	yes	characteristic
423	C₂	#20252264	1	2	yes	—
424	C₂	#20253870	1	1	yes	characteristic
425	C₂	#20253878	1	1	yes	characteristic
426	C₂	#20254024	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#495	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₈×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#495	D₄₇
hypocenter	C₄₇	#21696
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#495

Complements

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

N	H ≅ G/N	type
1. C₂×#15689224	C₂	semidirect
2. C₂×Q₁₆×Dic₄₇	C₂	semidirect
4. #20246101	C₂	semidirect
5. #20244271	C₂	semidirect
7. #20244250	C₂	semidirect
8. #20244205	C₂	semidirect
9. #20243548	C₂	semidirect
10. #20243074	C₂	semidirect
39. C₄₇×#495	C₄	semidirect
76. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
79. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
86. #124×C₄₇	C₂×C₄	semidirect
89. C₄×C₈×C₄₇	C₂×C₄	semidirect
231. #495	Dic₄₇	semidirect
254. C₄₇	#21696	semidirect
260. C₂×Q₁₆	C₂×Dic₄₇	semidirect
263. C₂×SD₁₆	C₂×Dic₄₇	semidirect
272. #124	C₂×Dic₄₇	semidirect
300. C₄×C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689224	2
C₂×Q₁₆×Dic₄₇	2
C₂×D₈×Dic₄₇	2
#20246101	2
#20244271	2
#20244255	2
#20244250	2
#20244205	2
#20243548	2
#20243074	2
C₂×C₄₇×#495	2
#21696	47