Subgroups — #26219609

Order 12032.

1038 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689160	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689160	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20245869	C₂	1	2	yes	maximal
5	#20244122	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244121	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244119	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244115	C₂	1	2	yes	maximal, complemented
9	#20244113	C₂	1	2	yes	maximal, complemented
10	#20243103	C₂	1	2	yes	maximal
11	C₄₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×#13093982	C₂²	1	2	yes	—
15	C₂×#13093982	C₂²	1	2	yes	—
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	#15689160	—	2	4	no	—
18	#15689160	C₄	1	8	yes	complemented
19	C₂×#13093958	C₂²	1	1	yes	characteristic
20	C₂×#13093958	C₂²	1	1	yes	characteristic
21	C₂×#13093955	C₂²	1	2	yes	—
22	C₂×#13093955	C₂²	1	2	yes	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₄₇	—	2	4	no	—
27	#15689022	C₂²	1	2	yes	—
28	#15689021	C₂²	1	2	yes	—
29	#15689019	C₂²	1	2	yes	—
30	#15688997	—	2	2	no	—
31	#15688994	—	2	2	no	—
32	C₄⋊C₄×Dic₄₇	—	2	2	no	—
33	#15688974	—	2	2	no	—
34	#15688886	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	#15688885	C₂²	1	2	yes	—
37	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#389	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
43	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₈×D₄₇	—	2	2	no	—
48	C₂×C₈×D₄₇	—	2	2	no	—
49	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
50	C₂×C₈×D₄₇	D₄	1	4	yes	—
51	C₂×C₈×D₄₇	Q₈	1	4	yes	—
52	C₂×C₈×D₄₇	Q₈	1	4	yes	—
53	#13093982	—	2	4	no	—
54	#13093982	—	2	4	no	—
55	#13093982	—	2	4	no	—
56	#13093982	C₂×C₄	1	8	yes	—
57	C₂×C₄⋊Dic₄₇	—	2	2	no	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
60	C₂×Dic₄₇⋊C₄	—	2	2	no	—
61	C₂×Dic₄₇⋊C₄	—	2	2	no	—
62	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
63	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	C₂×C₄×Dic₄₇	—	2	2	no	—
65	C₂×C₄×Dic₄₇	—	2	2	no	—
66	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
68	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
69	C₄²×D₄₇	—	2	2	no	—
70	C₄²×D₄₇	—	2	2	no	—
71	#13093958	—	2	2	no	—
72	#13093958	C₂×C₄	1	4	yes	complemented
73	#13093955	—	2	4	no	—
74	#13093955	C₂×C₄	1	8	yes	complemented
75	C₄×C₄₇⋊C₈	—	2	2	no	—
76	C₈×Dic₄₇	—	2	2	no	—
77	C₈×Dic₄₇	—	2	2	no	—
78	C₄₇⋊#95	—	2	2	no	—
79	C₄₇⋊#95	—	2	2	no	—
80	C₄₇⋊#95	—	2	2	no	—
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	#107×C₄₇	—	2	2	no	—
88	#107×C₄₇	C₂×C₄	1	4	yes	complemented
89	C₄×C₈×C₄₇	—	2	2	no	—
90	#95×C₄₇	—	2	2	no	—
91	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₄₇	—	2	2	no	—
103	C₂×C₄×D₄₇	—	2	2	no	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	—	2	2	no	—
106	C₂×C₄×D₄₇	—	2	2	no	—
107	C₂×C₄×D₄₇	—	2	2	no	—
108	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
109	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
110	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
111	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
112	C₂×C₄×D₄₇	#41	1	2	yes	—
113	C₂×C₄×D₄₇	#41	1	2	yes	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
119	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	4	4	no	—
124	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
125	C₄²×C₄₇	—	2	1	no	—
126	C₄²×C₄₇	—	2	1	no	—
127	(C₂×D₄₇)⋊C₄	—	2	8	no	—
128	(C₂×D₄₇)⋊C₄	—	4	4	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	—	4	4	no	—
133	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
134	Dic₄₇⋊C₄	—	4	4	no	—
135	Dic₄₇⋊C₄	—	4	4	no	—
136	C₄×Dic₄₇	—	2	1	no	—
137	C₄×Dic₄₇	—	2	1	no	—
138	C₄×Dic₄₇	—	2	8	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	4	4	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
146	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
147	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
148	C₈×D₄₇	—	2	8	no	—
149	C₈×D₄₇	C₄⋊C₄	1	16	yes	complemented
150	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	C₂²×D₄₇	—	2	1	no	—
152	C₂²×D₄₇	—	2	1	no	—
153	C₂²×D₄₇	—	2	1	no	—
154	C₂²×D₄₇	—	2	1	no	—
155	C₂²×D₄₇	C₄×D₄	1	2	yes	—
156	C₂²×D₄₇	#121	1	2	yes	—
157	C₂²×D₄₇	C₄⋊Q₈	1	2	yes	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	#135	1	2	yes	—
169	C₂×C₄×C₄₇	#135	1	2	yes	—
170	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	4	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	4	2	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
187	C₂×Dic₄₇	#121	1	2	yes	—
188	C₂×Dic₄₇	C₄⋊Q₈	1	2	yes	—
189	C₂×Dic₄₇	#135	1	2	yes	—
190	C₂×Dic₄₇	#135	1	2	yes	—
191	C₄×D₄₇	—	2	8	no	—
192	C₄×D₄₇	—	2	8	no	—
193	C₄×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
194	C₄×D₄₇	C₄×Q₈	1	4	yes	—
195	C₄×D₄₇	C₂²⋊Q₈	1	4	yes	—
196	C₄×D₄₇	#125	1	4	yes	—
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
199	C₄₇⋊C₈	—	2	2	no	—
200	C₄₇⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
201	#21151	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
207	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
209	C₂×D₄₇	—	2	2	no	—
210	C₂×D₄₇	—	2	2	no	—
211	C₂×D₄₇	—	2	2	no	—
212	C₂×D₄₇	—	2	2	no	—
213	C₂×D₄₇	—	2	2	no	—
214	C₂×D₄₇	—	2	2	no	—
215	C₂×D₄₇	#389	1	4	yes	—
216	C₄×C₄₇	—	2	2	no	—
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	4	4	no	—
219	C₄×C₄₇	—	8	2	no	—
220	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
221	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
222	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
223	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
224	Dic₄₇	—	2	2	no	—
225	Dic₄₇	—	2	2	no	—
226	Dic₄₇	—	4	4	no	—
227	Dic₄₇	—	8	2	no	—
228	Dic₄₇	#389	1	4	yes	—
229	C₂×#427	—	47	1	no	—
230	C₂×#427	—	47	1	no	—
231	C₂²×C₄×C₈	—	47	1	no	—
232	#2296	—	47	2	no	—
233	#1942	—	47	1	no	—
234	#1942	—	47	1	no	—
235	#1942	—	47	1	no	—
236	#1942	D₄₇	1	1	yes	characteristic, complemented
237	#1941	—	47	2	no	—
238	#1941	—	47	2	no	—
239	#1735	—	47	2	no	—
240	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
241	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
242	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
243	C₂×C₄₇	#3050	1	1	yes	characteristic
244	C₂×C₄₇	#3050	1	1	yes	characteristic
245	C₂×C₄₇	#3160	1	1	yes	characteristic
246	C₂×C₄₇	#3160	1	1	yes	characteristic
247	D₄₇	—	2	4	no	—
248	C₂³×C₈	—	47	1	no	—
249	C₂³×C₈	—	47	1	no	—
250	C₂×#117	—	47	2	no	—
251	C₂×#117	—	47	2	no	—
252	C₂²×C₄²	—	47	1	no	—
253	#427	—	47	8	no	—
254	#427	—	94	4	no	—
255	C₂×#107	—	47	1	no	—
256	C₂×#107	—	47	1	no	—
257	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
258	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
259	C₂×#106	—	47	2	no	—
260	C₂×#106	—	47	2	no	—
261	C₂×C₄×C₈	—	47	1	no	—
262	C₂×C₄×C₈	—	47	1	no	—
263	C₂×C₄×C₈	—	47	1	no	—
264	C₂×C₄×C₈	—	94	4	no	—
265	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
266	#389	—	47	2	no	—
267	#389	—	47	2	no	—
268	#389	—	47	2	no	—
269	#389	C₂×D₄₇	1	2	yes	—
270	#385	—	94	2	no	—
271	#385	—	94	2	no	—
272	C₄×C₄⋊C₄	—	94	2	no	—
273	C₄×C₄⋊C₄	—	94	2	no	—
274	#340	—	47	2	no	—
275	#340	—	47	2	no	—
276	#340	—	47	2	no	—
277	#340	C₂×D₄₇	1	2	yes	—
278	C₄₇	#21151	1	1	yes	characteristic, complemented, Sylow
279	C₂³×C₄	—	47	1	no	—
280	C₂³×C₄	—	47	1	no	—
281	C₂³×C₄	—	47	1	no	—
282	C₂²×C₈	—	47	1	no	—
283	C₂²×C₈	—	47	4	no	—
284	C₂²×C₈	—	47	4	no	—
285	C₂²×C₈	—	47	4	no	—
286	C₂²×C₈	—	47	1	no	—
287	C₂²×C₈	—	47	4	no	—
288	C₂²×C₈	—	94	2	no	—
289	C₂²×C₈	—	94	2	no	—
290	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
292	#117	—	47	8	no	—
293	#117	—	94	4	no	—
294	#117	—	94	4	no	—
295	#117	—	94	4	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	47	2	no	—
298	C₂×C₄⋊C₄	—	47	2	no	—
299	C₂×C₄⋊C₄	—	94	2	no	—
300	C₂×C₄⋊C₄	—	94	2	no	—
301	C₂×C₄⋊C₄	—	94	2	no	—
302	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
303	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
304	C₂×C₂²⋊C₄	—	94	2	no	—
305	C₂×C₂²⋊C₄	—	94	2	no	—
306	C₂×C₄²	—	47	1	no	—
307	C₂×C₄²	—	47	1	no	—
308	C₂×C₄²	—	47	1	no	—
309	C₂×C₄²	—	94	2	no	—
310	C₂×C₄²	—	94	2	no	—
311	C₂×C₄²	—	94	2	no	—
312	C₂×C₄²	—	94	2	no	—
313	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
314	#107	—	2	2	no	—
315	#107	—	47	4	no	—
316	#107	—	94	2	no	—
317	#107	C₄×D₄₇	1	4	yes	complemented
318	#106	—	47	8	no	—
319	#106	—	94	4	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	94	2	no	—
322	C₄×C₈	—	94	2	no	—
323	C₄×C₈	—	94	2	no	—
324	#95	—	2	2	no	—
325	#95	—	94	2	no	—
326	#95	—	94	2	no	—
327	#95	—	94	2	no	—
328	C₂⁴	—	47	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	47	1	no	—
332	C₂²×C₄	—	47	2	no	—
333	C₂²×C₄	—	47	2	no	—
334	C₂²×C₄	—	47	2	no	—
335	C₂²×C₄	—	47	2	no	—
336	C₂²×C₄	—	47	2	no	—
337	C₂²×C₄	—	47	2	no	—
338	C₂²×C₄	—	47	1	no	—
339	C₂²×C₄	—	47	1	no	—
340	C₂²×C₄	—	94	2	no	—
341	C₂²×C₄	—	94	2	no	—
342	C₂²×C₄	—	94	2	no	—
343	C₂²×C₄	—	94	2	no	—
344	C₂²×C₄	—	94	2	no	—
345	C₂²×C₄	—	94	2	no	—
346	C₂²×C₄	—	94	2	no	—
347	C₂²×C₄	—	94	2	no	—
348	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
349	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	47	2	no	—
354	C₂×C₈	—	47	2	no	—
355	C₂×C₈	—	47	2	no	—
356	C₂×C₈	—	47	16	no	—
357	C₂×C₈	—	47	2	no	—
358	C₂×C₈	—	94	8	no	—
359	C₂×C₈	—	94	1	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
362	C₂×C₈	D₄×D₄₇	1	2	yes	—
363	C₂×C₈	Q₈×D₄₇	1	2	yes	—
364	C₂×C₈	Q₈×D₄₇	1	2	yes	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	47	4	no	—
370	C₄⋊C₄	—	94	2	no	—
371	C₄⋊C₄	—	94	2	no	—
372	C₄⋊C₄	—	94	2	no	—
373	C₄⋊C₄	—	188	4	no	—
374	C₄⋊C₄	—	188	4	no	—
375	C₄⋊C₄	—	188	4	no	—
376	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
377	C₂²⋊C₄	—	94	8	no	—
378	C₂²⋊C₄	—	188	4	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	94	2	no	—
382	C₄²	—	94	2	no	—
383	C₄²	—	94	8	no	—
384	C₄²	—	94	1	no	—
385	C₄²	—	94	1	no	—
386	C₄²	—	188	4	no	—
387	C₂³	—	47	2	no	—
388	C₂³	—	47	2	no	—
389	C₂³	—	47	2	no	—
390	C₂³	—	94	1	no	—
391	C₂³	—	94	1	no	—
392	C₂³	—	94	1	no	—
393	C₂³	—	94	1	no	—
394	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	47	2	no	—
406	C₂×C₄	—	47	2	no	—
407	C₂×C₄	—	47	2	no	—
408	C₂×C₄	—	47	4	no	—
409	C₂×C₄	—	47	4	no	—
410	C₂×C₄	—	47	4	no	—
411	C₂×C₄	—	47	4	no	—
412	C₂×C₄	—	47	2	no	—
413	C₂×C₄	—	47	2	no	—
414	C₂×C₄	—	94	8	no	—
415	C₂×C₄	—	94	8	no	—
416	C₂×C₄	—	94	1	no	—
417	C₂×C₄	—	94	1	no	—
418	C₂×C₄	—	94	1	no	—
419	C₂×C₄	—	94	1	no	—
420	C₂×C₄	—	94	4	no	—
421	C₂×C₄	—	188	2	no	—
422	C₂×C₄	—	188	2	no	—
423	C₂×C₄	—	188	2	no	—
424	C₂×C₄	—	188	2	no	—
425	C₂×C₄	—	188	2	no	—
426	C₂×C₄	#13094043	1	2	yes	—
427	C₂×C₄	#13094047	1	2	yes	—
428	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
431	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
432	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
433	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	47	4	no	—
436	C₈	—	94	2	no	—
437	C₈	C₄⋊C₄×D₄₇	1	4	yes	—
438	C₂²	—	47	4	no	—
439	C₂²	—	94	2	no	—
440	C₂²	—	94	2	no	—
441	C₂²	—	94	2	no	—
442	C₂²	—	94	2	no	—
443	C₂²	—	94	2	no	—
444	C₂²	—	94	2	no	—
445	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
446	C₂²	#121×D₄₇	1	1	yes	characteristic
447	C₂²	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
448	C₂²	#135×D₄₇	1	1	yes	characteristic
449	C₂²	#135×D₄₇	1	1	yes	characteristic
450	C₂²	C₂×#13094043	1	1	yes	characteristic
451	C₂²	C₂×#13094047	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	4	4	no	—
455	C₄	—	8	2	no	—
456	C₄	—	47	4	no	—
457	C₄	—	94	2	no	—
458	C₄	—	94	2	no	—
459	C₄	—	376	2	no	—
460	C₄	—	188	4	no	—
461	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
462	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
463	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
464	C₄	#125×D₄₇	1	1	yes	characteristic
465	C₂	—	94	4	no	—
466	C₂	#389×D₄₇	1	1	yes	characteristic
467	C₂	C₄×#13094043	1	1	yes	characteristic
468	C₂	C₄×#13094047	1	1	yes	characteristic
469	C₂	#20252967	1	1	yes	characteristic
470	C₂	#20252971	1	1	yes	characteristic
471	C₂	#20253899	1	1	yes	characteristic
472	C₂	#20253901	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1942	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1942	D₄₇
hypocenter	C₄₇	#21151
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1942

Complements

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

N	H ≅ G/N	type
5. #20244122	C₂	semidirect
6. #20244121	C₂	semidirect
7. #20244119	C₂	semidirect
8. #20244115	C₂	semidirect
9. #20244113	C₂	semidirect
11. C₄₇×#1942	C₂	semidirect
18. #15689160	C₄	semidirect
72. #13093958	C₂×C₄	semidirect
74. #13093955	C₂×C₄	semidirect
88. #107×C₄₇	C₂×C₄	semidirect
149. C₈×D₄₇	C₄⋊C₄	semidirect
236. #1942	D₄₇	semidirect
278. C₄₇	#21151	semidirect
317. #107	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689160	2
C₂×C₄×C₈×D₄₇	2
#20245869	2
#20244122	2
#20244121	2
#20244119	2
#20244115	2
#20244113	2
#20243103	2
C₄₇×#1942	2
#21151	47