Subgroups — #26219695

Order 12032.

882 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#427×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20251949	C₂	1	2	yes	maximal
4	C₂×#15689077	C₂	1	1	yes	maximal, characteristic
5	#20244140	C₂	1	2	yes	maximal, complemented
6	#20244138	C₂	1	2	yes	maximal, complemented
7	#20244137	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244136	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244134	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243096	C₂	1	2	yes	maximal
11	C₄₇×#1945	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
14	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
15	C₂×#13093981	C₂²	1	1	yes	characteristic
16	#117×D₄₇	C₂²	1	2	yes	—
17	C₂×#13093960	C₂²	1	1	yes	characteristic
18	C₂×#13093959	C₂²	1	2	yes	—
19	#108×D₄₇	—	2	4	no	—
20	#15689161	C₂²	1	1	yes	characteristic
21	#15689160	C₄	1	2	yes	complemented
22	#15689159	C₂²	1	2	yes	—
23	#15689158	C₄	1	2	yes	complemented
24	#107×D₄₇	C₄	1	2	yes	complemented
25	#106×D₄₇	C₄	1	2	yes	complemented
26	#15689151	C₂²	1	2	yes	—
27	#15689150	C₂²	1	2	yes	—
28	#15689149	C₂²	1	2	yes	—
29	#15689148	—	2	4	no	—
30	#15689145	—	2	4	no	—
31	#15689077	—	2	4	no	—
32	C₂×#13093935	C₂²	1	1	yes	characteristic
33	C₂×#13093934	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	#15688884	C₂²	1	2	yes	—
36	#15688883	C₂²	1	2	yes	—
37	#15688882	C₂²	1	2	yes	—
38	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#427	C₂²	1	1	yes	characteristic
40	C₄₇×#424	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#339	C₂²	1	2	yes	—
43	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
44	C₂×#10625329	C₂³	1	2	yes	—
45	C₂×#10625324	—	2	2	no	—
46	C₂×#10625324	—	2	2	no	—
47	C₂×#10625324	—	2	2	no	—
48	C₂×#10625324	D₄	1	2	yes	—
49	C₂×#10625324	D₄	1	2	yes	—
50	M₁₆×D₄₇	—	2	4	no	—
51	M₁₆×D₄₇	—	2	4	no	—
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₄₇	—	2	2	no	—
55	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₄₇	D₄	1	4	yes	—
60	C₂×C₈×D₄₇	Q₈	1	4	yes	—
61	#13093983	C₂³	1	2	yes	—
62	#13093982	C₂×C₄	1	4	yes	—
63	#13093981	—	2	2	no	—
64	#13093981	—	2	2	no	—
65	#13093981	Q₈	1	4	yes	—
66	#13093980	—	2	2	no	—
67	C₂×Dic₄₇⋊C₄	—	2	1	no	—
68	C₄⋊C₄×D₄₇	C₂×C₄	1	4	yes	—
69	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
70	C₂²⋊C₄×D₄₇	—	2	2	no	—
71	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	C₄²×D₄₇	—	2	2	no	—
73	#13093960	—	2	2	no	—
74	#13093959	—	2	4	no	—
75	#13093958	C₂×C₄	1	2	yes	—
76	#13093957	C₂×C₄	1	4	yes	—
77	#13093956	C₂×C₄	1	2	yes	—
78	#13093955	C₂×C₄	1	4	yes	—
79	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
80	Dic₄₇⋊C₈	—	2	4	no	—
81	Dic₄₇⋊C₈	—	2	4	no	—
82	#13093935	—	2	2	no	—
83	#13093934	—	2	2	no	—
84	C₈×Dic₄₇	—	2	2	no	—
85	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
86	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	#117×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	#108×C₄₇	—	2	2	no	—
91	#107×C₄₇	C₂×C₄	1	2	yes	—
92	#106×C₄₇	C₂×C₄	1	2	yes	—
93	C₄⋊C₈×C₄₇	—	2	4	no	—
94	C₄×C₈×C₄₇	—	2	2	no	—
95	C₂³×D₄₇	#41	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₄₇	—	2	1	no	—
99	C₂²×Dic₄₇	#41	1	1	yes	characteristic
100	C₂×C₄×D₄₇	—	2	4	no	—
101	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
104	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
107	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
108	C₂×C₄×D₄₇	#41	1	2	yes	—
109	M₁₆×C₄₇	—	2	2	no	—
110	M₁₆×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
119	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
120	C₂²⋊C₄×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	—	2	1	no	—
123	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
124	C₂²⋊Dic₄₇	—	2	2	no	—
125	(C₂×D₄₇)⋊C₄	—	2	4	no	—
126	(C₂×D₄₇)⋊C₄	—	2	4	no	—
127	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
128	Dic₄₇⋊C₄	—	2	4	no	—
129	Dic₄₇⋊C₄	—	2	4	no	—
130	C₄×Dic₄₇	—	2	1	no	—
131	C₄×Dic₄₇	—	2	2	no	—
132	C₄×Dic₄₇	—	2	4	no	—
133	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
134	#10625329	—	2	2	no	—
135	#10625329	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
142	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
143	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
144	#10625324	—	2	4	no	—
145	#10625324	—	2	4	no	—
146	#10625324	—	4	4	no	—
147	C₈×D₄₇	—	4	4	no	—
148	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
149	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
150	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
151	C₈×D₄₇	C₄⋊C₄	1	4	yes	—
152	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂²×D₄₇	—	4	2	no	—
154	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
155	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
156	C₂²×D₄₇	C₂²⋊Q₈	1	2	yes	—
157	C₂²×D₄₇	#125	1	2	yes	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂×Dic₄₇	—	2	4	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
171	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
172	C₂×Dic₄₇	C₂²⋊Q₈	1	2	yes	—
173	C₂×Dic₄₇	#125	1	2	yes	—
174	C₄×D₄₇	—	8	4	no	—
175	C₄×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
176	C₄×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
177	C₄×D₄₇	C₄×Q₈	1	2	yes	—
178	C₄×D₄₇	C₄×Q₈	1	2	yes	—
179	C₄×D₄₇	#121	1	2	yes	—
180	C₄×D₄₇	#121	1	2	yes	—
181	C₄×D₄₇	C₄⋊Q₈	1	2	yes	—
182	C₄×D₄₇	C₄⋊Q₈	1	2	yes	—
183	C₈×C₄₇	—	2	2	no	—
184	C₈×C₄₇	—	4	2	no	—
185	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
186	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
187	C₄₇⋊C₈	—	2	2	no	—
188	C₄₇⋊C₈	—	4	2	no	—
189	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
190	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
191	#21163	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	2	2	no	—
193	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×#125	1	1	yes	characteristic
196	C₂×D₄₇	—	2	2	no	—
197	C₂×D₄₇	—	2	2	no	—
198	C₂×D₄₇	—	4	2	no	—
199	C₂×D₄₇	—	4	2	no	—
200	C₂×D₄₇	#389	1	2	yes	—
201	C₂×D₄₇	#389	1	2	yes	—
202	C₄×C₄₇	—	4	2	no	—
203	C₄×C₄₇	—	4	4	no	—
204	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
205	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
206	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
207	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
208	Dic₄₇	—	4	2	no	—
209	Dic₄₇	—	4	4	no	—
210	Dic₄₇	#389	1	2	yes	—
211	Dic₄₇	#389	1	2	yes	—
212	C₂²×#108	—	47	1	no	—
213	C₂×#427	—	47	1	no	—
214	#2905	—	47	2	no	—
215	C₂×#405	—	47	1	no	—
216	#1946	—	47	2	no	—
217	#1946	—	47	2	no	—
218	#1945	—	47	1	no	—
219	#1945	—	47	1	no	—
220	#1945	—	47	1	no	—
221	#1945	D₄₇	1	1	yes	characteristic, complemented
222	#1733	—	47	2	no	—
223	C₂×C₄₇	—	2	1	no	—
224	C₂×C₄₇	—	2	1	no	—
225	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
226	C₂×C₄₇	#2957	1	2	yes	—
227	D₄₇	—	2	2	no	—
228	D₄₇	—	2	2	no	—
229	C₂²×M₁₆	—	47	1	no	—
230	C₂²×M₁₆	—	47	2	no	—
231	C₂³×C₈	—	47	1	no	—
232	C₂×#117	—	47	1	no	—
233	C₂×#117	—	47	2	no	—
234	C₂×#108	—	47	2	no	—
235	C₂×#108	—	47	1	no	—
236	C₂×#108	—	94	4	no	—
237	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
238	#427	—	47	1	no	—
239	#427	—	47	2	no	—
240	#427	—	47	2	no	—
241	#427	—	47	2	no	—
242	#427	C₂×D₄₇	1	1	yes	characteristic
243	C₂×#107	—	47	2	no	—
244	C₂×#106	—	47	2	no	—
245	#424	—	47	2	no	—
246	#424	—	47	2	no	—
247	#424	—	47	2	no	—
248	#424	—	94	4	no	—
249	#424	C₂×D₄₇	1	2	yes	—
250	#423	—	94	4	no	—
251	#405	—	94	4	no	—
252	C₂×#97	—	47	1	no	—
253	C₂×#97	—	47	1	no	—
254	C₂×C₄×C₈	—	47	1	no	—
255	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
256	#339	—	47	2	no	—
257	#339	—	47	2	no	—
258	#339	—	47	2	no	—
259	#339	C₂×D₄₇	1	2	yes	—
260	C₄₇	#21163	1	1	yes	characteristic, complemented, Sylow
261	C₂³×C₄	—	47	1	no	—
262	C₂×M₁₆	—	47	2	no	—
263	C₂×M₁₆	—	47	2	no	—
264	C₂×M₁₆	—	47	2	no	—
265	C₂×M₁₆	—	94	2	no	—
266	C₂×M₁₆	—	94	2	no	—
267	C₂×M₁₆	—	94	2	no	—
268	C₂×M₁₆	—	94	4	no	—
269	C₂×M₁₆	—	94	4	no	—
270	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
271	C₂²×C₈	—	47	1	no	—
272	C₂²×C₈	—	47	1	no	—
273	C₂²×C₈	—	47	1	no	—
274	C₂²×C₈	—	47	1	no	—
275	C₂²×C₈	—	47	1	no	—
276	C₂²×C₈	—	47	4	no	—
277	C₂²×C₈	—	47	4	no	—
278	C₂²×C₈	—	47	1	no	—
279	C₂²×C₈	—	94	2	no	—
280	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
282	#117	—	47	4	no	—
283	#117	—	47	2	no	—
284	#117	—	47	4	no	—
285	#117	—	94	2	no	—
286	#117	—	94	2	no	—
287	#117	—	94	2	no	—
288	#117	C₂²×D₄₇	1	2	yes	—
289	C₂×C₄⋊C₄	—	47	4	no	—
290	C₂×C₄⋊C₄	—	94	1	no	—
291	C₂×C₂²⋊C₄	—	94	2	no	—
292	C₂×C₂²⋊C₄	—	94	1	no	—
293	C₂×C₄²	—	47	1	no	—
294	C₂×C₄²	—	94	2	no	—
295	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
296	#108	—	2	2	no	—
297	#108	—	94	4	no	—
298	#108	—	94	2	no	—
299	#107	—	47	2	no	—
300	#107	—	47	4	no	—
301	#107	C₄×D₄₇	1	2	yes	—
302	#106	—	47	2	no	—
303	#106	—	47	4	no	—
304	#106	C₄×D₄₇	1	2	yes	—
305	C₄⋊C₈	—	2	4	no	—
306	C₄⋊C₈	—	94	4	no	—
307	C₄⋊C₈	—	94	4	no	—
308	C₄⋊C₈	—	94	4	no	—
309	#97	—	94	2	no	—
310	#97	—	94	2	no	—
311	C₄×C₈	—	2	2	no	—
312	C₄×C₈	—	94	2	no	—
313	C₂⁴	—	47	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	47	1	no	—
316	C₂²×C₄	—	47	1	no	—
317	C₂²×C₄	—	47	1	no	—
318	C₂²×C₄	—	47	2	no	—
319	C₂²×C₄	—	47	1	no	—
320	C₂²×C₄	—	47	1	no	—
321	C₂²×C₄	—	47	2	no	—
322	C₂²×C₄	—	47	2	no	—
323	C₂²×C₄	—	47	2	no	—
324	C₂²×C₄	—	94	4	no	—
325	C₂²×C₄	—	94	1	no	—
326	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
327	M₁₆	—	2	2	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	94	4	no	—
330	M₁₆	—	94	4	no	—
331	M₁₆	—	94	2	no	—
332	M₁₆	—	94	2	no	—
333	M₁₆	—	188	4	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	47	1	no	—
338	C₂×C₈	—	47	1	no	—
339	C₂×C₈	—	47	2	no	—
340	C₂×C₈	—	47	2	no	—
341	C₂×C₈	—	47	4	no	—
342	C₂×C₈	—	47	4	no	—
343	C₂×C₈	—	47	4	no	—
344	C₂×C₈	—	47	4	no	—
345	C₂×C₈	—	47	2	no	—
346	C₂×C₈	—	94	1	no	—
347	C₂×C₈	—	94	1	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	188	4	no	—
350	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
351	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
352	C₂×C₈	D₄×D₄₇	1	2	yes	—
353	C₂×C₈	D₄×D₄₇	1	2	yes	—
354	C₂×C₈	Q₈×D₄₇	1	2	yes	—
355	C₄⋊C₄	—	47	4	no	—
356	C₄⋊C₄	—	94	4	no	—
357	C₄⋊C₄	—	94	4	no	—
358	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	94	4	no	—
361	C₂²⋊C₄	—	94	4	no	—
362	C₂²⋊C₄	—	94	2	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	47	2	no	—
366	C₄²	—	94	4	no	—
367	C₄²	—	94	1	no	—
368	C₄²	—	94	2	no	—
369	C₄²	Q₈×D₄₇	1	2	yes	—
370	C₂³	—	47	1	no	—
371	C₂³	—	47	1	no	—
372	C₂³	—	47	2	no	—
373	C₂³	—	47	2	no	—
374	C₂³	—	188	2	no	—
375	C₂³	#41×D₄₇	1	1	yes	characteristic
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	47	1	no	—
380	C₂×C₄	—	47	1	no	—
381	C₂×C₄	—	47	2	no	—
382	C₂×C₄	—	47	2	no	—
383	C₂×C₄	—	47	2	no	—
384	C₂×C₄	—	47	2	no	—
385	C₂×C₄	—	47	2	no	—
386	C₂×C₄	—	47	2	no	—
387	C₂×C₄	—	47	2	no	—
388	C₂×C₄	—	47	2	no	—
389	C₂×C₄	—	47	2	no	—
390	C₂×C₄	—	47	2	no	—
391	C₂×C₄	—	94	4	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	376	4	no	—
394	C₂×C₄	—	188	2	no	—
395	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
398	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
399	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
400	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	47	2	no	—
404	C₈	—	47	2	no	—
405	C₈	—	94	2	no	—
406	C₈	—	188	2	no	—
407	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
408	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
409	C₂²	—	2	2	no	—
410	C₂²	—	47	2	no	—
411	C₂²	—	47	2	no	—
412	C₂²	—	94	2	no	—
413	C₂²	—	94	2	no	—
414	C₂²	—	188	2	no	—
415	C₂²	—	188	2	no	—
416	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
417	C₂²	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
418	C₂²	#125×D₄₇	1	1	yes	characteristic
419	C₄	—	4	2	no	—
420	C₄	—	4	4	no	—
421	C₄	—	47	2	no	—
422	C₄	—	47	2	no	—
423	C₄	—	188	2	no	—
424	C₄	—	188	4	no	—
425	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
426	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
427	C₄	#121×D₄₇	1	1	yes	characteristic
428	C₄	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	—	94	2	no	—
432	C₂	—	94	2	no	—
433	C₂	#389×D₄₇	1	1	yes	characteristic
434	C₂	#20252300	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1945	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂³×D₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1945	D₄₇
hypocenter	C₄₇	#21163
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1945

Complements

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

N	H ≅ G/N	type
5. #20244140	C₂	semidirect
6. #20244138	C₂	semidirect
7. #20244137	C₂	semidirect
8. #20244136	C₂	semidirect
9. #20244134	C₂	semidirect
11. C₄₇×#1945	C₂	semidirect
21. #15689160	C₄	semidirect
23. #15689158	C₄	semidirect
24. #107×D₄₇	C₄	semidirect
25. #106×D₄₇	C₄	semidirect
221. #1945	D₄₇	semidirect
260. C₄₇	#21163	semidirect

Maximal subgroups

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

subgroup	index
C₂×#108×D₄₇	2
#427×D₄₇	2
#20251949	2
C₂×#15689077	2
#20244140	2
#20244138	2
#20244137	2
#20244136	2
#20244134	2
#20243096	2
C₄₇×#1945	2
#21163	47