Subgroups — #26226903

Order 12032.

724 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	#20252020	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689174	C₂	1	1	yes	maximal, characteristic
3	#423×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20244162	C₂	1	4	yes	maximal, complemented
5	#20243594	C₂	1	4	yes	maximal
6	#20243560	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243559	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243525	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1837	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
11	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
12	#15689179	—	2	1	no	—
13	#15689179	—	2	1	no	—
14	#15689175	—	2	1	no	—
15	#15689175	—	2	1	no	—
16	#15689174	C₄	1	2	yes	—
17	#15689174	C₄	1	2	yes	—
18	#15689174	C₄	1	2	yes	—
19	#15689174	C₄	1	2	yes	—
20	C₂×#13093960	C₂²	1	4	yes	—
21	C₂×#13093959	C₂²	1	4	yes	—
22	#15689147	C₂²	1	1	yes	characteristic
23	#15689147	C₂²	1	1	yes	characteristic
24	#15689146	C₂²	1	2	yes	—
25	#15689145	—	2	1	no	—
26	#15689145	—	2	1	no	—
27	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
28	C₄⋊C₈×D₄₇	—	2	1	no	—
29	C₄⋊C₈×D₄₇	—	2	1	no	—
30	#15689086	C₂²	1	2	yes	—
31	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
32	M₁₆×Dic₄₇	C₂²	1	2	yes	—
33	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	#15688887	C₂²	1	4	yes	—
35	C₄₇×#423	C₂²	1	1	yes	characteristic
36	C₄₇×#423	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#341	C₂²	1	4	yes	—
39	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
40	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
41	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
42	C₂×#10625329	C₂³	1	2	yes	—
43	C₂×#10625329	C₂³	1	2	yes	—
44	C₂×#10625324	—	2	2	no	—
45	M₁₆×D₄₇	—	4	4	no	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂×C₈×D₄₇	—	2	2	no	—
48	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
49	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
50	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
51	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₄₇	D₄	1	1	yes	characteristic
56	C₄²×D₄₇	D₄	1	1	yes	characteristic
57	C₄²×D₄₇	D₄	1	1	yes	characteristic
58	C₄²×D₄₇	D₄	1	1	yes	characteristic
59	#13093960	—	4	4	no	—
60	#13093959	—	4	4	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
62	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
63	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
64	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
65	Dic₄₇⋊C₈	—	2	2	no	—
66	Dic₄₇⋊C₈	—	2	2	no	—
67	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
68	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
69	(C₂×D₄₇)⋊C₈	—	2	2	no	—
70	(C₂×D₄₇)⋊C₈	—	2	2	no	—
71	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
72	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
73	#13093934	—	2	2	no	—
74	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
75	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
76	C₈×Dic₄₇	—	2	2	no	—
77	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
78	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
79	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₇	—	2	1	no	—
82	C₄⋊C₈×C₄₇	—	2	1	no	—
83	C₄⋊C₈×C₄₇	—	2	1	no	—
84	C₄⋊C₈×C₄₇	—	2	1	no	—
85	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
86	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
87	C₂³×D₄₇	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
92	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
93	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
94	C₂×C₄×D₄₇	—	2	2	no	—
95	C₂×C₄×D₄₇	—	2	2	no	—
96	C₂×C₄×D₄₇	—	2	4	no	—
97	C₂×C₄×D₄₇	—	4	2	no	—
98	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
110	M₁₆×C₄₇	—	2	4	no	—
111	M₁₆×C₄₇	—	2	4	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
117	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
132	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
133	#10625329	—	2	4	no	—
134	#10625329	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
140	#10625324	—	4	4	no	—
141	C₈×D₄₇	—	4	4	no	—
142	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
143	C₂²×D₄₇	—	2	2	no	—
144	C₂²×D₄₇	—	2	2	no	—
145	C₂²×D₄₇	—	4	1	no	—
146	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
157	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
158	C₂×Dic₄₇	—	2	2	no	—
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	—	4	1	no	—
161	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₄×D₄₇	—	2	2	no	—
168	C₄×D₄₇	—	2	2	no	—
169	C₄×D₄₇	—	2	2	no	—
170	C₄×D₄₇	—	2	1	no	—
171	C₄×D₄₇	—	2	1	no	—
172	C₄×D₄₇	—	2	1	no	—
173	C₄×D₄₇	—	2	1	no	—
174	C₄×D₄₇	—	2	2	no	—
175	C₄×D₄₇	—	2	2	no	—
176	C₄×D₄₇	—	2	2	no	—
177	C₄×D₄₇	—	2	2	no	—
178	C₄×D₄₇	—	4	1	no	—
179	C₄×D₄₇	—	4	1	no	—
180	C₄×D₄₇	#108	1	4	yes	complemented
181	C₈×C₄₇	—	2	4	no	—
182	C₈×C₄₇	—	4	2	no	—
183	C₈×C₄₇	—	4	2	no	—
184	C₄₇⋊C₈	—	2	4	no	—
185	C₄₇⋊C₈	—	4	2	no	—
186	C₄₇⋊C₈	—	4	2	no	—
187	#21993	—	47	1	no	maximal, Sylow
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
191	C₂²×C₄₇	#544	1	2	yes	—
192	C₂×D₄₇	—	2	1	no	—
193	C₂×D₄₇	—	2	1	no	—
194	C₂×D₄₇	—	2	1	no	—
195	C₂×D₄₇	—	2	1	no	—
196	C₂×D₄₇	—	2	1	no	—
197	C₂×D₄₇	—	4	4	no	—
198	C₂×D₄₇	C₂×#108	1	2	yes	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	C₂×#108	1	2	yes	—
202	C₄×C₄₇	#430	1	2	yes	—
203	C₄×C₄₇	#520	1	2	yes	—
204	C₄×C₄₇	#535	1	1	yes	characteristic
205	C₄×C₄₇	#536	1	1	yes	characteristic
206	Dic₄₇	—	2	1	no	—
207	Dic₄₇	—	2	1	no	—
208	Dic₄₇	—	2	1	no	—
209	Dic₄₇	—	2	1	no	—
210	Dic₄₇	—	2	1	no	—
211	Dic₄₇	C₂×#108	1	2	yes	—
212	#2920	—	47	1	no	—
213	C₂×#431	—	47	1	no	—
214	C₂×#423	—	47	1	no	—
215	#1950	—	47	4	no	—
216	#1855	—	47	4	no	—
217	#1848	—	47	1	no	—
218	#1848	—	47	1	no	—
219	#1837	—	47	1	no	—
220	#1837	D₄₇	1	1	yes	characteristic, complemented
221	C₂×C₄₇	—	2	2	no	—
222	C₂×C₄₇	#2317	1	1	yes	characteristic
223	C₂×C₄₇	C₂²×#108	1	1	yes	characteristic
224	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
225	D₄₇	—	2	2	no	—
226	D₄₇	—	4	1	no	—
227	C₂²×M₁₆	—	47	2	no	—
228	C₂²×C₄²	—	47	1	no	—
229	#432	—	94	1	no	—
230	#432	—	94	1	no	—
231	#431	—	47	2	no	—
232	#431	—	47	2	no	—
233	#431	—	47	2	no	—
234	#431	—	47	2	no	—
235	#431	—	94	1	no	—
236	#431	—	94	1	no	—
237	C₂×#108	—	47	4	no	—
238	C₂×#108	—	47	4	no	—
239	#423	—	47	2	no	—
240	#423	—	47	1	no	—
241	#423	—	47	1	no	—
242	#423	—	94	1	no	—
243	#423	—	94	1	no	—
244	#423	C₂×D₄₇	1	1	yes	characteristic
245	#423	C₂×D₄₇	1	1	yes	characteristic
246	C₂×C₄⋊C₈	—	47	2	no	—
247	C₂×C₄⋊C₈	—	94	1	no	—
248	C₂×C₄⋊C₈	—	94	1	no	—
249	#407	—	47	2	no	—
250	C₂×C₂²⋊C₈	—	47	2	no	—
251	C₄×M₁₆	—	47	2	no	—
252	C₂×C₄×C₈	—	47	1	no	—
253	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
254	#341	—	47	4	no	—
255	#341	C₂×D₄₇	1	4	yes	—
256	C₄₇	#21993	1	1	yes	characteristic, complemented, Sylow
257	C₂³×C₄	—	47	1	no	—
258	C₂³×C₄	—	47	1	no	—
259	C₂³×C₄	—	47	1	no	—
260	C₂×M₁₆	—	47	2	no	—
261	C₂×M₁₆	—	47	2	no	—
262	C₂×M₁₆	—	94	2	no	—
263	C₂×M₁₆	—	188	4	no	—
264	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
265	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
266	C₂²×C₈	—	47	2	no	—
267	C₂²×C₈	—	94	2	no	—
268	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
269	C₂×C₄²	—	47	1	no	—
270	C₂×C₄²	—	47	1	no	—
271	C₂×C₄²	—	47	1	no	—
272	C₂×C₄²	—	47	1	no	—
273	C₂×C₄²	—	47	1	no	—
274	C₂×C₄²	—	47	1	no	—
275	C₂×C₄²	—	47	1	no	—
276	C₂×C₄²	—	47	1	no	—
277	C₂×C₄²	—	47	1	no	—
278	C₂×C₄²	—	47	1	no	—
279	C₂×C₄²	—	47	1	no	—
280	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
281	#108	—	188	4	no	—
282	#108	—	188	4	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	47	4	no	—
288	C₄⋊C₈	—	47	4	no	—
289	C₄⋊C₈	—	94	2	no	—
290	C₄⋊C₈	—	94	2	no	—
291	C₄⋊C₈	—	94	1	no	—
292	C₄⋊C₈	—	94	1	no	—
293	C₄⋊C₈	—	94	1	no	—
294	C₄⋊C₈	—	94	1	no	—
295	C₂²⋊C₈	—	47	4	no	—
296	C₂²⋊C₈	—	47	4	no	—
297	C₂²⋊C₈	—	94	2	no	—
298	C₂²⋊C₈	—	94	2	no	—
299	#97	—	94	2	no	—
300	C₄×C₈	—	47	2	no	—
301	C₄×C₈	—	47	2	no	—
302	C₄×C₈	—	94	2	no	—
303	C₄×C₈	C₄×D₄₇	1	2	yes	—
304	C₄×C₈	C₄×D₄₇	1	2	yes	—
305	C₂⁴	—	47	1	no	—
306	C₂²×C₄	—	47	1	no	—
307	C₂²×C₄	—	47	1	no	—
308	C₂²×C₄	—	47	1	no	—
309	C₂²×C₄	—	47	1	no	—
310	C₂²×C₄	—	47	1	no	—
311	C₂²×C₄	—	47	1	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	47	1	no	—
314	C₂²×C₄	—	47	1	no	—
315	C₂²×C₄	—	47	1	no	—
316	C₂²×C₄	—	47	1	no	—
317	C₂²×C₄	—	47	1	no	—
318	C₂²×C₄	—	47	1	no	—
319	C₂²×C₄	—	47	1	no	—
320	C₂²×C₄	—	47	1	no	—
321	C₂²×C₄	—	94	4	no	—
322	C₂²×C₄	—	94	2	no	—
323	C₂²×C₄	—	94	2	no	—
324	C₂²×C₄	—	188	2	no	—
325	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
326	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
328	M₁₆	—	2	4	no	—
329	M₁₆	—	2	4	no	—
330	M₁₆	—	94	4	no	—
331	M₁₆	—	94	4	no	—
332	M₁₆	—	188	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	47	4	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	—	188	4	no	—
343	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
344	C₄²	—	47	1	no	—
345	C₄²	—	47	1	no	—
346	C₄²	—	47	1	no	—
347	C₄²	—	47	1	no	—
348	C₄²	—	47	1	no	—
349	C₄²	—	47	1	no	—
350	C₄²	—	47	1	no	—
351	C₄²	—	47	1	no	—
352	C₄²	—	47	1	no	—
353	C₄²	—	47	1	no	—
354	C₄²	—	47	1	no	—
355	C₄²	—	47	1	no	—
356	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
358	C₄²	D₄×D₄₇	1	1	yes	characteristic
359	C₄²	D₄×D₄₇	1	1	yes	characteristic
360	C₂³	—	47	1	no	—
361	C₂³	—	47	1	no	—
362	C₂³	—	94	2	no	—
363	C₂³	—	94	2	no	—
364	C₂³	—	188	1	no	—
365	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	47	1	no	—
369	C₂×C₄	—	47	4	no	—
370	C₂×C₄	—	47	1	no	—
371	C₂×C₄	—	47	1	no	—
372	C₂×C₄	—	47	1	no	—
373	C₂×C₄	—	47	1	no	—
374	C₂×C₄	—	47	1	no	—
375	C₂×C₄	—	94	2	no	—
376	C₂×C₄	—	94	2	no	—
377	C₂×C₄	—	94	2	no	—
378	C₂×C₄	—	94	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	—	94	1	no	—
385	C₂×C₄	—	94	1	no	—
386	C₂×C₄	—	94	1	no	—
387	C₂×C₄	—	94	1	no	—
388	C₂×C₄	—	188	1	no	—
389	C₂×C₄	—	188	1	no	—
390	C₂×C₄	—	188	1	no	—
391	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
394	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
397	C₂×C₄	#13094070	1	2	yes	—
398	C₂×C₄	#13094071	1	2	yes	—
399	C₈	—	2	4	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₈	—	94	4	no	—
403	C₈	—	188	2	no	—
404	C₈	—	188	2	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	47	2	no	—
408	C₂²	—	94	1	no	—
409	C₂²	—	94	1	no	—
410	C₂²	—	94	1	no	—
411	C₂²	—	94	1	no	—
412	C₂²	—	94	1	no	—
413	C₂²	—	188	4	no	—
414	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
415	C₂²	#15689753	1	2	yes	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	47	2	no	—
419	C₄	—	94	1	no	—
420	C₄	—	94	1	no	—
421	C₄	—	94	1	no	—
422	C₄	—	94	1	no	—
423	C₄	—	94	1	no	—
424	C₄	#108×D₄₇	1	2	yes	—
425	C₄	#15689170	1	2	yes	—
426	C₄	#15689603	1	2	yes	—
427	C₄	#15689691	1	1	yes	characteristic
428	C₄	#15689693	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	94	2	no	—
431	C₂	—	188	1	no	—
432	C₂	#20246013	1	1	yes	characteristic
433	C₂	C₂×#108×D₄₇	1	1	yes	characteristic
434	C₂	C₂×#15689170	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1837	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₇	C₂×Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1837	D₄₇
hypocenter	C₄₇	#21993
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

Complements

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

N	H ≅ G/N	type
4. #20244162	C₂	semidirect
6. #20243560	C₂	semidirect
7. #20243559	C₂	semidirect
8. #20243525	C₂	semidirect
9. C₄₇×#1837	C₂	semidirect
180. C₄×D₄₇	#108	semidirect
220. #1837	D₄₇	semidirect
256. C₄₇	#21993	semidirect

Maximal subgroups

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

subgroup	index
#20252020	2
C₂×#15689174	2
#423×D₄₇	2
#20244162	2
#20243594	2
#20243560	2
#20243559	2
#20243525	2
C₄₇×#1837	2
#21993	47