Subgroups — #26235065

Order 12032.

790 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×D₁₈₈	C₂	1	1	yes	maximal, characteristic
2	#20252123	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689200	C₂	1	1	yes	maximal, characteristic
4	#20244164	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243594	C₂	1	2	yes	maximal, complemented
6	#20243591	C₂	1	2	yes	maximal, complemented
7	#20243525	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243427	C₂	1	2	yes	maximal, complemented
9	C₄×#13093959	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243113	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	2	yes	—
13	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
14	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
15	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
16	#15689202	—	2	1	no	—
17	#15689200	—	2	1	no	—
18	#15689200	C₄	1	2	yes	—
19	#15689200	C₄	1	2	yes	—
20	#15689200	C₄	1	4	yes	—
21	#15689196	—	2	2	no	—
22	#15689193	—	2	2	no	—
23	C₈×D₁₈₈	—	2	1	no	—
24	#15689188	—	2	1	no	—
25	C₂×#13093960	C₂²	1	2	yes	—
26	C₂×#13093959	C₂²	1	1	yes	characteristic
27	C₂×#13093959	C₂²	1	1	yes	characteristic
28	#15689147	C₂²	1	1	yes	characteristic
29	#15689086	C₂²	1	2	yes	—
30	#15689086	C₂²	1	2	yes	—
31	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
32	C₄×#10625329	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	#15688888	C₂²	1	2	yes	—
35	#15688887	C₂²	1	2	yes	—
36	#15688887	C₂²	1	2	yes	—
37	#15688887	C₂²	1	1	yes	characteristic
38	#15688887	C₂²	1	1	yes	characteristic
39	C₂×#108×C₄₇	C₂²	1	2	yes	—
40	C₄₇×#423	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#341	C₂²	1	2	yes	—
44	C₂²×D₁₈₈	Q₈	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
46	C₂×#10625329	C₂³	1	1	yes	characteristic
47	C₂×#10625329	C₂³	1	2	yes	—
48	C₂×#10625329	C₂³	1	1	yes	characteristic
49	C₂×#10625324	—	2	2	no	—
50	C₂×#10625324	—	2	2	no	—
51	C₂×#10625324	—	4	2	no	—
52	C₂×#10625324	—	4	2	no	—
53	C₂×#10625324	C₂×C₄	1	4	yes	—
54	C₂×#10625324	C₂×C₄	1	4	yes	—
55	M₁₆×D₄₇	—	2	4	no	—
56	M₁₆×D₄₇	—	2	4	no	—
57	M₁₆×D₄₇	—	4	2	no	—
58	M₁₆×D₄₇	—	4	2	no	—
59	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₄₇	—	2	2	no	—
62	C₂×C₈×D₄₇	—	2	2	no	—
63	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
64	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
65	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
66	C₄×D₁₈₈	D₄	1	1	yes	characteristic
67	C₄×D₁₈₈	D₄	1	1	yes	characteristic
68	C₄×D₁₈₈	D₄	1	2	yes	—
69	C₂×C₄⋊Dic₄₇	Q₈	1	1	yes	characteristic
70	C₂×(C₂×D₄₇)⋊C₄	Q₈	1	2	yes	—
71	#13093960	—	4	2	no	—
72	#13093959	—	2	2	no	—
73	#13093959	—	2	2	no	—
74	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
75	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
76	(C₂×D₄₇)⋊C₈	—	2	2	no	—
77	(C₂×D₄₇)⋊C₈	—	2	2	no	—
78	(C₂×D₄₇)⋊C₈	—	2	2	no	—
79	(C₂×D₄₇)⋊C₈	—	2	2	no	—
80	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
81	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
82	#13093935	—	2	1	no	—
83	C₄×C₄₇⋊C₈	—	2	1	no	—
84	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
85	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
86	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
88	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	#108×C₄₇	—	4	2	no	—
92	C₄⋊C₈×C₄₇	—	2	1	no	—
93	C₄⋊C₈×C₄₇	—	2	1	no	—
94	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
95	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
96	#97×C₄₇	—	2	1	no	—
97	C₄×C₈×C₄₇	—	2	1	no	—
98	C₂³×D₄₇	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂×Q₈	1	2	yes	—
103	C₂×D₁₈₈	—	4	2	no	—
104	C₂×D₁₈₈	C₄⋊C₄	1	1	yes	characteristic
105	C₂×D₁₈₈	C₄⋊C₄	1	1	yes	characteristic
106	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
107	C₂×C₄×D₄₇	—	2	2	no	—
108	C₂×C₄×D₄₇	—	2	2	no	—
109	C₂×C₄×D₄₇	—	2	2	no	—
110	C₂×C₄×D₄₇	—	2	2	no	—
111	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
114	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
115	M₁₆×C₄₇	—	2	1	no	—
116	M₁₆×C₄₇	—	2	1	no	—
117	M₁₆×C₄₇	—	2	2	no	—
118	M₁₆×C₄₇	—	2	1	no	—
119	M₁₆×C₄₇	—	2	2	no	—
120	M₁₆×C₄₇	#41	1	2	yes	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
127	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
131	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
132	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
133	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
134	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
135	C₄⋊Dic₄₇	C₄⋊C₄	1	2	yes	—
136	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
137	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
138	#10625329	—	2	1	no	—
139	#10625329	—	2	1	no	—
140	#10625329	—	2	2	no	—
141	#10625329	—	2	1	no	—
142	#10625329	—	2	2	no	—
143	#10625329	#41	1	2	yes	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
153	#10625324	—	4	4	no	—
154	#10625324	—	4	4	no	—
155	#10625324	—	4	4	no	—
156	#10625324	—	4	4	no	—
157	C₈×D₄₇	—	4	4	no	—
158	C₈×D₄₇	—	4	4	no	—
159	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
160	C₂²×D₄₇	—	2	2	no	—
161	C₂²×D₄₇	—	2	2	no	—
162	C₂²×D₄₇	—	4	2	no	—
163	C₂²×D₄₇	—	4	2	no	—
164	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
165	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	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×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
181	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
182	D₁₈₈	—	2	2	no	—
183	D₁₈₈	—	2	2	no	—
184	D₁₈₈	—	4	2	no	—
185	C₄×D₄₇	—	2	2	no	—
186	C₄×D₄₇	—	2	2	no	—
187	C₄×D₄₇	—	2	2	no	—
188	C₄×D₄₇	—	2	2	no	—
189	C₄×D₄₇	—	2	2	no	—
190	C₄×D₄₇	—	2	2	no	—
191	C₄×D₄₇	—	2	2	no	—
192	C₄×D₄₇	—	2	2	no	—
193	C₈×C₄₇	—	2	4	no	—
194	C₈×C₄₇	—	2	2	no	—
195	C₈×C₄₇	—	4	2	no	—
196	C₈×C₄₇	—	4	1	no	—
197	C₄₇⋊C₈	—	2	2	no	—
198	C₄₇⋊C₈	—	2	2	no	—
199	C₄₇⋊C₈	—	2	2	no	—
200	C₄₇⋊C₈	—	4	2	no	—
201	C₄₇⋊C₈	—	4	1	no	—
202	#22719	—	47	1	no	maximal, Sylow
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	—	2	1	no	—
205	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
206	C₂²×C₄₇	#554	1	1	yes	characteristic
207	C₂²×C₄₇	#554	1	1	yes	characteristic
208	C₂×D₄₇	—	2	2	no	—
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	—	8	2	no	—
215	C₂×D₄₇	—	8	2	no	—
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	—	2	1	no	—
218	C₄×C₄₇	—	2	1	no	—
219	C₄×C₄₇	#430	1	2	yes	—
220	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
221	C₄×C₄₇	#518	1	1	yes	characteristic
222	C₄×C₄₇	#546	1	1	yes	characteristic
223	C₄×C₄₇	#546	1	1	yes	characteristic
224	Dic₄₇	—	2	2	no	—
225	Dic₄₇	—	2	2	no	—
226	D₄×M₁₆	—	47	1	no	—
227	D₄×M₁₆	—	47	1	no	—
228	C₂×#436	—	47	1	no	—
229	#1950	—	47	1	no	—
230	#1950	D₄₇	1	1	yes	characteristic, complemented
231	#1855	—	47	2	no	—
232	#1855	—	47	2	no	—
233	#1837	—	47	1	no	—
234	#1811	—	47	2	no	—
235	C₄×#108	—	47	1	no	—
236	#1738	—	47	2	no	—
237	C₂×C₄₇	—	2	1	no	—
238	C₂×C₄₇	—	2	1	no	—
239	C₂×C₄₇	#2349	1	1	yes	characteristic
240	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
241	C₂×C₄₇	#2916	1	1	yes	characteristic
242	D₄₇	—	4	2	no	—
243	D₄₇	—	4	2	no	—
244	C₂²×M₁₆	—	47	2	no	—
245	C₂²×M₁₆	—	47	2	no	—
246	C₂²×M₁₆	—	47	2	no	—
247	C₂×C₄×D₄	—	47	1	no	—
248	#436	—	47	2	no	—
249	#436	—	47	2	no	—
250	#436	—	47	4	no	—
251	#436	—	94	1	no	—
252	#436	—	94	1	no	—
253	#435	—	94	2	no	—
254	#435	—	94	2	no	—
255	C₈×D₄	—	94	1	no	—
256	C₈×D₄	—	94	1	no	—
257	C₂×#108	—	47	1	no	—
258	C₂×#108	—	47	1	no	—
259	C₂×#108	—	47	2	no	—
260	C₂×#108	C₂×D₄₇	1	2	yes	—
261	#423	—	47	1	no	—
262	#423	C₂×D₄₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
264	#407	—	47	2	no	—
265	#407	—	47	2	no	—
266	C₂×C₂²⋊C₈	—	47	2	no	—
267	C₄×M₁₆	—	47	1	no	—
268	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
269	C₂×C₄×C₈	—	47	1	no	—
270	#341	—	47	1	no	—
271	#341	—	47	2	no	—
272	#341	—	47	2	no	—
273	#341	—	47	1	no	—
274	#341	—	47	2	no	—
275	#341	C₂×D₄₇	1	2	yes	—
276	C₄₇	#22719	1	1	yes	characteristic, complemented, Sylow
277	C₂²×D₄	—	47	1	no	—
278	C₂³×C₄	—	47	2	no	—
279	C₂×M₁₆	—	47	4	no	—
280	C₂×M₁₆	—	47	4	no	—
281	C₂×M₁₆	—	47	1	no	—
282	C₂×M₁₆	—	47	2	no	—
283	C₂×M₁₆	—	47	1	no	—
284	C₂×M₁₆	—	94	2	no	—
285	C₂×M₁₆	—	94	2	no	—
286	C₂×M₁₆	—	94	4	no	—
287	C₂×M₁₆	—	94	4	no	—
288	C₂×M₁₆	—	188	2	no	—
289	C₂×M₁₆	—	188	2	no	—
290	C₂×M₁₆	—	188	2	no	—
291	C₂×M₁₆	—	188	2	no	—
292	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
293	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
294	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
295	C₂²×C₈	—	47	1	no	—
296	C₂²×C₈	—	47	1	no	—
297	C₂²×C₈	—	94	2	no	—
298	C₂²×C₈	—	94	2	no	—
299	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
300	C₄×D₄	—	47	1	no	—
301	C₄×D₄	—	47	1	no	—
302	C₄×D₄	—	47	2	no	—
303	C₄×D₄	—	47	1	no	—
304	C₄×D₄	—	47	1	no	—
305	C₄×D₄	—	47	2	no	—
306	C₂×C₄⋊C₄	—	47	1	no	—
307	C₂×C₂²⋊C₄	—	47	2	no	—
308	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
309	#108	—	4	2	no	—
310	#108	—	94	2	no	—
311	#108	—	94	2	no	—
312	#108	—	188	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	94	1	no	—
316	C₄⋊C₈	—	94	1	no	—
317	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
318	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
319	C₂²⋊C₈	—	47	4	no	—
320	C₂²⋊C₈	—	47	4	no	—
321	C₂²⋊C₈	—	94	2	no	—
322	C₂²⋊C₈	—	94	2	no	—
323	C₂²⋊C₈	—	94	2	no	—
324	C₂²⋊C₈	—	94	2	no	—
325	#97	—	2	1	no	—
326	#97	—	94	1	no	—
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	—	47	2	no	—
329	C₄×C₈	—	47	2	no	—
330	C₄×C₈	—	94	1	no	—
331	C₂⁴	—	47	2	no	—
332	C₂×D₄	—	47	1	no	—
333	C₂×D₄	—	47	1	no	—
334	C₂×D₄	—	47	2	no	—
335	C₂×D₄	—	188	2	no	—
336	C₂²×C₄	—	47	2	no	—
337	C₂²×C₄	—	47	2	no	—
338	C₂²×C₄	—	47	2	no	—
339	C₂²×C₄	—	47	2	no	—
340	C₂²×C₄	—	47	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	Q₈×D₄₇	1	1	yes	characteristic
346	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
347	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
348	M₁₆	—	2	1	no	—
349	M₁₆	—	2	1	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	47	2	no	—
354	M₁₆	—	94	1	no	—
355	M₁₆	—	94	1	no	—
356	M₁₆	—	94	2	no	—
357	M₁₆	—	94	1	no	—
358	M₁₆	—	94	2	no	—
359	M₁₆	—	188	4	no	—
360	M₁₆	—	188	4	no	—
361	M₁₆	—	188	4	no	—
362	M₁₆	—	188	4	no	—
363	M₁₆	#10625354	1	2	yes	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	47	2	no	—
370	C₂×C₈	—	47	2	no	—
371	C₂×C₈	—	94	1	no	—
372	C₂×C₈	—	94	1	no	—
373	C₂×C₈	—	94	1	no	—
374	C₂×C₈	—	94	1	no	—
375	C₂×C₈	—	94	1	no	—
376	C₂×C₈	—	94	1	no	—
377	C₂×C₈	—	94	2	no	—
378	C₂×C₈	—	188	4	no	—
379	C₂×C₈	—	188	4	no	—
380	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
381	C₄⋊C₄	—	47	2	no	—
382	C₄⋊C₄	—	47	1	no	—
383	C₄⋊C₄	—	47	1	no	—
384	C₂²⋊C₄	—	47	2	no	—
385	C₂²⋊C₄	—	47	2	no	—
386	C₂²⋊C₄	—	47	2	no	—
387	C₂²⋊C₄	—	47	2	no	—
388	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
389	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
390	C₄²	D₄×D₄₇	1	1	yes	characteristic
391	C₄²	D₄×D₄₇	1	1	yes	characteristic
392	C₂³	—	47	2	no	—
393	C₂³	—	47	2	no	—
394	C₂³	—	94	2	no	—
395	C₂³	—	94	2	no	—
396	C₂³	—	188	2	no	—
397	C₂³	—	188	2	no	—
398	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
399	D₄	—	94	2	no	—
400	D₄	—	94	2	no	—
401	D₄	—	188	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	47	2	no	—
405	C₂×C₄	—	47	2	no	—
406	C₂×C₄	—	94	2	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	2	no	—
409	C₂×C₄	—	94	2	no	—
410	C₂×C₄	—	94	2	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	94	2	no	—
414	C₂×C₄	—	94	2	no	—
415	C₂×C₄	—	94	2	no	—
416	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
417	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
418	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
419	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
422	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
424	C₂×C₄	#13094069	1	1	yes	characteristic
425	C₂×C₄	#13094070	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	2	4	no	—
428	C₈	—	4	2	no	—
429	C₈	—	4	1	no	—
430	C₈	—	94	2	no	—
431	C₈	—	94	2	no	—
432	C₈	—	94	2	no	—
433	C₈	—	188	2	no	—
434	C₈	—	188	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	94	2	no	—
438	C₂²	—	94	2	no	—
439	C₂²	—	94	2	no	—
440	C₂²	—	94	2	no	—
441	C₂²	—	94	2	no	—
442	C₂²	—	94	2	no	—
443	C₂²	—	376	2	no	—
444	C₂²	—	376	2	no	—
445	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
446	C₂²	#15689829	1	1	yes	characteristic
447	C₂²	#15689834	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	94	2	no	—
452	C₄	—	94	2	no	—
453	C₄	#15689170	1	2	yes	—
454	C₄	C₄×#10625354	1	1	yes	characteristic
455	C₄	#15689595	1	1	yes	characteristic
456	C₄	#15689764	1	1	yes	characteristic
457	C₄	#15689770	1	1	yes	characteristic
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	188	2	no	—
461	C₂	—	188	2	no	—
462	C₂	#20246297	1	1	yes	characteristic
463	C₂	C₂×#15689170	1	1	yes	characteristic
464	C₂	#20251998	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×#1950	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂²×D₁₈₈	Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1950	D₄₇
hypocenter	C₄₇	#22719
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
4. #20244164	C₂	semidirect
5. #20243594	C₂	semidirect
6. #20243591	C₂	semidirect
7. #20243525	C₂	semidirect
8. #20243427	C₂	semidirect
9. C₄×#13093959	C₂	semidirect
10. #20243113	C₂	semidirect
11. C₄₇×#1950	C₂	semidirect
230. #1950	D₄₇	semidirect
276. C₄₇	#22719	semidirect

Maximal subgroups

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

subgroup	index
M₁₆×D₁₈₈	2
#20252123	2
C₂×#15689200	2
#20244164	2
#20243594	2
#20243591	2
#20243525	2
#20243427	2
C₄×#13093959	2
#20243113	2
C₄₇×#1950	2
#22719	47