Subgroups — #26185729

Order 12032.

702 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252496	C₂	1	1	yes	maximal, characteristic
2	#20252468	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13094057	C₂	1	1	yes	maximal, characteristic
4	#20242208	C₂	1	2	yes	maximal, complemented
5	#20242202	C₂	1	2	yes	maximal, complemented
6	C₈×Dic₁₈₈	C₂	1	2	yes	maximal, complemented
7	C₈×#10625325	C₂	1	2	yes	maximal, complemented
8	#20242140	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241771	C₂	1	1	yes	maximal, characteristic
10	C₂×#15688855	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094057	C₄	1	1	yes	characteristic
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	C₈×Dic₉₄	C₂²	1	2	yes	—
16	C₈×Dic₉₄	C₂²	1	2	yes	—
17	C₈×Dic₉₄	C₂²	1	2	yes	—
18	#15689247	—	2	1	no	—
19	#15689247	—	2	1	no	—
20	#15689231	C₄	1	2	yes	—
21	#15689225	C₄	1	2	yes	—
22	C₄×Dic₁₈₈	C₂²	1	2	yes	—
23	C₄×#10625325	C₂²	1	2	yes	—
24	C₈×D₁₈₈	C₂²	1	2	yes	—
25	(C₂²⋊D₄₇)⋊C₈	—	2	2	no	—
26	#15689176	C₂²	1	1	yes	characteristic
27	#15689175	—	2	1	no	—
28	#15689173	—	2	2	no	—
29	#15689165	C₄	1	1	yes	characteristic
30	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
31	C₄⋊C₈×D₄₇	—	2	1	no	—
32	#15689133	C₄	1	1	yes	characteristic
33	#15689125	C₄	1	1	yes	characteristic
34	#15688876	C₂²	1	2	yes	—
35	#15688874	C₂²	1	2	yes	—
36	#15688855	C₂²	1	2	yes	—
37	#15688855	C₂²	1	1	yes	characteristic
38	#15688855	C₂²	1	2	yes	—
39	#15688855	C₂²	1	1	yes	characteristic
40	#15688852	C₂²	1	1	yes	characteristic
41	#15688852	C₂²	1	1	yes	characteristic
42	C₄₇×#431	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#322	C₂²	1	2	yes	—
46	C₈²×C₄₇	C₂²	1	2	yes	—
47	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
48	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
49	#13094057	C₈	1	8	yes	complemented
50	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
51	C₂×#10625325	C₂×C₄	1	2	yes	—
52	C₂²×C₄₇⋊C₈	—	2	1	no	—
53	C₂×C₈×D₄₇	—	2	2	no	—
54	C₄×Dic₉₄	—	2	1	no	—
55	C₄×Dic₉₄	—	2	1	no	—
56	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
57	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
58	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
59	C₄×Dic₉₄	C₂³	1	2	yes	—
60	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
61	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
62	C₄×C₂²⋊D₄₇	—	2	1	no	—
63	C₄×C₂²⋊D₄₇	—	2	1	no	—
64	#13093983	C₂×C₄	1	1	yes	characteristic
65	#13093981	—	2	1	no	—
66	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×Dic₄₇⋊C₄	—	2	1	no	—
68	C₂×C₄×Dic₄₇	—	2	1	no	—
69	C₄²×D₄₇	—	2	1	no	—
70	#13093958	C₂×C₄	1	2	yes	—
71	#13093956	C₂×C₄	1	2	yes	—
72	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
73	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
74	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
75	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
76	Dic₄₇⋊C₈	—	2	2	no	—
77	Dic₄₇⋊C₈	—	2	2	no	—
78	Dic₄₇⋊C₈	—	2	2	no	—
79	#13093949	C₂×C₄	1	2	yes	—
80	#13093949	C₂×C₄	1	2	yes	—
81	#13093949	C₂×C₄	1	2	yes	—
82	#13093946	C₂×C₄	1	2	yes	—
83	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
84	(C₂×D₄₇)⋊C₈	—	2	2	no	—
85	C₄×C₄₇⋊C₈	—	2	1	no	—
86	C₈×Dic₄₇	—	2	2	no	—
87	C₈×Dic₄₇	—	2	2	no	—
88	C₈×Dic₄₇	—	2	2	no	—
89	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
94	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
95	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
96	#97×C₄₇	C₂×C₄	1	2	yes	—
97	C₄×C₈×C₄₇	—	2	1	no	—
98	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	2	yes	—
101	C₄×C₈×C₄₇	C₂³	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₄₇	—	2	1	no	—
106	C₂²×Dic₄₇	—	2	1	no	—
107	C₂²×Dic₄₇	—	2	1	no	—
108	#10625350	—	2	2	no	—
109	#10625350	C₂×C₈	1	4	yes	—
110	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₄₇	—	2	1	no	—
112	C₂×C₄×D₄₇	—	2	1	no	—
113	C₂×C₄×D₄₇	—	2	1	no	—
114	C₂×Dic₉₄	—	2	1	no	—
115	C₂×Dic₉₄	—	2	2	no	—
116	C₂×Dic₉₄	C₂×C₈	1	4	yes	complemented
117	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
118	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
119	M₁₆×C₄₇	—	2	2	no	—
120	M₁₆×C₄₇	C₂×C₈	1	4	yes	complemented
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	4	2	no	—
124	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
128	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₇	#41	1	1	yes	characteristic
131	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₂²⋊Dic₄₇	—	2	1	no	—
133	(C₂×D₄₇)⋊C₄	—	2	1	no	—
134	(C₂×D₄₇)⋊C₄	—	2	1	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
137	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
139	Dic₄₇⋊C₄	—	2	2	no	—
140	Dic₄₇⋊C₄	—	2	1	no	—
141	Dic₄₇⋊C₄	—	2	2	no	—
142	Dic₄₇⋊C₄	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	2	no	—
146	C₄×Dic₄₇	—	2	1	no	—
147	C₄×Dic₄₇	—	2	2	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	—	8	1	no	—
152	Dic₁₈₈	C₂×C₈	1	8	yes	complemented
153	#10625325	C₂×C₈	1	8	yes	complemented
154	C₈×D₄₇	—	8	2	no	—
155	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
156	C₂²×D₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
164	C₂×C₄×C₄₇	#131	1	2	yes	—
165	C₂×C₄×C₄₇	C₂³×C₄	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	C₂²⋊D₄₇	—	2	4	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	1	no	—
171	C₂×Dic₄₇	—	2	4	no	—
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	1	no	—
174	C₂×Dic₄₇	—	2	1	no	—
175	C₂×Dic₄₇	—	8	1	no	—
176	D₁₈₈	—	2	1	no	—
177	D₁₈₈	C₂²×C₈	1	2	yes	—
178	C₄×D₄₇	—	2	4	no	—
179	C₄×D₄₇	—	4	1	no	—
180	C₄×D₄₇	—	4	1	no	—
181	C₄×D₄₇	—	8	1	no	—
182	Dic₉₄	—	2	2	no	—
183	Dic₉₄	—	2	1	no	—
184	Dic₉₄	—	2	4	no	—
185	Dic₉₄	C₂²×C₈	1	4	yes	—
186	Dic₉₄	C₂²×C₈	1	2	yes	—
187	C₈×C₄₇	—	2	2	no	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	—	2	2	no	—
190	C₈×C₄₇	—	2	2	no	—
191	C₈×C₄₇	—	4	1	no	—
192	C₈×C₄₇	C₂²×C₈	1	4	yes	—
193	C₄₇⋊C₈	—	4	2	no	—
194	C₄₇⋊C₈	—	4	1	no	—
195	C₄₇⋊C₈	—	4	1	no	—
196	#17853	—	47	1	no	maximal, Sylow
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	C₈×D₄	1	2	yes	—
200	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂×D₄₇	—	2	2	no	—
202	C₂×D₄₇	—	4	1	no	—
203	C₂×D₄₇	—	4	1	no	—
204	C₄×C₄₇	—	2	1	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	C₈×D₄	1	2	yes	—
208	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
209	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
210	C₄×C₄₇	#577	1	1	yes	characteristic
211	C₄×C₄₇	#578	1	1	yes	characteristic
212	Dic₄₇	—	2	4	no	—
213	Dic₄₇	—	2	2	no	—
214	Dic₄₇	—	4	1	no	—
215	Dic₄₇	—	4	1	no	—
216	Dic₄₇	—	4	2	no	—
217	#2988	—	47	1	no	—
218	#2982	—	47	1	no	—
219	C₄×#137	—	47	1	no	—
220	#1579	—	47	2	no	—
221	SD₁₆⋊C₈	—	47	2	no	—
222	C₈×Q₁₆	—	47	2	no	—
223	C₈×SD₁₆	—	47	2	no	—
224	#1565	—	47	1	no	—
225	#1476	—	47	1	no	—
226	C₂×Q₈⋊C₈	—	47	1	no	—
227	C₈×M₁₆	D₄₇	1	1	yes	characteristic, complemented
228	C₂×C₄₇	—	2	2	no	—
229	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
230	C₂×C₄₇	#2947	1	1	yes	characteristic
231	C₂×C₄₇	#2956	1	1	yes	characteristic
232	D₄₇	—	4	2	no	—
233	C₂×#137	—	47	1	no	—
234	C₄×#41	—	47	1	no	—
235	C₂×C₄×Q₈	—	47	1	no	—
236	C₈×Q₈	—	47	2	no	—
237	C₈×Q₈	—	47	2	no	—
238	C₈×Q₈	—	47	2	no	—
239	C₈×Q₈	—	94	1	no	—
240	C₈×Q₈	—	94	1	no	—
241	#441	—	47	2	no	—
242	#440	—	47	2	no	—
243	C₄×Q₁₆	—	47	2	no	—
244	C₄×SD₁₆	—	47	2	no	—
245	C₈×D₄	—	47	2	no	—
246	C₈×D₄	—	94	2	no	—
247	#431	—	47	1	no	—
248	#431	—	94	1	no	—
249	#431	—	94	2	no	—
250	#431	C₂×D₄₇	1	1	yes	characteristic
251	#428	—	47	1	no	—
252	C₂×C₄⋊C₈	—	47	1	no	—
253	C₂×C₄⋊C₈	—	94	1	no	—
254	#419	—	47	1	no	—
255	#417	—	47	1	no	—
256	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
258	#335	—	47	2	no	—
259	#334	—	47	2	no	—
260	Q₈⋊C₈	—	47	2	no	—
261	Q₈⋊C₈	—	47	1	no	—
262	Q₈⋊C₈	—	47	2	no	—
263	Q₈⋊C₈	—	47	1	no	—
264	D₄⋊C₈	—	47	1	no	—
265	D₄⋊C₈	—	47	1	no	—
266	#322	C₂×D₄₇	1	2	yes	—
267	C₈²	C₂×D₄₇	1	2	yes	—
268	C₄₇	#17853	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	47	1	no	—
270	C₂²×Q₈	—	47	1	no	—
271	#137	—	47	8	no	—
272	C₂×Q₁₆	—	47	2	no	—
273	C₂×SD₁₆	—	47	2	no	—
274	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
275	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	94	1	no	—
278	C₂²×C₈	—	94	2	no	—
279	C₄×Q₈	—	47	2	no	—
280	C₄×Q₈	—	47	1	no	—
281	C₄×Q₈	—	47	2	no	—
282	C₄×Q₈	—	47	1	no	—
283	C₄×Q₈	—	94	1	no	—
284	C₄×Q₈	—	94	1	no	—
285	C₄×D₄	—	47	1	no	—
286	C₄×D₄	—	47	1	no	—
287	C₄×D₄	—	94	1	no	—
288	C₄×D₄	—	94	1	no	—
289	#117	—	47	1	no	—
290	#117	—	94	1	no	—
291	C₂×C₄⋊C₄	—	47	1	no	—
292	C₂×C₄⋊C₄	—	94	1	no	—
293	C₂×C₄²	—	94	1	no	—
294	C₂×C₄²	—	94	1	no	—
295	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
296	#107	—	47	2	no	—
297	#106	—	47	2	no	—
298	C₄⋊C₈	—	47	1	no	—
299	C₄⋊C₈	—	47	1	no	—
300	C₄⋊C₈	—	47	2	no	—
301	C₄⋊C₈	—	94	2	no	—
302	C₄⋊C₈	—	94	2	no	—
303	C₄⋊C₈	—	94	2	no	—
304	C₄⋊C₈	—	94	1	no	—
305	C₄⋊C₈	D₁₈₈	1	1	yes	characteristic
306	C₄⋊C₈	D₁₈₈	1	1	yes	characteristic
307	#103	—	47	2	no	—
308	#103	—	47	2	no	—
309	#103	—	47	2	no	—
310	#102	—	47	2	no	—
311	C₂²⋊C₈	—	94	1	no	—
312	C₂²⋊C₈	—	94	2	no	—
313	C₂²⋊C₈	D₁₈₈	1	2	yes	—
314	#97	C₄×D₄₇	1	2	yes	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	94	2	no	—
317	C₄×C₈	—	94	2	no	—
318	C₄×C₈	—	94	2	no	—
319	C₄×C₈	—	94	1	no	—
320	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
321	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₄₇	1	2	yes	—
323	C₄×C₈	C₂²×D₄₇	1	2	yes	—
324	#41	—	47	4	no	—
325	#41	—	94	2	no	—
326	C₂×Q₈	—	47	4	no	—
327	C₂×Q₈	—	47	2	no	—
328	C₂×Q₈	—	47	1	no	—
329	C₂×Q₈	—	94	1	no	—
330	C₂×Q₈	—	94	2	no	—
331	C₂×D₄	—	47	1	no	—
332	C₂×D₄	—	94	1	no	—
333	C₂²×C₄	—	94	1	no	—
334	C₂²×C₄	—	94	1	no	—
335	C₂²×C₄	—	94	1	no	—
336	C₂²×C₄	—	94	1	no	—
337	C₂²×C₄	—	94	1	no	—
338	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
340	C₂²×C₄	#10625350	1	1	yes	characteristic
341	Q₁₆	—	47	8	no	—
342	SD₁₆	—	47	8	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	C₈×D₄₇	1	4	yes	complemented
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	—	94	1	no	—
349	C₂×C₈	—	94	1	no	—
350	C₂×C₈	—	94	2	no	—
351	C₂×C₈	—	376	2	no	—
352	C₂×C₈	—	376	1	no	—
353	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
354	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
355	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
356	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
357	C₄⋊C₄	—	47	2	no	—
358	C₄⋊C₄	—	47	1	no	—
359	C₄⋊C₄	—	47	1	no	—
360	C₄⋊C₄	—	94	2	no	—
361	C₄⋊C₄	—	94	1	no	—
362	C₄⋊C₄	—	94	1	no	—
363	C₄⋊C₄	—	94	2	no	—
364	C₄⋊C₄	—	94	1	no	—
365	C₂²⋊C₄	—	94	1	no	—
366	C₂²⋊C₄	—	94	1	no	—
367	C₂²⋊C₄	—	94	1	no	—
368	C₄²	—	94	1	no	—
369	C₄²	—	94	1	no	—
370	C₄²	—	94	2	no	—
371	C₄²	—	94	1	no	—
372	C₄²	—	94	2	no	—
373	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
374	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
375	C₄²	#10625350	1	1	yes	characteristic
376	C₄²	C₂³×D₄₇	1	1	yes	characteristic
377	C₂³	—	94	1	no	—
378	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
379	Q₈	—	47	4	no	—
380	Q₈	—	47	2	no	—
381	Q₈	—	94	2	no	—
382	Q₈	—	94	1	no	—
383	Q₈	—	94	4	no	—
384	D₄	—	47	2	no	—
385	D₄	—	94	4	no	—
386	D₄	—	94	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	94	1	no	—
391	C₂×C₄	—	94	2	no	—
392	C₂×C₄	—	94	4	no	—
393	C₂×C₄	—	94	4	no	—
394	C₂×C₄	—	94	1	no	—
395	C₂×C₄	—	94	1	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	—	376	1	no	—
398	C₂×C₄	—	376	1	no	—
399	C₂×C₄	—	188	1	no	—
400	C₂×C₄	—	188	1	no	—
401	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
402	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
403	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
404	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
405	C₂×C₄	#13094030	1	2	yes	—
406	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
408	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	188	1	no	—
415	C₈	—	188	2	no	—
416	C₈	—	188	1	no	—
417	C₈	C₂×C₈×D₄₇	1	4	yes	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	94	2	no	—
421	C₂²	—	188	1	no	—
422	C₂²	—	188	1	no	—
423	C₂²	C₈×D₁₈₈	1	2	yes	—
424	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	94	2	no	—
429	C₄	—	94	4	no	—
430	C₄	—	188	1	no	—
431	C₄	—	188	1	no	—
432	C₄	—	188	2	no	—
433	C₄	C₈×D₁₈₈	1	2	yes	—
434	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
435	C₄	C₂×#13094030	1	1	yes	characteristic
436	C₄	#15689935	1	1	yes	characteristic
437	C₄	#15689940	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	188	2	no	—
440	C₂	C₂×C₈×D₁₈₈	1	1	yes	characteristic
441	C₂	#20252233	1	1	yes	characteristic
442	C₂	#20252299	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#10625350	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₈×M₁₆	D₄₇
hypocenter	C₄₇	#17853
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. #20252468	C₂	semidirect
4. #20242208	C₂	semidirect
5. #20242202	C₂	semidirect
6. C₈×Dic₁₈₈	C₂	semidirect
7. C₈×#10625325	C₂	semidirect
8. #20242140	C₂	semidirect
10. C₂×#15688855	C₂	semidirect
11. C₈×M₁₆×C₄₇	C₂	semidirect
49. #13094057	C₈	semidirect
116. C₂×Dic₉₄	C₂×C₈	semidirect
120. M₁₆×C₄₇	C₂×C₈	semidirect
152. Dic₁₈₈	C₂×C₈	semidirect
153. #10625325	C₂×C₈	semidirect
227. C₈×M₁₆	D₄₇	semidirect
268. C₄₇	#17853	semidirect
344. M₁₆	C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252496	2
#20252468	2
C₄×#13094057	2
#20242208	2
#20242202	2
C₈×Dic₁₈₈	2
C₈×#10625325	2
#20242140	2
#20241771	2
C₂×#15688855	2
C₈×M₁₆×C₄₇	2
#17853	47