Subgroups — #26242819

Order 12032.

702 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20244329	C₂	1	2	yes	maximal, complemented
2	#20244003	C₂	1	2	yes	maximal, complemented
3	#20244003	C₂	1	2	yes	maximal, complemented
4	#20243686	C₂	1	1	yes	maximal, characteristic
5	#20243681	C₂	1	1	yes	maximal, characteristic
6	#20243573	C₂	1	2	yes	maximal, complemented
7	#20243568	C₂	1	2	yes	maximal, complemented
8	#20243508	C₂	1	2	yes	maximal, complemented
9	C₄₇×#2398	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×#13093935	C₂²	1	2	yes	—
20	#15688878	C₂²	1	2	yes	—
21	#15688878	C₂²	1	2	yes	—
22	#15688878	C₂²	1	2	yes	—
23	#15688878	C₂²	1	2	yes	—
24	#15688878	C₂²	1	2	yes	—
25	#15688878	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#400	C₄	1	2	yes	—
29	C₄₇×#397	C₄	1	1	yes	characteristic
30	C₄₇×#397	C₄	1	1	yes	characteristic
31	C₄₇×#394	C₄	1	2	yes	—
32	C₄₇×#393	C₄	1	1	yes	characteristic
33	C₄₇×#393	C₄	1	1	yes	characteristic
34	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
36	C₄₇×#376	C₂²	1	1	yes	characteristic
37	C₂×#10625329	—	4	2	no	—
38	C₂×#10625329	—	4	1	no	—
39	C₂²×C₄₇⋊C₈	—	4	2	no	—
40	C₂²×C₄₇⋊C₈	—	4	1	no	—
41	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
46	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
47	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
48	C₂²⋊(C₄₇⋊C₈)	—	4	1	no	—
49	C₂²⋊(C₄₇⋊C₈)	—	4	1	no	—
50	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
51	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
52	#13093935	—	4	2	no	—
53	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₄×Q₈×C₄₇	—	4	1	no	—
58	C₄×Q₈×C₄₇	—	4	1	no	—
59	C₄×D₄×C₄₇	—	4	1	no	—
60	C₄×D₄×C₄₇	—	4	1	no	—
61	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
73	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
74	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
75	#95×C₄₇	C₂×C₄	1	2	yes	—
76	#95×C₄₇	C₂×C₄	1	2	yes	—
77	#95×C₄₇	C₂×C₄	1	2	yes	—
78	#95×C₄₇	C₂×C₄	1	2	yes	—
79	#95×C₄₇	C₂×C₄	1	2	yes	—
80	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂×Q₈×C₄₇	—	4	1	no	—
83	C₂×Q₈×C₄₇	—	4	2	no	—
84	C₂×D₄×C₄₇	—	2	2	no	—
85	C₂×D₄×C₄₇	—	4	1	no	—
86	C₂×D₄×C₄₇	—	4	1	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₄⋊C₄×C₄₇	—	4	1	no	—
105	C₄⋊C₄×C₄₇	—	4	1	no	—
106	C₄⋊C₄×C₄₇	—	4	2	no	—
107	C₂²⋊C₄×C₄₇	—	2	4	no	—
108	C₂²⋊C₄×C₄₇	—	4	2	no	—
109	C₂²⋊C₄×C₄₇	—	4	2	no	—
110	C₂²⋊C₄×C₄₇	—	4	2	no	—
111	C₂²⋊C₄×C₄₇	—	4	1	no	—
112	C₂²⋊C₄×C₄₇	—	4	1	no	—
113	C₄²×C₄₇	—	2	1	no	—
114	C₄²×C₄₇	—	2	1	no	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	—	2	2	no	—
119	#10625329	—	4	4	no	—
120	C₂×C₄₇⋊C₈	—	2	2	no	—
121	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	4	4	no	—
133	C₂³×C₄₇	—	2	1	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	—	2	1	no	—
137	C₂³×C₄₇	—	2	1	no	—
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	—	2	1	no	—
140	C₂³×C₄₇	—	2	1	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	#131	1	2	yes	—
143	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
144	Q₈×C₄₇	—	4	4	no	—
145	D₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
176	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
177	C₄₇⋊C₈	—	4	2	no	—
178	C₄₇⋊C₈	—	4	2	no	—
179	C₄₇⋊C₈	—	4	2	no	—
180	C₄₇⋊C₈	—	4	2	no	—
181	#23354	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	4	no	—
184	C₂²×C₄₇	—	4	1	no	—
185	C₂²×C₄₇	—	4	1	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	4	1	no	—
188	C₂²×C₄₇	—	4	1	no	—
189	C₂²×C₄₇	—	4	1	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	4	2	no	—
192	C₂²×C₄₇	#518	1	1	yes	characteristic
193	C₂²×C₄₇	#520	1	2	yes	—
194	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
195	C₂²×C₄₇	#568	1	1	yes	characteristic
196	C₂²×C₄₇	#568	1	2	yes	—
197	C₄×C₄₇	—	4	1	no	—
198	C₄×C₄₇	—	4	1	no	—
199	C₄×C₄₇	—	4	2	no	—
200	C₄×C₄₇	—	4	1	no	—
201	C₄×C₄₇	—	4	1	no	—
202	C₄×C₄₇	—	4	2	no	—
203	C₄×C₄₇	—	4	2	no	—
204	C₄×C₄₇	—	4	2	no	—
205	C₄×C₄₇	H(3,𝔽₄)	1	1	yes	characteristic
206	C₄×C₄₇	#562	1	2	yes	—
207	C₄×C₄₇	#563	1	1	yes	characteristic
208	#2398	D₄₇	1	1	yes	characteristic
209	#1985	—	47	2	no	—
210	#1924	—	47	2	no	—
211	#1924	—	47	2	no	—
212	#1870	—	47	1	no	—
213	#1869	—	47	1	no	—
214	#1851	—	47	2	no	—
215	#1850	—	47	2	no	—
216	#1832	—	47	2	no	—
217	C₂×C₄₇	—	4	2	no	—
218	C₂×C₄₇	—	8	1	no	—
219	C₂×C₄₇	#2379	1	1	yes	characteristic
220	C₂×C₄₇	#2976	1	1	yes	characteristic
221	C₂×C₄₇	#2978	1	1	yes	characteristic
222	C₂×C₄₇	#2992	1	2	yes	—
223	C₂×C₄₇	#2995	1	2	yes	—
224	C₂²×M₁₆	—	47	1	no	—
225	C₂³×C₈	—	47	1	no	—
226	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
228	C₂×C₄⋊C₈	—	47	2	no	—
229	C₂×C₄⋊C₈	—	47	2	no	—
230	C₂×C₄⋊C₈	—	47	2	no	—
231	C₂×C₂²⋊C₈	—	47	2	no	—
232	C₂×C₂²⋊C₈	—	47	2	no	—
233	C₂×C₂²⋊C₈	—	47	1	no	—
234	C₂×C₂²⋊C₈	—	47	1	no	—
235	C₂×#97	—	47	2	no	—
236	#400	Dic₄₇	1	2	yes	—
237	#397	Dic₄₇	1	1	yes	characteristic
238	#397	Dic₄₇	1	1	yes	characteristic
239	#394	Dic₄₇	1	2	yes	—
240	#393	Dic₄₇	1	1	yes	characteristic
241	#393	Dic₄₇	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
243	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
244	#376	C₂×D₄₇	1	1	yes	characteristic
245	#336	—	47	2	no	—
246	#336	—	47	2	no	—
247	#336	—	47	2	no	—
248	#336	—	47	2	no	—
249	#336	—	47	2	no	—
250	#336	—	47	2	no	—
251	C₄₇	#23354	1	1	yes	characteristic, complemented, Sylow
252	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
253	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
254	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
255	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
256	C₂×M₁₆	—	188	1	no	—
257	C₂×M₁₆	—	188	2	no	—
258	C₂²×C₈	—	47	2	no	—
259	C₂²×C₈	—	47	2	no	—
260	C₂²×C₈	—	47	2	no	—
261	C₂²×C₈	—	47	2	no	—
262	C₂²×C₈	—	188	1	no	—
263	C₂²×C₈	—	188	2	no	—
264	C₄×Q₈	—	4	1	no	—
265	C₄×Q₈	—	4	1	no	—
266	C₄×D₄	—	4	1	no	—
267	C₄×D₄	—	4	1	no	—
268	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
272	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
275	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
276	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
277	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
278	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
279	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
280	C₄⋊C₈	—	188	2	no	—
281	C₄⋊C₈	—	188	2	no	—
282	C₄⋊C₈	—	188	2	no	—
283	C₂²⋊C₈	—	188	1	no	—
284	C₂²⋊C₈	—	188	1	no	—
285	C₂²⋊C₈	—	188	2	no	—
286	C₂²⋊C₈	—	188	2	no	—
287	#97	—	188	2	no	—
288	#95	C₂×Dic₄₇	1	1	yes	characteristic
289	#95	C₂×Dic₄₇	1	1	yes	characteristic
290	#95	C₂×Dic₄₇	1	2	yes	—
291	#95	C₂×Dic₄₇	1	2	yes	—
292	#95	C₂×Dic₄₇	1	2	yes	—
293	#95	C₂×Dic₄₇	1	2	yes	—
294	#95	C₂×Dic₄₇	1	2	yes	—
295	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
296	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
311	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
312	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
315	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
317	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
318	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
319	M₁₆	—	188	4	no	—
320	C₂×C₈	—	94	2	no	—
321	C₂×C₈	—	94	2	no	—
322	C₂×C₈	—	94	2	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	—	94	2	no	—
329	C₂×C₈	—	94	2	no	—
330	C₂×C₈	—	94	2	no	—
331	C₂×C₈	—	94	2	no	—
332	C₂×C₈	—	188	4	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	2	no	—
357	C₂³	#13094031	1	2	yes	—
358	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
359	Q₈	—	4	4	no	—
360	D₄	—	4	4	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	#13094069	1	1	yes	characteristic
389	C₂×C₄	#13094069	1	1	yes	characteristic
390	C₂×C₄	#13094070	1	2	yes	—
391	C₂×C₄	#13094071	1	2	yes	—
392	C₈	—	188	2	no	—
393	C₈	—	188	2	no	—
394	C₈	—	188	2	no	—
395	C₈	—	188	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	#15689598	1	1	yes	characteristic
407	C₂²	#15689606	1	2	yes	—
408	C₂²	C₂×#13094031	1	1	yes	characteristic
409	C₂²	#15689890	1	1	yes	characteristic
410	C₂²	#15689890	1	2	yes	—
411	C₄	—	4	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	#15689865	1	1	yes	characteristic
420	C₄	#15689867	1	2	yes	—
421	C₄	#15689873	1	1	yes	characteristic
422	C₂	—	4	2	no	—
423	C₂	—	8	1	no	—
424	C₂	#20246562	1	1	yes	characteristic
425	C₂	#20252436	1	1	yes	characteristic
426	C₂	#20252450	1	1	yes	characteristic
427	C₂	#20252527	1	2	yes	—
428	C₂	#20252558	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#2398	C₂
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2398	D₄₇
hypocenter	C₄₇	#23354
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2398

Complements

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

N	H ≅ G/N	type
1. #20244329	C₂	semidirect
2. #20244003	C₂	semidirect
3. #20244003	C₂	semidirect
6. #20243573	C₂	semidirect
7. #20243568	C₂	semidirect
8. #20243508	C₂	semidirect
251. C₄₇	#23354	semidirect

Maximal subgroups

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

subgroup	index
#20244329	2
#20244003	2
#20243686	2
#20243681	2
#20243573	2
#20243568	2
#20243508	2
C₄₇×#2398	2
#23354	47