Subgroups — #26216532

Order 12032.

818 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13093981	C₂	1	1	yes	maximal, characteristic
2	#20243532	C₂	1	2	yes	maximal, complemented
3	#20243532	C₂	1	2	yes	maximal, complemented
4	#20243531	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243530	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243530	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243083	C₂	1	2	yes	maximal
8	#20243083	C₂	1	2	yes	maximal
9	#20243080	C₂	1	1	yes	maximal, characteristic
10	#336×D₄₇	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1839	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	2	yes	—
13	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
14	C₂×#13093981	C₂²	1	1	yes	characteristic
15	C₂×#13093981	C₂²	1	1	yes	characteristic
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
18	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
19	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
20	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
21	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
22	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
23	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
24	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
25	#15688969	C₂²	1	1	yes	characteristic
26	#15688969	C₂²	1	1	yes	characteristic
27	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
28	#15688878	C₂²	1	1	yes	characteristic
29	#15688878	C₂²	1	1	yes	characteristic
30	#15688878	C₂²	1	2	yes	—
31	#15688878	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₄³×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#336	C₂²	1	1	yes	characteristic
40	C₄₇×#336	C₂²	1	1	yes	characteristic
41	C₄₇×#336	C₂²	1	2	yes	—
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
46	C₂×#10625324	—	2	4	no	—
47	C₂×#10625324	—	2	4	no	—
48	C₂×#10625324	—	2	4	no	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	C₂×C₈×D₄₇	—	2	4	no	—
52	C₂×C₈×D₄₇	—	2	4	no	—
53	C₂×C₈×D₄₇	—	2	4	no	—
54	#13093981	—	2	2	no	—
55	#13093981	—	2	4	no	—
56	#13093981	—	2	2	no	—
57	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
74	C₄²×D₄₇	—	2	4	no	—
75	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
76	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
77	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
78	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
79	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
80	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
81	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
82	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
84	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
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	—	4	1	no	—
112	C₂×C₄×D₄₇	—	4	1	no	—
113	C₂×C₄×D₄₇	#41	1	4	yes	—
114	C₂×C₄×D₄₇	#41	1	2	yes	—
115	C₂×C₄×D₄₇	#41	1	4	yes	—
116	C₂×C₄×D₄₇	#41	1	2	yes	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	2	1	no	—
128	C₄²×C₄₇	—	2	1	no	—
129	C₄²×C₄₇	—	4	1	no	—
130	C₄²×C₄₇	—	4	1	no	—
131	(C₂×D₄₇)⋊C₄	—	2	2	no	—
132	(C₂×D₄₇)⋊C₄	—	2	2	no	—
133	(C₂×D₄₇)⋊C₄	—	2	2	no	—
134	(C₂×D₄₇)⋊C₄	—	2	2	no	—
135	Dic₄₇⋊C₄	—	2	2	no	—
136	Dic₄₇⋊C₄	—	2	2	no	—
137	Dic₄₇⋊C₄	—	2	2	no	—
138	Dic₄₇⋊C₄	—	2	2	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	2	no	—
146	C₄×Dic₄₇	—	2	2	no	—
147	C₄×Dic₄₇	—	4	1	no	—
148	C₄×Dic₄₇	—	4	1	no	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	#10625324	—	4	8	no	—
156	C₈×D₄₇	—	4	8	no	—
157	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
158	C₂²×D₄₇	—	2	1	no	—
159	C₂²×D₄₇	—	2	1	no	—
160	C₂²×D₄₇	—	2	1	no	—
161	C₂²×D₄₇	—	2	1	no	—
162	C₂²×D₄₇	#117	1	2	yes	—
163	C₂²×D₄₇	#117	1	2	yes	—
164	C₂²×D₄₇	#117	1	2	yes	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	#131	1	2	yes	—
182	C₂×C₄×C₄₇	#131	1	2	yes	—
183	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
184	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂×Dic₄₇	—	2	1	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	1	no	—
192	C₂×Dic₄₇	—	2	1	no	—
193	C₂×Dic₄₇	—	2	1	no	—
194	C₂×Dic₄₇	—	2	1	no	—
195	C₂×Dic₄₇	—	2	1	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	1	no	—
198	C₂×Dic₄₇	—	2	1	no	—
199	C₂×Dic₄₇	—	2	1	no	—
200	C₂×Dic₄₇	—	2	1	no	—
201	C₂×Dic₄₇	—	2	1	no	—
202	C₂×Dic₄₇	—	2	1	no	—
203	C₂×Dic₄₇	—	2	1	no	—
204	C₂×Dic₄₇	—	2	1	no	—
205	C₂×Dic₄₇	#117	1	2	yes	—
206	C₂×Dic₄₇	#117	1	2	yes	—
207	C₂×Dic₄₇	#117	1	2	yes	—
208	C₄×D₄₇	—	4	4	no	—
209	C₄×D₄₇	—	4	4	no	—
210	C₄×D₄₇	#126	1	8	yes	—
211	C₄×D₄₇	#126	1	8	yes	—
212	C₈×C₄₇	—	4	2	no	—
213	C₈×C₄₇	—	4	2	no	—
214	C₄₇⋊C₈	—	4	2	no	—
215	C₄₇⋊C₈	—	4	2	no	—
216	#20774	—	47	1	no	maximal, Sylow
217	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
220	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
221	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
222	C₂²×C₄₇	#568	1	1	yes	characteristic
223	C₂²×C₄₇	#568	1	1	yes	characteristic
224	C₂×D₄₇	—	2	2	no	—
225	C₂×D₄₇	—	2	2	no	—
226	C₂×D₄₇	—	2	2	no	—
227	C₂×D₄₇	—	2	2	no	—
228	C₂×D₄₇	—	2	2	no	—
229	C₂×D₄₇	—	2	2	no	—
230	C₂×D₄₇	#383	1	4	yes	—
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	4	1	no	—
234	C₄×C₄₇	—	4	1	no	—
235	C₄×C₄₇	—	4	1	no	—
236	C₄×C₄₇	—	4	1	no	—
237	C₄×C₄₇	C₂×#126	1	2	yes	—
238	C₄×C₄₇	C₂×#126	1	2	yes	—
239	Dic₄₇	—	4	1	no	—
240	Dic₄₇	—	4	1	no	—
241	Dic₄₇	—	4	1	no	—
242	Dic₄₇	—	4	1	no	—
243	Dic₄₇	—	4	1	no	—
244	Dic₄₇	—	4	1	no	—
245	Dic₄₇	#383	1	4	yes	—
246	C₄×#117	—	47	1	no	—
247	#1840	—	47	2	no	—
248	#1840	—	47	2	no	—
249	#1839	—	47	1	no	—
250	#1839	—	47	1	no	—
251	#1839	—	47	1	no	—
252	#1839	D₄₇	1	1	yes	characteristic, complemented
253	#1729	—	47	2	no	—
254	#1729	—	47	2	no	—
255	#1728	—	47	1	no	—
256	C₂×#336	—	47	1	no	—
257	C₂×C₄₇	C₂×#383	1	1	yes	characteristic
258	C₂×C₄₇	#2922	1	1	yes	characteristic
259	C₂×C₄₇	#2923	1	1	yes	characteristic
260	C₂×C₄₇	#2924	1	1	yes	characteristic
261	C₂×C₄₇	#2924	1	1	yes	characteristic
262	C₂×C₄₇	#2925	1	1	yes	characteristic
263	C₂×C₄₇	#2925	1	1	yes	characteristic
264	D₄₇	—	2	4	no	—
265	C₂²×M₁₆	—	47	2	no	—
266	C₂³×C₈	—	47	2	no	—
267	C₂×#117	—	47	1	no	—
268	C₂×#117	—	47	1	no	—
269	C₂²×C₄²	—	47	1	no	—
270	C₄×C₄⋊C₄	—	47	1	no	—
271	C₄×C₄⋊C₄	—	47	1	no	—
272	C₄×C₄⋊C₄	—	47	1	no	—
273	C₄×C₄⋊C₄	—	47	1	no	—
274	C₄×C₂²⋊C₄	—	47	1	no	—
275	C₄×C₂²⋊C₄	—	47	1	no	—
276	C₄×C₂²⋊C₄	—	47	1	no	—
277	C₄×C₂²⋊C₄	—	47	1	no	—
278	#376	—	47	1	no	—
279	#376	—	47	1	no	—
280	C₄³	—	47	1	no	—
281	C₄³	C₂×D₄₇	1	1	yes	characteristic
282	#336	—	47	2	no	—
283	#336	—	47	2	no	—
284	#336	—	47	2	no	—
285	#336	—	47	2	no	—
286	#336	—	47	2	no	—
287	#336	—	47	2	no	—
288	#336	—	47	1	no	—
289	#336	—	47	1	no	—
290	#336	—	47	2	no	—
291	#336	—	47	2	no	—
292	#336	C₂×D₄₇	1	1	yes	characteristic
293	#336	C₂×D₄₇	1	1	yes	characteristic
294	#336	C₂×D₄₇	1	2	yes	—
295	#336	C₂×D₄₇	1	2	yes	—
296	C₄₇	#20774	1	1	yes	characteristic, complemented, Sylow
297	C₂³×C₄	—	47	1	no	—
298	C₂³×C₄	—	47	1	no	—
299	C₂³×C₄	—	47	1	no	—
300	C₂×M₁₆	—	94	4	no	—
301	C₂×M₁₆	—	94	4	no	—
302	C₂×M₁₆	—	94	4	no	—
303	C₂²×C₈	—	47	2	no	—
304	C₂²×C₈	—	47	2	no	—
305	C₂²×C₈	—	94	4	no	—
306	C₂²×C₈	—	94	4	no	—
307	C₂²×C₈	—	94	4	no	—
308	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
309	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
310	#117	—	94	2	no	—
311	#117	—	94	4	no	—
312	#117	—	94	2	no	—
313	C₂×C₄⋊C₄	—	47	1	no	—
314	C₂×C₄⋊C₄	—	47	1	no	—
315	C₂×C₄⋊C₄	—	47	1	no	—
316	C₂×C₄⋊C₄	—	47	1	no	—
317	C₂×C₂²⋊C₄	—	47	1	no	—
318	C₂×C₂²⋊C₄	—	47	1	no	—
319	C₂×C₂²⋊C₄	—	47	1	no	—
320	C₂×C₂²⋊C₄	—	47	1	no	—
321	C₂×C₄²	—	47	1	no	—
322	C₂×C₄²	—	47	1	no	—
323	C₂×C₄²	—	47	1	no	—
324	C₂×C₄²	—	47	1	no	—
325	C₂×C₄²	—	47	1	no	—
326	C₂×C₄²	—	47	1	no	—
327	C₂×C₄²	—	47	1	no	—
328	C₂×C₄²	—	47	1	no	—
329	C₂×C₄²	—	47	1	no	—
330	C₂×C₄²	—	94	4	no	—
331	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
332	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
333	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
334	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
335	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
336	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
337	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
338	#95	—	47	1	no	—
339	#95	—	47	1	no	—
340	#95	—	47	1	no	—
341	#95	—	47	1	no	—
342	#95	—	47	1	no	—
343	#95	—	47	1	no	—
344	#95	—	47	1	no	—
345	#95	—	47	1	no	—
346	C₂⁴	—	47	1	no	—
347	C₂²×C₄	—	47	1	no	—
348	C₂²×C₄	—	47	4	no	—
349	C₂²×C₄	—	47	2	no	—
350	C₂²×C₄	—	47	4	no	—
351	C₂²×C₄	—	47	2	no	—
352	C₂²×C₄	—	47	1	no	—
353	C₂²×C₄	—	47	1	no	—
354	C₂²×C₄	—	47	1	no	—
355	C₂²×C₄	—	47	1	no	—
356	C₂²×C₄	—	47	1	no	—
357	C₂²×C₄	—	47	1	no	—
358	C₂²×C₄	—	94	2	no	—
359	C₂²×C₄	—	94	2	no	—
360	C₂²×C₄	—	94	2	no	—
361	C₂²×C₄	—	94	2	no	—
362	C₂²×C₄	—	188	1	no	—
363	C₂²×C₄	—	188	1	no	—
364	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
370	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
371	M₁₆	—	188	8	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	94	2	no	—
381	C₂×C₈	—	94	2	no	—
382	C₂×C₈	—	94	2	no	—
383	C₂×C₈	—	94	2	no	—
384	C₂×C₈	—	188	8	no	—
385	C₄⋊C₄	—	94	2	no	—
386	C₄⋊C₄	—	94	2	no	—
387	C₄⋊C₄	—	94	2	no	—
388	C₄⋊C₄	—	94	2	no	—
389	C₂²⋊C₄	—	94	2	no	—
390	C₂²⋊C₄	—	94	2	no	—
391	C₂²⋊C₄	—	94	2	no	—
392	C₂²⋊C₄	—	94	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	4	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	—	94	2	no	—
402	C₄²	—	94	2	no	—
403	C₄²	—	94	2	no	—
404	C₄²	—	94	2	no	—
405	C₄²	—	94	2	no	—
406	C₄²	—	94	2	no	—
407	C₄²	—	94	1	no	—
408	C₄²	—	94	1	no	—
409	C₄²	—	188	1	no	—
410	C₄²	—	188	1	no	—
411	C₂³	—	47	2	no	—
412	C₂³	—	47	2	no	—
413	C₂³	—	47	2	no	—
414	C₂³	—	94	1	no	—
415	C₂³	—	94	1	no	—
416	C₂³	—	94	1	no	—
417	C₂³	—	94	1	no	—
418	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	47	2	no	—
436	C₂×C₄	—	47	2	no	—
437	C₂×C₄	—	47	2	no	—
438	C₂×C₄	—	47	8	no	—
439	C₂×C₄	—	47	8	no	—
440	C₂×C₄	—	94	1	no	—
441	C₂×C₄	—	94	1	no	—
442	C₂×C₄	—	94	1	no	—
443	C₂×C₄	—	94	1	no	—
444	C₂×C₄	—	94	1	no	—
445	C₂×C₄	—	94	1	no	—
446	C₂×C₄	—	94	1	no	—
447	C₂×C₄	—	94	1	no	—
448	C₂×C₄	—	94	1	no	—
449	C₂×C₄	—	94	1	no	—
450	C₂×C₄	—	94	1	no	—
451	C₂×C₄	—	94	1	no	—
452	C₂×C₄	—	94	1	no	—
453	C₂×C₄	—	94	1	no	—
454	C₂×C₄	—	94	1	no	—
455	C₂×C₄	—	94	1	no	—
456	C₂×C₄	—	94	1	no	—
457	C₂×C₄	—	94	1	no	—
458	C₂×C₄	—	188	4	no	—
459	C₂×C₄	—	188	4	no	—
460	C₂×C₄	#13094030	1	2	yes	—
461	C₂×C₄	#13094032	1	2	yes	—
462	C₂×C₄	#41×D₄₇	1	2	yes	—
463	C₂×C₄	#41×D₄₇	1	2	yes	—
464	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
465	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
466	C₈	—	4	2	no	—
467	C₈	—	4	2	no	—
468	C₈	—	188	2	no	—
469	C₈	—	188	2	no	—
470	C₂²	—	47	4	no	—
471	C₂²	—	94	2	no	—
472	C₂²	—	94	2	no	—
473	C₂²	—	94	2	no	—
474	C₂²	—	94	2	no	—
475	C₂²	—	94	2	no	—
476	C₂²	—	94	2	no	—
477	C₂²	#117×D₄₇	1	1	yes	characteristic
478	C₂²	#117×D₄₇	1	1	yes	characteristic
479	C₂²	#117×D₄₇	1	1	yes	characteristic
480	C₂²	C₂×#13094030	1	1	yes	characteristic
481	C₂²	C₂×#13094032	1	1	yes	characteristic
482	C₂²	#15689889	1	1	yes	characteristic
483	C₂²	#15689889	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	1	no	—
490	C₄	—	47	4	no	—
491	C₄	—	188	1	no	—
492	C₄	—	188	1	no	—
493	C₄	—	188	1	no	—
494	C₄	—	188	1	no	—
495	C₄	—	188	1	no	—
496	C₄	—	188	1	no	—
497	C₄	#126×D₄₇	1	2	yes	—
498	C₄	#126×D₄₇	1	2	yes	—
499	C₂	—	94	4	no	—
500	C₂	#383×D₄₇	1	1	yes	characteristic
501	C₂	#20252027	1	1	yes	characteristic
502	C₂	#20252034	1	1	yes	characteristic
503	C₂	#20252041	1	1	yes	characteristic
504	C₂	#20252047	1	1	yes	characteristic
505	C₂	#20252049	1	1	yes	characteristic
506	C₂	#20252055	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1839	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1839	D₄₇
hypocenter	C₄₇	#20774
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1839

Complements

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

N	H ≅ G/N	type
2. #20243532	C₂	semidirect
3. #20243532	C₂	semidirect
4. #20243531	C₂	semidirect
5. #20243530	C₂	semidirect
6. #20243530	C₂	semidirect
11. C₄₇×#1839	C₂	semidirect
252. #1839	D₄₇	semidirect
296. C₄₇	#20774	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13093981	2
#20243532	2
#20243531	2
#20243530	2
#20243083	2
#20243080	2
#336×D₄₇	2
C₄₇×#1839	2
#20774	47