Subgroups — #26216785

Order 12032.

854 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689181	C₂	1	2	yes	maximal
2	C₄×#13093983	C₂	1	1	yes	maximal, characteristic
3	#20243541	C₂	1	2	yes	maximal, complemented
4	#20243503	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243503	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243370	C₂	1	2	yes	maximal
7	#20243368	C₂	1	1	yes	maximal, characteristic
8	#20243247	C₂	1	2	yes	maximal, complemented
9	#20243240	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243236	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1797	C₂	1	1	yes	maximal, characteristic
12	C₂×#13093983	C₂²	1	1	yes	characteristic
13	C₂×#13093983	C₂²	1	1	yes	characteristic
14	#15689181	—	2	8	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
21	C₂×#13093934	C₂²	1	2	yes	—
22	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
23	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
24	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
25	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
26	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
27	C₄×C₂²⋊Dic₄₇	C₄	1	1	yes	characteristic
28	C₄×C₂²⋊Dic₄₇	C₄	1	1	yes	characteristic
29	C₄×C₂²⋊Dic₄₇	C₄	1	1	yes	characteristic
30	C₄×C₂²⋊Dic₄₇	C₄	1	1	yes	characteristic
31	#15688969	C₂²	1	1	yes	characteristic
32	#15688969	C₂²	1	1	yes	characteristic
33	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
35	#15688878	C₂²	1	1	yes	characteristic
36	#15688878	C₂²	1	1	yes	characteristic
37	#15688877	C₂²	1	2	yes	—
38	#15688877	C₂²	1	2	yes	—
39	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
41	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
42	C₄₇×#336	C₂²	1	1	yes	characteristic
43	C₄₇×#336	C₂²	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	#13093983	—	2	4	no	—
47	#13093983	D₄	1	4	yes	—
48	#13093983	Q₈	1	4	yes	—
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
69	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
70	Dic₄₇⋊C₈	—	2	4	no	—
71	Dic₄₇⋊C₈	—	2	4	no	—
72	Dic₄₇⋊C₈	—	2	4	no	—
73	Dic₄₇⋊C₈	—	2	4	no	—
74	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
75	#13093934	—	2	4	no	—
76	C₈×Dic₄₇	—	2	4	no	—
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	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
84	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
89	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₇	—	2	4	no	—
91	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₇	—	2	4	no	—
96	C₂²⋊C₈×C₄₇	—	2	4	no	—
97	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	4	1	no	—
105	C₂²×C₄×C₄₇	—	4	1	no	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
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	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	#41	1	4	yes	—
132	C₂²⋊Dic₄₇	—	2	2	no	—
133	C₂²⋊Dic₄₇	—	2	2	no	—
134	C₂²⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
135	C₂²⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
139	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	—	4	1	no	—
146	C₄×Dic₄₇	—	4	1	no	—
147	C₄×Dic₄₇	—	4	1	no	—
148	C₄×Dic₄₇	—	4	1	no	—
149	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
150	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
151	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
152	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
153	C₄×Dic₄₇	#41	1	4	yes	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂³×C₄₇	—	2	1	no	—
161	C₂³×C₄₇	—	2	1	no	—
162	C₂³×C₄₇	—	2	1	no	—
163	C₂³×C₄₇	—	2	1	no	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	—	2	1	no	—
166	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
167	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
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	4	no	—
179	C₂×C₄×C₄₇	—	2	4	no	—
180	C₂×C₄×C₄₇	—	4	4	no	—
181	C₂×C₄×C₄₇	—	4	4	no	—
182	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
183	C₂×C₄×C₄₇	#117	1	2	yes	—
184	C₂×C₄×C₄₇	#117	1	2	yes	—
185	C₂×C₄×C₄₇	#131	1	2	yes	—
186	C₂×C₄×C₄₇	#131	1	2	yes	—
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
190	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
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	—	2	1	no	—
206	C₂×Dic₄₇	—	2	1	no	—
207	C₂×Dic₄₇	—	2	1	no	—
208	C₂×Dic₄₇	—	2	1	no	—
209	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
210	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
211	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
212	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
213	C₂×Dic₄₇	#117	1	2	yes	—
214	C₂×Dic₄₇	#117	1	2	yes	—
215	C₈×C₄₇	—	4	2	no	—
216	C₈×C₄₇	—	4	2	no	—
217	C₄₇⋊C₈	—	4	2	no	—
218	C₄₇⋊C₈	—	4	2	no	—
219	#20813	—	47	1	no	maximal, Sylow
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	2	2	no	—
222	C₂²×C₄₇	—	2	2	no	—
223	C₂²×C₄₇	—	4	1	no	—
224	C₂²×C₄₇	—	4	1	no	—
225	C₂²×C₄₇	—	4	1	no	—
226	C₂²×C₄₇	—	4	1	no	—
227	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
228	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
229	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
230	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
231	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
232	C₂²×C₄₇	#568	1	1	yes	characteristic
233	C₂²×C₄₇	#568	1	1	yes	characteristic
234	C₄×C₄₇	—	2	2	no	—
235	C₄×C₄₇	—	2	2	no	—
236	C₄×C₄₇	—	2	2	no	—
237	C₄×C₄₇	—	2	2	no	—
238	C₄×C₄₇	—	2	2	no	—
239	C₄×C₄₇	#532	1	2	yes	—
240	C₄×C₄₇	#533	1	2	yes	—
241	Dic₄₇	—	2	2	no	—
242	Dic₄₇	—	2	2	no	—
243	Dic₄₇	—	2	2	no	—
244	Dic₄₇	—	2	2	no	—
245	Dic₄₇	—	2	2	no	—
246	Dic₄₇	—	2	2	no	—
247	Dic₄₇	—	4	1	no	—
248	Dic₄₇	—	4	1	no	—
249	C₂×#433	—	47	2	no	—
250	C₄×#117	—	47	1	no	—
251	#1843	—	47	2	no	—
252	#1831	—	47	1	no	—
253	#1831	—	47	1	no	—
254	#1798	—	47	2	no	—
255	#1797	—	47	1	no	—
256	#1797	D₄₇	1	1	yes	characteristic
257	#1768	—	47	2	no	—
258	#1767	—	47	1	no	—
259	C₄×C₄⋊C₈	—	47	1	no	—
260	C₂×C₄₇	—	4	2	no	—
261	C₂×C₄₇	#2285	1	1	yes	characteristic
262	C₂×C₄₇	#2906	1	1	yes	characteristic
263	C₂×C₄₇	#2906	1	1	yes	characteristic
264	C₂×C₄₇	#2922	1	1	yes	characteristic
265	C₂×C₄₇	#2923	1	1	yes	characteristic
266	C₂×C₄₇	#2924	1	1	yes	characteristic
267	C₂×C₄₇	#2924	1	1	yes	characteristic
268	C₂×#117	—	47	1	no	—
269	C₂×#117	—	47	1	no	—
270	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
271	#433	—	94	8	no	—
272	C₂×C₄⋊C₈	—	47	2	no	—
273	C₂×C₄⋊C₈	—	47	2	no	—
274	C₂×C₄⋊C₈	—	47	2	no	—
275	C₂×C₄⋊C₈	—	47	2	no	—
276	C₂×C₄⋊C₈	—	47	2	no	—
277	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
278	C₂×C₂²⋊C₈	—	47	2	no	—
279	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
280	C₂×#97	—	47	2	no	—
281	C₂×C₄×C₈	—	47	2	no	—
282	C₄×C₄⋊C₄	—	47	1	no	—
283	C₄×C₄⋊C₄	—	47	1	no	—
284	C₄×C₄⋊C₄	—	47	1	no	—
285	C₄×C₄⋊C₄	—	47	1	no	—
286	C₄×C₂²⋊C₄	—	47	1	no	—
287	C₄×C₂²⋊C₄	—	47	1	no	—
288	C₄×C₂²⋊C₄	—	47	1	no	—
289	C₄×C₂²⋊C₄	—	47	1	no	—
290	#376	—	47	1	no	—
291	#376	—	47	1	no	—
292	C₄³	—	47	1	no	—
293	C₄³	—	47	1	no	—
294	#336	—	47	2	no	—
295	#336	—	47	2	no	—
296	#336	—	47	1	no	—
297	#336	—	47	1	no	—
298	#336	C₂×D₄₇	1	1	yes	characteristic
299	#336	C₂×D₄₇	1	1	yes	characteristic
300	C₄₇	#20813	1	1	yes	characteristic, complemented, Sylow
301	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
302	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
303	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
304	C₂²×C₈	—	47	2	no	—
305	C₂²×C₈	—	47	2	no	—
306	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
307	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
308	#117	—	47	4	no	—
309	#117	—	47	4	no	—
310	#117	—	94	4	no	—
311	C₂×C₄⋊C₄	—	47	1	no	—
312	C₂×C₄⋊C₄	—	47	1	no	—
313	C₂×C₄⋊C₄	—	47	1	no	—
314	C₂×C₄⋊C₄	—	47	1	no	—
315	C₂×C₂²⋊C₄	—	47	1	no	—
316	C₂×C₂²⋊C₄	—	47	1	no	—
317	C₂×C₂²⋊C₄	—	47	1	no	—
318	C₂×C₂²⋊C₄	—	47	1	no	—
319	C₂×C₄²	—	2	4	no	—
320	C₂×C₄²	—	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	—	47	1	no	—
331	C₂×C₄²	—	47	1	no	—
332	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
333	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
334	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
335	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
336	C₄⋊C₈	—	2	4	no	—
337	C₄⋊C₈	—	94	4	no	—
338	C₄⋊C₈	—	94	4	no	—
339	C₄⋊C₈	—	94	4	no	—
340	C₄⋊C₈	—	94	4	no	—
341	C₄⋊C₈	—	94	4	no	—
342	C₂²⋊C₈	—	2	4	no	—
343	C₂²⋊C₈	—	94	4	no	—
344	#97	—	94	4	no	—
345	C₄×C₈	—	94	4	no	—
346	#95	—	47	1	no	—
347	#95	—	47	1	no	—
348	#95	—	47	1	no	—
349	#95	—	47	1	no	—
350	#95	—	47	1	no	—
351	#95	—	47	1	no	—
352	#95	—	47	1	no	—
353	#95	—	47	1	no	—
354	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	—	47	1	no	—
364	C₂²×C₄	—	47	1	no	—
365	C₂²×C₄	—	47	1	no	—
366	C₂²×C₄	—	47	1	no	—
367	C₂²×C₄	—	47	1	no	—
368	C₂²×C₄	—	47	1	no	—
369	C₂²×C₄	—	47	1	no	—
370	C₂²×C₄	—	47	1	no	—
371	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
376	C₂²×C₄	D₄×D₄₇	1	2	yes	—
377	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
378	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	94	2	no	—
386	C₂×C₈	—	94	2	no	—
387	C₂×C₈	—	94	2	no	—
388	C₂×C₈	—	94	2	no	—
389	C₂×C₈	—	94	2	no	—
390	C₂×C₈	—	94	2	no	—
391	C₄⋊C₄	—	47	4	no	—
392	C₄⋊C₄	—	47	4	no	—
393	C₄⋊C₄	—	94	2	no	—
394	C₄⋊C₄	—	94	2	no	—
395	C₂²⋊C₄	—	47	4	no	—
396	C₂²⋊C₄	—	47	4	no	—
397	C₂²⋊C₄	—	94	2	no	—
398	C₂²⋊C₄	—	94	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	47	2	no	—
403	C₄²	—	47	2	no	—
404	C₄²	—	47	2	no	—
405	C₄²	—	47	2	no	—
406	C₄²	—	47	4	no	—
407	C₄²	—	94	2	no	—
408	C₄²	—	94	2	no	—
409	C₄²	—	94	2	no	—
410	C₄²	—	94	2	no	—
411	C₄²	—	94	2	no	—
412	C₄²	—	188	1	no	—
413	C₄²	—	188	1	no	—
414	C₄²	—	188	1	no	—
415	C₄²	—	188	1	no	—
416	C₄²	#10625352	1	4	yes	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
424	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
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	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	47	2	no	—
440	C₂×C₄	—	47	2	no	—
441	C₂×C₄	—	47	2	no	—
442	C₂×C₄	—	47	2	no	—
443	C₂×C₄	—	47	2	no	—
444	C₂×C₄	—	47	2	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	—	94	1	no	—
459	C₂×C₄	—	94	1	no	—
460	C₂×C₄	—	94	1	no	—
461	C₂×C₄	—	94	1	no	—
462	C₂×C₄	—	94	1	no	—
463	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
464	C₂×C₄	#13093980	1	2	yes	—
465	C₂×C₄	#13093980	1	2	yes	—
466	C₂×C₄	#13094030	1	2	yes	—
467	C₂×C₄	#13094032	1	2	yes	—
468	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
469	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
470	C₂×C₄	#41×D₄₇	1	2	yes	—
471	C₂×C₄	C₂×#10625352	1	2	yes	—
472	C₈	—	4	2	no	—
473	C₈	—	4	2	no	—
474	C₈	—	188	2	no	—
475	C₈	—	188	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
484	C₂²	#117×D₄₇	1	1	yes	characteristic
485	C₂²	C₂×#13093980	1	1	yes	characteristic
486	C₂²	C₂×#13094030	1	1	yes	characteristic
487	C₂²	C₂×#13094032	1	1	yes	characteristic
488	C₂²	#15689889	1	1	yes	characteristic
489	C₂²	#15689889	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	94	2	no	—
496	C₄	—	94	2	no	—
497	C₄	—	94	2	no	—
498	C₄	—	94	2	no	—
499	C₄	—	94	2	no	—
500	C₄	—	94	2	no	—
501	C₄	—	188	1	no	—
502	C₄	—	188	1	no	—
503	C₄	#15689668	1	2	yes	—
504	C₄	#15689675	1	2	yes	—
505	C₂	—	4	2	no	—
506	C₂	#20245790	1	1	yes	characteristic
507	C₂	#20251953	1	1	yes	characteristic
508	C₂	#20251957	1	1	yes	characteristic
509	C₂	#20252027	1	1	yes	characteristic
510	C₂	#20252034	1	1	yes	characteristic
511	C₂	#20252042	1	1	yes	characteristic
512	C₂	#20252048	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1797	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1797	D₄₇
hypocenter	C₄₇	#20813
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1797

Complements

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

N	H ≅ G/N	type
3. #20243541	C₂	semidirect
4. #20243503	C₂	semidirect
5. #20243503	C₂	semidirect
8. #20243247	C₂	semidirect
9. #20243240	C₂	semidirect
10. #20243236	C₂	semidirect
300. C₄₇	#20813	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689181	2
C₄×#13093983	2
#20243541	2
#20243503	2
#20243370	2
#20243368	2
#20243247	2
#20243240	2
#20243236	2
C₄₇×#1797	2
#20813	47