Subgroups — #26379030

Order 12032.

2982 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246545	C₂	1	4	yes	maximal, complemented
2	#20246440	C₂	1	4	yes	maximal, complemented
3	#20246237	C₂	1	4	yes	maximal, complemented
4	D₄×C₂²⋊Dic₄₇	C₂	1	4	yes	maximal, complemented
5	#20246155	C₂	1	4	yes	maximal, complemented
6	#20246093	C₂	1	4	yes	maximal, complemented
7	#20245991	C₂	1	2	yes	maximal, complemented
8	#20245966	C₂	1	2	yes	maximal, complemented
9	#20245771	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688986	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#121×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₄₇	C₂²	1	8	yes	complemented
13	C₂×#13093983	C₂²	1	2	yes	—
14	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
15	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
16	#15689026	C₂²	1	8	yes	complemented
17	#15689016	C₂²	1	8	yes	complemented
18	#15689016	C₂²	1	8	yes	complemented
19	#15689009	C₂²	1	8	yes	complemented
20	#15689009	C₂²	1	8	yes	complemented
21	#15689003	C₂²	1	8	yes	complemented
22	#15689003	C₂²	1	8	yes	complemented
23	#15689003	C₂²	1	8	yes	complemented
24	#15689003	C₂²	1	8	yes	complemented
25	#15688998	C₂²	1	8	yes	complemented
26	#15688986	C₂²	1	2	yes	—
27	#15688986	C₂²	1	2	yes	—
28	#15688986	C₂²	1	2	yes	—
29	#15688986	C₂²	1	2	yes	complemented
30	#15688986	C₂²	1	2	yes	complemented
31	#15688983	C₂²	1	4	yes	—
32	#15688983	C₂²	1	2	yes	complemented
33	#15688983	C₂²	1	2	yes	complemented
34	#15688979	C₂²	1	2	yes	—
35	#15688979	C₂²	1	4	yes	—
36	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	complemented
37	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
38	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
39	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
40	C₂×C₄₇⋊#95	C₂²	1	2	yes	complemented
41	C₂×C₄₇⋊#95	C₂²	1	2	yes	complemented
42	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
43	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
44	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#121×C₄₇	C₄	1	16	yes	complemented
46	C₂×#121×C₄₇	C₂²	1	2	yes	—
47	C₂×#121×C₄₇	C₂²	1	2	yes	—
48	C₂×#121×C₄₇	C₂²	1	2	yes	—
49	C₂×#121×C₄₇	C₂²	1	2	yes	—
50	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
51	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
52	C₂³×Dic₄₇	C₂³	1	4	yes	—
53	C₂³×Dic₄₇	C₂³	1	8	yes	—
54	D₄×Dic₄₇	—	4	16	no	—
55	#13093983	—	4	4	no	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
58	C₂×C₂²⋊Dic₄₇	—	4	4	no	—
59	C₂×C₂²⋊Dic₄₇	—	4	8	no	—
60	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
61	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
62	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
63	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
64	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
65	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
66	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
67	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
68	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
69	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
70	C₄₇⋊#95	C₂³	1	4	yes	—
71	C₄₇⋊#95	C₂³	1	4	yes	—
72	C₄₇⋊#95	C₂³	1	4	yes	—
73	C₄₇⋊#95	C₂³	1	4	yes	—
74	C₄₇⋊#95	C₂³	1	8	yes	—
75	C₄₇⋊#95	C₂³	1	4	yes	—
76	C₄₇⋊#95	C₂³	1	4	yes	—
77	C₄₇⋊#95	C₂³	1	8	yes	—
78	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
79	C₂⁵×C₄₇	C₂³	1	2	yes	—
80	C₂²×D₄×C₄₇	—	4	4	no	—
81	C₂²×D₄×C₄₇	—	4	8	no	—
82	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
83	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
84	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
85	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
87	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
88	C₂³×C₄×C₄₇	—	4	4	no	—
89	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
95	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
97	#121×C₄₇	C₂×C₄	1	16	yes	complemented
98	#121×C₄₇	C₂×C₄	1	16	yes	complemented
99	#121×C₄₇	C₂×C₄	1	16	yes	complemented
100	#121×C₄₇	C₂×C₄	1	16	yes	complemented
101	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
102	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
104	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
105	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
107	C₂⁴×C₄₇	—	2	4	no	—
108	C₂⁴×C₄₇	—	2	4	no	—
109	C₂⁴×C₄₇	—	2	8	no	—
110	C₂⁴×C₄₇	—	4	2	no	—
111	C₂⁴×C₄₇	—	4	4	no	—
112	C₂⁴×C₄₇	—	4	4	no	—
113	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
114	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
115	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
116	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
118	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
119	C₂×D₄×C₄₇	—	2	16	no	—
120	C₂×D₄×C₄₇	—	4	16	no	—
121	C₂×D₄×C₄₇	—	4	8	no	—
122	C₂×D₄×C₄₇	—	4	2	no	—
123	C₂×D₄×C₄₇	—	4	4	no	—
124	C₂×D₄×C₄₇	—	4	2	no	—
125	C₂×D₄×C₄₇	—	4	32	no	—
126	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
127	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
128	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
129	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
130	C₂²×C₄×C₄₇	—	2	4	no	—
131	C₂²×C₄×C₄₇	—	2	4	no	—
132	C₂²×C₄×C₄₇	—	4	16	no	—
133	C₂²×C₄×C₄₇	—	4	2	no	—
134	C₂²×C₄×C₄₇	—	4	2	no	—
135	C₂²×C₄×C₄₇	—	4	2	no	—
136	C₂²×C₄×C₄₇	—	4	2	no	—
137	C₂²×C₄×C₄₇	—	4	4	no	—
138	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
139	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
141	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
150	C₂²×Dic₄₇	—	2	8	no	—
151	C₂²×Dic₄₇	—	4	8	no	—
152	C₂²×Dic₄₇	—	4	4	no	—
153	C₂²×Dic₄₇	—	4	8	no	—
154	C₂²×Dic₄₇	—	4	8	no	—
155	C₂²×Dic₄₇	—	4	4	no	—
156	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
157	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
158	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
159	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
160	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
161	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
162	C₂²⋊Dic₄₇	—	2	8	no	—
163	C₂²⋊Dic₄₇	—	2	8	no	—
164	C₂²⋊Dic₄₇	—	2	8	no	—
165	C₂²⋊Dic₄₇	—	4	8	no	—
166	C₂²⋊Dic₄₇	—	4	4	no	—
167	C₂²⋊Dic₄₇	—	4	4	no	—
168	C₂²⋊Dic₄₇	—	4	8	no	—
169	C₂²⋊Dic₄₇	—	4	8	no	—
170	C₄⋊Dic₄₇	—	4	4	no	—
171	C₄⋊Dic₄₇	—	4	8	no	—
172	C₄×Dic₄₇	—	4	4	no	—
173	C₄×Dic₄₇	—	4	8	no	—
174	C₂³×C₄₇	—	2	2	no	—
175	C₂³×C₄₇	—	2	2	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	2	no	—
178	C₂³×C₄₇	—	2	8	no	—
179	C₂³×C₄₇	—	2	8	no	—
180	C₂³×C₄₇	—	2	2	no	—
181	C₂³×C₄₇	—	2	4	no	—
182	C₂³×C₄₇	—	2	8	no	—
183	C₂³×C₄₇	—	2	4	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	2	2	no	—
186	C₂³×C₄₇	—	2	8	no	—
187	C₂³×C₄₇	—	2	16	no	—
188	C₂³×C₄₇	—	4	4	no	—
189	C₂³×C₄₇	—	4	8	no	—
190	C₂³×C₄₇	—	4	8	no	—
191	C₂³×C₄₇	—	4	16	no	—
192	C₂³×C₄₇	—	8	16	no	—
193	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
194	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
195	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
196	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
197	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
198	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
199	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
200	D₄×C₄₇	—	2	32	no	—
201	D₄×C₄₇	—	4	8	no	—
202	D₄×C₄₇	—	4	8	no	—
203	D₄×C₄₇	—	4	16	no	—
204	C₂×C₄×C₄₇	—	2	8	no	—
205	C₂×C₄×C₄₇	—	2	8	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	8	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	4	4	no	—
212	C₂×C₄×C₄₇	—	4	4	no	—
213	C₂×C₄×C₄₇	—	4	4	no	—
214	C₂×C₄×C₄₇	—	4	4	no	—
215	C₂×C₄×C₄₇	—	4	8	no	—
216	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
217	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
218	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
219	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
220	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
221	C₂×Dic₄₇	—	2	8	no	—
222	C₂×Dic₄₇	—	2	8	no	—
223	C₂×Dic₄₇	—	2	8	no	—
224	C₂×Dic₄₇	—	2	8	no	—
225	C₂×Dic₄₇	—	2	8	no	—
226	C₂×Dic₄₇	—	2	8	no	—
227	C₂×Dic₄₇	—	8	8	no	—
228	C₂×Dic₄₇	—	8	16	no	—
229	#34358	—	47	1	no	maximal, Sylow
230	C₂²×C₄₇	—	2	2	no	—
231	C₂²×C₄₇	—	2	2	no	—
232	C₂²×C₄₇	—	2	2	no	—
233	C₂²×C₄₇	—	2	2	no	—
234	C₂²×C₄₇	—	2	8	no	—
235	C₂²×C₄₇	—	2	8	no	—
236	C₂²×C₄₇	—	2	2	no	—
237	C₂²×C₄₇	—	2	8	no	—
238	C₂²×C₄₇	—	2	2	no	—
239	C₂²×C₄₇	—	2	8	no	—
240	C₂²×C₄₇	—	2	2	no	—
241	C₂²×C₄₇	—	2	8	no	—
242	C₂²×C₄₇	—	4	16	no	—
243	C₂²×C₄₇	—	4	8	no	—
244	C₂²×C₄₇	—	4	4	no	—
245	C₂²×C₄₇	—	4	8	no	—
246	C₂²×C₄₇	—	8	16	no	—
247	C₂²×C₄₇	#518	1	4	yes	—
248	C₂²×C₄₇	#518	1	4	yes	—
249	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
250	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
251	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
252	C₂²×C₄₇	#585	1	2	yes	—
253	C₄×C₄₇	—	2	2	no	—
254	C₄×C₄₇	—	2	2	no	—
255	C₄×C₄₇	—	2	2	no	—
256	C₄×C₄₇	—	2	2	no	—
257	C₄×C₄₇	—	2	8	no	—
258	Dic₄₇	—	4	8	no	—
259	Dic₄₇	—	4	8	no	—
260	C₂²×#121	D₄₇	1	1	yes	characteristic
261	#2377	—	47	4	no	—
262	#2364	—	47	4	no	—
263	#2342	—	47	4	no	—
264	D₄×C₂²⋊C₄	—	47	4	no	—
265	#2333	—	47	4	no	—
266	#2325	—	47	4	no	—
267	#2313	—	47	2	no	—
268	#2308	—	47	2	no	—
269	#2280	—	47	1	no	—
270	C₂×#381	—	47	1	no	—
271	C₂×C₄₇	—	2	4	no	—
272	C₂×C₄₇	—	2	4	no	—
273	C₂×C₄₇	—	4	2	no	—
274	C₂×C₄₇	—	4	8	no	—
275	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
276	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
277	C₂×C₄₇	#3428	1	1	yes	characteristic
278	C₂×C₄₇	#3534	1	4	yes	—
279	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
280	C₂³×D₄	C₂×D₄₇	1	2	yes	—
281	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
282	C₂×#121	Dic₄₇	1	16	yes	complemented
283	C₂×#121	C₂×D₄₇	1	2	yes	—
284	C₂×#121	C₂×D₄₇	1	2	yes	—
285	C₂×#121	C₂×D₄₇	1	2	yes	—
286	C₂×#121	C₂×D₄₇	1	2	yes	—
287	C₂×C₄×D₄	—	47	8	no	—
288	C₂×#117	—	47	2	no	—
289	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
290	C₂²×C₂²⋊C₄	—	47	4	no	—
291	C₂²×C₂²⋊C₄	—	47	2	no	—
292	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
293	#390	—	47	8	no	—
294	#388	—	47	8	no	—
295	#388	—	47	8	no	—
296	#387	—	47	8	no	—
297	#387	—	47	8	no	—
298	#386	—	47	8	no	—
299	#386	—	47	8	no	—
300	#386	—	47	8	no	—
301	#386	—	47	8	no	—
302	#385	—	47	8	no	—
303	#381	—	47	2	no	—
304	#381	—	47	2	no	—
305	#381	—	47	2	no	—
306	#381	—	47	2	no	—
307	#381	—	47	2	no	—
308	#380	—	47	4	no	—
309	#380	—	47	2	no	—
310	#380	—	47	2	no	—
311	#379	—	47	4	no	—
312	#379	—	47	2	no	—
313	C₄×C₂²⋊C₄	—	47	4	no	—
314	C₄×C₂²⋊C₄	—	47	2	no	—
315	C₄×C₂²⋊C₄	—	47	2	no	—
316	C₄×C₂²⋊C₄	—	47	8	no	—
317	C₂×#95	—	47	2	no	—
318	C₂×#95	—	47	2	no	—
319	C₄₇	#34358	1	1	yes	characteristic, complemented, Sylow
320	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
321	C₂⁵	C₂²×D₄₇	1	2	yes	—
322	C₂²×D₄	—	4	4	no	—
323	C₂²×D₄	—	4	8	no	—
324	C₂²×D₄	C₂×Dic₄₇	1	8	yes	complemented
325	C₂²×D₄	C₂×Dic₄₇	1	16	yes	complemented
326	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
327	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
328	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
329	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
330	C₂³×C₄	—	4	4	no	—
331	C₂³×C₄	—	47	4	no	—
332	C₂³×C₄	—	47	8	no	—
333	C₂³×C₄	C₂×Dic₄₇	1	8	yes	complemented
334	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
335	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
336	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
337	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
338	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
339	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
340	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
341	#121	C₂×Dic₄₇	1	16	yes	complemented
342	#121	C₂×Dic₄₇	1	16	yes	complemented
343	#121	C₂×Dic₄₇	1	16	yes	complemented
344	#121	C₂×Dic₄₇	1	16	yes	complemented
345	C₄×D₄	—	188	16	no	—
346	#117	—	188	4	no	—
347	C₂×C₄⋊C₄	—	47	4	no	—
348	C₂×C₄⋊C₄	—	47	8	no	—
349	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
350	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
351	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
352	C₂×C₂²⋊C₄	—	47	4	no	—
353	C₂×C₂²⋊C₄	—	47	4	no	—
354	C₂×C₂²⋊C₄	—	47	4	no	—
355	C₂×C₂²⋊C₄	—	47	4	no	—
356	C₂×C₂²⋊C₄	—	47	8	no	—
357	C₂×C₂²⋊C₄	—	47	8	no	—
358	C₂×C₂²⋊C₄	—	47	4	no	—
359	C₂×C₂²⋊C₄	—	47	8	no	—
360	C₂×C₂²⋊C₄	—	188	4	no	—
361	C₂×C₂²⋊C₄	—	188	8	no	—
362	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
363	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
364	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
365	C₂×C₄²	—	47	4	no	—
366	C₂×C₄²	—	47	8	no	—
367	#95	—	47	4	no	—
368	#95	—	47	4	no	—
369	#95	—	47	4	no	—
370	#95	—	47	4	no	—
371	#95	—	47	4	no	—
372	#95	—	47	4	no	—
373	#95	—	47	8	no	—
374	#95	—	47	8	no	—
375	C₂⁴	—	2	4	no	—
376	C₂⁴	—	2	4	no	—
377	C₂⁴	—	2	8	no	—
378	C₂⁴	—	4	2	no	—
379	C₂⁴	—	4	4	no	—
380	C₂⁴	—	4	4	no	—
381	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
382	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
383	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
384	C₂⁴	C₂³×D₄₇	1	4	yes	—
385	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
386	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
387	C₂×D₄	—	2	16	no	—
388	C₂×D₄	—	4	16	no	—
389	C₂×D₄	—	4	8	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	4	32	no	—
394	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
395	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
396	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
397	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	4	16	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	—	4	4	no	—
406	C₂²×C₄	—	47	8	no	—
407	C₂²×C₄	—	47	8	no	—
408	C₂²×C₄	—	94	8	no	—
409	C₂²×C₄	—	188	8	no	—
410	C₂²×C₄	—	188	4	no	—
411	C₂²×C₄	—	188	8	no	—
412	C₂²×C₄	—	188	8	no	—
413	C₂²×C₄	—	188	4	no	—
414	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
415	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
416	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
417	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
418	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
419	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
420	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
421	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
422	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
423	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
425	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
426	C₄⋊C₄	—	188	4	no	—
427	C₄⋊C₄	—	188	8	no	—
428	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
429	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
430	C₂²⋊C₄	—	94	8	no	—
431	C₂²⋊C₄	—	94	8	no	—
432	C₂²⋊C₄	—	94	8	no	—
433	C₂²⋊C₄	—	188	4	no	—
434	C₂²⋊C₄	—	188	8	no	—
435	C₂²⋊C₄	—	188	8	no	—
436	C₂²⋊C₄	—	188	4	no	—
437	C₂²⋊C₄	—	188	8	no	—
438	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
439	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
440	C₄²	—	188	4	no	—
441	C₄²	—	188	8	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	8	no	—
447	C₂³	—	2	8	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	8	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	8	no	—
455	C₂³	—	2	16	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	4	8	no	—
458	C₂³	—	4	8	no	—
459	C₂³	—	4	16	no	—
460	C₂³	—	8	16	no	—
461	C₂³	C₂³×Dic₄₇	1	8	yes	—
462	C₂³	C₂³×Dic₄₇	1	2	yes	—
463	C₂³	C₂³×Dic₄₇	1	2	yes	—
464	C₂³	C₂³×Dic₄₇	1	2	yes	—
465	C₂³	#13094069	1	4	yes	—
466	C₂³	#13094069	1	4	yes	—
467	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
468	D₄	—	2	32	no	—
469	D₄	—	4	8	no	—
470	D₄	—	4	8	no	—
471	D₄	—	4	16	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	8	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	8	no	—
484	C₂×C₄	—	94	8	no	—
485	C₂×C₄	—	94	8	no	—
486	C₂×C₄	—	94	8	no	—
487	C₂×C₄	—	94	8	no	—
488	C₂×C₄	—	94	8	no	—
489	C₂×C₄	—	94	8	no	—
490	C₂×C₄	—	376	8	no	—
491	C₂×C₄	—	376	16	no	—
492	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
493	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
494	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
495	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
496	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
497	C₂²	—	2	8	no	—
498	C₂²	—	2	8	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	8	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	8	no	—
509	C₂²	—	4	16	no	—
510	C₂²	—	4	8	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	8	no	—
513	C₂²	—	8	16	no	—
514	C₂²	#15689598	1	4	yes	—
515	C₂²	#15689598	1	4	yes	—
516	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
517	C₂²	C₂×#13094069	1	2	yes	—
518	C₂²	C₂×#13094069	1	2	yes	—
519	C₂²	#15689959	1	2	yes	—
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	8	no	—
525	C₄	—	188	8	no	—
526	C₄	—	188	8	no	—
527	C₂	—	2	4	no	—
528	C₂	—	2	4	no	—
529	C₂	—	4	2	no	—
530	C₂	—	4	8	no	—
531	C₂	C₂×#15689598	1	1	yes	characteristic
532	C₂	C₂×#15689598	1	1	yes	characteristic
533	C₂	#20256591	1	1	yes	characteristic
534	C₂	#20257578	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting, prime radical	C₂²×#121×C₄₇	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#121	D₄₇
hypocenter	C₄₇	#34358
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#121

Complements

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

N	H ≅ G/N	type
1. #20246545	C₂	semidirect
2. #20246440	C₂	semidirect
3. #20246237	C₂	semidirect
4. D₄×C₂²⋊Dic₄₇	C₂	semidirect
5. #20246155	C₂	semidirect
6. #20246093	C₂	semidirect
7. #20245991	C₂	semidirect
8. #20245966	C₂	semidirect
9. #20245771	C₂	semidirect
10. C₂×#15688986	C₂	semidirect
12. C₂×D₄×Dic₄₇	C₂²	semidirect
16. #15689026	C₂²	semidirect
17. #15689016	C₂²	semidirect
18. #15689016	C₂²	semidirect
19. #15689009	C₂²	semidirect
20. #15689009	C₂²	semidirect
21. #15689003	C₂²	semidirect
22. #15689003	C₂²	semidirect
23. #15689003	C₂²	semidirect
24. #15689003	C₂²	semidirect
25. #15688998	C₂²	semidirect
29. #15688986	C₂²	semidirect
30. #15688986	C₂²	semidirect
32. #15688983	C₂²	semidirect
33. #15688983	C₂²	semidirect
36. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
38. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
39. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
40. C₂×C₄₇⋊#95	C₂²	semidirect
41. C₂×C₄₇⋊#95	C₂²	semidirect
45. C₂×#121×C₄₇	C₄	semidirect
82. C₂²×D₄×C₄₇	C₂×C₄	semidirect
83. C₂²×D₄×C₄₇	C₂×C₄	semidirect
89. C₂³×C₄×C₄₇	C₂×C₄	semidirect
97. #121×C₄₇	C₂×C₄	semidirect
98. #121×C₄₇	C₂×C₄	semidirect
99. #121×C₄₇	C₂×C₄	semidirect
100. #121×C₄₇	C₂×C₄	semidirect
101. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
104. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
282. C₂×#121	Dic₄₇	semidirect
319. C₄₇	#34358	semidirect
324. C₂²×D₄	C₂×Dic₄₇	semidirect
325. C₂²×D₄	C₂×Dic₄₇	semidirect
333. C₂³×C₄	C₂×Dic₄₇	semidirect
341. #121	C₂×Dic₄₇	semidirect
342. #121	C₂×Dic₄₇	semidirect
343. #121	C₂×Dic₄₇	semidirect
344. #121	C₂×Dic₄₇	semidirect
349. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
362. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246545	2
#20246440	2
#20246237	2
D₄×C₂²⋊Dic₄₇	2
#20246155	2
#20246093	2
#20245991	2
#20245966	2
#20245771	2
C₂×#15688986	2
C₂²×#121×C₄₇	2
#34358	47