Subgroups — #26376494

Order 12032.

3014 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246337	C₂	1	2	yes	maximal, complemented
2	#20246317	C₂	1	4	yes	maximal, complemented
3	D₄×C₄⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
4	#20246265	C₂	1	2	yes	maximal, complemented
5	#20246237	C₂	1	4	yes	maximal, complemented
6	D₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
7	#20246031	C₂	1	2	yes	maximal, complemented
8	#20246021	C₂	1	4	yes	maximal, complemented
9	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
10	#20245786	C₂	1	1	yes	maximal, characteristic, complemented
11	#20245771	C₂	1	2	yes	maximal, complemented
12	C₂×#15688983	C₂	1	2	yes	maximal, complemented
13	#20245749	C₂	1	2	yes	maximal, complemented
14	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
15	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
16	C₂×#13093983	C₂²	1	2	yes	—
17	C₂×#13093983	C₂²	1	4	yes	complemented
18	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
19	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
20	#15689026	C₂²	1	4	yes	—
21	#15689022	C₂²	1	4	yes	complemented
22	#15689016	C₂²	1	8	yes	complemented
23	#15689016	C₂²	1	8	yes	complemented
24	#15689009	C₂²	1	8	yes	complemented
25	#15689003	C₂²	1	8	yes	—
26	#15688998	C₂²	1	8	yes	complemented
27	#15688993	C₂²	1	2	yes	complemented
28	#15688991	C₂²	1	2	yes	complemented
29	#15688989	C₂²	1	2	yes	complemented
30	#15688989	C₂²	1	2	yes	complemented
31	#15688986	C₂²	1	2	yes	—
32	#15688986	C₂²	1	4	yes	complemented
33	#15688983	C₂²	1	1	yes	characteristic
34	#15688983	C₂²	1	2	yes	—
35	#15688983	C₂²	1	4	yes	—
36	#15688983	C₂²	1	1	yes	characteristic
37	#15688983	C₂²	1	2	yes	—
38	#15688983	C₂²	1	4	yes	complemented
39	#15688983	C₂²	1	4	yes	complemented
40	#15688983	C₂²	1	4	yes	complemented
41	#15688979	C₂²	1	4	yes	—
42	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	complemented
43	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
44	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
45	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
46	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	complemented
47	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
48	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
49	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
50	#15688969	C₂²	1	2	yes	complemented
51	C₂×C₄₇⋊#95	C₂²	1	4	yes	complemented
52	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
53	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
54	C₂×C₄×D₄×C₄₇	C₄	1	16	yes	complemented
55	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
58	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
60	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
61	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
62	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
63	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
64	C₂³×Dic₄₇	C₂³	1	8	yes	—
65	D₄×Dic₄₇	—	2	16	no	—
66	#13093983	—	4	8	no	—
67	#13093983	—	4	4	no	—
68	C₂×C₄⋊Dic₄₇	—	4	8	no	—
69	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
70	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
71	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
72	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
73	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
74	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
75	C₂×C₂²⋊Dic₄₇	—	4	8	no	—
76	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
77	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
78	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
79	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
80	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
81	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
82	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
83	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
84	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
85	C₄₇⋊#95	C₂³	1	2	yes	—
86	C₄₇⋊#95	C₂³	1	4	yes	—
87	C₄₇⋊#95	C₂³	1	8	yes	—
88	C₄₇⋊#95	C₂³	1	2	yes	—
89	C₄₇⋊#95	C₂³	1	4	yes	—
90	C₄₇⋊#95	C₂³	1	8	yes	—
91	C₄₇⋊#95	C₂³	1	4	yes	—
92	C₄₇⋊#95	C₂³	1	4	yes	—
93	C₄₇⋊#95	C₂³	1	4	yes	—
94	C₂⁵×C₄₇	C₂³	1	2	yes	—
95	C₂²×D₄×C₄₇	—	2	8	no	—
96	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
97	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
98	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₄₇	—	4	8	no	—
101	C₂³×C₄×C₄₇	C₂×C₄	1	16	yes	complemented
102	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
105	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
106	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
108	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
109	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
110	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
111	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
112	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
113	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
114	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
115	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
116	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
117	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
121	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
125	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
126	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
130	C₂⁴×C₄₇	—	2	8	no	—
131	C₂⁴×C₄₇	—	2	4	no	—
132	C₂⁴×C₄₇	—	2	4	no	—
133	C₂⁴×C₄₇	—	4	4	no	—
134	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
135	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
136	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
137	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₄₇	—	2	8	no	—
139	C₂×D₄×C₄₇	—	2	32	no	—
140	C₂×D₄×C₄₇	—	2	4	no	—
141	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
142	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
143	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
144	C₂×D₄×C₄₇	#41	1	8	yes	—
145	C₂²×C₄×C₄₇	—	2	2	no	—
146	C₂²×C₄×C₄₇	—	2	2	no	—
147	C₂²×C₄×C₄₇	—	2	4	no	—
148	C₂²×C₄×C₄₇	—	2	4	no	—
149	C₂²×C₄×C₄₇	—	2	8	no	—
150	C₂²×C₄×C₄₇	—	2	8	no	—
151	C₂²×C₄×C₄₇	—	4	32	no	—
152	C₂²×C₄×C₄₇	—	4	4	no	—
153	C₂²×C₄×C₄₇	—	4	4	no	—
154	C₂²×C₄×C₄₇	—	4	4	no	—
155	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
156	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
157	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
158	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
159	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
160	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
161	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
162	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
163	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂²×Dic₄₇	—	2	16	no	—
172	C₂²×Dic₄₇	—	4	8	no	—
173	C₂²×Dic₄₇	—	4	8	no	—
174	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
175	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
176	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
177	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
178	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
179	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
180	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
181	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
182	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
183	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
184	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
185	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
186	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
187	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
188	C₂²⋊Dic₄₇	—	2	16	no	—
189	C₂²⋊Dic₄₇	—	2	4	no	—
190	C₂²⋊Dic₄₇	—	2	8	no	—
191	C₂²⋊Dic₄₇	—	2	4	no	—
192	C₂²⋊Dic₄₇	—	4	8	no	—
193	C₂²⋊Dic₄₇	—	4	8	no	—
194	C₄⋊Dic₄₇	—	2	8	no	—
195	C₄⋊Dic₄₇	—	2	4	no	—
196	C₄⋊Dic₄₇	—	2	8	no	—
197	C₄⋊Dic₄₇	—	2	4	no	—
198	C₄⋊Dic₄₇	—	4	8	no	—
199	C₄⋊Dic₄₇	—	4	4	no	—
200	C₄×Dic₄₇	—	2	8	no	—
201	C₄×Dic₄₇	—	4	8	no	—
202	C₄×Dic₄₇	—	4	4	no	—
203	C₂³×C₄₇	—	2	2	no	—
204	C₂³×C₄₇	—	2	2	no	—
205	C₂³×C₄₇	—	2	4	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	—	2	2	no	—
208	C₂³×C₄₇	—	2	16	no	—
209	C₂³×C₄₇	—	2	16	no	—
210	C₂³×C₄₇	—	2	4	no	—
211	C₂³×C₄₇	—	2	2	no	—
212	C₂³×C₄₇	—	2	4	no	—
213	C₂³×C₄₇	—	2	2	no	—
214	C₂³×C₄₇	—	4	8	no	—
215	C₂³×C₄₇	—	4	16	no	—
216	C₂³×C₄₇	—	4	16	no	—
217	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
218	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
219	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
220	C₂³×C₄₇	C₂×#41	1	8	yes	—
221	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
222	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
223	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
224	D₄×C₄₇	—	2	16	no	—
225	D₄×C₄₇	—	2	8	no	—
226	D₄×C₄₇	#117	1	16	yes	complemented
227	C₂×C₄×C₄₇	—	2	8	no	—
228	C₂×C₄×C₄₇	—	2	2	no	—
229	C₂×C₄×C₄₇	—	2	1	no	—
230	C₂×C₄×C₄₇	—	2	4	no	—
231	C₂×C₄×C₄₇	—	2	1	no	—
232	C₂×C₄×C₄₇	—	2	4	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	1	no	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	8	no	—
237	C₂×C₄×C₄₇	—	2	8	no	—
238	C₂×C₄×C₄₇	—	2	16	no	—
239	C₂×C₄×C₄₇	—	2	16	no	—
240	C₂×C₄×C₄₇	—	4	8	no	—
241	C₂×C₄×C₄₇	—	4	8	no	—
242	C₂×C₄×C₄₇	—	4	8	no	—
243	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
244	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
245	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
246	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
247	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
248	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
249	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
250	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
251	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
252	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
253	C₂×Dic₄₇	—	2	4	no	—
254	C₂×Dic₄₇	—	2	4	no	—
255	C₂×Dic₄₇	—	2	8	no	—
256	C₂×Dic₄₇	—	2	4	no	—
257	C₂×Dic₄₇	—	2	8	no	—
258	C₂×Dic₄₇	—	2	8	no	—
259	C₂×Dic₄₇	—	2	4	no	—
260	C₂×Dic₄₇	—	2	4	no	—
261	C₂×Dic₄₇	—	2	4	no	—
262	C₂×Dic₄₇	—	8	16	no	—
263	#34194	—	47	1	no	maximal, Sylow
264	C₂²×C₄₇	—	2	2	no	—
265	C₂²×C₄₇	—	2	2	no	—
266	C₂²×C₄₇	—	2	4	no	—
267	C₂²×C₄₇	—	2	4	no	—
268	C₂²×C₄₇	—	2	8	no	—
269	C₂²×C₄₇	—	2	4	no	—
270	C₂²×C₄₇	—	2	4	no	—
271	C₂²×C₄₇	—	2	8	no	—
272	C₂²×C₄₇	—	2	4	no	—
273	C₂²×C₄₇	—	2	4	no	—
274	C₂²×C₄₇	—	2	4	no	—
275	C₂²×C₄₇	—	4	32	no	—
276	C₂²×C₄₇	—	4	4	no	—
277	C₂²×C₄₇	—	4	4	no	—
278	C₂²×C₄₇	C₂×#117	1	8	yes	—
279	C₂²×C₄₇	#520	1	4	yes	—
280	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
281	C₂²×C₄₇	C₂²×#41	1	2	yes	—
282	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
283	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
284	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
285	C₄×C₄₇	—	2	2	no	—
286	C₄×C₄₇	—	2	2	no	—
287	C₄×C₄₇	—	2	4	no	—
288	C₄×C₄₇	—	2	4	no	—
289	C₄×C₄₇	—	2	2	no	—
290	C₄×C₄₇	—	2	2	no	—
291	C₄×C₄₇	C₂×#117	1	4	yes	—
292	C₄×C₄₇	#518	1	4	yes	—
293	Dic₄₇	—	4	8	no	—
294	Dic₄₇	—	4	4	no	—
295	Dic₄₇	—	4	4	no	—
296	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
297	#2354	—	47	2	no	—
298	#2352	—	47	4	no	—
299	D₄×C₄⋊C₄	—	47	2	no	—
300	#2345	—	47	2	no	—
301	#2342	—	47	4	no	—
302	D₄×C₂²⋊C₄	—	47	2	no	—
303	#2319	—	47	2	no	—
304	#2318	—	47	4	no	—
305	#2285	—	47	1	no	—
306	#2283	—	47	1	no	—
307	#2280	—	47	2	no	—
308	C₂×#380	—	47	2	no	—
309	#2275	—	47	2	no	—
310	C₂×C₄₇	—	2	4	no	—
311	C₂×C₄₇	—	2	8	no	—
312	C₂×C₄₇	—	4	4	no	—
313	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
314	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
315	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
316	C₂×C₄₇	#3519	1	2	yes	—
317	C₂×C₄₇	#3520	1	2	yes	—
318	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
319	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
320	C₂×C₄×D₄	—	47	4	no	—
321	C₂×C₄×D₄	Dic₄₇	1	16	yes	complemented
322	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
323	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
325	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
326	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
327	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
328	C₂×#117	—	47	2	no	—
329	C₂×#117	—	47	4	no	—
330	C₂²×C₄⋊C₄	—	47	4	no	—
331	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	—	47	4	no	—
333	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
334	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
335	#390	—	47	4	no	—
336	#389	—	47	4	no	—
337	#388	—	47	8	no	—
338	#388	—	47	8	no	—
339	#387	—	47	8	no	—
340	#386	—	47	8	no	—
341	#385	—	47	8	no	—
342	#384	—	47	2	no	—
343	#383	—	47	2	no	—
344	#382	—	47	2	no	—
345	#382	—	47	2	no	—
346	#381	—	47	4	no	—
347	#381	—	47	2	no	—
348	#380	—	47	4	no	—
349	#380	—	47	2	no	—
350	#380	—	47	4	no	—
351	#380	—	47	1	no	—
352	#380	—	47	2	no	—
353	#380	—	47	1	no	—
354	#380	—	47	4	no	—
355	#380	—	47	4	no	—
356	#379	—	47	4	no	—
357	C₄×C₄⋊C₄	—	47	4	no	—
358	C₄×C₄⋊C₄	—	47	2	no	—
359	C₄×C₄⋊C₄	—	47	2	no	—
360	C₄×C₄⋊C₄	—	47	2	no	—
361	C₄×C₂²⋊C₄	—	47	2	no	—
362	C₄×C₂²⋊C₄	—	47	4	no	—
363	C₄×C₂²⋊C₄	—	47	4	no	—
364	C₄×C₂²⋊C₄	—	47	8	no	—
365	#376	—	47	2	no	—
366	C₂×#95	—	47	4	no	—
367	C₄₇	#34194	1	1	yes	characteristic, complemented, Sylow
368	C₂⁵	C₂²×D₄₇	1	2	yes	—
369	C₂²×D₄	—	2	8	no	—
370	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
371	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
372	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
373	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
374	C₂³×C₄	—	4	8	no	—
375	C₂³×C₄	—	47	8	no	—
376	C₂³×C₄	C₂×Dic₄₇	1	16	yes	complemented
377	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
378	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
379	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
380	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
381	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
382	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
383	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
384	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
385	C₄×D₄	—	94	16	no	—
386	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
387	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
388	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
389	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
390	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
391	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
392	#117	—	188	4	no	—
393	#117	—	188	8	no	—
394	C₂×C₄⋊C₄	—	47	2	no	—
395	C₂×C₄⋊C₄	—	47	4	no	—
396	C₂×C₄⋊C₄	—	47	2	no	—
397	C₂×C₄⋊C₄	—	47	4	no	—
398	C₂×C₄⋊C₄	—	47	8	no	—
399	C₂×C₄⋊C₄	—	47	4	no	—
400	C₂×C₄⋊C₄	—	188	8	no	—
401	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
402	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
404	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	—	47	2	no	—
406	C₂×C₂²⋊C₄	—	47	4	no	—
407	C₂×C₂²⋊C₄	—	47	8	no	—
408	C₂×C₂²⋊C₄	—	47	2	no	—
409	C₂×C₂²⋊C₄	—	47	8	no	—
410	C₂×C₂²⋊C₄	—	47	8	no	—
411	C₂×C₂²⋊C₄	—	188	8	no	—
412	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
413	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
417	C₂×C₄²	—	47	4	no	—
418	C₂×C₄²	—	47	8	no	—
419	C₂×C₄²	—	47	4	no	—
420	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
421	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
422	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
423	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
424	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
425	#95	—	47	2	no	—
426	#95	—	47	4	no	—
427	#95	—	47	8	no	—
428	#95	—	47	2	no	—
429	#95	—	47	4	no	—
430	#95	—	47	8	no	—
431	#95	—	47	4	no	—
432	#95	—	47	4	no	—
433	#95	—	47	4	no	—
434	C₂⁴	—	2	8	no	—
435	C₂⁴	—	2	4	no	—
436	C₂⁴	—	2	4	no	—
437	C₂⁴	—	4	4	no	—
438	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
439	C₂⁴	C₂³×D₄₇	1	2	yes	—
440	C₂⁴	C₂³×D₄₇	1	2	yes	—
441	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
442	C₂×D₄	—	2	8	no	—
443	C₂×D₄	—	2	32	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	#10625350	1	8	yes	—
446	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
447	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
448	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	8	no	—
453	C₂²×C₄	—	2	8	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	4	32	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	4	no	—
458	C₂²×C₄	—	4	4	no	—
459	C₂²×C₄	—	47	4	no	—
460	C₂²×C₄	—	47	4	no	—
461	C₂²×C₄	—	47	8	no	—
462	C₂²×C₄	—	94	16	no	—
463	C₂²×C₄	—	188	8	no	—
464	C₂²×C₄	—	188	8	no	—
465	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
466	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
467	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
468	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
469	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
470	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
471	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
472	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
473	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
474	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
475	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
476	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
477	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
478	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
479	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
480	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
481	C₄⋊C₄	—	94	8	no	—
482	C₄⋊C₄	—	94	4	no	—
483	C₄⋊C₄	—	94	8	no	—
484	C₄⋊C₄	—	94	4	no	—
485	C₄⋊C₄	—	188	8	no	—
486	C₄⋊C₄	—	188	4	no	—
487	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
488	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
489	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
490	C₂²⋊C₄	—	94	16	no	—
491	C₂²⋊C₄	—	94	4	no	—
492	C₂²⋊C₄	—	94	8	no	—
493	C₂²⋊C₄	—	94	4	no	—
494	C₂²⋊C₄	—	188	8	no	—
495	C₂²⋊C₄	—	188	8	no	—
496	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
497	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
498	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
499	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
500	C₄²	—	94	8	no	—
501	C₄²	—	188	8	no	—
502	C₄²	—	188	4	no	—
503	C₄²	C₂²×Dic₄₇	1	4	yes	—
504	C₄²	C₂²×Dic₄₇	1	4	yes	—
505	C₄²	C₂²×Dic₄₇	1	4	yes	—
506	C₄²	C₂²×Dic₄₇	1	4	yes	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	16	no	—
513	C₂³	—	2	16	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	4	8	no	—
519	C₂³	—	4	16	no	—
520	C₂³	—	4	16	no	—
521	C₂³	C₂³×Dic₄₇	1	4	yes	—
522	C₂³	C₂³×Dic₄₇	1	4	yes	—
523	C₂³	C₂³×Dic₄₇	1	2	yes	—
524	C₂³	C₂×#10625350	1	8	yes	—
525	C₂³	#13094070	1	2	yes	—
526	C₂³	#13094071	1	2	yes	—
527	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
528	D₄	—	2	16	no	—
529	D₄	—	2	8	no	—
530	D₄	#13093983	1	16	yes	complemented
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	16	no	—
543	C₂×C₄	—	2	16	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	—	94	4	no	—
548	C₂×C₄	—	94	4	no	—
549	C₂×C₄	—	94	8	no	—
550	C₂×C₄	—	94	4	no	—
551	C₂×C₄	—	94	8	no	—
552	C₂×C₄	—	94	4	no	—
553	C₂×C₄	—	94	8	no	—
554	C₂×C₄	—	94	4	no	—
555	C₂×C₄	—	94	4	no	—
556	C₂×C₄	—	376	16	no	—
557	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
558	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
559	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
560	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
561	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
562	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
563	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
564	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
565	C₂×C₄	C₂×#10625350	1	4	yes	—
566	C₂×C₄	#13094069	1	4	yes	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	4	no	—
570	C₂²	—	2	4	no	—
571	C₂²	—	2	8	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	4	32	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	4	no	—
581	C₂²	C₂×#13093983	1	8	yes	—
582	C₂²	#15689606	1	4	yes	—
583	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
584	C₂²	C₂²×#10625350	1	2	yes	—
585	C₂²	C₂×#13094069	1	2	yes	—
586	C₂²	C₂×#13094070	1	1	yes	characteristic
587	C₂²	C₂×#13094071	1	1	yes	characteristic
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	4	no	—
591	C₄	—	2	4	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	188	4	no	—
595	C₄	—	188	8	no	—
596	C₄	—	188	4	no	—
597	C₄	C₂×#13093983	1	4	yes	—
598	C₄	#15689598	1	4	yes	—
599	C₂	—	2	4	no	—
600	C₂	—	2	8	no	—
601	C₂	—	4	4	no	—
602	C₂	C₂²×#13093983	1	1	yes	characteristic
603	C₂	C₂×#15689598	1	1	yes	characteristic
604	C₂	C₂×#15689606	1	1	yes	characteristic
605	C₂	#20257420	1	2	yes	—
606	C₂	#20257437	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂³×D₄×C₄₇	C₂²
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	#34194
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #20246337	C₂	semidirect
2. #20246317	C₂	semidirect
3. D₄×C₄⋊Dic₄₇	C₂	semidirect
4. #20246265	C₂	semidirect
5. #20246237	C₂	semidirect
7. #20246031	C₂	semidirect
8. #20246021	C₂	semidirect
9. #20245795	C₂	semidirect
10. #20245786	C₂	semidirect
11. #20245771	C₂	semidirect
12. C₂×#15688983	C₂	semidirect
13. #20245749	C₂	semidirect
17. C₂×#13093983	C₂²	semidirect
18. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
21. #15689022	C₂²	semidirect
22. #15689016	C₂²	semidirect
23. #15689016	C₂²	semidirect
24. #15689009	C₂²	semidirect
26. #15688998	C₂²	semidirect
27. #15688993	C₂²	semidirect
28. #15688991	C₂²	semidirect
29. #15688989	C₂²	semidirect
30. #15688989	C₂²	semidirect
32. #15688986	C₂²	semidirect
38. #15688983	C₂²	semidirect
39. #15688983	C₂²	semidirect
40. #15688983	C₂²	semidirect
42. C₄⋊C₄×Dic₄₇	C₂²	semidirect
43. C₄×C₄⋊Dic₄₇	C₂²	semidirect
44. C₄×C₄⋊Dic₄₇	C₂²	semidirect
45. C₄×C₄⋊Dic₄₇	C₂²	semidirect
46. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
49. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
50. #15688969	C₂²	semidirect
51. C₂×C₄₇⋊#95	C₂²	semidirect
54. C₂×C₄×D₄×C₄₇	C₄	semidirect
101. C₂³×C₄×C₄₇	C₂×C₄	semidirect
112. C₄×D₄×C₄₇	C₂×C₄	semidirect
113. C₄×D₄×C₄₇	C₂×C₄	semidirect
114. C₄×D₄×C₄₇	C₂×C₄	semidirect
115. C₄×D₄×C₄₇	C₂×C₄	semidirect
116. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
120. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
125. C₂×C₄²×C₄₇	C₂×C₄	semidirect
226. D₄×C₄₇	#117	semidirect
321. C₂×C₄×D₄	Dic₄₇	semidirect
367. C₄₇	#34194	semidirect
376. C₂³×C₄	C₂×Dic₄₇	semidirect
388. C₄×D₄	C₂×Dic₄₇	semidirect
389. C₄×D₄	C₂×Dic₄₇	semidirect
390. C₄×D₄	C₂×Dic₄₇	semidirect
391. C₄×D₄	C₂×Dic₄₇	semidirect
401. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
412. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
420. C₂×C₄²	C₂×Dic₄₇	semidirect
530. D₄	#13093983	semidirect

Maximal subgroups

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

subgroup	index
#20246337	2
#20246317	2
D₄×C₄⋊Dic₄₇	2
#20246265	2
#20246237	2
D₄×C₂²⋊Dic₄₇	2
#20246031	2
#20246021	2
#20245795	2
#20245786	2
#20245771	2
C₂×#15688983	2
#20245749	2
C₂²×C₄×D₄×C₄₇	2
#34194	47