Subgroups — #26375944

Order 12032.

2322 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246488	C₂	1	4	yes	maximal, complemented
2	#20246478	C₂	1	2	yes	maximal, complemented
3	#20246473	C₂	1	4	yes	maximal
4	#20246448	C₂	1	2	yes	maximal, complemented
5	#20246397	C₂	1	4	yes	maximal
6	#20245872	C₂	1	2	yes	maximal
7	#20245866	C₂	1	2	yes	maximal, complemented
8	#20245866	C₂	1	4	yes	maximal, complemented
9	C₄×Q₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
10	#117×Dic₄₇	C₂	1	2	yes	maximal
11	C₄×#13093983	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
14	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	—
15	C₂×#13093983	C₂²	1	1	yes	characteristic
16	C₂×#13093983	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
18	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
19	#15689030	C₂²	1	4	yes	—
20	#15689030	C₂²	1	8	yes	—
21	#15689022	C₂²	1	4	yes	—
22	#15689022	C₂²	1	8	yes	—
23	#15689022	C₂²	1	4	yes	—
24	#15689022	C₂²	1	4	yes	—
25	#15689009	C₂²	1	8	yes	—
26	#15689009	C₂²	1	8	yes	—
27	#15689009	C₂²	1	8	yes	—
28	#15688998	C₂²	1	8	yes	—
29	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	8	yes	—
32	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
33	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	—
34	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
36	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	—
37	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
38	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
39	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
40	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
41	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
42	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	—
43	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
44	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
45	#15688969	C₂²	1	2	yes	—
46	#15688969	C₂²	1	4	yes	—
47	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
48	C₄²×Dic₄₇	C₂²	1	2	yes	—
49	C₄²×Dic₄₇	C₂²	1	4	yes	—
50	C₄₇×#533	C₄	1	16	yes	complemented
51	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×#125×C₄₇	C₂²	1	2	yes	—
54	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
55	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
57	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
58	C₂×#117×C₄₇	C₂²	1	2	yes	—
59	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
60	C₂³×Dic₄₇	C₂³	1	4	yes	—
61	Q₈×Dic₄₇	—	2	16	no	—
62	#13093983	—	2	4	no	—
63	#13093983	Q₈	1	8	yes	complemented
64	C₂×C₄⋊Dic₄₇	—	2	8	no	—
65	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
66	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
68	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
69	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
70	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
71	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
72	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
73	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
74	C₂×C₄×Dic₄₇	—	2	8	no	—
75	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
76	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
77	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
78	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
79	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
80	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
81	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
82	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
83	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
84	C₄₇⋊#95	C₂³	1	2	yes	—
85	C₄₇⋊#95	C₂³	1	2	yes	—
86	C₄₇⋊#95	C₂³	1	4	yes	—
87	C₄₇⋊#95	C₂³	1	4	yes	—
88	C₄₇⋊#95	C₂³	1	4	yes	—
89	C₄₇⋊#95	C₂³	1	8	yes	—
90	C₄₇⋊#95	C₂³	1	8	yes	—
91	C₄₇⋊#95	C₂³	1	8	yes	—
92	C₄₇⋊#95	C₂³	1	8	yes	—
93	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
94	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
95	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
99	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
100	#125×C₄₇	C₂×C₄	1	16	yes	complemented
101	C₂²⋊Q₈×C₄₇	C₂×C₄	1	16	yes	—
102	C₂²⋊Q₈×C₄₇	C₂×C₄	1	16	yes	—
103	C₄×Q₈×C₄₇	C₂×C₄	1	16	yes	complemented
104	C₄×Q₈×C₄₇	C₂×C₄	1	16	yes	complemented
105	#117×C₄₇	C₂×C₄	1	16	yes	—
106	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
113	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
114	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
116	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
119	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂×Q₈×C₄₇	—	2	8	no	—
121	C₂×Q₈×C₄₇	—	4	4	no	—
122	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
123	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
124	C₂²×C₄×C₄₇	—	2	4	no	—
125	C₂²×C₄×C₄₇	—	4	2	no	—
126	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
127	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
128	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
130	C₂²×C₄×C₄₇	#41	1	4	yes	—
131	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
139	C₂²×Dic₄₇	—	2	8	no	—
140	C₂²×Dic₄₇	—	2	8	no	—
141	C₂²×Dic₄₇	—	4	4	no	—
142	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
143	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
144	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
145	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
146	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
147	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
148	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
149	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
150	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
151	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
152	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
153	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
154	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
155	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
156	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
157	C₄²×C₄₇	C₂²×C₄	1	16	yes	—
158	C₂²⋊Dic₄₇	—	2	4	no	—
159	C₂²⋊Dic₄₇	C₂×Q₈	1	8	yes	—
160	C₄⋊Dic₄₇	—	2	4	no	—
161	C₄⋊Dic₄₇	—	2	4	no	—
162	C₄⋊Dic₄₇	—	2	8	no	—
163	C₄⋊Dic₄₇	—	2	16	no	—
164	C₄⋊Dic₄₇	—	4	8	no	—
165	C₄⋊Dic₄₇	C₂×Q₈	1	8	yes	—
166	C₄⋊Dic₄₇	#41	1	8	yes	—
167	C₄×Dic₄₇	—	2	4	no	—
168	C₄×Dic₄₇	—	2	8	no	—
169	C₄×Dic₄₇	—	2	4	no	—
170	C₄×Dic₄₇	—	2	4	no	—
171	C₄×Dic₄₇	—	2	8	no	—
172	C₄×Dic₄₇	—	2	16	no	—
173	C₄×Dic₄₇	—	4	8	no	—
174	C₄×Dic₄₇	—	4	4	no	—
175	C₄×Dic₄₇	C₂×Q₈	1	8	yes	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	2	no	—
178	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
179	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
180	C₂³×C₄₇	C₂×#41	1	2	yes	—
181	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
182	Q₈×C₄₇	—	2	16	no	—
183	Q₈×C₄₇	—	4	8	no	—
184	C₂×C₄×C₄₇	—	2	8	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	8	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	8	no	—
190	C₂×C₄×C₄₇	—	4	4	no	—
191	C₂×C₄×C₄₇	C₄×Q₈	1	16	yes	complemented
192	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
193	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
194	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
195	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
196	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
197	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
198	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
199	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
200	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
201	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
202	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
203	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
204	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
205	C₂×Dic₄₇	—	2	4	no	—
206	C₂×Dic₄₇	—	2	4	no	—
207	C₂×Dic₄₇	—	2	4	no	—
208	C₂×Dic₄₇	—	2	4	no	—
209	C₂×Dic₄₇	—	2	4	no	—
210	C₂×Dic₄₇	—	2	4	no	—
211	C₂×Dic₄₇	—	2	4	no	—
212	C₂×Dic₄₇	—	2	4	no	—
213	C₂×Dic₄₇	—	2	4	no	—
214	C₂×Dic₄₇	—	2	4	no	—
215	C₂×Dic₄₇	—	4	16	no	—
216	C₂×Dic₄₇	C₂²×Q₈	1	8	yes	—
217	C₂×Dic₄₇	C₂×#41	1	8	yes	—
218	#34145	—	47	1	no	maximal, Sylow
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	2	4	no	—
222	C₂²×C₄₇	—	2	4	no	—
223	C₂²×C₄₇	C₂×C₄×Q₈	1	4	yes	—
224	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
225	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
226	C₂²×C₄₇	C₂²×#41	1	2	yes	—
227	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
228	C₂²×C₄₇	#585	1	2	yes	—
229	C₄×C₄₇	—	2	2	no	—
230	C₄×C₄₇	—	2	8	no	—
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	2	8	no	—
234	C₄×C₄₇	C₂×C₄×Q₈	1	4	yes	—
235	C₄×C₄₇	C₂×C₄×Q₈	1	4	yes	—
236	C₄×C₄₇	C₄×#41	1	4	yes	—
237	Dic₄₇	—	2	8	no	—
238	Dic₄₇	—	2	8	no	—
239	Dic₄₇	—	4	4	no	—
240	Dic₄₇	—	4	4	no	—
241	C₂×#533	D₄₇	1	1	yes	characteristic
242	#2370	—	47	4	no	—
243	#2369	—	47	2	no	—
244	#2368	—	47	4	no	—
245	#2365	—	47	2	no	—
246	#2360	—	47	4	no	—
247	#2296	—	47	2	no	—
248	#2295	—	47	2	no	—
249	#2295	—	47	4	no	—
250	C₄²×Q₈	—	47	2	no	—
251	C₄×#117	—	47	1	no	—
252	C₄×#117	—	47	2	no	—
253	C₂×C₄×C₄⋊C₄	—	47	1	no	—
254	C₂×C₄₇	—	2	4	no	—
255	C₂×C₄₇	C₂²×C₄×Q₈	1	1	yes	characteristic
256	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
257	C₂×C₄₇	#3428	1	1	yes	characteristic
258	C₂×C₄₇	#3475	1	2	yes	—
259	C₂×C₄₇	Q₈×#41	1	2	yes	—
260	#533	Dic₄₇	1	16	yes	complemented
261	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
262	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
263	C₂×#125	C₂×D₄₇	1	2	yes	—
264	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
265	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
266	C₂×C₄×Q₈	—	47	4	no	—
267	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
268	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
269	C₂×#117	—	47	1	no	—
270	C₂×#117	—	47	1	no	—
271	C₂×#117	C₂×D₄₇	1	2	yes	—
272	C₂²×C₄⋊C₄	—	47	2	no	—
273	C₂²×C₄²	—	47	2	no	—
274	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
275	#391	—	47	4	no	—
276	#391	—	47	8	no	—
277	#389	—	47	4	no	—
278	#389	—	47	8	no	—
279	#389	—	47	4	no	—
280	#389	—	47	4	no	—
281	#387	—	47	8	no	—
282	#387	—	47	8	no	—
283	#387	—	47	8	no	—
284	#385	—	47	8	no	—
285	C₄×C₄⋊C₄	—	47	4	no	—
286	C₄×C₄⋊C₄	—	47	4	no	—
287	C₄×C₄⋊C₄	—	47	8	no	—
288	C₄×C₄⋊C₄	—	47	4	no	—
289	C₄×C₄⋊C₄	—	47	2	no	—
290	C₄×C₄⋊C₄	—	47	2	no	—
291	C₄×C₄⋊C₄	—	47	2	no	—
292	C₄×C₄⋊C₄	—	47	2	no	—
293	C₄×C₄⋊C₄	—	47	1	no	—
294	C₄×C₄⋊C₄	—	47	1	no	—
295	C₄×C₄⋊C₄	—	47	2	no	—
296	C₄×C₄⋊C₄	—	47	4	no	—
297	C₄×C₄⋊C₄	—	47	4	no	—
298	C₄×C₂²⋊C₄	—	47	2	no	—
299	C₄×C₂²⋊C₄	—	47	2	no	—
300	C₄×C₂²⋊C₄	—	47	8	no	—
301	#376	—	47	2	no	—
302	#376	—	47	4	no	—
303	C₂×#95	—	47	2	no	—
304	C₄³	—	47	4	no	—
305	C₄³	—	47	2	no	—
306	C₄₇	#34145	1	1	yes	characteristic, complemented, Sylow
307	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
308	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
309	C₂³×C₄	—	47	4	no	—
310	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
311	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
312	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
313	C₄⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
314	C₄⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
315	#125	C₂×Dic₄₇	1	16	yes	complemented
316	C₂²⋊Q₈	C₂×Dic₄₇	1	16	yes	—
317	C₂²⋊Q₈	C₂×Dic₄₇	1	16	yes	—
318	C₄×Q₈	—	94	16	no	—
319	C₄×Q₈	C₂×Dic₄₇	1	16	yes	complemented
320	C₄×Q₈	C₂×Dic₄₇	1	16	yes	complemented
321	#117	—	47	8	no	—
322	#117	—	94	4	no	—
323	#117	C₂×Dic₄₇	1	16	yes	—
324	C₂×C₄⋊C₄	—	47	2	no	—
325	C₂×C₄⋊C₄	—	47	2	no	—
326	C₂×C₄⋊C₄	—	47	4	no	—
327	C₂×C₄⋊C₄	—	47	2	no	—
328	C₂×C₄⋊C₄	—	47	2	no	—
329	C₂×C₄⋊C₄	—	47	8	no	—
330	C₂×C₄⋊C₄	—	47	8	no	—
331	C₂×C₄⋊C₄	—	94	8	no	—
332	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
333	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
334	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
335	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
336	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
337	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
338	C₂×C₂²⋊C₄	—	47	2	no	—
339	C₂×C₂²⋊C₄	—	47	2	no	—
340	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
341	C₂×C₄²	—	47	2	no	—
342	C₂×C₄²	—	47	8	no	—
343	C₂×C₄²	—	47	4	no	—
344	C₂×C₄²	—	47	4	no	—
345	C₂×C₄²	—	47	2	no	—
346	C₂×C₄²	—	47	2	no	—
347	C₂×C₄²	—	47	2	no	—
348	C₂×C₄²	—	47	4	no	—
349	C₂×C₄²	—	47	8	no	—
350	C₂×C₄²	—	94	8	no	—
351	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
352	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
353	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
354	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
355	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
356	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
357	#95	—	47	2	no	—
358	#95	—	47	2	no	—
359	#95	—	47	4	no	—
360	#95	—	47	4	no	—
361	#95	—	47	8	no	—
362	#95	—	47	8	no	—
363	#95	—	47	4	no	—
364	#95	—	47	8	no	—
365	#95	—	47	8	no	—
366	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
367	C₂×Q₈	—	2	8	no	—
368	C₂×Q₈	—	4	4	no	—
369	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
370	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	47	4	no	—
374	C₂²×C₄	—	47	4	no	—
375	C₂²×C₄	—	47	4	no	—
376	C₂²×C₄	—	47	4	no	—
377	C₂²×C₄	—	94	8	no	—
378	C₂²×C₄	—	94	8	no	—
379	C₂²×C₄	—	188	4	no	—
380	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
381	C₂²×C₄	#10625354	1	4	yes	—
382	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
383	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
384	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
385	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
386	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
387	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
388	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
389	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
390	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
391	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
392	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
393	C₄⋊C₄	—	47	8	no	—
394	C₄⋊C₄	—	47	8	no	—
395	C₄⋊C₄	—	94	8	no	—
396	C₄⋊C₄	—	94	16	no	—
397	C₄⋊C₄	—	94	4	no	—
398	C₄⋊C₄	—	94	4	no	—
399	C₄⋊C₄	—	188	8	no	—
400	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
401	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
402	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	—
403	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	—
404	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
405	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
406	C₂²⋊C₄	—	47	8	no	—
407	C₂²⋊C₄	—	94	4	no	—
408	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
409	C₄²	—	47	8	no	—
410	C₄²	—	94	16	no	—
411	C₄²	—	94	8	no	—
412	C₄²	—	94	4	no	—
413	C₄²	—	94	8	no	—
414	C₄²	—	94	4	no	—
415	C₄²	—	94	4	no	—
416	C₄²	—	188	4	no	—
417	C₄²	—	188	8	no	—
418	C₄²	C₂²×Dic₄₇	1	4	yes	—
419	C₄²	C₂²×Dic₄₇	1	4	yes	—
420	C₄²	C₂²×Dic₄₇	1	4	yes	—
421	C₄²	C₂²×Dic₄₇	1	4	yes	—
422	C₄²	C₂²×Dic₄₇	1	16	yes	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	C₂³×Dic₄₇	1	2	yes	—
426	C₂³	C₂×Q₈×D₄₇	1	2	yes	—
427	C₂³	C₂×#10625354	1	2	yes	—
428	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
429	Q₈	—	2	16	no	—
430	Q₈	—	4	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	47	8	no	—
439	C₂×C₄	—	47	8	no	—
440	C₂×C₄	—	94	4	no	—
441	C₂×C₄	—	94	4	no	—
442	C₂×C₄	—	94	4	no	—
443	C₂×C₄	—	94	4	no	—
444	C₂×C₄	—	94	4	no	—
445	C₂×C₄	—	94	4	no	—
446	C₂×C₄	—	94	4	no	—
447	C₂×C₄	—	94	4	no	—
448	C₂×C₄	—	94	4	no	—
449	C₂×C₄	—	94	4	no	—
450	C₂×C₄	—	188	16	no	—
451	C₂×C₄	Q₈×Dic₄₇	1	16	yes	complemented
452	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
453	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
454	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
455	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
456	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
457	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
458	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
459	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
460	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
461	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
462	C₂×C₄	#41×D₄₇	1	4	yes	—
463	C₂×C₄	C₂×#10625354	1	2	yes	—
464	C₂×C₄	C₂×#10625354	1	2	yes	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	4	no	—
469	C₂²	C₂×Q₈×Dic₄₇	1	4	yes	—
470	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
471	C₂²	C₂²×Q₈×D₄₇	1	1	yes	characteristic
472	C₂²	C₂×#41×D₄₇	1	2	yes	—
473	C₂²	C₂²×#10625354	1	1	yes	characteristic
474	C₂²	#15689959	1	2	yes	—
475	C₄	—	2	2	no	—
476	C₄	—	2	8	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	8	no	—
480	C₄	—	94	8	no	—
481	C₄	—	94	8	no	—
482	C₄	—	188	4	no	—
483	C₄	—	188	4	no	—
484	C₄	C₂×Q₈×Dic₄₇	1	4	yes	—
485	C₄	C₂×Q₈×Dic₄₇	1	4	yes	—
486	C₄	#41×Dic₄₇	1	4	yes	—
487	C₂	—	2	4	no	—
488	C₂	C₂²×Q₈×Dic₄₇	1	1	yes	characteristic
489	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
490	C₂	#20256591	1	1	yes	characteristic
491	C₂	#20256955	1	2	yes	—
492	C₂	#20256966	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂⁴×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	#34145
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. #20246488	C₂	semidirect
2. #20246478	C₂	semidirect
4. #20246448	C₂	semidirect
7. #20245866	C₂	semidirect
8. #20245866	C₂	semidirect
9. C₄×Q₈×Dic₄₇	C₂	semidirect
50. C₄₇×#533	C₄	semidirect
63. #13093983	Q₈	semidirect
98. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
99. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
100. #125×C₄₇	C₂×C₄	semidirect
103. C₄×Q₈×C₄₇	C₂×C₄	semidirect
104. C₄×Q₈×C₄₇	C₂×C₄	semidirect
191. C₂×C₄×C₄₇	C₄×Q₈	semidirect
260. #533	Dic₄₇	semidirect
306. C₄₇	#34145	semidirect
313. C₄⋊Q₈	C₂×Dic₄₇	semidirect
314. C₄⋊Q₈	C₂×Dic₄₇	semidirect
315. #125	C₂×Dic₄₇	semidirect
319. C₄×Q₈	C₂×Dic₄₇	semidirect
320. C₄×Q₈	C₂×Dic₄₇	semidirect
451. C₂×C₄	Q₈×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246488	2
#20246478	2
#20246473	2
#20246448	2
#20246397	2
#20245872	2
#20245866	2
C₄×Q₈×Dic₄₇	2
#117×Dic₄₇	2
C₄×#13093983	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₄₇×#533	2
#34145	47