Subgroups — #532×Dic₄₇ #26374812

Order 12032.

3526 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	C₄⋊Q₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
3	#127×Dic₄₇	C₂	1	2	yes	maximal, complemented
4	#124×Dic₄₇	C₂	1	4	yes	maximal, complemented
5	#121×Dic₄₇	C₂	1	8	yes	maximal, complemented
6	#20245879	C₂	1	2	yes	maximal, complemented
7	#20245853	C₂	1	4	yes	maximal, complemented
8	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×D₄×Dic₄₇	C₂	1	4	yes	maximal, complemented
10	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
12	#41×Dic₄₇	—	2	16	no	—
13	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	—
14	C₂×D₄×Dic₄₇	C₂²	1	8	yes	—
15	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
16	C₂×D₄×Dic₄₇	C₂²	1	8	yes	—
17	C₂×#13093983	C₂²	1	2	yes	—
18	C₂×#13093983	C₂²	1	4	yes	—
19	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
20	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
22	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
23	#15689030	C₂²	1	4	yes	—
24	#15689026	C₂²	1	8	yes	—
25	#15689026	C₂²	1	4	yes	—
26	#15689022	C₂²	1	8	yes	—
27	#15689016	C₂²	1	16	yes	—
28	#15689003	C₂²	1	8	yes	—
29	#15688993	C₂²	1	2	yes	—
30	#15688989	C₂²	1	2	yes	—
31	#15688983	C₂²	1	4	yes	—
32	C₄⋊C₄×Dic₄₇	C₂²	1	8	yes	—
33	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	—
34	C₂²⋊C₄×Dic₄₇	C₂²	1	16	yes	—
35	C₄×C₂²⋊Dic₄₇	C₂²	1	8	yes	—
36	C₄²×Dic₄₇	C₂²	1	2	yes	—
37	C₄²×Dic₄₇	C₂²	1	2	yes	—
38	C₄²×Dic₄₇	C₂²	1	2	yes	—
39	C₄²×Dic₄₇	C₂²	1	2	yes	—
40	C₂²×#41×C₄₇	C₂²	1	2	yes	—
41	C₄₇×#532	C₄	1	16	yes	complemented
42	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#124×C₄₇	C₂²	1	2	yes	—
45	C₂×#121×C₄₇	C₂²	1	4	yes	—
46	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	—
47	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
48	C₂³×Dic₄₇	C₂³	1	8	yes	—
49	C₂³×Dic₄₇	C₂³	1	2	yes	—
50	C₂³×Dic₄₇	C₂³	1	2	yes	—
51	Q₈×Dic₄₇	—	2	16	no	—
52	D₄×Dic₄₇	—	2	32	no	—
53	D₄×Dic₄₇	—	2	16	no	—
54	D₄×Dic₄₇	—	2	32	no	—
55	#13093983	—	2	8	no	—
56	#13093983	—	2	16	no	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
60	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
61	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
62	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
63	C₂×C₄×Dic₄₇	—	2	4	no	—
64	C₂×C₄×Dic₄₇	—	2	16	no	—
65	C₂×C₄×Dic₄₇	—	2	16	no	—
66	C₂×C₄×Dic₄₇	D₄	1	8	yes	complemented
67	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
68	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
69	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
70	C₂×C₄×Dic₄₇	C₂³	1	4	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	1	yes	characteristic
75	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
77	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
78	C₄₇⋊#95	C₂³	1	16	yes	—
79	C₄₇⋊#95	C₂³	1	8	yes	—
80	C₂×#41×C₄₇	—	2	8	no	—
81	C₂×#41×C₄₇	—	2	8	no	—
82	C₂×#41×C₄₇	C₂×C₄	1	16	yes	complemented
83	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
84	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
85	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
86	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
87	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
88	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
89	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
91	#127×C₄₇	C₂×C₄	1	8	yes	complemented
92	#124×C₄₇	C₂×C₄	1	16	yes	complemented
93	#121×C₄₇	C₂×C₄	1	32	yes	complemented
94	C₄×D₄×C₄₇	C₂×C₄	1	32	yes	complemented
95	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
97	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
98	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
102	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
103	#41×C₄₇	—	2	64	no	—
104	C₂×Q₈×C₄₇	—	2	4	no	—
105	C₂×Q₈×C₄₇	—	2	4	no	—
106	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
107	C₂×D₄×C₄₇	—	2	8	no	—
108	C₂×D₄×C₄₇	—	2	8	no	—
109	C₂×D₄×C₄₇	—	2	4	no	—
110	C₂×D₄×C₄₇	—	2	4	no	—
111	C₂×D₄×C₄₇	—	2	16	no	—
112	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
113	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
114	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
115	C₂²×C₄×C₄₇	—	2	8	no	—
116	C₂²×C₄×C₄₇	—	2	8	no	—
117	C₂²×C₄×C₄₇	—	2	8	no	—
118	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
119	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
120	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₄₇	#41	1	4	yes	—
123	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
128	C₂²×Dic₄₇	—	2	4	no	—
129	C₂²×Dic₄₇	—	2	8	no	—
130	C₂²×Dic₄₇	—	2	8	no	—
131	C₂²×Dic₄₇	—	2	16	no	—
132	C₂²×Dic₄₇	—	2	32	no	—
133	C₂²×Dic₄₇	C₂×D₄	1	8	yes	—
134	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
135	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
136	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
137	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
138	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
139	C₂²⋊C₄×C₄₇	C₂²×C₄	1	32	yes	—
140	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
141	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
142	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
143	C₂²⋊Dic₄₇	—	2	8	no	—
144	C₂²⋊Dic₄₇	—	2	16	no	—
145	C₂²⋊Dic₄₇	—	2	32	no	—
146	C₄⋊Dic₄₇	—	2	8	no	—
147	C₄⋊Dic₄₇	—	2	16	no	—
148	C₄⋊Dic₄₇	—	2	16	no	—
149	C₄×Dic₄₇	—	2	8	no	—
150	C₄×Dic₄₇	—	2	8	no	—
151	C₄×Dic₄₇	—	2	4	no	—
152	C₄×Dic₄₇	—	2	4	no	—
153	C₄×Dic₄₇	—	2	16	no	—
154	C₄×Dic₄₇	—	2	8	no	—
155	C₄×Dic₄₇	—	2	8	no	—
156	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
157	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
158	C₄×Dic₄₇	C₂×D₄	1	8	yes	—
159	C₄×Dic₄₇	#41	1	16	yes	complemented
160	C₂³×C₄₇	—	2	4	no	—
161	C₂³×C₄₇	—	2	4	no	—
162	C₂³×C₄₇	—	2	16	no	—
163	C₂³×C₄₇	—	2	4	no	—
164	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
165	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
166	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
167	C₂³×C₄₇	C₂×#41	1	2	yes	—
168	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
169	Q₈×C₄₇	—	2	16	no	—
170	D₄×C₄₇	—	2	32	no	—
171	D₄×C₄₇	—	2	16	no	—
172	D₄×C₄₇	—	2	32	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	2	32	no	—
177	C₂×C₄×C₄₇	—	2	16	no	—
178	C₂×C₄×C₄₇	C₄×D₄	1	16	yes	complemented
179	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
180	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
181	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
182	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
183	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
184	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
187	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
188	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
189	C₂×Dic₄₇	—	2	16	no	—
190	C₂×Dic₄₇	—	2	4	no	—
191	C₂×Dic₄₇	—	2	4	no	—
192	C₂×Dic₄₇	—	2	4	no	—
193	C₂×Dic₄₇	—	2	16	no	—
194	C₂×Dic₄₇	—	2	8	no	—
195	C₂×Dic₄₇	—	2	16	no	—
196	C₂×Dic₄₇	—	4	32	no	—
197	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
198	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
199	C₂×Dic₄₇	C₂×#41	1	8	yes	—
200	C₂×Dic₄₇	C₂×#41	1	8	yes	—
201	C₄×#532	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	—	2	4	no	—
203	C₂²×C₄₇	—	2	4	no	—
204	C₂²×C₄₇	—	2	4	no	—
205	C₂²×C₄₇	—	2	8	no	—
206	C₂²×C₄₇	—	2	16	no	—
207	C₂²×C₄₇	—	4	8	no	—
208	C₂²×C₄₇	—	4	8	no	—
209	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
210	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
211	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
212	C₂²×C₄₇	C₂²×#41	1	4	yes	—
213	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
214	C₄×C₄₇	—	2	8	no	—
215	C₄×C₄₇	—	2	4	no	—
216	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
217	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
218	C₄×C₄₇	C₄×#41	1	8	yes	complemented
219	Dic₄₇	—	2	4	no	—
220	Dic₄₇	—	2	8	no	—
221	Dic₄₇	—	4	8	no	—
222	Dic₄₇	#532	1	8	yes	direct product factor
223	C₂×#532	D₄₇	1	1	yes	characteristic
224	C₂×C₄×#41	—	47	2	no	—
225	C₄×C₄⋊Q₈	—	47	2	no	—
226	C₄×#127	—	47	2	no	—
227	C₄×#124	—	47	4	no	—
228	C₄×#121	—	47	8	no	—
229	#2297	—	47	2	no	—
230	#2293	—	47	4	no	—
231	#2285	—	47	1	no	—
232	C₄²×D₄	—	47	4	no	—
233	C₂×C₄³	—	47	1	no	—
234	C₂×C₄₇	—	2	4	no	—
235	C₂×C₄₇	—	4	8	no	—
236	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
237	C₂×C₄₇	C₂×C₄×#41	1	2	yes	—
238	C₂×C₄₇	C₂×#532	1	2	yes	—
239	C₂×C₄₇	#3444	1	2	yes	—
240	C₂²×#41	C₂×D₄₇	1	2	yes	—
241	#532	Dic₄₇	1	16	yes	direct product factor
242	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
243	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
244	C₂×#124	C₂×D₄₇	1	2	yes	—
245	C₂×#121	C₂×D₄₇	1	4	yes	—
246	C₄×#41	—	94	16	no	—
247	C₂×C₄×Q₈	—	47	4	no	—
248	C₂×C₄×D₄	—	47	4	no	—
249	C₂×C₄×D₄	—	47	8	no	—
250	C₂×C₄×D₄	—	47	8	no	—
251	C₂×C₄×D₄	C₂×D₄₇	1	4	yes	—
252	C₂×#117	—	47	2	no	—
253	C₂×#117	—	47	4	no	—
254	C₂²×C₄²	—	47	1	no	—
255	C₂²×C₄²	—	47	4	no	—
256	C₂²×C₄²	—	47	1	no	—
257	C₂²×C₄²	—	47	4	no	—
258	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
259	#391	—	47	4	no	—
260	#390	—	47	8	no	—
261	#390	—	47	4	no	—
262	#389	—	47	8	no	—
263	#388	—	47	16	no	—
264	#386	—	47	8	no	—
265	#384	—	47	2	no	—
266	#382	—	47	2	no	—
267	#380	—	47	4	no	—
268	C₄×C₄⋊C₄	—	47	8	no	—
269	C₄×C₄⋊C₄	—	47	4	no	—
270	C₄×C₂²⋊C₄	—	47	8	no	—
271	C₄×C₂²⋊C₄	—	47	16	no	—
272	C₄³	—	47	2	no	—
273	C₄³	—	47	2	no	—
274	C₄³	—	47	2	no	—
275	C₄³	—	47	2	no	—
276	C₄₇	C₄×#532	1	1	yes	characteristic, complemented, Sylow
277	C₂×#41	—	2	8	no	—
278	C₂×#41	—	2	8	no	—
279	C₂×#41	C₂×Dic₄₇	1	16	yes	complemented
280	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
281	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
282	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
283	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
284	C₂³×C₄	—	47	2	no	—
285	C₂³×C₄	—	47	8	no	—
286	C₂³×C₄	—	47	2	no	—
287	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
288	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
289	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
290	C₄⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
291	#127	C₂×Dic₄₇	1	8	yes	complemented
292	#124	C₂×Dic₄₇	1	16	yes	complemented
293	#121	C₂×Dic₄₇	1	32	yes	complemented
294	C₄×Q₈	—	94	16	no	—
295	C₄×D₄	—	94	16	no	—
296	C₄×D₄	—	94	32	no	—
297	C₄×D₄	—	94	32	no	—
298	C₄×D₄	C₂×Dic₄₇	1	32	yes	complemented
299	#117	—	94	16	no	—
300	#117	—	94	8	no	—
301	C₂×C₄⋊C₄	—	47	4	no	—
302	C₂×C₄⋊C₄	—	47	8	no	—
303	C₂×C₄⋊C₄	—	47	8	no	—
304	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
305	C₂×C₂²⋊C₄	—	47	4	no	—
306	C₂×C₂²⋊C₄	—	47	8	no	—
307	C₂×C₂²⋊C₄	—	47	16	no	—
308	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
309	C₂×C₄²	—	47	8	no	—
310	C₂×C₄²	—	47	2	no	—
311	C₂×C₄²	—	47	4	no	—
312	C₂×C₄²	—	47	1	no	—
313	C₂×C₄²	—	47	1	no	—
314	C₂×C₄²	—	47	8	no	—
315	C₂×C₄²	—	47	4	no	—
316	C₂×C₄²	—	47	4	no	—
317	C₂×C₄²	—	47	4	no	—
318	C₂×C₄²	—	47	2	no	—
319	C₂×C₄²	—	47	4	no	—
320	C₂×C₄²	—	47	2	no	—
321	C₂×C₄²	—	94	16	no	—
322	C₂×C₄²	—	94	16	no	—
323	C₂×C₄²	—	94	4	no	—
324	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
325	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
326	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
327	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
328	#95	—	47	8	no	—
329	#95	—	47	16	no	—
330	C₂⁴	C₂³×D₄₇	1	4	yes	—
331	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
332	#41	—	2	64	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	4	no	—
335	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	16	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
342	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
343	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	47	2	no	—
348	C₂²×C₄	—	47	8	no	—
349	C₂²×C₄	—	47	4	no	—
350	C₂²×C₄	—	47	2	no	—
351	C₂²×C₄	—	47	8	no	—
352	C₂²×C₄	—	94	8	no	—
353	C₂²×C₄	—	94	8	no	—
354	C₂²×C₄	—	94	16	no	—
355	C₂²×C₄	—	94	32	no	—
356	C₂²×C₄	—	94	4	no	—
357	C₂²×C₄	D₄×D₄₇	1	4	yes	—
358	C₂²×C₄	#10625352	1	4	yes	—
359	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
360	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
361	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
362	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
363	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
364	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
366	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
367	C₄⋊C₄	—	94	16	no	—
368	C₄⋊C₄	—	94	8	no	—
369	C₄⋊C₄	—	94	16	no	—
370	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	—
371	C₂²⋊C₄	—	94	16	no	—
372	C₂²⋊C₄	—	94	32	no	—
373	C₂²⋊C₄	—	94	8	no	—
374	C₂²⋊C₄	C₂²×Dic₄₇	1	32	yes	—
375	C₄²	—	47	4	no	—
376	C₄²	—	47	4	no	—
377	C₄²	—	47	8	no	—
378	C₄²	—	47	16	no	—
379	C₄²	—	94	8	no	—
380	C₄²	—	94	8	no	—
381	C₄²	—	94	16	no	—
382	C₄²	—	94	8	no	—
383	C₄²	—	94	8	no	—
384	C₄²	—	94	4	no	—
385	C₄²	—	94	4	no	—
386	C₄²	C₂²×Dic₄₇	1	8	yes	—
387	C₄²	C₂²×Dic₄₇	1	4	yes	—
388	C₄²	C₂²×Dic₄₇	1	4	yes	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	16	no	—
392	C₂³	—	2	4	no	—
393	C₂³	C₂³×Dic₄₇	1	8	yes	—
394	C₂³	C₂³×Dic₄₇	1	2	yes	—
395	C₂³	C₂×D₄×D₄₇	1	2	yes	—
396	C₂³	C₂×#10625352	1	2	yes	—
397	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
398	Q₈	—	2	16	no	—
399	D₄	—	2	32	no	—
400	D₄	—	2	16	no	—
401	D₄	—	2	32	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	32	no	—
406	C₂×C₄	—	2	16	no	—
407	C₂×C₄	—	47	4	no	—
408	C₂×C₄	—	47	8	no	—
409	C₂×C₄	—	47	4	no	—
410	C₂×C₄	—	47	8	no	—
411	C₂×C₄	—	94	16	no	—
412	C₂×C₄	—	94	16	no	—
413	C₂×C₄	—	94	4	no	—
414	C₂×C₄	—	94	4	no	—
415	C₂×C₄	—	94	4	no	—
416	C₂×C₄	—	94	8	no	—
417	C₂×C₄	—	94	16	no	—
418	C₂×C₄	—	188	32	no	—
419	C₂×C₄	D₄×Dic₄₇	1	16	yes	complemented
420	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
421	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
422	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
423	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
424	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
425	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
426	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
427	C₂×C₄	#41×D₄₇	1	8	yes	—
428	C₂×C₄	C₂×#10625352	1	2	yes	—
429	C₂×C₄	C₂×#10625352	1	2	yes	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	8	no	—
434	C₂²	—	2	16	no	—
435	C₂²	—	4	8	no	—
436	C₂²	—	4	8	no	—
437	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
438	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
439	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
440	C₂²	C₂×#41×D₄₇	1	4	yes	—
441	C₂²	C₂²×#10625352	1	1	yes	characteristic
442	C₄	—	2	8	no	—
443	C₄	—	2	4	no	—
444	C₄	—	47	8	no	—
445	C₄	—	94	4	no	—
446	C₄	—	94	8	no	—
447	C₄	—	188	8	no	—
448	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
449	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
450	C₄	#41×Dic₄₇	1	8	yes	complemented
451	C₂	—	2	4	no	—
452	C₂	—	4	8	no	—
453	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
454	C₂	C₂×#41×Dic₄₇	1	2	yes	—
455	C₂	#532×D₄₇	1	2	yes	—
456	C₂	#20256683	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting, prime radical	C₂×C₄₇×#532	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	C₄×#532
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂×#41×Dic₄₇	C₂	semidirect
2. C₄⋊Q₈×Dic₄₇	C₂	semidirect
3. #127×Dic₄₇	C₂	semidirect
4. #124×Dic₄₇	C₂	semidirect
5. #121×Dic₄₇	C₂	semidirect
6. #20245879	C₂	semidirect
7. #20245853	C₂	semidirect
8. #20245795	C₂	semidirect
9. C₄×D₄×Dic₄₇	C₂	semidirect
10. C₂×C₄²×Dic₄₇	C₂	semidirect
41. C₄₇×#532	C₄	semidirect
66. C₂×C₄×Dic₄₇	D₄	semidirect
82. C₂×#41×C₄₇	C₂×C₄	semidirect
90. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
91. #127×C₄₇	C₂×C₄	semidirect
92. #124×C₄₇	C₂×C₄	semidirect
93. #121×C₄₇	C₂×C₄	semidirect
94. C₄×D₄×C₄₇	C₂×C₄	semidirect
97. C₂×C₄²×C₄₇	C₂×C₄	semidirect
159. C₄×Dic₄₇	#41	semidirect
178. C₂×C₄×C₄₇	C₄×D₄	semidirect
218. C₄×C₄₇	C₄×#41	semidirect
222. Dic₄₇	#532	direct (N × H)
241. #532	Dic₄₇	direct (N × H)
276. C₄₇	C₄×#532	semidirect
279. C₂×#41	C₂×Dic₄₇	semidirect
290. C₄⋊Q₈	C₂×Dic₄₇	semidirect
291. #127	C₂×Dic₄₇	semidirect
292. #124	C₂×Dic₄₇	semidirect
293. #121	C₂×Dic₄₇	semidirect
298. C₄×D₄	C₂×Dic₄₇	semidirect
324. C₂×C₄²	C₂×Dic₄₇	semidirect
419. C₂×C₄	D₄×Dic₄₇	semidirect
450. C₄	#41×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×Dic₄₇	2
C₄⋊Q₈×Dic₄₇	2
#127×Dic₄₇	2
#124×Dic₄₇	2
#121×Dic₄₇	2
#20245879	2
#20245853	2
#20245795	2
C₄×D₄×Dic₄₇	2
C₂×C₄²×Dic₄₇	2
C₂×C₄₇×#532	2
C₄×#532	47

Subgroups — #532×Dic47 #26374812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #532×Dic₄₇ #26374812