Subgroups — #26375903

Order 12032.

3298 conjugacy classes of subgroups.

The subgroup lattice has 564 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	#20246463	C₂	1	4	yes	maximal, complemented
3	#20246453	C₂	1	2	yes	maximal, complemented
4	#20246448	C₂	1	2	yes	maximal, complemented
5	#20246440	C₂	1	4	yes	maximal, complemented
6	#20246408	C₂	1	4	yes	maximal, complemented
7	#20245879	C₂	1	2	yes	maximal, complemented
8	#20245853	C₂	1	2	yes	maximal, complemented
9	#20245833	C₂	1	4	yes	maximal, complemented
10	C₄×D₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	C₄×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
14	#41×Dic₄₇	—	2	16	no	—
15	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	—
16	C₂×D₄×Dic₄₇	C₂²	1	8	yes	—
17	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
18	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
19	C₂×#13093983	C₂²	1	4	yes	—
20	C₂×#13093983	C₂²	1	1	yes	characteristic
21	C₂×#13093983	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
23	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
24	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
25	#15689030	C₂²	1	4	yes	—
26	#15689026	C₂²	1	4	yes	—
27	#15689026	C₂²	1	4	yes	—
28	#15689022	C₂²	1	4	yes	—
29	#15689016	C₂²	1	8	yes	—
30	#15689016	C₂²	1	8	yes	—
31	#15689009	C₂²	1	8	yes	—
32	#15689003	C₂²	1	8	yes	—
33	#15689003	C₂²	1	8	yes	—
34	#15688998	C₂²	1	8	yes	—
35	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
36	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
37	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
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	2	yes	—
42	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
43	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	—
44	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
45	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
46	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
47	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
48	#15688969	C₂²	1	2	yes	—
49	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
50	C₄²×Dic₄₇	C₂²	1	2	yes	—
51	C₂²×#41×C₄₇	C₂²	1	2	yes	—
52	C₄₇×#532	C₄	1	16	yes	complemented
53	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×#124×C₄₇	C₂²	1	2	yes	—
56	C₂×#121×C₄₇	C₂²	1	2	yes	—
57	C₂×#121×C₄₇	C₂²	1	2	yes	—
58	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
59	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
60	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
61	C₂³×Dic₄₇	C₂³	1	4	yes	—
62	C₂³×Dic₄₇	C₂³	1	8	yes	—
63	Q₈×Dic₄₇	—	2	16	no	—
64	D₄×Dic₄₇	—	2	32	no	—
65	D₄×Dic₄₇	—	2	16	no	—
66	D₄×Dic₄₇	—	2	16	no	—
67	#13093983	—	2	4	no	—
68	#13093983	—	2	16	no	—
69	#13093983	D₄	1	8	yes	complemented
70	C₂×C₄⋊Dic₄₇	—	2	8	no	—
71	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
72	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
73	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
75	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
76	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
77	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
78	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
79	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
80	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
81	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
82	C₂×C₄×Dic₄₇	—	2	8	no	—
83	C₂×C₄×Dic₄₇	—	2	16	no	—
84	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
85	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
86	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
87	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
88	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
89	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
90	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
91	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
92	C₄₇⋊#95	C₂³	1	2	yes	—
93	C₄₇⋊#95	C₂³	1	4	yes	—
94	C₄₇⋊#95	C₂³	1	2	yes	—
95	C₄₇⋊#95	C₂³	1	4	yes	—
96	C₄₇⋊#95	C₂³	1	4	yes	—
97	C₄₇⋊#95	C₂³	1	8	yes	—
98	C₄₇⋊#95	C₂³	1	8	yes	—
99	C₂×#41×C₄₇	—	2	8	no	—
100	C₂×#41×C₄₇	—	2	8	no	—
101	C₂×#41×C₄₇	C₂×C₄	1	16	yes	complemented
102	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
103	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
104	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
105	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
106	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
107	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
109	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
112	#127×C₄₇	C₂×C₄	1	8	yes	complemented
113	#124×C₄₇	C₂×C₄	1	16	yes	complemented
114	#121×C₄₇	C₂×C₄	1	16	yes	complemented
115	#121×C₄₇	C₂×C₄	1	16	yes	complemented
116	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
117	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
118	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
122	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
123	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
127	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
128	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
129	#41×C₄₇	—	2	64	no	—
130	C₂×Q₈×C₄₇	—	2	4	no	—
131	C₂×Q₈×C₄₇	—	2	4	no	—
132	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
133	C₂×D₄×C₄₇	—	2	8	no	—
134	C₂×D₄×C₄₇	—	2	8	no	—
135	C₂×D₄×C₄₇	—	2	4	no	—
136	C₂×D₄×C₄₇	—	2	4	no	—
137	C₂×D₄×C₄₇	—	2	8	no	—
138	C₂×D₄×C₄₇	—	4	4	no	—
139	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
140	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
141	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
142	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
143	C₂²×C₄×C₄₇	—	2	8	no	—
144	C₂²×C₄×C₄₇	—	2	8	no	—
145	C₂²×C₄×C₄₇	—	2	4	no	—
146	C₂²×C₄×C₄₇	—	4	2	no	—
147	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
149	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
150	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₄₇	#41	1	4	yes	—
153	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
160	C₂²×Dic₄₇	—	2	8	no	—
161	C₂²×Dic₄₇	—	2	16	no	—
162	C₂²×Dic₄₇	—	2	8	no	—
163	C₂²×Dic₄₇	—	2	16	no	—
164	C₂²×Dic₄₇	—	4	8	no	—
165	C₂²×Dic₄₇	—	4	4	no	—
166	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
167	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
168	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
169	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
170	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
171	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
172	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
173	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
174	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
175	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
176	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
177	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
178	C₂²⋊Dic₄₇	—	2	4	no	—
179	C₂²⋊Dic₄₇	—	2	16	no	—
180	C₂²⋊Dic₄₇	—	2	16	no	—
181	C₂²⋊Dic₄₇	—	4	8	no	—
182	C₂²⋊Dic₄₇	C₂×D₄	1	8	yes	—
183	C₄⋊Dic₄₇	—	2	4	no	—
184	C₄⋊Dic₄₇	—	2	4	no	—
185	C₄⋊Dic₄₇	—	2	16	no	—
186	C₄⋊Dic₄₇	—	2	8	no	—
187	C₄⋊Dic₄₇	C₂×D₄	1	8	yes	—
188	C₄⋊Dic₄₇	#41	1	8	yes	complemented
189	C₄×Dic₄₇	—	2	4	no	—
190	C₄×Dic₄₇	—	2	4	no	—
191	C₄×Dic₄₇	—	2	8	no	—
192	C₄×Dic₄₇	—	2	4	no	—
193	C₄×Dic₄₇	—	2	8	no	—
194	C₄×Dic₄₇	—	2	16	no	—
195	C₄×Dic₄₇	—	4	4	no	—
196	C₄×Dic₄₇	C₂×D₄	1	8	yes	—
197	C₂³×C₄₇	—	2	2	no	—
198	C₂³×C₄₇	—	2	2	no	—
199	C₂³×C₄₇	—	2	4	no	—
200	C₂³×C₄₇	—	2	8	no	—
201	C₂³×C₄₇	—	2	4	no	—
202	C₂³×C₄₇	—	2	8	no	—
203	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
204	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
205	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
206	C₂³×C₄₇	C₂×#41	1	2	yes	—
207	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
208	Q₈×C₄₇	—	2	16	no	—
209	D₄×C₄₇	—	2	32	no	—
210	D₄×C₄₇	—	2	16	no	—
211	D₄×C₄₇	—	2	16	no	—
212	D₄×C₄₇	—	4	8	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	2	4	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	32	no	—
219	C₂×C₄×C₄₇	—	2	8	no	—
220	C₂×C₄×C₄₇	—	4	4	no	—
221	C₂×C₄×C₄₇	C₄×D₄	1	16	yes	complemented
222	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
223	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
224	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
225	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
226	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
227	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
228	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
229	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
232	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
233	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
234	C₂×Dic₄₇	—	2	4	no	—
235	C₂×Dic₄₇	—	2	4	no	—
236	C₂×Dic₄₇	—	2	4	no	—
237	C₂×Dic₄₇	—	2	4	no	—
238	C₂×Dic₄₇	—	2	4	no	—
239	C₂×Dic₄₇	—	2	4	no	—
240	C₂×Dic₄₇	—	2	4	no	—
241	C₂×Dic₄₇	—	2	4	no	—
242	C₂×Dic₄₇	—	2	4	no	—
243	C₂×Dic₄₇	—	2	4	no	—
244	C₂×Dic₄₇	—	4	32	no	—
245	C₂×Dic₄₇	—	4	16	no	—
246	C₂×Dic₄₇	C₂²×D₄	1	8	yes	—
247	C₂×Dic₄₇	C₂×#41	1	8	yes	—
248	#34141	—	47	1	no	maximal, Sylow
249	C₂²×C₄₇	—	2	2	no	—
250	C₂²×C₄₇	—	2	2	no	—
251	C₂²×C₄₇	—	2	4	no	—
252	C₂²×C₄₇	—	2	4	no	—
253	C₂²×C₄₇	—	2	8	no	—
254	C₂²×C₄₇	—	2	8	no	—
255	C₂²×C₄₇	—	2	8	no	—
256	C₂²×C₄₇	—	4	8	no	—
257	C₂²×C₄₇	—	4	8	no	—
258	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
259	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
260	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
261	C₂²×C₄₇	C₂²×#41	1	2	yes	—
262	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
263	C₂²×C₄₇	#585	1	2	yes	—
264	C₄×C₄₇	—	2	8	no	—
265	C₄×C₄₇	—	2	2	no	—
266	C₄×C₄₇	—	2	2	no	—
267	C₄×C₄₇	—	2	2	no	—
268	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
269	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
270	C₄×C₄₇	C₄×#41	1	4	yes	complemented
271	Dic₄₇	—	2	8	no	—
272	Dic₄₇	—	2	8	no	—
273	Dic₄₇	—	4	4	no	—
274	Dic₄₇	—	4	4	no	—
275	C₂×#532	D₄₇	1	1	yes	characteristic
276	C₂×C₄×#41	—	47	2	no	—
277	#2367	—	47	4	no	—
278	#2366	—	47	2	no	—
279	#2365	—	47	2	no	—
280	#2364	—	47	4	no	—
281	#2361	—	47	4	no	—
282	#2297	—	47	2	no	—
283	#2293	—	47	2	no	—
284	#2290	—	47	4	no	—
285	C₄²×D₄	—	47	2	no	—
286	C₄×#117	—	47	1	no	—
287	C₂×C₄×C₄⋊C₄	—	47	1	no	—
288	C₂×C₄₇	—	2	4	no	—
289	C₂×C₄₇	—	4	8	no	—
290	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
291	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
292	C₂×C₄₇	#3428	1	1	yes	characteristic
293	C₂×C₄₇	D₄×#41	1	2	yes	—
294	C₂×C₄₇	#3480	1	2	yes	—
295	C₂²×#41	C₂×D₄₇	1	2	yes	—
296	#532	Dic₄₇	1	16	yes	complemented
297	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
298	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
299	C₂×#124	C₂×D₄₇	1	2	yes	—
300	C₂×#121	C₂×D₄₇	1	2	yes	—
301	C₂×#121	C₂×D₄₇	1	2	yes	—
302	C₄×#41	—	94	16	no	—
303	C₂×C₄×Q₈	—	47	4	no	—
304	C₂×C₄×D₄	—	47	8	no	—
305	C₂×C₄×D₄	—	47	4	no	—
306	C₂×C₄×D₄	—	47	4	no	—
307	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
308	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
309	C₂×#117	—	47	1	no	—
310	C₂×#117	—	47	4	no	—
311	C₂×#117	—	47	1	no	—
312	C₂²×C₄⋊C₄	—	47	2	no	—
313	C₂²×C₄²	—	47	2	no	—
314	C₂²×C₄²	—	47	4	no	—
315	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
316	#391	—	47	4	no	—
317	#390	—	47	4	no	—
318	#390	—	47	4	no	—
319	#389	—	47	4	no	—
320	#388	—	47	8	no	—
321	#388	—	47	8	no	—
322	#387	—	47	8	no	—
323	#386	—	47	8	no	—
324	#386	—	47	8	no	—
325	#385	—	47	8	no	—
326	C₄×C₄⋊C₄	—	47	4	no	—
327	C₄×C₄⋊C₄	—	47	2	no	—
328	C₄×C₄⋊C₄	—	47	2	no	—
329	C₄×C₄⋊C₄	—	47	2	no	—
330	C₄×C₄⋊C₄	—	47	2	no	—
331	C₄×C₄⋊C₄	—	47	1	no	—
332	C₄×C₄⋊C₄	—	47	2	no	—
333	C₄×C₄⋊C₄	—	47	1	no	—
334	C₄×C₂²⋊C₄	—	47	2	no	—
335	C₄×C₂²⋊C₄	—	47	2	no	—
336	C₄×C₂²⋊C₄	—	47	4	no	—
337	C₄×C₂²⋊C₄	—	47	4	no	—
338	C₄×C₂²⋊C₄	—	47	8	no	—
339	#376	—	47	2	no	—
340	C₂×#95	—	47	2	no	—
341	C₄³	—	47	2	no	—
342	C₄₇	#34141	1	1	yes	characteristic, complemented, Sylow
343	C₂×#41	—	2	8	no	—
344	C₂×#41	—	2	8	no	—
345	C₂×#41	C₂×Dic₄₇	1	16	yes	complemented
346	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
347	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
348	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
349	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
350	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
351	C₂³×C₄	—	47	4	no	—
352	C₂³×C₄	—	47	8	no	—
353	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
354	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
355	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
356	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
357	C₄⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
358	#127	C₂×Dic₄₇	1	8	yes	complemented
359	#124	C₂×Dic₄₇	1	16	yes	complemented
360	#121	C₂×Dic₄₇	1	16	yes	complemented
361	#121	C₂×Dic₄₇	1	16	yes	complemented
362	C₄×Q₈	—	94	16	no	—
363	C₄×D₄	—	94	32	no	—
364	C₄×D₄	—	94	16	no	—
365	C₄×D₄	—	94	16	no	—
366	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
367	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
368	#117	—	47	8	no	—
369	#117	—	94	16	no	—
370	#117	—	94	4	no	—
371	C₂×C₄⋊C₄	—	47	2	no	—
372	C₂×C₄⋊C₄	—	47	2	no	—
373	C₂×C₄⋊C₄	—	47	4	no	—
374	C₂×C₄⋊C₄	—	47	2	no	—
375	C₂×C₄⋊C₄	—	47	8	no	—
376	C₂×C₄⋊C₄	—	47	2	no	—
377	C₂×C₄⋊C₄	—	94	8	no	—
378	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
379	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
380	C₂×C₂²⋊C₄	—	47	2	no	—
381	C₂×C₂²⋊C₄	—	47	8	no	—
382	C₂×C₂²⋊C₄	—	47	2	no	—
383	C₂×C₂²⋊C₄	—	47	8	no	—
384	C₂×C₂²⋊C₄	—	47	8	no	—
385	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
387	C₂×C₄²	—	47	2	no	—
388	C₂×C₄²	—	47	8	no	—
389	C₂×C₄²	—	47	4	no	—
390	C₂×C₄²	—	47	4	no	—
391	C₂×C₄²	—	47	2	no	—
392	C₂×C₄²	—	47	2	no	—
393	C₂×C₄²	—	47	2	no	—
394	C₂×C₄²	—	47	4	no	—
395	C₂×C₄²	—	94	16	no	—
396	C₂×C₄²	—	94	8	no	—
397	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
398	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
399	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
400	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
401	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
402	#95	—	47	2	no	—
403	#95	—	47	4	no	—
404	#95	—	47	2	no	—
405	#95	—	47	4	no	—
406	#95	—	47	4	no	—
407	#95	—	47	8	no	—
408	#95	—	47	8	no	—
409	C₂⁴	C₂³×D₄₇	1	4	yes	—
410	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
411	#41	—	2	64	no	—
412	C₂×Q₈	—	2	4	no	—
413	C₂×Q₈	—	2	4	no	—
414	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	4	4	no	—
421	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
422	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
423	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
424	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	8	no	—
428	C₂²×C₄	—	4	2	no	—
429	C₂²×C₄	—	47	4	no	—
430	C₂²×C₄	—	47	4	no	—
431	C₂²×C₄	—	47	4	no	—
432	C₂²×C₄	—	47	4	no	—
433	C₂²×C₄	—	94	16	no	—
434	C₂²×C₄	—	94	8	no	—
435	C₂²×C₄	—	94	16	no	—
436	C₂²×C₄	—	94	8	no	—
437	C₂²×C₄	—	188	8	no	—
438	C₂²×C₄	—	188	4	no	—
439	C₂²×C₄	D₄×D₄₇	1	4	yes	—
440	C₂²×C₄	#10625352	1	4	yes	—
441	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
442	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
443	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
444	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
445	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
446	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
447	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
448	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
449	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
450	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
451	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
452	C₄⋊C₄	—	47	8	no	—
453	C₄⋊C₄	—	47	8	no	—
454	C₄⋊C₄	—	94	8	no	—
455	C₄⋊C₄	—	94	16	no	—
456	C₄⋊C₄	—	94	4	no	—
457	C₄⋊C₄	—	94	4	no	—
458	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
459	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
460	C₂²⋊C₄	—	47	8	no	—
461	C₂²⋊C₄	—	94	16	no	—
462	C₂²⋊C₄	—	94	16	no	—
463	C₂²⋊C₄	—	94	4	no	—
464	C₂²⋊C₄	—	188	8	no	—
465	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
466	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
467	C₄²	—	47	8	no	—
468	C₄²	—	94	16	no	—
469	C₄²	—	94	4	no	—
470	C₄²	—	94	4	no	—
471	C₄²	—	94	8	no	—
472	C₄²	—	94	8	no	—
473	C₄²	—	94	4	no	—
474	C₄²	—	188	4	no	—
475	C₄²	C₂²×Dic₄₇	1	4	yes	—
476	C₄²	C₂²×Dic₄₇	1	4	yes	—
477	C₄²	C₂²×Dic₄₇	1	4	yes	—
478	C₄²	C₂²×Dic₄₇	1	4	yes	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	8	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	8	no	—
485	C₂³	C₂³×Dic₄₇	1	8	yes	—
486	C₂³	C₂³×Dic₄₇	1	2	yes	—
487	C₂³	C₂×D₄×D₄₇	1	2	yes	—
488	C₂³	C₂×#10625352	1	2	yes	—
489	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
490	Q₈	—	2	16	no	—
491	D₄	—	2	32	no	—
492	D₄	—	2	16	no	—
493	D₄	—	2	16	no	—
494	D₄	—	4	8	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	32	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	47	8	no	—
504	C₂×C₄	—	47	8	no	—
505	C₂×C₄	—	94	4	no	—
506	C₂×C₄	—	94	4	no	—
507	C₂×C₄	—	94	4	no	—
508	C₂×C₄	—	94	4	no	—
509	C₂×C₄	—	94	4	no	—
510	C₂×C₄	—	94	4	no	—
511	C₂×C₄	—	94	4	no	—
512	C₂×C₄	—	94	4	no	—
513	C₂×C₄	—	94	4	no	—
514	C₂×C₄	—	94	4	no	—
515	C₂×C₄	—	188	32	no	—
516	C₂×C₄	—	188	16	no	—
517	C₂×C₄	D₄×Dic₄₇	1	16	yes	complemented
518	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
519	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
520	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
521	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
522	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
523	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
524	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
525	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
526	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
527	C₂×C₄	#41×D₄₇	1	4	yes	—
528	C₂×C₄	C₂×#10625352	1	2	yes	—
529	C₂×C₄	C₂×#10625352	1	2	yes	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	8	no	—
535	C₂²	—	2	8	no	—
536	C₂²	—	2	8	no	—
537	C₂²	—	4	8	no	—
538	C₂²	—	4	8	no	—
539	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
540	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
541	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
542	C₂²	C₂×#41×D₄₇	1	2	yes	—
543	C₂²	C₂²×#10625352	1	1	yes	characteristic
544	C₂²	#15689959	1	2	yes	—
545	C₄	—	2	8	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	94	8	no	—
550	C₄	—	94	8	no	—
551	C₄	—	188	4	no	—
552	C₄	—	188	4	no	—
553	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
554	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
555	C₄	#41×Dic₄₇	1	4	yes	complemented
556	C₂	—	2	4	no	—
557	C₂	—	4	8	no	—
558	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
559	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
560	C₂	#20256591	1	1	yes	characteristic
561	C₂	#20256874	1	2	yes	—
562	C₂	#20256985	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	#34141
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. #20246463	C₂	semidirect
3. #20246453	C₂	semidirect
4. #20246448	C₂	semidirect
5. #20246440	C₂	semidirect
6. #20246408	C₂	semidirect
7. #20245879	C₂	semidirect
8. #20245853	C₂	semidirect
9. #20245833	C₂	semidirect
10. C₄×D₄×Dic₄₇	C₂	semidirect
11. C₄×#13093983	C₂	semidirect
12. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
52. C₄₇×#532	C₄	semidirect
69. #13093983	D₄	semidirect
101. C₂×#41×C₄₇	C₂×C₄	semidirect
111. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
112. #127×C₄₇	C₂×C₄	semidirect
113. #124×C₄₇	C₂×C₄	semidirect
114. #121×C₄₇	C₂×C₄	semidirect
115. #121×C₄₇	C₂×C₄	semidirect
116. C₄×D₄×C₄₇	C₂×C₄	semidirect
117. C₄×D₄×C₄₇	C₂×C₄	semidirect
122. C₂×C₄²×C₄₇	C₂×C₄	semidirect
188. C₄⋊Dic₄₇	#41	semidirect
221. C₂×C₄×C₄₇	C₄×D₄	semidirect
270. C₄×C₄₇	C₄×#41	semidirect
296. #532	Dic₄₇	semidirect
342. C₄₇	#34141	semidirect
345. C₂×#41	C₂×Dic₄₇	semidirect
357. C₄⋊Q₈	C₂×Dic₄₇	semidirect
358. #127	C₂×Dic₄₇	semidirect
359. #124	C₂×Dic₄₇	semidirect
360. #121	C₂×Dic₄₇	semidirect
361. #121	C₂×Dic₄₇	semidirect
366. C₄×D₄	C₂×Dic₄₇	semidirect
367. C₄×D₄	C₂×Dic₄₇	semidirect
397. C₂×C₄²	C₂×Dic₄₇	semidirect
517. C₂×C₄	D₄×Dic₄₇	semidirect
555. 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
#20246463	2
#20246453	2
#20246448	2
#20246440	2
#20246408	2
#20245879	2
#20245853	2
#20245833	2
C₄×D₄×Dic₄₇	2
C₄×#13093983	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₄₇×#532	2
#34141	47