Subgroups — #26376645

Order 12032.

3170 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689606	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	#20246337	C₂	1	2	yes	maximal, complemented
6	#20246317	C₂	1	4	yes	maximal, complemented
7	D₄×C₄⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
8	#20246093	C₂	1	4	yes	maximal, complemented
9	#20245980	C₂	1	2	yes	maximal, complemented
10	#121×Dic₄₇	C₂	1	4	yes	maximal, complemented
11	#20245795	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	#15689606	—	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	2	yes	—
20	C₂×#13093983	C₂²	1	4	yes	—
21	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	—
22	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
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	#15688993	C₂²	1	1	yes	characteristic
36	#15688993	C₂²	1	1	yes	characteristic
37	#15688989	C₂²	1	2	yes	—
38	#15688983	C₂²	1	4	yes	—
39	#15688983	C₂²	1	2	yes	—
40	#15688983	C₂²	1	2	yes	—
41	#15688983	C₂²	1	4	yes	—
42	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
43	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
44	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
45	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
46	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
47	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
48	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
49	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	—
50	C₂×C₄₇⋊#95	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	2	yes	—
62	C₂³×Dic₄₇	C₂³	1	8	yes	—
63	C₂³×Dic₄₇	C₂³	1	2	yes	—
64	Q₈×Dic₄₇	—	2	16	no	—
65	D₄×Dic₄₇	—	2	32	no	—
66	D₄×Dic₄₇	—	2	16	no	—
67	D₄×Dic₄₇	—	4	8	no	—
68	#13093983	—	2	8	no	—
69	#13093983	—	2	16	no	—
70	C₂×C₄⋊Dic₄₇	—	2	4	no	—
71	C₂×C₄⋊Dic₄₇	—	2	16	no	—
72	C₂×C₄⋊Dic₄₇	D₄	1	8	yes	complemented
73	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
75	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
76	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
77	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
78	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
79	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
80	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
81	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
82	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
83	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
84	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
85	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
86	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
87	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
88	C₂×C₄×Dic₄₇	—	4	4	no	—
89	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
90	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
91	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
92	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
93	C₄₇⋊#95	C₂³	1	4	yes	—
94	C₄₇⋊#95	C₂³	1	4	yes	—
95	C₄₇⋊#95	C₂³	1	4	yes	—
96	C₄₇⋊#95	C₂³	1	8	yes	—
97	C₄₇⋊#95	C₂³	1	4	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	4	no	—
138	C₂×D₄×C₄₇	—	2	4	no	—
139	C₂×D₄×C₄₇	—	4	2	no	—
140	C₂×D₄×C₄₇	—	4	2	no	—
141	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
142	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
143	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
144	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
145	C₂²×C₄×C₄₇	—	2	8	no	—
146	C₂²×C₄×C₄₇	—	2	8	no	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	2	no	—
149	C₂²×C₄×C₄₇	—	4	1	no	—
150	C₂²×C₄×C₄₇	—	4	1	no	—
151	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
153	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
155	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₄₇	#41	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×C₄×C₄₇	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₂²×Dic₄₇	—	2	4	no	—
165	C₂²×Dic₄₇	—	2	16	no	—
166	C₂²×Dic₄₇	—	4	2	no	—
167	C₂²×Dic₄₇	—	4	2	no	—
168	C₂²×Dic₄₇	—	4	2	no	—
169	C₂²×Dic₄₇	—	4	2	no	—
170	C₂²×Dic₄₇	—	4	8	no	—
171	C₂²×Dic₄₇	—	4	8	no	—
172	C₂²×Dic₄₇	C₂×D₄	1	8	yes	—
173	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
174	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
175	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
176	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
177	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
178	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
179	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
180	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
181	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
182	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
183	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
184	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
185	C₂²⋊Dic₄₇	—	2	8	no	—
186	C₂²⋊Dic₄₇	—	2	16	no	—
187	C₂²⋊Dic₄₇	—	4	8	no	—
188	C₂²⋊Dic₄₇	—	4	8	no	—
189	C₄⋊Dic₄₇	—	2	4	no	—
190	C₄⋊Dic₄₇	—	2	4	no	—
191	C₄⋊Dic₄₇	—	2	4	no	—
192	C₄⋊Dic₄₇	—	2	4	no	—
193	C₄⋊Dic₄₇	—	2	4	no	—
194	C₄⋊Dic₄₇	—	2	4	no	—
195	C₄⋊Dic₄₇	—	2	16	no	—
196	C₄⋊Dic₄₇	—	4	2	no	—
197	C₄⋊Dic₄₇	—	4	2	no	—
198	C₄⋊Dic₄₇	C₂×D₄	1	8	yes	—
199	C₄⋊Dic₄₇	C₂×D₄	1	8	yes	—
200	C₄×Dic₄₇	—	2	8	no	—
201	C₄×Dic₄₇	—	2	8	no	—
202	C₄×Dic₄₇	—	2	16	no	—
203	C₄×Dic₄₇	—	4	4	no	—
204	C₂³×C₄₇	—	2	1	no	—
205	C₂³×C₄₇	—	2	1	no	—
206	C₂³×C₄₇	—	2	1	no	—
207	C₂³×C₄₇	—	2	1	no	—
208	C₂³×C₄₇	—	2	4	no	—
209	C₂³×C₄₇	—	2	4	no	—
210	C₂³×C₄₇	—	2	4	no	—
211	C₂³×C₄₇	—	2	4	no	—
212	C₂³×C₄₇	—	2	4	no	—
213	C₂³×C₄₇	—	2	4	no	—
214	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
215	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
216	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
217	C₂³×C₄₇	C₂×#41	1	2	yes	—
218	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
219	Q₈×C₄₇	—	2	16	no	—
220	D₄×C₄₇	—	2	32	no	—
221	D₄×C₄₇	—	2	16	no	—
222	D₄×C₄₇	—	2	16	no	—
223	D₄×C₄₇	—	4	8	no	—
224	C₂×C₄×C₄₇	—	2	4	no	—
225	C₂×C₄×C₄₇	—	2	4	no	—
226	C₂×C₄×C₄₇	—	2	1	no	—
227	C₂×C₄×C₄₇	—	2	1	no	—
228	C₂×C₄×C₄₇	—	2	1	no	—
229	C₂×C₄×C₄₇	—	2	1	no	—
230	C₂×C₄×C₄₇	—	2	1	no	—
231	C₂×C₄×C₄₇	—	2	1	no	—
232	C₂×C₄×C₄₇	—	2	32	no	—
233	C₂×C₄×C₄₇	—	2	8	no	—
234	C₂×C₄×C₄₇	—	4	4	no	—
235	C₂×C₄×C₄₇	C₄×D₄	1	16	yes	complemented
236	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
237	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
238	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
239	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
240	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
241	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
242	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
243	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
246	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
247	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
248	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
249	C₂×Dic₄₇	—	2	4	no	—
250	C₂×Dic₄₇	—	2	4	no	—
251	C₂×Dic₄₇	—	2	4	no	—
252	C₂×Dic₄₇	—	2	4	no	—
253	C₂×Dic₄₇	—	2	4	no	—
254	C₂×Dic₄₇	—	2	4	no	—
255	C₂×Dic₄₇	—	2	4	no	—
256	C₂×Dic₄₇	—	2	4	no	—
257	C₂×Dic₄₇	—	2	4	no	—
258	C₂×Dic₄₇	—	2	4	no	—
259	C₂×Dic₄₇	—	2	4	no	—
260	C₂×Dic₄₇	—	4	8	no	—
261	C₂×Dic₄₇	—	4	8	no	—
262	C₂×Dic₄₇	—	8	16	no	—
263	C₂×Dic₄₇	C₂²×D₄	1	8	yes	—
264	#34206	—	47	1	no	maximal, Sylow
265	C₂²×C₄₇	—	2	2	no	—
266	C₂²×C₄₇	—	2	2	no	—
267	C₂²×C₄₇	—	2	2	no	—
268	C₂²×C₄₇	—	2	2	no	—
269	C₂²×C₄₇	—	2	2	no	—
270	C₂²×C₄₇	—	2	2	no	—
271	C₂²×C₄₇	—	2	8	no	—
272	C₂²×C₄₇	—	2	8	no	—
273	C₂²×C₄₇	—	2	8	no	—
274	C₂²×C₄₇	—	4	4	no	—
275	C₂²×C₄₇	—	4	4	no	—
276	C₂²×C₄₇	—	4	4	no	—
277	C₂²×C₄₇	—	4	4	no	—
278	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
279	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
280	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
281	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
282	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
283	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
284	C₂²×C₄₇	#585	1	1	yes	characteristic
285	C₂²×C₄₇	#585	1	1	yes	characteristic
286	C₄×C₄₇	—	2	8	no	—
287	C₄×C₄₇	—	2	2	no	—
288	C₄×C₄₇	—	2	2	no	—
289	C₄×C₄₇	—	2	2	no	—
290	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
291	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
292	C₄×C₄₇	#520	1	4	yes	complemented
293	Dic₄₇	—	2	8	no	—
294	Dic₄₇	—	4	4	no	—
295	Dic₄₇	—	4	4	no	—
296	Dic₄₇	—	4	4	no	—
297	C₂×#532	D₄₇	1	1	yes	characteristic
298	C₂×#520	—	47	2	no	—
299	#2367	—	47	4	no	—
300	#2366	—	47	2	no	—
301	#2365	—	47	2	no	—
302	#2354	—	47	2	no	—
303	#2352	—	47	4	no	—
304	D₄×C₄⋊C₄	—	47	2	no	—
305	#2325	—	47	4	no	—
306	#2311	—	47	2	no	—
307	C₄×#121	—	47	4	no	—
308	#2285	—	47	1	no	—
309	C₂×C₄×C₄⋊C₄	—	47	1	no	—
310	C₂×C₄₇	—	2	4	no	—
311	C₂×C₄₇	—	4	8	no	—
312	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
313	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
314	C₂×C₄₇	#3428	1	1	yes	characteristic
315	C₂×C₄₇	#3496	1	1	yes	characteristic
316	C₂×C₄₇	#3497	1	1	yes	characteristic
317	C₂×C₄₇	#3506	1	1	yes	characteristic
318	C₂×C₄₇	#3507	1	1	yes	characteristic
319	C₂²×#41	C₂×D₄₇	1	2	yes	—
320	#532	Dic₄₇	1	16	yes	complemented
321	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
322	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
323	C₂×#124	C₂×D₄₇	1	2	yes	—
324	C₂×#121	C₂×D₄₇	1	2	yes	—
325	C₂×#121	C₂×D₄₇	1	2	yes	—
326	#520	—	94	16	no	—
327	C₂×C₄×Q₈	—	47	4	no	—
328	C₂×C₄×D₄	—	47	8	no	—
329	C₂×C₄×D₄	—	47	4	no	—
330	C₂×C₄×D₄	—	47	4	no	—
331	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
332	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
333	C₂×#117	—	47	2	no	—
334	C₂×#117	—	47	4	no	—
335	C₂²×C₄⋊C₄	—	47	1	no	—
336	C₂²×C₄⋊C₄	—	47	1	no	—
337	C₂²×C₄⋊C₄	—	47	4	no	—
338	C₂²×C₄²	—	47	2	no	—
339	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
340	#391	—	47	4	no	—
341	#390	—	47	4	no	—
342	#390	—	47	4	no	—
343	#389	—	47	4	no	—
344	#388	—	47	8	no	—
345	#388	—	47	8	no	—
346	#387	—	47	8	no	—
347	#386	—	47	8	no	—
348	#386	—	47	8	no	—
349	#385	—	47	8	no	—
350	#384	—	47	1	no	—
351	#384	—	47	1	no	—
352	#382	—	47	2	no	—
353	#380	—	47	4	no	—
354	#380	—	47	4	no	—
355	#380	—	47	2	no	—
356	#380	—	47	2	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×C₄⋊C₄	—	47	2	no	—
362	C₄×C₄⋊C₄	—	47	2	no	—
363	C₄×C₄⋊C₄	—	47	2	no	—
364	C₄×C₂²⋊C₄	—	47	8	no	—
365	C₂×#95	—	47	2	no	—
366	C₄₇	#34206	1	1	yes	characteristic, complemented, Sylow
367	C₂×#41	—	2	8	no	—
368	C₂×#41	—	2	8	no	—
369	C₂×#41	C₂×Dic₄₇	1	16	yes	complemented
370	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
371	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
372	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
373	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
374	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
375	C₂³×C₄	—	47	2	no	—
376	C₂³×C₄	—	47	8	no	—
377	C₂³×C₄	—	47	2	no	—
378	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
379	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
380	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
381	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
382	C₄⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
383	#127	C₂×Dic₄₇	1	8	yes	complemented
384	#124	C₂×Dic₄₇	1	16	yes	complemented
385	#121	C₂×Dic₄₇	1	16	yes	complemented
386	#121	C₂×Dic₄₇	1	16	yes	complemented
387	C₄×Q₈	—	94	16	no	—
388	C₄×D₄	—	94	16	no	—
389	C₄×D₄	—	94	32	no	—
390	C₄×D₄	—	188	8	no	—
391	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
392	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
393	#117	—	94	16	no	—
394	#117	—	94	8	no	—
395	C₂×C₄⋊C₄	—	47	8	no	—
396	C₂×C₄⋊C₄	—	47	2	no	—
397	C₂×C₄⋊C₄	—	47	2	no	—
398	C₂×C₄⋊C₄	—	47	2	no	—
399	C₂×C₄⋊C₄	—	47	8	no	—
400	C₂×C₄⋊C₄	—	47	2	no	—
401	C₂×C₄⋊C₄	—	47	2	no	—
402	C₂×C₄⋊C₄	—	47	2	no	—
403	C₂×C₄⋊C₄	—	47	2	no	—
404	C₂×C₄⋊C₄	—	47	2	no	—
405	C₂×C₄⋊C₄	—	47	2	no	—
406	C₂×C₄⋊C₄	—	47	2	no	—
407	C₂×C₄⋊C₄	—	94	16	no	—
408	C₂×C₄⋊C₄	—	94	4	no	—
409	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
410	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
411	C₂×C₂²⋊C₄	—	47	4	no	—
412	C₂×C₂²⋊C₄	—	47	8	no	—
413	C₂×C₂²⋊C₄	—	47	8	no	—
414	C₂×C₂²⋊C₄	—	47	8	no	—
415	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
417	C₂×C₄²	—	47	8	no	—
418	C₂×C₄²	—	47	4	no	—
419	C₂×C₄²	—	47	4	no	—
420	C₂×C₄²	—	47	4	no	—
421	C₂×C₄²	—	188	4	no	—
422	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
423	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
424	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
425	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
426	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
427	#95	—	47	4	no	—
428	#95	—	47	4	no	—
429	#95	—	47	4	no	—
430	#95	—	47	8	no	—
431	#95	—	47	4	no	—
432	#95	—	47	8	no	—
433	C₂⁴	C₂³×D₄₇	1	4	yes	—
434	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
435	#41	—	2	64	no	—
436	C₂×Q₈	—	2	4	no	—
437	C₂×Q₈	—	2	4	no	—
438	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	4	2	no	—
446	C₂×D₄	—	4	2	no	—
447	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
448	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
449	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
450	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	8	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	47	4	no	—
458	C₂²×C₄	—	47	8	no	—
459	C₂²×C₄	—	47	4	no	—
460	C₂²×C₄	—	47	4	no	—
461	C₂²×C₄	—	47	4	no	—
462	C₂²×C₄	—	94	16	no	—
463	C₂²×C₄	—	94	4	no	—
464	C₂²×C₄	—	188	8	no	—
465	C₂²×C₄	—	188	8	no	—
466	C₂²×C₄	—	188	2	no	—
467	C₂²×C₄	—	188	2	no	—
468	C₂²×C₄	—	188	2	no	—
469	C₂²×C₄	—	188	2	no	—
470	C₂²×C₄	D₄×D₄₇	1	4	yes	—
471	C₂²×C₄	#10625352	1	4	yes	—
472	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
473	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
474	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
475	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
476	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
477	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
478	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
479	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
480	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
481	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
482	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
483	C₄⋊C₄	—	47	8	no	—
484	C₄⋊C₄	—	47	8	no	—
485	C₄⋊C₄	—	94	16	no	—
486	C₄⋊C₄	—	94	4	no	—
487	C₄⋊C₄	—	94	4	no	—
488	C₄⋊C₄	—	94	4	no	—
489	C₄⋊C₄	—	94	4	no	—
490	C₄⋊C₄	—	94	4	no	—
491	C₄⋊C₄	—	94	4	no	—
492	C₄⋊C₄	—	188	2	no	—
493	C₄⋊C₄	—	188	2	no	—
494	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
495	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
496	C₂²⋊C₄	—	94	16	no	—
497	C₂²⋊C₄	—	94	8	no	—
498	C₂²⋊C₄	—	188	8	no	—
499	C₂²⋊C₄	—	188	8	no	—
500	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
501	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
502	C₄²	—	94	16	no	—
503	C₄²	—	94	8	no	—
504	C₄²	—	94	8	no	—
505	C₄²	—	188	4	no	—
506	C₄²	C₂²×Dic₄₇	1	4	yes	—
507	C₄²	C₂²×Dic₄₇	1	4	yes	—
508	C₄²	C₂²×Dic₄₇	1	4	yes	—
509	C₄²	C₂²×Dic₄₇	1	4	yes	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	4	no	—
520	C₂³	C₂³×Dic₄₇	1	8	yes	—
521	C₂³	C₂³×Dic₄₇	1	2	yes	—
522	C₂³	C₂×D₄×D₄₇	1	2	yes	—
523	C₂³	C₂×#10625352	1	2	yes	—
524	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
525	Q₈	—	2	16	no	—
526	D₄	—	2	32	no	—
527	D₄	—	2	16	no	—
528	D₄	—	2	16	no	—
529	D₄	—	4	8	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	32	no	—
539	C₂×C₄	—	2	8	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	47	8	no	—
542	C₂×C₄	—	94	4	no	—
543	C₂×C₄	—	94	4	no	—
544	C₂×C₄	—	94	4	no	—
545	C₂×C₄	—	94	4	no	—
546	C₂×C₄	—	94	4	no	—
547	C₂×C₄	—	94	4	no	—
548	C₂×C₄	—	94	4	no	—
549	C₂×C₄	—	94	4	no	—
550	C₂×C₄	—	94	4	no	—
551	C₂×C₄	—	94	4	no	—
552	C₂×C₄	—	94	4	no	—
553	C₂×C₄	—	376	16	no	—
554	C₂×C₄	—	188	8	no	—
555	C₂×C₄	—	188	8	no	—
556	C₂×C₄	D₄×Dic₄₇	1	16	yes	complemented
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	8	yes	—
561	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
562	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
563	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
564	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
565	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
566	C₂×C₄	C₂×#10625352	1	2	yes	—
567	C₂×C₄	C₂×#10625352	1	2	yes	—
568	C₂×C₄	#13094070	1	2	yes	—
569	C₂×C₄	#13094071	1	2	yes	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	8	no	—
578	C₂²	—	2	8	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	4	no	—
583	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
584	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
585	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
586	C₂²	C₂²×#10625352	1	1	yes	characteristic
587	C₂²	C₂×#13094070	1	1	yes	characteristic
588	C₂²	C₂×#13094071	1	1	yes	characteristic
589	C₂²	#15689959	1	1	yes	characteristic
590	C₂²	#15689959	1	1	yes	characteristic
591	C₄	—	2	8	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	94	8	no	—
596	C₄	—	188	4	no	—
597	C₄	—	188	4	no	—
598	C₄	—	188	4	no	—
599	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
600	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
601	C₄	#15689606	1	4	yes	complemented
602	C₂	—	2	4	no	—
603	C₂	—	4	8	no	—
604	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
605	C₂	C₂×#15689606	1	1	yes	characteristic
606	C₂	#20256591	1	1	yes	characteristic
607	C₂	#20257150	1	1	yes	characteristic
608	C₂	#20257154	1	1	yes	characteristic
609	C₂	#20257237	1	1	yes	characteristic
610	C₂	#20257250	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting, prime radical	C₂×C₄₇×#532	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	#34206
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂×#15689606	C₂	semidirect
2. #20246463	C₂	semidirect
3. #20246453	C₂	semidirect
4. #20246448	C₂	semidirect
5. #20246337	C₂	semidirect
6. #20246317	C₂	semidirect
7. D₄×C₄⋊Dic₄₇	C₂	semidirect
8. #20246093	C₂	semidirect
9. #20245980	C₂	semidirect
10. #121×Dic₄₇	C₂	semidirect
11. #20245795	C₂	semidirect
12. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
52. C₄₇×#532	C₄	semidirect
72. C₂×C₄⋊Dic₄₇	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
235. C₂×C₄×C₄₇	C₄×D₄	semidirect
292. C₄×C₄₇	#520	semidirect
320. #532	Dic₄₇	semidirect
366. C₄₇	#34206	semidirect
369. C₂×#41	C₂×Dic₄₇	semidirect
382. C₄⋊Q₈	C₂×Dic₄₇	semidirect
383. #127	C₂×Dic₄₇	semidirect
384. #124	C₂×Dic₄₇	semidirect
385. #121	C₂×Dic₄₇	semidirect
386. #121	C₂×Dic₄₇	semidirect
391. C₄×D₄	C₂×Dic₄₇	semidirect
392. C₄×D₄	C₂×Dic₄₇	semidirect
422. C₂×C₄²	C₂×Dic₄₇	semidirect
556. C₂×C₄	D₄×Dic₄₇	semidirect
601. C₄	#15689606	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689606	2
#20246463	2
#20246453	2
#20246448	2
#20246337	2
#20246317	2
D₄×C₄⋊Dic₄₇	2
#20246093	2
#20245980	2
#121×Dic₄₇	2
#20245795	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₄₇×#532	2
#34206	47