Subgroups — C₂×#20257287 #27124772

Order 12032.

7302 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	#20257287	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689855	C₂	1	4	yes	maximal, complemented
3	C₂×#15689847	C₂	1	4	yes	maximal, complemented
4	C₂×#15689796	C₂	1	8	yes	maximal, complemented
5	C₂×#15689746	C₂	1	4	yes	maximal, complemented
6	C₂×#15689687	C₂	1	1	yes	maximal, characteristic
7	C₂×#15689676	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15689659	C₂	1	4	yes	maximal, complemented
9	C₂²×#13094013	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15689601	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15689597	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
15	#15689855	C₂²	1	64	yes	complemented
16	#15689847	C₂²	1	64	yes	complemented
17	#15689796	C₂²	1	128	yes	complemented
18	#15689746	C₂²	1	64	yes	complemented
19	#15689687	C₂²	1	16	yes	—
20	#15689676	C₂²	1	16	yes	complemented
21	C₂×#13094023	C₂²	1	2	yes	complemented
22	C₂×#13094020	C₂²	1	2	yes	—
23	#15689659	C₂²	1	64	yes	complemented
24	C₂×#13094019	C₂²	1	8	yes	complemented
25	C₂×#13094019	C₂²	1	8	yes	complemented
26	C₂×#13094015	C₂²	1	2	yes	complemented
27	C₂×#13094013	C₂²	1	2	yes	—
28	C₂×#13094013	C₂²	1	2	yes	—
29	C₂×#13094013	C₂²	1	4	yes	—
30	C₂×#13094013	C₂²	1	2	yes	—
31	C₂×#13094013	C₂²	1	16	yes	complemented
32	C₂×#13094010	C₂²	1	8	yes	complemented
33	C₂×#13094008	C₂²	1	8	yes	complemented
34	C₂×#13094006	C₂²	1	8	yes	complemented
35	C₂×#13094004	C₂²	1	8	yes	complemented
36	C₂×#13094001	C₂²	1	4	yes	—
37	C₂×#13093998	C₂²	1	4	yes	—
38	C₂×#13093992	C₂²	1	4	yes	—
39	#15689601	C₂²	1	16	yes	complemented
40	#15689597	C₂²	1	16	yes	complemented
41	#41×Dic₄₇	C₂²	1	16	yes	complemented
42	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	complemented
43	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
44	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	complemented
45	C₂×C₄×Dic₉₄	C₂²	1	4	yes	complemented
46	C₂×C₄×D₁₈₈	C₂²	1	4	yes	—
47	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
48	C₂×D₄×Dic₄₇	C₂²	1	2	yes	complemented
49	C₂×#13093986	C₂²	1	4	yes	—
50	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	8	yes	complemented
51	C₂×#13093983	C₂²	1	1	yes	characteristic
52	C₂×#13093983	C₂²	1	4	yes	—
53	C₂×#13093983	C₂²	1	1	yes	characteristic
54	C₂×#13093983	C₂²	1	2	yes	complemented
55	C₂×#13093982	C₂²	1	8	yes	complemented
56	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
57	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
58	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
59	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	complemented
60	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
61	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
62	C₄₇×#536	C₂²	1	16	yes	complemented
63	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
64	C₂×#124×C₄₇	C₂²	1	2	yes	complemented
65	C₂×#123×C₄₇	C₂²	1	4	yes	—
66	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	complemented
67	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
68	C₂⁴×D₄₇	C₂³	1	2	yes	—
69	C₂²×Dic₉₄	C₂³	1	4	yes	—
70	C₂²×D₁₈₈	—	2	8	no	—
71	C₂²×D₁₈₈	C₂³	1	2	yes	—
72	C₂²×D₁₈₈	C₂³	1	2	yes	—
73	C₂²×D₁₈₈	C₂³	1	8	yes	—
74	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
75	C₂³×Dic₄₇	C₂³	1	2	yes	—
76	C₂³×Dic₄₇	C₂³	1	4	yes	—
77	C₂²×C₄×D₄₇	C₂³	1	8	yes	—
78	#13094023	C₂³	1	16	yes	complemented
79	#13094020	C₂³	1	16	yes	—
80	#13094019	C₂³	1	64	yes	complemented
81	#13094019	C₂³	1	64	yes	complemented
82	#13094015	C₂³	1	16	yes	complemented
83	#13094013	C₂³	1	16	yes	—
84	#13094013	C₂³	1	16	yes	—
85	#13094013	C₂³	1	32	yes	—
86	#13094013	C₂³	1	16	yes	—
87	#13094010	C₂³	1	64	yes	complemented
88	#13094008	C₂³	1	64	yes	complemented
89	#13094006	C₂³	1	64	yes	complemented
90	#13094004	C₂³	1	64	yes	complemented
91	#13094001	C₂³	1	32	yes	—
92	#13093998	C₂³	1	32	yes	—
93	#13093992	C₂³	1	32	yes	—
94	Q₈×Dic₄₇	C₂³	1	32	yes	complemented
95	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
96	Q₈×Dic₄₇	C₂³	1	32	yes	complemented
97	C₄×Dic₉₄	C₂³	1	32	yes	complemented
98	C₄×D₁₈₈	C₂³	1	32	yes	—
99	D₄×Dic₄₇	C₂³	1	32	yes	—
100	D₄×Dic₄₇	C₂³	1	16	yes	complemented
101	#13093986	C₂³	1	32	yes	—
102	(C₂²⋊D₄₇)⋊C₄	C₂³	1	64	yes	complemented
103	#13093983	C₂³	1	32	yes	—
104	#13093983	C₂³	1	8	yes	—
105	#13093983	C₂³	1	8	yes	—
106	#13093983	C₂³	1	16	yes	complemented
107	#13093982	C₂³	1	64	yes	complemented
108	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
109	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
110	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
111	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
112	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
113	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
114	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
115	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
118	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	32	yes	—
119	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
120	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
121	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
122	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
123	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	—
124	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
125	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
126	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
127	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
128	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
129	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
130	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
131	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
132	C₂×C₄×Dic₄₇	C₂³	1	16	yes	complemented
133	C₂×#41×C₄₇	—	2	8	no	—
134	C₂×#41×C₄₇	C₂³	1	8	yes	—
135	C₂²×Q₈×C₄₇	—	2	8	no	—
136	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
137	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
138	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₄₇	C₂³	1	8	yes	—
140	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
141	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈×C₄₇	C₂³	1	16	yes	complemented
146	#124×C₄₇	C₂³	1	16	yes	complemented
147	#123×C₄₇	C₂³	1	32	yes	—
148	C₂²⋊Q₈×C₄₇	C₂³	1	32	yes	complemented
149	#117×C₄₇	C₂³	1	8	yes	—
150	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
152	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
154	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
155	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
156	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
157	C₂³×D₄₇	—	2	8	no	—
158	C₂³×D₄₇	—	4	8	no	—
159	C₂³×D₄₇	C₂⁴	1	4	yes	—
160	C₂³×D₄₇	C₂⁴	1	8	yes	—
161	#41×C₄₇	—	2	32	no	—
162	C₂×Q₈×C₄₇	—	2	8	no	—
163	C₂×Q₈×C₄₇	—	2	8	no	—
164	C₂×Q₈×C₄₇	—	2	32	no	—
165	C₂×Q₈×C₄₇	—	2	4	no	—
166	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
167	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
168	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
169	C₂×D₄×C₄₇	—	2	8	no	—
170	C₂×D₄×C₄₇	—	2	4	no	—
171	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
172	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₄₇	—	2	8	no	—
174	C₂²×C₄×C₄₇	—	2	8	no	—
175	C₂²×C₄×C₄₇	#41	1	8	yes	—
176	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
180	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
181	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
184	C₂×C₂²⋊D₄₇	—	4	16	no	—
185	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
186	C₂²×Dic₄₇	—	4	4	no	—
187	C₂²×Dic₄₇	—	4	8	no	—
188	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
189	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
190	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
191	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
192	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
193	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
194	C₂×D₁₈₈	—	2	8	no	—
195	C₂×D₁₈₈	—	2	8	no	—
196	C₂×D₁₈₈	—	2	32	no	—
197	C₂×D₁₈₈	C₂⁴	1	8	yes	—
198	C₂×D₁₈₈	C₂⁴	1	8	yes	—
199	C₂×C₄×D₄₇	—	4	16	no	—
200	C₂×C₄×D₄₇	C₂⁴	1	32	yes	—
201	C₂×Dic₉₄	—	4	8	no	—
202	C₂×Dic₉₄	C₂⁴	1	16	yes	—
203	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
204	C₄⋊C₄×C₄₇	C₂⁴	1	32	yes	—
205	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
206	C₂²⋊C₄×C₄₇	C₂⁴	1	32	yes	—
207	C₄²×C₄₇	C₂⁴	1	8	yes	—
208	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
209	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
210	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
211	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
212	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
213	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
214	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
215	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
216	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
217	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
218	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
219	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
220	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
221	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
222	C₄×Dic₄₇	C₂⁴	1	4	yes	—
223	C₄×Dic₄₇	C₂⁴	1	4	yes	—
224	C₄×Dic₄₇	C₂⁴	1	8	yes	—
225	C₄×Dic₄₇	C₂⁴	1	16	yes	—
226	C₄×Dic₄₇	C₂⁴	1	8	yes	—
227	C₄×Dic₄₇	C₂⁴	1	32	yes	—
228	C₄×Dic₄₇	C₂⁴	1	8	yes	—
229	C₂³×C₄₇	—	2	4	no	—
230	C₂³×C₄₇	—	2	4	no	—
231	C₂³×C₄₇	—	2	8	no	—
232	C₂³×C₄₇	C₂×#41	1	4	yes	—
233	C₂³×C₄₇	C₂⁵	1	4	yes	—
234	C₂³×C₄₇	C₂⁵	1	2	yes	—
235	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
236	C₂²×D₄₇	—	2	8	no	—
237	C₂²×D₄₇	—	2	16	no	—
238	C₂²×D₄₇	—	2	16	no	—
239	C₂²×D₄₇	—	4	16	no	—
240	C₂²×D₄₇	—	8	16	no	—
241	C₂²×D₄₇	C₂⁵	1	8	yes	—
242	Q₈×C₄₇	—	2	16	no	—
243	Q₈×C₄₇	—	2	16	no	—
244	Q₈×C₄₇	—	2	8	no	—
245	D₄×C₄₇	—	2	16	no	—
246	D₄×C₄₇	—	2	8	no	—
247	C₂×C₄×C₄₇	—	2	4	no	—
248	C₂×C₄×C₄₇	—	2	16	no	—
249	C₂×C₄×C₄₇	—	2	8	no	—
250	C₂×C₄×C₄₇	—	2	8	no	—
251	C₂×C₄×C₄₇	—	2	16	no	—
252	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
253	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
254	C₂×C₄×C₄₇	C₂×#41	1	16	yes	—
255	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
256	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
257	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
258	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
259	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
260	C₂²⋊D₄₇	—	4	32	no	—
261	C₂×Dic₄₇	—	2	4	no	—
262	C₂×Dic₄₇	—	2	8	no	—
263	C₂×Dic₄₇	—	2	8	no	—
264	C₂×Dic₄₇	—	2	4	no	—
265	C₂×Dic₄₇	—	4	8	no	—
266	C₂×Dic₄₇	—	4	16	no	—
267	C₂×Dic₄₇	C₂⁵	1	4	yes	—
268	C₂×Dic₄₇	C₂⁵	1	8	yes	—
269	C₂×Dic₄₇	C₂⁵	1	8	yes	—
270	C₂×Dic₄₇	C₂⁵	1	4	yes	—
271	D₁₈₈	—	2	16	no	—
272	D₁₈₈	—	2	16	no	—
273	C₄×D₄₇	—	4	32	no	—
274	Dic₉₄	—	4	16	no	—
275	C₂×#3510	—	47	1	no	maximal, Sylow
276	C₂²×C₄₇	—	2	4	no	—
277	C₂²×C₄₇	—	2	8	no	—
278	C₂²×C₄₇	—	2	4	no	—
279	C₂²×C₄₇	—	2	8	no	—
280	C₂²×C₄₇	—	4	8	no	—
281	C₂²×C₄₇	C₂²×#41	1	4	yes	—
282	C₂²×C₄₇	C₂²×#41	1	2	yes	—
283	C₂²×C₄₇	#585	1	4	yes	—
284	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
285	C₂×D₄₇	—	2	8	no	—
286	C₂×D₄₇	—	2	16	no	—
287	C₂×D₄₇	—	4	16	no	—
288	C₂×D₄₇	—	8	16	no	—
289	C₄×C₄₇	—	2	4	no	—
290	C₄×C₄₇	—	2	8	no	—
291	C₄×C₄₇	—	2	8	no	—
292	C₄×C₄₇	C₂²×#41	1	4	yes	—
293	C₄×C₄₇	C₂²×#41	1	4	yes	—
294	Dic₄₇	—	2	4	no	—
295	Dic₄₇	—	2	8	no	—
296	Dic₄₇	—	2	8	no	—
297	Dic₄₇	—	2	4	no	—
298	#3510	—	47	32	no	—
299	C₂×#559	—	47	4	no	—
300	C₂×#556	—	47	4	no	—
301	C₂×#551	—	47	8	no	—
302	C₂×#542	—	47	4	no	—
303	C₂×#536	D₄₇	1	1	yes	characteristic, complemented
304	C₂×#535	—	47	1	no	—
305	C₂×#533	—	47	1	no	—
306	C₂×#529	—	47	4	no	—
307	C₂²×#124	—	47	1	no	—
308	C₂×#519	—	47	1	no	—
309	C₂×#518	—	47	1	no	—
310	C₂×C₄×#41	—	47	1	no	—
311	C₂×C₄₇	—	2	4	no	—
312	C₂×C₄₇	—	4	4	no	—
313	C₂×C₄₇	#3510	1	4	yes	complemented
314	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
315	C₂×C₄₇	C₂×#585	1	2	yes	—
316	D₄₇	—	4	8	no	—
317	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
318	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
319	C₂³×D₄	—	47	1	no	—
320	#559	—	47	64	no	—
321	#556	—	47	64	no	—
322	#551	—	47	128	no	—
323	#542	—	47	64	no	—
324	#536	C₂×D₄₇	1	16	yes	complemented
325	#535	—	47	16	no	—
326	#533	—	47	16	no	—
327	C₂×C₄⋊Q₈	—	47	2	no	—
328	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	complemented
329	C₂×#127	—	47	2	no	—
330	#529	—	47	64	no	—
331	C₂×#126	—	47	8	no	—
332	C₂×#126	—	47	8	no	—
333	C₂×#125	—	47	2	no	—
334	C₂×#124	—	47	2	no	—
335	C₂×#124	—	47	2	no	—
336	C₂×#124	—	47	4	no	—
337	C₂×#124	—	47	16	no	—
338	C₂×#124	—	47	2	no	—
339	C₂×#124	—	47	8	no	—
340	C₂×#124	C₂×D₄₇	1	2	yes	complemented
341	C₂×#123	—	47	8	no	—
342	C₂×#123	—	47	8	no	—
343	C₂×#123	C₂×D₄₇	1	4	yes	—
344	C₂×C₂²⋊Q₈	—	47	8	no	—
345	C₂×C₂²⋊Q₈	—	47	4	no	—
346	C₂×C₂²⋊Q₈	C₂×D₄₇	1	4	yes	complemented
347	C₂×#121	—	47	4	no	—
348	C₂×#120	—	47	4	no	—
349	#519	—	47	16	no	—
350	#518	—	47	16	no	—
351	C₄×#41	—	47	16	no	—
352	C₂×C₄×Q₈	—	47	2	no	—
353	C₂×C₄×Q₈	—	47	4	no	—
354	C₂×C₄×Q₈	—	47	4	no	—
355	C₂×C₄×Q₈	—	47	4	no	—
356	C₂×C₄×D₄	—	47	4	no	—
357	C₂×C₄×D₄	—	47	2	no	—
358	C₂×C₄×D₄	—	47	4	no	—
359	C₂×C₄×D₄	—	47	8	no	—
360	C₂×C₄×D₄	—	47	4	no	—
361	C₂×#117	—	47	1	no	—
362	C₂×#117	—	47	2	no	—
363	C₂×#117	—	47	1	no	—
364	C₂×#117	—	47	4	no	—
365	C₂×#117	—	47	8	no	—
366	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	—	47	4	no	—
368	C₂²×C₂²⋊C₄	—	47	4	no	—
369	C₂²×C₄²	—	47	1	no	—
370	C₂²×C₄²	—	47	2	no	—
371	C₄₇	C₂×#3510	1	1	yes	characteristic, complemented, Sylow
372	C₂⁵	—	47	2	no	—
373	C₂×#41	—	2	8	no	—
374	C₂×#41	C₂²×D₄₇	1	8	yes	—
375	C₂²×Q₈	—	2	8	no	—
376	C₂²×Q₈	—	47	4	no	—
377	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
378	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
379	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
380	C₂²×Q₈	C₂²×D₄₇	1	8	yes	—
381	C₂²×D₄	—	47	8	no	—
382	C₂²×D₄	—	47	2	no	—
383	C₂²×D₄	—	47	2	no	—
384	C₂²×D₄	—	47	8	no	—
385	C₂²×D₄	—	94	8	no	—
386	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
387	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
388	C₂³×C₄	—	47	2	no	—
389	C₂³×C₄	—	47	4	no	—
390	C₂³×C₄	—	47	8	no	—
391	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
392	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
393	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
394	C₄⋊Q₈	—	47	16	no	—
395	C₄⋊Q₈	C₂²×D₄₇	1	16	yes	complemented
396	#127	—	47	16	no	—
397	#126	—	47	64	no	—
398	#126	—	47	64	no	—
399	#125	—	47	16	no	—
400	#124	—	47	16	no	—
401	#124	—	47	16	no	—
402	#124	—	47	32	no	—
403	#124	—	47	16	no	—
404	#124	—	47	64	no	—
405	#124	C₂²×D₄₇	1	16	yes	complemented
406	#123	—	47	64	no	—
407	#123	—	47	64	no	—
408	#123	C₂²×D₄₇	1	32	yes	—
409	C₂²⋊Q₈	—	47	64	no	—
410	C₂²⋊Q₈	—	47	32	no	—
411	C₂²⋊Q₈	C₂²×D₄₇	1	32	yes	complemented
412	#121	—	47	32	no	—
413	#120	—	47	32	no	—
414	C₄×Q₈	—	47	16	no	—
415	C₄×Q₈	—	47	32	no	—
416	C₄×Q₈	—	47	32	no	—
417	C₄×Q₈	—	47	32	no	—
418	C₄×D₄	—	47	32	no	—
419	C₄×D₄	—	47	16	no	—
420	C₄×D₄	—	47	32	no	—
421	C₄×D₄	—	47	64	no	—
422	C₄×D₄	—	47	32	no	—
423	#117	—	47	8	no	—
424	#117	—	47	16	no	—
425	#117	—	47	8	no	—
426	#117	—	47	32	no	—
427	#117	—	47	64	no	—
428	#117	C₂²×D₄₇	1	8	yes	—
429	C₂×C₄⋊C₄	—	47	4	no	—
430	C₂×C₄⋊C₄	—	47	2	no	—
431	C₂×C₄⋊C₄	—	47	4	no	—
432	C₂×C₄⋊C₄	—	47	2	no	—
433	C₂×C₄⋊C₄	—	47	8	no	—
434	C₂×C₄⋊C₄	—	47	4	no	—
435	C₂×C₄⋊C₄	—	47	4	no	—
436	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	—
437	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
438	C₂×C₂²⋊C₄	—	47	2	no	—
439	C₂×C₂²⋊C₄	—	47	2	no	—
440	C₂×C₂²⋊C₄	—	47	4	no	—
441	C₂×C₂²⋊C₄	—	47	8	no	—
442	C₂×C₂²⋊C₄	—	47	8	no	—
443	C₂×C₂²⋊C₄	—	47	8	no	—
444	C₂×C₂²⋊C₄	—	47	32	no	—
445	C₂×C₂²⋊C₄	—	47	8	no	—
446	C₂×C₂²⋊C₄	—	47	32	no	—
447	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
449	C₂×C₄²	—	47	2	no	—
450	C₂×C₄²	—	47	8	no	—
451	C₂×C₄²	—	47	4	no	—
452	C₂×C₄²	—	47	1	no	—
453	C₂×C₄²	—	47	2	no	—
454	C₂×C₄²	—	47	2	no	—
455	C₂×C₄²	—	47	8	no	—
456	C₂×C₄²	—	47	16	no	—
457	C₂×C₄²	—	47	1	no	—
458	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
459	C₂⁴	—	47	4	no	—
460	C₂⁴	—	47	8	no	—
461	C₂⁴	—	94	8	no	—
462	C₂⁴	—	188	8	no	—
463	C₂⁴	C₂³×D₄₇	1	2	yes	—
464	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
465	#41	—	2	32	no	—
466	C₂×Q₈	—	2	8	no	—
467	C₂×Q₈	—	2	8	no	—
468	C₂×Q₈	—	2	32	no	—
469	C₂×Q₈	—	2	4	no	—
470	C₂×Q₈	—	47	16	no	—
471	C₂×Q₈	—	188	8	no	—
472	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
473	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
474	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
475	C₂×D₄	—	2	8	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	47	32	no	—
478	C₂×D₄	—	47	8	no	—
479	C₂×D₄	—	47	8	no	—
480	C₂×D₄	—	94	8	no	—
481	C₂×D₄	—	94	8	no	—
482	C₂×D₄	—	94	32	no	—
483	C₂×D₄	—	188	16	no	—
484	C₂×D₄	C₂³×D₄₇	1	8	yes	—
485	C₂×D₄	C₂³×D₄₇	1	4	yes	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	47	2	no	—
489	C₂²×C₄	—	47	4	no	—
490	C₂²×C₄	—	47	4	no	—
491	C₂²×C₄	—	47	2	no	—
492	C₂²×C₄	—	47	8	no	—
493	C₂²×C₄	—	47	16	no	—
494	C₂²×C₄	—	47	32	no	—
495	C₂²×C₄	—	188	16	no	—
496	C₂²×C₄	—	188	8	no	—
497	C₂²×C₄	—	188	4	no	—
498	C₂²×C₄	#10625352	1	8	yes	—
499	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
500	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
501	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
502	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
503	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
504	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
505	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
506	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
507	C₄⋊C₄	—	47	16	no	—
508	C₄⋊C₄	—	47	16	no	—
509	C₄⋊C₄	—	47	16	no	—
510	C₄⋊C₄	—	47	8	no	—
511	C₄⋊C₄	—	47	16	no	—
512	C₄⋊C₄	—	47	8	no	—
513	C₄⋊C₄	—	47	32	no	—
514	C₄⋊C₄	C₂³×D₄₇	1	32	yes	—
515	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
516	C₂²⋊C₄	—	47	8	no	—
517	C₂²⋊C₄	—	47	8	no	—
518	C₂²⋊C₄	—	47	16	no	—
519	C₂²⋊C₄	—	47	32	no	—
520	C₂²⋊C₄	—	47	32	no	—
521	C₂²⋊C₄	—	47	32	no	—
522	C₂²⋊C₄	—	47	32	no	—
523	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
524	C₂²⋊C₄	C₂³×D₄₇	1	32	yes	—
525	C₄²	—	47	4	no	—
526	C₄²	—	47	8	no	—
527	C₄²	—	47	16	no	—
528	C₄²	—	47	4	no	—
529	C₄²	—	47	8	no	—
530	C₄²	—	47	32	no	—
531	C₄²	—	47	8	no	—
532	C₄²	C₂³×D₄₇	1	8	yes	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	8	no	—
536	C₂³	—	47	8	no	—
537	C₂³	—	94	16	no	—
538	C₂³	—	94	8	no	—
539	C₂³	—	94	16	no	—
540	C₂³	—	376	16	no	—
541	C₂³	—	188	16	no	—
542	C₂³	C₂×#10625352	1	4	yes	—
543	C₂³	C₂⁴×D₄₇	1	4	yes	—
544	C₂³	C₂⁴×D₄₇	1	2	yes	—
545	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
546	Q₈	—	2	16	no	—
547	Q₈	—	2	16	no	—
548	Q₈	—	2	8	no	—
549	Q₈	—	188	16	no	—
550	D₄	—	2	16	no	—
551	D₄	—	2	8	no	—
552	D₄	—	94	16	no	—
553	D₄	—	94	16	no	—
554	D₄	—	188	32	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	16	no	—
560	C₂×C₄	—	47	4	no	—
561	C₂×C₄	—	47	8	no	—
562	C₂×C₄	—	47	8	no	—
563	C₂×C₄	—	47	4	no	—
564	C₂×C₄	—	94	8	no	—
565	C₂×C₄	—	94	4	no	—
566	C₂×C₄	—	94	4	no	—
567	C₂×C₄	—	94	8	no	—
568	C₂×C₄	—	188	32	no	—
569	C₂×C₄	—	188	16	no	—
570	C₂×C₄	—	188	8	no	—
571	C₂×C₄	C₂×#10625352	1	4	yes	—
572	C₂×C₄	C₂×#10625352	1	4	yes	—
573	C₂×C₄	C₂×#10625352	1	16	yes	—
574	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
575	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
576	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
577	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
578	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	8	no	—
583	C₂²	—	4	8	no	—
584	C₂²	—	94	8	no	—
585	C₂²	—	94	16	no	—
586	C₂²	—	376	16	no	—
587	C₂²	—	188	16	no	—
588	C₂²	C₂²×#10625352	1	4	yes	—
589	C₂²	C₂²×#10625352	1	2	yes	—
590	C₂²	#15689960	1	4	yes	—
591	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	2	8	no	—
594	C₄	—	2	8	no	—
595	C₄	—	94	8	no	—
596	C₄	—	94	4	no	—
597	C₄	—	94	4	no	—
598	C₄	—	94	8	no	—
599	C₄	C₂²×#10625352	1	4	yes	—
600	C₄	C₂²×#10625352	1	4	yes	—
601	C₂	—	2	4	no	—
602	C₂	—	4	4	no	—
603	C₂	—	188	8	no	—
604	C₂	#20257287	1	4	yes	direct product factor
605	C₂	C₂³×#10625352	1	1	yes	characteristic
606	C₂	C₂×#15689960	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#536	C₂
socle	C₂³×C₄₇	C₂⁵
prime radical	C₂×#15689687	C₂
hypercenter	C₂×#536	D₄₇
hypocenter	C₄₇	C₂×#3510
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#536

Complements

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

N	H ≅ G/N	type
1. #20257287	C₂	direct (N × H)
2. C₂×#15689855	C₂	semidirect
3. C₂×#15689847	C₂	semidirect
4. C₂×#15689796	C₂	semidirect
5. C₂×#15689746	C₂	semidirect
7. C₂×#15689676	C₂	semidirect
8. C₂×#15689659	C₂	semidirect
9. C₂²×#13094013	C₂	semidirect
10. C₂×#15689601	C₂	semidirect
11. C₂×#15689597	C₂	semidirect
12. C₂×#41×Dic₄₇	C₂	semidirect
13. C₂×C₄₇×#536	C₂	semidirect
15. #15689855	C₂²	semidirect
16. #15689847	C₂²	semidirect
17. #15689796	C₂²	semidirect
18. #15689746	C₂²	semidirect
20. #15689676	C₂²	semidirect
21. C₂×#13094023	C₂²	semidirect
23. #15689659	C₂²	semidirect
24. C₂×#13094019	C₂²	semidirect
25. C₂×#13094019	C₂²	semidirect
26. C₂×#13094015	C₂²	semidirect
31. C₂×#13094013	C₂²	semidirect
32. C₂×#13094010	C₂²	semidirect
33. C₂×#13094008	C₂²	semidirect
34. C₂×#13094006	C₂²	semidirect
35. C₂×#13094004	C₂²	semidirect
39. #15689601	C₂²	semidirect
40. #15689597	C₂²	semidirect
41. #41×Dic₄₇	C₂²	semidirect
42. C₂×Q₈×Dic₄₇	C₂²	semidirect
43. C₂×Q₈×Dic₄₇	C₂²	semidirect
44. C₂×Q₈×Dic₄₇	C₂²	semidirect
45. C₂×C₄×Dic₉₄	C₂²	semidirect
48. C₂×D₄×Dic₄₇	C₂²	semidirect
50. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
54. C₂×#13093983	C₂²	semidirect
55. C₂×#13093982	C₂²	semidirect
59. C₂²×C₄×Dic₄₇	C₂²	semidirect
62. C₄₇×#536	C₂²	semidirect
63. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
64. C₂×#124×C₄₇	C₂²	semidirect
66. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
78. #13094023	C₂³	semidirect
80. #13094019	C₂³	semidirect
81. #13094019	C₂³	semidirect
82. #13094015	C₂³	semidirect
87. #13094010	C₂³	semidirect
88. #13094008	C₂³	semidirect
89. #13094006	C₂³	semidirect
90. #13094004	C₂³	semidirect
94. Q₈×Dic₄₇	C₂³	semidirect
95. Q₈×Dic₄₇	C₂³	semidirect
96. Q₈×Dic₄₇	C₂³	semidirect
97. C₄×Dic₉₄	C₂³	semidirect
100. D₄×Dic₄₇	C₂³	semidirect
102. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
106. #13093983	C₂³	semidirect
107. #13093982	C₂³	semidirect
132. C₂×C₄×Dic₄₇	C₂³	semidirect
145. C₄⋊Q₈×C₄₇	C₂³	semidirect
146. #124×C₄₇	C₂³	semidirect
148. C₂²⋊Q₈×C₄₇	C₂³	semidirect
303. C₂×#536	D₄₇	semidirect
313. C₂×C₄₇	#3510	semidirect
324. #536	C₂×D₄₇	semidirect
328. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
340. C₂×#124	C₂×D₄₇	semidirect
346. C₂×C₂²⋊Q₈	C₂×D₄₇	semidirect
371. C₄₇	C₂×#3510	semidirect
395. C₄⋊Q₈	C₂²×D₄₇	semidirect
405. #124	C₂²×D₄₇	semidirect
411. C₂²⋊Q₈	C₂²×D₄₇	semidirect
604. C₂	#20257287	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257287	2
C₂×#15689855	2
C₂×#15689847	2
C₂×#15689796	2
C₂×#15689746	2
C₂×#15689687	2
C₂×#15689676	2
C₂×#15689659	2
C₂²×#13094013	2
C₂×#15689601	2
C₂×#15689597	2
C₂×#41×Dic₄₇	2
C₂×C₄₇×#536	2
C₂×#3510	47

Subgroups — C2×#20257287 #27124772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257287 #27124772