Subgroups — C₂×#20256810 #27123079

Order 12032.

7994 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256810	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689754	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689738	C₂	1	4	yes	maximal, complemented
4	C₂×#15689724	C₂	1	4	yes	maximal, complemented
5	C₂×#15689711	C₂	1	4	yes	maximal, complemented
6	C₂×#15689704	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689690	C₂	1	2	yes	maximal, complemented
8	C₂×#15689670	C₂	1	4	yes	maximal, complemented
9	C₂×#15689655	C₂	1	4	yes	maximal, complemented
10	C₂×#15689634	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×#10625350	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10625350	C₂²	1	2	yes	—
14	C₂²×#10625350	C₂²	1	4	yes	complemented
15	#15689754	C₂²	1	16	yes	complemented
16	#15689738	C₂²	1	64	yes	complemented
17	#15689724	C₂²	1	64	yes	complemented
18	#15689711	C₂²	1	64	yes	complemented
19	#15689704	C₂²	1	16	yes	complemented
20	#15689690	C₂²	1	32	yes	complemented
21	#15689670	C₂²	1	64	yes	complemented
22	C₂×#13094023	C₂²	1	4	yes	complemented
23	C₂×#13094020	C₂²	1	4	yes	—
24	#15689655	C₂²	1	64	yes	complemented
25	C₂×#13094017	C₂²	1	8	yes	complemented
26	C₂×#13094015	C₂²	1	4	yes	complemented
27	C₂×#13094011	C₂²	1	4	yes	—
28	C₂×#13094010	C₂²	1	8	yes	complemented
29	#15689634	C₂²	1	64	yes	complemented
30	C₂×#13094007	C₂²	1	8	yes	complemented
31	C₂×#13094006	C₂²	1	8	yes	complemented
32	C₂×#13094004	C₂²	1	4	yes	complemented
33	C₂×#13094003	C₂²	1	4	yes	—
34	C₂×#13094003	C₂²	1	4	yes	complemented
35	C₂×#13093999	C₂²	1	4	yes	complemented
36	C₂×#13093998	C₂²	1	4	yes	—
37	C₂×#13093998	C₂²	1	4	yes	complemented
38	C₂×#13093997	C₂²	1	8	yes	complemented
39	C₂×#13093995	C₂²	1	4	yes	—
40	C₂×#13093995	C₂²	1	4	yes	—
41	C₂×#13093993	C₂²	1	8	yes	—
42	C₄×#10625350	C₂²	1	32	yes	complemented
43	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
44	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
45	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
46	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
47	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
48	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
49	C₂×C₄×C₂²⋊D₄₇	C₂²	1	8	yes	complemented
50	C₂×#13093983	C₂²	1	2	yes	—
51	C₂×#13093983	C₂²	1	4	yes	complemented
52	C₂×#13093981	C₂²	1	4	yes	complemented
53	C₂×C₄²×D₄₇	C₂²	1	4	yes	complemented
54	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
55	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	—
57	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	—
58	C₂×C₄×D₄×C₄₇	C₂²	1	16	yes	complemented
59	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
60	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
61	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
62	C₂×#10625350	—	2	16	no	—
63	C₂×#10625350	—	4	16	no	—
64	C₂×#10625350	C₂³	1	16	yes	—
65	C₂×#10625350	C₂³	1	32	yes	complemented
66	C₂²×Dic₉₄	C₂³	1	2	yes	—
67	C₂²×Dic₉₄	C₂³	1	4	yes	—
68	C₂²×D₁₈₈	C₂³	1	2	yes	—
69	C₂²×D₁₈₈	C₂³	1	4	yes	—
70	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
71	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
72	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
73	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
74	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
75	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
76	#13094023	C₂³	1	32	yes	complemented
77	#13094020	C₂³	1	32	yes	—
78	#13094017	C₂³	1	64	yes	complemented
79	#13094015	C₂³	1	32	yes	complemented
80	#13094011	C₂³	1	32	yes	—
81	#13094010	C₂³	1	64	yes	complemented
82	#13094007	C₂³	1	64	yes	complemented
83	#13094006	C₂³	1	64	yes	complemented
84	#13094004	C₂³	1	32	yes	complemented
85	#13094003	C₂³	1	32	yes	—
86	#13094003	C₂³	1	32	yes	complemented
87	#13093999	C₂³	1	32	yes	complemented
88	#13093998	C₂³	1	32	yes	—
89	#13093998	C₂³	1	32	yes	complemented
90	#13093997	C₂³	1	64	yes	complemented
91	#13093995	C₂³	1	32	yes	—
92	#13093995	C₂³	1	32	yes	—
93	#13093993	C₂³	1	64	yes	—
94	C₄×Dic₉₄	C₂³	1	16	yes	complemented
95	C₄×Dic₉₄	C₂³	1	16	yes	complemented
96	C₄×D₁₈₈	C₂³	1	16	yes	complemented
97	C₄×D₁₈₈	C₂³	1	16	yes	complemented
98	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	—
99	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	—
100	C₄×C₂²⋊D₄₇	C₂³	1	64	yes	complemented
101	#13093983	C₂³	1	16	yes	—
102	#13093983	C₂³	1	32	yes	complemented
103	#13093981	C₂³	1	32	yes	complemented
104	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
105	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
106	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
107	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
108	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
109	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
110	C₂×Dic₄₇⋊C₄	C₂³	1	8	yes	—
111	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
112	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
113	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
114	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
115	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
116	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
117	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
118	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
119	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
120	C₄²×D₄₇	C₂³	1	32	yes	complemented
121	C₂⁵×C₄₇	C₂³	1	2	yes	—
122	C₂²×D₄×C₄₇	—	2	8	no	—
123	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
124	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
125	C₂³×C₄×C₄₇	—	4	8	no	—
126	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
128	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
131	C₂³×C₄×C₄₇	C₂³	1	16	yes	—
132	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₄₇	C₂³	1	32	yes	—
134	C₄×D₄×C₄₇	C₂³	1	32	yes	—
135	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
136	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
138	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
139	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
141	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
142	C₂⁴×C₄₇	—	2	8	no	—
143	C₂⁴×C₄₇	—	4	4	no	—
144	C₂⁴×C₄₇	—	4	4	no	—
145	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
146	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
147	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
148	C₂³×D₄₇	C₂⁴	1	4	yes	—
149	C₂×D₄×C₄₇	—	2	16	no	—
150	C₂×D₄×C₄₇	—	2	32	no	—
151	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
152	C₂²×C₄×C₄₇	—	2	4	no	—
153	C₂²×C₄×C₄₇	—	2	16	no	—
154	C₂²×C₄×C₄₇	—	4	32	no	—
155	C₂²×C₄×C₄₇	—	4	4	no	—
156	C₂²×C₄×C₄₇	—	4	8	no	—
157	C₂²×C₄×C₄₇	—	4	2	no	—
158	C₂²×C₄×C₄₇	#41	1	8	yes	complemented
159	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
164	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
166	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
167	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₂×C₂²⋊D₄₇	—	2	16	no	—
171	C₂×C₂²⋊D₄₇	—	4	16	no	—
172	C₂×C₂²⋊D₄₇	—	4	16	no	—
173	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
174	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
175	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
176	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
177	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
178	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
179	#10625350	—	2	64	no	—
180	#10625350	—	4	64	no	—
181	C₂×D₁₈₈	—	2	8	no	—
182	C₂×D₁₈₈	—	4	8	no	—
183	C₂×D₁₈₈	C₂⁴	1	8	yes	—
184	C₂×D₁₈₈	C₂⁴	1	16	yes	—
185	C₂×C₄×D₄₇	—	2	16	no	—
186	C₂×C₄×D₄₇	—	2	16	no	—
187	C₂×C₄×D₄₇	—	4	8	no	—
188	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
189	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
190	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
191	C₂×Dic₉₄	—	2	8	no	—
192	C₂×Dic₉₄	—	4	8	no	—
193	C₂×Dic₉₄	C₂⁴	1	8	yes	—
194	C₂×Dic₉₄	C₂⁴	1	16	yes	—
195	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
196	C₂²⋊C₄×C₄₇	C₂⁴	1	32	yes	—
197	C₄²×C₄₇	C₂⁴	1	8	yes	—
198	C₄²×C₄₇	C₂⁴	1	8	yes	—
199	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
200	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
201	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
202	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
203	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
204	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
205	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
206	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
207	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
208	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
209	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
210	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
211	Dic₄₇⋊C₄	C₂⁴	1	32	yes	—
212	C₄×Dic₄₇	C₂⁴	1	16	yes	—
213	C₄×Dic₄₇	C₂⁴	1	16	yes	—
214	C₄×Dic₄₇	C₂⁴	1	16	yes	—
215	C₂³×C₄₇	—	2	2	no	—
216	C₂³×C₄₇	—	2	2	no	—
217	C₂³×C₄₇	—	2	16	no	—
218	C₂³×C₄₇	—	2	8	no	—
219	C₂³×C₄₇	—	2	8	no	—
220	C₂³×C₄₇	—	2	8	no	—
221	C₂³×C₄₇	—	4	8	no	—
222	C₂³×C₄₇	—	4	8	no	—
223	C₂³×C₄₇	—	4	32	no	—
224	C₂³×C₄₇	C₂×#41	1	4	yes	—
225	C₂³×C₄₇	C₂⁵	1	8	yes	—
226	C₂³×C₄₇	C₂⁵	1	2	yes	—
227	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
228	C₂²×D₄₇	—	2	8	no	—
229	C₂²×D₄₇	—	2	8	no	—
230	C₂²×D₄₇	—	2	8	no	—
231	C₂²×D₄₇	C₂⁵	1	8	yes	—
232	D₄×C₄₇	—	2	32	no	—
233	C₂×C₄×C₄₇	—	2	8	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	4	no	—
236	C₂×C₄×C₄₇	—	2	32	no	—
237	C₂×C₄×C₄₇	—	2	8	no	—
238	C₂×C₄×C₄₇	—	4	8	no	—
239	C₂×C₄×C₄₇	—	4	16	no	—
240	C₂×C₄×C₄₇	—	4	4	no	—
241	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
242	C₂×C₄×C₄₇	C₂×#41	1	16	yes	complemented
243	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
244	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
245	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
246	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
247	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
248	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
249	C₂²⋊D₄₇	—	2	32	no	—
250	C₂²⋊D₄₇	—	4	32	no	—
251	C₂²⋊D₄₇	—	4	32	no	—
252	C₂×Dic₄₇	—	2	8	no	—
253	C₂×Dic₄₇	—	2	8	no	—
254	C₂×Dic₄₇	—	2	8	no	—
255	C₂×Dic₄₇	C₂⁵	1	8	yes	—
256	C₂×Dic₄₇	C₂⁵	1	8	yes	—
257	C₂×Dic₄₇	C₂⁵	1	8	yes	—
258	D₁₈₈	—	2	16	no	—
259	D₁₈₈	—	4	16	no	—
260	C₄×D₄₇	—	2	32	no	—
261	C₄×D₄₇	—	2	32	no	—
262	C₄×D₄₇	—	4	16	no	—
263	Dic₉₄	—	2	16	no	—
264	Dic₉₄	—	4	16	no	—
265	C₂×#3460	—	47	1	no	maximal, Sylow
266	C₂²×C₄₇	—	2	2	no	—
267	C₂²×C₄₇	—	2	2	no	—
268	C₂²×C₄₇	—	2	8	no	—
269	C₂²×C₄₇	—	2	8	no	—
270	C₂²×C₄₇	—	2	8	no	—
271	C₂²×C₄₇	—	2	8	no	—
272	C₂²×C₄₇	—	4	32	no	—
273	C₂²×C₄₇	—	4	16	no	—
274	C₂²×C₄₇	C₂²×#41	1	4	yes	—
275	C₂²×C₄₇	C₂²×#41	1	2	yes	—
276	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
277	C₂²×C₄₇	#585	1	2	yes	—
278	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
279	C₂×D₄₇	—	2	8	no	—
280	C₂×D₄₇	—	2	8	no	—
281	C₂×D₄₇	—	2	8	no	—
282	C₂×D₄₇	—	4	16	no	—
283	C₄×C₄₇	—	2	8	no	—
284	C₄×C₄₇	—	2	2	no	—
285	C₄×C₄₇	—	2	4	no	—
286	C₄×C₄₇	C₂²×#41	1	8	yes	—
287	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
288	Dic₄₇	—	2	8	no	—
289	Dic₄₇	—	2	8	no	—
290	Dic₄₇	—	2	8	no	—
291	#3460	—	47	32	no	—
292	C₂×#544	—	47	1	no	—
293	C₂×#542	—	47	4	no	—
294	C₂×#540	—	47	4	no	—
295	C₂×#538	—	47	4	no	—
296	C₂×#537	—	47	1	no	—
297	C₂×#535	—	47	2	no	—
298	C₂×#532	—	47	4	no	—
299	C₂×#529	—	47	4	no	—
300	C₂×#525	—	47	4	no	—
301	C₂×C₄×#41	—	47	2	no	—
302	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic, complemented
303	C₂×C₄₇	—	2	4	no	—
304	C₂×C₄₇	—	4	8	no	—
305	C₂×C₄₇	#3460	1	4	yes	complemented
306	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
307	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
309	D₄₇	—	4	8	no	—
310	C₂²×#41	—	47	2	no	—
311	C₂²×#41	—	47	4	no	—
312	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
313	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
314	#544	—	47	16	no	—
315	#542	—	47	64	no	—
316	#540	—	47	64	no	—
317	#538	—	47	64	no	—
318	#537	—	47	16	no	—
319	#535	—	47	32	no	—
320	#532	—	47	64	no	—
321	C₂×C₄⋊Q₈	—	47	4	no	—
322	C₂×#127	—	47	4	no	—
323	#529	—	47	64	no	—
324	C₂×#126	—	47	8	no	—
325	C₂×#125	—	47	4	no	—
326	C₂×#124	—	47	4	no	—
327	C₂×#124	—	47	8	no	—
328	#525	—	47	64	no	—
329	C₂×#123	—	47	8	no	—
330	C₂×#123	—	47	8	no	—
331	C₂×C₂²⋊Q₈	—	47	4	no	—
332	C₂×C₂²⋊Q₈	—	47	4	no	—
333	C₂×C₂²⋊Q₈	—	47	4	no	—
334	C₂×#121	—	47	4	no	—
335	C₂×#121	—	47	4	no	—
336	C₂×#121	—	47	4	no	—
337	C₂×#121	—	47	4	no	—
338	C₂×#121	—	47	4	no	—
339	C₂×#121	—	47	8	no	—
340	C₂×#120	—	47	8	no	—
341	C₄×#41	—	47	32	no	—
342	C₂×C₄×Q₈	—	47	2	no	—
343	C₂×C₄×Q₈	—	47	2	no	—
344	C₂×C₄×D₄	—	47	4	no	—
345	C₂×C₄×D₄	—	47	4	no	—
346	C₂×C₄×D₄	—	47	8	no	—
347	C₂×C₄×D₄	—	47	2	no	—
348	C₂×C₄×D₄	—	47	2	no	—
349	C₂×C₄×D₄	C₂×D₄₇	1	4	yes	—
350	C₂×C₄×D₄	C₂×D₄₇	1	4	yes	—
351	C₂×C₄×D₄	C₂×D₄₇	1	16	yes	complemented
352	C₂×#117	—	47	2	no	—
353	C₂×#117	—	47	4	no	—
354	C₂×#117	—	47	4	no	—
355	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
356	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
357	C₂²×C₄²	—	47	4	no	—
358	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
359	C₄₇	C₂×#3460	1	1	yes	characteristic, complemented, Sylow
360	C₂⁵	C₂²×D₄₇	1	2	yes	—
361	C₂×#41	—	47	16	no	—
362	C₂×#41	—	47	32	no	—
363	C₂×#41	—	94	16	no	—
364	C₂×#41	—	188	16	no	—
365	C₂²×Q₈	—	47	2	no	—
366	C₂²×Q₈	—	47	4	no	—
367	C₂²×D₄	—	2	8	no	—
368	C₂²×D₄	—	47	4	no	—
369	C₂²×D₄	—	47	8	no	—
370	C₂²×D₄	—	47	8	no	—
371	C₂²×D₄	—	47	2	no	—
372	C₂²×D₄	—	47	4	no	—
373	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
374	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
375	C₂³×C₄	—	4	8	no	—
376	C₂³×C₄	—	47	4	no	—
377	C₂³×C₄	—	47	4	no	—
378	C₂³×C₄	—	47	4	no	—
379	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
380	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
381	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
382	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
383	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
384	C₂³×C₄	C₂²×D₄₇	1	16	yes	—
385	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
386	C₄⋊Q₈	—	47	32	no	—
387	#127	—	47	32	no	—
388	#126	—	47	64	no	—
389	#125	—	47	32	no	—
390	#124	—	47	32	no	—
391	#124	—	47	64	no	—
392	#123	—	47	64	no	—
393	#123	—	47	64	no	—
394	C₂²⋊Q₈	—	47	32	no	—
395	C₂²⋊Q₈	—	47	32	no	—
396	C₂²⋊Q₈	—	47	32	no	—
397	#121	—	47	32	no	—
398	#121	—	47	32	no	—
399	#121	—	47	32	no	—
400	#121	—	47	32	no	—
401	#121	—	47	32	no	—
402	#121	—	47	64	no	—
403	#120	—	47	64	no	—
404	C₄×Q₈	—	47	16	no	—
405	C₄×Q₈	—	47	16	no	—
406	C₄×D₄	—	47	32	no	—
407	C₄×D₄	—	47	32	no	—
408	C₄×D₄	—	47	64	no	—
409	C₄×D₄	—	47	16	no	—
410	C₄×D₄	—	47	16	no	—
411	C₄×D₄	C₂²×D₄₇	1	32	yes	—
412	C₄×D₄	C₂²×D₄₇	1	32	yes	—
413	#117	—	47	16	no	—
414	#117	—	47	32	no	—
415	#117	—	47	32	no	—
416	C₂×C₄⋊C₄	—	47	2	no	—
417	C₂×C₄⋊C₄	—	47	2	no	—
418	C₂×C₄⋊C₄	—	47	4	no	—
419	C₂×C₄⋊C₄	—	47	4	no	—
420	C₂×C₄⋊C₄	—	47	4	no	—
421	C₂×C₄⋊C₄	—	47	4	no	—
422	C₂×C₄⋊C₄	—	47	8	no	—
423	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
424	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	—
425	C₂×C₂²⋊C₄	—	47	4	no	—
426	C₂×C₂²⋊C₄	—	47	8	no	—
427	C₂×C₂²⋊C₄	—	47	8	no	—
428	C₂×C₂²⋊C₄	—	47	4	no	—
429	C₂×C₂²⋊C₄	—	47	4	no	—
430	C₂×C₂²⋊C₄	—	47	8	no	—
431	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
432	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	—
433	C₂×C₄²	—	47	4	no	—
434	C₂×C₄²	—	47	4	no	—
435	C₂×C₄²	—	47	4	no	—
436	C₂×C₄²	—	47	32	no	—
437	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
438	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
439	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
440	C₂⁴	—	2	8	no	—
441	C₂⁴	—	4	4	no	—
442	C₂⁴	—	4	4	no	—
443	C₂⁴	—	47	4	no	—
444	C₂⁴	C₂³×D₄₇	1	4	yes	—
445	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
446	C₂⁴	C₂³×D₄₇	1	8	yes	—
447	#41	—	94	64	no	—
448	#41	—	188	64	no	—
449	C₂×Q₈	—	47	8	no	—
450	C₂×Q₈	—	47	16	no	—
451	C₂×Q₈	—	94	8	no	—
452	C₂×Q₈	—	188	8	no	—
453	C₂×D₄	—	2	16	no	—
454	C₂×D₄	—	2	32	no	—
455	C₂×D₄	—	47	16	no	—
456	C₂×D₄	—	47	32	no	—
457	C₂×D₄	—	47	32	no	—
458	C₂×D₄	—	47	8	no	—
459	C₂×D₄	—	47	16	no	—
460	C₂×D₄	—	94	16	no	—
461	C₂×D₄	—	94	8	no	—
462	C₂×D₄	—	188	8	no	—
463	C₂×D₄	—	188	16	no	—
464	C₂×D₄	—	188	16	no	—
465	C₂×D₄	C₂³×D₄₇	1	16	yes	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	16	no	—
468	C₂²×C₄	—	4	32	no	—
469	C₂²×C₄	—	4	8	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	47	4	no	—
473	C₂²×C₄	—	47	4	no	—
474	C₂²×C₄	—	47	4	no	—
475	C₂²×C₄	—	47	16	no	—
476	C₂²×C₄	—	47	16	no	—
477	C₂²×C₄	—	47	16	no	—
478	C₂²×C₄	—	94	16	no	—
479	C₂²×C₄	—	94	16	no	—
480	C₂²×C₄	—	188	8	no	—
481	C₂²×C₄	#10625350	1	8	yes	complemented
482	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
483	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
484	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
485	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
486	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
487	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
488	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
489	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
490	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
491	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
492	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
493	C₄⋊C₄	—	47	16	no	—
494	C₄⋊C₄	—	47	16	no	—
495	C₄⋊C₄	—	47	32	no	—
496	C₄⋊C₄	—	47	8	no	—
497	C₄⋊C₄	—	47	8	no	—
498	C₄⋊C₄	—	47	16	no	—
499	C₄⋊C₄	—	47	16	no	—
500	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
501	C₂²⋊C₄	—	47	16	no	—
502	C₂²⋊C₄	—	47	32	no	—
503	C₂²⋊C₄	—	47	32	no	—
504	C₂²⋊C₄	—	47	16	no	—
505	C₂²⋊C₄	—	47	16	no	—
506	C₂²⋊C₄	—	47	32	no	—
507	C₂²⋊C₄	C₂³×D₄₇	1	32	yes	—
508	C₄²	—	47	16	no	—
509	C₄²	—	47	16	no	—
510	C₄²	—	47	16	no	—
511	C₄²	C₂³×D₄₇	1	8	yes	—
512	C₄²	C₂³×D₄₇	1	8	yes	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	16	no	—
516	C₂³	—	2	8	no	—
517	C₂³	—	2	8	no	—
518	C₂³	—	2	8	no	—
519	C₂³	—	4	8	no	—
520	C₂³	—	4	8	no	—
521	C₂³	—	4	32	no	—
522	C₂³	—	47	8	no	—
523	C₂³	—	94	8	no	—
524	C₂³	—	94	8	no	—
525	C₂³	—	94	8	no	—
526	C₂³	C₂×#10625350	1	4	yes	—
527	C₂³	C₂⁴×D₄₇	1	8	yes	—
528	C₂³	C₂⁴×D₄₇	1	2	yes	—
529	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
530	Q₈	—	94	16	no	—
531	Q₈	—	188	16	no	—
532	D₄	—	2	32	no	—
533	D₄	—	94	32	no	—
534	D₄	—	94	16	no	—
535	D₄	—	188	16	no	—
536	D₄	—	188	32	no	—
537	D₄	—	188	32	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	8	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	32	no	—
543	C₂×C₄	—	4	16	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	47	8	no	—
547	C₂×C₄	—	47	8	no	—
548	C₂×C₄	—	47	8	no	—
549	C₂×C₄	—	94	8	no	—
550	C₂×C₄	—	94	8	no	—
551	C₂×C₄	—	94	8	no	—
552	C₂×C₄	—	94	32	no	—
553	C₂×C₄	—	94	32	no	—
554	C₂×C₄	—	188	16	no	—
555	C₂×C₄	C₂×#10625350	1	8	yes	—
556	C₂×C₄	C₂×#10625350	1	16	yes	complemented
557	C₂×C₄	#13094069	1	4	yes	—
558	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
559	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
560	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
561	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
562	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
563	C₂²	—	2	8	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	8	no	—
567	C₂²	—	2	8	no	—
568	C₂²	—	2	8	no	—
569	C₂²	—	4	32	no	—
570	C₂²	—	4	16	no	—
571	C₂²	—	94	8	no	—
572	C₂²	—	94	8	no	—
573	C₂²	—	94	8	no	—
574	C₂²	—	188	16	no	—
575	C₂²	C₂²×#10625350	1	4	yes	—
576	C₂²	C₂²×#10625350	1	2	yes	—
577	C₂²	C₂×#13094069	1	2	yes	—
578	C₂²	#15689959	1	2	yes	—
579	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	8	no	—
582	C₄	—	2	4	no	—
583	C₄	—	94	8	no	—
584	C₄	—	94	8	no	—
585	C₄	—	94	8	no	—
586	C₄	C₂²×#10625350	1	8	yes	—
587	C₄	C₂×#13094069	1	4	yes	—
588	C₂	—	2	4	no	—
589	C₂	—	4	8	no	—
590	C₂	—	188	8	no	—
591	C₂	#20256810	1	4	yes	direct product factor
592	C₂	C₂³×#10625350	1	1	yes	characteristic
593	C₂	C₂²×#13094069	1	1	yes	characteristic
594	C₂	C₂×#15689959	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂×#3460
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #20256810	C₂	direct (N × H)
2. C₂×#15689754	C₂	semidirect
3. C₂×#15689738	C₂	semidirect
4. C₂×#15689724	C₂	semidirect
5. C₂×#15689711	C₂	semidirect
6. C₂×#15689704	C₂	semidirect
7. C₂×#15689690	C₂	semidirect
8. C₂×#15689670	C₂	semidirect
9. C₂×#15689655	C₂	semidirect
10. C₂×#15689634	C₂	semidirect
11. C₂×C₄×#10625350	C₂	semidirect
12. C₂²×C₄×D₄×C₄₇	C₂	semidirect
14. C₂²×#10625350	C₂²	semidirect
15. #15689754	C₂²	semidirect
16. #15689738	C₂²	semidirect
17. #15689724	C₂²	semidirect
18. #15689711	C₂²	semidirect
19. #15689704	C₂²	semidirect
20. #15689690	C₂²	semidirect
21. #15689670	C₂²	semidirect
22. C₂×#13094023	C₂²	semidirect
24. #15689655	C₂²	semidirect
25. C₂×#13094017	C₂²	semidirect
26. C₂×#13094015	C₂²	semidirect
28. C₂×#13094010	C₂²	semidirect
29. #15689634	C₂²	semidirect
30. C₂×#13094007	C₂²	semidirect
31. C₂×#13094006	C₂²	semidirect
32. C₂×#13094004	C₂²	semidirect
34. C₂×#13094003	C₂²	semidirect
35. C₂×#13093999	C₂²	semidirect
37. C₂×#13093998	C₂²	semidirect
38. C₂×#13093997	C₂²	semidirect
42. C₄×#10625350	C₂²	semidirect
43. C₂×C₄×Dic₉₄	C₂²	semidirect
44. C₂×C₄×Dic₉₄	C₂²	semidirect
45. C₂×C₄×D₁₈₈	C₂²	semidirect
46. C₂×C₄×D₁₈₈	C₂²	semidirect
49. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
51. C₂×#13093983	C₂²	semidirect
52. C₂×#13093981	C₂²	semidirect
53. C₂×C₄²×D₄₇	C₂²	semidirect
58. C₂×C₄×D₄×C₄₇	C₂²	semidirect
65. C₂×#10625350	C₂³	semidirect
76. #13094023	C₂³	semidirect
78. #13094017	C₂³	semidirect
79. #13094015	C₂³	semidirect
81. #13094010	C₂³	semidirect
82. #13094007	C₂³	semidirect
83. #13094006	C₂³	semidirect
84. #13094004	C₂³	semidirect
86. #13094003	C₂³	semidirect
87. #13093999	C₂³	semidirect
89. #13093998	C₂³	semidirect
90. #13093997	C₂³	semidirect
94. C₄×Dic₉₄	C₂³	semidirect
95. C₄×Dic₉₄	C₂³	semidirect
96. C₄×D₁₈₈	C₂³	semidirect
97. C₄×D₁₈₈	C₂³	semidirect
100. C₄×C₂²⋊D₄₇	C₂³	semidirect
102. #13093983	C₂³	semidirect
103. #13093981	C₂³	semidirect
120. C₄²×D₄₇	C₂³	semidirect
158. C₂²×C₄×C₄₇	#41	semidirect
242. C₂×C₄×C₄₇	C₂×#41	semidirect
302. C₂²×C₄×D₄	D₄₇	semidirect
305. C₂×C₄₇	#3460	semidirect
351. C₂×C₄×D₄	C₂×D₄₇	semidirect
359. C₄₇	C₂×#3460	semidirect
481. C₂²×C₄	#10625350	semidirect
556. C₂×C₄	C₂×#10625350	semidirect
591. C₂	#20256810	direct (N × H)

Maximal subgroups

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

subgroup	index
#20256810	2
C₂×#15689754	2
C₂×#15689738	2
C₂×#15689724	2
C₂×#15689711	2
C₂×#15689704	2
C₂×#15689690	2
C₂×#15689670	2
C₂×#15689655	2
C₂×#15689634	2
C₂×C₄×#10625350	2
C₂²×C₄×D₄×C₄₇	2
C₂×#3460	47

Subgroups — C2×#20256810 #27123079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20256810 #27123079