Subgroups — C₂×#20257721 #27123871

Order 12032.

8814 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257721	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689860	C₂	1	4	yes	maximal, complemented
3	C₂×#15689859	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689793	C₂	1	2	yes	maximal, complemented
5	C₂×#15689767	C₂	1	4	yes	maximal, complemented
6	C₂×#15689758	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄×C₂²⋊D₄₇	C₂	1	4	yes	maximal, complemented
8	C₂×#15689727	C₂	1	4	yes	maximal, complemented
9	C₂×#15689686	C₂	1	4	yes	maximal, complemented
10	C₂×#15689682	C₂	1	4	yes	maximal, complemented
11	C₂×#15689657	C₂	1	2	yes	maximal, complemented
12	C₂²×#127×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10625352	C₂²	1	4	yes	complemented
14	C₂³×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
15	C₂²×D₄×D₄₇	C₂²	1	4	yes	complemented
16	#15689860	C₂²	1	64	yes	complemented
17	#15689859	C₂²	1	16	yes	complemented
18	#15689793	C₂²	1	32	yes	complemented
19	#15689767	C₂²	1	64	yes	complemented
20	#15689758	C₂²	1	16	yes	complemented
21	D₄×C₂²⋊D₄₇	C₂²	1	64	yes	complemented
22	#15689727	C₂²	1	64	yes	complemented
23	#15689686	C₂²	1	64	yes	complemented
24	#15689682	C₂²	1	64	yes	complemented
25	C₂×#13094020	C₂²	1	4	yes	complemented
26	#15689657	C₂²	1	32	yes	complemented
27	C₂×#13094018	C₂²	1	4	yes	complemented
28	C₂×#13094016	C₂²	1	2	yes	complemented
29	C₂×#13094012	C₂²	1	2	yes	complemented
30	C₂×#13094011	C₂²	1	4	yes	complemented
31	C₂×#13094007	C₂²	1	4	yes	complemented
32	C₂×#13094005	C₂²	1	8	yes	complemented
33	C₂×#13094005	C₂²	1	4	yes	complemented
34	C₂×#13094005	C₂²	1	4	yes	complemented
35	C₂×#13094003	C₂²	1	2	yes	complemented
36	C₂×#13093998	C₂²	1	2	yes	—
37	C₂×#13093996	C₂²	1	8	yes	complemented
38	C₂×#13093996	C₂²	1	8	yes	complemented
39	C₂×#13093996	C₂²	1	8	yes	complemented
40	C₂×#13093996	C₂²	1	8	yes	complemented
41	C₂×#13093995	C₂²	1	4	yes	complemented
42	C₂×#13093995	C₂²	1	4	yes	complemented
43	C₂×#13093993	C₂²	1	8	yes	complemented
44	C₂×#13093992	C₂²	1	8	yes	complemented
45	C₂×#13093992	C₂²	1	4	yes	complemented
46	C₂×#13093992	C₂²	1	4	yes	complemented
47	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
48	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
49	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
50	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
51	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
52	C₂×#13093981	C₂²	1	4	yes	complemented
53	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
54	C₂³×D₄×C₄₇	C₂²	1	4	yes	complemented
55	C₂³×D₄×C₄₇	C₂²	1	2	yes	complemented
56	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×#127×C₄₇	C₂²	1	4	yes	complemented
59	C₂×#127×C₄₇	C₂²	1	2	yes	complemented
60	C₂×#127×C₄₇	C₂²	1	16	yes	complemented
61	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic, complemented
62	C₂⁴×D₄₇	C₂³	1	4	yes	—
63	C₂×#10625352	—	4	16	no	—
64	C₂×#10625352	C₂³	1	32	yes	complemented
65	C₂²×Dic₉₄	C₂³	1	2	yes	—
66	C₂²×D₁₈₈	C₂³	1	2	yes	—
67	C₂²×C₂²⋊D₄₇	—	4	16	no	—
68	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
69	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
70	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
71	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
72	C₂²×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
73	C₂×D₄×D₄₇	—	4	16	no	—
74	C₂×D₄×D₄₇	C₂³	1	32	yes	complemented
75	C₂³×Dic₄₇	C₂³	1	8	yes	—
76	C₂³×Dic₄₇	C₂³	1	4	yes	—
77	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
78	#13094020	C₂³	1	32	yes	complemented
79	#13094018	C₂³	1	32	yes	complemented
80	#13094016	C₂³	1	16	yes	complemented
81	#13094012	C₂³	1	16	yes	complemented
82	#13094011	C₂³	1	32	yes	complemented
83	#13094007	C₂³	1	32	yes	complemented
84	#13094005	C₂³	1	64	yes	complemented
85	#13094005	C₂³	1	32	yes	complemented
86	#13094005	C₂³	1	32	yes	complemented
87	#13094003	C₂³	1	16	yes	complemented
88	#13093998	C₂³	1	16	yes	—
89	#13093996	C₂³	1	64	yes	complemented
90	#13093996	C₂³	1	64	yes	complemented
91	#13093996	C₂³	1	64	yes	complemented
92	#13093996	C₂³	1	64	yes	complemented
93	#13093995	C₂³	1	32	yes	complemented
94	#13093995	C₂³	1	32	yes	complemented
95	#13093993	C₂³	1	64	yes	complemented
96	#13093992	C₂³	1	64	yes	complemented
97	#13093992	C₂³	1	32	yes	complemented
98	#13093992	C₂³	1	32	yes	complemented
99	C₄×Dic₉₄	C₂³	1	16	yes	complemented
100	C₄×D₁₈₈	C₂³	1	16	yes	complemented
101	D₄×Dic₄₇	C₂³	1	32	yes	complemented
102	D₄×Dic₄₇	C₂³	1	32	yes	complemented
103	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
104	#13093981	C₂³	1	32	yes	complemented
105	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
106	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
107	C₂×Dic₄₇⋊C₄	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	4	yes	—
111	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
112	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
113	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
114	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
115	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
116	C₂×C₂²⋊Dic₄₇	C₂³	1	32	yes	complemented
117	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
118	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
119	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
120	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
121	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
122	C₂⁵×C₄₇	C₂³	1	4	yes	—
123	C₂²×D₄×C₄₇	—	4	16	no	—
124	C₂²×D₄×C₄₇	—	4	8	no	—
125	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
126	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
127	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
128	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
129	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
130	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
131	C₂²×D₄×C₄₇	C₂³	1	32	yes	complemented
132	C₂²×D₄×C₄₇	C₂³	1	16	yes	complemented
133	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
135	#127×C₄₇	C₂³	1	8	yes	—
136	#127×C₄₇	C₂³	1	8	yes	complemented
137	#127×C₄₇	C₂³	1	16	yes	complemented
138	#127×C₄₇	C₂³	1	32	yes	complemented
139	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
141	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₄₇	C₂³	1	8	yes	complemented
143	C₂⁴×C₄₇	—	2	16	no	—
144	C₂⁴×C₄₇	—	4	16	no	—
145	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
146	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
147	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₄₇	C₂⁴	1	16	yes	—
149	C₂³×D₄₇	—	4	16	no	—
150	C₂³×D₄₇	—	4	8	no	—
151	C₂³×D₄₇	C₂⁴	1	4	yes	—
152	C₂³×D₄₇	C₂⁴	1	16	yes	—
153	C₂×D₄×C₄₇	—	2	16	no	—
154	C₂×D₄×C₄₇	—	2	16	no	—
155	C₂×D₄×C₄₇	—	4	64	no	—
156	C₂×D₄×C₄₇	—	4	16	no	—
157	C₂×D₄×C₄₇	—	4	4	no	—
158	C₂×D₄×C₄₇	—	4	8	no	—
159	C₂×D₄×C₄₇	—	4	4	no	—
160	C₂×D₄×C₄₇	—	4	32	no	—
161	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
162	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
163	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
164	C₂×D₄×C₄₇	C₂⁴	1	32	yes	—
165	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
166	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
167	C₂²×C₄×C₄₇	—	2	4	no	—
168	C₂²×C₄×C₄₇	—	2	8	no	—
169	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
173	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
175	C₂×C₂²⋊D₄₇	—	2	16	no	—
176	C₂×C₂²⋊D₄₇	—	4	16	no	—
177	C₂×C₂²⋊D₄₇	—	4	16	no	—
178	C₂×C₂²⋊D₄₇	—	4	16	no	—
179	C₂×C₂²⋊D₄₇	—	4	64	no	—
180	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
181	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
182	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
183	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
184	C₂²×Dic₄₇	—	4	8	no	—
185	C₂²×Dic₄₇	—	4	16	no	—
186	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
187	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
188	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
189	C₂²×Dic₄₇	C₂⁴	1	32	yes	—
190	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
191	#10625352	—	4	64	no	—
192	D₄×D₄₇	—	4	64	no	—
193	C₂×D₁₈₈	—	2	8	no	—
194	C₂×D₁₈₈	C₂⁴	1	8	yes	—
195	C₂×C₄×D₄₇	—	2	16	no	—
196	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
197	C₂×Dic₉₄	—	2	8	no	—
198	C₂×Dic₉₄	C₂⁴	1	8	yes	—
199	C₄²×C₄₇	C₂⁴	1	4	yes	—
200	C₄²×C₄₇	C₂⁴	1	8	yes	—
201	C₄²×C₄₇	C₂⁴	1	4	yes	—
202	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
203	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
204	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
205	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
206	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
207	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
208	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
209	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
210	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
211	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
212	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
213	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
214	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
215	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
216	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
217	C₄×Dic₄₇	C₂⁴	1	16	yes	—
218	C₂³×C₄₇	—	2	4	no	—
219	C₂³×C₄₇	—	2	16	no	—
220	C₂³×C₄₇	—	2	8	no	—
221	C₂³×C₄₇	—	2	8	no	—
222	C₂³×C₄₇	—	2	16	no	—
223	C₂³×C₄₇	—	2	32	no	—
224	C₂³×C₄₇	—	4	32	no	—
225	C₂³×C₄₇	—	8	32	no	—
226	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
227	C₂³×C₄₇	C₂⁵	1	8	yes	—
228	C₂³×C₄₇	C₂⁵	1	8	yes	—
229	C₂³×C₄₇	C₂⁵	1	2	yes	—
230	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
231	C₂²×D₄₇	—	2	8	no	—
232	C₂²×D₄₇	—	2	8	no	—
233	C₂²×D₄₇	—	2	8	no	—
234	C₂²×D₄₇	—	4	32	no	—
235	C₂²×D₄₇	—	4	16	no	—
236	C₂²×D₄₇	—	8	32	no	—
237	C₂²×D₄₇	C₂⁵	1	8	yes	—
238	D₄×C₄₇	—	2	32	no	—
239	D₄×C₄₇	—	2	32	no	—
240	D₄×C₄₇	—	4	32	no	—
241	D₄×C₄₇	—	4	8	no	—
242	D₄×C₄₇	—	4	16	no	—
243	D₄×C₄₇	—	4	8	no	—
244	C₂×C₄×C₄₇	—	2	8	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	2	2	no	—
247	C₂×C₄×C₄₇	—	2	4	no	—
248	C₂×C₄×C₄₇	—	2	16	no	—
249	C₂×C₄×C₄₇	H(5,𝔽₂)	1	8	yes	—
250	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
251	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
252	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
253	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
254	C₂²⋊D₄₇	—	2	32	no	—
255	C₂²⋊D₄₇	—	4	32	no	—
256	C₂²⋊D₄₇	—	4	32	no	—
257	C₂²⋊D₄₇	—	4	32	no	—
258	C₂×Dic₄₇	—	2	8	no	—
259	C₂×Dic₄₇	—	2	8	no	—
260	C₂×Dic₄₇	—	2	8	no	—
261	C₂×Dic₄₇	—	4	32	no	—
262	C₂×Dic₄₇	—	4	16	no	—
263	C₂×Dic₄₇	C₂⁵	1	8	yes	—
264	C₂×Dic₄₇	C₂⁵	1	8	yes	—
265	C₂×Dic₄₇	C₂⁵	1	8	yes	—
266	D₁₈₈	—	2	16	no	—
267	C₄×D₄₇	—	2	32	no	—
268	Dic₉₄	—	2	16	no	—
269	C₂×#3543	—	47	1	no	maximal, Sylow
270	C₂²×C₄₇	—	2	4	no	—
271	C₂²×C₄₇	—	2	8	no	—
272	C₂²×C₄₇	—	2	16	no	—
273	C₂²×C₄₇	—	2	8	no	—
274	C₂²×C₄₇	—	2	8	no	—
275	C₂²×C₄₇	—	2	16	no	—
276	C₂²×C₄₇	—	4	16	no	—
277	C₂²×C₄₇	—	4	16	no	—
278	C₂²×C₄₇	—	8	32	no	—
279	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
280	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
281	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
282	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
283	C₂×D₄₇	—	2	8	no	—
284	C₂×D₄₇	—	2	8	no	—
285	C₂×D₄₇	—	2	8	no	—
286	C₂×D₄₇	—	4	16	no	—
287	C₂×D₄₇	—	8	32	no	—
288	C₄×C₄₇	—	2	2	no	—
289	C₄×C₄₇	—	2	2	no	—
290	C₄×C₄₇	—	2	4	no	—
291	C₄×C₄₇	C₂×H(5,𝔽₂)	1	8	yes	—
292	Dic₄₇	—	2	8	no	—
293	Dic₄₇	—	2	8	no	—
294	Dic₄₇	—	2	8	no	—
295	#3543	—	47	32	no	—
296	C₂×#560	—	47	4	no	—
297	C₂×#559	—	47	1	no	—
298	C₂×#550	—	47	2	no	—
299	C₂×#546	—	47	4	no	—
300	C₂×D₄²	—	47	4	no	—
301	C₂×D₄²	—	47	1	no	—
302	C₂×#540	—	47	4	no	—
303	C₂×#535	—	47	4	no	—
304	C₂×#534	—	47	4	no	—
305	C₂²×#127	D₄₇	1	1	yes	characteristic, complemented
306	C₂×#529	—	47	2	no	—
307	C₂×C₄₇	—	2	4	no	—
308	C₂×C₄₇	—	4	8	no	—
309	C₂×C₄₇	—	4	8	no	—
310	C₂×C₄₇	#3543	1	4	yes	complemented
311	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
312	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	2	yes	—
313	D₄₇	—	4	8	no	—
314	C₂²×#41	—	47	4	no	—
315	C₂³×D₄	—	47	4	no	—
316	C₂³×D₄	—	47	4	no	—
317	C₂³×D₄	C₂×D₄₇	1	2	yes	complemented
318	C₂³×D₄	C₂×D₄₇	1	4	yes	complemented
319	#560	—	47	64	no	—
320	#559	—	47	16	no	—
321	#550	—	47	32	no	—
322	#546	—	47	64	no	—
323	D₄²	—	47	64	no	—
324	D₄²	—	47	16	no	—
325	#540	—	47	64	no	—
326	#535	—	47	64	no	—
327	#534	—	47	64	no	—
328	C₂×#127	—	47	4	no	—
329	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
330	C₂×#127	C₂×D₄₇	1	4	yes	complemented
331	C₂×#127	C₂×D₄₇	1	1	yes	characteristic, complemented
332	C₂×#127	C₂×D₄₇	1	2	yes	complemented
333	C₂×#127	C₂×D₄₇	1	16	yes	complemented
334	#529	—	47	32	no	—
335	C₂×#126	—	47	4	no	—
336	C₂×#125	—	47	2	no	—
337	C₂×#124	—	47	4	no	—
338	C₂×#124	—	47	2	no	—
339	C₂×#123	—	47	4	no	—
340	C₂×#123	—	47	4	no	—
341	C₂×#123	—	47	8	no	—
342	C₂×#123	—	47	4	no	—
343	C₂×C₂²⋊Q₈	—	47	2	no	—
344	C₂×#121	—	47	8	no	—
345	C₂×#121	—	47	8	no	—
346	C₂×#121	—	47	8	no	—
347	C₂×#121	—	47	4	no	—
348	C₂×#121	—	47	4	no	—
349	C₂×#121	—	47	8	no	—
350	C₂×#121	—	47	2	no	—
351	C₂×#120	—	47	8	no	—
352	C₂×#120	—	47	4	no	—
353	C₂×#120	—	47	4	no	—
354	C₂×#120	—	47	8	no	—
355	C₂×C₄×Q₈	—	47	2	no	—
356	C₂×C₄×D₄	—	47	4	no	—
357	C₂×C₄×D₄	—	47	4	no	—
358	C₂×C₄×D₄	—	47	4	no	—
359	C₂×C₄×D₄	—	47	2	no	—
360	C₂×#117	—	47	4	no	—
361	C₂²×C₂²⋊C₄	—	47	4	no	—
362	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic, complemented
363	C₄₇	C₂×#3543	1	1	yes	characteristic, complemented, Sylow
364	C₂⁵	—	47	4	no	—
365	C₂⁵	C₂²×D₄₇	1	4	yes	—
366	C₂×#41	—	47	32	no	—
367	C₂×#41	—	188	16	no	—
368	C₂²×Q₈	—	47	2	no	—
369	C₂²×D₄	—	4	16	no	—
370	C₂²×D₄	—	4	8	no	—
371	C₂²×D₄	—	47	4	no	—
372	C₂²×D₄	—	47	8	no	—
373	C₂²×D₄	—	47	8	no	—
374	C₂²×D₄	—	47	8	no	—
375	C₂²×D₄	—	47	32	no	—
376	C₂²×D₄	—	47	32	no	—
377	C₂²×D₄	—	47	2	no	—
378	C₂²×D₄	—	188	16	no	—
379	C₂²×D₄	—	188	16	no	—
380	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
381	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
382	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
383	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
384	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
385	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
386	C₂²×D₄	C₂²×D₄₇	1	16	yes	complemented
387	C₂²×D₄	C₂²×D₄₇	1	32	yes	complemented
388	C₂³×C₄	—	47	8	no	—
389	C₂³×C₄	—	47	4	no	—
390	C₂³×C₄	—	47	4	no	—
391	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
392	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
393	#127	—	47	32	no	—
394	#127	C₂²×D₄₇	1	8	yes	—
395	#127	C₂²×D₄₇	1	32	yes	complemented
396	#127	C₂²×D₄₇	1	8	yes	complemented
397	#127	C₂²×D₄₇	1	16	yes	complemented
398	#126	—	47	32	no	—
399	#125	—	47	16	no	—
400	#124	—	47	32	no	—
401	#124	—	47	16	no	—
402	#123	—	47	32	no	—
403	#123	—	47	32	no	—
404	#123	—	47	64	no	—
405	#123	—	47	32	no	—
406	C₂²⋊Q₈	—	47	16	no	—
407	#121	—	47	64	no	—
408	#121	—	47	64	no	—
409	#121	—	47	64	no	—
410	#121	—	47	32	no	—
411	#121	—	47	32	no	—
412	#121	—	47	64	no	—
413	#121	—	47	16	no	—
414	#120	—	47	64	no	—
415	#120	—	47	32	no	—
416	#120	—	47	32	no	—
417	#120	—	47	64	no	—
418	C₄×Q₈	—	47	16	no	—
419	C₄×D₄	—	47	32	no	—
420	C₄×D₄	—	47	32	no	—
421	C₄×D₄	—	47	32	no	—
422	C₄×D₄	—	47	16	no	—
423	#117	—	47	32	no	—
424	C₂×C₄⋊C₄	—	47	4	no	—
425	C₂×C₄⋊C₄	—	47	4	no	—
426	C₂×C₄⋊C₄	—	47	2	no	—
427	C₂×C₄⋊C₄	—	47	2	no	—
428	C₂×C₄⋊C₄	—	47	4	no	—
429	C₂×C₄⋊C₄	—	47	4	no	—
430	C₂×C₂²⋊C₄	—	47	4	no	—
431	C₂×C₂²⋊C₄	—	47	4	no	—
432	C₂×C₂²⋊C₄	—	47	4	no	—
433	C₂×C₂²⋊C₄	—	47	32	no	—
434	C₂×C₂²⋊C₄	—	47	8	no	—
435	C₂×C₂²⋊C₄	—	47	8	no	—
436	C₂×C₂²⋊C₄	—	47	4	no	—
437	C₂×C₂²⋊C₄	—	47	4	no	—
438	C₂×C₂²⋊C₄	—	47	4	no	—
439	C₂×C₂²⋊C₄	—	47	4	no	—
440	C₂×C₄²	—	47	4	no	—
441	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
442	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
443	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
444	C₂×C₄²	C₂²×D₄₇	1	8	yes	complemented
445	C₂⁴	—	2	16	no	—
446	C₂⁴	—	4	16	no	—
447	C₂⁴	—	47	4	no	—
448	C₂⁴	—	47	16	no	—
449	C₂⁴	—	188	8	no	—
450	C₂⁴	—	188	16	no	—
451	C₂⁴	C₂³×D₄₇	1	4	yes	—
452	C₂⁴	C₂³×D₄₇	1	4	yes	—
453	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
454	C₂⁴	C₂³×D₄₇	1	16	yes	—
455	#41	—	188	64	no	—
456	C₂×Q₈	—	47	8	no	—
457	C₂×Q₈	—	94	8	no	—
458	C₂×D₄	—	2	16	no	—
459	C₂×D₄	—	2	16	no	—
460	C₂×D₄	—	4	64	no	—
461	C₂×D₄	—	4	16	no	—
462	C₂×D₄	—	4	4	no	—
463	C₂×D₄	—	4	8	no	—
464	C₂×D₄	—	4	4	no	—
465	C₂×D₄	—	4	32	no	—
466	C₂×D₄	—	47	16	no	—
467	C₂×D₄	—	47	32	no	—
468	C₂×D₄	—	47	32	no	—
469	C₂×D₄	—	47	32	no	—
470	C₂×D₄	—	47	8	no	—
471	C₂×D₄	—	94	16	no	—
472	C₂×D₄	—	94	8	no	—
473	C₂×D₄	—	188	64	no	—
474	C₂×D₄	—	188	16	no	—
475	C₂×D₄	—	188	16	no	—
476	C₂×D₄	—	188	16	no	—
477	C₂×D₄	—	188	64	no	—
478	C₂×D₄	C₂³×D₄₇	1	16	yes	—
479	C₂×D₄	C₂³×D₄₇	1	16	yes	—
480	C₂×D₄	C₂³×D₄₇	1	8	yes	—
481	C₂×D₄	C₂³×D₄₇	1	16	yes	—
482	C₂×D₄	C₂³×D₄₇	1	32	yes	—
483	C₂×D₄	C₂³×D₄₇	1	8	yes	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	8	no	—
486	C₂²×C₄	—	47	4	no	—
487	C₂²×C₄	—	47	4	no	—
488	C₂²×C₄	—	47	4	no	—
489	C₂²×C₄	—	47	32	no	—
490	C₂²×C₄	—	47	16	no	—
491	C₂²×C₄	—	47	16	no	—
492	C₂²×C₄	—	94	16	no	—
493	C₂²×C₄	—	188	8	no	—
494	C₂²×C₄	—	188	16	no	—
495	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
496	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
497	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
498	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
499	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
500	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
501	C₄⋊C₄	—	47	16	no	—
502	C₄⋊C₄	—	47	16	no	—
503	C₄⋊C₄	—	47	16	no	—
504	C₄⋊C₄	—	47	16	no	—
505	C₄⋊C₄	—	47	8	no	—
506	C₄⋊C₄	—	47	8	no	—
507	C₂²⋊C₄	—	47	16	no	—
508	C₂²⋊C₄	—	47	16	no	—
509	C₂²⋊C₄	—	47	16	no	—
510	C₂²⋊C₄	—	47	32	no	—
511	C₂²⋊C₄	—	47	32	no	—
512	C₂²⋊C₄	—	47	16	no	—
513	C₂²⋊C₄	—	47	16	no	—
514	C₂²⋊C₄	—	47	16	no	—
515	C₂²⋊C₄	—	47	16	no	—
516	C₄²	—	47	16	no	—
517	C₄²	C₂³×D₄₇	1	8	yes	—
518	C₄²	C₂³×D₄₇	1	4	yes	—
519	C₄²	C₂³×D₄₇	1	4	yes	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	16	no	—
522	C₂³	—	2	8	no	—
523	C₂³	—	2	16	no	—
524	C₂³	—	2	8	no	—
525	C₂³	—	2	32	no	—
526	C₂³	—	4	32	no	—
527	C₂³	—	8	32	no	—
528	C₂³	—	47	8	no	—
529	C₂³	—	94	8	no	—
530	C₂³	—	94	8	no	—
531	C₂³	—	94	8	no	—
532	C₂³	—	376	32	no	—
533	C₂³	—	188	16	no	—
534	C₂³	—	188	32	no	—
535	C₂³	#13094069	1	4	yes	—
536	C₂³	C₂⁴×D₄₇	1	8	yes	—
537	C₂³	C₂⁴×D₄₇	1	8	yes	—
538	C₂³	C₂⁴×D₄₇	1	2	yes	—
539	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
540	Q₈	—	94	16	no	—
541	D₄	—	2	32	no	—
542	D₄	—	2	32	no	—
543	D₄	—	4	32	no	—
544	D₄	—	4	8	no	—
545	D₄	—	4	16	no	—
546	D₄	—	4	8	no	—
547	D₄	—	94	32	no	—
548	D₄	—	94	16	no	—
549	D₄	—	188	32	no	—
550	D₄	—	188	32	no	—
551	D₄	—	188	32	no	—
552	C₂×C₄	—	2	8	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	47	8	no	—
558	C₂×C₄	—	47	8	no	—
559	C₂×C₄	—	47	8	no	—
560	C₂×C₄	—	94	8	no	—
561	C₂×C₄	—	94	8	no	—
562	C₂×C₄	—	94	8	no	—
563	C₂×C₄	—	94	32	no	—
564	C₂×C₄	—	188	16	no	—
565	C₂×C₄	—	188	32	no	—
566	C₂×C₄	#13094069	1	8	yes	—
567	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
568	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
569	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
570	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
571	C₂²	—	2	4	no	—
572	C₂²	—	2	8	no	—
573	C₂²	—	2	16	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	16	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	4	16	no	—
578	C₂²	—	4	16	no	—
579	C₂²	—	8	32	no	—
580	C₂²	—	94	8	no	—
581	C₂²	—	94	8	no	—
582	C₂²	—	94	8	no	—
583	C₂²	—	376	32	no	—
584	C₂²	—	188	16	no	—
585	C₂²	C₂×#13094069	1	4	yes	—
586	C₂²	C₂×#13094069	1	2	yes	—
587	C₂²	C₂×#13094069	1	4	yes	—
588	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	4	no	—
592	C₄	—	94	8	no	—
593	C₄	—	94	8	no	—
594	C₄	—	94	8	no	—
595	C₄	C₂×#13094069	1	8	yes	—
596	C₂	—	2	4	no	—
597	C₂	—	4	8	no	—
598	C₂	—	4	8	no	—
599	C₂	—	188	8	no	—
600	C₂	#20257721	1	4	yes	direct product factor
601	C₂	C₂²×#13094069	1	1	yes	characteristic
602	C₂	C₂²×#13094069	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×#127×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#127	D₄₇
hypocenter	C₄₇	C₂×#3543
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#127

Complements

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

N	H ≅ G/N	type
1. #20257721	C₂	direct (N × H)
2. C₂×#15689860	C₂	semidirect
3. C₂×#15689859	C₂	semidirect
4. C₂×#15689793	C₂	semidirect
5. C₂×#15689767	C₂	semidirect
6. C₂×#15689758	C₂	semidirect
7. C₂×D₄×C₂²⋊D₄₇	C₂	semidirect
8. C₂×#15689727	C₂	semidirect
9. C₂×#15689686	C₂	semidirect
10. C₂×#15689682	C₂	semidirect
11. C₂×#15689657	C₂	semidirect
12. C₂²×#127×C₄₇	C₂	semidirect
13. C₂²×#10625352	C₂²	semidirect
14. C₂³×C₂²⋊D₄₇	C₂²	semidirect
15. C₂²×D₄×D₄₇	C₂²	semidirect
16. #15689860	C₂²	semidirect
17. #15689859	C₂²	semidirect
18. #15689793	C₂²	semidirect
19. #15689767	C₂²	semidirect
20. #15689758	C₂²	semidirect
21. D₄×C₂²⋊D₄₇	C₂²	semidirect
22. #15689727	C₂²	semidirect
23. #15689686	C₂²	semidirect
24. #15689682	C₂²	semidirect
25. C₂×#13094020	C₂²	semidirect
26. #15689657	C₂²	semidirect
27. C₂×#13094018	C₂²	semidirect
28. C₂×#13094016	C₂²	semidirect
29. C₂×#13094012	C₂²	semidirect
30. C₂×#13094011	C₂²	semidirect
31. C₂×#13094007	C₂²	semidirect
32. C₂×#13094005	C₂²	semidirect
33. C₂×#13094005	C₂²	semidirect
34. C₂×#13094005	C₂²	semidirect
35. C₂×#13094003	C₂²	semidirect
37. C₂×#13093996	C₂²	semidirect
38. C₂×#13093996	C₂²	semidirect
39. C₂×#13093996	C₂²	semidirect
40. C₂×#13093996	C₂²	semidirect
41. C₂×#13093995	C₂²	semidirect
42. C₂×#13093995	C₂²	semidirect
43. C₂×#13093993	C₂²	semidirect
44. C₂×#13093992	C₂²	semidirect
45. C₂×#13093992	C₂²	semidirect
46. C₂×#13093992	C₂²	semidirect
47. C₂×C₄×Dic₉₄	C₂²	semidirect
48. C₂×C₄×D₁₈₈	C₂²	semidirect
49. C₂×D₄×Dic₄₇	C₂²	semidirect
50. C₂×D₄×Dic₄₇	C₂²	semidirect
51. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
52. C₂×#13093981	C₂²	semidirect
53. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
54. C₂³×D₄×C₄₇	C₂²	semidirect
55. C₂³×D₄×C₄₇	C₂²	semidirect
57. C₂×#127×C₄₇	C₂²	semidirect
58. C₂×#127×C₄₇	C₂²	semidirect
59. C₂×#127×C₄₇	C₂²	semidirect
60. C₂×#127×C₄₇	C₂²	semidirect
61. C₂²×C₄²×C₄₇	C₂²	semidirect
64. C₂×#10625352	C₂³	semidirect
72. C₂²×C₂²⋊D₄₇	C₂³	semidirect
74. C₂×D₄×D₄₇	C₂³	semidirect
78. #13094020	C₂³	semidirect
79. #13094018	C₂³	semidirect
80. #13094016	C₂³	semidirect
81. #13094012	C₂³	semidirect
82. #13094011	C₂³	semidirect
83. #13094007	C₂³	semidirect
84. #13094005	C₂³	semidirect
85. #13094005	C₂³	semidirect
86. #13094005	C₂³	semidirect
87. #13094003	C₂³	semidirect
89. #13093996	C₂³	semidirect
90. #13093996	C₂³	semidirect
91. #13093996	C₂³	semidirect
92. #13093996	C₂³	semidirect
93. #13093995	C₂³	semidirect
94. #13093995	C₂³	semidirect
95. #13093993	C₂³	semidirect
96. #13093992	C₂³	semidirect
97. #13093992	C₂³	semidirect
98. #13093992	C₂³	semidirect
99. C₄×Dic₉₄	C₂³	semidirect
100. C₄×D₁₈₈	C₂³	semidirect
101. D₄×Dic₄₇	C₂³	semidirect
102. D₄×Dic₄₇	C₂³	semidirect
103. C₄×C₂²⋊D₄₇	C₂³	semidirect
104. #13093981	C₂³	semidirect
116. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
131. C₂²×D₄×C₄₇	C₂³	semidirect
132. C₂²×D₄×C₄₇	C₂³	semidirect
136. #127×C₄₇	C₂³	semidirect
137. #127×C₄₇	C₂³	semidirect
138. #127×C₄₇	C₂³	semidirect
142. C₂×C₄²×C₄₇	C₂³	semidirect
305. C₂²×#127	D₄₇	semidirect
310. C₂×C₄₇	#3543	semidirect
317. C₂³×D₄	C₂×D₄₇	semidirect
318. C₂³×D₄	C₂×D₄₇	semidirect
330. C₂×#127	C₂×D₄₇	semidirect
331. C₂×#127	C₂×D₄₇	semidirect
332. C₂×#127	C₂×D₄₇	semidirect
333. C₂×#127	C₂×D₄₇	semidirect
362. C₂²×C₄²	C₂×D₄₇	semidirect
363. C₄₇	C₂×#3543	semidirect
386. C₂²×D₄	C₂²×D₄₇	semidirect
387. C₂²×D₄	C₂²×D₄₇	semidirect
395. #127	C₂²×D₄₇	semidirect
396. #127	C₂²×D₄₇	semidirect
397. #127	C₂²×D₄₇	semidirect
444. C₂×C₄²	C₂²×D₄₇	semidirect
600. C₂	#20257721	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257721	2
C₂×#15689860	2
C₂×#15689859	2
C₂×#15689793	2
C₂×#15689767	2
C₂×#15689758	2
C₂×D₄×C₂²⋊D₄₇	2
C₂×#15689727	2
C₂×#15689686	2
C₂×#15689682	2
C₂×#15689657	2
C₂²×#127×C₄₇	2
C₂×#3543	47

Subgroups — C2×#20257721 #27123871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257721 #27123871