Subgroups — C₂×#20246328 #26375617

Order 12032.

3374 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246328	C₂	1	16	yes	maximal, direct product factor
2	C₂×#15689016	C₂	1	2	yes	maximal, complemented
3	C₂×#15689009	C₂	1	2	yes	maximal, complemented
4	C₂×#15689003	C₂	1	2	yes	maximal
5	C₂×#15688991	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688986	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688983	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂²⋊C₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688969	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
13	C₂⁴×Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
15	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
17	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
18	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
19	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
20	#15689016	C₂²	1	16	yes	complemented
21	#15689009	C₂²	1	16	yes	complemented
22	#15689003	C₂²	1	16	yes	—
23	#15688991	C₂²	1	8	yes	complemented
24	#15688986	C₂²	1	8	yes	complemented
25	#15688983	C₂²	1	8	yes	complemented
26	C₂²⋊C₄×Dic₄₇	C₂²	1	16	yes	complemented
27	C₄×C₂²⋊Dic₄₇	C₂²	1	8	yes	complemented
28	#15688969	C₂²	1	8	yes	complemented
29	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
30	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
31	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
32	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
33	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
34	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
35	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
36	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
37	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
38	C₂×C₄₇⋊#95	C₂²	1	8	yes	complemented
39	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₄₇	C₄	1	16	yes	complemented
43	C₂×C₄×D₄×C₄₇	C₂²	1	8	yes	—
44	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
48	C₂³×Dic₄₇	—	2	8	no	—
49	C₂³×Dic₄₇	—	2	8	no	—
50	C₂³×Dic₄₇	—	4	4	no	—
51	C₂³×Dic₄₇	C₂³	1	2	yes	—
52	C₂³×Dic₄₇	C₂³	1	2	yes	—
53	C₂³×Dic₄₇	C₂³	1	2	yes	—
54	C₂³×Dic₄₇	C₂³	1	8	yes	—
55	C₂³×Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	—	4	4	no	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
58	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
59	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
60	C₂×C₂²⋊Dic₄₇	—	4	4	no	—
61	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
62	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
63	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
64	C₂×C₄×Dic₄₇	—	2	8	no	—
65	C₂×C₄×Dic₄₇	—	4	4	no	—
66	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
67	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
68	C₄₇⋊#95	C₂³	1	4	yes	—
69	C₄₇⋊#95	C₂³	1	4	yes	—
70	C₄₇⋊#95	C₂³	1	8	yes	—
71	C₄₇⋊#95	C₂³	1	4	yes	—
72	C₄₇⋊#95	C₂³	1	8	yes	—
73	C₄₇⋊#95	C₂³	1	4	yes	—
74	C₄₇⋊#95	C₂³	1	8	yes	—
75	C₄₇⋊#95	C₂³	1	8	yes	—
76	C₄₇⋊#95	C₂³	1	8	yes	—
77	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
78	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₄₇	—	2	4	no	—
80	C₂²×D₄×C₄₇	—	2	4	no	—
81	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
82	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
83	C₂³×C₄×C₄₇	—	4	4	no	—
84	C₂³×C₄×C₄₇	—	4	4	no	—
85	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
86	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
87	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
93	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
94	C₄×D₄×C₄₇	C₂×C₄	1	64	yes	complemented
95	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
96	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
98	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
99	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
101	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
102	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
103	C₂⁴×C₄₇	—	2	4	no	—
104	C₂⁴×C₄₇	—	2	4	no	—
105	C₂⁴×C₄₇	—	2	2	no	—
106	C₂⁴×C₄₇	—	2	2	no	—
107	C₂⁴×C₄₇	—	2	4	no	—
108	C₂⁴×C₄₇	—	2	4	no	—
109	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
110	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
111	C₂⁴×C₄₇	#41	1	4	yes	—
112	C₂⁴×C₄₇	#41	1	4	yes	—
113	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
114	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
115	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂×D₄×C₄₇	—	2	32	no	—
117	C₂×D₄×C₄₇	—	2	8	no	—
118	C₂×D₄×C₄₇	—	2	8	no	—
119	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	4	no	—
123	C₂²×C₄×C₄₇	—	2	4	no	—
124	C₂²×C₄×C₄₇	—	2	4	no	—
125	C₂²×C₄×C₄₇	—	2	4	no	—
126	C₂²×C₄×C₄₇	—	4	16	no	—
127	C₂²×C₄×C₄₇	—	4	16	no	—
128	C₂²×C₄×C₄₇	—	4	8	no	—
129	C₂²×C₄×C₄₇	—	4	8	no	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
136	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
137	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
142	C₂²×Dic₄₇	—	2	4	no	—
143	C₂²×Dic₄₇	—	2	4	no	—
144	C₂²×Dic₄₇	—	2	4	no	—
145	C₂²×Dic₄₇	—	2	4	no	—
146	C₂²×Dic₄₇	—	2	4	no	—
147	C₂²×Dic₄₇	—	2	4	no	—
148	C₂²×Dic₄₇	—	2	16	no	—
149	C₂²×Dic₄₇	—	2	4	no	—
150	C₂²×Dic₄₇	—	2	4	no	—
151	C₂²×Dic₄₇	—	2	4	no	—
152	C₂²×Dic₄₇	—	2	4	no	—
153	C₂²×Dic₄₇	—	2	4	no	—
154	C₂²×Dic₄₇	—	2	16	no	—
155	C₂²×Dic₄₇	—	4	8	no	—
156	C₂²×Dic₄₇	—	4	32	no	—
157	C₂²×Dic₄₇	#41	1	8	yes	—
158	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
159	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
160	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
161	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
162	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
163	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
164	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
165	C₄²×C₄₇	C₂²×C₄	1	16	yes	complemented
166	C₂²⋊Dic₄₇	—	2	16	no	—
167	C₂²⋊Dic₄₇	—	2	16	no	—
168	C₂²⋊Dic₄₇	—	4	8	no	—
169	C₄⋊Dic₄₇	—	4	8	no	—
170	C₄×Dic₄₇	—	2	16	no	—
171	C₄×Dic₄₇	—	4	8	no	—
172	C₂³×C₄₇	—	2	8	no	—
173	C₂³×C₄₇	—	2	8	no	—
174	C₂³×C₄₇	—	2	16	no	—
175	C₂³×C₄₇	—	2	16	no	—
176	C₂³×C₄₇	—	2	4	no	—
177	C₂³×C₄₇	—	2	4	no	—
178	C₂³×C₄₇	—	2	8	no	—
179	C₂³×C₄₇	—	2	8	no	—
180	C₂³×C₄₇	—	2	8	no	—
181	C₂³×C₄₇	—	2	4	no	—
182	C₂³×C₄₇	—	2	2	no	—
183	C₂³×C₄₇	—	2	2	no	—
184	C₂³×C₄₇	—	2	4	no	—
185	C₂³×C₄₇	—	4	8	no	—
186	C₂³×C₄₇	—	4	8	no	—
187	C₂³×C₄₇	#117	1	16	yes	—
188	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
189	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
190	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
191	C₂³×C₄₇	C₂×#41	1	4	yes	—
192	C₂³×C₄₇	C₂×#41	1	4	yes	—
193	C₂³×C₄₇	C₂×#41	1	4	yes	—
194	C₂³×C₄₇	C₂×#41	1	2	yes	—
195	C₂³×C₄₇	C₂×#41	1	2	yes	—
196	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
197	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
198	D₄×C₄₇	—	2	32	no	—
199	C₂×C₄×C₄₇	—	2	8	no	—
200	C₂×C₄×C₄₇	—	2	8	no	—
201	C₂×C₄×C₄₇	—	2	8	no	—
202	C₂×C₄×C₄₇	—	2	8	no	—
203	C₂×C₄×C₄₇	—	2	8	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	2	4	no	—
209	C₂×C₄×C₄₇	—	2	4	no	—
210	C₂×C₄×C₄₇	—	4	16	no	—
211	C₂×C₄×C₄₇	—	4	16	no	—
212	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
213	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
214	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
215	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
216	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
217	C₂×Dic₄₇	—	2	16	no	—
218	C₂×Dic₄₇	—	2	4	no	—
219	C₂×Dic₄₇	—	2	4	no	—
220	C₂×Dic₄₇	—	2	4	no	—
221	C₂×Dic₄₇	—	2	4	no	—
222	C₂×Dic₄₇	—	2	4	no	—
223	C₂×Dic₄₇	—	2	4	no	—
224	C₂×Dic₄₇	—	2	4	no	—
225	C₂×Dic₄₇	—	2	4	no	—
226	C₂×Dic₄₇	—	2	4	no	—
227	C₂×Dic₄₇	—	2	4	no	—
228	C₂×Dic₄₇	—	2	4	no	—
229	C₂×Dic₄₇	—	4	32	no	—
230	C₂×Dic₄₇	—	4	8	no	—
231	C₂×Dic₄₇	—	4	8	no	—
232	C₂×Dic₄₇	—	4	8	no	—
233	C₂×Dic₄₇	C₂×#41	1	8	yes	—
234	C₂×#2353	—	47	1	no	maximal, Sylow
235	C₂²×C₄₇	—	2	32	no	—
236	C₂²×C₄₇	—	2	4	no	—
237	C₂²×C₄₇	—	2	4	no	—
238	C₂²×C₄₇	—	2	8	no	—
239	C₂²×C₄₇	—	2	8	no	—
240	C₂²×C₄₇	—	2	4	no	—
241	C₂²×C₄₇	—	2	4	no	—
242	C₂²×C₄₇	—	2	4	no	—
243	C₂²×C₄₇	—	4	16	no	—
244	C₂²×C₄₇	—	4	4	no	—
245	C₂²×C₄₇	—	4	4	no	—
246	C₂²×C₄₇	C₂×#117	1	8	yes	—
247	C₂²×C₄₇	C₂×#117	1	4	yes	—
248	C₂²×C₄₇	C₄×#41	1	4	yes	—
249	C₂²×C₄₇	#518	1	4	yes	—
250	C₂²×C₄₇	#551	1	8	yes	—
251	C₂²×C₄₇	#553	1	8	yes	—
252	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
253	C₂²×C₄₇	C₂²×#41	1	2	yes	—
254	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
255	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
256	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
257	C₄×C₄₇	—	2	4	no	—
258	C₄×C₄₇	—	2	4	no	—
259	C₄×C₄₇	—	2	4	no	—
260	C₄×C₄₇	—	2	4	no	—
261	C₄×C₄₇	—	2	4	no	—
262	Dic₄₇	—	2	8	no	—
263	Dic₄₇	—	4	4	no	—
264	Dic₄₇	—	4	4	no	—
265	Dic₄₇	—	4	4	no	—
266	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
267	#2353	—	47	16	no	—
268	C₂×#388	—	47	2	no	—
269	C₂×#387	—	47	2	no	—
270	C₂×#386	—	47	2	no	—
271	C₂×#383	—	47	1	no	—
272	C₂×#381	—	47	1	no	—
273	C₂×#380	—	47	1	no	—
274	C₂×C₄×C₂²⋊C₄	—	47	1	no	—
275	C₂×C₄×C₂²⋊C₄	—	47	2	no	—
276	C₂×#376	—	47	1	no	—
277	C₂²×#95	—	47	1	no	—
278	C₂×C₄₇	—	2	8	no	—
279	C₂×C₄₇	—	4	4	no	—
280	C₂×C₄₇	#2353	1	8	yes	complemented
281	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
282	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
283	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
284	C₂×C₄₇	C₂×#551	1	2	yes	—
285	C₂×C₄₇	C₂×#553	1	2	yes	—
286	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
287	C₂⁴×C₄	—	47	2	no	—
288	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
289	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
290	C₂×C₄×D₄	Dic₄₇	1	16	yes	complemented
291	C₂×C₄×D₄	C₂×D₄₇	1	8	yes	—
292	C₂²×C₄⋊C₄	—	47	2	no	—
293	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
294	C₂²×C₂²⋊C₄	—	47	2	no	—
295	C₂²×C₂²⋊C₄	—	47	2	no	—
296	C₂²×C₂²⋊C₄	—	47	2	no	—
297	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
298	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
299	C₂²×C₄²	—	47	2	no	—
300	C₂²×C₄²	—	47	2	no	—
301	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
302	#388	—	47	16	no	—
303	#387	—	47	16	no	—
304	#386	—	47	16	no	—
305	#383	—	47	8	no	—
306	#381	—	47	8	no	—
307	#380	—	47	8	no	—
308	C₄×C₂²⋊C₄	—	47	8	no	—
309	C₄×C₂²⋊C₄	—	47	16	no	—
310	#376	—	47	8	no	—
311	C₂×#95	—	47	1	no	—
312	C₂×#95	—	47	1	no	—
313	C₂×#95	—	47	2	no	—
314	C₂×#95	—	47	1	no	—
315	C₂×#95	—	47	2	no	—
316	C₂×#95	—	47	1	no	—
317	C₂×#95	—	47	2	no	—
318	C₂×#95	—	47	2	no	—
319	C₂×#95	—	47	2	no	—
320	C₂×#95	—	47	8	no	—
321	C₄₇	C₂×#2353	1	1	yes	characteristic, complemented, Sylow
322	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
323	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
324	C₂²×D₄	—	2	4	no	—
325	C₂²×D₄	—	2	4	no	—
326	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
327	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
328	C₂³×C₄	—	4	4	no	—
329	C₂³×C₄	—	4	4	no	—
330	C₂³×C₄	—	47	2	no	—
331	C₂³×C₄	—	47	2	no	—
332	C₂³×C₄	—	47	2	no	—
333	C₂³×C₄	—	47	2	no	—
334	C₂³×C₄	—	47	8	no	—
335	C₂³×C₄	—	94	8	no	—
336	C₂³×C₄	—	94	8	no	—
337	C₂³×C₄	—	188	4	no	—
338	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
339	C₂³×C₄	C₂×Dic₄₇	1	8	yes	complemented
340	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
341	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
342	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
343	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
344	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
345	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
346	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
347	C₄×D₄	C₂×Dic₄₇	1	64	yes	complemented
348	C₂×C₄⋊C₄	—	47	8	no	—
349	C₂×C₄⋊C₄	—	188	4	no	—
350	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
351	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
352	C₂×C₂²⋊C₄	—	47	8	no	—
353	C₂×C₂²⋊C₄	—	47	8	no	—
354	C₂×C₂²⋊C₄	—	47	8	no	—
355	C₂×C₂²⋊C₄	—	94	8	no	—
356	C₂×C₂²⋊C₄	—	94	8	no	—
357	C₂×C₂²⋊C₄	—	188	4	no	—
358	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	8	yes	—
359	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
360	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
361	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
362	C₂×C₄²	—	47	8	no	—
363	C₂×C₄²	—	47	8	no	—
364	C₂×C₄²	—	94	8	no	—
365	C₂×C₄²	—	188	4	no	—
366	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
367	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
368	#95	—	47	4	no	—
369	#95	—	47	4	no	—
370	#95	—	47	8	no	—
371	#95	—	47	4	no	—
372	#95	—	47	8	no	—
373	#95	—	47	4	no	—
374	#95	—	47	8	no	—
375	#95	—	47	8	no	—
376	#95	—	47	8	no	—
377	C₂⁴	—	2	4	no	—
378	C₂⁴	—	2	4	no	—
379	C₂⁴	—	2	4	no	—
380	C₂⁴	—	2	2	no	—
381	C₂⁴	—	2	2	no	—
382	C₂⁴	—	2	4	no	—
383	C₂⁴	#10625350	1	4	yes	—
384	C₂⁴	#10625350	1	4	yes	—
385	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
386	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
387	C₂⁴	C₂³×D₄₇	1	2	yes	—
388	C₂⁴	C₂³×D₄₇	1	2	yes	—
389	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
390	C₂×D₄	—	2	32	no	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	4	16	no	—
401	C₂²×C₄	—	4	16	no	—
402	C₂²×C₄	—	4	8	no	—
403	C₂²×C₄	—	4	8	no	—
404	C₂²×C₄	—	47	8	no	—
405	C₂²×C₄	—	47	4	no	—
406	C₂²×C₄	—	47	4	no	—
407	C₂²×C₄	—	47	4	no	—
408	C₂²×C₄	—	47	4	no	—
409	C₂²×C₄	—	94	16	no	—
410	C₂²×C₄	—	94	4	no	—
411	C₂²×C₄	—	94	4	no	—
412	C₂²×C₄	—	94	4	no	—
413	C₂²×C₄	—	94	4	no	—
414	C₂²×C₄	—	94	4	no	—
415	C₂²×C₄	—	94	4	no	—
416	C₂²×C₄	—	94	4	no	—
417	C₂²×C₄	—	94	16	no	—
418	C₂²×C₄	—	94	4	no	—
419	C₂²×C₄	—	94	4	no	—
420	C₂²×C₄	—	94	4	no	—
421	C₂²×C₄	—	94	4	no	—
422	C₂²×C₄	—	188	8	no	—
423	C₂²×C₄	—	188	32	no	—
424	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
425	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
426	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
427	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
428	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
429	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
430	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	complemented
431	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
432	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
433	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
434	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
435	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
436	C₄⋊C₄	—	188	8	no	—
437	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	complemented
438	C₂²⋊C₄	—	94	16	no	—
439	C₂²⋊C₄	—	94	16	no	—
440	C₂²⋊C₄	—	188	8	no	—
441	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
442	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	complemented
443	C₄²	—	94	16	no	—
444	C₄²	—	188	8	no	—
445	C₄²	C₂²×Dic₄₇	1	16	yes	complemented
446	C₂³	—	2	16	no	—
447	C₂³	—	2	16	no	—
448	C₂³	—	2	8	no	—
449	C₂³	—	2	8	no	—
450	C₂³	—	2	4	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	8	no	—
453	C₂³	—	2	8	no	—
454	C₂³	—	2	8	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	4	8	no	—
460	C₂³	—	4	8	no	—
461	C₂³	#13093983	1	16	yes	—
462	C₂³	C₂³×Dic₄₇	1	4	yes	—
463	C₂³	C₂³×Dic₄₇	1	4	yes	—
464	C₂³	C₂³×Dic₄₇	1	2	yes	—
465	C₂³	#41×D₄₇	1	4	yes	—
466	C₂³	C₂×#10625350	1	4	yes	—
467	C₂³	C₂×#10625350	1	4	yes	—
468	C₂³	C₂×#10625350	1	2	yes	—
469	C₂³	C₂×#10625350	1	2	yes	—
470	C₂³	#13094069	1	4	yes	—
471	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
472	D₄	—	2	32	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	8	no	—
475	C₂×C₄	—	2	8	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	4	16	no	—
485	C₂×C₄	—	4	16	no	—
486	C₂×C₄	—	47	8	no	—
487	C₂×C₄	—	94	16	no	—
488	C₂×C₄	—	94	4	no	—
489	C₂×C₄	—	94	4	no	—
490	C₂×C₄	—	94	4	no	—
491	C₂×C₄	—	94	4	no	—
492	C₂×C₄	—	94	4	no	—
493	C₂×C₄	—	94	4	no	—
494	C₂×C₄	—	94	4	no	—
495	C₂×C₄	—	94	4	no	—
496	C₂×C₄	—	94	4	no	—
497	C₂×C₄	—	94	4	no	—
498	C₂×C₄	—	94	4	no	—
499	C₂×C₄	—	188	32	no	—
500	C₂×C₄	—	188	8	no	—
501	C₂×C₄	—	188	8	no	—
502	C₂×C₄	—	188	8	no	—
503	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
504	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
505	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
506	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
507	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
508	C₂²	—	2	32	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	8	no	—
512	C₂²	—	2	8	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	4	16	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	4	4	no	—
519	C₂²	C₂×#13093983	1	8	yes	—
520	C₂²	C₂×#13093983	1	4	yes	—
521	C₂²	#41×Dic₄₇	1	4	yes	—
522	C₂²	#15689598	1	4	yes	—
523	C₂²	#15689802	1	8	yes	—
524	C₂²	#15689822	1	8	yes	—
525	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
526	C₂²	C₂×#41×D₄₇	1	2	yes	—
527	C₂²	C₂²×#10625350	1	1	yes	characteristic
528	C₂²	C₂²×#10625350	1	1	yes	characteristic
529	C₂²	C₂×#13094069	1	2	yes	—
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	4	no	—
533	C₄	—	2	4	no	—
534	C₄	—	2	4	no	—
535	C₄	—	94	8	no	—
536	C₄	—	188	4	no	—
537	C₄	—	188	4	no	—
538	C₄	—	188	4	no	—
539	C₂	—	2	8	no	—
540	C₂	—	4	4	no	—
541	C₂	#20246328	1	8	yes	direct product factor
542	C₂	C₂²×#13093983	1	1	yes	characteristic
543	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
544	C₂	C₂×#15689598	1	1	yes	characteristic
545	C₂	C₂×#15689802	1	2	yes	—
546	C₂	C₂×#15689822	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂³×D₄×C₄₇	C₂²
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂×#2353
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #20246328	C₂	direct (N × H)
2. C₂×#15689016	C₂	semidirect
3. C₂×#15689009	C₂	semidirect
5. C₂×#15688991	C₂	semidirect
6. C₂×#15688986	C₂	semidirect
7. C₂×#15688983	C₂	semidirect
8. C₂×C₂²⋊C₄×Dic₄₇	C₂	semidirect
9. C₂×C₄×C₂²⋊Dic₄₇	C₂	semidirect
10. C₂×#15688969	C₂	semidirect
11. C₂²×C₄₇⋊#95	C₂	semidirect
20. #15689016	C₂²	semidirect
21. #15689009	C₂²	semidirect
23. #15688991	C₂²	semidirect
24. #15688986	C₂²	semidirect
25. #15688983	C₂²	semidirect
26. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
27. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
28. #15688969	C₂²	semidirect
38. C₂×C₄₇⋊#95	C₂²	semidirect
42. C₂×C₄×D₄×C₄₇	C₄	semidirect
86. C₂³×C₄×C₄₇	C₂×C₄	semidirect
94. C₄×D₄×C₄₇	C₂×C₄	semidirect
95. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
98. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
101. C₂×C₄²×C₄₇	C₂×C₄	semidirect
136. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
162. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
164. C₂²⋊C₄×C₄₇	C₂²×C₄	semidirect
165. C₄²×C₄₇	C₂²×C₄	semidirect
280. C₂×C₄₇	#2353	semidirect
290. C₂×C₄×D₄	Dic₄₇	semidirect
321. C₄₇	C₂×#2353	semidirect
339. C₂³×C₄	C₂×Dic₄₇	semidirect
347. C₄×D₄	C₂×Dic₄₇	semidirect
350. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
359. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
366. C₂×C₄²	C₂×Dic₄₇	semidirect
430. C₂²×C₄	C₂²×Dic₄₇	semidirect
437. C₄⋊C₄	C₂²×Dic₄₇	semidirect
442. C₂²⋊C₄	C₂²×Dic₄₇	semidirect
445. C₄²	C₂²×Dic₄₇	semidirect
541. C₂	#20246328	direct (N × H)

Maximal subgroups

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

subgroup	index
#20246328	2
C₂×#15689016	2
C₂×#15689009	2
C₂×#15689003	2
C₂×#15688991	2
C₂×#15688986	2
C₂×#15688983	2
C₂×C₂²⋊C₄×Dic₄₇	2
C₂×C₄×C₂²⋊Dic₄₇	2
C₂×#15688969	2
C₂²×C₄₇⋊#95	2
C₂²×C₄×D₄×C₄₇	2
C₂×#2353	47

Subgroups — C2×#20246328 #26375617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20246328 #26375617