Subgroups — C₂×#20252021 #27080003

Order 12032.

2806 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252021	C₂	1	16	yes	maximal, direct product factor
2	C₂×#15689180	C₂	1	4	yes	maximal, complemented
3	C₂×#15689176	C₂	1	4	yes	maximal, complemented
4	C₂×#15689147	C₂	1	2	yes	maximal, complemented
5	C₂×#15689087	C₂	1	2	yes	maximal
6	C₂×C₄×#10625329	C₂	1	2	yes	maximal, complemented
7	C₂³×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10625329	C₂²	1	4	yes	—
9	#15689180	C₂²	1	32	yes	complemented
10	#15689176	C₂²	1	32	yes	complemented
11	#15689147	C₂²	1	16	yes	complemented
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	8	yes	complemented
13	#15689087	C₂²	1	16	yes	—
14	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	8	yes	—
15	C₄×#10625329	C₂²	1	16	yes	complemented
16	C₂×#13093935	C₂²	1	4	yes	complemented
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	4	yes	complemented
18	C₂⁴×C₄×C₄₇	C₄	1	2	yes	—
19	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₇	C₄	1	8	yes	—
21	C₂²×C₄²×C₄₇	C₄	1	2	yes	—
22	C₂²×C₄²×C₄₇	C₄	1	2	yes	—
23	C₂²×C₄²×C₄₇	C₄	1	2	yes	—
24	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
26	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
27	C₂²×C₄²×C₄₇	C₂²	1	8	yes	—
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#10625329	—	2	16	no	—
30	C₂×#10625329	C₂³	1	16	yes	—
31	C₂²×C₄₇⋊C₈	C₂³	1	8	yes	—
32	C₄⋊(C₄₇⋊C₈)	C₂³	1	32	yes	complemented
33	C₂²⋊(C₄₇⋊C₈)	C₂³	1	32	yes	—
34	#13093935	C₂³	1	16	yes	complemented
35	C₄×C₄₇⋊C₈	C₂³	1	16	yes	complemented
36	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	—	2	16	no	—
38	C₂³×C₄×C₄₇	—	2	8	no	—
39	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₄₇	C₂×C₄	1	16	yes	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
54	C₂×C₄²×C₄₇	C₂×C₄	1	16	yes	—
55	C₂×C₄²×C₄₇	C₂×C₄	1	16	yes	—
56	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
59	C₂×C₄²×C₄₇	C₂×C₄	1	16	yes	—
60	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
68	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
71	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₂⁴×C₄₇	—	2	4	no	—
74	C₂⁴×C₄₇	—	2	8	no	—
75	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
76	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	8	no	—
80	C₂²×C₄×C₄₇	—	2	16	no	—
81	C₂²×C₄×C₄₇	—	2	8	no	—
82	C₂²×C₄×C₄₇	—	2	8	no	—
83	C₂²×C₄×C₄₇	—	2	8	no	—
84	C₂²×C₄×C₄₇	—	2	8	no	—
85	C₂²×C₄×C₄₇	—	2	8	no	—
86	C₂²×C₄×C₄₇	—	2	64	no	—
87	C₂²×C₄×C₄₇	—	2	8	no	—
88	C₂²×C₄×C₄₇	—	2	16	no	—
89	C₂²×C₄×C₄₇	M₁₆	1	16	yes	complemented
90	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
106	C₂²×C₄×C₄₇	#41	1	8	yes	—
107	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
110	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
111	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
112	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
113	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
114	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
115	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
116	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
117	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
118	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
119	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₇	C₂⁴	1	2	yes	—
121	C₄²×C₄₇	C₂⁴	1	2	yes	—
122	C₄²×C₄₇	C₂⁴	1	4	yes	—
123	#10625329	—	2	32	no	—
124	C₂×C₄₇⋊C₈	—	2	16	no	—
125	C₂×C₄₇⋊C₈	C₂⁴	1	16	yes	—
126	C₂³×C₄₇	—	2	32	no	—
127	C₂³×C₄₇	—	2	8	no	—
128	C₂³×C₄₇	—	2	4	no	—
129	C₂³×C₄₇	—	2	16	no	—
130	C₂³×C₄₇	—	2	4	no	—
131	C₂³×C₄₇	—	2	4	no	—
132	C₂³×C₄₇	#117	1	4	yes	—
133	C₂³×C₄₇	C₂×M₁₆	1	8	yes	—
134	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
135	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
136	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₇	—	2	8	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	16	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	8	no	—
143	C₂×C₄×C₄₇	—	2	16	no	—
144	C₂×C₄×C₄₇	—	2	16	no	—
145	C₂×C₄×C₄₇	—	2	16	no	—
146	C₂×C₄×C₄₇	—	2	16	no	—
147	C₂×C₄×C₄₇	—	2	16	no	—
148	C₂×C₄×C₄₇	—	2	8	no	—
149	C₂×C₄×C₄₇	#117	1	8	yes	—
150	C₂×C₄×C₄₇	#117	1	4	yes	—
151	C₂×C₄×C₄₇	C₂×M₁₆	1	8	yes	—
152	C₂×C₄×C₄₇	C₂×M₁₆	1	8	yes	—
153	C₂×C₄×C₄₇	C₂×M₁₆	1	32	yes	complemented
154	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
155	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
156	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
157	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
159	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
160	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
161	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
162	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
163	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
164	C₄₇⋊C₈	—	2	16	no	—
165	C₂×#2920	—	47	1	no	maximal, Sylow
166	C₂²×C₄₇	—	2	32	no	—
167	C₂²×C₄₇	—	2	4	no	—
168	C₂²×C₄₇	—	2	8	no	—
169	C₂²×C₄₇	—	2	16	no	—
170	C₂²×C₄₇	—	2	4	no	—
171	C₂²×C₄₇	—	2	4	no	—
172	C₂²×C₄₇	C₂×#117	1	4	yes	—
173	C₂²×C₄₇	C₂×#117	1	2	yes	—
174	C₂²×C₄₇	C₂²×M₁₆	1	8	yes	—
175	C₂²×C₄₇	C₂²×M₁₆	1	4	yes	—
176	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
177	C₄×C₄₇	—	2	4	no	—
178	C₄×C₄₇	—	2	4	no	—
179	C₄×C₄₇	—	2	4	no	—
180	C₄×C₄₇	C₂×#117	1	2	yes	—
181	C₄×C₄₇	C₂×#117	1	4	yes	—
182	C₄×C₄₇	C₂²×M₁₆	1	8	yes	—
183	C₄×C₄₇	C₂²×M₁₆	1	8	yes	—
184	C₄×C₄₇	C₂²×#41	1	2	yes	—
185	C₂³×C₄²	D₄₇	1	1	yes	characteristic
186	#2920	—	47	16	no	—
187	C₂×#432	—	47	4	no	—
188	C₂×#431	—	47	4	no	—
189	C₂×#423	—	47	2	no	—
190	C₂×#407	—	47	2	no	—
191	C₂×C₄×M₁₆	—	47	2	no	—
192	C₂×C₄₇	—	2	4	no	—
193	C₂×C₄₇	—	2	8	no	—
194	C₂×C₄₇	#2920	1	4	yes	complemented
195	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
196	C₂×C₄₇	C₂³×M₁₆	1	2	yes	—
197	C₂⁴×C₄	Dic₄₇	1	2	yes	—
198	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
199	C₂²×M₁₆	—	47	4	no	—
200	C₂²×C₄²	Dic₄₇	1	8	yes	—
201	C₂²×C₄²	Dic₄₇	1	2	yes	—
202	C₂²×C₄²	Dic₄₇	1	2	yes	—
203	C₂²×C₄²	Dic₄₇	1	2	yes	—
204	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
205	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
206	C₂²×C₄²	C₂×D₄₇	1	8	yes	—
207	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
208	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
209	#432	—	47	32	no	—
210	#431	—	47	32	no	—
211	#423	—	47	16	no	—
212	C₂×C₄⋊C₈	—	47	8	no	—
213	#407	—	47	16	no	—
214	C₂×C₂²⋊C₈	—	47	8	no	—
215	C₄×M₁₆	—	47	16	no	—
216	C₂×#97	—	47	4	no	—
217	C₂×C₄×C₈	—	47	4	no	—
218	C₄₇	C₂×#2920	1	1	yes	characteristic, complemented, Sylow
219	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
220	C₂³×C₄	—	2	16	no	—
221	C₂³×C₄	—	2	8	no	—
222	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
223	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
224	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
225	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
226	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
227	C₂³×C₄	C₂×Dic₄₇	1	16	yes	—
228	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
229	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
230	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
231	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
232	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
233	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
234	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
235	C₂×M₁₆	—	47	16	no	—
236	C₂×M₁₆	—	94	16	no	—
237	C₂²×C₈	—	47	8	no	—
238	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
239	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
240	C₂×C₄²	C₂×Dic₄₇	1	16	yes	—
241	C₂×C₄²	C₂×Dic₄₇	1	16	yes	—
242	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
243	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
244	C₂×C₄²	C₂×Dic₄₇	1	16	yes	—
245	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
246	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
247	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
248	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
249	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
250	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
251	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
252	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
253	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
254	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
255	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
256	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
257	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
258	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
259	C₄⋊C₈	—	47	32	no	—
260	C₂²⋊C₈	—	47	32	no	—
261	#97	—	47	16	no	—
262	C₄×C₈	—	47	16	no	—
263	C₂⁴	—	2	4	no	—
264	C₂⁴	—	2	8	no	—
265	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
266	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
267	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	16	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	64	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	16	no	—
279	C₂²×C₄	#10625329	1	16	yes	complemented
280	C₂²×C₄	#10625350	1	8	yes	—
281	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
282	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
283	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
284	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
285	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
286	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
287	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
288	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
289	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
290	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
291	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
292	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
293	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
295	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
296	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
297	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
298	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
299	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
300	M₁₆	—	94	32	no	—
301	C₂×C₈	—	47	16	no	—
302	C₂×C₈	—	94	16	no	—
303	C₄²	C₂²×Dic₄₇	1	8	yes	—
304	C₄²	C₂²×Dic₄₇	1	8	yes	—
305	C₄²	C₂²×Dic₄₇	1	8	yes	—
306	C₄²	C₂²×Dic₄₇	1	8	yes	—
307	C₄²	C₂²×Dic₄₇	1	2	yes	—
308	C₄²	C₂²×Dic₄₇	1	4	yes	—
309	C₄²	C₂²×Dic₄₇	1	8	yes	—
310	C₄²	C₂²×Dic₄₇	1	4	yes	—
311	C₄²	C₂²×Dic₄₇	1	4	yes	—
312	C₄²	C₂²×Dic₄₇	1	2	yes	—
313	C₄²	C₂³×D₄₇	1	2	yes	—
314	C₄²	C₂³×D₄₇	1	2	yes	—
315	C₄²	C₂³×D₄₇	1	4	yes	—
316	C₂³	—	2	32	no	—
317	C₂³	—	2	8	no	—
318	C₂³	—	2	4	no	—
319	C₂³	—	2	16	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	4	no	—
322	C₂³	#13093983	1	4	yes	—
323	C₂³	C₂×#10625329	1	8	yes	—
324	C₂³	C₂³×Dic₄₇	1	2	yes	—
325	C₂³	C₂³×Dic₄₇	1	4	yes	—
326	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	16	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	16	no	—
334	C₂×C₄	—	2	16	no	—
335	C₂×C₄	—	2	16	no	—
336	C₂×C₄	—	2	16	no	—
337	C₂×C₄	—	2	16	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	#13093983	1	8	yes	—
340	C₂×C₄	#13093983	1	4	yes	—
341	C₂×C₄	C₂×#10625329	1	8	yes	—
342	C₂×C₄	C₂×#10625329	1	8	yes	—
343	C₂×C₄	C₂×#10625329	1	32	yes	complemented
344	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
345	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
346	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
347	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
348	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
349	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
350	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
351	C₂×C₄	C₂×#10625350	1	4	yes	—
352	C₂×C₄	C₂×#10625350	1	8	yes	—
353	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
354	C₈	—	94	16	no	—
355	C₂²	—	2	32	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	8	no	—
360	C₂²	—	2	16	no	—
361	C₂²	C₂×#13093983	1	4	yes	—
362	C₂²	C₂×#13093983	1	2	yes	—
363	C₂²	C₂²×#10625329	1	8	yes	—
364	C₂²	C₂²×#10625329	1	4	yes	—
365	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
366	C₄	—	2	4	no	—
367	C₄	—	2	4	no	—
368	C₄	—	2	4	no	—
369	C₄	C₂×#13093983	1	2	yes	—
370	C₄	C₂×#13093983	1	4	yes	—
371	C₄	C₂²×#10625329	1	8	yes	—
372	C₄	C₂²×#10625329	1	8	yes	—
373	C₄	C₂²×#10625350	1	2	yes	—
374	C₂	—	2	4	no	—
375	C₂	—	2	8	no	—
376	C₂	#20252021	1	4	yes	direct product factor
377	C₂	C₂²×#13093983	1	1	yes	characteristic
378	C₂	C₂³×#10625329	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂³×C₄²×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁵×C₄₇	C₂×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂³×C₄²	D₄₇
hypocenter	C₄₇	C₂×#2920
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
1. #20252021	C₂	direct (N × H)
2. C₂×#15689180	C₂	semidirect
3. C₂×#15689176	C₂	semidirect
4. C₂×#15689147	C₂	semidirect
6. C₂×C₄×#10625329	C₂	semidirect
9. #15689180	C₂²	semidirect
10. #15689176	C₂²	semidirect
11. #15689147	C₂²	semidirect
12. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
15. C₄×#10625329	C₂²	semidirect
16. C₂×#13093935	C₂²	semidirect
17. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
32. C₄⋊(C₄₇⋊C₈)	C₂³	semidirect
34. #13093935	C₂³	semidirect
35. C₄×C₄₇⋊C₈	C₂³	semidirect
89. C₂²×C₄×C₄₇	M₁₆	semidirect
153. C₂×C₄×C₄₇	C₂×M₁₆	semidirect
194. C₂×C₄₇	#2920	semidirect
218. C₄₇	C₂×#2920	semidirect
279. C₂²×C₄	#10625329	semidirect
343. C₂×C₄	C₂×#10625329	semidirect
376. C₂	#20252021	direct (N × H)

Maximal subgroups

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

subgroup	index
#20252021	2
C₂×#15689180	2
C₂×#15689176	2
C₂×#15689147	2
C₂×#15689087	2
C₂×C₄×#10625329	2
C₂³×C₄²×C₄₇	2
C₂×#2920	47

Subgroups — C2×#20252021 #27080003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252021 #27080003