Subgroups — C₂×#20241990 #26184185

Order 12032.

1050 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689180	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
3	#20241990	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688865	C₂	1	4	yes	maximal, complemented
5	C₂²×#125×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	—	2	1	no	—
7	#15689180	—	2	2	no	—
8	#15689180	C₂²	1	4	yes	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
10	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
11	C₄×#10625329	—	2	2	no	—
12	C₄×#10625329	C₂²	1	4	yes	—
13	C₂×#13093935	C₂²	1	2	yes	—
14	C₂×#13093935	C₂²	1	2	yes	—
15	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
16	#15688865	C₂²	1	16	yes	complemented
17	C₂×#125×C₄₇	—	2	1	no	—
18	C₂×#125×C₄₇	—	2	2	no	—
19	C₂×#125×C₄₇	—	2	1	no	—
20	C₂×#125×C₄₇	—	2	2	no	—
21	C₂×#125×C₄₇	C₄	1	2	yes	—
22	C₂×#125×C₄₇	C₄	1	4	yes	—
23	C₂×#125×C₄₇	C₂²	1	2	yes	—
24	C₂×#125×C₄₇	C₂²	1	4	yes	—
25	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
26	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
27	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#10625329	—	2	8	no	—
31	C₂×#10625329	—	2	4	no	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
35	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
36	#13093935	—	2	2	no	—
37	#13093935	—	2	2	no	—
38	#13093935	C₂³	1	4	yes	—
39	#13093935	C₂³	1	4	yes	—
40	C₄×C₄₇⋊C₈	—	2	4	no	—
41	C₂³×C₄×C₄₇	—	2	1	no	—
42	C₂³×C₄×C₄₇	—	2	1	no	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	#125×C₄₇	—	2	4	no	—
47	#125×C₄₇	—	2	4	no	—
48	#125×C₄₇	—	2	4	no	—
49	#125×C₄₇	—	2	4	no	—
50	#125×C₄₇	—	2	2	no	—
51	#125×C₄₇	—	2	2	no	—
52	#125×C₄₇	—	2	4	no	—
53	#125×C₄₇	C₂×C₄	1	4	yes	—
54	#125×C₄₇	C₂×C₄	1	8	yes	—
55	#125×C₄₇	C₂³	1	4	yes	—
56	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
68	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
72	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	D₄	1	2	yes	—
76	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	D₄	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	4	2	no	—
88	C₂²×C₄×C₄₇	—	4	4	no	—
89	C₂²×C₄×C₄₇	—	4	4	no	—
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₄⋊C₄×C₄₇	—	2	4	no	—
103	C₄⋊C₄×C₄₇	—	2	8	no	—
104	C₄⋊C₄×C₄₇	—	2	8	no	—
105	C₄⋊C₄×C₄₇	—	2	4	no	—
106	C₄⋊C₄×C₄₇	—	2	2	no	—
107	C₄⋊C₄×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	2	4	no	—
109	C₄⋊C₄×C₄₇	—	2	4	no	—
110	C₄⋊C₄×C₄₇	—	2	4	no	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
113	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
114	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
115	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
116	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
117	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₄₇	C₂×D₄	1	2	yes	—
120	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	C₂×D₄	1	2	yes	—
123	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
124	#10625329	—	2	16	no	—
125	C₂×C₄₇⋊C₈	—	2	8	no	—
126	C₂×C₄₇⋊C₈	—	2	4	no	—
127	C₂×C₄₇⋊C₈	—	2	4	no	—
128	C₂×C₄₇⋊C₈	—	4	4	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	#104	1	4	yes	—
132	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	8	no	—
148	C₂×C₄×C₄₇	—	4	8	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	#101	1	4	yes	—
152	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₄₇⋊C₈	—	2	8	no	—
162	C₄₇⋊C₈	—	4	4	no	—
163	C₂×#1528	—	47	1	no	maximal, Sylow
164	C₂²×C₄₇	—	2	2	no	—
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	2	8	no	—
167	C₂²×C₄₇	C₂×#101	1	2	yes	—
168	C₂²×C₄₇	C₂×#104	1	4	yes	—
169	C₂²×C₄₇	C₂×#104	1	2	yes	—
170	C₂²×C₄₇	#421	1	2	yes	—
171	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
172	C₄×C₄₇	—	2	1	no	—
173	C₄×C₄₇	—	2	1	no	—
174	C₄×C₄₇	—	2	1	no	—
175	C₄×C₄₇	—	2	1	no	—
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	—	2	1	no	—
178	C₄×C₄₇	—	2	1	no	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	4	4	no	—
181	C₄×C₄₇	—	4	4	no	—
182	C₄×C₄₇	C₂×#101	1	4	yes	—
183	C₂²×#125	D₄₇	1	1	yes	characteristic
184	C₂×#432	—	47	1	no	—
185	C₂×C₄×M₁₆	—	47	1	no	—
186	#1528	—	47	8	no	—
187	C₂×#330	—	47	4	no	—
188	C₂×C₄₇	—	2	4	no	—
189	C₂×C₄₇	#1528	1	4	yes	complemented
190	C₂×C₄₇	C₂²×#101	1	1	yes	characteristic
191	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
192	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
193	C₂²×M₁₆	—	94	1	no	—
194	C₂×#125	—	2	1	no	—
195	C₂×#125	—	2	2	no	—
196	C₂×#125	—	2	1	no	—
197	C₂×#125	—	2	2	no	—
198	C₂×#125	Dic₄₇	1	4	yes	—
199	C₂×#125	Dic₄₇	1	2	yes	—
200	C₂×#125	C₂×D₄₇	1	2	yes	—
201	C₂×#125	C₂×D₄₇	1	4	yes	—
202	C₂²×C₄⋊C₄	—	2	1	no	—
203	C₂²×C₄⋊C₄	—	2	1	no	—
204	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
205	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
206	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
207	#432	—	47	4	no	—
208	#432	—	94	2	no	—
209	C₂×C₄⋊C₈	—	94	1	no	—
210	C₂×C₂²⋊C₈	—	94	1	no	—
211	C₄×M₁₆	—	47	4	no	—
212	C₄×M₁₆	—	94	2	no	—
213	C₂×#97	—	47	2	no	—
214	C₂×#97	—	47	2	no	—
215	C₂×C₄×C₈	—	94	1	no	—
216	#330	—	47	16	no	—
217	C₄₇	C₂×#1528	1	1	yes	characteristic, complemented, Sylow
218	C₂³×C₄	—	2	1	no	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
221	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
222	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
223	C₂×M₁₆	—	94	8	no	—
224	C₂×M₁₆	—	94	4	no	—
225	C₂²×C₈	—	94	2	no	—
226	C₂²×C₈	—	94	2	no	—
227	#125	—	2	4	no	—
228	#125	—	2	4	no	—
229	#125	—	2	4	no	—
230	#125	—	2	4	no	—
231	#125	—	2	2	no	—
232	#125	—	2	2	no	—
233	#125	—	2	4	no	—
234	#125	C₂×Dic₄₇	1	4	yes	—
235	#125	C₂×Dic₄₇	1	8	yes	—
236	#125	C₂²×D₄₇	1	4	yes	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
250	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
251	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
252	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
253	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
254	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
255	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
256	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
257	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
259	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
260	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
261	C₄⋊C₈	—	94	4	no	—
262	C₂²⋊C₈	—	94	4	no	—
263	#97	—	47	4	no	—
264	#97	—	47	4	no	—
265	#97	—	94	2	no	—
266	#97	—	94	2	no	—
267	C₄×C₈	—	94	4	no	—
268	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
279	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
280	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
283	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
285	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
287	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
290	M₁₆	—	94	16	no	—
291	C₂×C₈	—	94	8	no	—
292	C₂×C₈	—	94	4	no	—
293	C₂×C₈	—	94	4	no	—
294	C₂×C₈	—	188	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	—	2	8	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
306	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
307	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
308	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
309	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
310	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
311	C₄²	C₂²×Dic₄₇	1	2	yes	—
312	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
313	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
314	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
315	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
316	C₄²	C₂³×D₄₇	1	1	yes	characteristic
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	#13093951	1	4	yes	—
320	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
321	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	8	no	—
336	C₂×C₄	—	4	8	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	#13093943	1	4	yes	—
340	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
341	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
342	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
343	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
344	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
345	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
346	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
348	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
349	C₈	—	94	8	no	—
350	C₈	—	188	4	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	8	no	—
353	C₂²	—	2	2	no	—
354	C₂²	C₂×#13093943	1	2	yes	—
355	C₂²	C₂×#13093951	1	4	yes	—
356	C₂²	C₂×#13093951	1	2	yes	—
357	C₂²	#15689140	1	2	yes	—
358	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	4	4	no	—
368	C₄	—	4	4	no	—
369	C₄	C₂×#13093943	1	4	yes	—
370	C₂	—	2	4	no	—
371	C₂	#20241990	1	4	yes	direct product factor
372	C₂	C₂²×#13093943	1	1	yes	characteristic
373	C₂	C₂²×#13093951	1	1	yes	characteristic
374	C₂	C₂×#15689140	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂²×#125×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂²×#125	D₄₇
hypocenter	C₄₇	C₂×#1528
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×#125

Complements

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

N	H ≅ G/N	type
3. #20241990	C₂	direct (N × H)
4. C₂×#15688865	C₂	semidirect
16. #15688865	C₂²	semidirect
189. C₂×C₄₇	#1528	semidirect
217. C₄₇	C₂×#1528	semidirect
371. C₂	#20241990	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689180	2
C₂×C₄×#10625329	2
#20241990	2
C₂×#15688865	2
C₂²×#125×C₄₇	2
C₂×#1528	47

Subgroups — C2×#20241990 #26184185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241990 #26184185