Subgroups — C₂×#20252331 #27080654

Order 12032.

1938 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689680	C₂	1	1	yes	maximal, characteristic
2	#20252331	C₂	1	16	yes	maximal, direct product factor
3	C₂×#15689252	C₂	1	4	yes	maximal, complemented
4	C₂×#15689250	C₂	1	2	yes	maximal, complemented
5	C₂×#15689247	C₂	1	2	yes	maximal, complemented
6	C₂×#15689149	C₂	1	2	yes	maximal
7	C₂×#15689078	C₂	1	2	yes	maximal
8	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	#15689680	C₄	1	8	yes	—
13	#15689680	C₂²	1	8	yes	—
14	C₂×#13094024	C₄	1	1	yes	characteristic
15	C₂×#13094024	C₄	1	1	yes	characteristic
16	C₂×#13094016	C₄	1	2	yes	—
17	C₂×#13094003	C₄	1	2	yes	—
18	C₂×#13094003	C₄	1	2	yes	—
19	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
20	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
21	C₂×#13093983	C₂²	1	2	yes	—
22	#15689252	C₂²	1	32	yes	complemented
23	#15689250	C₂²	1	16	yes	complemented
24	#15689247	C₂²	1	16	yes	complemented
25	#15689149	C₂²	1	16	yes	—
26	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
27	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
28	#15689078	C₂²	1	16	yes	—
29	C₄×#10625329	C₂²	1	8	yes	—
30	C₂×#13093935	C₂²	1	2	yes	—
31	C₂×#13093934	C₂²	1	4	yes	—
32	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
33	C₂×C₈×Dic₄₇	C₂²	1	4	yes	—
34	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
35	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	8	yes	—
40	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
41	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
42	C₂×#10625329	—	2	4	no	—
43	C₂×#10625329	Q₈	1	8	yes	complemented
44	C₂×#10625329	C₂³	1	4	yes	—
45	C₂×#10625329	C₂³	1	4	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	#13094024	C₂×C₄	1	8	yes	—
49	#13094024	C₂×C₄	1	8	yes	—
50	#13094016	C₂×C₄	1	16	yes	—
51	#13094003	C₂×C₄	1	16	yes	—
52	#13094003	C₂×C₄	1	16	yes	—
53	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
54	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
55	C₄×Dic₉₄	C₂³	1	8	yes	—
56	C₄×Dic₉₄	C₂³	1	8	yes	—
57	#13093983	C₂×C₄	1	8	yes	—
58	#13093983	C₂³	1	8	yes	—
59	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
63	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
64	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
65	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
66	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
67	Dic₄₇⋊C₈	C₂³	1	16	yes	—
68	Dic₄₇⋊C₈	C₂³	1	16	yes	—
69	#13093935	C₂³	1	8	yes	—
70	#13093934	C₂³	1	16	yes	—
71	C₄×C₄₇⋊C₈	C₂³	1	8	yes	—
72	C₈×Dic₄₇	C₂³	1	16	yes	—
73	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₇	—	2	8	no	—
77	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
78	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
79	C₂²×C₈×C₄₇	C₂³	1	8	yes	—
80	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
86	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
87	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
88	C₄⋊C₈×C₄₇	C₂³	1	8	yes	—
89	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	4	2	no	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₄₇	#41	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
105	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
106	C₂×Dic₉₄	—	2	8	no	—
107	C₂×Dic₉₄	—	4	4	no	—
108	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
109	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
110	C₂×C₈×C₄₇	—	2	4	no	—
111	C₂×C₈×C₄₇	—	2	4	no	—
112	C₂×C₈×C₄₇	—	2	16	no	—
113	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
114	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
115	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
116	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
117	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
118	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
119	C₄²×C₄₇	C₂⁴	1	2	yes	—
120	C₄²×C₄₇	C₂⁴	1	2	yes	—
121	C₂²⋊Dic₄₇	C₂²×C₄	1	16	yes	—
122	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
123	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
124	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
125	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
126	Dic₄₇⋊C₄	C₂²×C₄	1	16	yes	—
127	Dic₄₇⋊C₄	C₂²×C₄	1	16	yes	—
128	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
129	C₄×Dic₄₇	C₂⁴	1	8	yes	—
130	#10625329	—	2	8	no	—
131	#10625329	C₂×Q₈	1	16	yes	complemented
132	C₂×C₄₇⋊C₈	—	2	4	no	—
133	C₂×C₄₇⋊C₈	C₂×Q₈	1	8	yes	—
134	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
135	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	C₄×Q₈	1	4	yes	—
139	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
140	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	8	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	C₄×Q₈	1	8	yes	—
147	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
148	C₂×C₄×C₄₇	#131	1	4	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
152	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
156	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
157	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
159	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
160	C₂×Dic₄₇	—	2	8	no	—
161	C₂×Dic₄₇	—	2	8	no	—
162	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
163	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
164	Dic₉₄	—	2	16	no	—
165	Dic₉₄	—	4	8	no	—
166	C₈×C₄₇	—	2	4	no	—
167	C₈×C₄₇	—	2	4	no	—
168	C₄₇⋊C₈	—	2	4	no	—
169	C₄₇⋊C₈	C₂²×Q₈	1	8	yes	—
170	C₂×#2962	—	47	1	no	maximal, Sylow
171	C₂²×C₄₇	—	2	8	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	C₂×C₄×Q₈	1	4	yes	—
175	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
176	C₂²×C₄₇	C₂×#131	1	2	yes	—
177	C₂²×C₄₇	#568	1	2	yes	—
178	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	2	2	no	—
181	C₄×C₄₇	—	2	2	no	—
182	C₄×C₄₇	C₂×C₄×Q₈	1	2	yes	—
183	C₄×C₄₇	C₂×C₄×Q₈	1	4	yes	—
184	C₄×C₄₇	C₂×#131	1	4	yes	—
185	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
186	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
187	Dic₄₇	—	2	8	no	—
188	Dic₄₇	—	2	8	no	—
189	C₂×#533	—	47	1	no	—
190	#2962	—	47	16	no	—
191	C₂×#446	—	47	2	no	—
192	C₂×#446	—	47	4	no	—
193	C₂×C₈×Q₈	—	47	2	no	—
194	C₂×#424	—	47	2	no	—
195	C₂²×C₄⋊C₈	D₄₇	1	1	yes	characteristic
196	C₂×#405	—	47	2	no	—
197	C₂×C₄×M₁₆	—	47	1	no	—
198	C₂×C₄₇	—	2	4	no	—
199	C₂×C₄₇	#2962	1	4	yes	complemented
200	C₂×C₄₇	C₂²×C₄×Q₈	1	1	yes	characteristic
201	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
202	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
203	C₂²×M₁₆	—	47	1	no	—
204	C₂²×M₁₆	—	47	1	no	—
205	C₂³×C₈	C₂×D₄₇	1	2	yes	—
206	#533	—	47	8	no	—
207	#533	—	47	8	no	—
208	C₂×C₄⋊Q₈	—	47	1	no	—
209	C₂×C₄⋊Q₈	—	47	1	no	—
210	C₂×#125	—	47	2	no	—
211	C₂×C₂²⋊Q₈	—	47	2	no	—
212	C₂×C₂²⋊Q₈	—	47	2	no	—
213	C₂×C₄×Q₈	—	47	2	no	—
214	C₂×C₄×Q₈	—	47	2	no	—
215	C₂×#117	—	47	2	no	—
216	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
217	#446	—	47	16	no	—
218	#446	—	47	32	no	—
219	C₈×Q₈	—	47	16	no	—
220	#424	—	47	16	no	—
221	C₂×C₄⋊C₈	—	47	4	no	—
222	C₂×C₄⋊C₈	—	47	4	no	—
223	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
226	C₂×C₄⋊C₈	C₂×D₄₇	1	8	yes	—
227	#405	—	47	16	no	—
228	C₄×M₁₆	—	47	8	no	—
229	C₂×#97	—	47	4	no	—
230	C₂×#97	—	47	2	no	—
231	C₂×C₄×C₈	—	47	4	no	—
232	C₂×C₄×C₈	—	47	2	no	—
233	C₄₇	C₂×#2962	1	1	yes	characteristic, complemented, Sylow
234	C₂²×Q₈	—	47	2	no	—
235	C₂²×Q₈	—	47	2	no	—
236	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
237	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
238	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
239	C₂×M₁₆	—	47	8	no	—
240	C₂×M₁₆	—	47	4	no	—
241	C₂×M₁₆	—	47	4	no	—
242	C₂×M₁₆	—	94	4	no	—
243	C₂²×C₈	—	2	8	no	—
244	C₂²×C₈	—	47	2	no	—
245	C₂²×C₈	—	47	2	no	—
246	C₂²×C₈	C₂²×D₄₇	1	8	yes	—
247	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
248	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
249	C₄⋊Q₈	—	47	8	no	—
250	C₄⋊Q₈	—	47	8	no	—
251	#125	—	47	16	no	—
252	C₂²⋊Q₈	—	47	16	no	—
253	C₂²⋊Q₈	—	47	16	no	—
254	C₄×Q₈	—	47	8	no	—
255	C₄×Q₈	—	47	8	no	—
256	C₄×Q₈	—	47	8	no	—
257	C₄×Q₈	—	47	8	no	—
258	#117	—	47	8	no	—
259	#117	—	47	8	no	—
260	C₂×C₄⋊C₄	—	47	2	no	—
261	C₂×C₄⋊C₄	—	47	2	no	—
262	C₂×C₄⋊C₄	—	47	4	no	—
263	C₂×C₄⋊C₄	—	47	4	no	—
264	C₂×C₄⋊C₄	—	47	2	no	—
265	C₂×C₄⋊C₄	—	47	2	no	—
266	C₂×C₂²⋊C₄	—	47	4	no	—
267	C₂×C₄²	—	47	4	no	—
268	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
269	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
270	C₂×C₄²	C₄×D₄₇	1	4	yes	—
271	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
272	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
273	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
274	C₄⋊C₈	—	47	16	no	—
275	C₄⋊C₈	—	47	16	no	—
276	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
277	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
278	C₄⋊C₈	C₂²×D₄₇	1	8	yes	—
279	#97	—	47	16	no	—
280	#97	—	47	8	no	—
281	C₄×C₈	—	47	16	no	—
282	C₄×C₈	—	47	8	no	—
283	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
284	C₂×Q₈	—	47	8	no	—
285	C₂×Q₈	—	47	8	no	—
286	C₂×Q₈	—	94	8	no	—
287	C₂×Q₈	—	188	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	47	4	no	—
291	C₂²×C₄	—	47	4	no	—
292	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
296	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
297	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
299	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
300	C₂²×C₄	#10625352	1	4	yes	—
301	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
302	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
303	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
304	M₁₆	—	47	16	no	—
305	M₁₆	—	94	8	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	16	no	—
309	C₂×C₈	—	47	8	no	—
310	C₂×C₈	—	47	4	no	—
311	C₂×C₈	—	47	4	no	—
312	C₂×C₈	—	94	4	no	—
313	C₂×C₈	C₂³×D₄₇	1	4	yes	—
314	C₂×C₈	C₂³×D₄₇	1	4	yes	—
315	C₄⋊C₄	—	47	16	no	—
316	C₄⋊C₄	—	47	16	no	—
317	C₄⋊C₄	—	47	8	no	—
318	C₄⋊C₄	—	47	8	no	—
319	C₄⋊C₄	—	47	8	no	—
320	C₄⋊C₄	—	47	8	no	—
321	C₂²⋊C₄	—	47	16	no	—
322	C₄²	—	47	8	no	—
323	C₄²	—	47	8	no	—
324	C₄²	C₂×C₄×D₄₇	1	2	yes	—
325	C₄²	C₂×C₄×D₄₇	1	2	yes	—
326	C₄²	C₂×C₄×D₄₇	1	4	yes	—
327	C₄²	C₂×C₄×D₄₇	1	4	yes	—
328	C₄²	C₂³×D₄₇	1	2	yes	—
329	C₄²	C₂³×D₄₇	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	#13093989	1	4	yes	—
333	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
334	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
335	Q₈	—	94	16	no	—
336	Q₈	—	188	8	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	47	8	no	—
343	C₂×C₄	—	47	8	no	—
344	C₂×C₄	—	94	8	no	—
345	C₂×C₄	—	94	8	no	—
346	C₂×C₄	#13093989	1	8	yes	—
347	C₂×C₄	#13093989	1	4	yes	—
348	C₂×C₄	#13094030	1	4	yes	—
349	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
350	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
351	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
352	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
354	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
355	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
356	C₂×C₄	C₂×Q₈×D₄₇	1	4	yes	—
357	C₂×C₄	C₂×#10625352	1	2	yes	—
358	C₂×C₄	C₂×#10625352	1	4	yes	—
359	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
360	C₈	—	2	4	no	—
361	C₈	—	2	4	no	—
362	C₈	—	47	8	no	—
363	C₈	—	94	4	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	8	no	—
367	C₂²	C₂×#13093989	1	4	yes	—
368	C₂²	C₂×#13093989	1	2	yes	—
369	C₂²	C₂×#13094030	1	2	yes	—
370	C₂²	#15689889	1	2	yes	—
371	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	94	8	no	—
376	C₄	—	94	8	no	—
377	C₄	C₂×#13093989	1	2	yes	—
378	C₄	C₂×#13093989	1	4	yes	—
379	C₄	C₂×#13094030	1	4	yes	—
380	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
381	C₄	C₂²×#10625352	1	1	yes	characteristic
382	C₂	—	2	4	no	—
383	C₂	#20252331	1	4	yes	direct product factor
384	C₂	C₂²×#13093989	1	1	yes	characteristic
385	C₂	C₂²×#13094030	1	1	yes	characteristic
386	C₂	C₂×#15689889	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂²×C₄⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂²×C₄⋊C₈	D₄₇
hypocenter	C₄₇	C₂×#2962
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #20252331	C₂	direct (N × H)
3. C₂×#15689252	C₂	semidirect
4. C₂×#15689250	C₂	semidirect
5. C₂×#15689247	C₂	semidirect
22. #15689252	C₂²	semidirect
23. #15689250	C₂²	semidirect
24. #15689247	C₂²	semidirect
43. C₂×#10625329	Q₈	semidirect
131. #10625329	C₂×Q₈	semidirect
199. C₂×C₄₇	#2962	semidirect
233. C₄₇	C₂×#2962	semidirect
383. C₂	#20252331	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×#15689680	2
#20252331	2
C₂×#15689252	2
C₂×#15689250	2
C₂×#15689247	2
C₂×#15689149	2
C₂×#15689078	2
C₂×C₄×#10625329	2
C₂²×C₄⋊C₈×C₄₇	2
C₂×#2962	47

Subgroups — C2×#20252331 #27080654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252331 #27080654