Subgroups — C₂×#20251740 #26422214

Order 12032.

3790 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094024	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13094003	C₂	1	2	yes	maximal
3	#20251740	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689029	C₂	1	2	yes	maximal, complemented
5	C₂×#15689021	C₂	1	4	yes	maximal, complemented
6	C₂×#15688993	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688983	C₂	1	4	yes	maximal
8	C₂³×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂³×Dic₉₄	C₂²	1	2	yes	—
10	C₂×#13094024	—	2	8	no	—
11	C₂×#13094024	C₂²	1	8	yes	complemented
12	C₂×#13094003	—	2	16	no	—
13	C₂×#13094003	C₂²	1	16	yes	—
14	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	—
15	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	—
16	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
17	C₂²×Dic₄₇⋊C₄	C₂²	1	4	yes	—
18	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
19	#15689029	C₂²	1	16	yes	complemented
20	#15689021	C₂²	1	32	yes	complemented
21	#15688993	C₂²	1	8	yes	complemented
22	#15688983	C₂²	1	32	yes	—
23	C₂×C₄₇⋊#95	C₂²	1	8	yes	—
24	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
26	C₂²×C₄²×C₄₇	—	2	8	no	—
27	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
28	C₂²×C₄²×C₄₇	C₂²	1	8	yes	—
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×Dic₉₄	—	2	8	no	—
32	C₂²×Dic₉₄	—	2	8	no	—
33	C₂²×Dic₉₄	—	2	8	no	—
34	C₂²×Dic₉₄	C₂³	1	8	yes	—
35	C₂³×Dic₄₇	C₂³	1	4	yes	—
36	C₂³×Dic₄₇	C₂³	1	4	yes	—
37	#13094024	—	2	32	no	—
38	#13094003	—	2	64	no	—
39	C₂×C₄⋊Dic₄₇	—	2	8	no	—
40	C₂×C₄⋊Dic₄₇	—	2	16	no	—
41	C₂×C₄⋊Dic₄₇	—	2	16	no	—
42	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	—
43	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	—
44	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
45	C₂×Dic₄₇⋊C₄	—	2	16	no	—
46	C₂×Dic₄₇⋊C₄	C₂³	1	16	yes	—
47	C₂×C₂²⋊Dic₄₇	—	2	16	no	—
48	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
49	C₄₇⋊#95	C₂³	1	32	yes	—
50	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	—	2	4	no	—
52	C₂³×C₄×C₄₇	—	2	8	no	—
53	C₂³×C₄×C₄₇	—	2	4	no	—
54	C₂³×C₄×C₄₇	—	2	8	no	—
55	C₂³×C₄×C₄₇	D₄	1	8	yes	—
56	C₂³×C₄×C₄₇	Q₈	1	16	yes	complemented
57	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
59	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
60	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
63	C₂×C₄²×C₄₇	—	2	4	no	—
64	C₂×C₄²×C₄₇	—	2	8	no	—
65	C₂×C₄²×C₄₇	—	2	32	no	—
66	C₂×C₄²×C₄₇	D₄	1	8	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
68	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
69	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
70	C₂⁴×C₄₇	—	2	2	no	—
71	C₂⁴×C₄₇	—	2	2	no	—
72	C₂⁴×C₄₇	—	2	4	no	—
73	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
74	C₂⁴×C₄₇	C₂×Q₈	1	8	yes	—
75	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
76	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	32	no	—
82	C₂²×C₄×C₄₇	—	2	64	no	—
83	C₂²×C₄×C₄₇	—	2	8	no	—
84	C₂²×C₄×C₄₇	—	2	16	no	—
85	C₂²×C₄×C₄₇	—	2	8	no	—
86	C₂²×C₄×C₄₇	—	2	16	no	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂×D₄	1	16	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
92	C₂²×C₄×C₄₇	C₂×Q₈	1	8	yes	—
93	C₂²×C₄×C₄₇	C₂×Q₈	1	8	yes	—
94	C₂²×C₄×C₄₇	C₂×Q₈	1	32	yes	complemented
95	C₂²×C₄×C₄₇	#41	1	4	yes	—
96	C₂²×C₄×C₄₇	#41	1	8	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
99	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
101	C₂²×Dic₄₇	—	2	8	no	—
102	C₂²×Dic₄₇	—	2	8	no	—
103	C₂²×Dic₄₇	—	2	8	no	—
104	C₂²×Dic₄₇	—	2	16	no	—
105	C₂²×Dic₄₇	—	2	8	no	—
106	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
107	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
108	C₂×Dic₉₄	—	2	16	no	—
109	C₂×Dic₉₄	—	2	16	no	—
110	C₂×Dic₉₄	—	2	16	no	—
111	C₂×Dic₉₄	—	4	32	no	—
112	C₄²×C₄₇	—	2	8	no	—
113	C₄²×C₄₇	—	2	16	no	—
114	C₄²×C₄₇	C₂×D₄	1	16	yes	—
115	C₂²⋊Dic₄₇	—	2	32	no	—
116	C₄⋊Dic₄₇	—	2	16	no	—
117	C₄⋊Dic₄₇	—	2	32	no	—
118	C₄⋊Dic₄₇	—	2	32	no	—
119	Dic₄₇⋊C₄	—	2	32	no	—
120	C₂³×C₄₇	—	2	8	no	—
121	C₂³×C₄₇	—	2	16	no	—
122	C₂³×C₄₇	—	2	8	no	—
123	C₂³×C₄₇	—	2	16	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	—	2	4	no	—
127	C₂³×C₄₇	C₄⋊Q₈	1	16	yes	complemented
128	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
129	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
130	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
131	C₂³×C₄₇	C₂²×Q₈	1	8	yes	—
132	C₂³×C₄₇	C₂²×Q₈	1	4	yes	—
133	C₂³×C₄₇	C₂×#41	1	2	yes	—
134	C₂³×C₄₇	C₂×#41	1	4	yes	—
135	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
136	C₂×C₄×C₄₇	—	2	8	no	—
137	C₂×C₄×C₄₇	—	2	16	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	32	no	—
143	C₂×C₄×C₄₇	—	2	64	no	—
144	C₂×C₄×C₄₇	#121	1	16	yes	—
145	C₂×C₄×C₄₇	C₂²⋊Q₈	1	32	yes	complemented
146	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
147	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
148	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
149	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
150	C₂×C₄×C₄₇	C₂²×Q₈	1	8	yes	—
151	C₂×C₄×C₄₇	C₂²×Q₈	1	8	yes	—
152	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
153	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
154	C₂×Dic₄₇	—	2	8	no	—
155	C₂×Dic₄₇	—	2	8	no	—
156	C₂×Dic₄₇	—	2	8	no	—
157	C₂×Dic₄₇	—	2	16	no	—
158	C₂×Dic₄₇	—	2	8	no	—
159	C₂×Dic₄₇	—	4	16	no	—
160	C₂×Dic₄₇	—	4	16	no	—
161	Dic₉₄	—	4	32	no	—
162	C₂×#2857	—	47	1	no	maximal, Sylow
163	C₂²×C₄₇	—	2	32	no	—
164	C₂²×C₄₇	—	2	4	no	—
165	C₂²×C₄₇	—	2	8	no	—
166	C₂²×C₄₇	—	2	4	no	—
167	C₂²×C₄₇	—	2	8	no	—
168	C₂²×C₄₇	C₂×#121	1	4	yes	—
169	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	8	yes	—
170	C₂²×C₄₇	C₂×C₄⋊Q₈	1	4	yes	—
171	C₂²×C₄₇	C₂×C₄⋊Q₈	1	8	yes	complemented
172	C₂²×C₄₇	#532	1	4	yes	—
173	C₂²×C₄₇	#533	1	8	yes	—
174	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
175	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
176	C₂²×C₄₇	C₂³×Q₈	1	2	yes	—
177	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
178	C₂²×C₄₇	C₂²×#41	1	2	yes	—
179	C₄×C₄₇	—	2	4	no	—
180	C₄×C₄₇	—	2	8	no	—
181	C₄×C₄₇	C₂×#121	1	8	yes	—
182	C₄×C₄₇	C₂×C₂²⋊Q₈	1	16	yes	complemented
183	Dic₄₇	—	4	8	no	—
184	Dic₄₇	—	4	8	no	—
185	C₂²×C₄⋊Q₈	—	47	1	no	—
186	C₂²×C₂²⋊Q₈	—	47	2	no	—
187	C₂³×C₄²	D₄₇	1	1	yes	characteristic
188	#2857	—	47	16	no	—
189	C₂×#391	—	47	2	no	—
190	C₂×#389	—	47	4	no	—
191	C₂×#384	—	47	1	no	—
192	C₂×#380	—	47	4	no	—
193	C₂×C₄₇	—	2	8	no	—
194	C₂×C₄₇	#2857	1	8	yes	complemented
195	C₂×C₄₇	C₂²×#121	1	1	yes	characteristic
196	C₂×C₄₇	C₂²×C₂²⋊Q₈	1	2	yes	—
197	C₂×C₄₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
198	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
199	C₂×C₄₇	C₂×#533	1	2	yes	—
200	C₂³×Q₈	—	47	2	no	—
201	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
202	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	—	47	8	no	—
204	C₂×C₄⋊Q₈	—	94	8	no	—
205	C₂×C₂²⋊Q₈	—	47	16	no	—
206	C₂×C₂²⋊Q₈	—	94	16	no	—
207	C₂²×C₄⋊C₄	—	47	4	no	—
208	C₂²×C₄⋊C₄	—	47	2	no	—
209	C₂²×C₄⋊C₄	—	47	4	no	—
210	C₂²×C₄⋊C₄	—	47	4	no	—
211	C₂²×C₂²⋊C₄	—	47	4	no	—
212	C₂²×C₄²	—	2	8	no	—
213	C₂²×C₄²	C₂×D₄₇	1	8	yes	—
214	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
215	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
216	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
217	#391	—	47	16	no	—
218	#389	—	47	32	no	—
219	#384	—	47	8	no	—
220	#380	—	47	32	no	—
221	C₂×#95	—	47	8	no	—
222	C₄₇	C₂×#2857	1	1	yes	characteristic, complemented, Sylow
223	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
224	C₂²×Q₈	—	47	8	no	—
225	C₂²×Q₈	—	94	8	no	—
226	C₂²×Q₈	—	94	8	no	—
227	C₂²×Q₈	—	94	8	no	—
228	C₂³×C₄	—	2	4	no	—
229	C₂³×C₄	—	2	8	no	—
230	C₂³×C₄	—	2	4	no	—
231	C₂³×C₄	—	2	8	no	—
232	C₂³×C₄	—	47	4	no	—
233	C₂³×C₄	—	47	4	no	—
234	C₂³×C₄	Dic₉₄	1	16	yes	complemented
235	C₂³×C₄	D₁₈₈	1	8	yes	—
236	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
237	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
238	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
239	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
240	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
241	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
242	C₄⋊Q₈	—	94	32	no	—
243	C₂²⋊Q₈	—	94	64	no	—
244	C₂×C₄⋊C₄	—	47	16	no	—
245	C₂×C₄⋊C₄	—	47	8	no	—
246	C₂×C₄⋊C₄	—	47	16	no	—
247	C₂×C₄⋊C₄	—	47	16	no	—
248	C₂×C₄⋊C₄	—	94	16	no	—
249	C₂×C₄⋊C₄	—	94	8	no	—
250	C₂×C₄⋊C₄	—	94	16	no	—
251	C₂×C₄⋊C₄	—	94	16	no	—
252	C₂×C₂²⋊C₄	—	47	16	no	—
253	C₂×C₂²⋊C₄	—	94	16	no	—
254	C₂×C₄²	—	2	4	no	—
255	C₂×C₄²	—	2	8	no	—
256	C₂×C₄²	—	2	32	no	—
257	C₂×C₄²	C₂²⋊D₄₇	1	8	yes	—
258	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
259	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
260	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
261	#95	—	47	32	no	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	—	2	2	no	—
264	C₂⁴	—	2	4	no	—
265	C₂⁴	C₂×Dic₉₄	1	8	yes	—
266	C₂⁴	C₂×D₁₈₈	1	4	yes	—
267	C₂⁴	C₂³×D₄₇	1	2	yes	—
268	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
269	C₂×Q₈	—	94	16	no	—
270	C₂×Q₈	—	94	16	no	—
271	C₂×Q₈	—	94	16	no	—
272	C₂×Q₈	—	188	32	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	32	no	—
278	C₂²×C₄	—	2	64	no	—
279	C₂²×C₄	—	2	8	no	—
280	C₂²×C₄	—	2	16	no	—
281	C₂²×C₄	—	2	8	no	—
282	C₂²×C₄	—	2	16	no	—
283	C₂²×C₄	—	47	8	no	—
284	C₂²×C₄	—	47	8	no	—
285	C₂²×C₄	—	94	8	no	—
286	C₂²×C₄	—	94	8	no	—
287	C₂²×C₄	—	94	8	no	—
288	C₂²×C₄	—	94	16	no	—
289	C₂²×C₄	—	94	8	no	—
290	C₂²×C₄	C₂×Dic₉₄	1	8	yes	—
291	C₂²×C₄	C₂×Dic₉₄	1	8	yes	—
292	C₂²×C₄	C₂×Dic₉₄	1	32	yes	complemented
293	C₂²×C₄	C₂×D₁₈₈	1	4	yes	—
294	C₂²×C₄	C₂×D₁₈₈	1	16	yes	—
295	C₂²×C₄	C₂×D₁₈₈	1	4	yes	—
296	C₂²×C₄	#10625350	1	4	yes	—
297	C₂²×C₄	#10625350	1	8	yes	—
298	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
300	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
301	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
302	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
303	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
304	C₄⋊C₄	—	94	32	no	—
305	C₄⋊C₄	—	94	32	no	—
306	C₄⋊C₄	—	94	16	no	—
307	C₄⋊C₄	—	94	32	no	—
308	C₂²⋊C₄	—	94	32	no	—
309	C₄²	—	2	8	no	—
310	C₄²	—	2	16	no	—
311	C₄²	C₂×C₂²⋊D₄₇	1	16	yes	—
312	C₂³	—	2	8	no	—
313	C₂³	—	2	16	no	—
314	C₂³	—	2	8	no	—
315	C₂³	—	2	16	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	4	no	—
319	C₂³	#13094024	1	16	yes	complemented
320	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
321	C₂³	C₂²×D₁₈₈	1	4	yes	—
322	C₂³	C₂²×D₁₈₈	1	2	yes	—
323	C₂³	C₂²×Dic₉₄	1	8	yes	—
324	C₂³	C₂²×Dic₉₄	1	4	yes	—
325	C₂³	C₂×#10625350	1	2	yes	—
326	C₂³	C₂×#10625350	1	4	yes	—
327	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
328	Q₈	—	188	32	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	16	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	32	no	—
336	C₂×C₄	—	2	64	no	—
337	C₂×C₄	—	94	8	no	—
338	C₂×C₄	—	94	8	no	—
339	C₂×C₄	—	94	8	no	—
340	C₂×C₄	—	94	16	no	—
341	C₂×C₄	—	94	8	no	—
342	C₂×C₄	—	188	16	no	—
343	C₂×C₄	—	188	16	no	—
344	C₂×C₄	#13093998	1	16	yes	—
345	C₂×C₄	#13094003	1	32	yes	complemented
346	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
347	C₂×C₄	C₂²×C₂²⋊D₄₇	1	8	yes	—
348	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
349	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
350	C₂×C₄	C₂²×Dic₉₄	1	8	yes	—
351	C₂×C₄	C₂²×Dic₉₄	1	8	yes	—
352	C₂×C₄	C₂×#10625350	1	4	yes	—
353	C₂×C₄	C₂×#10625350	1	8	yes	—
354	C₂²	—	2	32	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	8	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	8	no	—
359	C₂²	C₂×#13093998	1	4	yes	—
360	C₂²	C₂×#13094003	1	8	yes	—
361	C₂²	C₂×#13094024	1	4	yes	—
362	C₂²	C₂×#13094024	1	8	yes	complemented
363	C₂²	#15689673	1	4	yes	—
364	C₂²	#15689680	1	8	yes	—
365	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
366	C₂²	C₂³×D₁₈₈	1	1	yes	characteristic
367	C₂²	C₂³×Dic₉₄	1	2	yes	—
368	C₂²	C₂²×#10625350	1	1	yes	characteristic
369	C₂²	C₂²×#10625350	1	2	yes	—
370	C₄	—	2	4	no	—
371	C₄	—	2	8	no	—
372	C₄	—	188	8	no	—
373	C₄	—	188	8	no	—
374	C₄	C₂×#13093998	1	8	yes	—
375	C₄	C₂×#13094003	1	16	yes	complemented
376	C₂	—	2	8	no	—
377	C₂	#20251740	1	8	yes	direct product factor
378	C₂	C₂²×#13093998	1	1	yes	characteristic
379	C₂	C₂²×#13094003	1	2	yes	—
380	C₂	C₂²×#13094024	1	1	yes	characteristic
381	C₂	C₂×#15689673	1	1	yes	characteristic
382	C₂	C₂×#15689680	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator, cosocle	C₂³×C₄₇	C₂⁵
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂³×C₄²×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂⁵×C₄₇	C₂³
hypercenter	C₂³×C₄²	D₄₇
hypocenter	C₄₇	C₂×#2857
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×#13094024	C₂	semidirect
3. #20251740	C₂	direct (N × H)
4. C₂×#15689029	C₂	semidirect
5. C₂×#15689021	C₂	semidirect
6. C₂×#15688993	C₂	semidirect
11. C₂×#13094024	C₂²	semidirect
19. #15689029	C₂²	semidirect
20. #15689021	C₂²	semidirect
21. #15688993	C₂²	semidirect
56. C₂³×C₄×C₄₇	Q₈	semidirect
94. C₂²×C₄×C₄₇	C₂×Q₈	semidirect
127. C₂³×C₄₇	C₄⋊Q₈	semidirect
145. C₂×C₄×C₄₇	C₂²⋊Q₈	semidirect
171. C₂²×C₄₇	C₂×C₄⋊Q₈	semidirect
182. C₄×C₄₇	C₂×C₂²⋊Q₈	semidirect
194. C₂×C₄₇	#2857	semidirect
222. C₄₇	C₂×#2857	semidirect
234. C₂³×C₄	Dic₉₄	semidirect
292. C₂²×C₄	C₂×Dic₉₄	semidirect
319. C₂³	#13094024	semidirect
345. C₂×C₄	#13094003	semidirect
362. C₂²	C₂×#13094024	semidirect
375. C₄	C₂×#13094003	semidirect
377. C₂	#20251740	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13094024	2
C₂²×#13094003	2
#20251740	2
C₂×#15689029	2
C₂×#15689021	2
C₂×#15688993	2
C₂×#15688983	2
C₂³×C₄²×C₄₇	2
C₂×#2857	47

Subgroups — C2×#20251740 #26422214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20251740 #26422214