Subgroups — C₂×#20253935 #27085928

Order 12032.

2118 conjugacy classes of subgroups.

The subgroup lattice has 410 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
2	#20253935	C₂	1	16	yes	maximal, direct product factor
3	C₂×#15689533	C₂	1	4	yes	maximal, complemented
4	C₂×#15689526	C₂	1	2	yes	maximal, complemented
5	C₂×#15689519	C₂	1	2	yes	maximal, complemented
6	C₂×#15689166	C₂	1	4	yes	maximal
7	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
9	C₂³×Dic₉₄	—	2	1	no	—
10	C₂²×#10625329	C₂²	1	2	yes	—
11	C₂×#13094024	—	2	1	no	—
12	C₂×#13094024	—	2	1	no	—
13	C₂×#13094024	—	2	4	no	—
14	C₂×#13094024	C₂²	1	2	yes	—
15	C₂×#13094024	C₂²	1	2	yes	—
16	C₂×#13094024	C₂²	1	8	yes	—
17	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
18	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
19	#15689533	C₂²	1	32	yes	complemented
20	#15689526	C₂²	1	16	yes	complemented
21	#15689519	C₂²	1	16	yes	complemented
22	#15689166	C₂²	1	32	yes	—
23	C₂×#13093957	C₂²	1	8	yes	—
24	C₂×#13093955	C₂²	1	8	yes	—
25	C₄×#10625329	C₂²	1	8	yes	—
26	C₂×#13093935	C₂²	1	2	yes	—
27	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
28	C₄₇×#533	—	2	4	no	—
29	C₄₇×#533	C₂²	1	8	yes	—
30	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#125×C₄₇	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
35	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
36	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
37	C₂×#117×C₄₇	C₂²	1	2	yes	—
38	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×Dic₉₄	—	2	2	no	—
40	C₂²×Dic₉₄	—	2	8	no	—
41	C₂²×Dic₉₄	—	2	2	no	—
42	C₂²×Dic₉₄	—	4	8	no	—
43	C₂³×Dic₄₇	—	2	2	no	—
44	C₂×#10625329	Q₈	1	16	yes	complemented
45	C₂×#10625329	C₂³	1	8	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
47	#13094024	—	2	8	no	—
48	#13094024	—	2	8	no	—
49	#13094024	—	2	4	no	—
50	#13094024	—	2	4	no	—
51	#13094024	C₂³	1	8	yes	—
52	#13094024	C₂³	1	8	yes	—
53	C₂×C₄⋊Dic₄₇	—	2	2	no	—
54	C₂×C₄⋊Dic₄₇	—	2	8	no	—
55	C₂×C₄⋊Dic₄₇	—	2	2	no	—
56	C₂×C₄⋊Dic₄₇	—	2	2	no	—
57	C₂×C₄⋊Dic₄₇	—	2	4	no	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
60	#13093957	C₂³	1	32	yes	—
61	#13093955	C₂³	1	32	yes	—
62	#13093935	C₂³	1	8	yes	—
63	C₄×C₄₇⋊C₈	C₂³	1	8	yes	—
64	C₂²×Q₈×C₄₇	—	2	1	no	—
65	C₂²×Q₈×C₄₇	—	2	1	no	—
66	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₄⋊Q₈×C₄₇	—	2	2	no	—
70	C₄⋊Q₈×C₄₇	—	2	2	no	—
71	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
72	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
73	#125×C₄₇	—	2	4	no	—
74	#125×C₄₇	C₂³	1	8	yes	—
75	C₂²⋊Q₈×C₄₇	—	2	8	no	—
76	C₂²⋊Q₈×C₄₇	—	2	8	no	—
77	C₄×Q₈×C₄₇	—	2	8	no	—
78	C₄×Q₈×C₄₇	—	2	8	no	—
79	#117×C₄₇	—	2	4	no	—
80	#117×C₄₇	C₂³	1	8	yes	—
81	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₄²×C₄₇	—	2	2	no	—
89	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	D₄	1	4	yes	—
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
95	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₄₇	—	2	4	no	—
97	C₂×Q₈×C₄₇	—	2	4	no	—
98	C₂×Q₈×C₄₇	—	4	4	no	—
99	C₂×Q₈×C₄₇	—	4	4	no	—
100	C₂²×C₄×C₄₇	—	2	4	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×Q₈	1	8	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
115	C₂²×Dic₄₇	—	2	8	no	—
116	C₂²×Dic₄₇	—	2	4	no	—
117	C₂²×Dic₄₇	—	4	8	no	—
118	C₂×Dic₉₄	—	2	8	no	—
119	C₂×Dic₉₄	—	2	8	no	—
120	C₂×Dic₉₄	—	4	8	no	—
121	C₂×Dic₉₄	—	4	32	no	—
122	C₂×Dic₉₄	—	4	8	no	—
123	C₄⋊C₄×C₄₇	—	2	8	no	—
124	C₄⋊C₄×C₄₇	—	2	8	no	—
125	C₄⋊C₄×C₄₇	—	2	4	no	—
126	C₄⋊C₄×C₄₇	—	2	4	no	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
130	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
131	C₂²⋊C₄×C₄₇	—	2	8	no	—
132	C₄²×C₄₇	—	2	8	no	—
133	C₄²×C₄₇	C₂×D₄	1	4	yes	—
134	C₄²×C₄₇	C₂×D₄	1	4	yes	—
135	C₄²×C₄₇	C₂×D₄	1	2	yes	—
136	C₄²×C₄₇	C₂×D₄	1	2	yes	—
137	C₄²×C₄₇	C₂⁴	1	2	yes	—
138	C₄²×C₄₇	C₂⁴	1	2	yes	—
139	C₄⋊Dic₄₇	—	2	8	no	—
140	C₄⋊Dic₄₇	—	2	8	no	—
141	C₄⋊Dic₄₇	—	2	8	no	—
142	C₄⋊Dic₄₇	—	2	4	no	—
143	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
144	#10625329	C₂×Q₈	1	32	yes	complemented
145	C₂×C₄₇⋊C₈	C₂×Q₈	1	16	yes	complemented
146	C₂×C₄₇⋊C₈	C₂⁴	1	8	yes	—
147	C₂³×C₄₇	—	2	2	no	—
148	C₂³×C₄₇	—	2	2	no	—
149	C₂³×C₄₇	C₄⋊Q₈	1	4	yes	—
150	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
151	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₄₇	—	4	8	no	—
153	Q₈×C₄₇	—	4	8	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	8	no	—
157	C₂×C₄×C₄₇	—	2	8	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	—	4	4	no	—
162	C₂×C₄×C₄₇	C₄⋊Q₈	1	8	yes	—
163	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
164	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
165	C₂×C₄×C₄₇	#137	1	4	yes	—
166	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
173	C₂×C₄×C₄₇	C₂²×Q₈	1	8	yes	—
174	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
175	C₂×Dic₄₇	—	2	8	no	—
176	C₂×Dic₄₇	—	4	16	no	—
177	C₂×Dic₄₇	—	4	8	no	—
178	Dic₉₄	—	4	16	no	—
179	Dic₉₄	—	4	16	no	—
180	C₄₇⋊C₈	C₂²×Q₈	1	16	yes	complemented
181	C₂×#3165	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	—	2	8	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	C₂×C₄⋊Q₈	1	4	yes	—
186	C₂²×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
187	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
188	C₂²×C₄₇	C₂×#137	1	2	yes	—
189	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
190	C₄×C₄₇	—	2	2	no	—
191	C₄×C₄₇	—	2	2	no	—
192	C₄×C₄₇	—	4	4	no	—
193	C₄×C₄₇	—	4	4	no	—
194	C₄×C₄₇	C₂×C₄⋊Q₈	1	4	yes	—
195	C₄×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
196	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
197	C₄×C₄₇	C₂×#137	1	4	yes	—
198	C₄×C₄₇	C₂³×Q₈	1	2	yes	—
199	Dic₄₇	—	4	8	no	—
200	C₂×#533	D₄₇	1	1	yes	characteristic
201	C₂²×C₄⋊Q₈	—	47	1	no	—
202	#3165	—	47	16	no	—
203	C₂×#501	—	47	4	no	—
204	C₂×#500	—	47	2	no	—
205	C₂×#498	—	47	2	no	—
206	C₂×#428	—	47	4	no	—
207	C₂×C₄×M₁₆	—	47	1	no	—
208	C₂×C₄₇	—	2	4	no	—
209	C₂×C₄₇	#3165	1	4	yes	complemented
210	C₂×C₄₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
211	C₂×C₄₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂×C₄₇	C₂²×#137	1	1	yes	characteristic
213	C₂³×Q₈	—	94	1	no	—
214	C₂²×M₁₆	—	47	2	no	—
215	#533	—	2	4	no	—
216	#533	C₂×D₄₇	1	8	yes	—
217	C₂×C₄⋊Q₈	—	47	2	no	—
218	C₂×C₄⋊Q₈	—	47	2	no	—
219	C₂×C₄⋊Q₈	—	47	8	no	—
220	C₂×C₄⋊Q₈	—	94	1	no	—
221	C₂×C₄⋊Q₈	—	94	1	no	—
222	C₂×C₄⋊Q₈	—	94	4	no	—
223	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#125	C₂×D₄₇	1	2	yes	—
226	C₂×C₂²⋊Q₈	—	2	1	no	—
227	C₂×C₂²⋊Q₈	—	2	1	no	—
228	C₂×C₄×Q₈	—	2	1	no	—
229	C₂×C₄×Q₈	—	2	1	no	—
230	C₂×#117	C₂×D₄₇	1	2	yes	—
231	C₂²×C₄⋊C₄	—	47	2	no	—
232	C₂²×C₄⋊C₄	—	94	1	no	—
233	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
234	#501	—	47	32	no	—
235	#500	—	47	16	no	—
236	#498	—	47	16	no	—
237	#428	—	47	32	no	—
238	C₂×#107	—	47	8	no	—
239	C₂×#106	—	47	8	no	—
240	C₄×M₁₆	—	47	8	no	—
241	C₂×#97	—	47	2	no	—
242	C₂×C₄×C₈	—	47	2	no	—
243	C₄₇	C₂×#3165	1	1	yes	characteristic, complemented, Sylow
244	C₂²×Q₈	—	2	1	no	—
245	C₂²×Q₈	—	2	1	no	—
246	C₂²×Q₈	—	94	8	no	—
247	C₂²×Q₈	—	94	2	no	—
248	C₂²×Q₈	—	94	2	no	—
249	C₂²×Q₈	—	188	8	no	—
250	C₂³×C₄	—	94	2	no	—
251	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
252	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
253	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
254	C₂×M₁₆	—	47	16	no	—
255	C₂×M₁₆	—	47	8	no	—
256	C₂²×C₈	—	47	4	no	—
257	C₄⋊Q₈	—	2	2	no	—
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	—	47	8	no	—
260	C₄⋊Q₈	—	47	8	no	—
261	C₄⋊Q₈	—	94	8	no	—
262	C₄⋊Q₈	—	94	8	no	—
263	C₄⋊Q₈	—	94	4	no	—
264	C₄⋊Q₈	—	94	4	no	—
265	C₄⋊Q₈	C₂²×D₄₇	1	4	yes	—
266	C₄⋊Q₈	C₂²×D₄₇	1	4	yes	—
267	#125	—	2	4	no	—
268	#125	C₂²×D₄₇	1	8	yes	—
269	C₂²⋊Q₈	—	2	8	no	—
270	C₂²⋊Q₈	—	2	8	no	—
271	C₄×Q₈	—	2	8	no	—
272	C₄×Q₈	—	2	8	no	—
273	#117	—	2	4	no	—
274	#117	C₂²×D₄₇	1	8	yes	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	47	4	no	—
280	C₂×C₄⋊C₄	—	47	8	no	—
281	C₂×C₄⋊C₄	—	94	4	no	—
282	C₂×C₄⋊C₄	—	94	2	no	—
283	C₂×C₄⋊C₄	—	94	8	no	—
284	C₂×C₄⋊C₄	—	94	2	no	—
285	C₂×C₄⋊C₄	—	94	2	no	—
286	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
287	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
291	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
292	C₂×C₄²	C₂²⋊D₄₇	1	4	yes	—
293	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
296	#107	—	47	32	no	—
297	#106	—	47	32	no	—
298	#97	—	47	8	no	—
299	C₄×C₈	—	47	8	no	—
300	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	4	4	no	—
304	C₂×Q₈	—	4	4	no	—
305	C₂×Q₈	—	94	8	no	—
306	C₂×Q₈	—	94	8	no	—
307	C₂×Q₈	—	188	8	no	—
308	C₂×Q₈	—	188	32	no	—
309	C₂×Q₈	—	188	8	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	94	8	no	—
315	C₂²×C₄	—	94	4	no	—
316	C₂²×C₄	—	188	8	no	—
317	C₂²×C₄	Q₈×D₄₇	1	8	yes	—
318	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
319	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
320	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
323	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
327	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
328	M₁₆	—	47	32	no	—
329	C₂×C₈	—	47	16	no	—
330	C₂×C₈	—	47	8	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	47	8	no	—
338	C₄⋊C₄	—	94	8	no	—
339	C₄⋊C₄	—	94	4	no	—
340	C₄⋊C₄	—	94	8	no	—
341	C₄⋊C₄	—	94	8	no	—
342	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
343	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₄²	—	2	8	no	—
346	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
347	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
348	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
349	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
350	C₄²	C₂³×D₄₇	1	2	yes	—
351	C₄²	C₂³×D₄₇	1	2	yes	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	#13094022	1	4	yes	—
355	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
356	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
357	Q₈	—	4	8	no	—
358	Q₈	—	4	8	no	—
359	Q₈	—	188	16	no	—
360	Q₈	—	188	16	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	94	8	no	—
370	C₂×C₄	—	188	16	no	—
371	C₂×C₄	—	188	8	no	—
372	C₂×C₄	#13094022	1	8	yes	—
373	C₂×C₄	#13094022	1	4	yes	—
374	C₂×C₄	#13094049	1	4	yes	—
375	C₂×C₄	#13094054	1	4	yes	—
376	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
377	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
378	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
379	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
380	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
381	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂×Q₈×D₄₇	1	4	yes	—
383	C₂×C₄	C₂×Q₈×D₄₇	1	8	yes	—
384	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
385	C₈	—	47	16	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	8	no	—
389	C₂²	C₂×#13094022	1	4	yes	—
390	C₂²	C₂×#13094022	1	2	yes	—
391	C₂²	C₂×#13094049	1	2	yes	—
392	C₂²	C₂×#13094054	1	2	yes	—
393	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	4	4	no	—
397	C₄	—	4	4	no	—
398	C₄	—	188	8	no	—
399	C₄	C₂×#13094022	1	4	yes	—
400	C₄	C₂×#13094022	1	2	yes	—
401	C₄	C₂×#13094049	1	4	yes	—
402	C₄	C₂×#13094054	1	4	yes	—
403	C₄	C₂²×Q₈×D₄₇	1	2	yes	—
404	C₂	—	2	4	no	—
405	C₂	#20253935	1	4	yes	direct product factor
406	C₂	C₂²×#13094022	1	1	yes	characteristic
407	C₂	C₂²×#13094049	1	1	yes	characteristic
408	C₂	C₂²×#13094054	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	C₂×#3165
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
2. #20253935	C₂	direct (N × H)
3. C₂×#15689533	C₂	semidirect
4. C₂×#15689526	C₂	semidirect
5. C₂×#15689519	C₂	semidirect
19. #15689533	C₂²	semidirect
20. #15689526	C₂²	semidirect
21. #15689519	C₂²	semidirect
44. C₂×#10625329	Q₈	semidirect
144. #10625329	C₂×Q₈	semidirect
145. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
180. C₄₇⋊C₈	C₂²×Q₈	semidirect
209. C₂×C₄₇	#3165	semidirect
243. C₄₇	C₂×#3165	semidirect
405. C₂	#20253935	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
#20253935	2
C₂×#15689533	2
C₂×#15689526	2
C₂×#15689519	2
C₂×#15689166	2
C₂×C₄×#10625329	2
C₂×C₄₇×#533	2
C₂×#3165	47

Subgroups — C2×#20253935 #27085928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20253935 #27085928