Subgroups — C₂×#20241817 #26182677

Order 12032.

1282 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689176	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
3	#20241817	C₂	1	8	yes	maximal, direct product factor
4	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	—	2	1	no	—
7	#15689176	—	2	2	no	—
8	#15689176	C₂²	1	4	yes	—
9	#15689147	—	2	2	no	—
10	#15689147	C₂²	1	4	yes	—
11	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
12	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
15	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
16	Q₈⋊(C₄₇⋊C₈)	C₂²	1	16	yes	complemented
17	C₂³×Q₈×C₄₇	C₄	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
19	C₂×C₄×Q₈×C₄₇	—	2	2	no	—
20	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
21	C₂×C₄×Q₈×C₄₇	—	2	2	no	—
22	C₂×C₄×Q₈×C₄₇	C₄	1	4	yes	—
23	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	—
24	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₄₇	C₂²	1	4	yes	—
26	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
27	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
28	C₂²×C₄²×C₄₇	—	2	1	no	—
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#10625329	—	2	4	no	—
31	C₂×#10625329	—	4	4	no	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
35	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
36	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
37	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
38	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
39	C₄×C₄₇⋊C₈	—	2	2	no	—
40	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
41	C₂²×Q₈×C₄₇	—	2	8	no	—
42	C₂²×Q₈×C₄₇	—	2	2	no	—
43	C₂²×Q₈×C₄₇	—	2	1	no	—
44	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
45	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₄₇	—	2	1	no	—
47	C₂³×C₄×C₄₇	—	2	1	no	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
51	C₄×Q₈×C₄₇	—	2	4	no	—
52	C₄×Q₈×C₄₇	—	2	4	no	—
53	C₄×Q₈×C₄₇	—	2	4	no	—
54	C₄×Q₈×C₄₇	—	2	2	no	—
55	C₄×Q₈×C₄₇	—	2	4	no	—
56	C₄×Q₈×C₄₇	—	2	2	no	—
57	C₄×Q₈×C₄₇	—	2	4	no	—
58	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
59	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
60	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	4	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	C₂×C₄	1	4	yes	—
68	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₄₇	—	2	4	no	—
70	C₂×C₄²×C₄₇	—	2	2	no	—
71	C₂×C₄²×C₄₇	—	2	4	no	—
72	C₂×C₄²×C₄₇	—	2	2	no	—
73	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	D₄	1	2	yes	—
78	C₂×C₄²×C₄₇	D₄	1	2	yes	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
81	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×Q₈×C₄₇	—	2	16	no	—
83	C₂×Q₈×C₄₇	—	2	8	no	—
84	C₂×Q₈×C₄₇	—	2	16	no	—
85	C₂×Q₈×C₄₇	—	2	4	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	2	4	no	—
88	C₂×Q₈×C₄₇	M₁₆	1	8	yes	complemented
89	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	—	2	8	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	4	2	no	—
97	C₂²×C₄×C₄₇	—	4	4	no	—
98	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
105	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₄⋊C₄×C₄₇	—	2	8	no	—
113	C₄⋊C₄×C₄₇	—	2	4	no	—
114	C₄⋊C₄×C₄₇	—	2	4	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	2	4	no	—
117	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
118	C₄²×C₄₇	—	2	8	no	—
119	C₄²×C₄₇	—	2	4	no	—
120	C₄²×C₄₇	—	2	4	no	—
121	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
123	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₄₇	C₂×D₄	1	2	yes	—
128	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂×D₄	1	2	yes	—
130	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
131	#10625329	—	4	8	no	—
132	C₂×C₄₇⋊C₈	—	2	4	no	—
133	C₂×C₄₇⋊C₈	—	2	4	no	—
134	C₂×C₄₇⋊C₈	—	4	4	no	—
135	C₂×C₄₇⋊C₈	—	4	4	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	#103	1	4	yes	—
139	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	Q₈×C₄₇	—	2	16	no	—
142	Q₈×C₄₇	—	2	4	no	—
143	Q₈×C₄₇	—	2	8	no	—
144	Q₈×C₄₇	C₂×M₁₆	1	8	yes	complemented
145	C₂×C₄×C₄₇	—	2	16	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	8	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	8	no	—
157	C₂×C₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	#103	1	8	yes	—
159	C₂×C₄×C₄₇	#103	1	4	yes	—
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
167	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
168	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
169	C₂×C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
170	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
171	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₄₇⋊C₈	—	4	4	no	—
175	C₄₇⋊C₈	—	4	4	no	—
176	C₂×#1487	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	—	2	2	no	—
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	8	no	—
180	C₂²×C₄₇	#407	1	2	yes	—
181	C₂²×C₄₇	C₂×#103	1	4	yes	—
182	C₂²×C₄₇	C₂×#103	1	2	yes	—
183	C₂²×C₄₇	#421	1	2	yes	—
184	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
185	C₄×C₄₇	—	2	8	no	—
186	C₄×C₄₇	—	2	2	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	4	4	no	—
191	C₄×C₄₇	#407	1	2	yes	—
192	C₄×C₄₇	C₂×#103	1	2	yes	—
193	C₄×C₄₇	C₂×#103	1	4	yes	—
194	C₄×C₄₇	C₂²×M₁₆	1	2	yes	—
195	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
196	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
197	C₂²×C₄×Q₈	D₄₇	1	1	yes	characteristic
198	C₂×#431	—	47	1	no	—
199	C₂×#423	—	47	1	no	—
200	#1487	—	47	8	no	—
201	C₂×Q₈⋊C₈	—	47	4	no	—
202	C₂×C₄₇	—	2	4	no	—
203	C₂×C₄₇	#1487	1	4	yes	complemented
204	C₂×C₄₇	C₂×#407	1	1	yes	characteristic
205	C₂×C₄₇	C₂²×#103	1	1	yes	characteristic
206	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
207	C₂³×Q₈	Dic₄₇	1	1	yes	characteristic
208	C₂²×M₁₆	—	94	1	no	—
209	C₂×C₄×Q₈	—	2	1	no	—
210	C₂×C₄×Q₈	—	2	2	no	—
211	C₂×C₄×Q₈	—	2	2	no	—
212	C₂×C₄×Q₈	—	2	1	no	—
213	C₂×C₄×Q₈	Dic₄₇	1	4	yes	—
214	C₂×C₄×Q₈	Dic₄₇	1	2	yes	—
215	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
216	C₂×C₄×Q₈	C₂×D₄₇	1	4	yes	—
217	C₂²×C₄⋊C₄	—	2	1	no	—
218	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
219	C₂²×C₄²	—	2	1	no	—
220	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
221	#431	—	47	4	no	—
222	#431	—	94	2	no	—
223	#423	—	47	4	no	—
224	#423	—	94	2	no	—
225	C₂×C₄⋊C₈	—	47	2	no	—
226	C₂×C₄⋊C₈	—	94	1	no	—
227	C₂×C₄⋊C₈	—	94	1	no	—
228	C₂×C₂²⋊C₈	—	94	1	no	—
229	C₂×C₄×C₈	—	47	2	no	—
230	Q₈⋊C₈	—	47	16	no	—
231	C₄₇	C₂×#1487	1	1	yes	characteristic, complemented, Sylow
232	C₂²×Q₈	—	2	8	no	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	C₂×Dic₄₇	1	4	yes	—
236	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
237	C₂³×C₄	—	2	1	no	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
240	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
241	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
242	C₂×M₁₆	—	94	4	no	—
243	C₂×M₁₆	—	188	4	no	—
244	C₂²×C₈	—	94	2	no	—
245	C₂²×C₈	—	94	2	no	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	4	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×Q₈	—	2	4	no	—
253	C₄×Q₈	C₂×Dic₄₇	1	4	yes	—
254	C₄×Q₈	C₂×Dic₄₇	1	8	yes	—
255	C₄×Q₈	C₂²×D₄₇	1	4	yes	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	4	no	—
262	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
263	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	4	no	—
266	C₂×C₄²	—	2	4	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
269	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
270	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
271	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
272	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
273	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
275	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
276	C₄⋊C₈	—	47	4	no	—
277	C₄⋊C₈	—	94	2	no	—
278	C₄⋊C₈	—	94	4	no	—
279	C₄⋊C₈	—	94	4	no	—
280	C₂²⋊C₈	—	94	4	no	—
281	C₄×C₈	—	47	4	no	—
282	C₄×C₈	—	94	2	no	—
283	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
284	C₂×Q₈	—	2	16	no	—
285	C₂×Q₈	—	2	8	no	—
286	C₂×Q₈	—	2	16	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	#10625329	1	8	yes	complemented
291	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	#10625336	1	4	yes	—
301	C₂²×C₄	#10625337	1	4	yes	—
302	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
303	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
305	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
306	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
308	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
309	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
312	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
313	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
314	M₁₆	—	188	8	no	—
315	C₂×C₈	—	94	4	no	—
316	C₂×C₈	—	94	4	no	—
317	C₂×C₈	—	188	4	no	—
318	C₂×C₈	—	188	4	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
325	C₄²	—	2	8	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	4	no	—
328	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
329	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
330	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
331	C₄²	C₂²×Dic₄₇	1	2	yes	—
332	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
333	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
334	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
335	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
336	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
337	C₄²	C₂³×D₄₇	1	1	yes	characteristic
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	#13093948	1	4	yes	—
341	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
342	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
343	Q₈	—	2	16	no	—
344	Q₈	—	2	8	no	—
345	Q₈	—	2	4	no	—
346	Q₈	C₂×#10625329	1	8	yes	complemented
347	C₂×C₄	—	2	16	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	#13093948	1	8	yes	—
361	C₂×C₄	#13093948	1	4	yes	—
362	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
363	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
365	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
366	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂×#10625329	1	4	yes	—
369	C₂×C₄	C₂×#10625336	1	2	yes	—
370	C₂×C₄	C₂×#10625336	1	4	yes	—
371	C₂×C₄	C₂×#10625337	1	4	yes	—
372	C₂×C₄	C₂×#10625337	1	2	yes	—
373	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
376	C₈	—	188	4	no	—
377	C₈	—	188	4	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	8	no	—
380	C₂²	—	2	2	no	—
381	C₂²	#15689087	1	2	yes	—
382	C₂²	C₂×#13093948	1	4	yes	—
383	C₂²	C₂×#13093948	1	2	yes	—
384	C₂²	#15689140	1	2	yes	—
385	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	8	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	4	no	—
392	C₄	#15689087	1	2	yes	—
393	C₄	C₂×#13093948	1	4	yes	—
394	C₄	C₂×#13093948	1	2	yes	—
395	C₄	C₂²×#10625329	1	2	yes	—
396	C₄	C₂²×#10625336	1	1	yes	characteristic
397	C₄	C₂²×#10625337	1	1	yes	characteristic
398	C₂	—	2	4	no	—
399	C₂	#20241817	1	4	yes	direct product factor
400	C₂	C₂×#15689087	1	1	yes	characteristic
401	C₂	C₂²×#13093948	1	1	yes	characteristic
402	C₂	C₂×#15689140	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂²×C₄×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂²×C₄×Q₈	D₄₇
hypocenter	C₄₇	C₂×#1487
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
3. #20241817	C₂	direct (N × H)
4. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
16. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
88. C₂×Q₈×C₄₇	M₁₆	semidirect
144. Q₈×C₄₇	C₂×M₁₆	semidirect
203. C₂×C₄₇	#1487	semidirect
231. C₄₇	C₂×#1487	semidirect
290. C₂×Q₈	#10625329	semidirect
346. Q₈	C₂×#10625329	semidirect
399. C₂	#20241817	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×#15689176	2
C₂×#15689147	2
#20241817	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₂²×C₄×Q₈×C₄₇	2
C₂×#1487	47

Subgroups — C2×#20241817 #26182677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241817 #26182677