Subgroups — C₂×#20244334 #26220774

Order 12032.

1510 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094023	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20244334	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
6	C₂×#15688885	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688885	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#340	C₂	1	1	yes	maximal, characteristic
9	C₂³×Dic₉₄	—	2	1	no	—
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#13094023	—	2	2	no	—
12	C₂×#13094023	—	2	4	no	—
13	C₂×#13094023	C₄	1	8	yes	complemented
14	C₂×#13094023	C₂²	1	4	yes	—
15	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
17	C₂²×Dic₄₇⋊C₄	—	2	1	no	—
18	C₂²×C₄×Dic₄₇	—	2	1	no	—
19	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₇⋊C₈	—	2	4	no	—
21	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
22	C₄⋊C₄×Dic₄₇	—	2	2	no	—
23	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
24	C₂×C₄₇⋊#95	—	2	1	no	—
25	#15688886	C₂²	1	4	yes	—
26	#15688885	C₂²	1	4	yes	—
27	#15688885	C₂²	1	4	yes	—
28	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#340	C₂²	1	4	yes	—
32	C₂²×Dic₉₄	—	2	8	no	—
33	C₂²×Dic₉₄	—	2	4	no	—
34	C₂²×Dic₉₄	—	4	4	no	—
35	C₂²×Dic₉₄	—	4	4	no	—
36	C₂³×Dic₄₇	—	2	1	no	—
37	C₂³×Dic₄₇	—	2	1	no	—
38	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
39	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
40	C₂²×C₄₇⋊C₈	—	2	2	no	—
41	C₂²×C₄₇⋊C₈	—	2	2	no	—
42	C₂²×C₄₇⋊C₈	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	#13094023	—	2	16	no	—
45	#13094023	—	2	8	no	—
46	#13094023	C₂×C₄	1	16	yes	complemented
47	C₂×C₄⋊Dic₄₇	—	2	1	no	—
48	C₂×C₄⋊Dic₄₇	—	2	1	no	—
49	C₂×C₄⋊Dic₄₇	—	2	2	no	—
50	C₂×C₄⋊Dic₄₇	—	2	2	no	—
51	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊Dic₄₇	Q₈	1	4	yes	complemented
53	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
55	C₂×Dic₄₇⋊C₄	—	2	8	no	—
56	C₂×Dic₄₇⋊C₄	—	2	4	no	—
57	C₂×C₄×Dic₄₇	—	2	4	no	—
58	C₂×C₄×Dic₄₇	—	4	4	no	—
59	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
61	C₂×C₄×Dic₄₇	D₄	1	4	yes	—
62	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
63	Dic₄₇⋊C₈	—	2	8	no	—
64	C₄₇⋊#95	—	2	4	no	—
65	C₂³×C₄×C₄₇	—	2	1	no	—
66	C₂³×C₄×C₄₇	—	2	1	no	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₄₇	—	2	2	no	—
69	C₂²×C₈×C₄₇	—	2	2	no	—
70	C₂²×C₈×C₄₇	—	2	2	no	—
71	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
77	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	complemented
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
80	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	4	2	no	—
86	C₂²×C₄×C₄₇	—	4	2	no	—
87	C₂²×C₄×C₄₇	—	4	2	no	—
88	C₂²×C₄×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₄₇	#41	1	2	yes	—
95	C₂²×C₄×C₄₇	#41	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	—	2	4	no	—
100	C₂²×Dic₄₇	—	2	4	no	—
101	C₂²×Dic₄₇	—	2	2	no	—
102	C₂²×Dic₄₇	—	2	2	no	—
103	C₂²×Dic₄₇	—	4	2	no	—
104	C₂²×Dic₄₇	—	4	2	no	—
105	C₂²×Dic₄₇	—	4	2	no	—
106	C₂²×Dic₄₇	—	4	2	no	—
107	C₂²×Dic₄₇	C₂²⋊C₄	1	4	yes	—
108	C₂²×Dic₄₇	C₂²⋊C₄	1	4	yes	—
109	C₂²×Dic₄₇	SD₁₆	1	4	yes	—
110	C₂²×Dic₄₇	Q₁₆	1	4	yes	—
111	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
112	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
113	C₂×Dic₉₄	—	2	16	no	—
114	C₂×Dic₉₄	—	4	8	no	—
115	C₂×Dic₉₄	—	4	8	no	—
116	C₂×Dic₉₄	—	4	32	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	4	4	no	—
121	C₄⋊C₄×C₄₇	—	2	4	no	—
122	C₄⋊C₄×C₄₇	—	2	4	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
126	C₄⋊C₄×C₄₇	C₂×Q₈	1	4	yes	complemented
127	C₄⋊Dic₄₇	—	2	4	no	—
128	C₄⋊Dic₄₇	—	2	4	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
132	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	complemented
133	Dic₄₇⋊C₄	—	2	16	no	—
134	C₄×Dic₄₇	—	4	8	no	—
135	C₄×Dic₄₇	C₂²⋊C₄	1	8	yes	—
136	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
137	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	4	4	no	—
142	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
144	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
145	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
146	C₂³×C₄₇	C₂×Q₁₆	1	2	yes	—
147	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
148	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
149	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	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	8	no	—
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
160	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
161	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
162	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
163	C₂×C₄×C₄₇	#124	1	4	yes	—
164	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
165	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	8	no	—
174	C₂×Dic₄₇	—	2	4	no	—
175	C₂×Dic₄₇	—	2	4	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	C₂×Dic₄₇	—	4	2	no	—
180	C₂×Dic₄₇	—	4	8	no	—
181	C₂×Dic₄₇	—	4	8	no	—
182	C₂×Dic₄₇	#103	1	16	yes	—
183	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	4	yes	—
184	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	4	yes	—
185	C₂×Dic₄₇	C₂×SD₁₆	1	4	yes	—
186	C₂×Dic₄₇	C₂×Q₁₆	1	4	yes	—
187	Dic₉₄	—	4	32	no	—
188	C₈×C₄₇	—	4	2	no	—
189	C₄₇⋊C₈	—	4	2	no	—
190	C₂×#1987	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	#391	1	4	yes	—
192	C₂²×C₄₇	C₂×#103	1	4	yes	—
193	C₂²×C₄₇	#418	1	4	yes	—
194	C₂²×C₄₇	#476	1	4	yes	—
195	C₂²×C₄₇	#476	1	4	yes	—
196	C₂²×C₄₇	#477	1	4	yes	—
197	C₂²×C₄₇	#477	1	4	yes	—
198	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
200	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
201	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
202	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
203	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₄×C₄₇	—	4	4	no	—
206	C₄×C₄₇	—	4	4	no	—
207	C₄×C₄₇	#391	1	4	yes	—
208	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
209	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
210	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
211	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
212	Dic₄₇	—	2	4	no	—
213	Dic₄₇	—	4	4	no	—
214	Dic₄₇	—	4	4	no	—
215	Dic₄₇	C₂×#103	1	8	yes	—
216	C₂²×C₄⋊Q₈	—	47	1	no	—
217	C₂²×C₄⋊C₈	—	47	1	no	—
218	C₂×C₄×C₄⋊C₄	—	47	1	no	—
219	#1987	—	47	8	no	—
220	C₂×#340	—	47	1	no	—
221	C₂×#340	—	47	1	no	—
222	C₂×#340	—	47	1	no	—
223	C₂×#340	D₄₇	1	1	yes	characteristic
224	C₂×C₄₇	#1987	1	8	yes	complemented
225	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
226	C₂×C₄₇	C₂²×#103	1	1	yes	characteristic
227	C₂×C₄₇	C₂×#418	1	1	yes	characteristic
228	C₂×C₄₇	C₂×#476	1	1	yes	characteristic
229	C₂×C₄₇	C₂×#476	1	1	yes	characteristic
230	C₂×C₄₇	C₂×#477	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#477	1	1	yes	characteristic
232	C₂³×Q₈	—	94	1	no	—
233	C₂³×C₈	—	47	1	no	—
234	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
235	C₂×C₄⋊Q₈	—	47	8	no	—
236	C₂×C₄⋊Q₈	—	47	4	no	—
237	C₂×C₄⋊Q₈	—	94	2	no	—
238	C₂×C₄⋊Q₈	—	94	4	no	—
239	C₂²×C₄⋊C₄	—	47	1	no	—
240	C₂²×C₄⋊C₄	—	47	1	no	—
241	C₂²×C₄⋊C₄	—	94	1	no	—
242	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
244	C₂²×C₄²	—	47	1	no	—
245	C₂²×C₄²	—	94	1	no	—
246	C₂×C₄⋊C₈	—	47	4	no	—
247	C₂×C₄⋊C₈	—	94	4	no	—
248	C₄×C₄⋊C₄	—	47	4	no	—
249	C₄×C₄⋊C₄	—	94	2	no	—
250	C₂×#95	—	94	1	no	—
251	#340	—	47	4	no	—
252	#340	—	47	4	no	—
253	#340	—	47	4	no	—
254	#340	C₂×D₄₇	1	4	yes	—
255	C₄₇	C₂×#1987	1	1	yes	characteristic, complemented, Sylow
256	C₂²×Q₈	—	94	8	no	—
257	C₂²×Q₈	—	94	4	no	—
258	C₂²×Q₈	—	188	4	no	—
259	C₂²×Q₈	—	188	4	no	—
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	—	47	1	no	—
263	C₂³×C₄	—	47	1	no	—
264	C₂³×C₄	—	94	1	no	—
265	C₂³×C₄	—	94	1	no	—
266	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	47	2	no	—
271	C₂²×C₈	—	94	2	no	—
272	C₂²×C₈	—	94	2	no	—
273	C₂²×C₈	—	94	2	no	—
274	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
275	C₄⋊Q₈	—	47	16	no	—
276	C₄⋊Q₈	—	94	16	no	—
277	C₄⋊Q₈	—	94	8	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	47	4	no	—
283	C₂×C₄⋊C₄	—	47	4	no	—
284	C₂×C₄⋊C₄	—	47	2	no	—
285	C₂×C₄⋊C₄	—	47	2	no	—
286	C₂×C₄⋊C₄	—	94	8	no	—
287	C₂×C₄⋊C₄	—	94	4	no	—
288	C₂×C₄⋊C₄	—	94	2	no	—
289	C₂×C₄⋊C₄	—	94	1	no	—
290	C₂×C₄⋊C₄	—	94	2	no	—
291	C₂×C₄⋊C₄	—	94	1	no	—
292	C₂×C₄⋊C₄	Dic₉₄	1	4	yes	complemented
293	C₂×C₄⋊C₄	C₄×D₄₇	1	4	yes	—
294	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
295	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
296	C₂×C₄²	—	47	4	no	—
297	C₂×C₄²	—	47	2	no	—
298	C₂×C₄²	—	47	4	no	—
299	C₂×C₄²	—	47	2	no	—
300	C₂×C₄²	—	94	4	no	—
301	C₂×C₄²	—	188	4	no	—
302	C₄⋊C₈	—	94	8	no	—
303	#95	—	94	4	no	—
304	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
305	C₂×Q₈	—	94	16	no	—
306	C₂×Q₈	—	188	32	no	—
307	C₂×Q₈	—	188	8	no	—
308	C₂×Q₈	—	188	8	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	47	4	no	—
318	C₂²×C₄	—	47	4	no	—
319	C₂²×C₄	—	47	4	no	—
320	C₂²×C₄	—	47	2	no	—
321	C₂²×C₄	—	47	4	no	—
322	C₂²×C₄	—	47	2	no	—
323	C₂²×C₄	—	94	2	no	—
324	C₂²×C₄	—	94	2	no	—
325	C₂²×C₄	—	94	4	no	—
326	C₂²×C₄	—	94	4	no	—
327	C₂²×C₄	—	94	2	no	—
328	C₂²×C₄	—	94	2	no	—
329	C₂²×C₄	—	188	2	no	—
330	C₂²×C₄	—	188	2	no	—
331	C₂²×C₄	—	188	2	no	—
332	C₂²×C₄	—	188	2	no	—
333	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
334	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
335	C₂²×C₄	#10625350	1	2	yes	—
336	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
337	C₂²×C₄	D₄×D₄₇	1	2	yes	—
338	C₂²×C₄	#10625352	1	2	yes	—
339	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
340	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	4	4	no	—
345	C₂×C₈	—	94	2	no	—
346	C₂×C₈	—	94	2	no	—
347	C₂×C₈	—	94	2	no	—
348	C₂×C₈	—	188	4	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	47	4	no	—
354	C₄⋊C₄	—	47	4	no	—
355	C₄⋊C₄	—	94	16	no	—
356	C₄⋊C₄	—	94	4	no	—
357	C₄⋊C₄	—	94	4	no	—
358	C₄⋊C₄	—	94	2	no	—
359	C₄⋊C₄	—	94	2	no	—
360	C₄⋊C₄	C₂×Dic₉₄	1	4	yes	complemented
361	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
362	C₄²	—	47	8	no	—
363	C₄²	—	47	4	no	—
364	C₄²	—	47	4	no	—
365	C₄²	—	188	8	no	—
366	C₂³	C₂²⋊C₄×D₄₇	1	2	yes	—
367	C₂³	#13094001	1	2	yes	—
368	C₂³	#13094002	1	2	yes	—
369	C₂³	SD₁₆×D₄₇	1	2	yes	—
370	C₂³	Q₁₆×D₄₇	1	2	yes	—
371	C₂³	#13094048	1	2	yes	—
372	C₂³	#13094051	1	2	yes	—
373	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
374	Q₈	—	188	32	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	47	4	no	—
384	C₂×C₄	—	47	16	no	—
385	C₂×C₄	—	47	4	no	—
386	C₂×C₄	—	47	4	no	—
387	C₂×C₄	—	47	4	no	—
388	C₂×C₄	—	94	8	no	—
389	C₂×C₄	—	94	2	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	94	4	no	—
392	C₂×C₄	—	94	4	no	—
393	C₂×C₄	—	188	8	no	—
394	C₂×C₄	—	188	2	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	—	188	2	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	—	188	8	no	—
399	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
400	C₂×C₄	#13093989	1	4	yes	—
401	C₂×C₄	C₄×Dic₉₄	1	4	yes	—
402	C₂×C₄	#13094001	1	2	yes	—
403	C₂×C₄	#13094002	1	2	yes	—
404	C₂×C₄	#13094010	1	4	yes	—
405	C₂×C₄	#13094023	1	4	yes	—
406	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
409	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
410	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
411	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
412	C₈	—	4	2	no	—
413	C₈	—	188	2	no	—
414	C₂²	#15689027	1	4	yes	—
415	C₂²	#103×D₄₇	1	4	yes	—
416	C₂²	#15689126	1	4	yes	—
417	C₂²	#15689411	1	4	yes	—
418	C₂²	#15689412	1	4	yes	—
419	C₂²	#15689416	1	4	yes	—
420	C₂²	#15689417	1	4	yes	—
421	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
422	C₂²	C₂×#13094001	1	1	yes	characteristic
423	C₂²	C₂×#13094002	1	1	yes	characteristic
424	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
425	C₂²	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
426	C₂²	C₂×#13094048	1	1	yes	characteristic
427	C₂²	C₂×#13094051	1	1	yes	characteristic
428	C₄	—	4	4	no	—
429	C₄	—	4	4	no	—
430	C₄	—	47	8	no	—
431	C₄	—	94	4	no	—
432	C₄	—	188	4	no	—
433	C₄	—	188	4	no	—
434	C₄	#15689027	1	4	yes	—
435	C₄	C₂×#13093989	1	1	yes	characteristic
436	C₄	C₂×C₄×Dic₉₄	1	1	yes	characteristic
437	C₄	C₂×#13094010	1	1	yes	characteristic
438	C₄	C₂×#13094023	1	1	yes	characteristic
439	C₂	#20244334	1	8	yes	direct product factor
440	C₂	C₂×#15689027	1	1	yes	characteristic
441	C₂	C₂×#103×D₄₇	1	1	yes	characteristic
442	C₂	C₂×#15689126	1	1	yes	characteristic
443	C₂	C₂×#15689411	1	1	yes	characteristic
444	C₂	C₂×#15689412	1	1	yes	characteristic
445	C₂	C₂×#15689416	1	1	yes	characteristic
446	C₂	C₂×#15689417	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#340	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#340	D₄₇
hypocenter	C₄₇	C₂×#1987
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
4. #20244334	C₂	direct (N × H)
13. C₂×#13094023	C₄	semidirect
46. #13094023	C₂×C₄	semidirect
52. C₂×C₄⋊Dic₄₇	Q₈	semidirect
77. C₂×C₄⋊C₄×C₄₇	Q₈	semidirect
126. C₄⋊C₄×C₄₇	C₂×Q₈	semidirect
132. C₄⋊Dic₄₇	C₂×Q₈	semidirect
224. C₂×C₄₇	#1987	semidirect
255. C₄₇	C₂×#1987	semidirect
292. C₂×C₄⋊C₄	Dic₉₄	semidirect
360. C₄⋊C₄	C₂×Dic₉₄	semidirect
439. C₂	#20244334	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×#13094023	2
C₂²×Dic₄₇⋊C₈	2
C₂×C₄⋊C₄×Dic₄₇	2
#20244334	2
C₂×#15688886	2
C₂×#15688885	2
C₂×C₄₇×#340	2
C₂×#1987	47

Subgroups — C2×#20244334 #26220774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244334 #26220774