Subgroups — C₂×#20241913 #26183405

Order 12032.

1206 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689180	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241913	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688860	C₂	1	2	yes	maximal, complemented
5	C₂×#15688857	C₂	1	2	yes	maximal
6	C₂×C₄₇×#529	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
8	C₂²×C₄×Dic₄₇	—	2	1	no	—
9	#15689180	—	2	2	no	—
10	#15689180	C₂²	1	4	yes	complemented
11	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
12	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×#13093935	—	2	1	no	—
14	C₄×C₄⋊Dic₄₇	—	2	2	no	—
15	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
16	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
17	#15688860	C₂²	1	8	yes	complemented
18	#15688857	C₂²	1	8	yes	—
19	C₄₇×#529	—	2	2	no	—
20	C₄₇×#529	—	2	2	no	—
21	C₄₇×#529	C₄	1	4	yes	complemented
22	C₄₇×#529	C₂²	1	4	yes	—
23	C₂×#126×C₄₇	—	2	1	no	—
24	C₂×#125×C₄₇	C₄	1	1	yes	characteristic, complemented
25	C₂×#124×C₄₇	C₄	1	1	yes	characteristic, complemented
26	C₂×#123×C₄₇	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₄₇	—	2	1	no	—
31	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic, complemented
32	C₂×#117×C₄₇	—	2	1	no	—
33	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
34	C₂³×Dic₄₇	—	2	2	no	—
35	C₂²×C₄₇⋊C₈	—	2	2	no	—
36	C₂×C₄⋊Dic₄₇	—	2	8	no	—
37	C₂×C₄⋊Dic₄₇	—	2	4	no	—
38	C₂×C₄×Dic₄₇	—	2	4	no	—
39	C₂×C₄×Dic₄₇	—	4	4	no	—
40	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
41	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
43	#13093935	—	2	4	no	—
44	C₄₇⋊#95	—	2	2	no	—
45	C₄₇⋊#95	C₂³	1	4	yes	—
46	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₄₇	—	2	1	no	—
48	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	—	2	1	no	—
50	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	#126×C₄₇	—	2	4	no	—
54	#126×C₄₇	—	2	4	no	—
55	#125×C₄₇	—	2	2	no	—
56	#125×C₄₇	C₂×C₄	1	4	yes	complemented
57	#124×C₄₇	—	2	2	no	—
58	#124×C₄₇	C₂×C₄	1	4	yes	complemented
59	#123×C₄₇	—	2	4	no	—
60	#123×C₄₇	—	2	4	no	—
61	C₂²⋊Q₈×C₄₇	—	2	1	no	—
62	C₂²⋊Q₈×C₄₇	—	2	1	no	—
63	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
64	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
65	#121×C₄₇	—	2	1	no	—
66	#121×C₄₇	—	2	1	no	—
67	#121×C₄₇	C₂×C₄	1	2	yes	—
68	#121×C₄₇	C₂³	1	2	yes	—
69	C₄×Q₈×C₄₇	—	2	2	no	—
70	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
71	C₄×D₄×C₄₇	—	2	4	no	—
72	C₄×D₄×C₄₇	—	2	4	no	—
73	C₄×D₄×C₄₇	—	2	2	no	—
74	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
75	#117×C₄₇	—	2	4	no	—
76	#117×C₄₇	—	2	4	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
92	C₂×C₄²×C₄₇	D₄	1	2	yes	—
93	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	D₄	1	2	yes	—
96	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
97	C₂⁴×C₄₇	—	2	1	no	—
98	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₄₇	—	2	1	no	—
100	C₂×Q₈×C₄₇	—	4	2	no	—
101	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	2	1	no	—
105	C₂×D₄×C₄₇	—	4	2	no	—
106	C₂×D₄×C₄₇	—	4	2	no	—
107	C₂×D₄×C₄₇	—	4	2	no	—
108	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	4	no	—
116	C₂²×C₄×C₄₇	—	4	2	no	—
117	C₂²×C₄×C₄₇	—	4	4	no	—
118	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
122	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₂²×Dic₄₇	—	2	8	no	—
133	C₂²×Dic₄₇	—	2	4	no	—
134	C₂²×Dic₄₇	—	4	4	no	—
135	C₂²×Dic₄₇	—	4	4	no	—
136	C₄⋊C₄×C₄₇	—	2	2	no	—
137	C₄⋊C₄×C₄₇	—	2	4	no	—
138	C₄⋊C₄×C₄₇	—	2	4	no	—
139	C₄⋊C₄×C₄₇	—	2	4	no	—
140	C₄⋊C₄×C₄₇	—	2	1	no	—
141	C₄⋊C₄×C₄₇	—	2	1	no	—
142	C₄⋊C₄×C₄₇	—	2	2	no	—
143	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
145	C₂²⋊C₄×C₄₇	—	2	2	no	—
146	C₂²⋊C₄×C₄₇	—	2	2	no	—
147	C₂²⋊C₄×C₄₇	—	2	2	no	—
148	C₂²⋊C₄×C₄₇	—	2	4	no	—
149	C₂²⋊C₄×C₄₇	—	2	4	no	—
150	C₂²⋊C₄×C₄₇	—	2	4	no	—
151	C₂²⋊C₄×C₄₇	—	2	2	no	—
152	C₄²×C₄₇	—	2	4	no	—
153	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
154	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
155	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
156	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
157	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
158	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
159	C₄²×C₄₇	C₂×D₄	1	2	yes	—
160	C₄²×C₄₇	C₂×D₄	1	2	yes	—
161	C₄⋊Dic₄₇	—	2	16	no	—
162	C₄×Dic₄₇	—	4	8	no	—
163	C₂×C₄₇⋊C₈	—	2	4	no	—
164	C₂×C₄₇⋊C₈	—	4	4	no	—
165	C₂³×C₄₇	—	2	2	no	—
166	C₂³×C₄₇	—	2	2	no	—
167	C₂³×C₄₇	—	2	2	no	—
168	C₂³×C₄₇	—	4	2	no	—
169	C₂³×C₄₇	—	4	2	no	—
170	C₂³×C₄₇	—	4	2	no	—
171	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
174	C₂³×C₄₇	#137	1	2	yes	—
175	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₄₇	—	4	2	no	—
177	Q₈×C₄₇	—	4	2	no	—
178	D₄×C₄₇	—	4	2	no	—
179	D₄×C₄₇	—	4	2	no	—
180	D₄×C₄₇	—	4	2	no	—
181	D₄×C₄₇	—	4	2	no	—
182	D₄×C₄₇	—	4	4	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	4	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	4	no	—
192	C₂×C₄×C₄₇	—	2	4	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	4	1	no	—
197	C₂×C₄×C₄₇	—	4	1	no	—
198	C₂×C₄×C₄₇	—	4	1	no	—
199	C₂×C₄×C₄₇	—	4	1	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	—	4	8	no	—
204	C₂×C₄×C₄₇	#104	1	4	yes	—
205	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
211	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×Dic₄₇	—	2	8	no	—
214	C₂×Dic₄₇	—	4	4	no	—
215	C₂×Dic₄₇	—	4	16	no	—
216	C₂×Dic₄₇	—	4	4	no	—
217	C₄₇⋊C₈	—	4	4	no	—
218	C₂×#1509	—	47	1	no	maximal, Sylow
219	C₂²×C₄₇	—	2	1	no	—
220	C₂²×C₄₇	—	2	1	no	—
221	C₂²×C₄₇	—	2	1	no	—
222	C₂²×C₄₇	—	2	1	no	—
223	C₂²×C₄₇	—	2	4	no	—
224	C₂²×C₄₇	—	2	4	no	—
225	C₂²×C₄₇	—	4	2	no	—
226	C₂²×C₄₇	—	4	2	no	—
227	C₂²×C₄₇	—	4	2	no	—
228	C₂²×C₄₇	—	8	4	no	—
229	C₂²×C₄₇	#410	1	2	yes	—
230	C₂²×C₄₇	#417	1	2	yes	—
231	C₂²×C₄₇	#417	1	2	yes	—
232	C₂²×C₄₇	C₂×#104	1	2	yes	—
233	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
234	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
236	C₄×C₄₇	—	2	1	no	—
237	C₄×C₄₇	—	2	1	no	—
238	C₄×C₄₇	—	2	1	no	—
239	C₄×C₄₇	—	2	1	no	—
240	C₄×C₄₇	—	2	2	no	—
241	C₄×C₄₇	—	2	2	no	—
242	C₄×C₄₇	—	2	2	no	—
243	C₄×C₄₇	—	4	2	no	—
244	C₄×C₄₇	—	4	2	no	—
245	C₄×C₄₇	—	4	2	no	—
246	C₄×C₄₇	C₂×#104	1	4	yes	—
247	Dic₄₇	—	4	8	no	—
248	C₂×#529	D₄₇	1	1	yes	characteristic
249	C₂×#432	—	47	1	no	—
250	C₂×C₄×C₄⋊C₄	—	47	1	no	—
251	#1509	—	47	8	no	—
252	C₂×#328	—	47	2	no	—
253	C₂×#327	—	47	2	no	—
254	C₂×C₄₇	—	2	1	no	—
255	C₂×C₄₇	—	2	1	no	—
256	C₂×C₄₇	—	2	2	no	—
257	C₂×C₄₇	—	8	2	no	—
258	C₂×C₄₇	#1509	1	4	yes	complemented
259	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
260	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
261	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
262	#529	—	2	2	no	—
263	#529	—	2	2	no	—
264	#529	Dic₄₇	1	4	yes	complemented
265	#529	C₂×D₄₇	1	4	yes	—
266	C₂×#126	—	2	1	no	—
267	C₂×#125	Dic₄₇	1	1	yes	characteristic, complemented
268	C₂×#124	Dic₄₇	1	1	yes	characteristic, complemented
269	C₂×#123	—	2	1	no	—
270	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
271	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
272	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic, complemented
273	C₂×C₄×D₄	—	2	1	no	—
274	C₂×C₄×D₄	Dic₄₇	1	1	yes	characteristic, complemented
275	C₂×#117	—	2	1	no	—
276	C₂²×C₄⋊C₄	—	94	1	no	—
277	C₂²×C₄²	—	94	1	no	—
278	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
279	#432	—	47	4	no	—
280	#432	—	94	2	no	—
281	C₂×C₄⋊C₈	—	94	1	no	—
282	C₂×C₂²⋊C₈	—	47	2	no	—
283	C₂×#97	—	94	1	no	—
284	C₄×C₄⋊C₄	—	47	4	no	—
285	C₄×C₄⋊C₄	—	94	2	no	—
286	C₂×#95	—	47	2	no	—
287	#328	—	47	8	no	—
288	#327	—	47	8	no	—
289	C₄₇	C₂×#1509	1	1	yes	characteristic, complemented, Sylow
290	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
293	C₂³×C₄	—	2	1	no	—
294	C₂³×C₄	—	94	2	no	—
295	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
296	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
298	C₂²×C₈	—	94	2	no	—
299	#126	—	2	4	no	—
300	#126	—	2	4	no	—
301	#125	—	2	2	no	—
302	#125	C₂×Dic₄₇	1	4	yes	complemented
303	#124	—	2	2	no	—
304	#124	C₂×Dic₄₇	1	4	yes	complemented
305	#123	—	2	4	no	—
306	#123	—	2	4	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
310	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
311	#121	—	2	1	no	—
312	#121	—	2	1	no	—
313	#121	C₂×Dic₄₇	1	2	yes	—
314	#121	C₂²×D₄₇	1	2	yes	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
321	#117	—	2	4	no	—
322	#117	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	94	8	no	—
328	C₂×C₄⋊C₄	—	94	4	no	—
329	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	94	4	no	—
338	C₂×C₄²	—	188	4	no	—
339	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
340	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
341	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
342	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
343	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
344	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
345	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
346	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
347	C₄⋊C₈	—	94	4	no	—
348	C₂²⋊C₈	—	47	4	no	—
349	C₂²⋊C₈	—	94	2	no	—
350	#97	—	94	4	no	—
351	#95	—	47	4	no	—
352	#95	—	94	2	no	—
353	C₂⁴	—	2	1	no	—
354	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	94	8	no	—
375	C₂²×C₄	—	94	4	no	—
376	C₂²×C₄	—	188	4	no	—
377	C₂²×C₄	—	188	4	no	—
378	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
379	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
380	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
381	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
382	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
383	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
384	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
385	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
387	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
388	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
391	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
392	C₂×C₈	—	94	4	no	—
393	C₂×C₈	—	188	4	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	94	16	no	—
402	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
403	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	188	8	no	—
413	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
414	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
415	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
416	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
417	C₄²	C₂²×Dic₄₇	1	2	yes	—
418	C₄²	C₂²×Dic₄₇	1	2	yes	—
419	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
420	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
428	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
429	C₂³	#13094049	1	2	yes	—
430	C₂³	#13094054	1	2	yes	—
431	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	4	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	8	no	—
460	C₂×C₄	—	94	8	no	—
461	C₂×C₄	—	188	4	no	—
462	C₂×C₄	—	188	16	no	—
463	C₂×C₄	—	188	4	no	—
464	C₂×C₄	#13093951	1	4	yes	—
465	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
466	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
467	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
468	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
469	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
470	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
471	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
473	C₈	—	188	4	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	8	4	no	—
484	C₂²	#15689097	1	2	yes	—
485	C₂²	#15689124	1	2	yes	—
486	C₂²	#15689124	1	2	yes	—
487	C₂²	C₂×#13093951	1	2	yes	—
488	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
489	C₂²	C₂×#13094049	1	1	yes	characteristic
490	C₂²	C₂×#13094054	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	188	8	no	—
502	C₄	C₂×#13093951	1	4	yes	—
503	C₂	—	2	1	no	—
504	C₂	—	2	2	no	—
505	C₂	—	2	1	no	—
506	C₂	—	8	2	no	—
507	C₂	#20241913	1	4	yes	direct product factor
508	C₂	C₂×#15689097	1	1	yes	characteristic
509	C₂	C₂×#15689124	1	1	yes	characteristic
510	C₂	C₂²×#13093951	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#529	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂×#121×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#529	D₄₇
hypocenter	C₄₇	C₂×#1509
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. C₂×#15689180	C₂	semidirect
2. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
3. #20241913	C₂	direct (N × H)
4. C₂×#15688860	C₂	semidirect
10. #15689180	C₂²	semidirect
15. C₄×C₄⋊Dic₄₇	C₂²	semidirect
17. #15688860	C₂²	semidirect
21. C₄₇×#529	C₄	semidirect
24. C₂×#125×C₄₇	C₄	semidirect
25. C₂×#124×C₄₇	C₄	semidirect
29. C₂×C₄×Q₈×C₄₇	C₄	semidirect
31. C₂×C₄×D₄×C₄₇	C₄	semidirect
56. #125×C₄₇	C₂×C₄	semidirect
58. #124×C₄₇	C₂×C₄	semidirect
70. C₄×Q₈×C₄₇	C₂×C₄	semidirect
74. C₄×D₄×C₄₇	C₂×C₄	semidirect
258. C₂×C₄₇	#1509	semidirect
264. #529	Dic₄₇	semidirect
267. C₂×#125	Dic₄₇	semidirect
268. C₂×#124	Dic₄₇	semidirect
272. C₂×C₄×Q₈	Dic₄₇	semidirect
274. C₂×C₄×D₄	Dic₄₇	semidirect
289. C₄₇	C₂×#1509	semidirect
302. #125	C₂×Dic₄₇	semidirect
304. #124	C₂×Dic₄₇	semidirect
316. C₄×Q₈	C₂×Dic₄₇	semidirect
320. C₄×D₄	C₂×Dic₄₇	semidirect
507. C₂	#20241913	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×#15689180	2
C₂×C₄×C₄⋊Dic₄₇	2
#20241913	2
C₂×#15688860	2
C₂×#15688857	2
C₂×C₄₇×#529	2
C₂×#1509	47

Subgroups — C2×#20241913 #26183405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241913 #26183405