Subgroups — C₄×#15689323 #26222476

Order 12032.

1152 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689323	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625336	C₂	1	2	yes	maximal, complemented
3	C₄×#13094021	C₂	1	1	yes	maximal, characteristic
4	#20244315	C₂	1	1	yes	maximal, characteristic
5	#20244151	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244015	C₂	1	2	yes	maximal, complemented
7	#20243743	C₂	1	2	yes	maximal, complemented
8	#20243393	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093944	C₂	1	2	yes	maximal, complemented
11	C₄²×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625336	C₂²	1	2	yes	—
13	C₂×#13094021	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₈₈	—	2	1	no	—
15	C₂×C₄×D₁₈₈	—	2	1	no	—
16	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
17	#15689323	C₄	1	8	yes	direct product factor
18	C₄×#10625336	—	2	8	no	—
19	C₂×#13093955	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#13093948	C₂²	1	2	yes	—
23	C₂×#13093944	C₂²	1	2	yes	—
24	C₂×#13093944	C₂²	1	2	yes	—
25	C₂×#13093944	C₂²	1	2	yes	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
27	#15689025	—	2	1	no	—
28	#15689025	—	2	1	no	—
29	#15689025	C₂²	1	2	yes	—
30	#15688993	C₂²	1	1	yes	characteristic
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	#15688878	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
38	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄³×C₄₇	—	2	1	no	—
44	C₄³×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×D₁₈₈	—	2	1	no	—
46	C₂²×D₁₈₈	—	2	1	no	—
47	C₂²×D₁₈₈	C₂³	1	2	yes	—
48	C₂²×C₄×D₄₇	—	2	2	no	—
49	C₂×#10625336	—	2	4	no	—
50	C₂×#10625336	—	2	4	no	—
51	C₂×#10625336	C₂×C₄	1	8	yes	complemented
52	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
53	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
54	#13094021	—	2	2	no	—
55	#13094021	C₂×C₄	1	4	yes	—
56	C₄×D₁₈₈	—	2	4	no	—
57	C₄×D₁₈₈	—	2	4	no	—
58	C₄×D₁₈₈	—	4	4	no	—
59	C₄×D₁₈₈	—	4	4	no	—
60	C₂×C₄⋊Dic₄₇	—	2	1	no	—
61	C₂×C₄⋊Dic₄₇	—	2	1	no	—
62	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
63	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
65	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
66	#13093955	—	2	4	no	—
67	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
68	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
69	#13093948	—	2	4	no	—
70	#13093944	—	2	4	no	—
71	#13093944	—	2	4	no	—
72	#13093944	C₂×C₄	1	8	yes	complemented
73	C₄×C₄₇⋊C₈	—	2	4	no	—
74	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×Q₈×C₄₇	—	2	2	no	—
76	C₄×Q₈×C₄₇	—	2	2	no	—
77	C₄×Q₈×C₄₇	—	2	2	no	—
78	C₄×Q₈×C₄₇	—	2	2	no	—
79	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
80	C₄×Q₈×C₄₇	D₄	1	4	yes	complemented
81	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	—	2	1	no	—
90	C₂×C₄²×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	—	2	1	no	—
93	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	#95×C₄₇	—	2	1	no	—
101	#95×C₄₇	—	2	1	no	—
102	#95×C₄₇	—	2	1	no	—
103	C₂³×D₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂×Q₈×C₄₇	—	2	1	no	—
106	C₂×Q₈×C₄₇	—	2	1	no	—
107	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₄₇	#41	1	2	yes	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
121	C₂²×Dic₄₇	—	2	2	no	—
122	C₂×D₁₈₈	—	2	2	no	—
123	C₂×D₁₈₈	—	2	2	no	—
124	C₂×D₁₈₈	—	2	2	no	—
125	C₂×D₁₈₈	—	2	2	no	—
126	C₂×D₁₈₈	—	2	4	no	—
127	C₂×D₁₈₈	—	2	4	no	—
128	C₂×D₁₈₈	—	2	2	no	—
129	C₂×D₁₈₈	—	4	2	no	—
130	C₂×D₁₈₈	—	4	2	no	—
131	C₂×D₁₈₈	—	4	2	no	—
132	C₂×D₁₈₈	—	4	2	no	—
133	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
134	C₂×C₄×D₄₇	—	4	4	no	—
135	C₂×C₄×D₄₇	—	4	4	no	—
136	C₂×C₄×D₄₇	—	4	4	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	1	no	—
143	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₄₇	#41	1	2	yes	—
146	C₄²×C₄₇	—	2	4	no	—
147	C₄²×C₄₇	—	2	4	no	—
148	C₄²×C₄₇	—	2	4	no	—
149	C₄²×C₄₇	—	2	2	no	—
150	C₄²×C₄₇	—	2	2	no	—
151	C₄²×C₄₇	—	2	1	no	—
152	C₄²×C₄₇	—	2	1	no	—
153	C₄²×C₄₇	—	4	1	no	—
154	C₄²×C₄₇	—	4	2	no	—
155	C₄²×C₄₇	—	4	2	no	—
156	C₄²×C₄₇	—	4	2	no	—
157	C₄²×C₄₇	SD₁₆	1	4	yes	complemented
158	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
159	C₄²×C₄₇	C₂×D₄	1	2	yes	—
160	C₄²×C₄₇	#41	1	2	yes	—
161	C₄²×C₄₇	#41	1	2	yes	—
162	#10625336	—	2	16	no	—
163	(C₂×D₄₇)⋊C₄	—	4	4	no	—
164	(C₂×D₄₇)⋊C₄	—	4	4	no	—
165	(C₂×D₄₇)⋊C₄	—	4	4	no	—
166	C₄⋊Dic₄₇	—	2	2	no	—
167	C₄⋊Dic₄₇	—	2	2	no	—
168	C₄⋊Dic₄₇	—	4	2	no	—
169	C₄⋊Dic₄₇	—	4	2	no	—
170	C₂×C₄₇⋊C₈	—	2	2	no	—
171	C₂×C₄₇⋊C₈	—	2	2	no	—
172	C₂×C₄₇⋊C₈	—	2	2	no	—
173	C₂×C₄₇⋊C₈	—	2	2	no	—
174	C₂×C₄₇⋊C₈	—	2	2	no	—
175	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
176	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂²×D₄₇	—	2	4	no	—
178	C₂²×D₄₇	—	4	2	no	—
179	C₂²×D₄₇	—	4	2	no	—
180	C₂²×D₄₇	—	4	2	no	—
181	C₂²×D₄₇	—	4	2	no	—
182	C₂²×D₄₇	—	4	2	no	—
183	C₂²×D₄₇	—	4	2	no	—
184	Q₈×C₄₇	—	2	2	no	—
185	Q₈×C₄₇	—	2	2	no	—
186	Q₈×C₄₇	—	2	2	no	—
187	Q₈×C₄₇	C₄×D₄	1	4	yes	complemented
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	1	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	2	1	no	—
194	C₂×C₄×C₄₇	—	2	1	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	1	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	1	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	1	no	—
202	C₂×C₄×C₄₇	—	2	1	no	—
203	C₂×C₄×C₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	4	1	no	—
205	C₂×C₄×C₄₇	—	4	1	no	—
206	C₂×C₄×C₄₇	—	4	1	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₄₇	#121	1	2	yes	—
212	C₂×C₄×C₄₇	#121	1	2	yes	—
213	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
214	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
215	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
216	C₂×C₄×C₄₇	#135	1	2	yes	—
217	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
224	C₂×Dic₄₇	—	4	2	no	—
225	C₂×Dic₄₇	—	4	2	no	—
226	C₂×Dic₄₇	—	4	2	no	—
227	D₁₈₈	—	2	4	no	—
228	D₁₈₈	—	2	4	no	—
229	D₁₈₈	—	4	8	no	—
230	D₁₈₈	—	4	2	no	—
231	D₁₈₈	—	4	2	no	—
232	D₁₈₈	—	4	8	no	—
233	C₄×D₄₇	—	8	8	no	—
234	C₄₇⋊C₈	—	2	4	no	—
235	C₄₇⋊C₈	—	4	2	no	—
236	C₄×#460	—	47	1	no	maximal, Sylow
237	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
238	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
239	C₂²×C₄₇	#525	1	1	yes	characteristic
240	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
241	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
242	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂²×C₄₇	#575	1	1	yes	characteristic
244	C₂×D₄₇	—	4	4	no	—
245	C₂×D₄₇	—	4	4	no	—
246	C₂×D₄₇	—	4	4	no	—
247	C₂×D₄₇	—	8	2	no	—
248	C₂×D₄₇	—	8	2	no	—
249	C₂×D₄₇	—	8	2	no	—
250	C₂×D₄₇	—	8	2	no	—
251	C₄×C₄₇	—	2	2	no	—
252	C₄×C₄₇	—	2	2	no	—
253	C₄×C₄₇	—	2	2	no	—
254	C₄×C₄₇	—	2	4	no	—
255	C₄×C₄₇	—	4	1	no	—
256	C₄×C₄₇	—	4	2	no	—
257	C₄×C₄₇	—	4	2	no	—
258	C₄×C₄₇	—	4	2	no	—
259	C₄×C₄₇	C₄×SD₁₆	1	4	yes	complemented
260	C₄×C₄₇	#460	1	4	yes	complemented
261	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
262	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
263	C₄×C₄₇	#529	1	1	yes	characteristic
264	C₄×C₄₇	#532	1	1	yes	characteristic
265	Dic₄₇	—	8	2	no	—
266	C₂×#460	—	47	1	no	—
267	C₂×C₄×SD₁₆	—	47	2	no	—
268	C₄×#127	—	47	1	no	—
269	C₄²×Q₈	D₄₇	1	1	yes	characteristic, complemented
270	#1982	—	47	1	no	—
271	#1948	—	47	1	no	—
272	#1926	—	47	2	no	—
273	#1880	—	47	2	no	—
274	#1803	—	47	1	no	—
275	C₄×C₄⋊C₈	—	47	1	no	—
276	C₄×#102	—	47	2	no	—
277	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
278	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
279	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
280	C₂×C₄₇	C₂×#460	1	1	yes	characteristic
281	C₂×C₄₇	#3035	1	1	yes	characteristic
282	C₂×C₄₇	#3103	1	1	yes	characteristic
283	C₂×C₄₇	#3106	1	1	yes	characteristic
284	D₄₇	—	8	4	no	—
285	C₂²×SD₁₆	—	47	2	no	—
286	C₂×#127	—	47	1	no	—
287	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
288	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
289	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
290	C₂×C₄×D₄	—	47	2	no	—
291	C₂×C₄×D₄	—	94	1	no	—
292	C₂×C₄×D₄	—	94	1	no	—
293	#460	—	47	8	no	—
294	C₄×SD₁₆	—	94	8	no	—
295	C₂×#106	—	47	2	no	—
296	C₂×C₄⋊C₈	—	47	1	no	—
297	C₂×C₄⋊C₈	—	47	1	no	—
298	C₂×#103	—	47	2	no	—
299	C₂×#102	—	47	2	no	—
300	C₂×#102	—	47	2	no	—
301	C₂×#102	—	47	2	no	—
302	C₂×C₄×C₈	—	47	2	no	—
303	#390	—	47	2	no	—
304	#390	—	94	1	no	—
305	#390	—	94	1	no	—
306	#384	—	47	1	no	—
307	C₄×C₄⋊C₄	—	2	1	no	—
308	C₄×C₄⋊C₄	—	2	1	no	—
309	C₄×C₄⋊C₄	—	2	1	no	—
310	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
311	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
312	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
313	C₄³	—	2	1	no	—
314	C₄³	C₂×D₄₇	1	1	yes	characteristic
315	#340	—	47	2	no	—
316	#340	—	47	2	no	—
317	#336	—	47	2	no	—
318	C₄₇	C₄×#460	1	1	yes	characteristic, complemented, Sylow
319	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
320	C₂²×D₄	—	47	2	no	—
321	C₂²×D₄	—	94	1	no	—
322	C₂²×D₄	—	94	1	no	—
323	C₂³×C₄	—	94	2	no	—
324	C₂×SD₁₆	—	47	8	no	—
325	C₂×SD₁₆	—	94	4	no	—
326	C₂×SD₁₆	—	94	4	no	—
327	C₂²×C₈	—	47	2	no	—
328	C₂²×C₈	—	47	2	no	—
329	#127	—	47	4	no	—
330	#127	—	94	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	C₄×D₄₇	1	4	yes	complemented
336	C₄×Q₈	D₁₈₈	1	4	yes	complemented
337	C₄×D₄	—	94	4	no	—
338	C₄×D₄	—	94	4	no	—
339	C₄×D₄	—	188	4	no	—
340	C₄×D₄	—	188	4	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	47	2	no	—
345	C₂×C₄⋊C₄	—	94	1	no	—
346	C₂×C₄⋊C₄	—	94	1	no	—
347	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	—	94	2	no	—
351	C₂×C₂²⋊C₄	—	94	2	no	—
352	C₂×C₂²⋊C₄	—	94	2	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
362	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
363	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
364	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
365	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
366	#106	—	94	4	no	—
367	C₄⋊C₈	—	47	4	no	—
368	C₄⋊C₈	—	94	2	no	—
369	#103	—	94	4	no	—
370	#102	—	47	8	no	—
371	#102	—	94	4	no	—
372	#102	—	94	4	no	—
373	C₄×C₈	—	94	4	no	—
374	#95	—	2	1	no	—
375	#95	—	2	1	no	—
376	#95	—	2	1	no	—
377	C₂⁴	—	94	2	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
382	C₂×Q₈	C₂×D₁₈₈	1	2	yes	—
383	C₂×Q₈	#10625350	1	2	yes	—
384	C₂×D₄	—	47	4	no	—
385	C₂×D₄	—	94	4	no	—
386	C₂×D₄	—	94	4	no	—
387	C₂×D₄	—	94	2	no	—
388	C₂×D₄	—	94	2	no	—
389	C₂×D₄	—	94	2	no	—
390	C₂×D₄	—	94	2	no	—
391	C₂×D₄	—	94	2	no	—
392	C₂×D₄	—	188	2	no	—
393	C₂×D₄	—	188	2	no	—
394	C₂×D₄	—	188	2	no	—
395	C₂×D₄	—	188	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	94	2	no	—
401	C₂²×C₄	—	188	4	no	—
402	C₂²×C₄	—	188	4	no	—
403	C₂²×C₄	—	188	4	no	—
404	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
407	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
408	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
410	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
411	SD₁₆	—	94	16	no	—
412	C₂×C₈	—	47	4	no	—
413	C₂×C₈	—	94	2	no	—
414	C₂×C₈	—	94	2	no	—
415	C₂×C₈	—	94	2	no	—
416	C₂×C₈	—	94	2	no	—
417	C₂×C₈	—	94	2	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	94	2	no	—
425	C₄⋊C₄	—	94	2	no	—
426	C₄⋊C₄	—	188	2	no	—
427	C₄⋊C₄	—	188	2	no	—
428	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
429	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
430	C₄⋊C₄	#10625350	1	2	yes	—
431	C₂²⋊C₄	—	188	4	no	—
432	C₂²⋊C₄	—	188	4	no	—
433	C₂²⋊C₄	—	188	4	no	—
434	C₄²	—	2	4	no	—
435	C₄²	—	2	4	no	—
436	C₄²	—	2	4	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	4	1	no	—
442	C₄²	—	4	2	no	—
443	C₄²	—	4	2	no	—
444	C₄²	—	4	2	no	—
445	C₄²	#10625336	1	4	yes	complemented
446	C₄²	C₂×C₄×D₄₇	1	2	yes	—
447	C₄²	C₂×D₁₈₈	1	2	yes	—
448	C₄²	#10625350	1	2	yes	—
449	C₄²	#10625350	1	2	yes	—
450	C₂³	—	94	4	no	—
451	C₂³	—	188	2	no	—
452	C₂³	—	188	2	no	—
453	C₂³	—	188	2	no	—
454	C₂³	—	188	2	no	—
455	C₂³	—	188	2	no	—
456	C₂³	—	188	2	no	—
457	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
458	Q₈	—	2	2	no	—
459	Q₈	—	2	2	no	—
460	Q₈	—	2	2	no	—
461	Q₈	C₄×D₁₈₈	1	4	yes	complemented
462	D₄	—	94	4	no	—
463	D₄	—	94	4	no	—
464	D₄	—	188	8	no	—
465	D₄	—	188	2	no	—
466	D₄	—	188	2	no	—
467	D₄	—	188	8	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	376	8	no	—
490	C₂×C₄	—	188	2	no	—
491	C₂×C₄	—	188	2	no	—
492	C₂×C₄	—	188	2	no	—
493	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
494	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
495	C₂×C₄	#13093998	1	2	yes	—
496	C₂×C₄	#13093998	1	2	yes	—
497	C₂×C₄	C₂×#10625336	1	2	yes	—
498	C₂×C₄	C₂×#10625336	1	2	yes	—
499	C₂×C₄	C₂×#10625336	1	2	yes	—
500	C₂×C₄	#13094044	1	2	yes	—
501	C₂×C₄	#13094049	1	2	yes	—
502	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
504	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
505	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
506	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
507	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
508	C₈	—	94	4	no	—
509	C₈	—	188	2	no	—
510	C₂²	—	376	2	no	—
511	C₂²	—	376	2	no	—
512	C₂²	—	376	2	no	—
513	C₂²	—	376	2	no	—
514	C₂²	—	188	4	no	—
515	C₂²	—	188	4	no	—
516	C₂²	—	188	4	no	—
517	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
518	C₂²	C₂×#13093998	1	1	yes	characteristic
519	C₂²	#15689634	1	1	yes	characteristic
520	C₂²	C₂²×#10625336	1	1	yes	characteristic
521	C₂²	C₂×#13094044	1	1	yes	characteristic
522	C₂²	C₂×#13094049	1	1	yes	characteristic
523	C₂²	#15689921	1	1	yes	characteristic
524	C₄	—	2	2	no	—
525	C₄	—	2	4	no	—
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	376	2	no	—
533	C₄	C₄×#10625336	1	4	yes	complemented
534	C₄	#15689323	1	4	yes	direct product factor
535	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
536	C₄	C₄×#10625350	1	1	yes	characteristic
537	C₄	#15689657	1	1	yes	characteristic
538	C₄	#15689673	1	1	yes	characteristic
539	C₂	—	376	4	no	—
540	C₂	C₄×#13093998	1	1	yes	characteristic
541	C₂	C₂×C₄×#10625336	1	1	yes	characteristic
542	C₂	C₄×#13094049	1	1	yes	characteristic
543	C₂	C₂×#15689323	1	1	yes	characteristic
544	C₂	#20252843	1	1	yes	characteristic
545	C₂	#20253419	1	1	yes	characteristic
546	C₂	#20253448	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄²×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#13094021	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄²×Q₈	D₄₇
hypocenter	C₄₇	C₄×#460
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#10625336	C₂	semidirect
5. #20244151	C₂	semidirect
6. #20244015	C₂	semidirect
7. #20243743	C₂	semidirect
8. #20243393	C₂	semidirect
9. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
10. C₄×#13093944	C₂	semidirect
11. C₄²×Q₈×C₄₇	C₂	semidirect
17. #15689323	C₄	direct (N × H)
51. C₂×#10625336	C₂×C₄	semidirect
68. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
72. #13093944	C₂×C₄	semidirect
79. C₄×Q₈×C₄₇	C₂×C₄	semidirect
80. C₄×Q₈×C₄₇	D₄	semidirect
157. C₄²×C₄₇	SD₁₆	semidirect
187. Q₈×C₄₇	C₄×D₄	semidirect
259. C₄×C₄₇	C₄×SD₁₆	semidirect
260. C₄×C₄₇	#460	semidirect
269. C₄²×Q₈	D₄₇	semidirect
318. C₄₇	C₄×#460	semidirect
335. C₄×Q₈	C₄×D₄₇	semidirect
336. C₄×Q₈	D₁₈₈	semidirect
445. C₄²	#10625336	semidirect
461. Q₈	C₄×D₁₈₈	semidirect
533. C₄	C₄×#10625336	semidirect
534. C₄	#15689323	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×#15689323	2
C₂×C₄×#10625336	2
C₄×#13094021	2
#20244315	2
#20244151	2
#20244015	2
#20243743	2
#20243393	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₄×#13093944	2
C₄²×Q₈×C₄₇	2
C₄×#460	47

Subgroups — C4×#15689323 #26222476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689323 #26222476