Subgroups — C₄⋊C₄×#10625336 #26234682

Order 12032.

1030 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625336	C₂	1	2	yes	maximal
2	C₂×C₄×#10625336	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic
4	#20244113	C₂	1	2	yes	maximal, complemented
5	#20243656	C₂	1	2	yes	maximal, complemented
6	#20243648	C₂	1	2	yes	maximal
7	#20243544	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243393	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243385	C₂	1	1	yes	maximal, characteristic
10	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625336	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×D₄₇	—	2	1	no	—
16	C₄×#10625336	—	2	8	no	—
17	C₄×#10625336	C₄	1	8	yes	complemented
18	C₂×#13093955	C₂²	1	2	yes	—
19	C₂×#13093955	C₂²	1	2	yes	—
20	C₂×#13093955	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#13093948	C₂²	1	2	yes	—
23	C₂×#13093948	C₂²	1	1	yes	characteristic
24	C₂×#13093944	C₂²	1	2	yes	—
25	C₂×#13093944	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
27	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	#15689021	C₂²	1	2	yes	—
29	#15688997	—	2	2	no	—
30	#15688993	C₂²	1	1	yes	characteristic
31	#15688980	—	2	1	no	—
32	#15688885	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688878	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#389	—	2	2	no	—
38	C₄₇×#389	C₂²	1	2	yes	—
39	C₄₇×#384	—	2	1	no	—
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	—	2	1	no	—
45	C₂²×C₄×D₄₇	—	2	2	no	—
46	C₂×#10625336	C₂×C₄	1	4	yes	—
47	C₂×#10625336	D₄	1	4	yes	—
48	C₂×#10625336	Q₈	1	4	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	C₄×D₁₈₈	—	2	2	no	—
53	C₄×D₁₈₈	—	2	4	no	—
54	C₄×D₁₈₈	—	4	2	no	—
55	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊Dic₄₇	—	2	1	no	—
57	C₂×C₄⋊Dic₄₇	—	2	1	no	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×Dic₄₇⋊C₄	—	2	2	no	—
61	C₄⋊C₄×D₄₇	—	4	4	no	—
62	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
63	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	#13093955	—	2	4	no	—
65	#13093955	—	4	2	no	—
66	#13093955	C₂×C₄	1	4	yes	complemented
67	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
68	#13093948	—	2	4	no	—
69	#13093948	C₂×C₄	1	4	yes	complemented
70	#13093944	—	2	4	no	—
71	#13093944	C₂×C₄	1	4	yes	—
72	C₄×C₄₇⋊C₈	—	2	4	no	—
73	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
74	C₄₇⋊#95	—	2	2	no	—
75	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₄×Q₈×C₄₇	—	2	2	no	—
77	C₄×Q₈×C₄₇	—	2	4	no	—
78	C₄×Q₈×C₄₇	—	4	2	no	—
79	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
80	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	—	2	1	no	—
90	C₂×C₄²×C₄₇	—	2	2	no	—
91	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	#95×C₄₇	—	2	2	no	—
94	#95×C₄₇	D₄	1	2	yes	—
95	C₂³×D₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×Q₈×C₄₇	—	2	1	no	—
99	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
101	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
110	C₂²×Dic₄₇	—	2	1	no	—
111	C₂²×Dic₄₇	—	2	2	no	—
112	C₂×D₁₈₈	—	2	1	no	—
113	C₂×D₁₈₈	—	2	1	no	—
114	C₂×D₁₈₈	—	2	1	no	—
115	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
116	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
117	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
118	C₂×C₄×D₄₇	—	2	4	no	—
119	C₂×C₄×D₄₇	—	4	2	no	—
120	C₂×C₄×D₄₇	—	4	2	no	—
121	C₂×C₄×D₄₇	—	4	4	no	—
122	C₂×C₄×D₄₇	—	4	4	no	—
123	C₂×C₄×D₄₇	—	8	2	no	—
124	C₄⋊C₄×C₄₇	—	2	4	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	4	4	no	—
130	C₄⋊C₄×C₄₇	—	4	2	no	—
131	C₄⋊C₄×C₄₇	—	8	1	no	—
132	C₄⋊C₄×C₄₇	—	8	2	no	—
133	C₄⋊C₄×C₄₇	SD₁₆	1	4	yes	complemented
134	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
135	C₄²×C₄₇	—	2	4	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	—	2	2	no	—
138	C₄²×C₄₇	—	4	4	no	—
139	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
140	C₄²×C₄₇	#41	1	2	yes	—
141	#10625336	C₄⋊C₄	1	16	yes	direct product factor
142	(C₂×D₄₇)⋊C₄	—	2	4	no	—
143	(C₂×D₄₇)⋊C₄	—	4	4	no	—
144	C₄⋊Dic₄₇	—	2	1	no	—
145	C₄⋊Dic₄₇	—	2	2	no	—
146	C₄⋊Dic₄₇	—	2	2	no	—
147	C₄⋊Dic₄₇	—	4	2	no	—
148	C₄⋊Dic₄₇	—	8	1	no	—
149	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
150	Dic₄₇⋊C₄	—	4	4	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
157	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
158	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
159	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
160	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂²×D₄₇	—	2	2	no	—
162	C₂²×D₄₇	—	2	2	no	—
163	C₂²×D₄₇	—	2	2	no	—
164	C₂²×D₄₇	—	4	1	no	—
165	C₂²×D₄₇	—	4	1	no	—
166	C₂²×D₄₇	—	4	1	no	—
167	C₂²×D₄₇	—	4	1	no	—
168	Q₈×C₄₇	—	2	2	no	—
169	Q₈×C₄₇	—	2	2	no	—
170	Q₈×C₄₇	—	2	2	no	—
171	Q₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	complemented
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
191	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
192	C₂×C₄×C₄₇	#135	1	2	yes	—
193	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
199	C₂×Dic₄₇	—	2	2	no	—
200	C₂×Dic₄₇	—	4	1	no	—
201	C₂×Dic₄₇	—	4	1	no	—
202	C₂×Dic₄₇	—	4	2	no	—
203	C₂×Dic₄₇	—	4	2	no	—
204	C₂×Dic₄₇	—	4	2	no	—
205	D₁₈₈	—	2	2	no	—
206	D₁₈₈	—	2	2	no	—
207	D₁₈₈	—	2	2	no	—
208	D₁₈₈	C₂×C₄⋊C₄	1	4	yes	—
209	C₄×D₄₇	—	4	8	no	—
210	C₄×D₄₇	—	8	8	no	—
211	C₄₇⋊C₈	—	2	2	no	—
212	C₄₇⋊C₈	—	4	2	no	—
213	C₄₇⋊C₈	C₂×C₄⋊C₄	1	4	yes	complemented
214	C₄⋊C₄×SD₁₆	—	47	1	no	maximal, Sylow
215	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
216	C₂²×C₄₇	D₄²	1	1	yes	characteristic
217	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
218	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
220	C₂²×C₄₇	#577	1	1	yes	characteristic
221	C₂²×C₄₇	#577	1	1	yes	characteristic
222	C₂×D₄₇	—	2	4	no	—
223	C₂×D₄₇	—	4	2	no	—
224	C₂×D₄₇	—	4	2	no	—
225	C₂×D₄₇	—	4	2	no	—
226	C₂×D₄₇	—	4	2	no	—
227	C₂×D₄₇	—	4	2	no	—
228	C₂×D₄₇	—	4	2	no	—
229	C₄×C₄₇	—	2	4	no	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	—	2	4	no	—
232	C₄×C₄₇	—	4	2	no	—
233	C₄×C₄₇	—	4	2	no	—
234	C₄×C₄₇	—	8	2	no	—
235	C₄×C₄₇	C₄×SD₁₆	1	4	yes	complemented
236	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
237	C₄×C₄₇	#520	1	1	yes	characteristic
238	C₄×C₄₇	#547	1	1	yes	characteristic
239	C₄×C₄₇	#554	1	1	yes	characteristic
240	Dic₄₇	—	4	2	no	—
241	Dic₄₇	—	8	2	no	—
242	C₂×C₄×SD₁₆	—	47	1	no	—
243	C₂×C₄×SD₁₆	—	47	2	no	—
244	Q₈×C₄⋊C₄	D₄₇	1	1	yes	characteristic, complemented
245	D₄×C₄⋊C₄	—	47	1	no	—
246	#1941	—	47	2	no	—
247	#1865	—	47	2	no	—
248	#1864	—	47	2	no	—
249	#1844	—	47	1	no	—
250	#1803	—	47	1	no	—
251	#1802	—	47	1	no	—
252	C₈×C₄⋊C₄	—	47	1	no	—
253	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
254	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
255	C₂×C₄₇	#2952	1	1	yes	characteristic
256	C₂×C₄₇	D₄×SD₁₆	1	1	yes	characteristic
257	C₂×C₄₇	#3284	1	1	yes	characteristic
258	C₂×C₄₇	Q₈×SD₁₆	1	1	yes	characteristic
259	C₂×C₄₇	#3381	1	1	yes	characteristic
260	D₄₇	—	4	4	no	—
261	C₂²×SD₁₆	—	47	1	no	—
262	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
263	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
264	C₂×C₄×D₄	—	47	1	no	—
265	C₂×C₄×D₄	—	47	2	no	—
266	C₂²×C₄⋊C₄	—	94	1	no	—
267	C₄×SD₁₆	—	47	8	no	—
268	C₄×SD₁₆	—	94	8	no	—
269	C₂×#106	—	47	1	no	—
270	C₂×#106	—	47	2	no	—
271	C₂×#106	—	47	2	no	—
272	C₂×C₄⋊C₈	—	47	1	no	—
273	C₂×#103	—	47	1	no	—
274	C₂×#103	—	47	2	no	—
275	C₂×#102	—	47	1	no	—
276	C₂×#102	—	47	2	no	—
277	C₂×C₄×C₈	—	47	1	no	—
278	C₂×C₄×C₈	—	47	2	no	—
279	#389	—	2	2	no	—
280	#389	—	47	2	no	—
281	#389	C₂×D₄₇	1	2	yes	—
282	#385	—	94	2	no	—
283	#384	—	2	1	no	—
284	#384	—	47	1	no	—
285	#384	C₂×D₄₇	1	1	yes	characteristic
286	#380	—	94	1	no	—
287	C₄×C₄⋊C₄	—	2	1	no	—
288	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
289	#340	—	47	2	no	—
290	#340	—	47	2	no	—
291	#336	—	47	2	no	—
292	C₄₇	C₄⋊C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
293	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
294	C₂²×D₄	—	47	1	no	—
295	C₂³×C₄	—	94	1	no	—
296	C₂³×C₄	—	94	2	no	—
297	C₂×SD₁₆	—	47	4	no	—
298	C₂×SD₁₆	—	47	4	no	—
299	C₂×SD₁₆	—	47	4	no	—
300	C₂²×C₈	—	47	1	no	—
301	C₂²×C₈	—	47	1	no	—
302	C₂²×C₈	—	47	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	4	no	—
305	C₄×Q₈	—	4	2	no	—
306	C₄×Q₈	C₄×D₄₇	1	4	yes	complemented
307	C₄×D₄	—	47	4	no	—
308	C₄×D₄	—	94	4	no	—
309	C₄×D₄	—	94	2	no	—
310	C₄×D₄	—	188	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	47	1	no	—
317	C₂×C₄⋊C₄	—	47	2	no	—
318	C₂×C₄⋊C₄	—	94	1	no	—
319	C₂×C₄⋊C₄	—	94	2	no	—
320	C₂×C₄⋊C₄	—	94	1	no	—
321	C₂×C₄⋊C₄	—	188	4	no	—
322	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
325	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	94	1	no	—
327	C₂×C₂²⋊C₄	—	94	2	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
331	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
332	#106	—	47	4	no	—
333	#106	—	94	4	no	—
334	#106	—	188	2	no	—
335	C₄⋊C₈	—	94	2	no	—
336	#103	—	47	4	no	—
337	#103	—	94	4	no	—
338	#102	—	47	4	no	—
339	#102	—	94	4	no	—
340	C₄×C₈	—	47	4	no	—
341	C₄×C₈	—	94	4	no	—
342	#95	—	2	2	no	—
343	#95	—	94	2	no	—
344	#95	C₂²⋊D₄₇	1	2	yes	—
345	C₂⁴	—	94	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
350	C₂×Q₈	D₄×D₄₇	1	2	yes	—
351	C₂×Q₈	Q₈×D₄₇	1	2	yes	—
352	C₂×D₄	—	47	2	no	—
353	C₂×D₄	—	47	2	no	—
354	C₂×D₄	—	47	2	no	—
355	C₂×D₄	—	94	1	no	—
356	C₂×D₄	—	94	1	no	—
357	C₂×D₄	—	94	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	94	1	no	—
362	C₂²×C₄	—	94	4	no	—
363	C₂²×C₄	—	94	2	no	—
364	C₂²×C₄	—	376	2	no	—
365	C₂²×C₄	—	188	4	no	—
366	C₂²×C₄	—	188	4	no	—
367	C₂²×C₄	—	188	2	no	—
368	C₂²×C₄	—	188	2	no	—
369	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
370	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
372	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
373	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
374	SD₁₆	—	47	16	no	—
375	C₂×C₈	—	47	2	no	—
376	C₂×C₈	—	47	2	no	—
377	C₂×C₈	—	47	2	no	—
378	C₂×C₈	—	47	2	no	—
379	C₂×C₈	—	94	1	no	—
380	C₂×C₈	—	94	1	no	—
381	C₂×C₈	—	94	2	no	—
382	C₂×C₈	—	94	2	no	—
383	C₂×C₈	—	94	2	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	8	1	no	—
392	C₄⋊C₄	—	8	2	no	—
393	C₄⋊C₄	—	47	2	no	—
394	C₄⋊C₄	—	94	1	no	—
395	C₄⋊C₄	—	94	2	no	—
396	C₄⋊C₄	—	94	2	no	—
397	C₄⋊C₄	—	376	1	no	—
398	C₄⋊C₄	—	188	4	no	—
399	C₄⋊C₄	—	188	2	no	—
400	C₄⋊C₄	#10625336	1	4	yes	direct product factor
401	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
402	C₂²⋊C₄	—	94	4	no	—
403	C₂²⋊C₄	—	188	4	no	—
404	C₄²	—	2	4	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	4	4	no	—
408	C₄²	C₂×C₄×D₄₇	1	2	yes	—
409	C₄²	#10625350	1	2	yes	—
410	C₂³	—	94	2	no	—
411	C₂³	—	94	2	no	—
412	C₂³	—	94	2	no	—
413	C₂³	—	188	1	no	—
414	C₂³	—	188	1	no	—
415	C₂³	—	188	1	no	—
416	C₂³	—	188	1	no	—
417	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	2	2	no	—
421	Q₈	C₄⋊C₄×D₄₇	1	4	yes	complemented
422	D₄	—	47	4	no	—
423	D₄	—	94	2	no	—
424	D₄	—	94	2	no	—
425	D₄	—	94	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	94	2	no	—
443	C₂×C₄	—	376	8	no	—
444	C₂×C₄	—	188	2	no	—
445	C₂×C₄	—	188	2	no	—
446	C₂×C₄	—	188	2	no	—
447	C₂×C₄	—	188	1	no	—
448	C₂×C₄	—	188	1	no	—
449	C₂×C₄	—	188	8	no	—
450	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
451	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
452	C₂×C₄	C₂×#10625336	1	4	yes	—
453	C₂×C₄	C₂×#10625336	1	2	yes	—
454	C₂×C₄	#13094044	1	2	yes	—
455	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
456	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
457	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
458	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
459	C₂×C₄	#13094069	1	1	yes	characteristic
460	C₂×C₄	#13094072	1	1	yes	characteristic
461	C₈	—	47	4	no	—
462	C₈	—	94	2	no	—
463	C₈	—	188	2	no	—
464	C₂²	—	94	4	no	—
465	C₂²	—	188	2	no	—
466	C₂²	—	188	2	no	—
467	C₂²	—	188	2	no	—
468	C₂²	—	188	2	no	—
469	C₂²	—	188	2	no	—
470	C₂²	—	188	2	no	—
471	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
472	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
473	C₂²	Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
474	C₂²	C₂²×#10625336	1	1	yes	characteristic
475	C₂²	C₂×#13094044	1	1	yes	characteristic
476	C₂²	#15689931	1	1	yes	characteristic
477	C₂²	#15689934	1	1	yes	characteristic
478	C₄	—	2	4	no	—
479	C₄	—	2	4	no	—
480	C₄	—	2	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	2	no	—
484	C₄	—	376	2	no	—
485	C₄	—	188	2	no	—
486	C₄	C₄×#10625336	1	4	yes	complemented
487	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
488	C₄	#15689604	1	1	yes	characteristic
489	C₄	#15689774	1	1	yes	characteristic
490	C₄	#15689828	1	1	yes	characteristic
491	C₂	—	188	4	no	—
492	C₂	C₄⋊C₄×C₂²⋊D₄₇	1	1	yes	characteristic
493	C₂	C₂×C₄×#10625336	1	1	yes	characteristic
494	C₂	#20252269	1	1	yes	characteristic
495	C₂	D₄×#10625336	1	1	yes	characteristic
496	C₂	#20255118	1	1	yes	characteristic
497	C₂	Q₈×#10625336	1	1	yes	characteristic
498	C₂	#20256259	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	Q₈×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	Q₈×C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₄⋊C₄×SD₁₆
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ Q₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #20244113	C₂	semidirect
5. #20243656	C₂	semidirect
7. #20243544	C₂	semidirect
8. #20243393	C₂	semidirect
10. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
11. Q₈×C₄⋊C₄×C₄₇	C₂	semidirect
17. C₄×#10625336	C₄	semidirect
66. #13093955	C₂×C₄	semidirect
69. #13093948	C₂×C₄	semidirect
73. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
79. C₄×Q₈×C₄₇	C₂×C₄	semidirect
133. C₄⋊C₄×C₄₇	SD₁₆	semidirect
141. #10625336	C₄⋊C₄	direct (N × H)
171. Q₈×C₄₇	C₂×C₄⋊C₄	semidirect
213. C₄₇⋊C₈	C₂×C₄⋊C₄	semidirect
235. C₄×C₄₇	C₄×SD₁₆	semidirect
244. Q₈×C₄⋊C₄	D₄₇	semidirect
292. C₄₇	C₄⋊C₄×SD₁₆	semidirect
306. C₄×Q₈	C₄×D₄₇	semidirect
400. C₄⋊C₄	#10625336	direct (N × H)
421. Q₈	C₄⋊C₄×D₄₇	semidirect
486. C₄	C₄×#10625336	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×#10625336	2
C₄⋊C₄×D₁₈₈	2
#20244113	2
#20243656	2
#20243648	2
#20243544	2
#20243393	2
#20243385	2
C₄⋊C₄×C₄₇⋊C₈	2
Q₈×C₄⋊C₄×C₄₇	2
C₄⋊C₄×SD₁₆	47

Subgroups — C4⋊C4×#10625336 #26234682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×#10625336 #26234682