Subgroups — C₄⋊C₄×#10621885 #25115026

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10621885	C₂	1	2	yes	maximal
2	C₂×C₄×#10621885	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
4	#19135325	C₂	1	2	yes	maximal
5	#19134849	C₂	1	2	yes	maximal
6	#19134848	C₂	1	2	yes	maximal
7	#19134754	C₂	1	1	yes	maximal, characteristic
8	#19134600	C₂	1	1	yes	maximal, characteristic
9	#19134597	C₂	1	1	yes	maximal, characteristic
10	C₄⋊C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
11	Q₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10621885	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
14	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
15	C₄×#10621885	—	2	8	no	—
16	C₄×#10621885	C₄	1	8	yes	complemented
17	C₂×#13063258	C₂²	1	2	yes	—
18	C₂×#13063258	C₂²	1	2	yes	—
19	C₂×#13063258	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#13063249	C₂²	1	2	yes	—
22	C₂×#13063249	C₂²	1	1	yes	characteristic
23	C₂×#13063248	C₂²	1	2	yes	—
24	C₂×#13063248	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
26	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
27	#14582797	C₂²	1	2	yes	—
28	#14582796	—	2	2	no	—
29	#14582769	C₂²	1	1	yes	characteristic
30	#14582768	—	2	1	no	—
31	C₄⋊C₄×Dic₄₃	—	2	1	no	—
32	#14582661	C₂²	1	2	yes	—
33	#14582661	C₂²	1	2	yes	—
34	#14582654	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#389	—	2	2	no	—
38	C₄₃×#389	C₂²	1	2	yes	—
39	C₄₃×#384	—	2	1	no	—
40	C₄₃×#384	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
42	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
44	C₂×#10621885	C₂×C₄	1	4	yes	—
45	C₂×#10621885	D₄	1	4	yes	—
46	C₂×#10621885	Q₈	1	4	yes	—
47	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
50	C₄×Dic₈₆	—	2	2	no	—
51	C₄×Dic₈₆	—	2	4	no	—
52	C₄×Dic₈₆	—	4	2	no	—
53	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊Dic₄₃	—	2	1	no	—
55	C₂×C₄⋊Dic₄₃	—	2	1	no	—
56	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
58	C₂×Dic₄₃⋊C₄	—	2	1	no	—
59	C₂×Dic₄₃⋊C₄	—	2	2	no	—
60	C₂×Dic₄₃⋊C₄	—	2	2	no	—
61	C₂×C₄×Dic₄₃	—	2	1	no	—
62	C₂×C₄×Dic₄₃	—	2	2	no	—
63	#13063258	—	2	4	no	—
64	#13063258	—	4	2	no	—
65	#13063258	C₂×C₄	1	4	yes	—
66	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
67	#13063249	—	2	4	no	—
68	#13063249	C₂×C₄	1	4	yes	—
69	#13063248	—	2	4	no	—
70	#13063248	C₂×C₄	1	4	yes	—
71	C₄×C₄₃⋊C₈	—	2	4	no	—
72	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
73	C₄₃⋊#95	—	2	2	no	—
74	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
75	C₄×Q₈×C₄₃	—	2	2	no	—
76	C₄×Q₈×C₄₃	—	2	4	no	—
77	C₄×Q₈×C₄₃	—	4	2	no	—
78	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	—	2	1	no	—
89	C₂×C₄²×C₄₃	—	2	2	no	—
90	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	#95×C₄₃	—	2	2	no	—
93	#95×C₄₃	D₄	1	2	yes	—
94	C₂×Q₈×C₄₃	—	2	1	no	—
95	C₂×Q₈×C₄₃	—	2	1	no	—
96	C₂×Q₈×C₄₃	—	2	1	no	—
97	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
99	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	C₂²×Dic₄₃	—	2	1	no	—
109	C₂²×Dic₄₃	—	2	1	no	—
110	C₂²×Dic₄₃	—	2	2	no	—
111	C₂×Dic₈₆	—	2	1	no	—
112	C₂×Dic₈₆	—	2	1	no	—
113	C₂×Dic₈₆	—	2	1	no	—
114	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
115	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
116	C₂×Dic₈₆	C₂×Q₈	1	2	yes	—
117	C₄⋊C₄×C₄₃	—	2	4	no	—
118	C₄⋊C₄×C₄₃	—	2	2	no	—
119	C₄⋊C₄×C₄₃	—	2	1	no	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	—	2	2	no	—
122	C₄⋊C₄×C₄₃	—	4	4	no	—
123	C₄⋊C₄×C₄₃	—	4	2	no	—
124	C₄⋊C₄×C₄₃	—	8	1	no	—
125	C₄⋊C₄×C₄₃	—	8	2	no	—
126	C₄⋊C₄×C₄₃	Q₁₆	1	4	yes	complemented
127	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₃	—	2	4	no	—
129	C₄²×C₄₃	—	2	2	no	—
130	C₄²×C₄₃	—	2	2	no	—
131	C₄²×C₄₃	—	4	4	no	—
132	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
133	C₄²×C₄₃	#41	1	2	yes	—
134	#10621885	C₄⋊C₄	1	16	yes	direct product factor
135	C₄⋊Dic₄₃	—	2	1	no	—
136	C₄⋊Dic₄₃	—	2	2	no	—
137	C₄⋊Dic₄₃	—	2	2	no	—
138	C₄⋊Dic₄₃	—	4	2	no	—
139	C₄⋊Dic₄₃	—	8	1	no	—
140	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
141	Dic₄₃⋊C₄	—	2	4	no	—
142	Dic₄₃⋊C₄	—	4	4	no	—
143	Dic₄₃⋊C₄	—	8	2	no	—
144	C₄×Dic₄₃	—	2	4	no	—
145	C₄×Dic₄₃	—	4	4	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	1	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
154	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
155	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₄₃	—	2	2	no	—
157	Q₈×C₄₃	—	2	2	no	—
158	Q₈×C₄₃	—	2	2	no	—
159	Q₈×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₂×Q₁₆	1	4	yes	—
179	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
180	C₂×C₄×C₄₃	#135	1	2	yes	—
181	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×Dic₄₃	—	2	2	no	—
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	2	no	—
190	C₂×Dic₄₃	—	2	2	no	—
191	C₂×Dic₄₃	—	4	1	no	—
192	C₂×Dic₄₃	—	4	1	no	—
193	C₂×Dic₄₃	—	4	2	no	—
194	C₂×Dic₄₃	—	4	2	no	—
195	C₂×Dic₄₃	—	4	2	no	—
196	Dic₈₆	—	2	2	no	—
197	Dic₈₆	—	2	2	no	—
198	Dic₈₆	—	2	2	no	—
199	Dic₈₆	C₂×C₄⋊C₄	1	4	yes	—
200	C₄₃⋊C₈	—	2	2	no	—
201	C₄₃⋊C₈	—	4	2	no	—
202	C₄₃⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
203	C₄⋊C₄×Q₁₆	—	43	1	no	maximal, Sylow
204	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₄₃	D₄²	1	1	yes	characteristic
206	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
207	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
208	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
209	C₂²×C₄₃	#576	1	1	yes	characteristic
210	C₂²×C₄₃	#578	1	1	yes	characteristic
211	C₄×C₄₃	—	2	4	no	—
212	C₄×C₄₃	—	2	2	no	—
213	C₄×C₄₃	—	2	4	no	—
214	C₄×C₄₃	—	4	2	no	—
215	C₄×C₄₃	—	4	2	no	—
216	C₄×C₄₃	—	8	2	no	—
217	C₄×C₄₃	C₄×Q₁₆	1	4	yes	complemented
218	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
219	C₄×C₄₃	#520	1	1	yes	characteristic
220	C₄×C₄₃	#547	1	1	yes	characteristic
221	C₄×C₄₃	#554	1	1	yes	characteristic
222	Dic₄₃	—	2	4	no	—
223	Dic₄₃	—	4	2	no	—
224	Dic₄₃	—	8	2	no	—
225	C₂×C₄×Q₁₆	—	43	1	no	—
226	C₂×C₄×Q₁₆	—	43	2	no	—
227	Q₈×C₄⋊C₄	—	43	1	no	—
228	Q₈×C₄⋊C₄	D₄₃	1	1	yes	characteristic
229	#1942	—	43	2	no	—
230	#1863	—	43	2	no	—
231	#1863	—	43	2	no	—
232	#1845	—	43	1	no	—
233	#1803	—	43	1	no	—
234	#1803	—	43	1	no	—
235	C₈×C₄⋊C₄	—	43	1	no	—
236	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
237	C₂×C₄₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
238	C₂×C₄₃	#2951	1	1	yes	characteristic
239	C₂×C₄₃	D₄×Q₁₆	1	1	yes	characteristic
240	C₂×C₄₃	#3287	1	1	yes	characteristic
241	C₂×C₄₃	Q₈×Q₁₆	1	1	yes	characteristic
242	C₂×C₄₃	#3383	1	1	yes	characteristic
243	C₂²×Q₁₆	—	43	1	no	—
244	C₂×C₄×Q₈	—	43	1	no	—
245	C₂×C₄×Q₈	—	43	2	no	—
246	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
247	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
248	C₄×Q₁₆	—	43	8	no	—
249	C₄×Q₁₆	—	86	8	no	—
250	C₂×#107	—	43	1	no	—
251	C₂×#107	—	43	2	no	—
252	C₂×#107	—	43	2	no	—
253	C₂×C₄⋊C₈	—	43	1	no	—
254	C₂×#103	—	43	1	no	—
255	C₂×#103	—	43	1	no	—
256	C₂×#103	—	43	2	no	—
257	C₂×#103	—	43	2	no	—
258	C₂×C₄×C₈	—	43	1	no	—
259	C₂×C₄×C₈	—	43	2	no	—
260	#389	—	2	2	no	—
261	#389	—	43	2	no	—
262	#389	—	86	2	no	—
263	#389	C₂×D₄₃	1	2	yes	—
264	#384	—	2	1	no	—
265	#384	—	43	1	no	—
266	#384	—	86	1	no	—
267	#384	C₂×D₄₃	1	1	yes	characteristic
268	C₄×C₄⋊C₄	—	2	1	no	—
269	C₄×C₄⋊C₄	—	86	1	no	—
270	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
271	#340	—	43	2	no	—
272	#340	—	43	2	no	—
273	#336	—	43	2	no	—
274	C₄₃	C₄⋊C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
275	C₂²×Q₈	—	43	1	no	—
276	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
277	C₂×Q₁₆	—	43	4	no	—
278	C₂×Q₁₆	—	43	4	no	—
279	C₂×Q₁₆	—	43	4	no	—
280	C₂²×C₈	—	43	1	no	—
281	C₂²×C₈	—	43	1	no	—
282	C₂²×C₈	—	43	2	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	—	4	2	no	—
286	C₄×Q₈	—	43	4	no	—
287	C₄×Q₈	—	86	4	no	—
288	C₄×Q₈	—	86	2	no	—
289	C₄×Q₈	—	172	2	no	—
290	C₄×Q₈	C₄×D₄₃	1	4	yes	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	43	1	no	—
297	C₂×C₄⋊C₄	—	43	2	no	—
298	C₂×C₄⋊C₄	—	86	1	no	—
299	C₂×C₄⋊C₄	—	86	2	no	—
300	C₂×C₄⋊C₄	—	86	1	no	—
301	C₂×C₄⋊C₄	—	86	2	no	—
302	C₂×C₄⋊C₄	—	86	1	no	—
303	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
306	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	—	86	1	no	—
310	C₂×C₄²	—	86	2	no	—
311	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
312	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
313	#107	—	43	4	no	—
314	#107	—	86	4	no	—
315	#107	—	172	2	no	—
316	C₄⋊C₈	—	86	2	no	—
317	#103	—	43	4	no	—
318	#103	—	43	4	no	—
319	#103	—	86	4	no	—
320	#103	—	86	4	no	—
321	C₄×C₈	—	43	4	no	—
322	C₄×C₈	—	86	4	no	—
323	#95	—	2	2	no	—
324	#95	—	86	2	no	—
325	#95	C₂²⋊D₄₃	1	2	yes	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	43	2	no	—
330	C₂×Q₈	—	43	2	no	—
331	C₂×Q₈	—	43	2	no	—
332	C₂×Q₈	—	86	1	no	—
333	C₂×Q₈	—	86	1	no	—
334	C₂×Q₈	—	86	1	no	—
335	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
336	C₂×Q₈	D₄×D₄₃	1	2	yes	—
337	C₂×Q₈	Q₈×D₄₃	1	2	yes	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	86	1	no	—
342	C₂²×C₄	—	86	1	no	—
343	C₂²×C₄	—	86	2	no	—
344	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
345	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
347	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
348	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
349	Q₁₆	—	43	16	no	—
350	C₂×C₈	—	43	2	no	—
351	C₂×C₈	—	43	2	no	—
352	C₂×C₈	—	43	2	no	—
353	C₂×C₈	—	43	2	no	—
354	C₂×C₈	—	86	1	no	—
355	C₂×C₈	—	86	1	no	—
356	C₂×C₈	—	86	2	no	—
357	C₂×C₈	—	86	2	no	—
358	C₂×C₈	—	86	2	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	8	1	no	—
367	C₄⋊C₄	—	8	2	no	—
368	C₄⋊C₄	—	43	2	no	—
369	C₄⋊C₄	—	86	4	no	—
370	C₄⋊C₄	—	86	1	no	—
371	C₄⋊C₄	—	86	2	no	—
372	C₄⋊C₄	—	86	2	no	—
373	C₄⋊C₄	—	344	2	no	—
374	C₄⋊C₄	—	344	1	no	—
375	C₄⋊C₄	—	172	4	no	—
376	C₄⋊C₄	—	172	2	no	—
377	C₄⋊C₄	#10621885	1	4	yes	direct product factor
378	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
379	C₄²	—	2	4	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	4	4	no	—
383	C₄²	—	86	4	no	—
384	C₄²	—	172	4	no	—
385	C₄²	C₂×C₄×D₄₃	1	2	yes	—
386	C₄²	#10621898	1	2	yes	—
387	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	43	4	no	—
392	Q₈	—	86	2	no	—
393	Q₈	—	86	2	no	—
394	Q₈	—	86	2	no	—
395	Q₈	C₄⋊C₄×D₄₃	1	4	yes	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	86	2	no	—
413	C₂×C₄	—	86	2	no	—
414	C₂×C₄	—	86	2	no	—
415	C₂×C₄	—	86	2	no	—
416	C₂×C₄	—	172	2	no	—
417	C₂×C₄	—	172	2	no	—
418	C₂×C₄	—	172	2	no	—
419	C₂×C₄	—	172	1	no	—
420	C₂×C₄	—	172	1	no	—
421	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
422	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
423	C₂×C₄	C₂×#10621885	1	4	yes	—
424	C₂×C₄	C₂×#10621885	1	2	yes	—
425	C₂×C₄	#13063345	1	2	yes	—
426	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
427	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
428	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
430	C₂×C₄	#13063370	1	1	yes	characteristic
431	C₂×C₄	#13063373	1	1	yes	characteristic
432	C₈	—	43	4	no	—
433	C₈	—	86	2	no	—
434	C₈	—	172	2	no	—
435	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
436	C₂²	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
437	C₂²	Q₈×C₂²⋊D₄₃	1	1	yes	characteristic
438	C₂²	C₂²×#10621885	1	1	yes	characteristic
439	C₂²	C₂×#13063345	1	1	yes	characteristic
440	C₂²	#14583702	1	1	yes	characteristic
441	C₂²	#14583714	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	4	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	8	2	no	—
448	C₄	—	86	4	no	—
449	C₄	—	344	2	no	—
450	C₄	—	172	2	no	—
451	C₄	C₄×#10621885	1	4	yes	complemented
452	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
453	C₄	#14583380	1	1	yes	characteristic
454	C₄	#14583550	1	1	yes	characteristic
455	C₄	#14583604	1	1	yes	characteristic
456	C₂	C₄⋊C₄×C₂²⋊D₄₃	1	1	yes	characteristic
457	C₂	C₂×C₄×#10621885	1	1	yes	characteristic
458	C₂	#19143468	1	1	yes	characteristic
459	C₂	D₄×#10621885	1	1	yes	characteristic
460	C₂	#19146351	1	1	yes	characteristic
461	C₂	Q₈×#10621885	1	1	yes	characteristic
462	C₂	#19147482	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	Q₈×C₄⋊C₄×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	Q₈×C₄⋊C₄	D₄₃
hypocenter	C₄₃	C₄⋊C₄×Q₁₆
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
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
16. C₄×#10621885	C₄	semidirect
126. C₄⋊C₄×C₄₃	Q₁₆	semidirect
134. #10621885	C₄⋊C₄	direct (N × H)
217. C₄×C₄₃	C₄×Q₁₆	semidirect
274. C₄₃	C₄⋊C₄×Q₁₆	semidirect
377. C₄⋊C₄	#10621885	direct (N × H)
451. C₄	C₄×#10621885	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10621885	2
C₄⋊C₄×Dic₈₆	2
#19135325	2
#19134849	2
#19134848	2
#19134754	2
#19134600	2
#19134597	2
C₄⋊C₄×C₄₃⋊C₈	2
Q₈×C₄⋊C₄×C₄₃	2
C₄⋊C₄×Q₁₆	43

Subgroups — C4⋊C4×#10621885 #25115026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×#10621885 #25115026