Subgroups — #25118864

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583106	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10621885	C₂	1	2	yes	maximal
3	C₄⋊C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
4	#19135398	C₂	1	1	yes	maximal, characteristic
5	#19135353	C₂	1	1	yes	maximal, characteristic
6	#19135274	C₂	1	2	yes	maximal
7	#19134939	C₂	1	2	yes	maximal
8	#19134849	C₂	1	2	yes	maximal
9	C₄⋊C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
10	C₄×#13063248	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#2365	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10621885	C₂²	1	2	yes	—
13	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
14	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
15	#14583106	C₄	1	8	yes	complemented
16	C₄×#10621885	—	2	8	no	—
17	C₂×#13063258	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#13063249	C₂²	1	2	yes	—
20	C₂×#13063249	C₂²	1	2	yes	—
21	C₂×#13063249	C₂²	1	2	yes	—
22	C₂×#13063248	C₂²	1	1	yes	characteristic
23	C₂×#13063248	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
25	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
26	#14582797	C₂²	1	2	yes	—
27	#14582796	—	2	2	no	—
28	#14582769	C₂²	1	1	yes	characteristic
29	#14582768	—	2	1	no	—
30	C₄⋊C₄×Dic₄₃	—	2	1	no	—
31	#14582661	C₂²	1	1	yes	characteristic
32	#14582661	C₂²	1	2	yes	—
33	#14582661	C₂²	1	1	yes	characteristic
34	#14582654	C₂²	1	2	yes	—
35	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
37	C₄₃×#391	C₂²	1	2	yes	—
38	C₄₃×#389	—	2	1	no	—
39	C₄₃×#387	—	2	2	no	—
40	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
44	C₂×#10621885	—	2	4	no	—
45	C₂×#10621885	—	2	4	no	—
46	C₂×#10621885	C₂×C₄	1	8	yes	—
47	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
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	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
65	#13063249	—	2	4	no	—
66	#13063249	—	4	2	no	—
67	#13063249	C₂×C₄	1	8	yes	—
68	#13063248	—	2	2	no	—
69	#13063248	D₄	1	4	yes	—
70	C₄×C₄₃⋊C₈	—	2	2	no	—
71	C₄×C₄₃⋊C₈	—	2	4	no	—
72	C₄₃⋊#95	—	2	2	no	—
73	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
74	C₄⋊Q₈×C₄₃	—	2	2	no	—
75	C₄⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
76	C₄×Q₈×C₄₃	—	2	4	no	—
77	C₄×Q₈×C₄₃	—	4	2	no	—
78	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₃	—	2	2	no	—
86	C₂×C₄²×C₄₃	—	2	1	no	—
87	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
88	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
89	#95×C₄₃	—	2	2	no	—
90	#95×C₄₃	—	2	1	no	—
91	#95×C₄₃	—	2	2	no	—
92	#95×C₄₃	D₄	1	2	yes	—
93	C₂×Q₈×C₄₃	—	2	2	no	—
94	C₂×Q₈×C₄₃	—	2	2	no	—
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
107	C₂²×Dic₄₃	—	2	1	no	—
108	C₂²×Dic₄₃	—	2	1	no	—
109	C₂²×Dic₄₃	—	2	2	no	—
110	C₂×Dic₈₆	—	2	1	no	—
111	C₂×Dic₈₆	—	2	1	no	—
112	C₂×Dic₈₆	—	2	1	no	—
113	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
114	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
115	C₂×Dic₈₆	#41	1	2	yes	—
116	C₄⋊C₄×C₄₃	—	2	4	no	—
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	1	no	—
121	C₄⋊C₄×C₄₃	—	2	1	no	—
122	C₄⋊C₄×C₄₃	—	4	4	no	—
123	C₄⋊C₄×C₄₃	Q₁₆	1	4	yes	complemented
124	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
125	C₄²×C₄₃	—	2	2	no	—
126	C₄²×C₄₃	—	2	2	no	—
127	C₄²×C₄₃	—	4	4	no	—
128	C₄²×C₄₃	—	4	2	no	—
129	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
130	C₄²×C₄₃	#41	1	2	yes	—
131	#10621885	—	2	16	no	—
132	C₄⋊Dic₄₃	—	2	1	no	—
133	C₄⋊Dic₄₃	—	2	2	no	—
134	C₄⋊Dic₄₃	—	2	2	no	—
135	C₄⋊Dic₄₃	—	4	2	no	—
136	C₄⋊Dic₄₃	—	8	1	no	—
137	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
138	Dic₄₃⋊C₄	—	2	4	no	—
139	Dic₄₃⋊C₄	—	4	4	no	—
140	Dic₄₃⋊C₄	—	8	2	no	—
141	C₄×Dic₄₃	—	2	4	no	—
142	C₄×Dic₄₃	—	4	4	no	—
143	C₂×C₄₃⋊C₈	—	2	2	no	—
144	C₂×C₄₃⋊C₈	—	2	1	no	—
145	C₂×C₄₃⋊C₈	—	2	2	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	1	no	—
148	C₂×C₄₃⋊C₈	—	2	1	no	—
149	C₂×C₄₃⋊C₈	—	2	1	no	—
150	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
151	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
152	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₄₃	—	2	4	no	—
154	Q₈×C₄₃	—	2	4	no	—
155	Q₈×C₄₃	—	4	2	no	—
156	Q₈×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₄₃	C₂×Q₁₆	1	4	yes	—
176	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
177	C₂×C₄×C₄₃	#135	1	2	yes	—
178	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂×Dic₄₃	—	2	2	no	—
185	C₂×Dic₄₃	—	2	2	no	—
186	C₂×Dic₄₃	—	2	2	no	—
187	C₂×Dic₄₃	—	2	2	no	—
188	C₂×Dic₄₃	—	4	1	no	—
189	C₂×Dic₄₃	—	4	1	no	—
190	C₂×Dic₄₃	—	4	2	no	—
191	C₂×Dic₄₃	—	4	2	no	—
192	C₂×Dic₄₃	—	4	2	no	—
193	Dic₈₆	—	2	2	no	—
194	Dic₈₆	—	2	2	no	—
195	Dic₈₆	—	2	2	no	—
196	Dic₈₆	C₄×D₄	1	4	yes	—
197	C₄₃⋊C₈	—	2	4	no	—
198	C₄₃⋊C₈	—	2	2	no	—
199	C₄₃⋊C₈	—	4	1	no	—
200	#22998	—	43	1	no	maximal, Sylow
201	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂²×C₄₃	D₄²	1	1	yes	characteristic
203	C₂²×C₄₃	#548	1	1	yes	characteristic
204	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
205	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
206	C₂²×C₄₃	#577	1	1	yes	characteristic
207	C₂²×C₄₃	#578	1	1	yes	characteristic
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	2	4	no	—
210	C₄×C₄₃	—	4	4	no	—
211	C₄×C₄₃	—	4	2	no	—
212	C₄×C₄₃	—	4	2	no	—
213	C₄×C₄₃	—	8	1	no	—
214	C₄×C₄₃	C₄×Q₁₆	1	4	yes	complemented
215	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₄₃	#520	1	1	yes	characteristic
217	C₄×C₄₃	#547	1	1	yes	characteristic
218	C₄×C₄₃	#553	1	1	yes	characteristic
219	Dic₄₃	—	2	4	no	—
220	Dic₄₃	—	4	2	no	—
221	Dic₄₃	—	8	2	no	—
222	C₂×#462	—	43	1	no	—
223	C₂×C₄×Q₁₆	—	43	2	no	—
224	#2365	D₄₃	1	1	yes	characteristic
225	Q₈×C₄⋊C₄	—	43	1	no	—
226	#1956	—	43	1	no	—
227	#1947	—	43	1	no	—
228	#1933	—	43	2	no	—
229	#1878	—	43	2	no	—
230	#1863	—	43	2	no	—
231	C₈×C₄⋊C₄	—	43	1	no	—
232	C₄×#103	—	43	1	no	—
233	C₂×C₄₃	#2361	1	1	yes	characteristic
234	C₂×C₄₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
235	C₂×C₄₃	#2947	1	1	yes	characteristic
236	C₂×C₄₃	#3284	1	1	yes	characteristic
237	C₂×C₄₃	D₄×Q₁₆	1	1	yes	characteristic
238	C₂×C₄₃	#3363	1	1	yes	characteristic
239	C₂×C₄₃	#3364	1	1	yes	characteristic
240	C₂²×Q₁₆	—	43	2	no	—
241	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
242	C₂×C₄×Q₈	—	43	1	no	—
243	C₂×C₄×Q₈	—	43	2	no	—
244	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
245	#462	—	43	8	no	—
246	C₄×Q₁₆	—	86	8	no	—
247	C₂×#107	—	43	2	no	—
248	C₂×C₄⋊C₈	—	43	1	no	—
249	C₂×#103	—	43	2	no	—
250	C₂×#103	—	43	1	no	—
251	C₂×#103	—	43	2	no	—
252	C₂×#103	—	43	1	no	—
253	C₂×#103	—	43	2	no	—
254	C₂×C₄×C₈	—	43	2	no	—
255	C₂×C₄×C₈	—	43	1	no	—
256	#391	C₂×D₄₃	1	2	yes	—
257	#389	—	2	1	no	—
258	#389	—	43	2	no	—
259	#389	—	86	2	no	—
260	#387	—	2	2	no	—
261	#384	—	43	1	no	—
262	#384	—	86	1	no	—
263	C₄×C₄⋊C₄	—	2	1	no	—
264	C₄×C₄⋊C₄	—	86	1	no	—
265	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
266	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
267	#340	—	43	1	no	—
268	#340	—	43	2	no	—
269	#340	—	43	1	no	—
270	#336	—	43	2	no	—
271	C₄₃	#22998	1	1	yes	characteristic, complemented, Sylow
272	C₂²×Q₈	—	43	1	no	—
273	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
274	C₂×Q₁₆	—	43	8	no	—
275	C₂×Q₁₆	—	86	4	no	—
276	C₂×Q₁₆	—	86	4	no	—
277	C₂²×C₈	—	43	2	no	—
278	C₂²×C₈	—	43	1	no	—
279	C₂²×C₈	—	43	1	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	C₄×D₄₃	1	4	yes	—
282	C₄×Q₈	—	2	4	no	—
283	C₄×Q₈	—	4	2	no	—
284	C₄×Q₈	—	43	4	no	—
285	C₄×Q₈	—	86	4	no	—
286	C₄×Q₈	—	86	2	no	—
287	C₄×Q₈	—	172	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	43	1	no	—
292	C₂×C₄⋊C₄	—	43	2	no	—
293	C₂×C₄⋊C₄	—	86	1	no	—
294	C₂×C₄⋊C₄	—	86	2	no	—
295	C₂×C₄⋊C₄	—	86	1	no	—
296	C₂×C₄⋊C₄	—	86	2	no	—
297	C₂×C₄⋊C₄	—	86	1	no	—
298	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	86	1	no	—
305	C₂×C₄²	—	86	2	no	—
306	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
307	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
308	#107	—	86	4	no	—
309	C₄⋊C₈	—	43	4	no	—
310	#103	—	43	8	no	—
311	#103	—	43	4	no	—
312	#103	—	86	2	no	—
313	#103	—	86	4	no	—
314	#103	—	172	2	no	—
315	C₄×C₈	—	86	4	no	—
316	C₄×C₈	—	86	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	2	no	—
320	#95	—	86	2	no	—
321	#95	C₂²⋊D₄₃	1	2	yes	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	43	2	no	—
328	C₂×Q₈	—	43	2	no	—
329	C₂×Q₈	—	43	2	no	—
330	C₂×Q₈	—	86	1	no	—
331	C₂×Q₈	—	86	1	no	—
332	C₂×Q₈	—	86	1	no	—
333	C₂×Q₈	C₂×C₄×D₄₃	1	4	yes	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	86	1	no	—
338	C₂²×C₄	—	86	1	no	—
339	C₂²×C₄	—	86	2	no	—
340	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
341	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
343	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
345	Q₁₆	—	86	16	no	—
346	C₂×C₈	—	43	4	no	—
347	C₂×C₈	—	43	2	no	—
348	C₂×C₈	—	86	2	no	—
349	C₂×C₈	—	86	2	no	—
350	C₂×C₈	—	86	1	no	—
351	C₂×C₈	—	86	1	no	—
352	C₂×C₈	—	86	1	no	—
353	C₂×C₈	—	86	1	no	—
354	C₂×C₈	—	86	1	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	—	43	2	no	—
363	C₄⋊C₄	—	86	4	no	—
364	C₄⋊C₄	—	86	1	no	—
365	C₄⋊C₄	—	86	2	no	—
366	C₄⋊C₄	—	86	2	no	—
367	C₄⋊C₄	—	344	2	no	—
368	C₄⋊C₄	—	344	1	no	—
369	C₄⋊C₄	—	172	4	no	—
370	C₄⋊C₄	—	172	2	no	—
371	C₄⋊C₄	#10621885	1	4	yes	complemented
372	C₄⋊C₄	D₄×D₄₃	1	2	yes	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	4	4	no	—
376	C₄²	—	4	2	no	—
377	C₄²	—	86	4	no	—
378	C₄²	—	172	4	no	—
379	C₄²	C₂×C₄×D₄₃	1	2	yes	—
380	C₄²	#10621898	1	2	yes	—
381	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
382	Q₈	—	2	4	no	—
383	Q₈	—	2	4	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	43	4	no	—
387	Q₈	—	86	2	no	—
388	Q₈	—	86	2	no	—
389	Q₈	—	86	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	86	2	no	—
407	C₂×C₄	—	86	2	no	—
408	C₂×C₄	—	86	2	no	—
409	C₂×C₄	—	86	2	no	—
410	C₂×C₄	—	172	2	no	—
411	C₂×C₄	—	172	2	no	—
412	C₂×C₄	—	172	2	no	—
413	C₂×C₄	—	172	1	no	—
414	C₂×C₄	—	172	1	no	—
415	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
416	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
417	C₂×C₄	C₂×#10621885	1	4	yes	—
418	C₂×C₄	C₂×#10621885	1	2	yes	—
419	C₂×C₄	#13063345	1	2	yes	—
420	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
421	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
422	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
423	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
424	C₂×C₄	#13063370	1	1	yes	characteristic
425	C₂×C₄	#13063372	1	1	yes	characteristic
426	C₈	—	86	2	no	—
427	C₈	—	86	4	no	—
428	C₈	—	172	1	no	—
429	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
430	C₂²	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
431	C₂²	#14583556	1	1	yes	characteristic
432	C₂²	C₂²×#10621885	1	1	yes	characteristic
433	C₂²	C₂×#13063345	1	1	yes	characteristic
434	C₂²	#14583707	1	1	yes	characteristic
435	C₂²	#14583714	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	4	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	86	4	no	—
443	C₄	—	344	2	no	—
444	C₄	—	172	2	no	—
445	C₄	C₄×#10621885	1	4	yes	complemented
446	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
447	C₄	#14583378	1	1	yes	characteristic
448	C₄	#14583554	1	1	yes	characteristic
449	C₄	#14583599	1	1	yes	characteristic
450	C₂	#19137607	1	1	yes	characteristic
451	C₂	C₂×C₄×#10621885	1	1	yes	characteristic
452	C₂	#19143438	1	1	yes	characteristic
453	C₂	#19146321	1	1	yes	characteristic
454	C₂	D₄×#10621885	1	1	yes	characteristic
455	C₂	#19147269	1	1	yes	characteristic
456	C₂	#19147276	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2365	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2365	D₄₃
hypocenter	C₄₃	#22998
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2365

Complements

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

N	H ≅ G/N	type
15. #14583106	C₄	semidirect
123. C₄⋊C₄×C₄₃	Q₁₆	semidirect
214. C₄×C₄₃	C₄×Q₁₆	semidirect
271. C₄₃	#22998	semidirect
371. C₄⋊C₄	#10621885	semidirect
445. 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×#14583106	2
C₂×C₄×#10621885	2
C₄⋊C₄×Dic₈₆	2
#19135398	2
#19135353	2
#19135274	2
#19134939	2
#19134849	2
C₄⋊C₄×C₄₃⋊C₈	2
C₄×#13063248	2
C₄₃×#2365	2
#22998	43