Subgroups — #25138188

Order 11008.

914 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583109	C₂	1	2	yes	maximal
2	C₂×#14583109	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#10621885	C₂	1	1	yes	maximal, characteristic
4	#19139583	C₂	1	1	yes	maximal, characteristic
5	#19135987	C₂	1	2	yes	maximal
6	#19135841	C₂	1	2	yes	maximal
7	#19135396	C₂	1	1	yes	maximal, characteristic
8	#19135314	C₂	1	1	yes	maximal, characteristic
9	#19134936	C₂	1	2	yes	maximal
10	#19134597	C₂	1	1	yes	maximal, characteristic
11	Q₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10621885	C₂²	1	2	yes	—
13	C₂²×#10621885	C₂²	1	1	yes	characteristic
14	C₂×#13063325	C₂²	1	1	yes	characteristic
15	C₂×#13063325	C₂²	1	2	yes	—
16	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
17	#14583109	—	2	8	no	—
18	#14583109	—	2	4	no	—
19	C₄×#10621885	—	2	4	no	—
20	C₂×#13063258	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
23	C₂×#13063249	C₂²	1	1	yes	characteristic
24	C₂×#13063248	C₂²	1	2	yes	—
25	C₂×#13063248	C₂²	1	2	yes	—
26	C₂×#13063248	C₂²	1	2	yes	—
27	C₂×#13063248	C₂²	1	1	yes	characteristic
28	C₂×#13063248	C₂²	1	2	yes	—
29	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
30	#14582831	—	2	2	no	—
31	#14582805	C₂²	1	2	yes	—
32	#14582798	—	2	1	no	—
33	#14582798	—	2	1	no	—
34	#14582661	C₂²	1	2	yes	—
35	#14582654	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₄₃×#389	—	2	2	no	—
39	C₄₃×#389	C₂²	1	2	yes	—
40	C₄₃×#384	—	2	1	no	—
41	C₄₃×#384	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
43	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
44	C₂²×Dic₈₆	C₂³	1	2	yes	—
45	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
46	C₂×#10621885	—	2	2	no	—
47	C₂×#10621885	—	2	2	no	—
48	C₂×#10621885	—	2	4	no	—
49	C₂×#10621885	—	2	4	no	—
50	C₂×#10621885	—	2	4	no	—
51	C₂×#10621885	D₄	1	4	yes	—
52	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
54	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
55	#13063325	—	2	4	no	—
56	#13063325	—	2	2	no	—
57	#13063325	—	2	2	no	—
58	#13063325	—	4	2	no	—
59	C₄×Dic₈₆	—	2	2	no	—
60	C₄×Dic₈₆	—	2	2	no	—
61	C₂×C₄⋊Dic₄₃	—	2	1	no	—
62	C₂×C₄⋊Dic₄₃	—	2	2	no	—
63	C₂×C₄⋊Dic₄₃	—	2	2	no	—
64	C₂×C₄⋊Dic₄₃	—	2	1	no	—
65	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
66	C₂×Dic₄₃⋊C₄	—	2	1	no	—
67	C₂×C₄×Dic₄₃	—	2	1	no	—
68	#13063258	—	2	2	no	—
69	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
70	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
71	#13063249	—	2	2	no	—
72	#13063248	—	2	4	no	—
73	#13063248	—	2	4	no	—
74	#13063248	—	2	2	no	—
75	#13063248	—	2	4	no	—
76	#13063248	—	4	2	no	—
77	C₄×C₄₃⋊C₈	—	2	2	no	—
78	C₄₃⋊#95	—	2	2	no	—
79	C₄₃⋊#95	—	2	2	no	—
80	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₄×Q₈×C₄₃	—	2	2	no	—
82	C₄×Q₈×C₄₃	—	2	4	no	—
83	C₄×Q₈×C₄₃	—	4	2	no	—
84	C₄×Q₈×C₄₃	D₄	1	4	yes	—
85	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	—	2	1	no	—
95	C₂×C₄²×C₄₃	—	2	2	no	—
96	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	#95×C₄₃	—	2	2	no	—
99	#95×C₄₃	D₄	1	2	yes	—
100	C₂×Q₈×C₄₃	—	2	1	no	—
101	C₂×Q₈×C₄₃	—	2	1	no	—
102	C₂×Q₈×C₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
105	C₂×Q₈×C₄₃	#41	1	2	yes	—
106	C₂²×C₄×C₄₃	—	2	1	no	—
107	C₂²×C₄×C₄₃	—	2	1	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₄₃	—	2	1	no	—
115	C₂²×Dic₄₃	—	2	1	no	—
116	C₂²×Dic₄₃	—	2	2	no	—
117	C₂×Dic₈₆	—	2	1	no	—
118	C₂×Dic₈₆	—	2	1	no	—
119	C₂×Dic₈₆	—	2	1	no	—
120	C₂×Dic₈₆	—	2	1	no	—
121	C₂×Dic₈₆	—	2	1	no	—
122	C₂×Dic₈₆	—	2	2	no	—
123	C₂×Dic₈₆	—	2	2	no	—
124	C₂×Dic₈₆	—	2	2	no	—
125	C₂×Dic₈₆	—	2	2	no	—
126	C₂×Dic₈₆	—	2	2	no	—
127	C₂×Dic₈₆	—	2	2	no	—
128	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₄₃	—	2	4	no	—
130	C₄⋊C₄×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	4	4	no	—
135	C₄⋊C₄×C₄₃	—	4	2	no	—
136	C₄⋊C₄×C₄₃	—	8	1	no	—
137	C₄⋊C₄×C₄₃	—	8	2	no	—
138	C₄⋊C₄×C₄₃	Q₁₆	1	4	yes	complemented
139	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
140	C₄²×C₄₃	—	2	4	no	—
141	C₄²×C₄₃	—	2	2	no	—
142	C₄²×C₄₃	—	2	2	no	—
143	C₄²×C₄₃	—	4	4	no	—
144	C₄²×C₄₃	C₂×D₄	1	2	yes	—
145	C₄²×C₄₃	#41	1	2	yes	—
146	#10621885	—	2	8	no	—
147	#10621885	—	4	8	no	—
148	C₄⋊Dic₄₃	—	2	1	no	—
149	C₄⋊Dic₄₃	—	2	1	no	—
150	C₄⋊Dic₄₃	—	4	4	no	—
151	C₄⋊Dic₄₃	—	4	4	no	—
152	C₄⋊Dic₄₃	—	4	2	no	—
153	C₄⋊Dic₄₃	—	4	2	no	—
154	Dic₄₃⋊C₄	—	4	2	no	—
155	C₄×Dic₄₃	—	4	2	no	—
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	1	no	—
158	C₂×C₄₃⋊C₈	—	2	1	no	—
159	C₂×C₄₃⋊C₈	—	2	2	no	—
160	C₂×C₄₃⋊C₈	—	2	2	no	—
161	C₂×C₄₃⋊C₈	—	2	2	no	—
162	C₂×C₄₃⋊C₈	—	2	1	no	—
163	C₂×C₄₃⋊C₈	—	2	1	no	—
164	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
165	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₄₃	—	2	2	no	—
167	Q₈×C₄₃	—	2	2	no	—
168	Q₈×C₄₃	—	2	2	no	—
169	Q₈×C₄₃	#121	1	4	yes	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	4	1	no	—
182	C₂×C₄×C₄₃	—	4	1	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	#121	1	2	yes	—
187	C₂×C₄×C₄₃	#121	1	2	yes	—
188	C₂×C₄×C₄₃	C₂×Q₁₆	1	4	yes	—
189	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
190	C₂×C₄×C₄₃	#137	1	2	yes	—
191	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
197	C₂×Dic₄₃	—	2	2	no	—
198	C₂×Dic₄₃	—	4	1	no	—
199	C₂×Dic₄₃	—	4	1	no	—
200	C₂×Dic₄₃	—	4	1	no	—
201	C₂×Dic₄₃	—	4	2	no	—
202	C₂×Dic₄₃	—	4	2	no	—
203	C₂×Dic₄₃	—	4	2	no	—
204	C₂×Dic₄₃	—	4	1	no	—
205	C₂×Dic₄₃	—	4	1	no	—
206	Dic₈₆	—	2	2	no	—
207	Dic₈₆	—	2	2	no	—
208	Dic₈₆	—	4	1	no	—
209	Dic₈₆	—	4	1	no	—
210	Dic₈₆	—	4	2	no	—
211	Dic₈₆	—	4	2	no	—
212	Dic₈₆	—	4	2	no	—
213	Dic₈₆	—	4	2	no	—
214	C₄₃⋊C₈	—	2	2	no	—
215	C₄₃⋊C₈	—	4	2	no	—
216	C₄₃⋊C₈	—	4	1	no	—
217	#24732	—	43	1	no	maximal, Sylow
218	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
219	C₂²×C₄₃	D₄²	1	1	yes	characteristic
220	C₂²×C₄₃	#548	1	1	yes	characteristic
221	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
222	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
223	C₂²×C₄₃	#577	1	1	yes	characteristic
224	C₂²×C₄₃	#578	1	1	yes	characteristic
225	C₄×C₄₃	—	2	4	no	—
226	C₄×C₄₃	—	2	4	no	—
227	C₄×C₄₃	—	2	2	no	—
228	C₄×C₄₃	—	4	2	no	—
229	C₄×C₄₃	—	4	2	no	—
230	C₄×C₄₃	—	8	2	no	—
231	C₄×C₄₃	#462	1	4	yes	complemented
232	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
233	C₄×C₄₃	#537	1	1	yes	characteristic
234	C₄×C₄₃	#547	1	1	yes	characteristic
235	C₄×C₄₃	#553	1	1	yes	characteristic
236	Dic₄₃	—	4	2	no	—
237	Dic₄₃	—	8	2	no	—
238	Dic₄₃	—	8	1	no	—
239	C₂×#462	—	43	2	no	—
240	C₂×#462	—	43	1	no	—
241	C₂×C₄×Q₁₆	—	43	1	no	—
242	#2546	—	43	1	no	—
243	Q₈×C₄⋊C₄	D₄₃	1	1	yes	characteristic
244	#2068	—	43	2	no	—
245	#2043	—	43	2	no	—
246	#1956	—	43	1	no	—
247	#1939	—	43	1	no	—
248	#1878	—	43	2	no	—
249	#1803	—	43	1	no	—
250	C₂×C₄₃	#2416	1	1	yes	characteristic
251	C₂×C₄₃	C₂×#462	1	1	yes	characteristic
252	C₂×C₄₃	#3046	1	1	yes	characteristic
253	C₂×C₄₃	#3278	1	1	yes	characteristic
254	C₂×C₄₃	D₄×Q₁₆	1	1	yes	characteristic
255	C₂×C₄₃	#3363	1	1	yes	characteristic
256	C₂×C₄₃	#3374	1	1	yes	characteristic
257	C₂²×Q₁₆	—	43	1	no	—
258	C₂²×Q₁₆	—	43	2	no	—
259	C₂×C₄⋊Q₈	—	43	1	no	—
260	C₂×C₄⋊Q₈	—	43	2	no	—
261	C₂×C₄×Q₈	—	43	1	no	—
262	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
263	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
264	#462	—	86	8	no	—
265	#462	—	86	4	no	—
266	C₄×Q₁₆	—	86	4	no	—
267	C₂×#107	—	43	1	no	—
268	C₂×C₄⋊C₈	—	43	1	no	—
269	C₂×C₄⋊C₈	—	43	2	no	—
270	C₂×#103	—	43	1	no	—
271	C₂×#103	—	43	2	no	—
272	C₂×#103	—	43	2	no	—
273	C₂×#103	—	43	2	no	—
274	C₂×#103	—	43	1	no	—
275	C₂×#103	—	43	2	no	—
276	C₂×C₄×C₈	—	43	1	no	—
277	#398	—	86	2	no	—
278	#391	—	43	2	no	—
279	#389	—	2	2	no	—
280	#389	—	86	1	no	—
281	#389	—	86	1	no	—
282	#389	C₂×D₄₃	1	2	yes	—
283	#384	—	2	1	no	—
284	#384	C₂×D₄₃	1	1	yes	characteristic
285	C₄×C₄⋊C₄	—	2	1	no	—
286	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
287	#340	—	43	2	no	—
288	#336	—	43	2	no	—
289	C₄₃	#24732	1	1	yes	characteristic, complemented, Sylow
290	C₂²×Q₈	—	43	1	no	—
291	C₂²×Q₈	—	43	2	no	—
292	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
293	C₂×Q₁₆	—	43	4	no	—
294	C₂×Q₁₆	—	86	2	no	—
295	C₂×Q₁₆	—	86	2	no	—
296	C₂×Q₁₆	—	86	4	no	—
297	C₂×Q₁₆	—	86	4	no	—
298	C₂×Q₁₆	—	86	4	no	—
299	C₂²×C₈	—	43	1	no	—
300	C₂²×C₈	—	43	2	no	—
301	C₂²×C₈	—	43	1	no	—
302	C₄⋊Q₈	—	86	4	no	—
303	C₄⋊Q₈	—	86	2	no	—
304	C₄⋊Q₈	—	86	2	no	—
305	C₄⋊Q₈	—	172	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	4	no	—
308	C₄×Q₈	—	4	2	no	—
309	C₄×Q₈	—	86	2	no	—
310	C₄×Q₈	—	86	2	no	—
311	C₄×Q₈	D₁₇₂	1	4	yes	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	43	1	no	—
318	C₂×C₄⋊C₄	—	86	1	no	—
319	C₂×C₄⋊C₄	—	86	1	no	—
320	C₂×C₄⋊C₄	—	86	2	no	—
321	C₂×C₄⋊C₄	—	86	2	no	—
322	C₂×C₄⋊C₄	—	86	1	no	—
323	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
326	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	2	no	—
329	C₂×C₄²	—	86	1	no	—
330	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
331	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
332	#107	—	86	2	no	—
333	C₄⋊C₈	—	86	4	no	—
334	C₄⋊C₈	—	86	2	no	—
335	#103	—	86	4	no	—
336	#103	—	86	4	no	—
337	#103	—	86	2	no	—
338	#103	—	86	2	no	—
339	#103	—	86	4	no	—
340	#103	—	172	2	no	—
341	C₄×C₈	—	86	2	no	—
342	#95	—	2	2	no	—
343	#95	—	86	2	no	—
344	#95	—	86	2	no	—
345	#95	C₂²⋊D₄₃	1	2	yes	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	43	2	no	—
350	C₂×Q₈	—	86	1	no	—
351	C₂×Q₈	—	86	2	no	—
352	C₂×Q₈	—	86	1	no	—
353	C₂×Q₈	—	86	2	no	—
354	C₂×Q₈	—	86	1	no	—
355	C₂×Q₈	—	86	2	no	—
356	C₂×Q₈	—	86	1	no	—
357	C₂×Q₈	—	86	2	no	—
358	C₂×Q₈	—	86	2	no	—
359	C₂×Q₈	—	86	1	no	—
360	C₂×Q₈	—	86	2	no	—
361	C₂×Q₈	C₂×D₁₇₂	1	2	yes	—
362	C₂×Q₈	D₄×D₄₃	1	2	yes	—
363	C₂×Q₈	#10621902	1	2	yes	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	86	1	no	—
368	C₂²×C₄	—	86	1	no	—
369	C₂²×C₄	—	86	2	no	—
370	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
371	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
373	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
374	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
375	Q₁₆	—	86	8	no	—
376	Q₁₆	—	172	8	no	—
377	C₂×C₈	—	43	2	no	—
378	C₂×C₈	—	86	1	no	—
379	C₂×C₈	—	86	1	no	—
380	C₂×C₈	—	86	2	no	—
381	C₂×C₈	—	86	1	no	—
382	C₂×C₈	—	86	2	no	—
383	C₂×C₈	—	86	2	no	—
384	C₂×C₈	—	86	1	no	—
385	C₂×C₈	—	86	1	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	4	4	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	8	1	no	—
394	C₄⋊C₄	—	8	2	no	—
395	C₄⋊C₄	—	86	1	no	—
396	C₄⋊C₄	—	86	1	no	—
397	C₄⋊C₄	—	172	4	no	—
398	C₄⋊C₄	—	172	4	no	—
399	C₄⋊C₄	—	172	2	no	—
400	C₄⋊C₄	—	172	2	no	—
401	C₄⋊C₄	—	172	2	no	—
402	C₄⋊C₄	#10621885	1	4	yes	complemented
403	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
404	C₄²	—	2	4	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	4	4	no	—
408	C₄²	—	172	2	no	—
409	C₄²	C₂×D₁₇₂	1	2	yes	—
410	C₄²	#10621898	1	2	yes	—
411	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	2	2	no	—
415	Q₈	—	86	2	no	—
416	Q₈	—	86	2	no	—
417	Q₈	—	172	2	no	—
418	Q₈	—	172	2	no	—
419	Q₈	—	172	2	no	—
420	Q₈	—	172	2	no	—
421	Q₈	—	172	1	no	—
422	Q₈	—	172	1	no	—
423	Q₈	#13063300	1	4	yes	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	86	2	no	—
441	C₂×C₄	—	172	2	no	—
442	C₂×C₄	—	172	1	no	—
443	C₂×C₄	—	172	2	no	—
444	C₂×C₄	—	172	1	no	—
445	C₂×C₄	—	172	1	no	—
446	C₂×C₄	—	172	2	no	—
447	C₂×C₄	—	172	1	no	—
448	C₂×C₄	—	172	1	no	—
449	C₂×C₄	#13063299	1	2	yes	—
450	C₂×C₄	#13063299	1	2	yes	—
451	C₂×C₄	C₂×#10621885	1	4	yes	—
452	C₂×C₄	C₂×#10621885	1	2	yes	—
453	C₂×C₄	#13063355	1	2	yes	—
454	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
456	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
457	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
458	C₂×C₄	#13063370	1	1	yes	characteristic
459	C₂×C₄	#13063373	1	1	yes	characteristic
460	C₈	—	86	2	no	—
461	C₈	—	172	2	no	—
462	C₈	—	172	1	no	—
463	C₂²	C₂×#13063299	1	1	yes	characteristic
464	C₂²	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
465	C₂²	#14583560	1	1	yes	characteristic
466	C₂²	C₂²×#10621885	1	1	yes	characteristic
467	C₂²	C₂×#13063355	1	1	yes	characteristic
468	C₂²	#14583710	1	1	yes	characteristic
469	C₂²	#14583714	1	1	yes	characteristic
470	C₄	—	2	4	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	4	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	2	no	—
476	C₄	—	344	1	no	—
477	C₄	—	344	2	no	—
478	C₄	—	172	2	no	—
479	C₄	#14583109	1	4	yes	complemented
480	C₄	C₂×#13063300	1	1	yes	characteristic
481	C₄	#14583480	1	1	yes	characteristic
482	C₄	#14583550	1	1	yes	characteristic
483	C₄	#14583597	1	1	yes	characteristic
484	C₂	#19138029	1	1	yes	characteristic
485	C₂	C₂×#14583109	1	1	yes	characteristic
486	C₂	#19144145	1	1	yes	characteristic
487	C₂	#19146261	1	1	yes	characteristic
488	C₂	D₄×#10621885	1	1	yes	characteristic
489	C₂	#19147273	1	1	yes	characteristic
490	C₂	#19147398	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	Q₈×C₄⋊C₄×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	Q₈×C₄⋊C₄	D₄₃
hypocenter	C₄₃	#24732
LCS	G ▷ C₂²×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
138. C₄⋊C₄×C₄₃	Q₁₆	semidirect
231. C₄×C₄₃	#462	semidirect
289. C₄₃	#24732	semidirect
402. C₄⋊C₄	#10621885	semidirect
479. C₄	#14583109	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583109	2
C₂×C₄×#10621885	2
#19139583	2
#19135987	2
#19135841	2
#19135396	2
#19135314	2
#19134936	2
#19134597	2
Q₈×C₄⋊C₄×C₄₃	2
#24732	43