Subgroups — #25106157

Order 11008.

1100 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583456	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063284	C₂	1	1	yes	maximal, characteristic
3	#19135571	C₂	1	4	yes	maximal, complemented
4	#19135539	C₂	1	4	yes	maximal, complemented
5	#19134692	C₂	1	4	yes	maximal
6	C₄₃×#2920	C₂	1	1	yes	maximal, characteristic
7	#14583456	—	2	1	no	—
8	#14583456	—	2	1	no	—
9	#14583456	—	2	1	no	—
10	#14583456	—	2	1	no	—
11	#14583456	C₄	1	2	yes	complemented
12	#14583456	C₄	1	2	yes	complemented
13	#14583456	C₂²	1	2	yes	—
14	#14583456	C₂²	1	2	yes	—
15	C₂×#13063325	C₄	1	1	yes	characteristic, complemented
16	C₂×#13063325	C₄	1	1	yes	characteristic, complemented
17	C₂×#13063317	C₄	1	2	yes	complemented
18	C₂×#13063304	—	2	1	no	—
19	C₂×#13063304	—	2	1	no	—
20	C₂×C₄×Dic₈₆	—	2	1	no	—
21	C₂×C₄×Dic₈₆	—	2	1	no	—
22	C₂×#13063284	—	2	1	no	—
23	C₂×#13063284	C₂²	1	2	yes	—
24	C₄×C₄⋊Dic₄₃	—	2	1	no	—
25	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
26	C₄×C₂²⋊Dic₄₃	—	2	1	no	—
27	C₄×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
28	#14582745	—	2	1	no	—
29	C₄²×Dic₄₃	C₂²	1	2	yes	—
30	#14582660	C₂²	1	16	yes	—
31	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#432	—	2	1	no	—
33	C₄₃×#432	—	2	1	no	—
34	C₄₃×#431	—	2	1	no	—
35	C₄₃×#431	—	2	1	no	—
36	C₄₃×#423	C₂²	1	2	yes	—
37	C₄₃×#407	C₂²	1	2	yes	—
38	C₄×M₁₆×C₄₃	C₂²	1	2	yes	—
39	C₂²×Dic₈₆	—	2	1	no	—
40	C₂²×Dic₈₆	—	2	1	no	—
41	#13063325	—	2	1	no	—
42	#13063325	—	2	1	no	—
43	#13063325	—	2	1	no	—
44	#13063325	—	2	1	no	—
45	#13063325	C₂×C₄	1	2	yes	—
46	#13063325	C₂×C₄	1	2	yes	—
47	#13063325	C₂×C₄	1	2	yes	—
48	#13063325	C₂×C₄	1	2	yes	—
49	#13063317	—	2	2	no	—
50	#13063317	—	2	2	no	—
51	#13063317	C₂×C₄	1	4	yes	—
52	#13063317	C₂×C₄	1	4	yes	—
53	#13063304	—	2	2	no	—
54	#13063304	—	2	2	no	—
55	#13063304	—	2	2	no	—
56	#13063304	—	2	2	no	—
57	#13063304	—	2	2	no	—
58	#13063304	—	2	2	no	—
59	#13063304	—	2	2	no	—
60	#13063304	—	2	2	no	—
61	C₄×Dic₈₆	—	2	2	no	—
62	C₄×Dic₈₆	—	2	2	no	—
63	C₄×Dic₈₆	—	2	2	no	—
64	C₄×Dic₈₆	—	2	2	no	—
65	C₄×Dic₈₆	—	2	2	no	—
66	C₄×Dic₈₆	—	2	2	no	—
67	C₄×Dic₈₆	—	2	2	no	—
68	C₄×Dic₈₆	—	2	2	no	—
69	#13063284	—	2	8	no	—
70	#13063284	—	2	2	no	—
71	#13063284	—	2	2	no	—
72	#13063284	C₂×C₄	1	4	yes	—
73	#13063284	C₂³	1	4	yes	—
74	C₂×C₄⋊Dic₄₃	—	2	1	no	—
75	C₂×C₄⋊Dic₄₃	—	2	1	no	—
76	C₂×C₄⋊Dic₄₃	—	2	2	no	—
77	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
78	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
79	C₂×Dic₄₃⋊C₄	—	2	2	no	—
80	C₂×Dic₄₃⋊C₄	—	2	2	no	—
81	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
82	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
83	C₂×C₄×Dic₄₃	—	2	2	no	—
84	C₂×C₄×Dic₄₃	—	2	2	no	—
85	C₂×C₄×Dic₄₃	—	2	2	no	—
86	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
87	C₄₃⋊#95	—	2	2	no	—
88	C₄₃⋊#95	—	2	2	no	—
89	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
90	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
91	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
93	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₄₃	—	2	2	no	—
106	C₄⋊C₈×C₄₃	—	2	2	no	—
107	C₂²⋊C₈×C₄₃	—	2	2	no	—
108	C₂²⋊C₈×C₄₃	—	2	2	no	—
109	#97×C₄₃	—	2	2	no	—
110	C₄×C₈×C₄₃	—	2	2	no	—
111	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	—	2	4	no	—
113	C₂²×C₄×C₄₃	—	2	4	no	—
114	C₂²×C₄×C₄₃	—	4	2	no	—
115	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
133	C₂²×Dic₄₃	—	2	2	no	—
134	C₂²×Dic₄₃	—	2	2	no	—
135	C₂²×Dic₄₃	—	2	4	no	—
136	C₂×Dic₈₆	—	2	2	no	—
137	C₂×Dic₈₆	—	2	2	no	—
138	C₂×Dic₈₆	—	2	2	no	—
139	C₂×Dic₈₆	—	2	2	no	—
140	C₂×Dic₈₆	—	4	4	no	—
141	C₂×Dic₈₆	—	4	4	no	—
142	M₁₆×C₄₃	—	2	8	no	—
143	C₂×C₈×C₄₃	—	2	4	no	—
144	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
145	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
146	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
147	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
149	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
160	C₂²⋊Dic₄₃	—	2	8	no	—
161	C₂²⋊Dic₄₃	—	2	4	no	—
162	C₂²⋊Dic₄₃	—	2	4	no	—
163	C₄⋊Dic₄₃	—	2	8	no	—
164	C₄⋊Dic₄₃	—	2	2	no	—
165	C₄⋊Dic₄₃	—	2	2	no	—
166	C₄⋊Dic₄₃	—	2	2	no	—
167	C₄⋊Dic₄₃	—	2	2	no	—
168	C₄⋊Dic₄₃	—	2	2	no	—
169	C₄⋊Dic₄₃	—	2	2	no	—
170	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
171	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
172	Dic₄₃⋊C₄	—	2	4	no	—
173	Dic₄₃⋊C₄	—	2	4	no	—
174	Dic₄₃⋊C₄	—	2	4	no	—
175	Dic₄₃⋊C₄	—	2	4	no	—
176	C₄×Dic₄₃	—	2	8	no	—
177	C₄×Dic₄₃	—	2	4	no	—
178	C₄×Dic₄₃	—	2	4	no	—
179	C₄×Dic₄₃	—	2	8	no	—
180	C₄×Dic₄₃	—	4	4	no	—
181	C₂³×C₄₃	—	2	2	no	—
182	C₂³×C₄₃	—	2	2	no	—
183	C₂³×C₄₃	—	4	1	no	—
184	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	2	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	—	2	2	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	2	2	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	4	1	no	—
203	C₂×C₄×C₄₃	#104	1	4	yes	—
204	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	2₋¹⁺⁴	1	4	yes	—
217	C₂×Dic₄₃	—	2	8	no	—
218	C₂×Dic₄₃	—	2	4	no	—
219	C₂×Dic₄₃	—	2	4	no	—
220	C₂×Dic₄₃	—	4	4	no	—
221	C₂×Dic₄₃	—	4	4	no	—
222	C₂×Dic₄₃	—	4	4	no	—
223	C₂×Dic₄₃	—	4	4	no	—
224	Dic₈₆	—	4	4	no	—
225	Dic₈₆	—	4	4	no	—
226	Dic₈₆	—	4	4	no	—
227	Dic₈₆	—	4	4	no	—
228	C₈×C₄₃	—	4	4	no	—
229	#21844	—	43	1	no	maximal, Sylow
230	C₂²×C₄₃	—	2	1	no	—
231	C₂²×C₄₃	—	2	1	no	—
232	C₂²×C₄₃	—	2	1	no	—
233	C₂²×C₄₃	—	2	1	no	—
234	C₂²×C₄₃	—	2	1	no	—
235	C₂²×C₄₃	—	2	1	no	—
236	C₂²×C₄₃	—	2	1	no	—
237	C₂²×C₄₃	—	4	4	no	—
238	C₂²×C₄₃	C₂×#104	1	2	yes	—
239	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₄₃	#536	1	2	yes	—
241	C₄×C₄₃	—	2	1	no	—
242	C₄×C₄₃	—	2	1	no	—
243	C₄×C₄₃	—	2	1	no	—
244	C₄×C₄₃	—	2	1	no	—
245	C₄×C₄₃	—	2	1	no	—
246	C₄×C₄₃	—	2	1	no	—
247	C₄×C₄₃	—	2	1	no	—
248	C₄×C₄₃	C₂×#104	1	2	yes	—
249	C₄×C₄₃	C₂×#104	1	2	yes	—
250	C₄×C₄₃	#421	1	2	yes	—
251	C₄×C₄₃	#519	1	2	yes	—
252	C₄×C₄₃	#536	1	2	yes	—
253	Dic₄₃	—	4	8	no	—
254	Dic₄₃	—	4	4	no	—
255	Dic₄₃	—	4	4	no	—
256	C₂×#533	—	43	1	no	—
257	#2920	D₄₃	1	1	yes	characteristic
258	C₄×#117	—	43	1	no	—
259	#1994	—	43	4	no	—
260	#1986	—	43	4	no	—
261	#1826	—	43	4	no	—
262	C₂×C₄₃	—	2	2	no	—
263	C₂×C₄₃	—	2	2	no	—
264	C₂×C₄₃	—	4	1	no	—
265	C₂×C₄₃	#2310	1	1	yes	characteristic
266	C₂×C₄₃	C₂²×#104	1	1	yes	characteristic
267	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
268	#533	—	43	2	no	—
269	#533	—	43	2	no	—
270	#533	—	43	2	no	—
271	#533	—	43	2	no	—
272	#533	—	86	1	no	—
273	#533	—	86	1	no	—
274	#533	—	86	1	no	—
275	#533	—	86	1	no	—
276	C₂×C₄⋊Q₈	—	43	1	no	—
277	C₂×C₄⋊Q₈	—	43	1	no	—
278	C₂×#125	—	43	2	no	—
279	C₂×C₂²⋊Q₈	—	86	1	no	—
280	C₂×C₂²⋊Q₈	—	86	1	no	—
281	C₂×C₄×Q₈	—	86	1	no	—
282	C₂×C₄×Q₈	—	86	1	no	—
283	C₂×#117	—	43	2	no	—
284	C₂×#117	—	86	1	no	—
285	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
286	#432	—	2	1	no	—
287	#432	—	2	1	no	—
288	#431	—	2	1	no	—
289	#431	—	2	1	no	—
290	#423	C₂×D₄₃	1	2	yes	—
291	#407	C₂×D₄₃	1	2	yes	—
292	C₄×M₁₆	C₂×D₄₃	1	2	yes	—
293	C₄×C₄⋊C₄	—	43	2	no	—
294	C₄×C₄⋊C₄	—	86	1	no	—
295	C₄×C₂²⋊C₄	—	43	2	no	—
296	C₄×C₂²⋊C₄	—	86	1	no	—
297	#376	—	86	1	no	—
298	C₄³	—	43	2	no	—
299	#339	—	43	16	no	—
300	C₄₃	#21844	1	1	yes	characteristic, complemented, Sylow
301	C₂²×Q₈	—	86	1	no	—
302	C₂²×Q₈	—	86	1	no	—
303	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
304	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
305	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
306	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
307	C₄⋊Q₈	—	43	2	no	—
308	C₄⋊Q₈	—	43	2	no	—
309	C₄⋊Q₈	—	43	2	no	—
310	C₄⋊Q₈	—	43	2	no	—
311	C₄⋊Q₈	—	86	1	no	—
312	C₄⋊Q₈	—	86	1	no	—
313	C₄⋊Q₈	—	86	1	no	—
314	C₄⋊Q₈	—	86	1	no	—
315	#125	—	43	4	no	—
316	#125	—	43	4	no	—
317	#125	—	86	2	no	—
318	#125	—	86	2	no	—
319	C₂²⋊Q₈	—	86	2	no	—
320	C₂²⋊Q₈	—	86	2	no	—
321	C₂²⋊Q₈	—	86	2	no	—
322	C₂²⋊Q₈	—	86	2	no	—
323	C₂²⋊Q₈	—	86	2	no	—
324	C₂²⋊Q₈	—	86	2	no	—
325	C₂²⋊Q₈	—	86	2	no	—
326	C₂²⋊Q₈	—	86	2	no	—
327	C₄×Q₈	—	86	2	no	—
328	C₄×Q₈	—	86	2	no	—
329	C₄×Q₈	—	86	2	no	—
330	C₄×Q₈	—	86	2	no	—
331	C₄×Q₈	—	86	2	no	—
332	C₄×Q₈	—	86	2	no	—
333	C₄×Q₈	—	86	2	no	—
334	C₄×Q₈	—	86	2	no	—
335	#117	—	43	4	no	—
336	#117	—	43	4	no	—
337	#117	—	86	8	no	—
338	#117	—	86	2	no	—
339	#117	—	86	2	no	—
340	C₂×C₄⋊C₄	—	43	2	no	—
341	C₂×C₄⋊C₄	—	43	2	no	—
342	C₂×C₄⋊C₄	—	86	2	no	—
343	C₂×C₄⋊C₄	—	86	2	no	—
344	C₂×C₄⋊C₄	—	86	1	no	—
345	C₂×C₄⋊C₄	—	86	1	no	—
346	C₂×C₄⋊C₄	—	86	2	no	—
347	C₂×C₂²⋊C₄	—	86	2	no	—
348	C₂×C₂²⋊C₄	—	86	2	no	—
349	C₂×C₄²	—	43	4	no	—
350	C₂×C₄²	—	86	2	no	—
351	C₂×C₄²	—	86	2	no	—
352	C₂×C₄²	—	86	2	no	—
353	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
354	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
355	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
356	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
357	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
358	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
359	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
360	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
361	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
362	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
363	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
364	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
365	C₄⋊C₈	—	2	2	no	—
366	C₄⋊C₈	—	2	2	no	—
367	C₂²⋊C₈	—	2	2	no	—
368	C₂²⋊C₈	—	2	2	no	—
369	#97	—	2	2	no	—
370	C₄×C₈	—	2	2	no	—
371	#95	—	86	2	no	—
372	#95	—	86	2	no	—
373	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
374	C₂×Q₈	—	86	2	no	—
375	C₂×Q₈	—	86	2	no	—
376	C₂×Q₈	—	86	2	no	—
377	C₂×Q₈	—	86	2	no	—
378	C₂×Q₈	—	172	4	no	—
379	C₂×Q₈	—	172	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	86	2	no	—
384	C₂²×C₄	—	86	2	no	—
385	C₂²×C₄	—	86	4	no	—
386	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
387	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
388	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
389	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
390	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
391	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
392	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
393	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
403	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
404	M₁₆	—	2	8	no	—
405	C₂×C₈	—	2	4	no	—
406	C₄⋊C₄	—	43	4	no	—
407	C₄⋊C₄	—	43	4	no	—
408	C₄⋊C₄	—	86	8	no	—
409	C₄⋊C₄	—	86	2	no	—
410	C₄⋊C₄	—	86	2	no	—
411	C₄⋊C₄	—	86	4	no	—
412	C₄⋊C₄	—	86	4	no	—
413	C₄⋊C₄	—	86	4	no	—
414	C₄⋊C₄	—	86	4	no	—
415	C₄⋊C₄	—	86	2	no	—
416	C₄⋊C₄	—	86	2	no	—
417	C₄⋊C₄	—	86	2	no	—
418	C₄⋊C₄	—	86	2	no	—
419	C₂²⋊C₄	—	86	8	no	—
420	C₂²⋊C₄	—	86	4	no	—
421	C₂²⋊C₄	—	86	4	no	—
422	C₄²	—	86	8	no	—
423	C₄²	—	86	4	no	—
424	C₄²	—	86	4	no	—
425	C₄²	—	86	8	no	—
426	C₄²	—	172	4	no	—
427	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
428	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
429	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
430	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
431	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
432	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
433	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
434	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
435	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
436	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
437	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
438	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
439	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
440	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
441	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
442	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	4	1	no	—
446	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
447	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
448	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
449	Q₈	—	172	4	no	—
450	Q₈	—	172	4	no	—
451	Q₈	—	172	4	no	—
452	Q₈	—	172	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	86	8	no	—
470	C₂×C₄	—	86	4	no	—
471	C₂×C₄	—	86	4	no	—
472	C₂×C₄	—	172	4	no	—
473	C₂×C₄	—	172	4	no	—
474	C₂×C₄	—	172	4	no	—
475	C₂×C₄	—	172	4	no	—
476	C₂×C₄	#13063251	1	4	yes	—
477	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
478	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
479	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
480	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
481	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
482	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
483	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
484	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
485	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
486	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
487	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
488	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
489	C₂×C₄	#13063372	1	4	yes	—
490	C₈	—	4	4	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	4	4	no	—
499	C₂²	C₂×#13063251	1	2	yes	—
500	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
501	C₂²	#14583475	1	2	yes	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	172	8	no	—
510	C₄	—	172	4	no	—
511	C₄	—	172	4	no	—
512	C₄	C₂×#13063251	1	2	yes	—
513	C₄	C₂×#13063251	1	2	yes	—
514	C₄	#14582915	1	2	yes	—
515	C₄	#14583376	1	2	yes	—
516	C₄	#14583470	1	2	yes	—
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	1	no	—
520	C₂	#19137179	1	1	yes	characteristic
521	C₂	C₂²×#13063251	1	1	yes	characteristic
522	C₂	C₂×#14582915	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2920	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2920	D₄₃
hypocenter	C₄₃	#21844
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #19135571	C₂	semidirect
4. #19135539	C₂	semidirect
11. #14583456	C₄	semidirect
12. #14583456	C₄	semidirect
15. C₂×#13063325	C₄	semidirect
16. C₂×#13063325	C₄	semidirect
17. C₂×#13063317	C₄	semidirect
300. C₄₃	#21844	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583456	2
C₄×#13063284	2
#19135571	2
#19135539	2
#19134692	2
C₄₃×#2920	2
#21844	43