Subgroups — #25105993

Order 11008.

1352 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583449	C₂	1	1	yes	maximal, characteristic
2	#19136993	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135514	C₂	1	4	yes	maximal, complemented
4	#19135426	C₂	1	4	yes	maximal, complemented
5	#19134538	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#10621898	C₂²	1	2	yes	—
8	#14583449	—	2	1	no	—
9	#14583449	—	2	1	no	—
10	#14583449	—	2	1	no	—
11	#14583449	—	2	1	no	—
12	#14583449	C₄	1	2	yes	complemented
13	#14583449	C₄	1	2	yes	complemented
14	#14583449	C₂²	1	2	yes	—
15	#14583449	C₂²	1	2	yes	—
16	C₂×#13063325	C₄	1	1	yes	characteristic, complemented
17	C₂×#13063322	C₄	1	1	yes	characteristic, complemented
18	C₂×#13063313	C₄	1	2	yes	complemented
19	C₂×#13063299	—	2	1	no	—
20	C₂×#13063299	—	2	1	no	—
21	C₂×C₄×D₁₇₂	—	2	1	no	—
22	C₂×C₄×D₁₇₂	—	2	1	no	—
23	C₂×#13063251	C₂²	1	16	yes	complemented
24	#14582767	—	2	1	no	—
25	#14582765	—	2	1	no	—
26	#14582762	—	2	1	no	—
27	#14582759	—	2	1	no	—
28	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	complemented
29	C₄×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
30	#14582745	C₂²	1	2	yes	complemented
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	complemented
37	C₄₃×#407	C₂²	1	2	yes	—
38	C₄×M₁₆×C₄₃	C₂²	1	2	yes	complemented
39	C₂×#10621898	—	2	2	no	—
40	C₂×#10621898	—	2	2	no	—
41	C₂×#10621898	—	4	8	no	—
42	C₂×#10621898	C₂×C₄	1	4	yes	—
43	C₂×#10621898	C₂³	1	4	yes	—
44	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
45	C₂²×D₁₇₂	—	2	1	no	—
46	C₂²×D₁₇₂	—	2	1	no	—
47	C₂²×D₁₇₂	C₂×C₄	1	2	yes	—
48	C₂²×C₂²⋊D₄₃	—	2	2	no	—
49	C₂²×C₄×D₄₃	—	2	2	no	—
50	#13063325	—	2	1	no	—
51	#13063325	—	2	1	no	—
52	#13063325	C₂×C₄	1	2	yes	—
53	#13063325	C₂×C₄	1	2	yes	—
54	#13063322	—	2	1	no	—
55	#13063322	—	2	1	no	—
56	#13063322	C₂×C₄	1	2	yes	—
57	#13063322	C₂×C₄	1	2	yes	—
58	#13063313	—	2	2	no	—
59	#13063313	—	2	2	no	—
60	#13063313	C₂×C₄	1	4	yes	—
61	#13063313	C₂×C₄	1	4	yes	—
62	#13063299	—	2	2	no	—
63	#13063299	—	2	2	no	—
64	#13063299	—	2	2	no	—
65	#13063299	—	2	2	no	—
66	#13063299	—	2	2	no	—
67	#13063299	—	2	2	no	—
68	#13063299	—	2	2	no	—
69	#13063299	—	2	2	no	—
70	C₄×D₁₇₂	—	2	2	no	—
71	C₄×D₁₇₂	—	2	2	no	—
72	C₄×D₁₇₂	—	2	2	no	—
73	C₄×D₁₇₂	—	2	2	no	—
74	C₄×D₁₇₂	—	2	2	no	—
75	C₄×D₁₇₂	—	2	2	no	—
76	C₄×D₁₇₂	—	2	2	no	—
77	C₄×D₁₇₂	—	2	2	no	—
78	C₂×C₄⋊Dic₄₃	—	2	1	no	—
79	C₂×C₄⋊Dic₄₃	—	2	1	no	—
80	C₂×C₄⋊Dic₄₃	—	2	2	no	—
81	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
82	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
83	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
84	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
85	#13063251	—	4	16	no	—
86	C₄₃⋊#95	—	2	2	no	—
87	C₄₃⋊#95	—	2	2	no	—
88	C₄₃⋊#95	—	2	2	no	—
89	C₄₃⋊#95	—	2	2	no	—
90	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
91	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
92	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
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	C₂×C₄	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	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₄₃	—	2	2	no	—
107	C₄⋊C₈×C₄₃	—	2	2	no	—
108	C₂²⋊C₈×C₄₃	—	2	2	no	—
109	C₂²⋊C₈×C₄₃	—	2	2	no	—
110	#97×C₄₃	—	2	2	no	—
111	C₄×C₈×C₄₃	—	2	2	no	—
112	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂³×D₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	—	2	4	no	—
115	C₂²×C₄×C₄₃	—	4	2	no	—
116	C₂²×C₄×C₄₃	—	4	2	no	—
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	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
135	C₂×C₂²⋊D₄₃	—	2	4	no	—
136	C₂×C₂²⋊D₄₃	—	2	4	no	—
137	C₂×C₂²⋊D₄₃	—	4	8	no	—
138	C₂²×Dic₄₃	—	2	2	no	—
139	C₂²×Dic₄₃	—	2	4	no	—
140	#10621898	—	2	16	no	—
141	#10621898	—	4	8	no	—
142	#10621898	—	4	8	no	—
143	#10621898	—	4	8	no	—
144	C₂×D₁₇₂	—	2	2	no	—
145	C₂×D₁₇₂	—	2	2	no	—
146	C₂×D₁₇₂	—	2	2	no	—
147	C₂×D₁₇₂	—	2	2	no	—
148	C₂×D₁₇₂	—	2	2	no	—
149	C₂×D₁₇₂	—	4	4	no	—
150	C₂×D₁₇₂	—	4	4	no	—
151	C₂×D₁₇₂	—	4	4	no	—
152	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
153	C₂×C₄×D₄₃	—	2	4	no	—
154	C₂×C₄×D₄₃	—	2	4	no	—
155	C₂×C₄×D₄₃	—	4	8	no	—
156	C₂×Dic₈₆	—	2	2	no	—
157	C₂×Dic₈₆	—	4	4	no	—
158	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
159	M₁₆×C₄₃	—	2	8	no	—
160	C₂×C₈×C₄₃	—	2	4	no	—
161	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
162	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
164	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
165	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
177	C₂²⋊Dic₄₃	—	4	4	no	—
178	(C₂×D₄₃)⋊C₄	—	2	4	no	—
179	(C₂×D₄₃)⋊C₄	—	2	4	no	—
180	(C₂×D₄₃)⋊C₄	—	2	4	no	—
181	(C₂×D₄₃)⋊C₄	—	2	4	no	—
182	C₄⋊Dic₄₃	—	2	2	no	—
183	C₄⋊Dic₄₃	—	2	2	no	—
184	C₄⋊Dic₄₃	—	2	2	no	—
185	C₄⋊Dic₄₃	—	2	2	no	—
186	C₄⋊Dic₄₃	—	4	4	no	—
187	C₄×Dic₄₃	—	2	8	no	—
188	C₂³×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	4	1	no	—
191	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
194	C₂²×D₄₃	—	2	4	no	—
195	C₂²×D₄₃	—	4	4	no	—
196	C₂²×D₄₃	—	4	4	no	—
197	C₂²×D₄₃	—	4	4	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	2	no	—
203	C₂×C₄×C₄₃	—	2	2	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	1	no	—
210	C₂×C₄×C₄₃	—	4	1	no	—
211	C₂×C₄×C₄₃	—	4	1	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
228	C₂²⋊D₄₃	—	4	8	no	—
229	C₂²⋊D₄₃	—	4	8	no	—
230	C₂×Dic₄₃	—	2	4	no	—
231	C₂×Dic₄₃	—	4	4	no	—
232	C₂×Dic₄₃	—	4	4	no	—
233	C₂×Dic₄₃	—	4	4	no	—
234	C₂×Dic₄₃	—	4	4	no	—
235	D₁₇₂	—	2	8	no	—
236	D₁₇₂	—	4	4	no	—
237	D₁₇₂	—	4	4	no	—
238	D₁₇₂	—	4	4	no	—
239	D₁₇₂	—	4	4	no	—
240	D₁₇₂	—	4	4	no	—
241	C₄×D₄₃	—	4	8	no	—
242	C₄×D₄₃	—	4	8	no	—
243	Dic₈₆	—	2	8	no	—
244	Dic₈₆	—	4	4	no	—
245	C₈×C₄₃	—	4	4	no	—
246	#21816	—	43	1	no	maximal, Sylow
247	C₂²×C₄₃	—	2	1	no	—
248	C₂²×C₄₃	—	2	1	no	—
249	C₂²×C₄₃	—	2	1	no	—
250	C₂²×C₄₃	—	2	1	no	—
251	C₂²×C₄₃	—	2	1	no	—
252	C₂²×C₄₃	—	2	1	no	—
253	C₂²×C₄₃	—	2	1	no	—
254	C₂²×C₄₃	—	4	4	no	—
255	C₂²×C₄₃	#421	1	2	yes	—
256	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₄₃	#535	1	2	yes	—
258	C₂×D₄₃	—	4	4	no	—
259	C₂×D₄₃	—	4	4	no	—
260	C₂×D₄₃	—	4	4	no	—
261	C₂×D₄₃	—	8	8	no	—
262	C₄×C₄₃	—	2	1	no	—
263	C₄×C₄₃	—	2	1	no	—
264	C₄×C₄₃	—	2	1	no	—
265	C₄×C₄₃	—	2	1	no	—
266	C₄×C₄₃	—	2	1	no	—
267	C₄×C₄₃	—	2	1	no	—
268	C₄×C₄₃	—	2	1	no	—
269	C₄×C₄₃	—	2	1	no	—
270	C₄×C₄₃	—	2	1	no	—
271	C₄×C₄₃	#421	1	2	yes	—
272	C₄×C₄₃	#518	1	2	yes	—
273	C₄×C₄₃	#535	1	2	yes	—
274	Dic₄₃	—	4	4	no	—
275	Dic₄₃	—	8	4	no	—
276	C₂×#532	—	43	1	no	—
277	#2920	D₄₃	1	1	yes	characteristic, complemented
278	#2283	—	43	1	no	—
279	#1980	—	43	4	no	—
280	#1963	—	43	4	no	—
281	#1789	—	43	4	no	—
282	C₂×C₄₃	—	2	2	no	—
283	C₂×C₄₃	—	2	2	no	—
284	C₂×C₄₃	—	4	1	no	—
285	C₂×C₄₃	#2309	1	1	yes	characteristic
286	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
287	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
288	D₄₃	—	8	4	no	—
289	C₂²×#41	—	43	2	no	—
290	#532	—	43	2	no	—
291	#532	—	43	2	no	—
292	#532	—	43	2	no	—
293	#532	—	43	2	no	—
294	#532	—	86	1	no	—
295	#532	—	86	1	no	—
296	#532	—	86	1	no	—
297	#532	—	86	1	no	—
298	C₂×C₄⋊Q₈	—	43	1	no	—
299	C₂×#127	—	43	1	no	—
300	C₂×#124	—	43	2	no	—
301	C₂×#121	—	86	1	no	—
302	C₂×#121	—	86	1	no	—
303	C₂×C₄×D₄	—	86	1	no	—
304	C₂×C₄×D₄	—	86	1	no	—
305	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
306	#432	—	2	1	no	—
307	#432	—	2	1	no	—
308	#431	—	2	1	no	—
309	#431	—	2	1	no	—
310	#423	C₂×D₄₃	1	2	yes	complemented
311	C₂×#104	—	43	16	no	—
312	#407	C₂×D₄₃	1	2	yes	—
313	C₄×M₁₆	C₂×D₄₃	1	2	yes	complemented
314	#383	—	86	1	no	—
315	#382	—	86	1	no	—
316	#381	—	86	1	no	—
317	#380	—	86	1	no	—
318	C₄×C₄⋊C₄	—	43	2	no	—
319	C₄×C₂²⋊C₄	—	43	2	no	—
320	#376	—	43	2	no	—
321	C₄₃	#21816	1	1	yes	characteristic, complemented, Sylow
322	C₂×#41	—	43	4	no	—
323	C₂×#41	—	43	4	no	—
324	C₂×#41	—	86	2	no	—
325	C₂×#41	—	86	2	no	—
326	C₂×#41	—	172	8	no	—
327	C₂²×Q₈	—	43	2	no	—
328	C₂²×D₄	—	43	2	no	—
329	C₂²×D₄	—	86	2	no	—
330	C₂²×D₄	—	86	1	no	—
331	C₂²×D₄	—	86	1	no	—
332	C₂³×C₄	—	86	2	no	—
333	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
334	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
335	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
336	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
337	C₄⋊Q₈	—	43	2	no	—
338	C₄⋊Q₈	—	43	2	no	—
339	C₄⋊Q₈	—	86	1	no	—
340	C₄⋊Q₈	—	86	1	no	—
341	#127	—	43	2	no	—
342	#127	—	43	2	no	—
343	#127	—	86	1	no	—
344	#127	—	86	1	no	—
345	#124	—	43	4	no	—
346	#124	—	43	4	no	—
347	#124	—	86	2	no	—
348	#124	—	86	2	no	—
349	#121	—	86	2	no	—
350	#121	—	86	2	no	—
351	#121	—	86	2	no	—
352	#121	—	86	2	no	—
353	#121	—	86	2	no	—
354	#121	—	86	2	no	—
355	#121	—	86	2	no	—
356	#121	—	86	2	no	—
357	C₄×D₄	—	86	2	no	—
358	C₄×D₄	—	86	2	no	—
359	C₄×D₄	—	86	2	no	—
360	C₄×D₄	—	86	2	no	—
361	C₄×D₄	—	86	2	no	—
362	C₄×D₄	—	86	2	no	—
363	C₄×D₄	—	86	2	no	—
364	C₄×D₄	—	86	2	no	—
365	C₂×C₄⋊C₄	—	86	1	no	—
366	C₂×C₄⋊C₄	—	86	1	no	—
367	C₂×C₄⋊C₄	—	86	2	no	—
368	C₂×C₂²⋊C₄	—	86	2	no	—
369	C₂×C₂²⋊C₄	—	86	2	no	—
370	C₂×C₂²⋊C₄	—	86	2	no	—
371	C₂×C₄²	—	43	4	no	—
372	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
373	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
374	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
375	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
376	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
377	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
378	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
379	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
380	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
381	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
382	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
383	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
384	C₄⋊C₈	—	2	2	no	—
385	C₄⋊C₈	—	2	2	no	—
386	#104	—	172	16	no	—
387	C₂²⋊C₈	—	2	2	no	—
388	C₂²⋊C₈	—	2	2	no	—
389	#97	—	2	2	no	—
390	C₄×C₈	—	2	2	no	—
391	#95	—	86	2	no	—
392	#95	—	86	2	no	—
393	#95	—	86	2	no	—
394	#95	—	86	2	no	—
395	C₂⁴	—	86	2	no	—
396	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
397	#41	—	86	16	no	—
398	#41	—	172	8	no	—
399	#41	—	172	8	no	—
400	#41	—	172	8	no	—
401	C₂×Q₈	—	43	4	no	—
402	C₂×Q₈	—	86	2	no	—
403	C₂×Q₈	—	172	4	no	—
404	C₂×D₄	—	43	4	no	—
405	C₂×D₄	—	86	4	no	—
406	C₂×D₄	—	86	4	no	—
407	C₂×D₄	—	86	2	no	—
408	C₂×D₄	—	86	2	no	—
409	C₂×D₄	—	86	2	no	—
410	C₂×D₄	—	86	2	no	—
411	C₂×D₄	—	86	2	no	—
412	C₂×D₄	—	172	4	no	—
413	C₂×D₄	—	172	4	no	—
414	C₂×D₄	—	172	4	no	—
415	C₂×D₄	—	172	8	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	86	2	no	—
420	C₂²×C₄	—	86	4	no	—
421	C₂²×C₄	—	86	4	no	—
422	C₂²×C₄	—	86	4	no	—
423	C₂²×C₄	—	172	8	no	—
424	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
425	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
426	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
427	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
428	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
429	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
430	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
431	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
441	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
442	M₁₆	—	2	8	no	—
443	C₂×C₈	—	2	4	no	—
444	C₄⋊C₄	—	86	2	no	—
445	C₄⋊C₄	—	86	2	no	—
446	C₄⋊C₄	—	86	2	no	—
447	C₄⋊C₄	—	86	2	no	—
448	C₄⋊C₄	—	172	4	no	—
449	C₂²⋊C₄	—	86	4	no	—
450	C₂²⋊C₄	—	86	4	no	—
451	C₂²⋊C₄	—	86	4	no	—
452	C₂²⋊C₄	—	86	4	no	—
453	C₂²⋊C₄	—	172	4	no	—
454	C₄²	—	86	8	no	—
455	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
456	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
457	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
458	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
459	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
460	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
461	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
462	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
463	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
464	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
465	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
466	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
467	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
468	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
469	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
470	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
471	C₂³	—	2	2	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	86	4	no	—
475	C₂³	—	172	4	no	—
476	C₂³	—	172	4	no	—
477	C₂³	—	172	4	no	—
478	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
479	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
480	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
481	Q₈	—	86	8	no	—
482	Q₈	—	172	4	no	—
483	D₄	—	86	8	no	—
484	D₄	—	172	4	no	—
485	D₄	—	172	4	no	—
486	D₄	—	172	4	no	—
487	D₄	—	172	4	no	—
488	D₄	—	172	8	no	—
489	D₄	—	172	8	no	—
490	D₄	—	172	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	86	4	no	—
509	C₂×C₄	—	172	8	no	—
510	C₂×C₄	—	172	4	no	—
511	C₂×C₄	—	172	4	no	—
512	C₂×C₄	—	172	4	no	—
513	C₂×C₄	—	172	4	no	—
514	C₂×C₄	—	172	8	no	—
515	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
516	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
517	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
518	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
519	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
520	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
521	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
522	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
523	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
524	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
525	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
526	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
527	C₂×C₄	#13063371	1	4	yes	—
528	C₈	—	4	4	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	344	8	no	—
538	C₂²	—	172	4	no	—
539	C₂²	—	172	4	no	—
540	C₂²	—	172	4	no	—
541	C₂²	#14582915	1	2	yes	—
542	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
543	C₂²	#14583468	1	2	yes	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	344	4	no	—
554	C₄	—	172	4	no	—
555	C₄	#14582915	1	2	yes	—
556	C₄	#14583373	1	2	yes	—
557	C₄	#14583463	1	2	yes	—
558	C₂	—	2	2	no	—
559	C₂	—	2	2	no	—
560	C₂	—	4	1	no	—
561	C₂	—	344	4	no	—
562	C₂	#19137175	1	1	yes	characteristic
563	C₂	C₂×#14582915	1	1	yes	characteristic
564	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	C₂×#14583449	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2920	D₄₃
hypocenter	C₄₃	#21816
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
2. #19136993	C₂	semidirect
3. #19135514	C₂	semidirect
4. #19135426	C₂	semidirect
5. #19134538	C₂	semidirect
6. C₄₃×#2920	C₂	semidirect
12. #14583449	C₄	semidirect
13. #14583449	C₄	semidirect
16. C₂×#13063325	C₄	semidirect
17. C₂×#13063322	C₄	semidirect
18. C₂×#13063313	C₄	semidirect
23. C₂×#13063251	C₂²	semidirect
28. C₄×C₄⋊Dic₄₃	C₂²	semidirect
30. #14582745	C₂²	semidirect
36. C₄₃×#423	C₂²	semidirect
38. C₄×M₁₆×C₄₃	C₂²	semidirect
277. #2920	D₄₃	semidirect
310. #423	C₂×D₄₃	semidirect
313. C₄×M₁₆	C₂×D₄₃	semidirect
321. C₄₃	#21816	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583449	2
#19136993	2
#19135514	2
#19135426	2
#19134538	2
C₄₃×#2920	2
#21816	43