Subgroups — #24989299

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137056	C₂	1	1	yes	maximal, characteristic
2	#19134746	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582628	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582626	C₂	1	1	yes	maximal, characteristic
6	#19132436	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#13063282	—	2	1	no	—
10	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₃⋊C₈	—	2	1	no	—
12	C₂×Dic₄₃⋊C₈	—	2	1	no	—
13	C₂×Dic₄₃⋊C₈	—	2	1	no	—
14	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	#14582800	C₄	1	1	yes	characteristic
16	#14582800	C₄	1	1	yes	characteristic
17	#14582795	C₄	1	1	yes	characteristic
18	#14582795	C₄	1	1	yes	characteristic
19	#14582788	—	2	1	no	—
20	#14582788	—	2	1	no	—
21	C₄×(C₂×D₄₃)⋊C₄	—	2	1	no	—
22	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
23	#14582653	—	2	1	no	—
24	#14582628	—	2	2	no	—
25	#14582626	—	2	2	no	—
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₃	—	2	1	no	—
31	C₂²×C₄₃⋊C₈	—	2	1	no	—
32	C₂²×C₄₃⋊C₈	—	2	1	no	—
33	C₄×D₁₇₂	—	2	1	no	—
34	C₄×D₁₇₂	—	2	1	no	—
35	C₄×D₁₇₂	D₄	1	2	yes	—
36	C₄×D₁₇₂	Q₈	1	2	yes	—
37	#13063282	—	4	2	no	—
38	#13063282	—	4	2	no	—
39	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂×Dic₄₃⋊C₄	—	2	1	no	—
41	C₂×Dic₄₃⋊C₄	—	2	1	no	—
42	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
43	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
44	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
45	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
46	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
47	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
51	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
53	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
55	Dic₄₃⋊C₈	—	2	4	no	—
56	Dic₄₃⋊C₈	—	4	2	no	—
57	Dic₄₃⋊C₈	—	4	2	no	—
58	C₄×C₄₃⋊C₈	—	2	1	no	—
59	C₄×C₄₃⋊C₈	—	2	1	no	—
60	C₄₃⋊#95	—	2	1	no	—
61	C₄₃⋊#95	—	2	1	no	—
62	C₂²×C₈×C₄₃	—	2	1	no	—
63	C₂²×C₈×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₃	—	2	1	no	—
67	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₃	—	2	1	no	—
69	C₄⋊C₈×C₄₃	—	2	1	no	—
70	C₄×C₈×C₄₃	—	2	1	no	—
71	C₄×C₈×C₄₃	—	2	1	no	—
72	#95×C₄₃	—	2	1	no	—
73	C₂³×D₄₃	—	2	1	no	—
74	C₂²×C₄×C₄₃	—	2	1	no	—
75	C₂²×C₄×C₄₃	—	2	1	no	—
76	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×Dic₄₃	—	2	1	no	—
80	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×D₁₇₂	—	2	1	no	—
85	C₂×D₁₇₂	—	2	1	no	—
86	C₂×D₁₇₂	—	2	1	no	—
87	C₂×D₁₇₂	—	2	1	no	—
88	C₂×D₁₇₂	—	2	1	no	—
89	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	—
90	C₂×C₄×D₄₃	—	2	2	no	—
91	C₂×C₄×D₄₃	—	2	2	no	—
92	C₂×C₄×D₄₃	—	4	1	no	—
93	C₂×C₄×D₄₃	—	4	1	no	—
94	C₂×C₄×D₄₃	—	4	1	no	—
95	C₂×C₄×D₄₃	—	4	1	no	—
96	C₂×C₈×C₄₃	—	2	2	no	—
97	C₂×C₈×C₄₃	—	4	1	no	—
98	C₂×C₈×C₄₃	—	4	1	no	—
99	C₂×C₈×C₄₃	—	4	1	no	—
100	C₂×C₈×C₄₃	—	4	1	no	—
101	C₂×C₈×C₄₃	—	4	1	no	—
102	C₄⋊C₄×C₄₃	—	2	1	no	—
103	C₄⋊C₄×C₄₃	—	2	1	no	—
104	C₄⋊C₄×C₄₃	—	2	1	no	—
105	C₄⋊C₄×C₄₃	—	2	1	no	—
106	C₄²×C₄₃	—	4	1	no	—
107	C₄²×C₄₃	—	4	1	no	—
108	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
110	C₄²×C₄₃	#41	1	1	yes	characteristic
111	C₄²×C₄₃	#41	1	1	yes	characteristic
112	(C₂×D₄₃)⋊C₄	—	2	2	no	—
113	(C₂×D₄₃)⋊C₄	—	2	2	no	—
114	(C₂×D₄₃)⋊C₄	—	4	2	no	—
115	(C₂×D₄₃)⋊C₄	—	4	2	no	—
116	(C₂×D₄₃)⋊C₄	—	4	2	no	—
117	(C₂×D₄₃)⋊C₄	—	4	2	no	—
118	C₄⋊Dic₄₃	—	2	1	no	—
119	C₄⋊Dic₄₃	C₄⋊C₄	1	2	yes	—
120	Dic₄₃⋊C₄	—	4	2	no	—
121	Dic₄₃⋊C₄	—	4	2	no	—
122	C₄×Dic₄₃	—	2	1	no	—
123	C₄×Dic₄₃	—	2	1	no	—
124	C₄×Dic₄₃	—	2	1	no	—
125	C₄×Dic₄₃	—	2	1	no	—
126	C₄×Dic₄₃	—	2	1	no	—
127	C₄×Dic₄₃	—	2	1	no	—
128	C₄×Dic₄₃	—	2	2	no	—
129	C₄×Dic₄₃	—	4	1	no	—
130	C₄×Dic₄₃	D₈	1	2	yes	—
131	C₄×Dic₄₃	SD₁₆	1	2	yes	—
132	C₂×C₄₃⋊C₈	—	2	2	no	—
133	C₂×C₄₃⋊C₈	—	4	1	no	—
134	C₂×C₄₃⋊C₈	—	4	1	no	—
135	C₂×C₄₃⋊C₈	—	4	1	no	—
136	C₂×C₄₃⋊C₈	—	4	1	no	—
137	C₂×C₄₃⋊C₈	—	4	1	no	—
138	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×D₄₃	—	2	2	no	—
140	C₂²×D₄₃	—	4	1	no	—
141	C₂²×D₄₃	—	4	1	no	—
142	C₂²×D₄₃	—	4	1	no	—
143	C₂²×D₄₃	—	4	1	no	—
144	C₂²×D₄₃	—	4	1	no	—
145	C₂²×D₄₃	—	4	1	no	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	1	no	—
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	—	4	1	no	—
154	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
156	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
157	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
161	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
162	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
163	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
166	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
168	C₂×Dic₄₃	—	2	1	no	—
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	—	2	1	no	—
172	C₂×Dic₄₃	—	2	1	no	—
173	C₂×Dic₄₃	—	2	1	no	—
174	C₂×Dic₄₃	—	2	2	no	—
175	C₂×Dic₄₃	—	2	1	no	—
176	C₂×Dic₄₃	—	2	1	no	—
177	C₂×Dic₄₃	—	2	1	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	—	4	1	no	—
180	C₂×Dic₄₃	#102	1	2	yes	—
181	C₂×Dic₄₃	#102	1	2	yes	—
182	C₂×Dic₄₃	#104	1	2	yes	—
183	D₁₇₂	—	2	2	no	—
184	D₁₇₂	—	2	2	no	—
185	D₁₇₂	—	4	1	no	—
186	D₁₇₂	—	4	1	no	—
187	C₄×D₄₃	—	4	2	no	—
188	C₄×D₄₃	—	4	2	no	—
189	C₄×D₄₃	—	4	2	no	—
190	C₄×D₄₃	—	4	2	no	—
191	C₈×C₄₃	—	4	2	no	—
192	C₈×C₄₃	—	8	1	no	—
193	C₄₃⋊C₈	—	4	2	no	—
194	C₄₃⋊C₈	—	8	1	no	—
195	#8567	—	43	1	no	maximal, Sylow
196	C₂²×C₄₃	#380	1	1	yes	characteristic
197	C₂²×C₄₃	#408	1	1	yes	characteristic
198	C₂²×C₄₃	#408	1	1	yes	characteristic
199	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
200	C₂²×C₄₃	#417	1	1	yes	characteristic
201	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
202	C₂²×C₄₃	#421	1	1	yes	characteristic
203	C₂×D₄₃	—	4	2	no	—
204	C₂×D₄₃	—	4	2	no	—
205	C₂×D₄₃	—	4	2	no	—
206	C₂×D₄₃	—	8	1	no	—
207	C₂×D₄₃	—	8	1	no	—
208	C₂×D₄₃	—	8	1	no	—
209	C₂×D₄₃	—	8	1	no	—
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	—	8	1	no	—
213	C₄×C₄₃	—	8	1	no	—
214	C₄×C₄₃	#424	1	1	yes	characteristic
215	C₄×C₄₃	#424	1	1	yes	characteristic
216	C₄×C₄₃	#433	1	1	yes	characteristic
217	C₄×C₄₃	#433	1	1	yes	characteristic
218	C₄×C₄₃	#459	1	1	yes	characteristic
219	C₄×C₄₃	#461	1	1	yes	characteristic
220	C₄×C₄₃	#474	1	1	yes	characteristic
221	C₄×C₄₃	#476	1	1	yes	characteristic
222	Dic₄₃	—	2	2	no	—
223	Dic₄₃	—	2	2	no	—
224	Dic₄₃	—	2	2	no	—
225	Dic₄₃	—	4	2	no	—
226	Dic₄₃	—	4	1	no	—
227	#2293	—	43	1	no	—
228	#1842	—	43	1	no	—
229	C₄×C₄⋊C₈	—	43	1	no	—
230	C₂×D₄⋊C₈	—	43	1	no	—
231	C₂×D₄⋊C₈	—	43	1	no	—
232	#1279	—	43	1	no	—
233	#1279	D₄₃	1	1	yes	characteristic, complemented
234	C₂×C₄₃	#1480	1	1	yes	characteristic
235	C₂×C₄₃	#1483	1	1	yes	characteristic
236	C₂×C₄₃	#1492	1	1	yes	characteristic
237	C₂×C₄₃	#1495	1	1	yes	characteristic
238	C₂×C₄₃	#1798	1	1	yes	characteristic
239	C₂×C₄₃	#1802	1	1	yes	characteristic
240	C₂×C₄₃	#1806	1	1	yes	characteristic
241	D₄₃	—	8	2	no	—
242	C₂×C₄×D₄	—	43	1	no	—
243	C₂×#117	—	86	1	no	—
244	C₂×C₄⋊C₈	—	43	1	no	—
245	C₂×C₄⋊C₈	—	86	1	no	—
246	C₂×C₄⋊C₈	—	86	1	no	—
247	C₂×C₄⋊C₈	—	86	1	no	—
248	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
249	C₂×C₄×C₈	—	43	1	no	—
250	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
251	#390	—	43	1	no	—
252	#390	—	43	1	no	—
253	#389	—	43	1	no	—
254	#389	—	43	1	no	—
255	#388	—	86	1	no	—
256	#388	—	86	1	no	—
257	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
258	C₄×C₂²⋊C₄	—	86	1	no	—
259	C₄³	—	43	1	no	—
260	#336	—	86	1	no	—
261	D₄⋊C₈	—	86	2	no	—
262	D₄⋊C₈	—	86	2	no	—
263	C₄₃	#8567	1	1	yes	characteristic, complemented, Sylow
264	C₂²×D₄	—	43	1	no	—
265	C₂³×C₄	—	86	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	86	1	no	—
269	C₂²×C₈	—	86	1	no	—
270	C₄×D₄	—	43	2	no	—
271	C₄×D₄	—	43	2	no	—
272	C₄×D₄	—	86	1	no	—
273	C₄×D₄	—	86	1	no	—
274	#117	—	172	2	no	—
275	#117	—	172	2	no	—
276	C₂×C₄⋊C₄	—	43	1	no	—
277	C₂×C₄⋊C₄	—	86	1	no	—
278	C₂×C₄⋊C₄	—	86	1	no	—
279	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	86	1	no	—
282	C₂×C₂²⋊C₄	—	86	1	no	—
283	C₂×C₂²⋊C₄	—	86	1	no	—
284	C₂×C₂²⋊C₄	—	86	1	no	—
285	C₂×C₂²⋊C₄	—	86	1	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	43	1	no	—
288	C₂×C₄²	—	43	1	no	—
289	C₂×C₄²	—	43	1	no	—
290	C₂×C₄²	—	43	1	no	—
291	C₂×C₄²	—	43	1	no	—
292	C₂×C₄²	—	43	1	no	—
293	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	86	4	no	—
297	C₄⋊C₈	—	86	1	no	—
298	C₄⋊C₈	—	86	1	no	—
299	C₄⋊C₈	—	172	2	no	—
300	C₄⋊C₈	—	172	2	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	86	1	no	—
304	C₄×C₈	—	86	1	no	—
305	#95	—	2	1	no	—
306	#95	—	86	1	no	—
307	#95	—	86	1	no	—
308	C₂⁴	—	86	1	no	—
309	C₂×D₄	—	43	2	no	—
310	C₂×D₄	—	86	1	no	—
311	C₂×D₄	—	86	1	no	—
312	C₂×D₄	—	86	1	no	—
313	C₂×D₄	—	86	1	no	—
314	C₂×D₄	—	86	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	43	1	no	—
318	C₂²×C₄	—	43	1	no	—
319	C₂²×C₄	—	43	1	no	—
320	C₂²×C₄	—	43	1	no	—
321	C₂²×C₄	—	86	1	no	—
322	C₂²×C₄	—	86	2	no	—
323	C₂²×C₄	—	86	2	no	—
324	C₂²×C₄	—	172	1	no	—
325	C₂²×C₄	—	172	1	no	—
326	C₂²×C₄	—	172	1	no	—
327	C₂²×C₄	—	172	1	no	—
328	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
329	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
330	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	86	2	no	—
338	C₂×C₈	—	172	1	no	—
339	C₂×C₈	—	172	1	no	—
340	C₂×C₈	—	172	1	no	—
341	C₂×C₈	—	172	1	no	—
342	C₂×C₈	—	172	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	43	2	no	—
348	C₄⋊C₄	—	86	1	no	—
349	C₄⋊C₄	—	172	2	no	—
350	C₄⋊C₄	—	172	2	no	—
351	C₂²⋊C₄	—	86	2	no	—
352	C₂²⋊C₄	—	86	2	no	—
353	C₂²⋊C₄	—	172	2	no	—
354	C₂²⋊C₄	—	172	2	no	—
355	C₂²⋊C₄	—	172	2	no	—
356	C₂²⋊C₄	—	172	2	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	4	1	no	—
359	C₄²	—	43	2	no	—
360	C₄²	—	43	2	no	—
361	C₄²	—	86	2	no	—
362	C₄²	—	86	1	no	—
363	C₄²	—	86	1	no	—
364	C₄²	—	86	1	no	—
365	C₄²	—	86	1	no	—
366	C₄²	—	86	1	no	—
367	C₄²	—	86	1	no	—
368	C₄²	—	172	1	no	—
369	C₄²	#10621898	1	1	yes	characteristic
370	C₄²	#10621898	1	1	yes	characteristic
371	C₄²	D₄×D₄₃	1	1	yes	characteristic
372	C₄²	Q₈×D₄₃	1	1	yes	characteristic
373	C₂³	—	86	2	no	—
374	C₂³	—	172	1	no	—
375	C₂³	—	172	1	no	—
376	C₂³	—	172	1	no	—
377	C₂³	—	172	1	no	—
378	C₂³	—	172	1	no	—
379	C₂³	—	172	1	no	—
380	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
381	D₄	—	86	2	no	—
382	D₄	—	86	2	no	—
383	D₄	—	172	1	no	—
384	D₄	—	172	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	43	2	no	—
394	C₂×C₄	—	43	2	no	—
395	C₂×C₄	—	43	2	no	—
396	C₂×C₄	—	86	1	no	—
397	C₂×C₄	—	86	1	no	—
398	C₂×C₄	—	86	1	no	—
399	C₂×C₄	—	86	1	no	—
400	C₂×C₄	—	86	1	no	—
401	C₂×C₄	—	86	1	no	—
402	C₂×C₄	—	86	1	no	—
403	C₂×C₄	—	86	1	no	—
404	C₂×C₄	—	86	1	no	—
405	C₂×C₄	—	86	2	no	—
406	C₂×C₄	—	172	1	no	—
407	C₂×C₄	—	172	1	no	—
408	C₂×C₄	—	172	2	no	—
409	C₂×C₄	—	172	2	no	—
410	C₂×C₄	—	172	2	no	—
411	C₂×C₄	—	172	2	no	—
412	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
413	C₂×C₄	#13063282	1	1	yes	characteristic
414	C₂×C₄	#13063298	1	1	yes	characteristic
415	C₂×C₄	#13063298	1	1	yes	characteristic
416	C₂×C₄	#13063303	1	1	yes	characteristic
417	C₂×C₄	#13063303	1	1	yes	characteristic
418	C₂×C₄	#13063331	1	1	yes	characteristic
419	C₂×C₄	#13063331	1	1	yes	characteristic
420	C₂×C₄	#13063333	1	1	yes	characteristic
421	C₂×C₄	#13063333	1	1	yes	characteristic
422	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
423	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
424	C₂×C₄	#13063352	1	1	yes	characteristic
425	C₂×C₄	#13063357	1	1	yes	characteristic
426	C₈	—	4	2	no	—
427	C₈	—	8	1	no	—
428	C₈	—	344	1	no	—
429	C₈	—	172	2	no	—
430	C₂²	—	344	1	no	—
431	C₂²	—	344	1	no	—
432	C₂²	—	344	1	no	—
433	C₂²	—	344	1	no	—
434	C₂²	—	172	2	no	—
435	C₂²	—	172	2	no	—
436	C₂²	—	172	2	no	—
437	C₂²	#14582758	1	1	yes	characteristic
438	C₂²	#14582864	1	1	yes	characteristic
439	C₂²	#14582864	1	1	yes	characteristic
440	C₂²	#102×D₄₃	1	1	yes	characteristic
441	C₂²	#14582899	1	1	yes	characteristic
442	C₂²	#104×D₄₃	1	1	yes	characteristic
443	C₂²	#14582914	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	1	no	—
448	C₄	—	86	2	no	—
449	C₄	—	86	2	no	—
450	C₄	—	86	2	no	—
451	C₄	—	172	2	no	—
452	C₄	—	172	1	no	—
453	C₄	#14582924	1	1	yes	characteristic
454	C₄	#14582924	1	1	yes	characteristic
455	C₄	#14582958	1	1	yes	characteristic
456	C₄	#14582961	1	1	yes	characteristic
457	C₄	#14583093	1	1	yes	characteristic
458	C₄	#14583103	1	1	yes	characteristic
459	C₄	#14583178	1	1	yes	characteristic
460	C₄	#14583188	1	1	yes	characteristic
461	C₂	—	344	2	no	—
462	C₂	#19132992	1	1	yes	characteristic
463	C₂	#19133007	1	1	yes	characteristic
464	C₂	#19133044	1	1	yes	characteristic
465	C₂	#19133059	1	1	yes	characteristic
466	C₂	#19134578	1	1	yes	characteristic
467	C₂	#19134594	1	1	yes	characteristic
468	C₂	#19134614	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1279	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₁₇₂	C₂×C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1279	D₄₃
hypocenter	C₄₃	#8567
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. #19134746	C₂	semidirect
3. C₄×Dic₄₃⋊C₈	C₂	semidirect
6. #19132436	C₂	semidirect
7. C₄₃×#1279	C₂	semidirect
233. #1279	D₄₃	semidirect
263. C₄₃	#8567	semidirect

Maximal subgroups

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

subgroup	index
#19137056	2
#19134746	2
C₄×Dic₄₃⋊C₈	2
C₂×#14582628	2
C₂×#14582626	2
#19132436	2
C₄₃×#1279	2
#8567	43