Subgroups — #24987596

Order 11008.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143290	C₂	1	1	yes	maximal, characteristic
2	#19134374	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133086	C₂	1	1	yes	maximal, characteristic
5	#19132483	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132481	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1501	C₂	1	1	yes	maximal, characteristic
8	C₂×#13063332	C₄	1	1	yes	characteristic, complemented
9	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	#14582971	—	2	1	no	—
11	#14582971	—	2	1	no	—
12	D₄×C₄₃⋊C₈	—	2	1	no	—
13	D₄×C₄₃⋊C₈	—	2	1	no	—
14	#14582926	C₄	1	1	yes	characteristic, complemented
15	#14582866	C₄	1	1	yes	characteristic, complemented
16	#14582863	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
18	#14582855	C₄	1	1	yes	characteristic, complemented
19	C₂×#13063235	—	2	1	no	—
20	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
21	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
22	#14582654	—	2	1	no	—
23	#14582653	—	2	1	no	—
24	#14582636	C₄	1	2	yes	complemented
25	#14582633	C₄	1	2	yes	complemented
26	C₄₃×#525	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#328	C₄	1	2	yes	complemented
30	C₄₃×#327	C₄	1	2	yes	complemented
31	#13063332	—	4	2	no	—
32	C₂×#10621877	—	2	1	no	—
33	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
34	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	C₂²×C₄₃⋊C₈	—	2	1	no	—
37	C₂²×C₄₃⋊C₈	—	4	2	no	—
38	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
41	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
42	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
43	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
44	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
45	C₂×C₄×Dic₄₃	—	2	1	no	—
46	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
47	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
48	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
49	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
50	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
51	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
52	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
53	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
54	#13063236	—	2	1	no	—
55	#13063235	—	4	2	no	—
56	C₄×C₄₃⋊C₈	—	2	1	no	—
57	C₄×C₄₃⋊C₈	—	4	2	no	—
58	C₄₃⋊#95	C₂×C₄	1	2	yes	—
59	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₄₃	—	2	1	no	—
62	#123×C₄₃	—	2	1	no	—
63	C₂²⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
64	C₂²⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
65	#121×C₄₃	C₂×C₄	1	1	yes	characteristic
66	#121×C₄₃	C₂×C₄	1	1	yes	characteristic
67	#120×C₄₃	—	2	1	no	—
68	C₄×D₄×C₄₃	—	2	1	no	—
69	C₄×D₄×C₄₃	—	2	1	no	—
70	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄²×C₄₃	—	2	1	no	—
73	C₂²⋊C₈×C₄₃	—	2	1	no	—
74	C₂²⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
75	#95×C₄₃	C₂×C₄	1	2	yes	—
76	C₂⁴×C₄₃	#41	1	1	yes	characteristic
77	#41×C₄₃	—	4	1	no	—
78	#41×C₄₃	—	4	1	no	—
79	C₂×Q₈×C₄₃	C₄²	1	1	yes	characteristic
80	C₂×D₄×C₄₃	—	2	1	no	—
81	C₂×D₄×C₄₃	—	2	1	no	—
82	C₂×D₄×C₄₃	—	2	1	no	—
83	C₂×D₄×C₄₃	C₄²	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	—	2	2	no	—
86	C₂²×C₄×C₄₃	—	4	1	no	—
87	C₂²×C₄×C₄₃	—	4	1	no	—
88	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
94	C₂²×Dic₄₃	—	2	2	no	—
95	C₂×C₈×C₄₃	—	2	2	no	—
96	C₂×C₈×C₄₃	—	4	1	no	—
97	C₂×C₈×C₄₃	—	4	1	no	—
98	C₄⋊C₄×C₄₃	—	2	1	no	—
99	C₄⋊C₄×C₄₃	—	2	1	no	—
100	C₄⋊C₄×C₄₃	C₄²	1	1	yes	characteristic
101	C₄⋊C₄×C₄₃	C₄²	1	1	yes	characteristic
102	C₂²⋊C₄×C₄₃	—	2	4	no	—
103	C₂²⋊C₄×C₄₃	—	2	1	no	—
104	C₂²⋊C₄×C₄₃	—	2	1	no	—
105	C₂²⋊C₄×C₄₃	—	2	1	no	—
106	C₂²⋊C₄×C₄₃	—	2	1	no	—
107	C₂²⋊C₄×C₄₃	—	2	1	no	—
108	C₄²×C₄₃	—	2	1	no	—
109	C₄²×C₄₃	—	4	1	no	—
110	C₄²×C₄₃	—	4	1	no	—
111	C₂²⋊Dic₄₃	—	4	2	no	—
112	C₄×Dic₄₃	—	4	1	no	—
113	C₄×Dic₄₃	—	4	1	no	—
114	#10621877	—	4	2	no	—
115	#10621877	—	4	1	no	—
116	#10621877	—	4	1	no	—
117	C₂×C₄₃⋊C₈	—	2	2	no	—
118	C₂×C₄₃⋊C₈	—	2	2	no	—
119	C₂×C₄₃⋊C₈	—	2	2	no	—
120	C₂×C₄₃⋊C₈	—	2	1	no	—
121	C₂×C₄₃⋊C₈	—	2	1	no	—
122	C₂×C₄₃⋊C₈	—	2	2	no	—
123	C₂×C₄₃⋊C₈	—	4	1	no	—
124	C₂×C₄₃⋊C₈	—	4	1	no	—
125	C₂×C₄₃⋊C₈	—	4	1	no	—
126	C₂×C₄₃⋊C₈	—	4	2	no	—
127	C₂×C₄₃⋊C₈	—	4	1	no	—
128	C₂×C₄₃⋊C₈	—	4	1	no	—
129	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₄₃	—	2	2	no	—
134	C₂³×C₄₃	—	2	2	no	—
135	C₂³×C₄₃	—	2	1	no	—
136	C₂³×C₄₃	—	4	1	no	—
137	C₂³×C₄₃	#117	1	1	yes	characteristic
138	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
139	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
140	Q₈×C₄₃	—	4	1	no	—
141	D₄×C₄₃	—	4	1	no	—
142	D₄×C₄₃	—	4	2	no	—
143	D₄×C₄₃	—	4	2	no	—
144	D₄×C₄₃	—	4	2	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	2	1	no	—
151	C₂×C₄×C₄₃	—	2	4	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	4	1	no	—
156	C₂×C₄×C₄₃	—	4	1	no	—
157	C₂×C₄×C₄₃	—	4	1	no	—
158	C₂×C₄×C₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	—	4	2	no	—
160	C₂×C₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
166	C₂×Dic₄₃	—	4	2	no	—
167	C₂×Dic₄₃	—	4	2	no	—
168	C₂×Dic₄₃	—	4	2	no	—
169	C₈×C₄₃	—	4	2	no	—
170	C₄₃⋊C₈	—	2	1	no	—
171	C₄₃⋊C₈	—	2	1	no	—
172	C₄₃⋊C₈	—	2	1	no	—
173	C₄₃⋊C₈	—	4	2	no	—
174	C₄₃⋊C₈	—	4	1	no	—
175	C₄₃⋊C₈	—	4	1	no	—
176	C₄₃⋊C₈	#99	1	2	yes	—
177	#8240	—	43	1	no	maximal, Sylow
178	C₂²×C₄₃	—	2	1	no	—
179	C₂²×C₄₃	—	2	1	no	—
180	C₂²×C₄₃	—	2	1	no	—
181	C₂²×C₄₃	—	2	1	no	—
182	C₂²×C₄₃	—	2	1	no	—
183	C₂²×C₄₃	—	2	1	no	—
184	C₂²×C₄₃	—	2	1	no	—
185	C₂²×C₄₃	—	4	4	no	—
186	C₂²×C₄₃	—	4	1	no	—
187	C₂²×C₄₃	—	4	1	no	—
188	C₂²×C₄₃	—	4	1	no	—
189	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₄₃	#443	1	2	yes	—
191	C₂²×C₄₃	#444	1	2	yes	—
192	C₄×C₄₃	—	2	1	no	—
193	C₄×C₄₃	—	2	1	no	—
194	C₄×C₄₃	—	2	1	no	—
195	C₄×C₄₃	—	4	4	no	—
196	C₄×C₄₃	—	4	1	no	—
197	C₄×C₄₃	—	4	1	no	—
198	C₄×C₄₃	—	4	1	no	—
199	C₄×C₄₃	C₂×#99	1	1	yes	characteristic
200	C₄×C₄₃	#410	1	1	yes	characteristic
201	Dic₄₃	—	8	2	no	—
202	#2929	—	43	1	no	—
203	#1752	—	43	1	no	—
204	C₈×C₂²⋊C₄	—	43	1	no	—
205	#1501	—	43	1	no	—
206	#1501	D₄₃	1	1	yes	characteristic
207	#1298	—	43	1	no	—
208	#1297	—	43	1	no	—
209	C₂×C₄₃	—	2	2	no	—
210	C₂×C₄₃	—	2	2	no	—
211	C₂×C₄₃	—	4	1	no	—
212	C₂×C₄₃	—	8	1	no	—
213	C₂×C₄₃	C₄×#99	1	1	yes	characteristic
214	C₂×C₄₃	#1764	1	1	yes	characteristic
215	C₂×C₄₃	#1765	1	1	yes	characteristic
216	C₂×#131	—	43	1	no	—
217	C₂³×C₈	—	43	1	no	—
218	#525	C₂×D₄₃	1	1	yes	characteristic
219	#435	—	86	1	no	—
220	#435	—	86	1	no	—
221	C₈×D₄	—	86	1	no	—
222	C₈×D₄	—	86	1	no	—
223	#424	—	43	1	no	—
224	#408	—	43	1	no	—
225	#407	—	43	1	no	—
226	C₂×C₂²⋊C₈	—	43	1	no	—
227	C₂×C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
228	#405	—	43	1	no	—
229	C₂×#97	—	86	1	no	—
230	C₂×C₄×C₈	—	86	1	no	—
231	C₄×C₂²⋊C₄	—	43	1	no	—
232	C₄×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
233	#336	—	86	1	no	—
234	#336	—	86	1	no	—
235	#328	—	43	2	no	—
236	#328	Dic₄₃	1	2	yes	complemented
237	#327	—	43	2	no	—
238	#327	Dic₄₃	1	2	yes	complemented
239	C₄₃	#8240	1	1	yes	characteristic, complemented, Sylow
240	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
241	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
242	#131	—	172	2	no	—
243	C₂×M₁₆	—	43	1	no	—
244	C₂×M₁₆	—	43	1	no	—
245	C₂×M₁₆	—	86	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	43	1	no	—
248	C₂²×C₈	—	43	1	no	—
249	C₂²×C₈	—	43	1	no	—
250	C₂²×C₈	—	43	1	no	—
251	C₂²×C₈	—	43	1	no	—
252	C₂²×C₈	—	43	1	no	—
253	C₂²×C₈	—	86	1	no	—
254	C₂²×C₈	—	86	1	no	—
255	C₂²×C₈	—	172	2	no	—
256	#123	—	2	1	no	—
257	C₂²⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
258	C₂²⋊Q₈	C₂×Dic₄₃	1	1	yes	characteristic
259	#121	C₄×D₄₃	1	1	yes	characteristic
260	#121	C₂×Dic₄₃	1	1	yes	characteristic
261	#120	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	#117	C₄×D₄₃	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	86	1	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	86	1	no	—
269	C₄⋊C₈	—	86	1	no	—
270	C₄⋊C₈	—	86	1	no	—
271	C₂²⋊C₈	—	2	1	no	—
272	C₂²⋊C₈	—	43	2	no	—
273	C₂²⋊C₈	—	86	1	no	—
274	C₂²⋊C₈	—	86	1	no	—
275	C₂²⋊C₈	—	86	1	no	—
276	C₂²⋊C₈	—	86	1	no	—
277	C₂²⋊C₈	—	86	1	no	—
278	C₂²⋊C₈	C₂×Dic₄₃	1	2	yes	—
279	#97	—	86	1	no	—
280	#97	—	172	2	no	—
281	C₄×C₈	—	86	1	no	—
282	C₄×C₈	—	172	2	no	—
283	#95	—	43	2	no	—
284	#95	C₂×Dic₄₃	1	2	yes	—
285	C₂⁴	#10621900	1	1	yes	characteristic
286	#41	—	4	1	no	—
287	#41	—	4	1	no	—
288	C₂×Q₈	C₄×Dic₄₃	1	1	yes	characteristic
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	C₄×Dic₄₃	1	1	yes	characteristic
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	86	2	no	—
298	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
301	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
302	C₂²×C₄	#10621900	1	1	yes	characteristic
303	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
304	M₁₆	—	172	2	no	—
305	M₁₆	—	172	1	no	—
306	M₁₆	—	172	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	43	1	no	—
311	C₂×C₈	—	43	1	no	—
312	C₂×C₈	—	43	1	no	—
313	C₂×C₈	—	43	1	no	—
314	C₂×C₈	—	86	2	no	—
315	C₂×C₈	—	86	2	no	—
316	C₂×C₈	—	86	2	no	—
317	C₂×C₈	—	86	1	no	—
318	C₂×C₈	—	86	1	no	—
319	C₂×C₈	—	86	2	no	—
320	C₂×C₈	—	172	1	no	—
321	C₂×C₈	—	172	1	no	—
322	C₂×C₈	—	172	1	no	—
323	C₂×C₈	—	172	2	no	—
324	C₂×C₈	—	172	1	no	—
325	C₂×C₈	—	172	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	C₄×Dic₄₃	1	1	yes	characteristic
329	C₄⋊C₄	C₄×Dic₄₃	1	1	yes	characteristic
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	172	2	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	4	1	no	—
339	C₄²	—	4	1	no	—
340	C₄²	—	172	1	no	—
341	C₄²	—	172	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	#13063281	1	1	yes	characteristic
347	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
348	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	172	2	no	—
372	C₂×C₄	—	172	2	no	—
373	C₂×C₄	—	172	2	no	—
374	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
375	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
376	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
377	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
378	C₈	—	4	2	no	—
379	C₈	—	43	2	no	—
380	C₈	—	86	1	no	—
381	C₈	—	86	1	no	—
382	C₈	—	86	1	no	—
383	C₈	—	172	2	no	—
384	C₈	—	172	1	no	—
385	C₈	—	172	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
398	C₂²	#14583013	1	2	yes	—
399	C₂²	#14583021	1	2	yes	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	1	no	—
407	C₄	—	344	2	no	—
408	C₄	#99×D₄₃	1	1	yes	characteristic
409	C₄	#14582871	1	1	yes	characteristic
410	C₂	—	2	2	no	—
411	C₂	—	2	2	no	—
412	C₂	—	4	1	no	—
413	C₂	—	8	1	no	—
414	C₂	#99×Dic₄₃	1	1	yes	characteristic
415	C₂	#19134433	1	1	yes	characteristic
416	C₂	#19134442	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄₃×#1501	C₂
socle	C₂²×C₄₃	C₄×C₂²⋊C₄
prime radical	C₄₃×#525	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	#1501	D₄₃
hypocenter	C₄₃	#8240
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1501

Complements

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

N	H ≅ G/N	type
2. #19134374	C₂	semidirect
3. C₂²⋊C₄×C₄₃⋊C₈	C₂	semidirect
5. #19132483	C₂	semidirect
6. #19132481	C₂	semidirect
8. C₂×#13063332	C₄	semidirect
14. #14582926	C₄	semidirect
15. #14582866	C₄	semidirect
18. #14582855	C₄	semidirect
24. #14582636	C₄	semidirect
25. #14582633	C₄	semidirect
29. C₄₃×#328	C₄	semidirect
30. C₄₃×#327	C₄	semidirect
236. #328	Dic₄₃	semidirect
238. #327	Dic₄₃	semidirect
239. C₄₃	#8240	semidirect

Maximal subgroups

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

subgroup	index
#19143290	2
#19134374	2
C₂²⋊C₄×C₄₃⋊C₈	2
#19133086	2
#19132483	2
#19132481	2
C₄₃×#1501	2
#8240	43