Subgroups — #24997804

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583101	C₂	1	1	yes	maximal, characteristic
2	#19139549	C₂	1	1	yes	maximal, characteristic
3	#19135548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582645	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582628	C₂	1	1	yes	maximal, characteristic
6	#19132435	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621884	—	2	1	no	—
9	C₂×#13063301	—	2	2	no	—
10	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
11	#14583101	—	2	2	no	—
12	#14583101	—	2	2	no	—
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#13063249	—	2	1	no	—
16	#14582834	—	2	2	no	—
17	#14582800	—	2	1	no	—
18	#14582768	—	2	1	no	—
19	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
20	#14582661	—	2	2	no	—
21	#14582645	—	2	2	no	—
22	#14582628	—	2	2	no	—
23	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#498	—	2	2	no	—
26	C₄₃×#498	—	2	2	no	—
27	C₂×#106×C₄₃	—	2	2	no	—
28	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₃	—	2	1	no	—
31	C₂×#10621884	—	2	4	no	—
32	C₂×#10621884	—	4	2	no	—
33	C₂×#10621884	—	4	2	no	—
34	C₂²×C₄₃⋊C₈	—	2	1	no	—
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	#13063301	—	4	4	no	—
37	#13063301	—	4	4	no	—
38	C₄×D₁₇₂	—	2	1	no	—
39	C₄×D₁₇₂	—	2	1	no	—
40	C₄×D₁₇₂	—	2	1	no	—
41	C₄×D₁₇₂	—	2	1	no	—
42	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
43	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
44	C₂×Dic₄₃⋊C₄	—	2	4	no	—
45	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
46	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
47	C₂×C₄×Dic₄₃	—	2	1	no	—
48	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
49	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
50	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
51	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
52	#13063249	—	2	4	no	—
53	C₄₃⋊#95	—	2	1	no	—
54	C₂²×Q₈×C₄₃	—	2	1	no	—
55	C₂²×Q₈×C₄₃	—	2	1	no	—
56	C₂²×C₈×C₄₃	—	2	1	no	—
57	C₄⋊Q₈×C₄₃	—	2	1	no	—
58	C₄⋊Q₈×C₄₃	—	2	1	no	—
59	C₄⋊Q₈×C₄₃	—	2	1	no	—
60	C₄⋊Q₈×C₄₃	—	2	1	no	—
61	C₄⋊Q₈×C₄₃	—	2	1	no	—
62	C₄⋊Q₈×C₄₃	—	2	1	no	—
63	C₄⋊Q₈×C₄₃	—	2	1	no	—
64	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	#106×C₄₃	—	2	8	no	—
71	C₄×C₈×C₄₃	—	2	1	no	—
72	C₄×C₈×C₄₃	D₄	1	2	yes	—
73	C₂³×D₄₃	—	2	1	no	—
74	C₂×Q₈×C₄₃	—	2	2	no	—
75	C₂×Q₈×C₄₃	—	4	1	no	—
76	C₂×Q₈×C₄₃	—	4	1	no	—
77	C₂×Q₈×C₄₃	—	4	1	no	—
78	C₂×Q₈×C₄₃	—	4	2	no	—
79	C₂×Q₈×C₄₃	—	4	2	no	—
80	C₂×Q₈×C₄₃	—	4	1	no	—
81	C₂×Q₈×C₄₃	—	4	1	no	—
82	C₂×Q₈×C₄₃	—	4	1	no	—
83	C₂×Q₈×C₄₃	—	4	1	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	—	4	1	no	—
86	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×Dic₄₃	—	2	2	no	—
90	C₂²×Dic₄₃	—	2	1	no	—
91	C₂×D₁₇₂	—	2	1	no	—
92	C₂×D₁₇₂	—	2	1	no	—
93	C₂×D₁₇₂	—	2	1	no	—
94	C₂×D₁₇₂	—	2	1	no	—
95	C₂×D₁₇₂	—	2	1	no	—
96	C₂×D₁₇₂	SD₁₆	1	2	yes	—
97	C₂×C₄×D₄₃	—	4	1	no	—
98	C₂×C₄×D₄₃	—	4	1	no	—
99	C₂×C₄×D₄₃	—	4	2	no	—
100	C₂×C₄×D₄₃	—	4	2	no	—
101	C₂×C₈×C₄₃	—	2	4	no	—
102	C₂×C₈×C₄₃	—	2	2	no	—
103	C₄⋊C₄×C₄₃	—	2	2	no	—
104	C₄⋊C₄×C₄₃	—	2	2	no	—
105	C₄⋊C₄×C₄₃	—	2	2	no	—
106	C₄⋊C₄×C₄₃	—	2	2	no	—
107	C₄⋊C₄×C₄₃	—	4	1	no	—
108	C₄⋊C₄×C₄₃	—	4	1	no	—
109	C₄⋊C₄×C₄₃	—	4	1	no	—
110	C₄⋊C₄×C₄₃	—	4	1	no	—
111	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₄₃	#41	1	1	yes	characteristic
115	#10621884	—	4	8	no	—
116	(C₂×D₄₃)⋊C₄	—	4	8	no	—
117	(C₂×D₄₃)⋊C₄	—	4	1	no	—
118	(C₂×D₄₃)⋊C₄	—	4	1	no	—
119	C₄⋊Dic₄₃	—	2	2	no	—
120	C₄⋊Dic₄₃	—	2	1	no	—
121	C₄⋊Dic₄₃	—	2	1	no	—
122	C₄⋊Dic₄₃	SD₁₆	1	4	yes	complemented
123	Dic₄₃⋊C₄	—	4	8	no	—
124	C₄×Dic₄₃	—	4	1	no	—
125	C₄×Dic₄₃	—	4	1	no	—
126	C₂×C₄₃⋊C₈	—	2	2	no	—
127	C₂×C₄₃⋊C₈	—	4	1	no	—
128	C₂×C₄₃⋊C₈	—	4	1	no	—
129	C₂×C₄₃⋊C₈	—	4	1	no	—
130	C₂×C₄₃⋊C₈	—	4	2	no	—
131	C₂³×C₄₃	#120	1	1	yes	characteristic
132	C₂²×D₄₃	—	2	2	no	—
133	C₂²×D₄₃	—	4	1	no	—
134	C₂²×D₄₃	—	4	1	no	—
135	C₂²×D₄₃	—	4	2	no	—
136	C₂²×D₄₃	—	4	2	no	—
137	Q₈×C₄₃	—	4	2	no	—
138	Q₈×C₄₃	—	4	2	no	—
139	Q₈×C₄₃	—	8	2	no	—
140	Q₈×C₄₃	—	8	1	no	—
141	Q₈×C₄₃	—	8	1	no	—
142	Q₈×C₄₃	—	8	1	no	—
143	Q₈×C₄₃	—	8	1	no	—
144	C₂×C₄×C₄₃	—	2	2	no	—
145	C₂×C₄×C₄₃	—	4	2	no	—
146	C₂×C₄×C₄₃	—	4	2	no	—
147	C₂×C₄×C₄₃	—	4	4	no	—
148	C₂×C₄×C₄₃	—	8	1	no	—
149	C₂×C₄×C₄₃	—	8	1	no	—
150	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
151	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
152	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
153	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
154	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
155	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
158	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
159	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
162	C₂×Dic₄₃	—	2	4	no	—
163	C₂×Dic₄₃	—	4	2	no	—
164	C₂×Dic₄₃	—	4	2	no	—
165	C₂×Dic₄₃	—	4	1	no	—
166	C₂×Dic₄₃	—	4	2	no	—
167	D₁₇₂	—	2	2	no	—
168	D₁₇₂	—	2	2	no	—
169	D₁₇₂	—	4	1	no	—
170	D₁₇₂	—	4	1	no	—
171	C₄×D₄₃	—	8	2	no	—
172	C₄×D₄₃	—	8	1	no	—
173	C₄×D₄₃	—	8	1	no	—
174	C₈×C₄₃	—	2	4	no	—
175	C₄₃⋊C₈	—	4	2	no	—
176	C₄₃⋊C₈	—	8	1	no	—
177	#10068	—	43	1	no	maximal, Sylow
178	C₂²×C₄₃	#392	1	1	yes	characteristic
179	C₂²×C₄₃	#448	1	1	yes	characteristic
180	C₂²×C₄₃	#449	1	1	yes	characteristic
181	C₂²×C₄₃	#450	1	2	yes	—
182	C₂²×C₄₃	#456	1	2	yes	—
183	C₂×D₄₃	—	4	4	no	—
184	C₂×D₄₃	—	4	2	no	—
185	C₂×D₄₃	—	8	2	no	—
186	C₂×D₄₃	—	8	1	no	—
187	C₂×D₄₃	—	8	1	no	—
188	C₄×C₄₃	—	2	1	no	—
189	C₄×C₄₃	—	2	1	no	—
190	C₄×C₄₃	—	8	2	no	—
191	C₄×C₄₃	—	8	2	no	—
192	C₄×C₄₃	#450	1	1	yes	characteristic
193	C₄×C₄₃	#452	1	1	yes	characteristic
194	C₄×C₄₃	#460	1	2	yes	—
195	C₄×C₄₃	#465	1	1	yes	characteristic
196	C₄×C₄₃	#468	1	1	yes	characteristic
197	C₄×C₄₃	#492	1	1	yes	characteristic
198	C₄×C₄₃	#496	1	1	yes	characteristic
199	Dic₄₃	—	4	4	no	—
200	Dic₄₃	—	8	1	no	—
201	C₂×#498	D₄₃	1	1	yes	characteristic, complemented
202	C₂×#461	—	43	1	no	—
203	#2542	—	43	1	no	—
204	#1988	—	43	1	no	—
205	C₂×#332	—	43	1	no	—
206	C₂×D₄⋊C₈	—	43	1	no	—
207	#1279	—	43	1	no	—
208	C₂×C₄₃	#1651	1	2	yes	—
209	C₂×C₄₃	#1654	1	2	yes	—
210	C₂×C₄₃	#2000	1	1	yes	characteristic
211	C₂×C₄₃	#2005	1	1	yes	characteristic
212	C₂×C₄₃	#2014	1	1	yes	characteristic
213	D₄₃	—	8	2	no	—
214	C₂²×SD₁₆	—	86	1	no	—
215	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	—	86	2	no	—
218	C₂×C₄×D₄	—	43	1	no	—
219	#498	—	2	2	no	—
220	#498	—	2	2	no	—
221	#461	—	86	2	no	—
222	#461	—	86	2	no	—
223	C₂×#106	—	2	2	no	—
224	C₂×C₄⋊C₈	—	43	1	no	—
225	C₂×C₄⋊C₈	—	43	1	no	—
226	C₂×#103	—	86	1	no	—
227	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
228	#399	—	86	2	no	—
229	#390	—	86	1	no	—
230	#384	—	86	1	no	—
231	C₄×C₄⋊C₄	—	43	1	no	—
232	#340	—	86	2	no	—
233	#332	—	86	2	no	—
234	D₄⋊C₈	—	86	2	no	—
235	C₄₃	#10068	1	1	yes	characteristic, complemented, Sylow
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	—	2	1	no	—
238	C₂²×D₄	—	43	1	no	—
239	C₂³×C₄	—	86	1	no	—
240	C₂×SD₁₆	—	86	4	no	—
241	C₂×SD₁₆	—	172	2	no	—
242	C₂×SD₁₆	—	172	2	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	86	1	no	—
245	C₂²×C₈	—	86	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	C₂²⋊D₄₃	1	2	yes	—
254	C₂²⋊Q₈	—	172	4	no	—
255	C₂²⋊Q₈	—	172	4	no	—
256	C₄×D₄	—	86	1	no	—
257	C₄×D₄	—	86	1	no	—
258	C₄×D₄	—	86	1	no	—
259	C₄×D₄	—	86	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	43	2	no	—
264	C₂×C₄⋊C₄	—	43	1	no	—
265	C₂×C₄⋊C₄	—	86	4	no	—
266	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
267	C₂×C₂²⋊C₄	—	86	4	no	—
268	C₂×C₂²⋊C₄	—	86	1	no	—
269	C₂×C₄²	—	86	1	no	—
270	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
271	#106	—	2	8	no	—
272	C₄⋊C₈	—	43	2	no	—
273	C₄⋊C₈	—	86	1	no	—
274	C₄⋊C₈	—	86	1	no	—
275	C₄⋊C₈	—	86	1	no	—
276	#103	—	86	4	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
279	#95	—	86	1	no	—
280	C₂⁴	—	86	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	—	4	1	no	—
284	C₂×Q₈	—	4	1	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×D₄	—	43	2	no	—
292	C₂×D₄	—	86	1	no	—
293	C₂×D₄	—	86	1	no	—
294	C₂×D₄	—	86	1	no	—
295	C₂×D₄	—	86	1	no	—
296	C₂×D₄	—	86	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	86	2	no	—
300	C₂²×C₄	—	86	1	no	—
301	C₂²×C₄	—	172	1	no	—
302	C₂²×C₄	—	172	1	no	—
303	C₂²×C₄	—	172	2	no	—
304	C₂²×C₄	—	172	2	no	—
305	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
306	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
308	SD₁₆	—	172	8	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	86	2	no	—
312	C₂×C₈	—	172	1	no	—
313	C₂×C₈	—	172	2	no	—
314	C₂×C₈	—	172	1	no	—
315	C₂×C₈	—	172	1	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	43	4	no	—
325	C₄⋊C₄	—	86	2	no	—
326	C₄⋊C₄	—	86	1	no	—
327	C₄⋊C₄	—	86	1	no	—
328	C₄⋊C₄	—	172	8	no	—
329	C₂²⋊C₄	—	172	8	no	—
330	C₂²⋊C₄	—	172	1	no	—
331	C₂²⋊C₄	—	172	1	no	—
332	C₄²	—	172	1	no	—
333	C₄²	—	172	1	no	—
334	C₄²	D₄×D₄₃	1	1	yes	characteristic
335	C₄²	#10621900	1	1	yes	characteristic
336	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
337	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
338	C₂³	—	86	2	no	—
339	C₂³	—	172	1	no	—
340	C₂³	—	172	2	no	—
341	C₂³	—	172	1	no	—
342	C₂³	—	172	2	no	—
343	C₂³	#13063293	1	1	yes	characteristic
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	8	2	no	—
347	Q₈	—	8	1	no	—
348	Q₈	—	8	1	no	—
349	Q₈	—	8	1	no	—
350	Q₈	—	8	1	no	—
351	D₄	—	86	2	no	—
352	D₄	—	86	2	no	—
353	D₄	—	172	1	no	—
354	D₄	—	172	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	8	1	no	—
360	C₂×C₄	—	8	1	no	—
361	C₂×C₄	—	86	4	no	—
362	C₂×C₄	—	344	2	no	—
363	C₂×C₄	—	344	1	no	—
364	C₂×C₄	—	344	1	no	—
365	C₂×C₄	—	172	2	no	—
366	C₂×C₄	—	172	1	no	—
367	C₂×C₄	—	172	2	no	—
368	C₂×C₄	—	172	2	no	—
369	C₂×C₄	#13063293	1	1	yes	characteristic
370	C₂×C₄	#13063294	1	1	yes	characteristic
371	C₂×C₄	#13063296	1	1	yes	characteristic
372	C₂×C₄	#13063297	1	1	yes	characteristic
373	C₂×C₄	#13063297	1	1	yes	characteristic
374	C₂×C₄	#13063321	1	1	yes	characteristic
375	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
376	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
377	C₂×C₄	#13063346	1	1	yes	characteristic
378	C₂×C₄	#13063352	1	1	yes	characteristic
379	C₂×C₄	#13063352	1	2	yes	—
380	C₂×C₄	#13063354	1	1	yes	characteristic
381	C₈	—	2	4	no	—
382	C₈	—	344	1	no	—
383	C₈	—	172	2	no	—
384	C₂²	—	344	1	no	—
385	C₂²	—	344	2	no	—
386	C₂²	—	344	1	no	—
387	C₂²	—	172	2	no	—
388	C₂²	—	172	4	no	—
389	C₂²	#14582807	1	1	yes	characteristic
390	C₂²	#14583036	1	1	yes	characteristic
391	C₂²	#14583043	1	1	yes	characteristic
392	C₂²	#14583048	1	2	yes	—
393	C₂²	#14583081	1	2	yes	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	344	1	no	—
399	C₄	—	172	4	no	—
400	C₄	#14583048	1	1	yes	characteristic
401	C₄	#14583058	1	1	yes	characteristic
402	C₄	#14583097	1	2	yes	—
403	C₄	#14583125	1	1	yes	characteristic
404	C₄	#14583142	1	1	yes	characteristic
405	C₄	#14583270	1	1	yes	characteristic
406	C₄	#14583285	1	1	yes	characteristic
407	C₂	—	344	2	no	—
408	C₂	#19133855	1	2	yes	—
409	C₂	#19133876	1	2	yes	—
410	C₂	#19135595	1	1	yes	characteristic
411	C₂	#19135631	1	1	yes	characteristic
412	C₂	#19135681	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063293
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#498	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂²×D₁₇₂	D₄
hypercenter	C₂×#498	D₄₃
hypocenter	C₄₃	#10068
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#498

Complements

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

N	H ≅ G/N	type
3. #19135548	C₂	semidirect
4. C₂×#14582645	C₂	semidirect
6. #19132435	C₂	semidirect
7. C₂×C₄₃×#498	C₂	semidirect
122. C₄⋊Dic₄₃	SD₁₆	semidirect
201. C₂×#498	D₄₃	semidirect
235. C₄₃	#10068	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583101	2
#19139549	2
#19135548	2
C₂×#14582645	2
C₂×#14582628	2
#19132435	2
C₂×C₄₃×#498	2
#10068	43