Subgroups — #25107169

Order 11008.

830 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137002	C₂	1	1	yes	maximal, characteristic
2	#19137002	C₂	1	1	yes	maximal, characteristic
3	#19135359	C₂	1	2	yes	maximal, complemented
4	#19135354	C₂	1	2	yes	maximal, complemented
5	#19134796	C₂	1	4	yes	maximal
6	#19134763	C₂	1	2	yes	maximal, complemented
7	#19134729	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₃×#432	C₂	1	1	yes	maximal, characteristic
9	C₂×#13063284	—	2	1	no	—
10	C₂×#13063284	C₂²	1	2	yes	—
11	C₂×#13063259	C₂²	1	4	yes	—
12	C₂×#13063257	C₂²	1	4	yes	—
13	#14582769	C₂²	1	1	yes	characteristic
14	#14582769	C₂²	1	1	yes	characteristic
15	#14582769	C₂²	1	1	yes	characteristic
16	#14582769	C₂²	1	1	yes	characteristic
17	#14582765	—	2	1	no	—
18	#14582765	C₂²	1	2	yes	—
19	#14582759	—	2	1	no	—
20	#14582759	—	2	1	no	—
21	#14582759	—	2	1	no	—
22	#14582759	C₂²	1	2	yes	—
23	C₄×C₄⋊Dic₄₃	—	2	1	no	—
24	C₄×C₄⋊Dic₄₃	—	2	1	no	—
25	C₄×C₄⋊Dic₄₃	—	2	1	no	—
26	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
27	#14582662	C₂²	1	4	yes	—
28	#14582662	C₂²	1	4	yes	—
29	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#432	C₄	1	8	yes	complemented
31	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
33	C₂×#97×C₄₃	C₂²	1	2	yes	—
34	#13063284	—	4	4	no	—
35	#13063284	—	4	4	no	—
36	C₂×C₄⋊Dic₄₃	—	2	1	no	—
37	C₂×C₄⋊Dic₄₃	—	2	1	no	—
38	C₂×C₄⋊Dic₄₃	—	2	1	no	—
39	C₂×C₄⋊Dic₄₃	—	2	1	no	—
40	C₂×C₄⋊Dic₄₃	—	2	1	no	—
41	C₂×C₄⋊Dic₄₃	—	2	1	no	—
42	C₂×C₄⋊Dic₄₃	—	2	1	no	—
43	C₂×C₄⋊Dic₄₃	—	2	1	no	—
44	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
45	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
47	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
48	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
49	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
50	C₂×C₄×Dic₄₃	—	2	2	no	—
51	C₂×C₄×Dic₄₃	—	2	2	no	—
52	#13063259	—	4	4	no	—
53	#13063257	—	4	4	no	—
54	C₄₃⋊#95	—	2	2	no	—
55	C₄₃⋊#95	—	2	2	no	—
56	C₄₃⋊#95	—	2	2	no	—
57	C₄₃⋊#95	—	2	2	no	—
58	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
62	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₃	Q₈	1	4	yes	—
66	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₃	C₂×C₄	1	8	yes	—
69	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	—
70	#97×C₄₃	C₂×C₄	1	8	yes	—
71	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₃	—	2	2	no	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
74	C₂²×C₄×C₄₃	—	2	2	no	—
75	C₂²×C₄×C₄₃	—	2	2	no	—
76	C₂²×C₄×C₄₃	—	4	1	no	—
77	C₂²×C₄×C₄₃	—	4	1	no	—
78	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
79	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
80	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
88	C₂²×Dic₄₃	—	2	2	no	—
89	C₂²×Dic₄₃	—	2	2	no	—
90	C₂²×Dic₄₃	—	2	2	no	—
91	C₂²×Dic₄₃	—	2	2	no	—
92	C₂×C₈×C₄₃	—	2	4	no	—
93	C₂×C₈×C₄₃	—	2	4	no	—
94	C₂×C₈×C₄₃	C₂²×C₄	1	8	yes	—
95	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
96	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
97	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
98	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
99	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
100	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
101	C₂²⋊Dic₄₃	—	4	4	no	—
102	C₂²⋊Dic₄₃	—	4	4	no	—
103	C₄⋊Dic₄₃	—	2	2	no	—
104	C₄⋊Dic₄₃	—	2	4	no	—
105	C₄⋊Dic₄₃	—	2	2	no	—
106	C₄⋊Dic₄₃	—	2	4	no	—
107	C₄⋊Dic₄₃	—	2	4	no	—
108	C₄⋊Dic₄₃	—	4	2	no	—
109	C₄⋊Dic₄₃	—	4	2	no	—
110	C₄⋊Dic₄₃	—	4	2	no	—
111	C₄⋊Dic₄₃	—	4	2	no	—
112	C₄⋊Dic₄₃	—	4	2	no	—
113	C₄⋊Dic₄₃	—	4	2	no	—
114	C₄⋊Dic₄₃	—	4	2	no	—
115	C₄⋊Dic₄₃	—	4	2	no	—
116	C₄×Dic₄₃	—	4	4	no	—
117	C₄×Dic₄₃	—	4	4	no	—
118	C₂³×C₄₃	—	2	1	no	—
119	C₂³×C₄₃	—	2	1	no	—
120	C₂³×C₄₃	—	2	1	no	—
121	C₂³×C₄₃	—	2	1	no	—
122	C₂³×C₄₃	—	2	1	no	—
123	C₂³×C₄₃	—	2	1	no	—
124	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
125	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
126	C₂×C₄×C₄₃	—	2	1	no	—
127	C₂×C₄×C₄₃	—	2	1	no	—
128	C₂×C₄×C₄₃	—	2	1	no	—
129	C₂×C₄×C₄₃	—	2	1	no	—
130	C₂×C₄×C₄₃	—	2	1	no	—
131	C₂×C₄×C₄₃	—	2	1	no	—
132	C₂×C₄×C₄₃	—	2	1	no	—
133	C₂×C₄×C₄₃	—	2	1	no	—
134	C₂×C₄×C₄₃	—	2	4	no	—
135	C₂×C₄×C₄₃	—	2	4	no	—
136	C₂×C₄×C₄₃	—	2	8	no	—
137	C₂×C₄×C₄₃	—	4	4	no	—
138	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
144	C₂×C₄×C₄₃	#137	1	2	yes	—
145	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
148	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
149	C₂×Dic₄₃	—	4	2	no	—
150	C₂×Dic₄₃	—	4	2	no	—
151	C₂×Dic₄₃	—	4	2	no	—
152	C₂×Dic₄₃	—	4	2	no	—
153	C₂×Dic₄₃	—	4	2	no	—
154	C₂×Dic₄₃	—	4	2	no	—
155	C₂×Dic₄₃	—	4	2	no	—
156	C₂×Dic₄₃	—	4	2	no	—
157	C₂×Dic₄₃	—	4	2	no	—
158	C₂×Dic₄₃	—	4	2	no	—
159	C₂×Dic₄₃	—	4	2	no	—
160	C₂×Dic₄₃	—	4	2	no	—
161	C₈×C₄₃	—	2	8	no	—
162	#21988	—	43	1	no	maximal, Sylow
163	C₂²×C₄₃	—	2	2	no	—
164	C₂²×C₄₃	—	2	2	no	—
165	C₂²×C₄₃	—	2	2	no	—
166	C₂²×C₄₃	—	4	1	no	—
167	C₂²×C₄₃	—	4	1	no	—
168	C₂²×C₄₃	—	4	1	no	—
169	C₂²×C₄₃	—	4	1	no	—
170	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
171	C₂²×C₄₃	#535	1	1	yes	characteristic
172	C₂²×C₄₃	#536	1	1	yes	characteristic
173	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
175	C₂²×C₄₃	#575	1	1	yes	characteristic
176	C₂²×C₄₃	#575	1	1	yes	characteristic
177	C₄×C₄₃	—	2	2	no	—
178	C₄×C₄₃	—	2	2	no	—
179	C₄×C₄₃	—	2	2	no	—
180	C₄×C₄₃	—	2	2	no	—
181	C₄×C₄₃	#428	1	4	yes	—
182	C₄×C₄₃	#520	1	2	yes	—
183	C₄×C₄₃	#544	1	2	yes	—
184	Dic₄₃	—	8	2	no	—
185	Dic₄₃	—	8	2	no	—
186	Dic₄₃	—	8	2	no	—
187	Dic₄₃	—	8	2	no	—
188	C₂×#432	D₄₃	1	1	yes	characteristic
189	#2285	—	43	1	no	—
190	#2285	—	43	1	no	—
191	#1948	—	43	2	no	—
192	#1947	—	43	2	no	—
193	#1854	—	43	4	no	—
194	#1847	—	43	2	no	—
195	#1836	—	43	2	no	—
196	C₂×C₄₃	—	4	2	no	—
197	C₂×C₄₃	#2317	1	1	yes	characteristic
198	C₂×C₄₃	C₂×#428	1	1	yes	characteristic
199	C₂×C₄₃	#2911	1	1	yes	characteristic
200	C₂×C₄₃	#3214	1	1	yes	characteristic
201	C₂×C₄₃	#3216	1	1	yes	characteristic
202	C₂×C₄₃	#3235	1	1	yes	characteristic
203	C₂×C₄₃	#3237	1	1	yes	characteristic
204	C₂×#117	—	43	2	no	—
205	C₂×#117	—	86	1	no	—
206	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
207	#432	Dic₄₃	1	8	yes	complemented
208	C₂×#107	—	43	4	no	—
209	C₂×#106	—	43	4	no	—
210	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
211	C₂×C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
212	C₂×#97	C₂×D₄₃	1	2	yes	—
213	#384	—	43	1	no	—
214	#384	—	43	1	no	—
215	#384	—	43	1	no	—
216	#384	—	43	1	no	—
217	#382	—	43	2	no	—
218	#382	—	86	1	no	—
219	#380	—	43	2	no	—
220	#380	—	86	1	no	—
221	#380	—	86	1	no	—
222	#380	—	86	1	no	—
223	C₄×C₄⋊C₄	—	43	2	no	—
224	C₄×C₄⋊C₄	—	86	1	no	—
225	C₄×C₄⋊C₄	—	86	1	no	—
226	C₄×C₄⋊C₄	—	86	1	no	—
227	#340	—	43	4	no	—
228	#340	—	43	4	no	—
229	C₄₃	#21988	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
231	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
232	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
233	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
234	#117	—	172	4	no	—
235	#117	—	172	4	no	—
236	C₂×C₄⋊C₄	—	43	2	no	—
237	C₂×C₄⋊C₄	—	43	2	no	—
238	C₂×C₄⋊C₄	—	43	2	no	—
239	C₂×C₄⋊C₄	—	43	2	no	—
240	C₂×C₄⋊C₄	—	86	1	no	—
241	C₂×C₄⋊C₄	—	86	1	no	—
242	C₂×C₄⋊C₄	—	86	1	no	—
243	C₂×C₄⋊C₄	—	86	1	no	—
244	C₂×C₄⋊C₄	—	86	1	no	—
245	C₂×C₄⋊C₄	—	86	1	no	—
246	C₂×C₄⋊C₄	—	86	1	no	—
247	C₂×C₄⋊C₄	—	86	1	no	—
248	C₂×C₂²⋊C₄	—	86	2	no	—
249	C₂×C₂²⋊C₄	—	86	2	no	—
250	C₂×C₄²	—	86	2	no	—
251	C₂×C₄²	—	86	2	no	—
252	C₂×C₄²	Dic₈₆	1	4	yes	—
253	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
254	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
255	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
256	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
257	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
258	#107	—	172	4	no	—
259	#106	—	172	4	no	—
260	C₄⋊C₈	C₂×Dic₄₃	1	8	yes	—
261	C₂²⋊C₈	C₂×Dic₄₃	1	8	yes	—
262	#97	C₂×Dic₄₃	1	8	yes	—
263	#95	—	86	2	no	—
264	#95	—	86	2	no	—
265	#95	—	86	2	no	—
266	#95	—	86	2	no	—
267	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	—	86	2	no	—
275	C₂²×C₄	—	86	2	no	—
276	C₂²×C₄	—	86	2	no	—
277	C₂²×C₄	—	86	2	no	—
278	C₂²×C₄	C₄⋊Dic₄₃	1	4	yes	—
279	C₂²×C₄	C₄⋊Dic₄₃	1	4	yes	—
280	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
281	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
286	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
287	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	C₂²×Dic₄₃	1	8	yes	—
291	C₄⋊C₄	—	86	2	no	—
292	C₄⋊C₄	—	86	4	no	—
293	C₄⋊C₄	—	86	2	no	—
294	C₄⋊C₄	—	86	4	no	—
295	C₄⋊C₄	—	86	4	no	—
296	C₄⋊C₄	—	172	2	no	—
297	C₄⋊C₄	—	172	2	no	—
298	C₄⋊C₄	—	172	2	no	—
299	C₄⋊C₄	—	172	2	no	—
300	C₄⋊C₄	—	172	2	no	—
301	C₄⋊C₄	—	172	2	no	—
302	C₄⋊C₄	—	172	2	no	—
303	C₄⋊C₄	—	172	2	no	—
304	C₂²⋊C₄	—	172	4	no	—
305	C₂²⋊C₄	—	172	4	no	—
306	C₄²	—	172	4	no	—
307	C₄²	—	172	4	no	—
308	C₄²	C₄⋊Dic₄₃	1	4	yes	—
309	C₄²	C₄⋊Dic₄₃	1	4	yes	—
310	C₄²	C₂×Dic₈₆	1	2	yes	—
311	C₄²	C₂×Dic₈₆	1	2	yes	—
312	C₄²	C₂²×Dic₄₃	1	2	yes	—
313	C₄²	C₂²×Dic₄₃	1	2	yes	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	C₂×C₄⋊Dic₄₃	1	2	yes	—
321	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	172	2	no	—
335	C₂×C₄	—	172	2	no	—
336	C₂×C₄	—	172	2	no	—
337	C₂×C₄	—	172	2	no	—
338	C₂×C₄	—	172	2	no	—
339	C₂×C₄	—	172	2	no	—
340	C₂×C₄	—	172	2	no	—
341	C₂×C₄	—	172	2	no	—
342	C₂×C₄	—	172	2	no	—
343	C₂×C₄	—	172	2	no	—
344	C₂×C₄	—	172	2	no	—
345	C₂×C₄	—	172	2	no	—
346	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
347	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
348	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
349	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
350	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
351	C₂×C₄	#13063353	1	2	yes	—
352	C₂×C₄	#13063358	1	2	yes	—
353	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
354	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
355	C₂×C₄	#13063371	1	2	yes	—
356	C₂×C₄	#13063372	1	2	yes	—
357	C₈	—	2	8	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
366	C₂²	#14583468	1	1	yes	characteristic
367	C₂²	#14583475	1	1	yes	characteristic
368	C₂²	C₂×#13063353	1	1	yes	characteristic
369	C₂²	C₂×#13063358	1	1	yes	characteristic
370	C₂²	#14583699	1	1	yes	characteristic
371	C₂²	#14583699	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	344	2	no	—
377	C₄	—	344	2	no	—
378	C₄	—	344	2	no	—
379	C₄	—	344	2	no	—
380	C₄	#14582941	1	4	yes	—
381	C₄	#14583382	1	2	yes	—
382	C₄	#14583527	1	2	yes	—
383	C₂	—	4	2	no	—
384	C₂	#19137218	1	1	yes	characteristic
385	C₂	C₂×#14582941	1	1	yes	characteristic
386	C₂	#19143185	1	1	yes	characteristic
387	C₂	#19145592	1	1	yes	characteristic
388	C₂	#19145608	1	1	yes	characteristic
389	C₂	#19145795	1	1	yes	characteristic
390	C₂	#19145811	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#432	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#432	D₄₃
hypocenter	C₄₃	#21988
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#432

Complements

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

N	H ≅ G/N	type
3. #19135359	C₂	semidirect
4. #19135354	C₂	semidirect
6. #19134763	C₂	semidirect
7. #19134729	C₂	semidirect
30. C₄₃×#432	C₄	semidirect
207. #432	Dic₄₃	semidirect
229. C₄₃	#21988	semidirect

Maximal subgroups

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

subgroup	index
#19137002	2
#19135359	2
#19135354	2
#19134796	2
#19134763	2
#19134729	2
C₂×C₄₃×#432	2
#21988	43