Subgroups — C₂×#19135356 #25100043

Order 11008.

1230 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063256	C₂	1	2	yes	maximal
2	C₂²×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	#19135356	C₂	1	8	yes	maximal, direct product factor
5	C₂×#14582661	C₂	1	2	yes	maximal
6	C₂×C₄₃×#384	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄₃⋊C₈	C₂²	1	2	yes	—
8	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₄₃	—	2	1	no	—
11	C₂×#13063256	—	2	8	no	—
12	C₂×#13063256	C₂²	1	8	yes	—
13	C₂×C₄⋊(C₄₃⋊C₈)	C₄	1	8	yes	complemented
14	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
15	C₄×C₄⋊Dic₄₃	—	2	2	no	—
16	C₄×C₄⋊Dic₄₃	C₂²	1	4	yes	—
17	C₂×C₄₃⋊#95	—	2	1	no	—
18	#14582661	C₂²	1	8	yes	—
19	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
21	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
22	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#384	—	2	2	no	—
24	C₄₃×#384	C₂²	1	4	yes	—
25	C₂³×Dic₄₃	—	2	1	no	—
26	C₂³×Dic₄₃	—	2	1	no	—
27	C₂²×C₄₃⋊C₈	—	2	4	no	—
28	C₂²×C₄₃⋊C₈	—	2	4	no	—
29	C₂²×C₄₃⋊C₈	C₂×C₄	1	8	yes	—
30	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
31	C₂×C₄⋊Dic₄₃	—	2	1	no	—
32	C₂×C₄⋊Dic₄₃	—	2	1	no	—
33	C₂×C₄⋊Dic₄₃	—	2	2	no	—
34	C₂×C₄⋊Dic₄₃	—	2	2	no	—
35	C₂×C₄⋊Dic₄₃	D₄	1	4	yes	—
36	C₂×C₄⋊Dic₄₃	Q₈	1	4	yes	—
37	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
38	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
39	C₂×C₄×Dic₄₃	—	2	4	no	—
40	C₂×C₄×Dic₄₃	—	4	4	no	—
41	#13063256	—	2	16	no	—
42	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	16	yes	complemented
43	C₄₃⋊#95	—	2	4	no	—
44	C₂³×C₄×C₄₃	—	2	2	no	—
45	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
54	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
55	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
56	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₄₃	D₄	1	2	yes	—
58	C₂×C₄²×C₄₃	Q₈	1	4	yes	—
59	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
60	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₃	—	2	2	no	—
62	C₂²×C₄×C₄₃	—	2	2	no	—
63	C₂²×C₄×C₄₃	—	2	4	no	—
64	C₂²×C₄×C₄₃	—	4	4	no	—
65	C₂²×C₄×C₄₃	—	4	4	no	—
66	C₂²×C₄×C₄₃	—	4	4	no	—
67	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
68	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
69	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	—
70	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	—
71	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
72	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
73	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
74	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
77	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
78	C₂²×C₄×C₄₃	#41	1	2	yes	—
79	C₂²×C₄×C₄₃	#41	1	2	yes	—
80	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
81	C₂²×Dic₄₃	—	2	4	no	—
82	C₂²×Dic₄₃	—	2	4	no	—
83	C₂²×Dic₄₃	—	2	2	no	—
84	C₂²×Dic₄₃	—	2	2	no	—
85	C₂²×Dic₄₃	—	4	2	no	—
86	C₂²×Dic₄₃	—	4	2	no	—
87	C₂²×Dic₄₃	—	4	2	no	—
88	C₂²×Dic₄₃	—	4	2	no	—
89	C₄⋊C₄×C₄₃	—	2	4	no	—
90	C₄⋊C₄×C₄₃	—	2	4	no	—
91	C₄⋊C₄×C₄₃	—	4	8	no	—
92	C₄⋊C₄×C₄₃	—	4	4	no	—
93	C₄⋊C₄×C₄₃	—	4	8	no	—
94	C₄²×C₄₃	C₄⋊C₄	1	8	yes	—
95	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
96	C₄²×C₄₃	C₂×Q₈	1	4	yes	—
97	C₄⋊Dic₄₃	—	2	4	no	—
98	C₄⋊Dic₄₃	—	2	4	no	—
99	C₄⋊Dic₄₃	—	2	2	no	—
100	C₄⋊Dic₄₃	—	2	2	no	—
101	C₄⋊Dic₄₃	C₂×D₄	1	4	yes	—
102	C₄⋊Dic₄₃	C₂×Q₈	1	4	yes	—
103	C₄×Dic₄₃	—	4	8	no	—
104	C₂×C₄₃⋊C₈	—	2	16	no	—
105	C₂×C₄₃⋊C₈	—	2	4	no	—
106	C₂×C₄₃⋊C₈	—	2	4	no	—
107	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
108	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
109	C₂³×C₄₃	#121	1	2	yes	—
110	C₂³×C₄₃	C₂²⋊Q₈	1	2	yes	—
111	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
112	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
113	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
114	C₂³×C₄₃	#137	1	2	yes	—
115	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
116	C₂×C₄×C₄₃	—	2	2	no	—
117	C₂×C₄×C₄₃	—	2	2	no	—
118	C₂×C₄×C₄₃	—	2	8	no	—
119	C₂×C₄×C₄₃	—	4	4	no	—
120	C₂×C₄×C₄₃	—	4	4	no	—
121	C₂×C₄×C₄₃	—	4	4	no	—
122	C₂×C₄×C₄₃	—	8	8	no	—
123	C₂×C₄×C₄₃	#106	1	16	yes	complemented
124	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
125	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
127	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
128	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
129	C₂×C₄×C₄₃	#121	1	2	yes	—
130	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
131	C₂×C₄×C₄₃	#125	1	4	yes	—
132	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
133	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
134	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
135	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
138	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
139	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
140	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
141	C₂×Dic₄₃	—	2	4	no	—
142	C₂×Dic₄₃	—	2	4	no	—
143	C₂×Dic₄₃	—	4	2	no	—
144	C₂×Dic₄₃	—	4	2	no	—
145	C₂×Dic₄₃	—	4	2	no	—
146	C₂×Dic₄₃	—	4	2	no	—
147	C₂×Dic₄₃	—	4	8	no	—
148	C₂×Dic₄₃	—	4	8	no	—
149	C₄₃⋊C₈	—	2	8	no	—
150	C₂×#1948	—	43	1	no	maximal, Sylow
151	C₂²×C₄₃	#389	1	4	yes	—
152	C₂²×C₄₃	C₂×#106	1	4	yes	—
153	C₂²×C₄₃	#428	1	4	yes	—
154	C₂²×C₄₃	#460	1	4	yes	—
155	C₂²×C₄₃	#461	1	4	yes	—
156	C₂²×C₄₃	#475	1	4	yes	—
157	C₂²×C₄₃	#476	1	4	yes	—
158	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
160	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
161	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
162	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
163	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
165	C₄×C₄₃	—	2	4	no	—
166	C₄×C₄₃	—	8	4	no	—
167	C₄×C₄₃	#389	1	4	yes	—
168	C₄×C₄₃	C₂×#106	1	8	yes	complemented
169	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
170	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
171	C₄×C₄₃	C₂×#125	1	1	yes	characteristic
172	C₄×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
173	Dic₄₃	—	4	4	no	—
174	Dic₄₃	—	4	4	no	—
175	C₂²×#106	—	43	2	no	—
176	C₂²×C₄⋊C₈	—	43	1	no	—
177	C₂×#384	D₄₃	1	1	yes	characteristic
178	C₂×C₄×C₄⋊C₄	—	43	1	no	—
179	#1948	—	43	8	no	—
180	C₂×#340	—	43	2	no	—
181	C₂×C₄₃	#1948	1	8	yes	complemented
182	C₂×C₄₃	C₂×#389	1	1	yes	characteristic
183	C₂×C₄₃	C₂²×#106	1	1	yes	characteristic
184	C₂×C₄₃	C₂×#428	1	1	yes	characteristic
185	C₂×C₄₃	C₂×#461	1	1	yes	characteristic
186	C₂×C₄₃	C₂×#460	1	1	yes	characteristic
187	C₂×C₄₃	C₂×#476	1	1	yes	characteristic
188	C₂×C₄₃	C₂×#475	1	1	yes	characteristic
189	C₂³×C₈	—	43	2	no	—
190	C₂²×C₄⋊C₄	—	2	1	no	—
191	C₂²×C₄⋊C₄	—	2	1	no	—
192	C₂²×C₄⋊C₄	—	43	1	no	—
193	C₂²×C₄⋊C₄	—	43	1	no	—
194	C₂²×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
195	C₂²×C₄²	—	86	1	no	—
196	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
197	C₂×#106	—	43	8	no	—
198	C₂×#106	—	86	8	no	—
199	C₂×C₄⋊C₈	—	43	4	no	—
200	C₂×C₄⋊C₈	—	43	8	no	—
201	#384	—	2	2	no	—
202	#384	C₂×D₄₃	1	4	yes	—
203	C₄×C₄⋊C₄	—	43	4	no	—
204	C₄×C₄⋊C₄	—	86	2	no	—
205	C₂×#95	—	86	1	no	—
206	#340	—	43	8	no	—
207	C₄₃	C₂×#1948	1	1	yes	characteristic, complemented, Sylow
208	C₂³×C₄	—	2	2	no	—
209	C₂³×C₄	—	86	1	no	—
210	C₂³×C₄	—	86	1	no	—
211	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
212	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
213	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
214	C₂²×C₈	—	43	8	no	—
215	C₂²×C₈	—	43	4	no	—
216	C₂²×C₈	—	86	4	no	—
217	C₂²×C₈	—	86	4	no	—
218	C₂×C₄⋊C₄	—	2	4	no	—
219	C₂×C₄⋊C₄	—	2	4	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	4	4	no	—
224	C₂×C₄⋊C₄	—	4	4	no	—
225	C₂×C₄⋊C₄	—	43	4	no	—
226	C₂×C₄⋊C₄	—	43	4	no	—
227	C₂×C₄⋊C₄	—	43	2	no	—
228	C₂×C₄⋊C₄	—	43	2	no	—
229	C₂×C₄⋊C₄	—	86	2	no	—
230	C₂×C₄⋊C₄	—	86	2	no	—
231	C₂×C₄⋊C₄	—	86	1	no	—
232	C₂×C₄⋊C₄	—	86	1	no	—
233	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
234	C₂×C₄²	—	86	4	no	—
235	C₂×C₄²	—	172	4	no	—
236	C₂×C₄²	Dic₈₆	1	4	yes	—
237	C₂×C₄²	C₄×D₄₃	1	4	yes	—
238	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
239	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
240	#106	—	86	16	no	—
241	C₄⋊C₈	—	43	16	no	—
242	#95	—	86	4	no	—
243	C₂⁴	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	4	4	no	—
248	C₂²×C₄	—	4	4	no	—
249	C₂²×C₄	—	4	4	no	—
250	C₂²×C₄	—	86	4	no	—
251	C₂²×C₄	—	86	4	no	—
252	C₂²×C₄	—	86	2	no	—
253	C₂²×C₄	—	86	2	no	—
254	C₂²×C₄	—	172	2	no	—
255	C₂²×C₄	—	172	2	no	—
256	C₂²×C₄	—	172	2	no	—
257	C₂²×C₄	—	172	2	no	—
258	C₂²×C₄	Dic₄₃⋊C₄	1	4	yes	—
259	C₂²×C₄	Dic₄₃⋊C₄	1	4	yes	—
260	C₂²×C₄	#10621883	1	4	yes	—
261	C₂²×C₄	#10621884	1	4	yes	—
262	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
263	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
264	C₂²×C₄	D₄×D₄₃	1	2	yes	—
265	C₂²×C₄	#10621900	1	2	yes	—
266	C₂²×C₄	Q₈×D₄₃	1	2	yes	—
267	C₂²×C₄	#10621902	1	2	yes	—
268	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
269	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
271	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
272	C₂×C₈	—	43	8	no	—
273	C₂×C₈	—	86	16	no	—
274	C₂×C₈	—	86	4	no	—
275	C₂×C₈	—	86	4	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	4	8	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	4	8	no	—
281	C₄⋊C₄	—	43	4	no	—
282	C₄⋊C₄	—	43	4	no	—
283	C₄⋊C₄	—	86	4	no	—
284	C₄⋊C₄	—	86	4	no	—
285	C₄⋊C₄	—	86	2	no	—
286	C₄⋊C₄	—	86	2	no	—
287	C₄²	—	172	8	no	—
288	C₄²	Dic₄₃⋊C₄	1	8	yes	—
289	C₄²	C₂×Dic₈₆	1	4	yes	—
290	C₄²	C₂×C₄×D₄₃	1	4	yes	—
291	C₂³	C₂×Dic₄₃⋊C₄	1	2	yes	—
292	C₂³	#13063296	1	2	yes	—
293	C₂³	#13063301	1	2	yes	—
294	C₂³	C₂×#10621884	1	2	yes	—
295	C₂³	C₂×#10621883	1	2	yes	—
296	C₂³	#13063351	1	2	yes	—
297	C₂³	#13063356	1	2	yes	—
298	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	4	4	no	—
305	C₂×C₄	—	8	8	no	—
306	C₂×C₄	—	86	4	no	—
307	C₂×C₄	—	86	4	no	—
308	C₂×C₄	—	172	8	no	—
309	C₂×C₄	—	172	2	no	—
310	C₂×C₄	—	172	2	no	—
311	C₂×C₄	—	172	2	no	—
312	C₂×C₄	—	172	2	no	—
313	C₂×C₄	—	172	8	no	—
314	C₂×C₄	#13063256	1	16	yes	complemented
315	C₂×C₄	C₂×Dic₄₃⋊C₄	1	4	yes	—
316	C₂×C₄	C₂×Dic₄₃⋊C₄	1	2	yes	—
317	C₂×C₄	C₂×Dic₄₃⋊C₄	1	4	yes	—
318	C₂×C₄	#13063287	1	4	yes	—
319	C₂×C₄	#13063290	1	4	yes	—
320	C₂×C₄	#13063296	1	2	yes	—
321	C₂×C₄	#13063301	1	2	yes	—
322	C₂×C₄	#13063316	1	4	yes	—
323	C₂×C₄	#13063324	1	4	yes	—
324	C₂×C₄	C₂×#10621884	1	4	yes	—
325	C₂×C₄	C₂×#10621883	1	4	yes	—
326	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
327	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
328	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
329	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
330	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
331	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
332	C₈	—	86	8	no	—
333	C₂²	#14582795	1	4	yes	—
334	C₂²	C₂×#13063256	1	4	yes	—
335	C₂²	#14582939	1	4	yes	—
336	C₂²	#14583096	1	4	yes	—
337	C₂²	#14583101	1	4	yes	—
338	C₂²	#14583181	1	4	yes	—
339	C₂²	#14583186	1	4	yes	—
340	C₂²	C₂²×Dic₄₃⋊C₄	1	1	yes	characteristic
341	C₂²	C₂×#13063296	1	1	yes	characteristic
342	C₂²	C₂×#13063301	1	1	yes	characteristic
343	C₂²	C₂²×#10621884	1	1	yes	characteristic
344	C₂²	C₂²×#10621883	1	1	yes	characteristic
345	C₂²	C₂×#13063351	1	1	yes	characteristic
346	C₂²	C₂×#13063356	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	8	4	no	—
349	C₄	—	172	4	no	—
350	C₄	—	172	4	no	—
351	C₄	#14582795	1	4	yes	—
352	C₄	C₂×#13063256	1	8	yes	complemented
353	C₄	C₂×#13063287	1	1	yes	characteristic
354	C₄	C₂×#13063290	1	1	yes	characteristic
355	C₄	C₂×#13063316	1	1	yes	characteristic
356	C₄	C₂×#13063324	1	1	yes	characteristic
357	C₂	#19135356	1	8	yes	direct product factor
358	C₂	C₂×#14582795	1	1	yes	characteristic
359	C₂	C₂²×#13063256	1	1	yes	characteristic
360	C₂	C₂×#14582939	1	1	yes	characteristic
361	C₂	C₂×#14583101	1	1	yes	characteristic
362	C₂	C₂×#14583096	1	1	yes	characteristic
363	C₂	C₂×#14583186	1	1	yes	characteristic
364	C₂	C₂×#14583181	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#384	C₂
socle, prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#384	D₄₃
hypocenter	C₄₃	C₂×#1948
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
4. #19135356	C₂	direct (N × H)
13. C₂×C₄⋊(C₄₃⋊C₈)	C₄	semidirect
42. C₄⋊(C₄₃⋊C₈)	C₂×C₄	semidirect
123. C₂×C₄×C₄₃	#106	semidirect
168. C₄×C₄₃	C₂×#106	semidirect
181. C₂×C₄₃	#1948	semidirect
207. C₄₃	C₂×#1948	semidirect
314. C₂×C₄	#13063256	semidirect
352. C₄	C₂×#13063256	semidirect
357. C₂	#19135356	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13063256	2
C₂²×C₄⋊(C₄₃⋊C₈)	2
C₂×C₄×C₄⋊Dic₄₃	2
#19135356	2
C₂×#14582661	2
C₂×C₄₃×#384	2
C₂×#1948	43

Subgroups — C2×#19135356 #25100043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19135356 #25100043