Subgroups — #533×Dic₄₃ #25255141

Order 11008.

2550 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	C₄⋊Q₈×Dic₄₃	C₂	1	4	yes	maximal, complemented
2	#125×Dic₄₃	C₂	1	4	yes	maximal, complemented
3	C₂²⋊Q₈×Dic₄₃	C₂	1	8	yes	maximal
4	#19137079	C₂	1	2	yes	maximal
5	#19137073	C₂	1	4	yes	maximal, complemented
6	#19137002	C₂	1	1	yes	maximal, characteristic
7	C₄×Q₈×Dic₄₃	C₂	1	4	yes	maximal, complemented
8	#117×Dic₄₃	C₂	1	2	yes	maximal
9	C₂×C₄²×Dic₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄₃×#533	C₂	1	1	yes	maximal, characteristic
11	C₂×Q₈×Dic₄₃	C₂²	1	8	yes	—
12	C₂×#13063284	C₂²	1	2	yes	—
13	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄×Dic₄₃	C₂²	1	4	yes	—
15	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
16	#14582806	C₂²	1	8	yes	—
17	#14582798	C₂²	1	8	yes	—
18	#14582798	C₂²	1	8	yes	—
19	#14582785	C₂²	1	16	yes	—
20	#14582774	C₂²	1	8	yes	—
21	#14582769	C₂²	1	2	yes	—
22	#14582765	C₂²	1	2	yes	—
23	#14582759	C₂²	1	4	yes	—
24	C₄⋊C₄×Dic₄₃	C₂²	1	16	yes	—
25	C₄⋊C₄×Dic₄₃	C₂²	1	8	yes	—
26	C₄⋊C₄×Dic₄₃	C₂²	1	8	yes	—
27	C₄×C₄⋊Dic₄₃	C₂²	1	8	yes	—
28	C₄×C₄⋊Dic₄₃	C₂²	1	4	yes	—
29	C₂²⋊C₄×Dic₄₃	C₂²	1	8	yes	—
30	#14582745	C₂²	1	4	yes	—
31	C₄²×Dic₄₃	C₂²	1	2	yes	—
32	C₄²×Dic₄₃	C₂²	1	2	yes	—
33	C₄²×Dic₄₃	C₂²	1	2	yes	—
34	C₄²×Dic₄₃	C₂²	1	2	yes	—
35	C₄²×Dic₄₃	C₂²	1	4	yes	—
36	C₄₃×#533	C₄	1	16	yes	complemented
37	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
38	C₂×#125×C₄₃	C₂²	1	2	yes	—
39	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	—
40	C₂×C₄×Q₈×C₄₃	C₂²	1	4	yes	—
41	C₂×#117×C₄₃	C₂²	1	2	yes	—
42	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
43	C₂³×Dic₄₃	C₂³	1	2	yes	—
44	C₂³×Dic₄₃	C₂³	1	2	yes	—
45	Q₈×Dic₄₃	—	2	32	no	—
46	#13063284	—	2	8	no	—
47	C₂×C₄⋊Dic₄₃	C₂³	1	16	yes	—
48	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
49	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
50	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
51	C₂×C₄×Dic₄₃	—	2	4	no	—
52	C₂×C₄×Dic₄₃	—	2	16	no	—
53	C₂×C₄×Dic₄₃	Q₈	1	8	yes	complemented
54	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
55	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
56	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
57	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
58	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
59	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
60	C₂×C₄×Dic₄₃	C₂³	1	16	yes	—
61	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
64	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
65	C₄₃⋊#95	C₂³	1	16	yes	—
66	C₄₃⋊#95	C₂³	1	8	yes	—
67	C₄₃⋊#95	C₂³	1	16	yes	—
68	C₂²×Q₈×C₄₃	C₂³	1	4	yes	—
69	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₄⋊Q₈×C₄₃	C₂×C₄	1	16	yes	complemented
72	#125×C₄₃	C₂×C₄	1	16	yes	complemented
73	C₂²⋊Q₈×C₄₃	C₂×C₄	1	32	yes	—
74	C₄×Q₈×C₄₃	C₂×C₄	1	32	yes	complemented
75	#117×C₄₃	C₂×C₄	1	16	yes	—
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
80	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
81	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
85	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
86	C₂×Q₈×C₄₃	—	2	16	no	—
87	C₂×Q₈×C₄₃	C₂²×C₄	1	16	yes	—
88	C₂²×C₄×C₄₃	—	2	8	no	—
89	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
90	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
92	C₂²×C₄×C₄₃	#41	1	4	yes	—
93	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
95	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
97	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₄₃	—	2	8	no	—
99	C₂²×Dic₄₃	—	2	8	no	—
100	C₂²×Dic₄₃	—	2	4	no	—
101	C₂²×Dic₄₃	C₂×Q₈	1	8	yes	—
102	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
103	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
104	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
105	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
106	C₄⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
107	C₄⋊C₄×C₄₃	C₂²×C₄	1	32	yes	—
108	C₄⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
109	C₂²⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
110	C₄²×C₄₃	C₂²×C₄	1	8	yes	—
111	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
112	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
113	C₄²×C₄₃	C₂²×C₄	1	16	yes	—
114	C₂²⋊Dic₄₃	—	2	8	no	—
115	C₄⋊Dic₄₃	—	2	8	no	—
116	C₄⋊Dic₄₃	—	2	16	no	—
117	C₄⋊Dic₄₃	—	2	32	no	—
118	C₄×Dic₄₃	—	2	8	no	—
119	C₄×Dic₄₃	—	2	4	no	—
120	C₄×Dic₄₃	—	2	4	no	—
121	C₄×Dic₄₃	—	2	8	no	—
122	C₄×Dic₄₃	—	2	8	no	—
123	C₄×Dic₄₃	—	2	8	no	—
124	C₄×Dic₄₃	—	2	32	no	—
125	C₄×Dic₄₃	C₂×Q₈	1	4	yes	—
126	C₄×Dic₄₃	C₂×Q₈	1	8	yes	—
127	C₄×Dic₄₃	C₂×Q₈	1	4	yes	—
128	C₄×Dic₄₃	#41	1	16	yes	—
129	C₂³×C₄₃	—	2	4	no	—
130	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
131	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
132	C₂³×C₄₃	C₂×#41	1	2	yes	—
133	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
134	Q₈×C₄₃	—	2	32	no	—
135	C₂×C₄×C₄₃	—	2	4	no	—
136	C₂×C₄×C₄₃	—	2	16	no	—
137	C₂×C₄×C₄₃	—	2	16	no	—
138	C₂×C₄×C₄₃	C₄×Q₈	1	16	yes	complemented
139	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
140	C₂×C₄×C₄₃	C₂³×C₄	1	16	yes	—
141	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
142	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
143	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
144	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
145	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
146	C₂×C₄×C₄₃	C₂×#41	1	8	yes	—
147	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
148	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
149	C₂×Dic₄₃	—	2	16	no	—
150	C₂×Dic₄₃	—	2	4	no	—
151	C₂×Dic₄₃	—	2	4	no	—
152	C₂×Dic₄₃	—	2	4	no	—
153	C₂×Dic₄₃	—	2	16	no	—
154	C₂×Dic₄₃	—	2	16	no	—
155	C₂×Dic₄₃	—	2	8	no	—
156	C₂×Dic₄₃	C₂²×Q₈	1	4	yes	—
157	C₂×Dic₄₃	C₂²×Q₈	1	4	yes	—
158	C₂×Dic₄₃	C₂×#41	1	8	yes	—
159	C₂×Dic₄₃	C₂×#41	1	8	yes	—
160	C₄×#533	—	43	1	no	maximal, Sylow
161	C₂²×C₄₃	—	2	4	no	—
162	C₂²×C₄₃	—	2	4	no	—
163	C₂²×C₄₃	—	2	4	no	—
164	C₂²×C₄₃	C₂×C₄×Q₈	1	4	yes	—
165	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
166	C₂²×C₄₃	C₂³×Q₈	1	1	yes	characteristic
167	C₂²×C₄₃	C₂²×#41	1	4	yes	—
168	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
169	C₄×C₄₃	—	2	4	no	—
170	C₄×C₄₃	—	2	16	no	—
171	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	—
172	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	—
173	C₄×C₄₃	C₄×#41	1	8	yes	—
174	Dic₄₃	—	2	4	no	—
175	Dic₄₃	—	2	8	no	—
176	Dic₄₃	—	4	8	no	—
177	Dic₄₃	#533	1	8	yes	direct product factor
178	C₂×#533	D₄₃	1	1	yes	characteristic
179	C₄×C₄⋊Q₈	—	43	4	no	—
180	C₄×#125	—	43	4	no	—
181	C₄×C₂²⋊Q₈	—	43	8	no	—
182	#2296	—	43	2	no	—
183	#2295	—	43	4	no	—
184	#2285	—	43	1	no	—
185	C₄²×Q₈	—	43	4	no	—
186	C₄×#117	—	43	2	no	—
187	C₂×C₄³	—	43	1	no	—
188	C₂×C₄₃	—	2	4	no	—
189	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
190	C₂×C₄₃	C₂×C₄×#41	1	2	yes	—
191	C₂×C₄₃	C₂×#533	1	2	yes	—
192	C₂×C₄₃	#3444	1	2	yes	—
193	#533	Dic₄₃	1	16	yes	direct product factor
194	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
195	C₂×#125	C₂×D₄₃	1	2	yes	—
196	C₂×C₂²⋊Q₈	C₂×D₄₃	1	4	yes	—
197	C₂×C₄×Q₈	—	43	8	no	—
198	C₂×C₄×Q₈	C₂×D₄₃	1	4	yes	—
199	C₂×#117	—	43	2	no	—
200	C₂×#117	C₂×D₄₃	1	2	yes	—
201	C₂²×C₄²	—	43	1	no	—
202	C₂²×C₄²	—	43	1	no	—
203	C₂²×C₄²	—	43	4	no	—
204	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
205	#391	—	43	8	no	—
206	#389	—	43	8	no	—
207	#389	—	43	8	no	—
208	#387	—	43	16	no	—
209	#385	—	43	8	no	—
210	#384	—	43	2	no	—
211	#382	—	43	2	no	—
212	#380	—	43	4	no	—
213	C₄×C₄⋊C₄	—	43	8	no	—
214	C₄×C₄⋊C₄	—	43	16	no	—
215	C₄×C₄⋊C₄	—	43	8	no	—
216	C₄×C₄⋊C₄	—	43	4	no	—
217	C₄×C₄⋊C₄	—	43	8	no	—
218	C₄×C₂²⋊C₄	—	43	8	no	—
219	#376	—	43	4	no	—
220	C₄³	—	43	2	no	—
221	C₄³	—	43	2	no	—
222	C₄³	—	43	2	no	—
223	C₄³	—	43	2	no	—
224	C₄³	—	43	4	no	—
225	C₄₃	C₄×#533	1	1	yes	characteristic, complemented, Sylow
226	C₂²×Q₈	C₂²×D₄₃	1	4	yes	—
227	C₂³×C₄	—	43	2	no	—
228	C₂³×C₄	—	43	2	no	—
229	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
230	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
231	C₄⋊Q₈	C₂×Dic₄₃	1	16	yes	complemented
232	#125	C₂×Dic₄₃	1	16	yes	complemented
233	C₂²⋊Q₈	C₂×Dic₄₃	1	32	yes	—
234	C₄×Q₈	—	86	32	no	—
235	C₄×Q₈	C₂×Dic₄₃	1	32	yes	complemented
236	#117	—	86	8	no	—
237	#117	C₂×Dic₄₃	1	16	yes	—
238	C₂×C₄⋊C₄	—	43	4	no	—
239	C₂×C₄⋊C₄	—	43	8	no	—
240	C₂×C₄⋊C₄	—	43	16	no	—
241	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
242	C₂×C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
243	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
244	C₂×C₂²⋊C₄	—	43	4	no	—
245	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
246	C₂×C₄²	—	43	8	no	—
247	C₂×C₄²	—	43	4	no	—
248	C₂×C₄²	—	43	2	no	—
249	C₂×C₄²	—	43	1	no	—
250	C₂×C₄²	—	43	1	no	—
251	C₂×C₄²	—	43	16	no	—
252	C₂×C₄²	—	43	4	no	—
253	C₂×C₄²	—	43	4	no	—
254	C₂×C₄²	—	43	2	no	—
255	C₂×C₄²	—	43	4	no	—
256	C₂×C₄²	—	43	4	no	—
257	C₂×C₄²	—	43	2	no	—
258	C₂×C₄²	—	86	16	no	—
259	C₂×C₄²	—	86	4	no	—
260	C₂×C₄²	C₂×Dic₄₃	1	8	yes	—
261	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
263	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
264	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
265	#95	—	43	16	no	—
266	#95	—	43	8	no	—
267	#95	—	43	16	no	—
268	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
269	C₂×Q₈	—	2	16	no	—
270	C₂×Q₈	C₂²×Dic₄₃	1	16	yes	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	43	2	no	—
273	C₂²×C₄	—	43	8	no	—
274	C₂²×C₄	—	43	2	no	—
275	C₂²×C₄	—	43	4	no	—
276	C₂²×C₄	—	43	8	no	—
277	C₂²×C₄	—	86	8	no	—
278	C₂²×C₄	—	86	8	no	—
279	C₂²×C₄	—	86	4	no	—
280	C₂²×C₄	Q₈×D₄₃	1	4	yes	—
281	C₂²×C₄	#10621902	1	4	yes	—
282	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
283	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
284	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
285	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
286	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
287	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
288	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
289	C₄⋊C₄	—	86	32	no	—
290	C₄⋊C₄	—	86	16	no	—
291	C₄⋊C₄	—	86	8	no	—
292	C₄⋊C₄	C₂²×Dic₄₃	1	16	yes	—
293	C₄⋊C₄	C₂²×Dic₄₃	1	32	yes	—
294	C₄⋊C₄	C₂²×Dic₄₃	1	16	yes	—
295	C₂²⋊C₄	—	86	8	no	—
296	C₂²⋊C₄	C₂²×Dic₄₃	1	16	yes	—
297	C₄²	—	43	4	no	—
298	C₄²	—	43	8	no	—
299	C₄²	—	43	4	no	—
300	C₄²	—	43	16	no	—
301	C₄²	—	86	8	no	—
302	C₄²	—	86	8	no	—
303	C₄²	—	86	32	no	—
304	C₄²	—	86	8	no	—
305	C₄²	—	86	4	no	—
306	C₄²	—	86	4	no	—
307	C₄²	—	86	8	no	—
308	C₄²	C₂²×Dic₄₃	1	8	yes	—
309	C₄²	C₂²×Dic₄₃	1	4	yes	—
310	C₄²	C₂²×Dic₄₃	1	4	yes	—
311	C₄²	C₂²×Dic₄₃	1	16	yes	—
312	C₂³	—	2	4	no	—
313	C₂³	C₂³×Dic₄₃	1	2	yes	—
314	C₂³	C₂×Q₈×D₄₃	1	2	yes	—
315	C₂³	C₂×#10621902	1	2	yes	—
316	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
317	Q₈	—	2	32	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	16	no	—
320	C₂×C₄	—	2	16	no	—
321	C₂×C₄	—	43	4	no	—
322	C₂×C₄	—	43	8	no	—
323	C₂×C₄	—	43	4	no	—
324	C₂×C₄	—	43	8	no	—
325	C₂×C₄	—	86	16	no	—
326	C₂×C₄	—	86	16	no	—
327	C₂×C₄	—	86	4	no	—
328	C₂×C₄	—	86	4	no	—
329	C₂×C₄	—	86	4	no	—
330	C₂×C₄	—	86	16	no	—
331	C₂×C₄	—	86	8	no	—
332	C₂×C₄	Q₈×Dic₄₃	1	16	yes	complemented
333	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
334	C₂×C₄	C₂³×Dic₄₃	1	16	yes	—
335	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
336	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
337	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
338	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
339	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
340	C₂×C₄	#41×D₄₃	1	8	yes	—
341	C₂×C₄	C₂×#10621902	1	2	yes	—
342	C₂×C₄	C₂×#10621902	1	2	yes	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	C₂×Q₈×Dic₄₃	1	4	yes	—
347	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
348	C₂²	C₂²×Q₈×D₄₃	1	1	yes	characteristic
349	C₂²	C₂×#41×D₄₃	1	4	yes	—
350	C₂²	C₂²×#10621902	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	2	16	no	—
353	C₄	—	43	8	no	—
354	C₄	—	86	4	no	—
355	C₄	—	86	8	no	—
356	C₄	—	172	8	no	—
357	C₄	C₂×Q₈×Dic₄₃	1	4	yes	—
358	C₄	C₂×Q₈×Dic₄₃	1	4	yes	—
359	C₄	#41×Dic₄₃	1	8	yes	—
360	C₂	—	2	4	no	—
361	C₂	C₂²×Q₈×Dic₄₃	1	1	yes	characteristic
362	C₂	C₂×#41×Dic₄₃	1	2	yes	—
363	C₂	#533×D₄₃	1	2	yes	—
364	C₂	#19147892	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#533	C₂
socle, cosocle	C₂³×C₄₃	C₂⁵
prime radical	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂×#533	D₄₃
hypocenter	C₄₃	C₄×#533
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. C₄⋊Q₈×Dic₄₃	C₂	semidirect
2. #125×Dic₄₃	C₂	semidirect
5. #19137073	C₂	semidirect
7. C₄×Q₈×Dic₄₃	C₂	semidirect
36. C₄₃×#533	C₄	semidirect
53. C₂×C₄×Dic₄₃	Q₈	semidirect
71. C₄⋊Q₈×C₄₃	C₂×C₄	semidirect
72. #125×C₄₃	C₂×C₄	semidirect
74. C₄×Q₈×C₄₃	C₂×C₄	semidirect
138. C₂×C₄×C₄₃	C₄×Q₈	semidirect
177. Dic₄₃	#533	direct (N × H)
193. #533	Dic₄₃	direct (N × H)
225. C₄₃	C₄×#533	semidirect
231. C₄⋊Q₈	C₂×Dic₄₃	semidirect
232. #125	C₂×Dic₄₃	semidirect
235. C₄×Q₈	C₂×Dic₄₃	semidirect
332. C₂×C₄	Q₈×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊Q₈×Dic₄₃	2
#125×Dic₄₃	2
C₂²⋊Q₈×Dic₄₃	2
#19137079	2
#19137073	2
#19137002	2
C₄×Q₈×Dic₄₃	2
#117×Dic₄₃	2
C₂×C₄²×Dic₄₃	2
C₂×C₄₃×#533	2
C₄×#533	43

Subgroups — #533×Dic43 #25255141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #533×Dic₄₃ #25255141