Subgroups — C₄×C₄₃×#391 #24933785

Order 11008.

2110 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#391	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1436	C₂	1	4	yes	maximal
6	C₄₃×C₄⋊#95	C₂	1	2	yes	maximal
7	C₄×#95×C₄₃	C₂	1	4	yes	maximal
8	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₄₃	—	2	4	no	—
10	C₂×C₄×Q₈×C₄₃	—	2	4	no	—
11	C₂×C₄×Q₈×C₄₃	C₄	1	8	yes	complemented
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#391	C₄	1	16	yes	direct product factor
22	C₄×C₄⋊C₄×C₄₃	—	2	4	no	—
23	C₂×#95×C₄₃	C₂²	1	8	yes	—
24	C₂×#95×C₄₃	C₂²	1	2	yes	—
25	C₂×#95×C₄₃	C₂²	1	8	yes	—
26	C₄³×C₄₃	—	2	4	no	—
27	C₂²×Q₈×C₄₃	—	2	2	no	—
28	C₂²×Q₈×C₄₃	—	2	2	no	—
29	C₂²×Q₈×C₄₃	—	2	4	no	—
30	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	—
31	C₂²×Q₈×C₄₃	C₂×C₄	1	8	yes	—
32	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
34	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
37	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₄×Q₈×C₄₃	—	2	32	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
48	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
49	C₂×C₄²×C₄₃	—	2	4	no	—
50	C₂×C₄²×C₄₃	—	2	4	no	—
51	C₂×C₄²×C₄₃	—	2	4	no	—
52	C₂×C₄²×C₄₃	—	2	4	no	—
53	C₂×C₄²×C₄₃	—	2	4	no	—
54	C₂×C₄²×C₄₃	—	2	8	no	—
55	C₂×C₄²×C₄₃	—	2	4	no	—
56	C₂×C₄²×C₄₃	—	2	4	no	—
57	C₂×C₄²×C₄₃	—	2	4	no	—
58	C₂×C₄²×C₄₃	—	2	8	no	—
59	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
60	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
61	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₄₃	D₄	1	4	yes	—
63	C₂×C₄²×C₄₃	D₄	1	4	yes	—
64	C₂×C₄²×C₄₃	Q₈	1	8	yes	complemented
65	#95×C₄₃	—	2	4	no	—
66	#95×C₄₃	—	2	16	no	—
67	#95×C₄₃	C₂×C₄	1	32	yes	—
68	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
69	C₂×Q₈×C₄₃	—	2	8	no	—
70	C₂×Q₈×C₄₃	—	2	8	no	—
71	C₂×Q₈×C₄₃	—	2	16	no	—
72	C₂×Q₈×C₄₃	—	2	16	no	—
73	C₂×Q₈×C₄₃	C₄²	1	16	yes	complemented
74	C₂²×C₄×C₄₃	—	2	4	no	—
75	C₂²×C₄×C₄₃	—	2	2	no	—
76	C₂²×C₄×C₄₃	—	2	2	no	—
77	C₂²×C₄×C₄₃	—	2	4	no	—
78	C₂²×C₄×C₄₃	—	2	2	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	4	no	—
81	C₂²×C₄×C₄₃	—	2	4	no	—
82	C₂²×C₄×C₄₃	—	2	4	no	—
83	C₂²×C₄×C₄₃	—	2	4	no	—
84	C₂²×C₄×C₄₃	—	2	4	no	—
85	C₂²×C₄×C₄₃	—	2	8	no	—
86	C₂²×C₄×C₄₃	—	2	8	no	—
87	C₂²×C₄×C₄₃	—	2	8	no	—
88	C₂²×C₄×C₄₃	—	2	4	no	—
89	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
90	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
92	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
95	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×Q₈	1	8	yes	—
105	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
106	C₂²×C₄×C₄₃	#41	1	8	yes	—
107	C₂²×C₄×C₄₃	#41	1	4	yes	—
108	C₂²×C₄×C₄₃	#41	1	4	yes	—
109	C₄⋊C₄×C₄₃	—	2	16	no	—
110	C₄⋊C₄×C₄₃	—	2	8	no	—
111	C₄⋊C₄×C₄₃	—	2	16	no	—
112	C₄²×C₄₃	—	2	16	no	—
113	C₄²×C₄₃	—	2	16	no	—
114	C₄²×C₄₃	—	2	16	no	—
115	C₄²×C₄₃	—	2	16	no	—
116	C₄²×C₄₃	—	4	8	no	—
117	C₄²×C₄₃	C₂²⋊C₄	1	16	yes	—
118	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
119	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
120	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
121	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
122	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
123	C₂³×C₄₃	C₂×#41	1	2	yes	—
124	C₂³×C₄₃	C₂×#41	1	2	yes	—
125	C₂³×C₄₃	C₂×#41	1	4	yes	—
126	Q₈×C₄₃	—	2	32	no	—
127	C₂×C₄×C₄₃	—	2	4	no	—
128	C₂×C₄×C₄₃	—	2	4	no	—
129	C₂×C₄×C₄₃	—	2	8	no	—
130	C₂×C₄×C₄₃	—	2	8	no	—
131	C₂×C₄×C₄₃	—	2	8	no	—
132	C₂×C₄×C₄₃	—	2	4	no	—
133	C₂×C₄×C₄₃	—	2	8	no	—
134	C₂×C₄×C₄₃	—	2	8	no	—
135	C₂×C₄×C₄₃	—	2	4	no	—
136	C₂×C₄×C₄₃	—	2	8	no	—
137	C₂×C₄×C₄₃	—	2	8	no	—
138	C₂×C₄×C₄₃	—	2	4	no	—
139	C₂×C₄×C₄₃	—	2	8	no	—
140	C₂×C₄×C₄₃	—	2	4	no	—
141	C₂×C₄×C₄₃	—	2	8	no	—
142	C₂×C₄×C₄₃	—	2	8	no	—
143	C₂×C₄×C₄₃	—	2	16	no	—
144	C₂×C₄×C₄₃	—	4	4	no	—
145	C₂×C₄×C₄₃	—	4	4	no	—
146	C₂×C₄×C₄₃	—	4	8	no	—
147	C₂×C₄×C₄₃	—	4	4	no	—
148	C₂×C₄×C₄₃	—	4	4	no	—
149	C₂×C₄×C₄₃	C₂×C₄²	1	8	yes	—
150	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
151	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
152	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
153	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
154	C₂×C₄×C₄₃	#117	1	4	yes	—
155	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
156	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
157	C₂×C₄×C₄₃	C₄×Q₈	1	8	yes	—
158	C₂×C₄×C₄₃	C₄×Q₈	1	16	yes	complemented
159	C₂×C₄×C₄₃	C₂²⋊Q₈	1	8	yes	—
160	C₂×C₄×C₄₃	#124	1	4	yes	—
161	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
162	C₄×#391	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
164	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
166	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
167	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
168	C₂²×C₄₃	C₂×C₄×Q₈	1	4	yes	—
169	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
170	C₂²×C₄₃	C₄×#41	1	2	yes	—
171	C₂²×C₄₃	C₄×#41	1	4	yes	—
172	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
173	C₂²×C₄₃	#525	1	2	yes	—
174	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
175	C₂²×C₄₃	#529	1	4	yes	—
176	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
177	C₂²×C₄₃	#532	1	2	yes	—
178	C₂²×C₄₃	#533	1	4	yes	—
179	C₄×C₄₃	—	2	8	no	—
180	C₄×C₄₃	—	2	4	no	—
181	C₄×C₄₃	—	2	16	no	—
182	C₄×C₄₃	—	4	4	no	—
183	C₄×C₄₃	—	4	8	no	—
184	C₄×C₄₃	C₄×C₂²⋊C₄	1	8	yes	—
185	C₄×C₄₃	#391	1	8	yes	direct product factor
186	C₂²×C₄×Q₈	C₂×C₄₃	1	1	yes	characteristic
187	C₂×#391	C₂×C₄₃	1	2	yes	—
188	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
189	C₂×C₄³	C₂×C₄₃	1	1	yes	characteristic
190	#1436	C₂×C₄₃	1	4	yes	—
191	C₄⋊#95	C₂×C₄₃	1	2	yes	—
192	C₄×#95	C₂×C₄₃	1	4	yes	—
193	C₂×C₄₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄₃	C₄²×Q₈	1	2	yes	—
195	C₂×C₄₃	C₂×#391	1	1	yes	characteristic
196	C₂×C₄₃	#2295	1	2	yes	—
197	C₂×C₄₃	#2297	1	1	yes	characteristic
198	C₂×C₄₃	C₄×C₂²⋊Q₈	1	4	yes	—
199	C₂×C₄₃	C₄×#124	1	2	yes	—
200	C₂×C₄₃	C₄×C₄⋊Q₈	1	2	yes	—
201	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
202	C₂×C₄×Q₈	—	2	4	no	—
203	C₂×C₄×Q₈	—	2	4	no	—
204	C₂×C₄×Q₈	C₄×C₄₃	1	8	yes	complemented
205	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
208	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
209	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
210	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
211	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
212	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
213	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
214	#391	C₄×C₄₃	1	16	yes	direct product factor
215	C₄×C₄⋊C₄	—	2	4	no	—
216	C₂×#95	C₂²×C₄₃	1	8	yes	—
217	C₂×#95	C₂²×C₄₃	1	2	yes	—
218	C₂×#95	C₂²×C₄₃	1	8	yes	—
219	C₄³	—	2	4	no	—
220	C₄₃	C₄×#391	1	1	yes	characteristic, direct product factor, Sylow
221	C₂²×Q₈	—	2	2	no	—
222	C₂²×Q₈	—	2	2	no	—
223	C₂²×Q₈	—	2	4	no	—
224	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	—
225	C₂²×Q₈	C₂×C₄×C₄₃	1	8	yes	—
226	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
227	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
228	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
229	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
231	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
233	C₄×Q₈	—	2	32	no	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
242	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	—	2	4	no	—
246	C₂×C₄²	—	2	4	no	—
247	C₂×C₄²	—	2	4	no	—
248	C₂×C₄²	—	2	8	no	—
249	C₂×C₄²	—	2	4	no	—
250	C₂×C₄²	—	2	4	no	—
251	C₂×C₄²	—	2	4	no	—
252	C₂×C₄²	—	2	8	no	—
253	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
254	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
255	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
256	C₂×C₄²	D₄×C₄₃	1	4	yes	—
257	C₂×C₄²	D₄×C₄₃	1	4	yes	—
258	C₂×C₄²	Q₈×C₄₃	1	8	yes	complemented
259	#95	—	2	4	no	—
260	#95	—	2	16	no	—
261	#95	C₂×C₄×C₄₃	1	32	yes	—
262	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
263	C₂×Q₈	—	2	8	no	—
264	C₂×Q₈	—	2	8	no	—
265	C₂×Q₈	—	2	16	no	—
266	C₂×Q₈	—	2	16	no	—
267	C₂×Q₈	C₄²×C₄₃	1	16	yes	complemented
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	8	no	—
280	C₂²×C₄	—	2	8	no	—
281	C₂²×C₄	—	2	8	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
284	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
285	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
286	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
287	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
289	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
291	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
298	C₂²×C₄	C₂×Q₈×C₄₃	1	8	yes	—
299	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
300	C₂²×C₄	#41×C₄₃	1	8	yes	—
301	C₂²×C₄	#41×C₄₃	1	4	yes	—
302	C₂²×C₄	#41×C₄₃	1	4	yes	—
303	C₄⋊C₄	—	2	16	no	—
304	C₄⋊C₄	—	2	8	no	—
305	C₄⋊C₄	—	2	16	no	—
306	C₄²	—	2	16	no	—
307	C₄²	—	2	16	no	—
308	C₄²	—	2	16	no	—
309	C₄²	—	2	16	no	—
310	C₄²	—	4	8	no	—
311	C₄²	C₂²⋊C₄×C₄₃	1	16	yes	—
312	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
313	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
314	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
315	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
316	C₂³	C₂²×Q₈×C₄₃	1	2	yes	—
317	C₂³	C₂×#41×C₄₃	1	2	yes	—
318	C₂³	C₂×#41×C₄₃	1	2	yes	—
319	C₂³	C₂×#41×C₄₃	1	4	yes	—
320	Q₈	—	2	32	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	16	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	8	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	C₂×C₄²×C₄₃	1	8	yes	—
344	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
345	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
346	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
347	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
348	C₂×C₄	#117×C₄₃	1	4	yes	—
349	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
350	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
351	C₂×C₄	C₄×Q₈×C₄₃	1	8	yes	—
352	C₂×C₄	C₄×Q₈×C₄₃	1	16	yes	complemented
353	C₂×C₄	C₂²⋊Q₈×C₄₃	1	8	yes	—
354	C₂×C₄	#124×C₄₃	1	4	yes	—
355	C₂×C₄	C₄⋊Q₈×C₄₃	1	4	yes	—
356	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
357	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
358	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
359	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
360	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
361	C₂²	C₂×C₄×Q₈×C₄₃	1	2	yes	—
362	C₂²	C₂×C₄×Q₈×C₄₃	1	4	yes	—
363	C₂²	C₄×#41×C₄₃	1	2	yes	—
364	C₂²	C₄×#41×C₄₃	1	4	yes	—
365	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
366	C₂²	C₄₃×#525	1	2	yes	—
367	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
368	C₂²	C₄₃×#529	1	4	yes	—
369	C₂²	C₂×C₄⋊Q₈×C₄₃	1	1	yes	characteristic
370	C₂²	C₄₃×#532	1	2	yes	—
371	C₂²	C₄₃×#533	1	4	yes	—
372	C₄	—	2	8	no	—
373	C₄	—	2	4	no	—
374	C₄	—	2	16	no	—
375	C₄	—	4	4	no	—
376	C₄	—	4	8	no	—
377	C₄	C₄×C₂²⋊C₄×C₄₃	1	8	yes	—
378	C₄	C₄₃×#391	1	8	yes	direct product factor
379	C₂	C₂×C₄×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
380	C₂	C₄²×Q₈×C₄₃	1	2	yes	—
381	C₂	C₂×C₄₃×#391	1	1	yes	characteristic
382	C₂	C₄₃×#2295	1	2	yes	—
383	C₂	C₄₃×#2297	1	1	yes	characteristic
384	C₂	C₄×C₂²⋊Q₈×C₄₃	1	4	yes	—
385	C₂	C₄×#124×C₄₃	1	2	yes	—
386	C₂	C₄×C₄⋊Q₈×C₄₃	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₃	C₂³
commutator	C₂²	C₂²×C₄²×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
socle, prime radical	C₂⁴×C₄₃	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₂×C₄×Q₈×C₄₃	C₄	semidirect
21. C₄₃×#391	C₄	direct (N × H)
64. C₂×C₄²×C₄₃	Q₈	semidirect
73. C₂×Q₈×C₄₃	C₄²	semidirect
158. C₂×C₄×C₄₃	C₄×Q₈	semidirect
162. C₄×#391	C₄₃	direct (N × H)
185. C₄×C₄₃	#391	direct (N × H)
204. C₂×C₄×Q₈	C₄×C₄₃	semidirect
214. #391	C₄×C₄₃	direct (N × H)
220. C₄₃	C₄×#391	direct (N × H)
258. C₂×C₄²	Q₈×C₄₃	semidirect
267. C₂×Q₈	C₄²×C₄₃	semidirect
352. C₂×C₄	C₄×Q₈×C₄₃	semidirect
378. C₄	C₄₃×#391	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×C₄×Q₈×C₄₃	2
C₂×C₄₃×#391	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₂×C₄³×C₄₃	2
C₄₃×#1436	2
C₄₃×C₄⋊#95	2
C₄×#95×C₄₃	2
C₄×#391	43

Subgroups — C4×C43×#391 #24933785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₃×#391 #24933785