Subgroups — C₄×#14582636 #24987476

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582636	C₂	1	2	yes	maximal
3	C₄×C₄₃⋊#95	C₂	1	1	yes	maximal, characteristic
4	#19132473	C₂	1	2	yes	maximal
5	C₄×C₂²⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×Dic₄₃	—	2	1	no	—
7	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
9	C₂×C₄₃⋊#95	—	2	1	no	—
10	C₂×C₄₃⋊#95	C₂²	1	2	yes	—
11	#14582654	—	2	1	no	—
12	#14582636	C₄	1	8	yes	direct product factor
13	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₃	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#391	C₄	1	1	yes	characteristic, complemented
17	C₄₃×#389	C₄	1	1	yes	characteristic, complemented
18	C₄₃×#387	—	2	1	no	—
19	C₄₃×#385	—	2	1	no	—
20	C₄₃×#380	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
22	C₄×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic, complemented
23	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
24	C₂³×Dic₄₃	—	2	2	no	—
25	C₂²×C₄₃⋊C₈	—	2	2	no	—
26	C₂×C₄×Dic₄₃	—	2	4	no	—
27	C₂×C₄×Dic₄₃	—	4	2	no	—
28	C₂×C₄×Dic₄₃	—	4	2	no	—
29	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
30	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
31	C₄×C₄₃⋊C₈	—	4	2	no	—
32	C₄₃⋊#95	—	2	4	no	—
33	C₄₃⋊#95	—	2	2	no	—
34	C₄₃⋊#95	C₂×C₄	1	4	yes	—
35	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂²⋊Q₈×C₄₃	—	2	2	no	—
40	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
41	C₄×Q₈×C₄₃	—	4	2	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
45	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
50	C₂×C₄²×C₄₃	—	2	1	no	—
51	C₂×C₄²×C₄₃	—	2	1	no	—
52	C₂×C₄²×C₄₃	—	4	2	no	—
53	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
57	#95×C₄₃	—	2	1	no	—
58	#95×C₄₃	—	2	1	no	—
59	#95×C₄₃	—	2	1	no	—
60	#95×C₄₃	—	2	1	no	—
61	#95×C₄₃	—	2	1	no	—
62	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
63	C₂×Q₈×C₄₃	—	2	1	no	—
64	C₂×Q₈×C₄₃	—	4	1	no	—
65	C₂×Q₈×C₄₃	—	4	1	no	—
66	C₂×Q₈×C₄₃	C₄²	1	2	yes	complemented
67	C₂²×C₄×C₄₃	—	2	2	no	—
68	C₂²×C₄×C₄₃	—	2	2	no	—
69	C₂²×C₄×C₄₃	—	2	2	no	—
70	C₂²×C₄×C₄₃	—	2	1	no	—
71	C₂²×C₄×C₄₃	—	2	1	no	—
72	C₂²×C₄×C₄₃	—	2	1	no	—
73	C₂²×C₄×C₄₃	—	2	1	no	—
74	C₂²×C₄×C₄₃	—	2	2	no	—
75	C₂²×C₄×C₄₃	—	4	1	no	—
76	C₂²×C₄×C₄₃	—	4	1	no	—
77	C₂²×C₄×C₄₃	—	4	1	no	—
78	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	SD₁₆	1	2	yes	—
83	C₂²×C₄×C₄₃	Q₁₆	1	2	yes	—
84	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	#41	1	2	yes	—
88	C₂²×Dic₄₃	—	2	4	no	—
89	C₂²×Dic₄₃	—	2	4	no	—
90	C₂²×Dic₄₃	—	2	4	no	—
91	C₂²×Dic₄₃	—	4	2	no	—
92	C₂²×Dic₄₃	—	4	2	no	—
93	C₂²×Dic₄₃	—	4	2	no	—
94	C₂²×Dic₄₃	—	4	2	no	—
95	C₄⋊C₄×C₄₃	—	2	1	no	—
96	C₄⋊C₄×C₄₃	—	2	4	no	—
97	C₄⋊C₄×C₄₃	—	4	1	no	—
98	C₄⋊C₄×C₄₃	—	4	1	no	—
99	C₄⋊C₄×C₄₃	—	4	2	no	—
100	C₄⋊C₄×C₄₃	—	4	2	no	—
101	C₄⋊C₄×C₄₃	C₄²	1	2	yes	complemented
102	C₂²⋊C₄×C₄₃	—	2	4	no	—
103	C₂²⋊C₄×C₄₃	—	4	2	no	—
104	C₄²×C₄₃	—	2	2	no	—
105	C₄²×C₄₃	—	2	2	no	—
106	C₄²×C₄₃	—	4	1	no	—
107	C₄²×C₄₃	—	4	1	no	—
108	C₄²×C₄₃	—	4	2	no	—
109	C₄²×C₄₃	—	4	2	no	—
110	C₄×Dic₄₃	—	4	8	no	—
111	C₂×C₄₃⋊C₈	—	2	4	no	—
112	C₂×C₄₃⋊C₈	—	4	2	no	—
113	C₂×C₄₃⋊C₈	—	4	2	no	—
114	C₂³×C₄₃	—	2	1	no	—
115	C₂³×C₄₃	—	2	1	no	—
116	C₂³×C₄₃	—	2	1	no	—
117	C₂³×C₄₃	—	2	1	no	—
118	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₄₃	C₄×D₄	1	2	yes	—
120	C₂³×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
121	C₂³×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
122	C₂³×C₄₃	#135	1	2	yes	—
123	Q₈×C₄₃	—	4	2	no	—
124	Q₈×C₄₃	—	4	2	no	—
125	C₂×C₄×C₄₃	—	2	1	no	—
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	4	no	—
134	C₂×C₄×C₄₃	—	2	4	no	—
135	C₂×C₄×C₄₃	—	2	2	no	—
136	C₂×C₄×C₄₃	—	2	2	no	—
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	2	1	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	4	2	no	—
141	C₂×C₄×C₄₃	—	4	2	no	—
142	C₂×C₄×C₄₃	—	4	4	no	—
143	C₂×C₄×C₄₃	—	4	1	no	—
144	C₂×C₄×C₄₃	—	4	1	no	—
145	C₂×C₄×C₄₃	—	4	1	no	—
146	C₂×C₄×C₄₃	—	4	1	no	—
147	C₂×C₄×C₄₃	—	4	1	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	1	no	—
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	#99	1	2	yes	—
154	C₂×C₄×C₄₃	#103	1	2	yes	—
155	C₂×C₄×C₄₃	#103	1	2	yes	—
156	C₂×C₄×C₄₃	#104	1	2	yes	—
157	C₂×C₄×C₄₃	#104	1	2	yes	—
158	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
161	C₂×Dic₄₃	—	2	8	no	—
162	C₂×Dic₄₃	—	4	4	no	—
163	C₂×Dic₄₃	—	4	4	no	—
164	C₂×Dic₄₃	—	4	4	no	—
165	C₂×Dic₄₃	—	4	4	no	—
166	C₂×Dic₄₃	—	4	4	no	—
167	C₂×Dic₄₃	—	4	4	no	—
168	C₄₃⋊C₈	—	4	4	no	—
169	C₄×#328	—	43	1	no	maximal, Sylow
170	C₂²×C₄₃	—	2	2	no	—
171	C₂²×C₄₃	—	2	1	no	—
172	C₂²×C₄₃	—	2	1	no	—
173	C₂²×C₄₃	—	2	2	no	—
174	C₂²×C₄₃	—	2	2	no	—
175	C₂²×C₄₃	—	2	2	no	—
176	C₂²×C₄₃	—	2	1	no	—
177	C₂²×C₄₃	—	2	1	no	—
178	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₄₃	C₂×#99	1	1	yes	characteristic
180	C₂²×C₄₃	#410	1	1	yes	characteristic
181	C₂²×C₄₃	C₂×#103	1	1	yes	characteristic
182	C₂²×C₄₃	#416	1	1	yes	characteristic
183	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
184	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
185	C₂²×C₄₃	C₄×SD₁₆	1	2	yes	—
186	C₂²×C₄₃	C₄×Q₁₆	1	2	yes	—
187	C₄×C₄₃	—	2	2	no	—
188	C₄×C₄₃	—	2	1	no	—
189	C₄×C₄₃	—	2	1	no	—
190	C₄×C₄₃	—	2	2	no	—
191	C₄×C₄₃	—	2	2	no	—
192	C₄×C₄₃	—	4	2	no	—
193	C₄×C₄₃	—	4	1	no	—
194	C₄×C₄₃	—	4	2	no	—
195	C₄×C₄₃	—	8	1	no	—
196	C₄×C₄₃	—	8	1	no	—
197	C₄×C₄₃	#328	1	4	yes	complemented
198	Dic₄₃	—	4	8	no	—
199	C₄×C₂²⋊Q₈	D₄₃	1	1	yes	characteristic
200	C₄×C₂²⋊C₈	—	43	1	no	—
201	C₂×#328	—	43	2	no	—
202	C₄×#95	—	43	1	no	—
203	#1294	—	43	2	no	—
204	C₂×C₄₃	—	2	2	no	—
205	C₂×C₄₃	—	2	2	no	—
206	C₂×C₄₃	C₂×#328	1	1	yes	characteristic
207	C₂×C₄₃	#1500	1	1	yes	characteristic
208	C₂×C₄₃	#1501	1	1	yes	characteristic
209	C₂×C₄₃	#1503	1	1	yes	characteristic
210	C₂×C₄₃	C₄×#99	1	1	yes	characteristic
211	C₂×C₄₃	C₄×#104	1	1	yes	characteristic
212	C₂×C₄₃	C₄×#103	1	1	yes	characteristic
213	C₂×C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
214	C₂×C₄×Q₈	Dic₄₃	1	1	yes	characteristic, complemented
215	C₂²×C₄²	—	86	1	no	—
216	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
217	C₂×C₂²⋊C₈	—	43	2	no	—
218	C₂×C₄×C₈	—	86	1	no	—
219	#391	Dic₄₃	1	1	yes	characteristic, complemented
220	#389	Dic₄₃	1	1	yes	characteristic, complemented
221	#387	—	2	1	no	—
222	#385	—	2	1	no	—
223	#380	C₂×D₄₃	1	1	yes	characteristic
224	C₄×C₄⋊C₄	—	2	1	no	—
225	C₄×C₄⋊C₄	Dic₄₃	1	1	yes	characteristic, complemented
226	C₄×C₂²⋊C₄	—	2	1	no	—
227	C₂×#95	—	43	2	no	—
228	C₂×#95	—	86	1	no	—
229	#336	—	86	1	no	—
230	#328	—	43	8	no	—
231	C₄₃	C₄×#328	1	1	yes	characteristic, complemented, Sylow
232	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
233	C₂³×C₄	—	86	2	no	—
234	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
235	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
236	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
237	C₂²×C₈	—	86	2	no	—
238	C₂²⋊Q₈	—	2	2	no	—
239	C₂²⋊Q₈	C₄×D₄₃	1	4	yes	—
240	C₄×Q₈	—	4	2	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	4	2	no	—
252	C₂×C₄²	—	86	4	no	—
253	C₂×C₄²	—	172	2	no	—
254	C₂×C₄²	—	172	2	no	—
255	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
256	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
257	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
259	C₂²⋊C₈	—	43	4	no	—
260	C₂²⋊C₈	—	86	2	no	—
261	C₄×C₈	—	172	2	no	—
262	#95	—	2	1	no	—
263	#95	—	2	1	no	—
264	#95	—	2	1	no	—
265	#95	—	2	1	no	—
266	#95	—	2	1	no	—
267	#95	—	43	4	no	—
268	#95	—	86	4	no	—
269	#95	—	86	2	no	—
270	C₂⁴	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×Q₈	C₄×Dic₄₃	1	2	yes	complemented
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	86	4	no	—
287	C₂²×C₄	—	86	4	no	—
288	C₂²×C₄	—	86	4	no	—
289	C₂²×C₄	—	172	2	no	—
290	C₂²×C₄	—	172	2	no	—
291	C₂²×C₄	—	172	2	no	—
292	C₂²×C₄	—	172	2	no	—
293	C₂²×C₄	#10621884	1	2	yes	—
294	C₂²×C₄	#10621885	1	2	yes	—
295	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
296	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
297	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
300	C₂²×C₄	#10621898	1	2	yes	—
301	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
303	C₂×C₈	—	86	4	no	—
304	C₂×C₈	—	172	2	no	—
305	C₂×C₈	—	172	2	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	C₄×Dic₄₃	1	2	yes	complemented
313	C₂²⋊C₄	—	2	4	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	4	1	no	—
319	C₄²	—	4	2	no	—
320	C₄²	—	4	2	no	—
321	C₄²	—	172	8	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
327	C₂³	C₄×C₂²⋊D₄₃	1	2	yes	—
328	C₂³	C₂×#10621884	1	1	yes	characteristic
329	C₂³	C₂×#10621885	1	1	yes	characteristic
330	C₂³	#13063345	1	2	yes	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	86	8	no	—
362	C₂×C₄	—	172	4	no	—
363	C₂×C₄	—	172	4	no	—
364	C₂×C₄	—	172	4	no	—
365	C₂×C₄	—	172	4	no	—
366	C₂×C₄	—	172	4	no	—
367	C₂×C₄	—	172	4	no	—
368	C₂×C₄	#13063240	1	2	yes	—
369	C₂×C₄	#13063249	1	2	yes	—
370	C₂×C₄	#13063249	1	2	yes	—
371	C₂×C₄	#13063252	1	2	yes	—
372	C₂×C₄	#13063252	1	2	yes	—
373	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
374	C₂×C₄	#13063284	1	1	yes	characteristic
375	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
376	C₈	—	172	4	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	C₄×C₂²⋊Dic₄₃	1	1	yes	characteristic
386	C₂²	C₂×#13063240	1	1	yes	characteristic
387	C₂²	#14582873	1	1	yes	characteristic
388	C₂²	C₂×#13063249	1	1	yes	characteristic
389	C₂²	#14582895	1	1	yes	characteristic
390	C₂²	C₂×#13063252	1	1	yes	characteristic
391	C₂²	C₂×#13063252	1	1	yes	characteristic
392	C₂²	C₄×#10621884	1	2	yes	—
393	C₂²	C₄×#10621885	1	2	yes	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	1	no	—
404	C₄	—	172	8	no	—
405	C₄	#14582636	1	4	yes	direct product factor
406	C₂	—	2	2	no	—
407	C₂	—	2	2	no	—
408	C₂	C₂×#14582636	1	1	yes	characteristic
409	C₂	#19133081	1	1	yes	characteristic
410	C₂	#19133086	1	1	yes	characteristic
411	C₂	#19133094	1	1	yes	characteristic
412	C₂	C₄×#13063240	1	1	yes	characteristic
413	C₂	C₄×#13063252	1	1	yes	characteristic
414	C₂	C₄×#13063249	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄×C₂²⋊Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₄₃
hypocenter	C₄₃	C₄×#328
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
12. #14582636	C₄	direct (N × H)
14. C₂×C₄×Q₈×C₄₃	C₄	semidirect
16. C₄₃×#391	C₄	semidirect
17. C₄₃×#389	C₄	semidirect
22. C₄×C₄⋊C₄×C₄₃	C₄	semidirect
66. C₂×Q₈×C₄₃	C₄²	semidirect
101. C₄⋊C₄×C₄₃	C₄²	semidirect
197. C₄×C₄₃	#328	semidirect
214. C₂×C₄×Q₈	Dic₄₃	semidirect
219. #391	Dic₄₃	semidirect
220. #389	Dic₄₃	semidirect
225. C₄×C₄⋊C₄	Dic₄₃	semidirect
231. C₄₃	C₄×#328	semidirect
274. C₂×Q₈	C₄×Dic₄₃	semidirect
312. C₄⋊C₄	C₄×Dic₄₃	semidirect
405. C₄	#14582636	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₂²⋊(C₄₃⋊C₈)	2
C₂×#14582636	2
C₄×C₄₃⋊#95	2
#19132473	2
C₄×C₂²⋊Q₈×C₄₃	2
C₄×#328	43

Subgroups — C4×#14582636 #24987476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#14582636 #24987476