Subgroups — #25065235

Order 11008.

996 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583456	C₂	1	1	yes	maximal, characteristic
2	#19143228	C₂	1	1	yes	maximal, characteristic
3	#19133323	C₂	1	4	yes	maximal, complemented
4	#19133283	C₂	1	4	yes	maximal, complemented
5	#19133277	C₂	1	2	yes	maximal, complemented
6	#19133268	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₃×#423	C₂	1	1	yes	maximal, characteristic
8	#14583456	—	2	1	no	—
9	#14583456	—	2	1	no	—
10	#14583456	—	2	1	no	—
11	#14583456	—	2	1	no	—
12	#14583456	C₄	1	2	yes	—
13	#14583456	C₄	1	2	yes	—
14	#14583456	C₂²	1	2	yes	—
15	#14583456	C₂²	1	2	yes	—
16	C₂×#13063325	C₂²	1	1	yes	characteristic
17	C₂×#13063325	C₂²	1	1	yes	characteristic
18	C₂×#13063317	—	2	1	no	—
19	C₂×#13063304	—	2	1	no	—
20	C₂×#13063304	C₄	1	2	yes	—
21	C₂×C₄×Dic₈₆	—	2	1	no	—
22	C₂×C₄×Dic₈₆	C₄	1	2	yes	—
23	C₂×#13063284	—	2	1	no	—
24	#14582956	—	2	1	no	—
25	#14582956	C₂²	1	2	yes	—
26	#14582952	—	2	1	no	—
27	#14582952	C₂²	1	2	yes	—
28	#14582923	C₂²	1	2	yes	—
29	#14582863	—	2	1	no	—
30	C₄×#10621877	—	2	1	no	—
31	#14582647	C₂²	1	8	yes	complemented
32	#14582646	C₂²	1	8	yes	complemented
33	C₂²×M₁₆×C₄₃	—	2	1	no	—
34	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
35	C₄₃×#423	—	2	1	no	—
36	C₄₃×#423	—	2	1	no	—
37	C₄₃×#423	C₂²	1	2	yes	—
38	C₄₃×#423	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
40	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
41	C₂²×Dic₈₆	—	2	1	no	—
42	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
43	C₂×#10621877	—	2	2	no	—
44	#13063325	—	2	1	no	—
45	#13063325	—	2	1	no	—
46	#13063325	—	2	1	no	—
47	#13063325	—	2	1	no	—
48	#13063325	C₂×C₄	1	2	yes	—
49	#13063325	C₂×C₄	1	2	yes	—
50	#13063325	C₂³	1	2	yes	—
51	#13063325	C₂³	1	2	yes	—
52	#13063317	—	2	2	no	—
53	#13063317	—	2	2	no	—
54	#13063317	—	2	2	no	—
55	#13063317	—	2	2	no	—
56	#13063304	—	2	2	no	—
57	#13063304	—	2	2	no	—
58	#13063304	—	2	2	no	—
59	#13063304	—	2	2	no	—
60	#13063304	—	2	2	no	—
61	#13063304	—	2	2	no	—
62	#13063304	C₂×C₄	1	4	yes	—
63	#13063304	C₂×C₄	1	4	yes	—
64	C₄×Dic₈₆	—	2	2	no	—
65	C₄×Dic₈₆	—	2	2	no	—
66	C₄×Dic₈₆	—	2	2	no	—
67	C₄×Dic₈₆	—	2	2	no	—
68	C₄×Dic₈₆	—	2	2	no	—
69	C₄×Dic₈₆	—	2	2	no	—
70	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
71	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
72	#13063284	—	2	2	no	—
73	#13063284	—	2	2	no	—
74	#13063284	—	2	2	no	—
75	#13063284	—	2	2	no	—
76	C₂×C₄⋊Dic₄₃	—	2	1	no	—
77	C₂×C₄⋊Dic₄₃	—	2	1	no	—
78	C₂×C₄⋊Dic₄₃	—	2	1	no	—
79	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
80	C₂×Dic₄₃⋊C₄	—	2	2	no	—
81	C₂×Dic₄₃⋊C₄	—	2	2	no	—
82	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
83	C₂×C₄×Dic₄₃	—	2	2	no	—
84	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
85	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
86	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
87	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
88	#13063236	—	2	2	no	—
89	C₄×C₄₃⋊C₈	—	2	2	no	—
90	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
91	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
92	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
93	C₂×M₁₆×C₄₃	—	2	2	no	—
94	C₂×M₁₆×C₄₃	—	2	2	no	—
95	C₂×M₁₆×C₄₃	—	4	4	no	—
96	C₂²×C₈×C₄₃	—	2	2	no	—
97	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
109	C₄⋊C₈×C₄₃	—	2	2	no	—
110	C₄⋊C₈×C₄₃	—	2	2	no	—
111	C₄⋊C₈×C₄₃	—	2	2	no	—
112	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
113	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	4	no	—
117	C₂²×C₄×C₄₃	—	4	2	no	—
118	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×Dic₄₃	—	2	2	no	—
137	C₂²×Dic₄₃	—	2	2	no	—
138	C₂×Dic₈₆	—	2	2	no	—
139	C₂×Dic₈₆	—	2	2	no	—
140	C₂×Dic₈₆	—	2	2	no	—
141	C₂×Dic₈₆	—	4	2	no	—
142	C₂×Dic₈₆	—	4	2	no	—
143	C₂×Dic₈₆	—	4	4	no	—
144	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
145	M₁₆×C₄₃	—	4	4	no	—
146	M₁₆×C₄₃	—	4	4	no	—
147	C₂×C₈×C₄₃	—	2	4	no	—
148	C₂×C₈×C₄₃	—	4	4	no	—
149	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
153	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
165	C₂²⋊Dic₄₃	—	2	4	no	—
166	C₂²⋊Dic₄₃	—	2	4	no	—
167	C₄⋊Dic₄₃	—	2	2	no	—
168	C₄⋊Dic₄₃	—	2	2	no	—
169	C₄⋊Dic₄₃	—	2	2	no	—
170	C₄⋊Dic₄₃	—	2	2	no	—
171	C₄⋊Dic₄₃	—	2	2	no	—
172	C₄⋊Dic₄₃	—	2	2	no	—
173	C₄⋊Dic₄₃	—	2	2	no	—
174	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
175	Dic₄₃⋊C₄	—	2	4	no	—
176	Dic₄₃⋊C₄	—	2	4	no	—
177	Dic₄₃⋊C₄	—	2	4	no	—
178	Dic₄₃⋊C₄	—	2	4	no	—
179	C₄×Dic₄₃	—	2	4	no	—
180	C₄×Dic₄₃	—	2	4	no	—
181	#10621877	—	4	4	no	—
182	C₂×C₄₃⋊C₈	—	2	4	no	—
183	C₂³×C₄₃	—	2	2	no	—
184	C₂³×C₄₃	—	2	2	no	—
185	C₂³×C₄₃	—	4	1	no	—
186	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	1	no	—
193	C₂×C₄×C₄₃	—	2	1	no	—
194	C₂×C₄×C₄₃	—	2	1	no	—
195	C₂×C₄×C₄₃	—	2	2	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	2	2	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	2	no	—
203	C₂×C₄×C₄₃	—	2	2	no	—
204	C₂×C₄×C₄₃	—	4	1	no	—
205	C₂×C₄×C₄₃	—	4	1	no	—
206	C₂×C₄×C₄₃	—	4	1	no	—
207	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
217	C₂×C₄×C₄₃	#137	1	2	yes	—
218	C₂×C₄×C₄₃	#137	1	4	yes	—
219	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×Dic₄₃	—	2	4	no	—
223	C₂×Dic₄₃	—	2	4	no	—
224	C₂×Dic₄₃	—	4	4	no	—
225	C₂×Dic₄₃	—	4	4	no	—
226	Dic₈₆	—	4	2	no	—
227	Dic₈₆	—	4	2	no	—
228	Dic₈₆	—	4	4	no	—
229	Dic₈₆	—	4	4	no	—
230	Dic₈₆	—	4	4	no	—
231	C₈×C₄₃	—	4	4	no	—
232	C₄₃⋊C₈	—	4	4	no	—
233	#17749	—	43	1	no	maximal, Sylow
234	C₂²×C₄₃	—	2	1	no	—
235	C₂²×C₄₃	—	2	1	no	—
236	C₂²×C₄₃	—	2	1	no	—
237	C₂²×C₄₃	—	2	1	no	—
238	C₂²×C₄₃	—	2	1	no	—
239	C₂²×C₄₃	—	2	1	no	—
240	C₂²×C₄₃	—	2	1	no	—
241	C₂²×C₄₃	—	4	4	no	—
242	C₂²×C₄₃	#417	1	2	yes	—
243	C₂²×C₄₃	#419	1	2	yes	—
244	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
245	C₄×C₄₃	—	2	1	no	—
246	C₄×C₄₃	—	2	1	no	—
247	C₄×C₄₃	—	2	1	no	—
248	C₄×C₄₃	—	2	1	no	—
249	C₄×C₄₃	—	2	1	no	—
250	C₄×C₄₃	—	2	1	no	—
251	C₄×C₄₃	—	2	1	no	—
252	C₄×C₄₃	#413	1	2	yes	—
253	C₄×C₄₃	#417	1	2	yes	—
254	C₄×C₄₃	#419	1	2	yes	—
255	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
257	C₄×C₄₃	C₂×#137	1	2	yes	—
258	Dic₄₃	—	4	4	no	—
259	Dic₄₃	—	4	4	no	—
260	C₂×#533	—	43	1	no	—
261	#2920	—	43	1	no	—
262	C₂×#423	D₄₃	1	1	yes	characteristic
263	#1559	—	43	4	no	—
264	#1550	—	43	4	no	—
265	#1548	—	43	2	no	—
266	#1546	—	43	2	no	—
267	C₂×C₄₃	—	2	2	no	—
268	C₂×C₄₃	—	2	2	no	—
269	C₂×C₄₃	—	4	1	no	—
270	C₂×C₄₃	C₂×#413	1	1	yes	characteristic
271	C₂×C₄₃	C₂×#419	1	1	yes	characteristic
272	C₂×C₄₃	C₂×#417	1	1	yes	characteristic
273	C₂²×M₁₆	—	2	1	no	—
274	#533	—	43	2	no	—
275	#533	—	43	2	no	—
276	#533	—	43	2	no	—
277	#533	—	43	2	no	—
278	#533	—	86	1	no	—
279	#533	—	86	1	no	—
280	#533	—	86	1	no	—
281	#533	—	86	1	no	—
282	C₂×C₄⋊Q₈	—	43	1	no	—
283	C₂×C₄⋊Q₈	—	43	1	no	—
284	C₂×#125	—	86	1	no	—
285	C₂×C₂²⋊Q₈	—	43	2	no	—
286	C₂×C₂²⋊Q₈	—	86	1	no	—
287	C₂×C₄×Q₈	—	43	2	no	—
288	C₂×C₄×Q₈	—	86	1	no	—
289	C₂×#117	—	86	1	no	—
290	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
291	#432	—	43	2	no	—
292	#432	—	86	1	no	—
293	#431	—	43	2	no	—
294	#431	—	86	1	no	—
295	#423	—	2	1	no	—
296	#423	—	2	1	no	—
297	#423	—	43	2	no	—
298	#423	C₂×D₄₃	1	2	yes	—
299	#423	C₂×D₄₃	1	2	yes	—
300	C₂×C₄⋊C₈	—	2	1	no	—
301	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
302	#407	—	86	1	no	—
303	C₄×M₁₆	—	86	1	no	—
304	#333	—	43	8	no	—
305	#332	—	43	8	no	—
306	C₄₃	#17749	1	1	yes	characteristic, complemented, Sylow
307	C₂²×Q₈	—	43	2	no	—
308	C₂²×Q₈	—	86	1	no	—
309	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
310	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
311	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
312	C₂×M₁₆	—	2	2	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	—	4	4	no	—
315	C₂×M₁₆	—	86	2	no	—
316	C₂²×C₈	—	2	2	no	—
317	C₄⋊Q₈	—	43	2	no	—
318	C₄⋊Q₈	—	43	2	no	—
319	C₄⋊Q₈	—	43	2	no	—
320	C₄⋊Q₈	—	43	2	no	—
321	C₄⋊Q₈	—	86	1	no	—
322	C₄⋊Q₈	—	86	1	no	—
323	C₄⋊Q₈	—	86	1	no	—
324	C₄⋊Q₈	—	86	1	no	—
325	#125	—	86	2	no	—
326	#125	—	86	2	no	—
327	#125	—	86	2	no	—
328	#125	—	86	2	no	—
329	C₂²⋊Q₈	—	43	4	no	—
330	C₂²⋊Q₈	—	43	4	no	—
331	C₂²⋊Q₈	—	86	2	no	—
332	C₂²⋊Q₈	—	86	2	no	—
333	C₂²⋊Q₈	—	86	2	no	—
334	C₂²⋊Q₈	—	86	2	no	—
335	C₂²⋊Q₈	—	86	2	no	—
336	C₂²⋊Q₈	—	86	2	no	—
337	C₄×Q₈	—	43	4	no	—
338	C₄×Q₈	—	43	4	no	—
339	C₄×Q₈	—	86	2	no	—
340	C₄×Q₈	—	86	2	no	—
341	C₄×Q₈	—	86	2	no	—
342	C₄×Q₈	—	86	2	no	—
343	C₄×Q₈	—	86	2	no	—
344	C₄×Q₈	—	86	2	no	—
345	#117	—	86	2	no	—
346	#117	—	86	2	no	—
347	#117	—	86	2	no	—
348	#117	—	86	2	no	—
349	C₂×C₄⋊C₄	—	43	2	no	—
350	C₂×C₄⋊C₄	—	86	2	no	—
351	C₂×C₄⋊C₄	—	86	2	no	—
352	C₂×C₄⋊C₄	—	86	1	no	—
353	C₂×C₄⋊C₄	—	86	1	no	—
354	C₂×C₄⋊C₄	—	86	1	no	—
355	C₂×C₂²⋊C₄	—	86	2	no	—
356	C₂×C₄²	—	86	2	no	—
357	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
358	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
359	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
360	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
361	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
362	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
363	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
364	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
365	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
366	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
367	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
368	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
369	C₄⋊C₈	—	2	2	no	—
370	C₄⋊C₈	—	2	2	no	—
371	C₄⋊C₈	—	2	2	no	—
372	C₄⋊C₈	—	43	4	no	—
373	C₄⋊C₈	—	86	2	no	—
374	C₄⋊C₈	C₂²×D₄₃	1	4	yes	—
375	C₂²⋊C₈	—	86	2	no	—
376	C₂²⋊C₈	—	86	2	no	—
377	#97	—	86	2	no	—
378	C₄×C₈	—	86	2	no	—
379	C₂⁴	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
380	C₂×Q₈	—	43	4	no	—
381	C₂×Q₈	—	86	2	no	—
382	C₂×Q₈	—	86	2	no	—
383	C₂×Q₈	—	86	2	no	—
384	C₂×Q₈	—	172	4	no	—
385	C₂×Q₈	—	172	2	no	—
386	C₂×Q₈	—	172	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	86	2	no	—
392	C₂²×C₄	—	86	2	no	—
393	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
394	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
395	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
396	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
397	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
398	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
399	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
400	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
401	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
403	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
408	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
410	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
411	M₁₆	—	4	4	no	—
412	M₁₆	—	4	4	no	—
413	M₁₆	—	172	4	no	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	4	4	no	—
416	C₂×C₈	—	86	4	no	—
417	C₄⋊C₄	—	43	4	no	—
418	C₄⋊C₄	—	86	2	no	—
419	C₄⋊C₄	—	86	2	no	—
420	C₄⋊C₄	—	86	2	no	—
421	C₄⋊C₄	—	86	4	no	—
422	C₄⋊C₄	—	86	4	no	—
423	C₄⋊C₄	—	86	4	no	—
424	C₄⋊C₄	—	86	4	no	—
425	C₄⋊C₄	—	86	2	no	—
426	C₄⋊C₄	—	86	2	no	—
427	C₄⋊C₄	—	86	2	no	—
428	C₄⋊C₄	—	86	2	no	—
429	C₂²⋊C₄	—	86	4	no	—
430	C₂²⋊C₄	—	86	4	no	—
431	C₄²	—	86	4	no	—
432	C₄²	—	86	4	no	—
433	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
434	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
435	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
436	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
437	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
438	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
439	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
440	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
441	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
442	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
443	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
444	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
445	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
446	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
447	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
448	C₄²	C₂³×D₄₃	1	1	yes	characteristic
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	4	1	no	—
452	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
453	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
454	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
455	Q₈	—	172	4	no	—
456	Q₈	—	172	4	no	—
457	Q₈	—	172	4	no	—
458	Q₈	—	172	2	no	—
459	Q₈	—	172	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	86	4	no	—
479	C₂×C₄	—	86	4	no	—
480	C₂×C₄	—	172	4	no	—
481	C₂×C₄	—	172	4	no	—
482	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
483	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
484	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
485	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
486	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
487	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
488	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
489	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
490	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
491	C₂×C₄	#13063351	1	2	yes	—
492	C₂×C₄	#13063356	1	2	yes	—
493	C₂×C₄	#13063358	1	4	yes	—
494	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
495	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
497	C₈	—	4	4	no	—
498	C₈	—	172	4	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	4	4	no	—
507	C₂²	#14582898	1	2	yes	—
508	C₂²	#14582909	1	2	yes	—
509	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	172	4	no	—
518	C₄	—	172	4	no	—
519	C₄	#14582881	1	2	yes	—
520	C₄	#14582898	1	2	yes	—
521	C₄	#14582909	1	2	yes	—
522	C₄	C₂×#13063351	1	1	yes	characteristic
523	C₄	C₂×#13063356	1	1	yes	characteristic
524	C₄	C₂×#13063358	1	2	yes	—
525	C₂	—	2	2	no	—
526	C₂	—	2	2	no	—
527	C₂	—	4	1	no	—
528	C₂	C₂×#14582881	1	1	yes	characteristic
529	C₂	C₂×#14582909	1	1	yes	characteristic
530	C₂	C₂×#14582898	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#423	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₄₃	C₂²⋊C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₂×#423	D₄₃
hypocenter	C₄₃	#17749
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #19133323	C₂	semidirect
4. #19133283	C₂	semidirect
5. #19133277	C₂	semidirect
6. #19133268	C₂	semidirect
31. #14582647	C₂²	semidirect
32. #14582646	C₂²	semidirect
306. C₄₃	#17749	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583456	2
#19143228	2
#19133323	2
#19133283	2
#19133277	2
#19133268	2
C₂×C₄₃×#423	2
#17749	43