Subgroups — #25105987

Order 11008.

1444 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583449	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063284	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135514	C₂	1	4	yes	maximal, complemented
4	#19135422	C₂	1	4	yes	maximal, complemented
5	#19134538	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#10621898	C₂²	1	2	yes	—
8	#14583449	—	2	1	no	—
9	#14583449	—	2	1	no	—
10	#14583449	—	2	1	no	—
11	#14583449	—	2	1	no	—
12	#14583449	C₄	1	2	yes	complemented
13	#14583449	C₄	1	2	yes	complemented
14	#14583449	C₂²	1	2	yes	—
15	#14583449	C₂²	1	2	yes	—
16	C₂×#13063325	C₄	1	1	yes	characteristic, complemented
17	C₂×#13063322	C₄	1	1	yes	characteristic, complemented
18	C₂×#13063313	C₄	1	2	yes	complemented
19	C₂×#13063299	—	2	1	no	—
20	C₂×#13063299	—	2	1	no	—
21	C₂×C₄×D₁₇₂	—	2	1	no	—
22	C₂×C₄×D₁₇₂	—	2	1	no	—
23	C₂×#13063284	—	2	1	no	—
24	C₂×#13063251	C₂²	1	16	yes	complemented
25	C₄×C₄⋊Dic₄₃	—	2	1	no	—
26	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	complemented
27	C₄×C₂²⋊Dic₄₃	—	2	1	no	—
28	C₄×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
29	#14582745	—	2	1	no	—
30	C₄²×Dic₄₃	C₂²	1	2	yes	complemented
31	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#432	—	2	1	no	—
33	C₄₃×#432	—	2	1	no	—
34	C₄₃×#431	—	2	1	no	—
35	C₄₃×#431	—	2	1	no	—
36	C₄₃×#423	C₂²	1	2	yes	complemented
37	C₄₃×#407	C₂²	1	2	yes	—
38	C₄×M₁₆×C₄₃	C₂²	1	2	yes	complemented
39	C₂×#10621898	—	2	2	no	—
40	C₂×#10621898	—	2	2	no	—
41	C₂×#10621898	—	4	8	no	—
42	C₂×#10621898	C₂×C₄	1	4	yes	—
43	C₂×#10621898	C₂³	1	4	yes	—
44	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
45	C₂²×D₁₇₂	—	2	1	no	—
46	C₂²×D₁₇₂	—	2	1	no	—
47	C₂²×D₁₇₂	C₂×C₄	1	2	yes	—
48	C₂²×C₂²⋊D₄₃	—	2	2	no	—
49	C₂²×C₄×D₄₃	—	2	2	no	—
50	#13063325	—	2	1	no	—
51	#13063325	—	2	1	no	—
52	#13063325	C₂×C₄	1	2	yes	—
53	#13063325	C₂×C₄	1	2	yes	—
54	#13063322	—	2	1	no	—
55	#13063322	—	2	1	no	—
56	#13063322	C₂×C₄	1	2	yes	—
57	#13063322	C₂×C₄	1	2	yes	—
58	#13063313	—	2	2	no	—
59	#13063313	—	2	2	no	—
60	#13063313	C₂×C₄	1	4	yes	—
61	#13063313	C₂×C₄	1	4	yes	—
62	#13063299	—	2	2	no	—
63	#13063299	—	2	2	no	—
64	#13063299	—	2	2	no	—
65	#13063299	—	2	2	no	—
66	#13063299	—	2	2	no	—
67	#13063299	—	2	2	no	—
68	#13063299	—	2	2	no	—
69	#13063299	—	2	2	no	—
70	C₄×D₁₇₂	—	2	2	no	—
71	C₄×D₁₇₂	—	2	2	no	—
72	C₄×D₁₇₂	—	2	2	no	—
73	C₄×D₁₇₂	—	2	2	no	—
74	C₄×D₁₇₂	—	2	2	no	—
75	C₄×D₁₇₂	—	2	2	no	—
76	C₄×D₁₇₂	—	2	2	no	—
77	C₄×D₁₇₂	—	2	2	no	—
78	#13063284	—	2	8	no	—
79	C₂×C₄⋊Dic₄₃	—	2	1	no	—
80	C₂×C₄⋊Dic₄₃	—	2	1	no	—
81	C₂×C₄⋊Dic₄₃	—	2	2	no	—
82	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
83	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
84	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
85	C₂×C₄×Dic₄₃	—	2	2	no	—
86	C₂×C₄×Dic₄₃	—	2	2	no	—
87	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
88	#13063251	—	4	16	no	—
89	C₄₃⋊#95	—	2	2	no	—
90	C₄₃⋊#95	—	2	2	no	—
91	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
92	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
95	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₃	D₄	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	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	C₄⋊C₈×C₄₃	—	2	2	no	—
108	C₄⋊C₈×C₄₃	—	2	2	no	—
109	C₂²⋊C₈×C₄₃	—	2	2	no	—
110	C₂²⋊C₈×C₄₃	—	2	2	no	—
111	#97×C₄₃	—	2	2	no	—
112	C₄×C₈×C₄₃	—	2	2	no	—
113	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂³×D₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	4	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	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
136	C₂×C₂²⋊D₄₃	—	2	4	no	—
137	C₂×C₂²⋊D₄₃	—	2	4	no	—
138	C₂×C₂²⋊D₄₃	—	4	8	no	—
139	C₂²×Dic₄₃	—	2	2	no	—
140	C₂²×Dic₄₃	—	2	4	no	—
141	#10621898	—	2	16	no	—
142	#10621898	—	4	8	no	—
143	#10621898	—	4	8	no	—
144	#10621898	—	4	8	no	—
145	C₂×D₁₇₂	—	2	2	no	—
146	C₂×D₁₇₂	—	2	2	no	—
147	C₂×D₁₇₂	—	2	2	no	—
148	C₂×D₁₇₂	—	2	2	no	—
149	C₂×D₁₇₂	—	2	2	no	—
150	C₂×D₁₇₂	—	4	4	no	—
151	C₂×D₁₇₂	—	4	4	no	—
152	C₂×D₁₇₂	—	4	4	no	—
153	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
154	C₂×C₄×D₄₃	—	2	4	no	—
155	C₂×C₄×D₄₃	—	2	4	no	—
156	C₂×C₄×D₄₃	—	4	8	no	—
157	C₂×Dic₈₆	—	2	2	no	—
158	C₂×Dic₈₆	—	4	4	no	—
159	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
160	M₁₆×C₄₃	—	2	8	no	—
161	C₂×C₈×C₄₃	—	2	4	no	—
162	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
164	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
165	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
178	C₂²⋊Dic₄₃	—	2	8	no	—
179	(C₂×D₄₃)⋊C₄	—	2	4	no	—
180	(C₂×D₄₃)⋊C₄	—	2	4	no	—
181	(C₂×D₄₃)⋊C₄	—	2	4	no	—
182	(C₂×D₄₃)⋊C₄	—	2	4	no	—
183	C₄⋊Dic₄₃	—	2	8	no	—
184	C₄⋊Dic₄₃	—	2	2	no	—
185	C₄⋊Dic₄₃	—	2	2	no	—
186	C₄⋊Dic₄₃	—	2	2	no	—
187	C₄⋊Dic₄₃	—	2	2	no	—
188	C₄×Dic₄₃	—	2	8	no	—
189	C₄×Dic₄₃	—	2	8	no	—
190	C₄×Dic₄₃	—	4	4	no	—
191	C₂³×C₄₃	—	2	2	no	—
192	C₂³×C₄₃	—	2	2	no	—
193	C₂³×C₄₃	—	4	1	no	—
194	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
197	C₂²×D₄₃	—	2	4	no	—
198	C₂²×D₄₃	—	4	4	no	—
199	C₂²×D₄₃	—	4	4	no	—
200	C₂²×D₄₃	—	4	4	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	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	2	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	2	no	—
211	C₂×C₄×C₄₃	—	2	2	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	—	4	1	no	—
216	C₂×C₄×C₄₃	—	4	1	no	—
217	C₂×C₄×C₄₃	#104	1	4	yes	complemented
218	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
231	C₂²⋊D₄₃	—	4	8	no	—
232	C₂²⋊D₄₃	—	4	8	no	—
233	C₂×Dic₄₃	—	2	8	no	—
234	C₂×Dic₄₃	—	2	4	no	—
235	C₂×Dic₄₃	—	4	4	no	—
236	C₂×Dic₄₃	—	4	4	no	—
237	C₂×Dic₄₃	—	4	4	no	—
238	D₁₇₂	—	2	8	no	—
239	D₁₇₂	—	4	4	no	—
240	D₁₇₂	—	4	4	no	—
241	D₁₇₂	—	4	4	no	—
242	D₁₇₂	—	4	4	no	—
243	D₁₇₂	—	4	4	no	—
244	C₄×D₄₃	—	4	8	no	—
245	C₄×D₄₃	—	4	8	no	—
246	Dic₈₆	—	2	8	no	—
247	Dic₈₆	—	4	4	no	—
248	C₈×C₄₃	—	4	4	no	—
249	#21815	—	43	1	no	maximal, Sylow
250	C₂²×C₄₃	—	2	1	no	—
251	C₂²×C₄₃	—	2	1	no	—
252	C₂²×C₄₃	—	2	1	no	—
253	C₂²×C₄₃	—	2	1	no	—
254	C₂²×C₄₃	—	2	1	no	—
255	C₂²×C₄₃	—	2	1	no	—
256	C₂²×C₄₃	—	2	1	no	—
257	C₂²×C₄₃	—	4	4	no	—
258	C₂²×C₄₃	C₂×#104	1	2	yes	—
259	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₄₃	#535	1	2	yes	—
261	C₂×D₄₃	—	4	4	no	—
262	C₂×D₄₃	—	4	4	no	—
263	C₂×D₄₃	—	4	4	no	—
264	C₂×D₄₃	—	8	8	no	—
265	C₄×C₄₃	—	2	1	no	—
266	C₄×C₄₃	—	2	1	no	—
267	C₄×C₄₃	—	2	1	no	—
268	C₄×C₄₃	—	2	1	no	—
269	C₄×C₄₃	—	2	1	no	—
270	C₄×C₄₃	—	2	1	no	—
271	C₄×C₄₃	—	2	1	no	—
272	C₄×C₄₃	C₂×#104	1	2	yes	—
273	C₄×C₄₃	C₂×#104	1	2	yes	—
274	C₄×C₄₃	#421	1	2	yes	—
275	C₄×C₄₃	#518	1	2	yes	—
276	C₄×C₄₃	#535	1	2	yes	—
277	Dic₄₃	—	4	8	no	—
278	Dic₄₃	—	4	4	no	—
279	C₂×#532	—	43	1	no	—
280	#2920	D₄₃	1	1	yes	characteristic, complemented
281	C₄×#117	—	43	1	no	—
282	#1980	—	43	4	no	—
283	#1962	—	43	4	no	—
284	#1789	—	43	4	no	—
285	C₂×C₄₃	—	2	2	no	—
286	C₂×C₄₃	—	2	2	no	—
287	C₂×C₄₃	—	4	1	no	—
288	C₂×C₄₃	#2309	1	1	yes	characteristic
289	C₂×C₄₃	C₂²×#104	1	1	yes	characteristic
290	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
291	D₄₃	—	8	4	no	—
292	C₂²×#41	—	43	2	no	—
293	#532	—	43	2	no	—
294	#532	—	43	2	no	—
295	#532	—	43	2	no	—
296	#532	—	43	2	no	—
297	#532	—	86	1	no	—
298	#532	—	86	1	no	—
299	#532	—	86	1	no	—
300	#532	—	86	1	no	—
301	C₂×C₄⋊Q₈	—	43	1	no	—
302	C₂×#127	—	43	1	no	—
303	C₂×#124	—	43	2	no	—
304	C₂×#121	—	86	1	no	—
305	C₂×#121	—	86	1	no	—
306	C₂×C₄×D₄	—	86	1	no	—
307	C₂×C₄×D₄	—	86	1	no	—
308	C₂×#117	—	86	1	no	—
309	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
310	#432	—	2	1	no	—
311	#432	—	2	1	no	—
312	#431	—	2	1	no	—
313	#431	—	2	1	no	—
314	#423	C₂×D₄₃	1	2	yes	complemented
315	C₂×#104	—	43	16	no	—
316	#407	C₂×D₄₃	1	2	yes	—
317	C₄×M₁₆	C₂×D₄₃	1	2	yes	complemented
318	C₄×C₄⋊C₄	—	43	2	no	—
319	C₄×C₄⋊C₄	—	86	1	no	—
320	C₄×C₂²⋊C₄	—	43	2	no	—
321	C₄×C₂²⋊C₄	—	86	1	no	—
322	#376	—	86	1	no	—
323	C₄³	—	43	2	no	—
324	C₄₃	#21815	1	1	yes	characteristic, complemented, Sylow
325	C₂×#41	—	43	4	no	—
326	C₂×#41	—	43	4	no	—
327	C₂×#41	—	86	2	no	—
328	C₂×#41	—	86	2	no	—
329	C₂×#41	—	172	8	no	—
330	C₂²×Q₈	—	43	2	no	—
331	C₂²×D₄	—	43	2	no	—
332	C₂²×D₄	—	86	2	no	—
333	C₂²×D₄	—	86	1	no	—
334	C₂²×D₄	—	86	1	no	—
335	C₂³×C₄	—	86	2	no	—
336	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
337	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
338	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
339	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
340	C₄⋊Q₈	—	43	2	no	—
341	C₄⋊Q₈	—	43	2	no	—
342	C₄⋊Q₈	—	86	1	no	—
343	C₄⋊Q₈	—	86	1	no	—
344	#127	—	43	2	no	—
345	#127	—	43	2	no	—
346	#127	—	86	1	no	—
347	#127	—	86	1	no	—
348	#124	—	43	4	no	—
349	#124	—	43	4	no	—
350	#124	—	86	2	no	—
351	#124	—	86	2	no	—
352	#121	—	86	2	no	—
353	#121	—	86	2	no	—
354	#121	—	86	2	no	—
355	#121	—	86	2	no	—
356	#121	—	86	2	no	—
357	#121	—	86	2	no	—
358	#121	—	86	2	no	—
359	#121	—	86	2	no	—
360	C₄×D₄	—	86	2	no	—
361	C₄×D₄	—	86	2	no	—
362	C₄×D₄	—	86	2	no	—
363	C₄×D₄	—	86	2	no	—
364	C₄×D₄	—	86	2	no	—
365	C₄×D₄	—	86	2	no	—
366	C₄×D₄	—	86	2	no	—
367	C₄×D₄	—	86	2	no	—
368	#117	—	86	8	no	—
369	C₂×C₄⋊C₄	—	86	1	no	—
370	C₂×C₄⋊C₄	—	86	1	no	—
371	C₂×C₄⋊C₄	—	86	2	no	—
372	C₂×C₂²⋊C₄	—	86	2	no	—
373	C₂×C₂²⋊C₄	—	86	2	no	—
374	C₂×C₂²⋊C₄	—	86	2	no	—
375	C₂×C₄²	—	43	4	no	—
376	C₂×C₄²	—	86	2	no	—
377	C₂×C₄²	—	86	2	no	—
378	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
379	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
380	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
381	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
382	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
383	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
384	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
385	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
386	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
387	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
388	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
389	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
390	C₄⋊C₈	—	2	2	no	—
391	C₄⋊C₈	—	2	2	no	—
392	#104	—	172	16	no	—
393	C₂²⋊C₈	—	2	2	no	—
394	C₂²⋊C₈	—	2	2	no	—
395	#97	—	2	2	no	—
396	C₄×C₈	—	2	2	no	—
397	#95	—	86	2	no	—
398	#95	—	86	2	no	—
399	C₂⁴	—	86	2	no	—
400	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
401	#41	—	86	16	no	—
402	#41	—	172	8	no	—
403	#41	—	172	8	no	—
404	#41	—	172	8	no	—
405	C₂×Q₈	—	43	4	no	—
406	C₂×Q₈	—	86	2	no	—
407	C₂×Q₈	—	172	4	no	—
408	C₂×D₄	—	43	4	no	—
409	C₂×D₄	—	86	4	no	—
410	C₂×D₄	—	86	4	no	—
411	C₂×D₄	—	86	2	no	—
412	C₂×D₄	—	86	2	no	—
413	C₂×D₄	—	86	2	no	—
414	C₂×D₄	—	86	2	no	—
415	C₂×D₄	—	86	2	no	—
416	C₂×D₄	—	172	4	no	—
417	C₂×D₄	—	172	4	no	—
418	C₂×D₄	—	172	8	no	—
419	C₂×D₄	—	172	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	86	2	no	—
424	C₂²×C₄	—	86	4	no	—
425	C₂²×C₄	—	86	4	no	—
426	C₂²×C₄	—	86	4	no	—
427	C₂²×C₄	—	172	8	no	—
428	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
429	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
430	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
431	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
432	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
433	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
434	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
435	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
445	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
446	M₁₆	—	2	8	no	—
447	C₂×C₈	—	2	4	no	—
448	C₄⋊C₄	—	86	8	no	—
449	C₄⋊C₄	—	86	2	no	—
450	C₄⋊C₄	—	86	2	no	—
451	C₄⋊C₄	—	86	2	no	—
452	C₄⋊C₄	—	86	2	no	—
453	C₂²⋊C₄	—	86	8	no	—
454	C₂²⋊C₄	—	86	4	no	—
455	C₂²⋊C₄	—	86	4	no	—
456	C₂²⋊C₄	—	86	4	no	—
457	C₂²⋊C₄	—	86	4	no	—
458	C₄²	—	86	8	no	—
459	C₄²	—	86	8	no	—
460	C₄²	—	172	4	no	—
461	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
462	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
463	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
464	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
465	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
466	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
467	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
468	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
469	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
470	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
471	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
472	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
473	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
474	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
475	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
476	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	86	4	no	—
481	C₂³	—	172	4	no	—
482	C₂³	—	172	4	no	—
483	C₂³	—	172	4	no	—
484	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
485	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
486	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
487	Q₈	—	86	8	no	—
488	Q₈	—	172	4	no	—
489	D₄	—	86	8	no	—
490	D₄	—	172	4	no	—
491	D₄	—	172	4	no	—
492	D₄	—	172	8	no	—
493	D₄	—	172	8	no	—
494	D₄	—	172	4	no	—
495	D₄	—	172	4	no	—
496	D₄	—	172	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	86	8	no	—
514	C₂×C₄	—	86	4	no	—
515	C₂×C₄	—	172	8	no	—
516	C₂×C₄	—	172	4	no	—
517	C₂×C₄	—	172	4	no	—
518	C₂×C₄	—	172	4	no	—
519	C₂×C₄	—	172	8	no	—
520	C₂×C₄	#13063251	1	4	yes	complemented
521	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
522	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
523	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
524	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
525	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
526	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
527	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
528	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
529	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
530	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
531	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
533	C₂×C₄	#13063371	1	4	yes	—
534	C₈	—	4	4	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	344	8	no	—
544	C₂²	—	172	4	no	—
545	C₂²	—	172	4	no	—
546	C₂²	—	172	4	no	—
547	C₂²	C₂×#13063251	1	2	yes	—
548	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
549	C₂²	#14583468	1	2	yes	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	172	8	no	—
558	C₄	—	172	4	no	—
559	C₄	C₂×#13063251	1	2	yes	—
560	C₄	C₂×#13063251	1	2	yes	—
561	C₄	#14582915	1	2	yes	—
562	C₄	#14583373	1	2	yes	—
563	C₄	#14583463	1	2	yes	—
564	C₂	—	2	2	no	—
565	C₂	—	2	2	no	—
566	C₂	—	4	1	no	—
567	C₂	—	344	4	no	—
568	C₂	#19137175	1	1	yes	characteristic
569	C₂	C₂²×#13063251	1	1	yes	characteristic
570	C₂	C₂×#14582915	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2920	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₂×#14583449	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2920	D₄₃
hypocenter	C₄₃	#21815
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
2. C₄×#13063284	C₂	semidirect
3. #19135514	C₂	semidirect
4. #19135422	C₂	semidirect
5. #19134538	C₂	semidirect
6. C₄₃×#2920	C₂	semidirect
12. #14583449	C₄	semidirect
13. #14583449	C₄	semidirect
16. C₂×#13063325	C₄	semidirect
17. C₂×#13063322	C₄	semidirect
18. C₂×#13063313	C₄	semidirect
24. C₂×#13063251	C₂²	semidirect
26. C₄×C₄⋊Dic₄₃	C₂²	semidirect
30. C₄²×Dic₄₃	C₂²	semidirect
36. C₄₃×#423	C₂²	semidirect
38. C₄×M₁₆×C₄₃	C₂²	semidirect
217. C₂×C₄×C₄₃	#104	semidirect
280. #2920	D₄₃	semidirect
314. #423	C₂×D₄₃	semidirect
317. C₄×M₁₆	C₂×D₄₃	semidirect
324. C₄₃	#21815	semidirect
520. C₂×C₄	#13063251	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583449	2
C₄×#13063284	2
#19135514	2
#19135422	2
#19134538	2
C₄₃×#2920	2
#21815	43