Subgroups — #25114392

Order 11008.

744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19136999	C₂	1	1	yes	maximal, characteristic
2	#19135312	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135310	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135158	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135154	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135153	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134578	C₂	1	1	yes	maximal, characteristic
8	#19134576	C₂	1	1	yes	maximal, characteristic
9	#19134574	C₂	1	1	yes	maximal, characteristic
10	#19134463	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134456	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134364	C₂	1	1	yes	maximal, characteristic
13	#19134360	C₂	1	1	yes	maximal, characteristic
14	#19134352	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#1917	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063282	C₂²	1	1	yes	characteristic
17	C₂×#13063282	C₂²	1	1	yes	characteristic
18	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×#13063235	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
33	#14582768	C₄	1	1	yes	characteristic
34	#14582768	C₄	1	1	yes	characteristic
35	#14582763	C₄	1	1	yes	characteristic
36	#14582763	C₄	1	1	yes	characteristic
37	#14582758	C₄	1	1	yes	characteristic
38	#14582758	C₄	1	1	yes	characteristic
39	#14582756	C₄	1	1	yes	characteristic
40	#14582756	C₄	1	1	yes	characteristic
41	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
44	#14582654	C₂²	1	1	yes	characteristic
45	#14582654	C₂²	1	1	yes	characteristic
46	#14582654	C₂²	1	1	yes	characteristic
47	#14582654	C₂²	1	1	yes	characteristic
48	#14582653	C₂²	1	1	yes	characteristic
49	#14582653	C₂²	1	1	yes	characteristic
50	#14582653	C₂²	1	1	yes	characteristic
51	#14582653	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
55	C₄₃×#336	C₂²	1	1	yes	characteristic
56	C₄₃×#336	C₂²	1	1	yes	characteristic
57	C₄₃×#336	C₂²	1	1	yes	characteristic
58	C₄₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
62	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
66	#13063282	—	4	1	no	—
67	#13063282	—	4	1	no	—
68	#13063282	—	4	1	no	—
69	#13063282	—	4	1	no	—
70	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
72	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
87	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
88	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
89	C₄²×D₄₃	—	2	2	no	—
90	C₄²×D₄₃	—	2	2	no	—
91	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
92	Dic₄₃⋊C₈	—	2	2	no	—
93	Dic₄₃⋊C₈	—	2	2	no	—
94	Dic₄₃⋊C₈	—	4	1	no	—
95	Dic₄₃⋊C₈	—	4	1	no	—
96	(C₂×D₄₃)⋊C₈	—	2	2	no	—
97	(C₂×D₄₃)⋊C₈	—	2	2	no	—
98	(C₂×D₄₃)⋊C₈	—	2	2	no	—
99	(C₂×D₄₃)⋊C₈	Q₈	1	4	yes	—
100	#13063235	—	4	1	no	—
101	C₄×C₄₃⋊C₈	—	4	1	no	—
102	C₈×Dic₄₃	—	2	2	no	—
103	C₈×Dic₄₃	—	2	2	no	—
104	C₈×Dic₄₃	—	4	1	no	—
105	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
108	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
109	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
110	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
111	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
120	C₄⋊C₈×C₄₃	—	4	1	no	—
121	#97×C₄₃	—	4	1	no	—
122	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
123	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
124	C₂³×D₄₃	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	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
132	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₄₃	—	2	1	no	—
140	C₂×C₄×D₄₃	—	2	1	no	—
141	C₂×C₄×D₄₃	—	2	1	no	—
142	C₂×C₄×D₄₃	—	2	1	no	—
143	C₂×C₄×D₄₃	—	2	2	no	—
144	C₂×C₄×D₄₃	—	2	2	no	—
145	C₂×C₄×D₄₃	—	2	2	no	—
146	C₂×C₄×D₄₃	—	2	2	no	—
147	C₂×C₄×D₄₃	—	2	2	no	—
148	C₂×C₄×D₄₃	—	4	1	no	—
149	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
150	C₂×C₄×D₄₃	#41	1	2	yes	—
151	C₂×C₈×C₄₃	—	2	1	no	—
152	C₂×C₈×C₄₃	—	2	1	no	—
153	C₂×C₈×C₄₃	—	2	1	no	—
154	C₂×C₈×C₄₃	—	2	1	no	—
155	C₂×C₈×C₄₃	—	2	1	no	—
156	C₂×C₈×C₄₃	—	2	1	no	—
157	C₂×C₈×C₄₃	—	2	1	no	—
158	C₂×C₈×C₄₃	—	2	1	no	—
159	C₂×C₈×C₄₃	—	2	1	no	—
160	C₂×C₈×C₄₃	—	2	1	no	—
161	C₂×C₈×C₄₃	—	2	1	no	—
162	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
163	C₄⋊C₄×C₄₃	—	2	2	no	—
164	C₄⋊C₄×C₄₃	—	4	1	no	—
165	C₄²×C₄₃	—	2	1	no	—
166	C₄²×C₄₃	—	2	1	no	—
167	C₄²×C₄₃	—	2	1	no	—
168	C₄²×C₄₃	—	2	1	no	—
169	C₄²×C₄₃	—	2	1	no	—
170	C₄²×C₄₃	—	2	1	no	—
171	(C₂×D₄₃)⋊C₄	—	4	1	no	—
172	(C₂×D₄₃)⋊C₄	—	4	1	no	—
173	(C₂×D₄₃)⋊C₄	—	4	1	no	—
174	(C₂×D₄₃)⋊C₄	—	4	1	no	—
175	C₄⋊Dic₄₃	—	2	2	no	—
176	C₄⋊Dic₄₃	—	4	1	no	—
177	Dic₄₃⋊C₄	—	2	2	no	—
178	Dic₄₃⋊C₄	—	2	2	no	—
179	Dic₄₃⋊C₄	—	2	2	no	—
180	Dic₄₃⋊C₄	—	2	2	no	—
181	Dic₄₃⋊C₄	—	4	1	no	—
182	Dic₄₃⋊C₄	—	4	1	no	—
183	Dic₄₃⋊C₄	—	4	1	no	—
184	Dic₄₃⋊C₄	—	4	1	no	—
185	C₄×Dic₄₃	—	2	1	no	—
186	C₄×Dic₄₃	—	2	1	no	—
187	C₄×Dic₄₃	—	2	1	no	—
188	C₄×Dic₄₃	—	2	1	no	—
189	C₄×Dic₄₃	—	2	2	no	—
190	C₄×Dic₄₃	—	2	2	no	—
191	C₄×Dic₄₃	#41	1	2	yes	—
192	C₄×Dic₄₃	#41	1	2	yes	—
193	C₂×C₄₃⋊C₈	—	2	1	no	—
194	C₂×C₄₃⋊C₈	—	2	1	no	—
195	C₂×C₄₃⋊C₈	—	2	1	no	—
196	C₂×C₄₃⋊C₈	—	2	1	no	—
197	C₂×C₄₃⋊C₈	—	2	1	no	—
198	C₂×C₄₃⋊C₈	—	2	1	no	—
199	C₂×C₄₃⋊C₈	—	2	1	no	—
200	C₂×C₄₃⋊C₈	—	2	1	no	—
201	C₂×C₄₃⋊C₈	—	2	1	no	—
202	C₂×C₄₃⋊C₈	—	2	1	no	—
203	C₂×C₄₃⋊C₈	—	2	1	no	—
204	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
205	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
206	C₂²×D₄₃	—	2	1	no	—
207	C₂²×D₄₃	—	2	1	no	—
208	C₂²×D₄₃	—	2	1	no	—
209	C₂²×D₄₃	—	2	1	no	—
210	C₂²×D₄₃	—	2	1	no	—
211	C₂²×D₄₃	—	2	1	no	—
212	C₂²×D₄₃	C₄×Q₈	1	2	yes	—
213	C₂×C₄×C₄₃	—	2	1	no	—
214	C₂×C₄×C₄₃	—	2	1	no	—
215	C₂×C₄×C₄₃	—	2	1	no	—
216	C₂×C₄×C₄₃	—	2	1	no	—
217	C₂×C₄×C₄₃	—	2	1	no	—
218	C₂×C₄×C₄₃	—	2	1	no	—
219	C₂×C₄×C₄₃	—	2	1	no	—
220	C₂×C₄×C₄₃	—	2	1	no	—
221	C₂×C₄×C₄₃	—	2	1	no	—
222	C₂×C₄×C₄₃	—	2	1	no	—
223	C₂×C₄×C₄₃	—	2	1	no	—
224	C₂×C₄×C₄₃	—	2	1	no	—
225	C₂×C₄×C₄₃	—	2	1	no	—
226	C₂×C₄×C₄₃	—	2	1	no	—
227	C₂×C₄×C₄₃	—	2	1	no	—
228	C₂×C₄×C₄₃	—	2	1	no	—
229	C₂×C₄×C₄₃	—	2	1	no	—
230	C₂×C₄×C₄₃	#131	1	2	yes	—
231	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×Dic₄₃	—	2	1	no	—
238	C₂×Dic₄₃	—	2	1	no	—
239	C₂×Dic₄₃	—	2	1	no	—
240	C₂×Dic₄₃	—	2	1	no	—
241	C₂×Dic₄₃	—	2	1	no	—
242	C₂×Dic₄₃	—	2	1	no	—
243	C₂×Dic₄₃	—	2	1	no	—
244	C₂×Dic₄₃	—	2	1	no	—
245	C₂×Dic₄₃	—	2	1	no	—
246	C₂×Dic₄₃	—	2	1	no	—
247	C₂×Dic₄₃	—	2	1	no	—
248	C₂×Dic₄₃	—	2	1	no	—
249	C₂×Dic₄₃	—	2	1	no	—
250	C₂×Dic₄₃	—	2	1	no	—
251	C₂×Dic₄₃	—	2	1	no	—
252	C₂×Dic₄₃	—	2	1	no	—
253	C₂×Dic₄₃	#117	1	2	yes	—
254	C₂×Dic₄₃	#117	1	2	yes	—
255	C₂×Dic₄₃	C₄×Q₈	1	2	yes	—
256	C₂×Dic₄₃	#131	1	2	yes	—
257	C₂×Dic₄₃	#131	1	2	yes	—
258	C₄×D₄₃	—	2	2	no	—
259	C₄×D₄₃	—	2	2	no	—
260	C₄×D₄₃	—	2	2	no	—
261	C₄×D₄₃	—	2	2	no	—
262	C₄×D₄₃	—	4	4	no	—
263	C₄×D₄₃	—	4	4	no	—
264	C₈×C₄₃	—	2	2	no	—
265	C₈×C₄₃	—	4	1	no	—
266	C₈×C₄₃	—	4	1	no	—
267	C₈×C₄₃	—	4	1	no	—
268	C₄₃⋊C₈	—	2	2	no	—
269	C₄₃⋊C₈	—	4	1	no	—
270	C₄₃⋊C₈	—	4	1	no	—
271	C₄₃⋊C₈	—	4	1	no	—
272	#22626	—	43	1	no	maximal, Sylow
273	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
274	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
275	C₂²×C₄₃	#518	1	1	yes	characteristic
276	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
277	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
278	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
279	C₂²×C₄₃	#568	1	1	yes	characteristic
280	C₂×D₄₃	—	2	2	no	—
281	C₂×D₄₃	—	2	2	no	—
282	C₂×D₄₃	—	2	2	no	—
283	C₂×D₄₃	—	4	1	no	—
284	C₂×D₄₃	—	4	1	no	—
285	C₂×D₄₃	—	4	1	no	—
286	C₂×D₄₃	—	4	1	no	—
287	C₄×C₄₃	—	2	2	no	—
288	C₄×C₄₃	—	4	1	no	—
289	C₄×C₄₃	—	4	1	no	—
290	C₄×C₄₃	—	4	1	no	—
291	C₄×C₄₃	—	4	1	no	—
292	C₄×C₄₃	—	4	1	no	—
293	C₄×C₄₃	#553	1	1	yes	characteristic
294	C₄×C₄₃	#553	1	1	yes	characteristic
295	C₄×C₄₃	#554	1	1	yes	characteristic
296	C₄×C₄₃	#554	1	1	yes	characteristic
297	Dic₄₃	—	2	2	no	—
298	Dic₄₃	—	2	2	no	—
299	Dic₄₃	—	4	1	no	—
300	Dic₄₃	—	4	1	no	—
301	Dic₄₃	—	4	1	no	—
302	Dic₄₃	—	4	1	no	—
303	Dic₄₃	#433	1	4	yes	—
304	#2285	—	43	1	no	—
305	#1939	—	43	1	no	—
306	#1939	—	43	1	no	—
307	#1917	—	43	1	no	—
308	#1917	D₄₃	1	1	yes	characteristic, complemented
309	#1916	—	43	1	no	—
310	#1916	—	43	1	no	—
311	#1798	—	43	1	no	—
312	#1798	—	43	1	no	—
313	#1797	—	43	1	no	—
314	#1770	—	43	1	no	—
315	C₈×C₄⋊C₄	—	43	1	no	—
316	#1750	—	43	1	no	—
317	#1750	—	43	1	no	—
318	C₄×C₂²⋊C₈	—	43	1	no	—
319	C₂×C₄₃	#2345	1	1	yes	characteristic
320	C₂×C₄₃	C₂×#433	1	1	yes	characteristic
321	C₂×C₄₃	#2924	1	1	yes	characteristic
322	C₂×C₄₃	#2960	1	1	yes	characteristic
323	C₂×C₄₃	#2962	1	1	yes	characteristic
324	C₂×C₄₃	#2979	1	1	yes	characteristic
325	C₂×C₄₃	#2981	1	1	yes	characteristic
326	D₄₃	—	4	2	no	—
327	C₂×#117	—	43	1	no	—
328	C₂×#117	—	43	1	no	—
329	C₂²×C₄²	—	43	1	no	—
330	C₂×C₄⋊C₈	—	43	1	no	—
331	C₂×C₄⋊C₈	—	43	1	no	—
332	C₂×C₄⋊C₈	—	43	1	no	—
333	C₂×C₄⋊C₈	—	43	1	no	—
334	C₂×C₄⋊C₈	—	43	1	no	—
335	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
336	C₂×C₂²⋊C₈	—	43	1	no	—
337	C₂×C₂²⋊C₈	—	43	1	no	—
338	C₂×C₂²⋊C₈	—	43	1	no	—
339	C₂×C₂²⋊C₈	—	43	1	no	—
340	C₂×#97	—	43	1	no	—
341	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
342	C₂×C₄×C₈	—	43	1	no	—
343	C₂×C₄×C₈	—	43	1	no	—
344	C₂×C₄×C₈	—	43	1	no	—
345	C₂×C₄×C₈	—	43	1	no	—
346	#384	—	43	1	no	—
347	#384	—	43	1	no	—
348	#382	—	43	1	no	—
349	#382	—	43	1	no	—
350	#380	—	43	1	no	—
351	#380	—	43	1	no	—
352	#380	—	43	1	no	—
353	#380	—	43	1	no	—
354	C₄×C₄⋊C₄	—	43	1	no	—
355	C₄×C₄⋊C₄	—	43	1	no	—
356	C₄×C₄⋊C₄	—	43	1	no	—
357	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
358	#336	—	43	1	no	—
359	#336	—	43	1	no	—
360	#336	—	43	1	no	—
361	#336	—	43	1	no	—
362	#336	—	43	1	no	—
363	#336	—	43	1	no	—
364	#336	—	43	1	no	—
365	#336	—	43	1	no	—
366	#336	C₂×D₄₃	1	1	yes	characteristic
367	#336	C₂×D₄₃	1	1	yes	characteristic
368	#336	C₂×D₄₃	1	1	yes	characteristic
369	#336	C₂×D₄₃	1	1	yes	characteristic
370	C₄₃	#22626	1	1	yes	characteristic, complemented, Sylow
371	C₂³×C₄	—	43	1	no	—
372	C₂³×C₄	—	43	1	no	—
373	C₂³×C₄	—	43	1	no	—
374	C₂²×C₈	—	43	1	no	—
375	C₂²×C₈	—	43	1	no	—
376	C₂²×C₈	—	43	1	no	—
377	C₂²×C₈	—	43	1	no	—
378	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
379	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
380	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
381	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
382	#117	—	172	1	no	—
383	#117	—	172	1	no	—
384	#117	—	172	1	no	—
385	#117	—	172	1	no	—
386	C₂×C₄⋊C₄	—	43	1	no	—
387	C₂×C₄⋊C₄	—	43	1	no	—
388	C₂×C₄⋊C₄	—	43	1	no	—
389	C₂×C₄⋊C₄	—	43	1	no	—
390	C₂×C₄⋊C₄	—	43	1	no	—
391	C₂×C₄⋊C₄	—	43	1	no	—
392	C₂×C₄⋊C₄	—	43	1	no	—
393	C₂×C₄⋊C₄	—	43	1	no	—
394	C₂×C₄⋊C₄	—	43	1	no	—
395	C₂×C₄⋊C₄	—	43	1	no	—
396	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	—	43	1	no	—
399	C₂×C₂²⋊C₄	—	43	1	no	—
400	C₂×C₂²⋊C₄	—	43	1	no	—
401	C₂×C₂²⋊C₄	—	43	1	no	—
402	C₂×C₄²	—	43	1	no	—
403	C₂×C₄²	—	43	1	no	—
404	C₂×C₄²	—	43	1	no	—
405	C₂×C₄²	—	43	1	no	—
406	C₂×C₄²	—	43	1	no	—
407	C₂×C₄²	—	86	2	no	—
408	C₂×C₄²	—	86	2	no	—
409	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
410	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
411	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
412	C₄⋊C₈	—	4	1	no	—
413	C₄⋊C₈	—	86	2	no	—
414	C₄⋊C₈	—	86	2	no	—
415	C₄⋊C₈	—	172	1	no	—
416	C₄⋊C₈	—	172	1	no	—
417	C₄⋊C₈	—	172	1	no	—
418	C₂²⋊C₈	—	43	4	no	—
419	C₂²⋊C₈	—	86	2	no	—
420	C₂²⋊C₈	—	86	2	no	—
421	C₂²⋊C₈	—	86	2	no	—
422	#97	—	4	1	no	—
423	#97	—	172	1	no	—
424	C₄×C₈	—	86	2	no	—
425	C₄×C₈	—	86	2	no	—
426	C₄×C₈	—	172	1	no	—
427	C₄×C₈	—	172	1	no	—
428	#95	—	43	1	no	—
429	#95	—	43	1	no	—
430	#95	—	43	1	no	—
431	#95	—	43	1	no	—
432	#95	—	43	1	no	—
433	#95	—	43	1	no	—
434	#95	C₄×D₄₃	1	1	yes	characteristic
435	#95	C₄×D₄₃	1	1	yes	characteristic
436	C₂⁴	—	43	1	no	—
437	C₂²×C₄	—	43	1	no	—
438	C₂²×C₄	—	43	1	no	—
439	C₂²×C₄	—	43	1	no	—
440	C₂²×C₄	—	43	2	no	—
441	C₂²×C₄	—	43	2	no	—
442	C₂²×C₄	—	43	1	no	—
443	C₂²×C₄	—	43	1	no	—
444	C₂²×C₄	—	43	1	no	—
445	C₂²×C₄	—	43	1	no	—
446	C₂²×C₄	—	86	2	no	—
447	C₂²×C₄	—	86	2	no	—
448	C₂²×C₄	—	86	2	no	—
449	C₂²×C₄	—	86	2	no	—
450	C₂²×C₄	—	86	1	no	—
451	C₂²×C₄	—	86	1	no	—
452	C₂²×C₄	—	86	1	no	—
453	C₂²×C₄	—	86	1	no	—
454	C₂²×C₄	—	86	2	no	—
455	C₂²×C₄	—	172	1	no	—
456	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
462	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	43	2	no	—
475	C₂×C₈	—	86	1	no	—
476	C₂×C₈	—	86	1	no	—
477	C₂×C₈	—	86	1	no	—
478	C₂×C₈	—	86	1	no	—
479	C₂×C₈	—	86	1	no	—
480	C₂×C₈	—	86	1	no	—
481	C₂×C₈	—	86	1	no	—
482	C₂×C₈	—	86	1	no	—
483	C₂×C₈	—	86	1	no	—
484	C₂×C₈	—	86	1	no	—
485	C₂×C₈	—	86	1	no	—
486	C₂×C₈	Q₈×D₄₃	1	2	yes	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	86	2	no	—
490	C₄⋊C₄	—	86	2	no	—
491	C₄⋊C₄	—	86	2	no	—
492	C₄⋊C₄	—	86	2	no	—
493	C₄⋊C₄	—	86	2	no	—
494	C₄⋊C₄	—	172	1	no	—
495	C₄⋊C₄	—	172	1	no	—
496	C₄⋊C₄	—	172	1	no	—
497	C₄⋊C₄	—	172	1	no	—
498	C₄⋊C₄	—	172	1	no	—
499	C₂²⋊C₄	—	172	1	no	—
500	C₂²⋊C₄	—	172	1	no	—
501	C₂²⋊C₄	—	172	1	no	—
502	C₂²⋊C₄	—	172	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	43	2	no	—
510	C₄²	—	43	2	no	—
511	C₄²	—	86	2	no	—
512	C₄²	—	86	2	no	—
513	C₄²	—	86	1	no	—
514	C₄²	—	86	1	no	—
515	C₄²	—	86	1	no	—
516	C₄²	—	86	1	no	—
517	C₂³	—	43	2	no	—
518	C₂³	—	86	1	no	—
519	C₂³	—	86	1	no	—
520	C₂³	—	86	1	no	—
521	C₂³	—	86	1	no	—
522	C₂³	—	86	1	no	—
523	C₂³	—	86	1	no	—
524	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	43	2	no	—
543	C₂×C₄	—	43	2	no	—
544	C₂×C₄	—	43	2	no	—
545	C₂×C₄	—	43	2	no	—
546	C₂×C₄	—	43	2	no	—
547	C₂×C₄	—	86	1	no	—
548	C₂×C₄	—	86	1	no	—
549	C₂×C₄	—	86	1	no	—
550	C₂×C₄	—	86	1	no	—
551	C₂×C₄	—	86	2	no	—
552	C₂×C₄	—	86	2	no	—
553	C₂×C₄	—	86	2	no	—
554	C₂×C₄	—	86	2	no	—
555	C₂×C₄	—	86	1	no	—
556	C₂×C₄	—	86	1	no	—
557	C₂×C₄	—	86	1	no	—
558	C₂×C₄	—	86	1	no	—
559	C₂×C₄	—	86	1	no	—
560	C₂×C₄	—	86	1	no	—
561	C₂×C₄	—	86	1	no	—
562	C₂×C₄	—	86	1	no	—
563	C₂×C₄	—	86	1	no	—
564	C₂×C₄	—	86	1	no	—
565	C₂×C₄	—	86	1	no	—
566	C₂×C₄	—	86	1	no	—
567	C₂×C₄	—	172	4	no	—
568	C₂×C₄	—	172	4	no	—
569	C₂×C₄	#13063333	1	2	yes	—
570	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
571	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
572	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
573	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
574	C₂×C₄	#13063370	1	1	yes	characteristic
575	C₂×C₄	#13063371	1	1	yes	characteristic
576	C₈	—	2	2	no	—
577	C₈	—	4	1	no	—
578	C₈	—	4	1	no	—
579	C₈	—	4	1	no	—
580	C₈	—	86	2	no	—
581	C₈	—	172	1	no	—
582	C₈	—	172	1	no	—
583	C₈	—	172	1	no	—
584	C₂²	—	86	2	no	—
585	C₂²	—	86	2	no	—
586	C₂²	—	86	2	no	—
587	C₂²	—	172	1	no	—
588	C₂²	—	172	1	no	—
589	C₂²	—	172	1	no	—
590	C₂²	—	172	1	no	—
591	C₂²	#117×D₄₃	1	1	yes	characteristic
592	C₂²	C₄×Q₈×D₄₃	1	1	yes	characteristic
593	C₂²	#14583371	1	1	yes	characteristic
594	C₂²	#131×D₄₃	1	1	yes	characteristic
595	C₂²	#131×D₄₃	1	1	yes	characteristic
596	C₂²	C₂×#13063333	1	1	yes	characteristic
597	C₂²	#14583665	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	43	4	no	—
605	C₄	—	86	2	no	—
606	C₄	—	86	2	no	—
607	C₄	—	172	1	no	—
608	C₄	—	172	1	no	—
609	C₄	—	172	1	no	—
610	C₄	—	172	1	no	—
611	C₄	#14583594	1	1	yes	characteristic
612	C₄	#14583600	1	1	yes	characteristic
613	C₄	#14583603	1	1	yes	characteristic
614	C₄	#14583605	1	1	yes	characteristic
615	C₂	—	172	2	no	—
616	C₂	#19137469	1	1	yes	characteristic
617	C₂	#433×D₄₃	1	1	yes	characteristic
618	C₂	#19143254	1	1	yes	characteristic
619	C₂	#19143526	1	1	yes	characteristic
620	C₂	#19143540	1	1	yes	characteristic
621	C₂	#19143660	1	1	yes	characteristic
622	C₂	#19143667	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1917	C₂
prime radical	C₂³×D₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1917	D₄₃
hypocenter	C₄₃	#22626
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1917

Complements

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

N	H ≅ G/N	type
2. #19135312	C₂	semidirect
3. #19135310	C₂	semidirect
4. #19135158	C₂	semidirect
5. #19135154	C₂	semidirect
6. #19135153	C₂	semidirect
10. #19134463	C₂	semidirect
11. #19134456	C₂	semidirect
15. C₄₃×#1917	C₂	semidirect
308. #1917	D₄₃	semidirect
370. C₄₃	#22626	semidirect

Maximal subgroups

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

subgroup	index
#19136999	2
#19135312	2
#19135310	2
#19135158	2
#19135154	2
#19135153	2
#19134578	2
#19134576	2
#19134574	2
#19134463	2
#19134456	2
#19134364	2
#19134360	2
#19134352	2
C₄₃×#1917	2
#22626	43