Subgroups — #19149022

Order 5504.

1050 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583648	C₂	1	2	yes	maximal, complemented
2	#14583636	C₂	1	2	yes	maximal, complemented
3	#14583611	C₂	1	2	yes	maximal, complemented
4	#14583595	C₂	1	2	yes	maximal, complemented
5	#14583589	C₂	1	2	yes	maximal, complemented
6	#14583579	C₂	1	2	yes	maximal, complemented
7	#14583558	C₂	1	2	yes	maximal, complemented
8	#14583545	C₂	1	2	yes	maximal, complemented
9	#14583499	C₂	1	4	yes	maximal, complemented
10	#14583481	C₂	1	4	yes	maximal, complemented
11	#14583477	C₂	1	2	yes	maximal, complemented
12	#14583470	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583463	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583433	C₂	1	2	yes	maximal, complemented
15	C₄₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10621898	C₂²	1	2	yes	—
17	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
19	#13063323	C₂²	1	2	yes	complemented
20	#13063321	C₂²	1	2	yes	—
21	#13063320	C₂²	1	4	yes	complemented
22	#13063319	C₂²	1	4	yes	complemented
23	#13063318	C₂²	1	4	yes	—
24	#13063317	C₂²	1	2	yes	complemented
25	#13063315	C₂²	1	4	yes	complemented
26	#13063314	C₂²	1	2	yes	—
27	#13063313	C₂²	1	2	yes	—
28	#13063312	C₂²	1	2	yes	—
29	#13063311	C₂²	1	4	yes	complemented
30	#13063310	C₂²	1	4	yes	—
31	#13063308	C₂²	1	4	yes	complemented
32	#13063307	C₂²	1	4	yes	complemented
33	#13063306	C₂²	1	2	yes	—
34	#13063306	C₂²	1	4	yes	—
35	#13063306	C₂²	1	2	yes	complemented
36	#13063304	C₂²	1	2	yes	—
37	#13063304	C₂²	1	2	yes	complemented
38	#13063304	C₂²	1	2	yes	complemented
39	#13063303	C₂²	1	4	yes	complemented
40	#13063301	C₂²	1	4	yes	complemented
41	#13063299	C₂²	1	2	yes	—
42	#13063299	C₂²	1	2	yes	—
43	#13063299	C₂²	1	2	yes	—
44	#13063298	C₂²	1	4	yes	—
45	#13063297	C₂²	1	4	yes	complemented
46	#13063297	C₂²	1	4	yes	complemented
47	#13063297	C₂²	1	4	yes	complemented
48	#13063297	C₂²	1	4	yes	complemented
49	#13063296	C₂²	1	4	yes	complemented
50	#13063293	C₂²	1	2	yes	—
51	#13063293	C₂²	1	4	yes	—
52	#13063293	C₂²	1	2	yes	—
53	C₄×Dic₈₆	C₂²	1	2	yes	complemented
54	C₄×D₁₇₂	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
56	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
57	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
58	#13063284	C₂²	1	1	yes	characteristic
59	#13063284	C₂²	1	1	yes	characteristic, complemented
60	#13063282	C₂²	1	4	yes	complemented
61	#13063281	C₂²	1	4	yes	complemented
62	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	complemented
63	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	—
64	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
65	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
66	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
67	#127×C₄₃	C₂²	1	1	yes	characteristic
68	#124×C₄₃	C₂²	1	1	yes	characteristic
69	#124×C₄₃	C₂²	1	1	yes	characteristic, complemented
70	#121×C₄₃	C₂²	1	2	yes	—
71	#121×C₄₃	C₂²	1	2	yes	complemented
72	C₄×D₄×C₄₃	C₂²	1	2	yes	—
73	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
74	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₄₃	C₂³	1	2	yes	—
76	#41×C₄₃	—	4	2	no	—
77	#41×C₄₃	—	4	2	no	—
78	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×D₄×C₄₃	C₂³	1	2	yes	—
81	C₂×D₄×C₄₃	C₂³	1	2	yes	—
82	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₄₃	C₂³	1	2	yes	—
84	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
90	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
96	C₂²×Dic₄₃	C₂³	1	4	yes	—
97	C₂²×Dic₄₃	C₂³	1	2	yes	—
98	#10621898	—	4	4	no	—
99	C₂×D₁₇₂	—	4	2	no	—
100	C₂×D₁₇₂	C₂³	1	2	yes	—
101	C₂×D₁₇₂	C₂³	1	2	yes	—
102	C₂×C₄×D₄₃	C₂³	1	4	yes	—
103	C₂×C₄×D₄₃	C₂³	1	4	yes	—
104	C₂×Dic₈₆	—	4	2	no	—
105	C₂×Dic₈₆	C₂³	1	2	yes	—
106	C₂×Dic₈₆	C₂³	1	2	yes	—
107	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
108	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
109	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
110	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
111	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
112	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
113	C₄²×C₄₃	C₂³	1	2	yes	—
114	C₄²×C₄₃	C₂³	1	1	yes	characteristic
115	C₄²×C₄₃	C₂³	1	1	yes	characteristic
116	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
117	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
118	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
119	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
120	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
121	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
127	C₄⋊Dic₄₃	C₂³	1	2	yes	—
128	C₄⋊Dic₄₃	C₂³	1	2	yes	—
129	C₄⋊Dic₄₃	C₂³	1	4	yes	—
130	Dic₄₃⋊C₄	C₂³	1	4	yes	—
131	Dic₄₃⋊C₄	C₂³	1	4	yes	—
132	Dic₄₃⋊C₄	C₂³	1	4	yes	—
133	Dic₄₃⋊C₄	C₂³	1	4	yes	—
134	Dic₄₃⋊C₄	C₂³	1	4	yes	—
135	Dic₄₃⋊C₄	C₂³	1	4	yes	—
136	C₄×Dic₄₃	C₂³	1	2	yes	—
137	C₄×Dic₄₃	C₂³	1	4	yes	—
138	C₄×Dic₄₃	C₂³	1	2	yes	—
139	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
140	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
141	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
142	C₂³×C₄₃	C₂⁴	1	2	yes	—
143	C₂²×D₄₃	—	4	2	no	—
144	C₂²×D₄₃	—	4	4	no	—
145	C₂²×D₄₃	C₂⁴	1	4	yes	—
146	Q₈×C₄₃	—	4	1	no	—
147	Q₈×C₄₃	—	4	1	no	—
148	D₄×C₄₃	—	4	2	no	—
149	D₄×C₄₃	—	4	2	no	—
150	D₄×C₄₃	—	4	1	no	—
151	D₄×C₄₃	—	4	2	no	—
152	D₄×C₄₃	—	4	1	no	—
153	D₄×C₄₃	—	4	1	no	—
154	D₄×C₄₃	—	4	1	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	4	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	4	2	no	—
160	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
162	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
164	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
166	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂²⋊D₄₃	—	4	4	no	—
168	C₂²⋊D₄₃	—	4	4	no	—
169	C₂²⋊D₄₃	—	4	4	no	—
170	C₂²⋊D₄₃	—	4	4	no	—
171	C₂×Dic₄₃	—	4	2	no	—
172	C₂×Dic₄₃	—	4	4	no	—
173	C₂×Dic₄₃	C₂⁴	1	4	yes	—
174	C₂×Dic₄₃	C₂⁴	1	4	yes	—
175	C₂×Dic₄₃	C₂⁴	1	4	yes	—
176	D₁₇₂	—	2	4	no	—
177	D₁₇₂	—	4	2	no	—
178	C₄×D₄₃	—	4	4	no	—
179	C₄×D₄₃	—	4	4	no	—
180	Dic₈₆	—	2	4	no	—
181	Dic₈₆	—	4	2	no	—
182	C₂²×C₄₃	—	2	1	no	—
183	C₂²×C₄₃	—	2	1	no	—
184	C₂²×C₄₃	—	2	2	no	—
185	C₂²×C₄₃	—	2	1	no	—
186	C₂²×C₄₃	—	2	2	no	—
187	C₂²×C₄₃	—	2	2	no	—
188	C₂²×C₄₃	—	2	2	no	—
189	C₂²×C₄₃	—	2	2	no	—
190	C₂²×C₄₃	—	2	2	no	—
191	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
192	C₂×D₄₃	—	2	4	no	—
193	C₂×D₄₃	—	2	4	no	—
194	C₂×D₄₃	—	2	4	no	—
195	C₂×D₄₃	—	8	4	no	—
196	C₄×C₄₃	—	2	1	no	—
197	C₄×C₄₃	—	2	2	no	—
198	C₄×C₄₃	—	2	1	no	—
199	C₄×C₄₃	—	2	1	no	—
200	C₄×C₄₃	—	2	2	no	—
201	C₄×C₄₃	—	2	2	no	—
202	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
203	Dic₄₃	—	2	4	no	—
204	Dic₄₃	—	2	4	no	—
205	Dic₄₃	—	2	4	no	—
206	#3551	—	43	1	no	maximal, Sylow
207	C₂×C₄₃	—	4	1	no	—
208	C₂×C₄₃	—	4	1	no	—
209	C₂×C₄₃	—	4	2	no	—
210	C₂×C₄₃	—	4	1	no	—
211	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄₃	#585	1	2	yes	—
213	D₄₃	—	4	4	no	—
214	#563	—	43	2	no	—
215	#560	—	43	2	no	—
216	#555	—	43	2	no	—
217	#553	—	43	2	no	—
218	#552	—	43	2	no	—
219	#551	—	43	2	no	—
220	#548	—	43	2	no	—
221	#546	—	43	2	no	—
222	#540	—	43	4	no	—
223	#538	—	43	4	no	—
224	#537	—	43	2	no	—
225	#536	—	43	1	no	—
226	#535	—	43	1	no	—
227	#532	D₄₃	1	1	yes	characteristic, complemented
228	#529	—	43	2	no	—
229	C₄₃	#3551	1	1	yes	characteristic, complemented, Sylow
230	C₂×#41	—	43	2	no	—
231	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
232	C₂×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
233	C₂²×Q₈	—	43	1	no	—
234	C₂²×D₄	—	43	1	no	—
235	C₄⋊Q₈	—	43	2	no	—
236	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
237	#127	—	43	2	no	—
238	#127	C₂×D₄₃	1	1	yes	characteristic
239	#126	—	43	4	no	—
240	#126	—	43	4	no	—
241	#126	—	43	4	no	—
242	#125	—	43	4	no	—
243	#125	—	43	2	no	—
244	#124	—	43	2	no	—
245	#124	—	43	2	no	—
246	#124	—	43	4	no	—
247	#124	—	43	2	no	—
248	#124	C₂×D₄₃	1	1	yes	characteristic
249	#124	C₂×D₄₃	1	1	yes	characteristic, complemented
250	#123	—	43	2	no	—
251	#123	—	43	2	no	—
252	#123	—	43	4	no	—
253	#123	—	43	4	no	—
254	#123	—	43	4	no	—
255	#123	—	43	4	no	—
256	C₂²⋊Q₈	—	43	4	no	—
257	C₂²⋊Q₈	—	43	2	no	—
258	C₂²⋊Q₈	—	43	2	no	—
259	C₂²⋊Q₈	—	43	2	no	—
260	C₂²⋊Q₈	—	43	4	no	—
261	#121	—	43	4	no	—
262	#121	—	43	4	no	—
263	#121	—	43	4	no	—
264	#121	—	43	4	no	—
265	#121	—	43	4	no	—
266	#121	—	43	2	no	—
267	#121	—	43	2	no	—
268	#121	—	43	2	no	—
269	#121	—	43	4	no	—
270	#121	C₂×D₄₃	1	2	yes	—
271	#121	C₂×D₄₃	1	2	yes	complemented
272	#120	—	43	2	no	—
273	#120	—	43	2	no	—
274	#120	—	43	4	no	—
275	C₄×Q₈	—	43	2	no	—
276	C₄×D₄	—	43	4	no	—
277	C₄×D₄	—	43	4	no	—
278	C₄×D₄	—	43	4	no	—
279	C₄×D₄	—	43	2	no	—
280	C₄×D₄	C₂×D₄₃	1	2	yes	—
281	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
282	#117	—	43	1	no	—
283	#117	—	43	1	no	—
284	#117	—	43	4	no	—
285	#117	—	43	4	no	—
286	C₂×C₄⋊C₄	—	43	2	no	—
287	C₂×C₂²⋊C₄	—	43	4	no	—
288	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic, complemented
289	C₂⁴	—	43	2	no	—
290	#41	—	4	2	no	—
291	#41	—	4	2	no	—
292	#41	—	172	4	no	—
293	C₂×Q₈	—	43	2	no	—
294	C₂×Q₈	—	43	2	no	—
295	C₂×Q₈	—	172	2	no	—
296	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
297	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
298	C₂×D₄	—	43	4	no	—
299	C₂×D₄	—	43	4	no	—
300	C₂×D₄	—	43	4	no	—
301	C₂×D₄	—	43	4	no	—
302	C₂×D₄	—	43	2	no	—
303	C₂×D₄	—	43	2	no	—
304	C₂×D₄	—	172	2	no	—
305	C₂×D₄	C₂²×D₄₃	1	2	yes	—
306	C₂×D₄	C₂²×D₄₃	1	2	yes	—
307	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
308	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
309	C₂×D₄	C₂²×D₄₃	1	2	yes	—
310	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
311	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
312	C₂²×C₄	—	43	4	no	—
313	C₂²×C₄	—	43	2	no	—
314	C₂²×C₄	—	43	4	no	—
315	C₂²×C₄	—	43	4	no	—
316	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
317	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
318	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
321	C₄⋊C₄	—	43	2	no	—
322	C₄⋊C₄	—	43	2	no	—
323	C₄⋊C₄	—	43	4	no	—
324	C₄⋊C₄	—	43	4	no	—
325	C₄⋊C₄	—	43	4	no	—
326	C₄⋊C₄	—	43	4	no	—
327	C₄⋊C₄	—	43	4	no	—
328	C₄⋊C₄	—	43	4	no	—
329	C₄⋊C₄	—	43	4	no	—
330	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
331	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
332	C₂²⋊C₄	—	43	4	no	—
333	C₂²⋊C₄	—	43	2	no	—
334	C₂²⋊C₄	—	43	4	no	—
335	C₂²⋊C₄	—	43	2	no	—
336	C₂²⋊C₄	—	43	4	no	—
337	C₂²⋊C₄	—	43	4	no	—
338	C₂²⋊C₄	—	43	4	no	—
339	C₂²⋊C₄	—	43	4	no	—
340	C₂²⋊C₄	—	43	4	no	—
341	C₂²⋊C₄	—	43	4	no	—
342	C₂²⋊C₄	—	43	4	no	—
343	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
344	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
345	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
346	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
347	C₄²	—	43	2	no	—
348	C₄²	—	43	4	no	—
349	C₄²	—	43	2	no	—
350	C₄²	C₂²×D₄₃	1	1	yes	characteristic
351	C₄²	C₂²×D₄₃	1	2	yes	—
352	C₄²	C₂²×D₄₃	1	1	yes	characteristic
353	C₂³	—	43	4	no	—
354	C₂³	—	172	2	no	—
355	C₂³	—	172	4	no	—
356	C₂³	C₂³×D₄₃	1	1	yes	characteristic
357	C₂³	C₂³×D₄₃	1	1	yes	characteristic
358	C₂³	C₂³×D₄₃	1	1	yes	characteristic
359	C₂³	C₂³×D₄₃	1	2	yes	—
360	Q₈	—	4	1	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	86	4	no	—
363	Q₈	—	172	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	1	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	86	4	no	—
372	D₄	—	172	2	no	—
373	D₄	—	172	4	no	—
374	D₄	—	172	4	no	—
375	D₄	—	172	4	no	—
376	D₄	—	172	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	43	4	no	—
383	C₂×C₄	—	43	4	no	—
384	C₂×C₄	—	43	4	no	—
385	C₂×C₄	—	172	4	no	—
386	C₂×C₄	—	172	4	no	—
387	C₂×C₄	—	172	2	no	—
388	C₂×C₄	—	172	4	no	—
389	C₂×C₄	C₂³×D₄₃	1	2	yes	—
390	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₄₃	1	2	yes	—
393	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₄₃	1	2	yes	—
395	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	86	4	no	—
406	C₂²	—	86	4	no	—
407	C₂²	—	86	4	no	—
408	C₂²	—	344	4	no	—
409	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	86	4	no	—
417	C₄	—	86	4	no	—
418	C₄	—	86	4	no	—
419	C₄	#13063370	1	2	yes	—
420	C₂	—	4	1	no	—
421	C₂	—	4	1	no	—
422	C₂	—	4	1	no	—
423	C₂	—	4	2	no	—
424	C₂	—	172	4	no	—
425	C₂	C₂×#13063370	1	1	yes	characteristic
426	C₂	#14583735	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#532	C₂
hypercenter	#532	D₄₃
hypocenter	C₄₃	#3551
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #14583648	C₂	semidirect
2. #14583636	C₂	semidirect
3. #14583611	C₂	semidirect
4. #14583595	C₂	semidirect
5. #14583589	C₂	semidirect
6. #14583579	C₂	semidirect
7. #14583558	C₂	semidirect
8. #14583545	C₂	semidirect
9. #14583499	C₂	semidirect
10. #14583481	C₂	semidirect
11. #14583477	C₂	semidirect
12. #14583470	C₂	semidirect
13. #14583463	C₂	semidirect
14. #14583433	C₂	semidirect
15. C₄₃×#532	C₂	semidirect
17. C₂²×Dic₈₆	C₂²	semidirect
19. #13063323	C₂²	semidirect
21. #13063320	C₂²	semidirect
22. #13063319	C₂²	semidirect
24. #13063317	C₂²	semidirect
25. #13063315	C₂²	semidirect
29. #13063311	C₂²	semidirect
31. #13063308	C₂²	semidirect
32. #13063307	C₂²	semidirect
35. #13063306	C₂²	semidirect
37. #13063304	C₂²	semidirect
38. #13063304	C₂²	semidirect
39. #13063303	C₂²	semidirect
40. #13063301	C₂²	semidirect
45. #13063297	C₂²	semidirect
46. #13063297	C₂²	semidirect
47. #13063297	C₂²	semidirect
48. #13063297	C₂²	semidirect
49. #13063296	C₂²	semidirect
53. C₄×Dic₈₆	C₂²	semidirect
55. C₄×C₂²⋊D₄₃	C₂²	semidirect
56. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
57. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
59. #13063284	C₂²	semidirect
60. #13063282	C₂²	semidirect
61. #13063281	C₂²	semidirect
62. C₂×C₄⋊Dic₄₃	C₂²	semidirect
65. C₂×#41×C₄₃	C₂²	semidirect
66. C₄⋊Q₈×C₄₃	C₂²	semidirect
69. #124×C₄₃	C₂²	semidirect
71. #121×C₄₃	C₂²	semidirect
73. C₄×D₄×C₄₃	C₂²	semidirect
74. C₂×C₄²×C₄₃	C₂²	semidirect
227. #532	D₄₃	semidirect
229. C₄₃	#3551	semidirect
232. C₂×#41	C₂×D₄₃	semidirect
236. C₄⋊Q₈	C₂×D₄₃	semidirect
249. #124	C₂×D₄₃	semidirect
271. #121	C₂×D₄₃	semidirect
281. C₄×D₄	C₂×D₄₃	semidirect
288. C₂×C₄²	C₂×D₄₃	semidirect