Subgroups — #25079039

Order 11008.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144377	C₂	1	2	yes	maximal
2	C₈×#10621898	C₂	1	1	yes	maximal, characteristic
3	#19134050	C₂	1	2	yes	maximal, complemented
4	#19134043	C₂	1	2	yes	maximal, complemented
5	#19133996	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133991	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133962	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14582652	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133252	C₂	1	2	yes	maximal, complemented
11	C₄₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10621898	C₂²	1	1	yes	characteristic
13	#14583203	—	2	2	no	—
14	#14583196	—	2	2	no	—
15	#14583191	C₂²	1	2	yes	—
16	#14583186	C₂²	1	2	yes	—
17	#14583181	C₂²	1	2	yes	—
18	#14583176	C₂²	1	2	yes	—
19	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
20	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
21	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
22	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₄₃	—	2	1	no	—
24	C₈×C₂²⋊D₄₃	—	2	1	no	—
25	#14582952	C₂²	1	1	yes	characteristic
26	#14582950	—	2	1	no	—
27	#14582935	—	2	2	no	—
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
29	#14582893	—	2	2	no	—
30	C₄×C₈×D₄₃	—	2	1	no	—
31	#14582652	C₂²	1	1	yes	characteristic
32	#14582652	C₂²	1	1	yes	characteristic
33	#14582652	C₂²	1	2	yes	—
34	#14582648	C₂²	1	2	yes	—
35	#14582648	C₂²	1	2	yes	—
36	#14582645	C₂²	1	2	yes	—
37	#14582645	C₂²	1	2	yes	—
38	C₄₃×#533	C₂²	1	2	yes	—
39	C₄₃×#500	C₂²	1	1	yes	characteristic
40	C₄₃×#494	C₂²	1	1	yes	characteristic
41	C₄₃×#487	C₂²	1	2	yes	—
42	C₄₃×#467	—	2	1	no	—
43	C₄₃×#467	—	2	1	no	—
44	C₄×Q₁₆×C₄₃	—	2	1	no	—
45	C₄×Q₁₆×C₄₃	—	2	1	no	—
46	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	D₄	1	1	yes	characteristic
48	C₂²×C₄₃⋊C₈	—	2	2	no	—
49	C₂×C₈×D₄₃	—	2	1	no	—
50	C₂×C₈×D₄₃	—	2	1	no	—
51	C₄×Dic₈₆	D₄	1	1	yes	characteristic
52	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
53	C₄×D₁₇₂	D₄	1	1	yes	characteristic
54	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
55	C₄×C₂²⋊D₄₃	—	2	1	no	—
56	C₄×C₂²⋊D₄₃	—	2	1	no	—
57	#13063284	D₄	1	1	yes	characteristic
58	#13063282	—	2	1	no	—
59	C₄²×D₄₃	—	2	1	no	—
60	#13063258	—	2	2	no	—
61	#13063258	—	2	2	no	—
62	#13063256	—	2	2	no	—
63	#13063256	—	2	2	no	—
64	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
65	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
69	Dic₄₃⋊C₈	—	2	1	no	—
70	Dic₄₃⋊C₈	—	2	1	no	—
71	#13063248	—	2	2	no	—
72	#13063248	—	2	2	no	—
73	#13063245	—	2	2	no	—
74	#13063245	—	2	2	no	—
75	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
76	(C₂×D₄₃)⋊C₈	—	2	1	no	—
77	(C₂×D₄₃)⋊C₈	—	2	1	no	—
78	C₄×C₄₃⋊C₈	—	2	1	no	—
79	C₈×Dic₄₃	—	2	1	no	—
80	C₈×Dic₄₃	—	2	1	no	—
81	C₂×Q₁₆×C₄₃	—	2	1	no	—
82	C₂×Q₁₆×C₄₃	—	2	1	no	—
83	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
85	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
86	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
87	#125×C₄₃	—	2	2	no	—
88	C₂²⋊Q₈×C₄₃	—	2	2	no	—
89	C₂²⋊Q₈×C₄₃	—	2	2	no	—
90	C₄×Q₈×C₄₃	—	2	2	no	—
91	C₄×Q₈×C₄₃	—	2	2	no	—
92	#117×C₄₃	—	2	2	no	—
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	#107×C₄₃	—	2	1	no	—
95	#107×C₄₃	—	2	1	no	—
96	#103×C₄₃	—	2	2	no	—
97	#103×C₄₃	—	2	2	no	—
98	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₄₃	—	2	2	no	—
103	C₂×Q₈×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
107	C₂×C₂²⋊D₄₃	—	2	1	no	—
108	#10621898	—	2	2	no	—
109	#10621898	Q₁₆	1	4	yes	complemented
110	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₄₃	—	2	1	no	—
112	C₂×C₄×D₄₃	—	2	1	no	—
113	C₂×C₄×D₄₃	—	2	1	no	—
114	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
115	Q₁₆×C₄₃	—	4	2	no	—
116	Q₁₆×C₄₃	—	4	2	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	—	4	1	no	—
119	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	4	2	no	—
128	C₄⋊C₄×C₄₃	—	4	2	no	—
129	C₂²⋊C₄×C₄₃	—	4	2	no	—
130	C₄²×C₄₃	—	4	2	no	—
131	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₃	#41	1	1	yes	characteristic
134	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₄₃	—	2	1	no	—
136	(C₂×D₄₃)⋊C₄	—	2	1	no	—
137	(C₂×D₄₃)⋊C₄	—	2	1	no	—
138	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
140	Dic₄₃⋊C₄	—	2	1	no	—
141	Dic₄₃⋊C₄	—	2	1	no	—
142	C₄×Dic₄₃	—	2	1	no	—
143	C₄×Dic₄₃	—	2	1	no	—
144	C₄×Dic₄₃	—	2	1	no	—
145	C₂×C₄₃⋊C₈	—	2	1	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	2	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	4	4	no	—
150	C₈×D₄₃	—	4	2	no	—
151	C₈×D₄₃	—	4	2	no	—
152	C₂³×C₄₃	#121	1	1	yes	characteristic
153	C₂²×D₄₃	—	2	1	no	—
154	Q₈×C₄₃	—	4	2	no	—
155	Q₈×C₄₃	—	4	2	no	—
156	Q₈×C₄₃	—	8	2	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
166	C₂×C₄×C₄₃	#135	1	2	yes	—
167	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
170	C₂²⋊D₄₃	—	2	4	no	—
171	C₂×Dic₄₃	—	2	1	no	—
172	C₂×Dic₄₃	—	2	1	no	—
173	C₂×Dic₄₃	—	2	1	no	—
174	D₁₇₂	—	2	1	no	—
175	D₁₇₂	C₂×Q₁₆	1	2	yes	—
176	C₄×D₄₃	—	2	4	no	—
177	C₄×D₄₃	—	4	2	no	—
178	C₄×D₄₃	—	4	1	no	—
179	C₄×D₄₃	—	4	1	no	—
180	Dic₈₆	—	2	1	no	—
181	Dic₈₆	C₂×Q₁₆	1	2	yes	—
182	C₈×C₄₃	—	2	1	no	—
183	C₈×C₄₃	—	2	1	no	—
184	C₈×C₄₃	—	2	1	no	—
185	C₈×C₄₃	#135	1	2	yes	—
186	C₄₃⋊C₈	—	4	1	no	—
187	C₄₃⋊C₈	—	4	2	no	—
188	C₄₃⋊C₈	—	4	2	no	—
189	C₄₃⋊C₈	—	4	1	no	—
190	#19126	—	43	1	no	maximal, Sylow
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	#467	1	2	yes	—
194	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
195	C₂×D₄₃	—	2	2	no	—
196	C₂×D₄₃	—	4	1	no	—
197	C₂×D₄₃	—	4	1	no	—
198	C₄×C₄₃	—	2	1	no	—
199	C₄×C₄₃	—	2	1	no	—
200	C₄×C₄₃	—	2	1	no	—
201	C₄×C₄₃	—	8	2	no	—
202	C₄×C₄₃	—	8	2	no	—
203	C₄×C₄₃	#467	1	2	yes	—
204	C₄×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
205	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
206	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
207	C₄×C₄₃	#575	1	1	yes	characteristic
208	Dic₄₃	—	2	2	no	—
209	Dic₄₃	—	4	1	no	—
210	Dic₄₃	—	4	1	no	—
211	#3170	D₄₃	1	1	yes	characteristic, complemented
212	#3076	—	43	2	no	—
213	C₈×#41	—	43	1	no	—
214	#1684	—	43	2	no	—
215	#1683	—	43	2	no	—
216	#1676	—	43	1	no	—
217	#1675	—	43	1	no	—
218	#1670	—	43	1	no	—
219	#1669	—	43	1	no	—
220	C₂×#335	—	43	1	no	—
221	#1542	—	43	2	no	—
222	C₂×C₄₃	—	2	2	no	—
223	C₂×C₄₃	#3035	1	1	yes	characteristic
224	C₂×C₄₃	C₂×#467	1	1	yes	characteristic
225	C₂×C₄₃	#3067	1	1	yes	characteristic
226	D₄₃	—	4	2	no	—
227	#533	C₂×D₄₃	1	2	yes	—
228	C₄×#41	—	43	1	no	—
229	#500	C₂×D₄₃	1	1	yes	characteristic
230	#494	C₂×D₄₃	1	1	yes	characteristic
231	#487	C₂×D₄₃	1	2	yes	—
232	#479	—	86	2	no	—
233	#478	—	86	2	no	—
234	#477	—	43	2	no	—
235	#476	—	43	2	no	—
236	#475	—	43	2	no	—
237	#474	—	43	2	no	—
238	#467	—	2	1	no	—
239	#467	—	2	1	no	—
240	C₈×Q₈	—	43	1	no	—
241	C₈×Q₈	—	43	1	no	—
242	C₄×Q₁₆	—	2	1	no	—
243	C₄×Q₁₆	—	2	1	no	—
244	C₈×D₄	—	43	1	no	—
245	C₈×D₄	—	43	1	no	—
246	C₈×D₄	—	86	1	no	—
247	C₈×D₄	—	86	1	no	—
248	#431	—	43	1	no	—
249	#431	—	86	1	no	—
250	#427	—	86	2	no	—
251	C₂×C₄⋊C₈	—	43	2	no	—
252	#416	—	86	2	no	—
253	C₂×C₄×C₈	—	86	1	no	—
254	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
255	#335	—	43	1	no	—
256	#335	—	43	1	no	—
257	#335	—	43	2	no	—
258	#333	—	43	2	no	—
259	#333	—	43	2	no	—
260	#332	—	43	2	no	—
261	#332	—	43	2	no	—
262	C₄₃	#19126	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	43	1	no	—
264	C₂×Q₁₆	—	2	1	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂²×C₈	—	86	2	no	—
267	C₂²×C₈	—	86	1	no	—
268	C₂²×C₈	—	86	1	no	—
269	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
270	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
271	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
272	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
273	#125	—	2	2	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×Q₈	—	43	1	no	—
279	C₄×Q₈	—	43	1	no	—
280	C₄×D₄	—	43	1	no	—
281	C₄×D₄	—	43	1	no	—
282	C₄×D₄	—	86	1	no	—
283	C₄×D₄	—	86	1	no	—
284	#117	—	2	2	no	—
285	#117	—	43	1	no	—
286	#117	—	86	1	no	—
287	C₂×C₄²	—	86	1	no	—
288	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
289	#107	—	2	1	no	—
290	#107	—	2	1	no	—
291	#107	—	86	2	no	—
292	#107	—	86	2	no	—
293	#106	—	86	2	no	—
294	#106	—	86	2	no	—
295	C₄⋊C₈	—	43	1	no	—
296	C₄⋊C₈	—	43	1	no	—
297	C₄⋊C₈	—	43	2	no	—
298	C₄⋊C₈	—	43	2	no	—
299	C₄⋊C₈	—	86	1	no	—
300	C₄⋊C₈	—	86	1	no	—
301	C₄⋊C₈	—	86	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#103	—	86	2	no	—
305	#103	—	86	2	no	—
306	#102	—	86	2	no	—
307	#102	—	86	2	no	—
308	C₂²⋊C₈	—	86	1	no	—
309	C₂²⋊C₈	—	86	1	no	—
310	C₂²⋊C₈	—	86	1	no	—
311	C₄×C₈	—	86	1	no	—
312	C₄×C₈	—	86	1	no	—
313	C₄×C₈	—	86	1	no	—
314	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
315	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
318	#41	—	43	4	no	—
319	#41	—	86	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	43	1	no	—
323	C₂×D₄	—	43	1	no	—
324	C₂×D₄	—	86	1	no	—
325	C₂²×C₄	—	86	1	no	—
326	C₂²×C₄	—	86	1	no	—
327	C₂²×C₄	—	86	1	no	—
328	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
329	C₂²×C₄	#10621900	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
331	Q₁₆	—	4	2	no	—
332	Q₁₆	—	4	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	86	2	no	—
336	C₂×C₈	—	86	2	no	—
337	C₂×C₈	—	86	1	no	—
338	C₂×C₈	—	86	1	no	—
339	C₂×C₈	—	172	2	no	—
340	C₂×C₈	—	172	4	no	—
341	C₂×C₈	—	172	2	no	—
342	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	43	1	no	—
353	C₄⋊C₄	—	43	1	no	—
354	C₄⋊C₄	—	86	1	no	—
355	C₄⋊C₄	—	86	1	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	86	1	no	—
358	C₂²⋊C₄	—	86	1	no	—
359	C₂²⋊C₄	—	86	1	no	—
360	C₄²	—	4	2	no	—
361	C₄²	—	86	1	no	—
362	C₄²	—	86	1	no	—
363	C₄²	—	86	1	no	—
364	C₄²	D₄×D₄₃	1	1	yes	characteristic
365	C₄²	#10621900	1	1	yes	characteristic
366	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
367	C₄²	C₂³×D₄₃	1	1	yes	characteristic
368	C₂³	—	86	1	no	—
369	C₂³	#13063296	1	1	yes	characteristic
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	8	2	no	—
373	Q₈	—	43	2	no	—
374	Q₈	—	86	1	no	—
375	D₄	—	43	2	no	—
376	D₄	—	86	4	no	—
377	D₄	—	86	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	86	1	no	—
384	C₂×C₄	—	86	4	no	—
385	C₂×C₄	—	86	1	no	—
386	C₂×C₄	—	86	1	no	—
387	C₂×C₄	—	172	2	no	—
388	C₂×C₄	—	172	1	no	—
389	C₂×C₄	—	172	1	no	—
390	C₂×C₄	#13063296	1	1	yes	characteristic
391	C₂×C₄	#13063296	1	1	yes	characteristic
392	C₂×C₄	#13063296	1	1	yes	characteristic
393	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
394	C₂×C₄	#13063348	1	2	yes	—
395	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
397	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	172	1	no	—
402	C₈	—	172	2	no	—
403	C₈	—	172	2	no	—
404	C₈	—	172	1	no	—
405	C₈	#13063345	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	86	2	no	—
409	C₂²	—	172	1	no	—
410	C₂²	—	172	1	no	—
411	C₂²	#14583137	1	2	yes	—
412	C₂²	C₂×#13063296	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	8	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	86	2	no	—
419	C₄	—	172	1	no	—
420	C₄	—	172	1	no	—
421	C₄	#14583137	1	2	yes	—
422	C₄	C₂×Q₁₆×D₄₃	1	1	yes	characteristic
423	C₄	C₂×#13063345	1	1	yes	characteristic
424	C₄	C₂×#13063348	1	1	yes	characteristic
425	C₄	#14583697	1	1	yes	characteristic
426	C₂	—	2	2	no	—
427	C₂	—	172	2	no	—
428	C₂	#19144044	1	1	yes	characteristic
429	C₂	C₂×#14583137	1	1	yes	characteristic
430	C₂	#19144311	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063296
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3170	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂×#10621898	D₄
hypercenter	#3170	D₄₃
hypocenter	C₄₃	#19126
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

Complements

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

N	H ≅ G/N	type
3. #19134050	C₂	semidirect
4. #19134043	C₂	semidirect
5. #19133996	C₂	semidirect
6. #19133991	C₂	semidirect
7. #19133962	C₂	semidirect
8. #19133957	C₂	semidirect
9. C₂×#14582652	C₂	semidirect
10. #19133252	C₂	semidirect
11. C₄₃×#3170	C₂	semidirect
109. #10621898	Q₁₆	semidirect
211. #3170	D₄₃	semidirect
262. C₄₃	#19126	semidirect

Maximal subgroups

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

subgroup	index
#19144377	2
C₈×#10621898	2
#19134050	2
#19134043	2
#19133996	2
#19133991	2
#19133962	2
#19133957	2
C₂×#14582652	2
#19133252	2
C₄₃×#3170	2
#19126	43