Subgroups — #25080180

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145907	C₂	1	1	yes	maximal, characteristic
2	#19145736	C₂	1	1	yes	maximal, characteristic, complemented
3	#19145054	C₂	1	1	yes	maximal, characteristic
4	#19134089	C₂	1	2	yes	maximal, complemented
5	#19134067	C₂	1	2	yes	maximal, complemented
6	#19133965	C₂	1	2	yes	maximal, complemented
7	#19133943	C₂	1	2	yes	maximal, complemented
8	#19133347	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133245	C₂	1	1	yes	maximal, characteristic
10	C₂×#14582646	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063358	—	2	1	no	—
13	C₂×#13063358	—	2	1	no	—
14	#14583449	C₂²	1	1	yes	characteristic
15	C₂×#13063325	C₂²	1	1	yes	characteristic
16	#14583295	—	2	1	no	—
17	#14583293	—	2	2	no	—
18	#14583279	C₂²	1	2	yes	—
19	#14583272	C₂²	1	2	yes	—
20	#14583249	—	2	1	no	—
21	#14583227	—	2	2	no	—
22	#14583186	—	2	1	no	—
23	#14583184	C₂²	1	2	yes	—
24	#14583184	C₂²	1	2	yes	—
25	#14583184	C₂²	1	2	yes	—
26	#14583130	—	2	2	no	—
27	#14583101	—	2	1	no	—
28	#14583099	C₂²	1	2	yes	—
29	#14582952	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
31	#14582652	C₂²	1	2	yes	—
32	#14582650	C₂²	1	2	yes	—
33	#14582646	C₂²	1	1	yes	characteristic
34	#14582646	C₂²	1	2	yes	—
35	#14582646	C₂²	1	2	yes	—
36	#14582646	C₂²	1	1	yes	characteristic
37	#14582642	C₂²	1	1	yes	characteristic
38	#14582642	C₂²	1	1	yes	characteristic
39	C₄₃×#533	C₂²	1	1	yes	characteristic
40	C₄₃×#446	—	2	2	no	—
41	C₄₃×#446	C₂²	1	2	yes	—
42	C₈×Q₈×C₄₃	C₂²	1	2	yes	—
43	C₄₃×#424	—	2	1	no	—
44	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#405	—	2	1	no	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	C₂²×Dic₈₆	—	2	1	no	—
49	#13063358	—	4	4	no	—
50	#13063358	—	4	4	no	—
51	C₂×Dic₁₇₂	—	2	2	no	—
52	C₂×Dic₁₇₂	—	2	2	no	—
53	C₂×#10621873	—	2	2	no	—
54	C₂×#10621873	—	2	2	no	—
55	C₂×#10621884	—	2	2	no	—
56	C₂²×C₄₃⋊C₈	—	2	1	no	—
57	#13063325	—	2	1	no	—
58	#13063325	—	2	1	no	—
59	#13063325	—	2	1	no	—
60	#13063325	C₂³	1	2	yes	—
61	#13063325	C₂³	1	1	yes	characteristic
62	#13063322	C₂³	1	1	yes	characteristic
63	#13063313	—	2	1	no	—
64	#13063299	—	2	1	no	—
65	#13063299	—	2	1	no	—
66	C₄×D₁₇₂	—	2	1	no	—
67	C₄×D₁₇₂	—	2	1	no	—
68	C₂×C₄⋊Dic₄₃	—	2	1	no	—
69	C₂×C₄⋊Dic₄₃	—	2	1	no	—
70	#13063256	—	2	2	no	—
71	#13063256	—	2	2	no	—
72	#13063256	—	2	2	no	—
73	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
74	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
75	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
77	#13063249	—	2	2	no	—
78	#13063249	—	2	2	no	—
79	#13063249	—	2	2	no	—
80	#13063245	—	2	2	no	—
81	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
82	C₄×C₄₃⋊C₈	—	2	1	no	—
83	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
84	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₃	—	2	1	no	—
86	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
87	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
88	#125×C₄₃	—	2	1	no	—
89	C₂²⋊Q₈×C₄₃	—	2	1	no	—
90	C₂²⋊Q₈×C₄₃	D₄	1	2	yes	—
91	C₄×Q₈×C₄₃	—	2	1	no	—
92	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
93	#117×C₄₃	—	2	1	no	—
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₃	—	2	2	no	—
96	C₄⋊C₈×C₄₃	—	2	2	no	—
97	C₄⋊C₈×C₄₃	—	2	1	no	—
98	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
100	#97×C₄₃	—	2	2	no	—
101	#97×C₄₃	D₄	1	2	yes	—
102	C₄×C₈×C₄₃	—	2	2	no	—
103	C₄×C₈×C₄₃	C₂³	1	2	yes	—
104	C₂×Q₈×C₄₃	—	2	1	no	—
105	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
109	C₂×C₂²⋊D₄₃	—	4	1	no	—
110	C₂²×Dic₄₃	—	4	1	no	—
111	#10621898	—	4	2	no	—
112	#10621898	—	4	2	no	—
113	C₂×D₁₇₂	—	2	1	no	—
114	C₂×D₁₇₂	—	2	1	no	—
115	C₂×D₁₇₂	—	2	1	no	—
116	C₂×C₄×D₄₃	—	4	1	no	—
117	C₂×Dic₈₆	—	2	1	no	—
118	C₂×Dic₈₆	—	2	2	no	—
119	C₂×Dic₈₆	—	4	2	no	—
120	C₂×Dic₈₆	—	4	2	no	—
121	C₂×Dic₈₆	—	4	1	no	—
122	M₁₆×C₄₃	—	2	2	no	—
123	M₁₆×C₄₃	SD₁₆	1	4	yes	complemented
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	1	no	—
126	C₂×C₈×C₄₃	—	4	2	no	—
127	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
135	C₂²⋊C₄×C₄₃	—	2	2	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₃	#41	1	1	yes	characteristic
140	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
141	#10621884	—	8	2	no	—
142	(C₂×D₄₃)⋊C₄	—	4	1	no	—
143	(C₂×D₄₃)⋊C₄	—	4	1	no	—
144	C₄⋊Dic₄₃	—	2	2	no	—
145	C₄⋊Dic₄₃	—	2	1	no	—
146	C₄⋊Dic₄₃	—	2	2	no	—
147	C₄⋊Dic₄₃	—	2	1	no	—
148	C₄⋊Dic₄₃	—	4	1	no	—
149	C₄⋊Dic₄₃	—	4	1	no	—
150	C₂×C₄₃⋊C₈	—	2	1	no	—
151	C₂×C₄₃⋊C₈	—	2	1	no	—
152	C₂×C₄₃⋊C₈	—	2	2	no	—
153	C₂×C₄₃⋊C₈	—	8	1	no	—
154	Dic₁₇₂	—	4	4	no	—
155	Dic₁₇₂	—	4	4	no	—
156	#10621873	—	4	4	no	—
157	#10621873	—	4	4	no	—
158	C₂³×C₄₃	#121	1	1	yes	characteristic
159	C₂²×D₄₃	—	4	1	no	—
160	Q₈×C₄₃	—	2	2	no	—
161	Q₈×C₄₃	—	2	2	no	—
162	Q₈×C₄₃	—	8	1	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
169	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
172	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₄₃	—	8	2	no	—
177	C₂×Dic₄₃	—	4	2	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	—	8	2	no	—
180	D₁₇₂	—	4	1	no	—
181	D₁₇₂	—	4	1	no	—
182	D₁₇₂	—	4	1	no	—
183	D₁₇₂	—	4	1	no	—
184	D₁₇₂	—	8	1	no	—
185	C₄×D₄₃	—	8	2	no	—
186	Dic₈₆	—	4	2	no	—
187	Dic₈₆	—	4	1	no	—
188	Dic₈₆	—	4	2	no	—
189	Dic₈₆	—	4	1	no	—
190	Dic₈₆	—	8	2	no	—
191	C₈×C₄₃	—	2	2	no	—
192	C₈×C₄₃	—	4	1	no	—
193	C₈×C₄₃	—	4	1	no	—
194	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
195	C₄₃⋊C₈	—	4	1	no	—
196	C₄₃⋊C₈	—	4	2	no	—
197	C₄₃⋊C₈	—	4	1	no	—
198	#19239	—	43	1	no	maximal, Sylow
199	C₂²×C₄₃	—	2	1	no	—
200	C₂²×C₄₃	—	2	1	no	—
201	C₂²×C₄₃	#460	1	2	yes	—
202	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
203	C₂×D₄₃	—	8	1	no	—
204	C₂×D₄₃	—	8	1	no	—
205	C₂×D₄₃	—	8	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	—	4	2	no	—
210	C₄×C₄₃	—	4	2	no	—
211	C₄×C₄₃	#460	1	2	yes	—
212	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
213	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₄×C₄₃	#577	1	1	yes	characteristic
215	C₄×C₄₃	#578	1	1	yes	characteristic
216	Dic₄₃	—	8	2	no	—
217	Dic₄₃	—	8	1	no	—
218	#3246	—	43	1	no	—
219	#3229	—	43	1	no	—
220	#3152	—	43	1	no	—
221	#2962	D₄₃	1	1	yes	characteristic, complemented
222	#1690	—	43	2	no	—
223	#1686	—	43	2	no	—
224	#1670	—	43	2	no	—
225	#1666	—	43	2	no	—
226	#1565	—	43	1	no	—
227	#1540	—	43	1	no	—
228	C₂×#332	—	43	1	no	—
229	C₂×C₄₃	—	2	2	no	—
230	C₂×C₄₃	C₂×#460	1	1	yes	characteristic
231	C₂×C₄₃	#3063	1	1	yes	characteristic
232	C₂×C₄₃	#3069	1	1	yes	characteristic
233	D₄₃	—	16	1	no	—
234	C₂×#137	—	86	1	no	—
235	C₂×#137	—	86	1	no	—
236	#533	C₂×D₄₃	1	1	yes	characteristic
237	#532	—	43	1	no	—
238	C₂×C₄⋊Q₈	—	43	1	no	—
239	#498	—	86	1	no	—
240	#497	—	86	2	no	—
241	#494	—	43	2	no	—
242	#492	—	43	2	no	—
243	#487	—	86	1	no	—
244	#483	—	86	2	no	—
245	#476	—	86	1	no	—
246	#475	—	43	2	no	—
247	#475	—	43	2	no	—
248	#475	—	43	2	no	—
249	#465	—	86	2	no	—
250	#461	—	86	1	no	—
251	#460	—	43	2	no	—
252	#446	—	2	2	no	—
253	#446	C₂×D₄₃	1	2	yes	—
254	C₈×Q₈	C₂×D₄₃	1	2	yes	—
255	#431	—	43	1	no	—
256	#424	—	2	1	no	—
257	C₂×C₄⋊C₈	—	43	1	no	—
258	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
259	#405	—	2	1	no	—
260	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
261	#335	—	43	2	no	—
262	#334	—	43	2	no	—
263	#332	—	43	2	no	—
264	#332	—	43	2	no	—
265	#332	—	43	1	no	—
266	#332	—	43	1	no	—
267	#331	—	43	1	no	—
268	#331	—	43	1	no	—
269	C₄₃	#19239	1	1	yes	characteristic, complemented, Sylow
270	C₂×#41	—	86	1	no	—
271	C₂²×Q₈	—	86	1	no	—
272	#137	—	172	4	no	—
273	#137	—	172	4	no	—
274	C₂×Q₁₆	—	86	2	no	—
275	C₂×Q₁₆	—	86	2	no	—
276	C₂×SD₁₆	—	86	2	no	—
277	C₂×SD₁₆	—	86	2	no	—
278	C₂×SD₁₆	—	86	2	no	—
279	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
280	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	86	1	no	—
283	C₄⋊Q₈	—	43	2	no	—
284	C₄⋊Q₈	—	43	1	no	—
285	C₄⋊Q₈	—	86	1	no	—
286	C₄⋊Q₈	—	86	1	no	—
287	C₄⋊Q₈	—	86	1	no	—
288	C₄⋊Q₈	D₁₇₂	1	1	yes	characteristic
289	C₄⋊Q₈	D₁₇₂	1	1	yes	characteristic
290	#127	—	43	1	no	—
291	#125	—	2	1	no	—
292	#124	—	86	1	no	—
293	C₂²⋊Q₈	—	2	1	no	—
294	C₂²⋊Q₈	D₁₇₂	1	2	yes	—
295	#121	—	86	1	no	—
296	#121	—	86	1	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
299	C₄×D₄	—	86	1	no	—
300	C₄×D₄	—	86	1	no	—
301	#117	—	2	1	no	—
302	C₂×C₄⋊C₄	—	86	1	no	—
303	C₂×C₄⋊C₄	—	86	1	no	—
304	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
305	#106	—	86	2	no	—
306	#106	—	86	2	no	—
307	#106	—	86	2	no	—
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	2	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	43	1	no	—
312	C₄⋊C₈	—	43	1	no	—
313	C₄⋊C₈	—	43	2	no	—
314	C₄⋊C₈	—	86	1	no	—
315	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
317	#103	—	86	2	no	—
318	#103	—	86	2	no	—
319	#103	—	86	2	no	—
320	#102	—	86	2	no	—
321	C₂²⋊C₈	—	86	1	no	—
322	#97	—	2	2	no	—
323	#97	C₂²⋊D₄₃	1	2	yes	—
324	C₄×C₈	—	2	2	no	—
325	C₄×C₈	—	86	1	no	—
326	C₄×C₈	C₂²×D₄₃	1	2	yes	—
327	#41	—	172	2	no	—
328	#41	—	172	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	86	1	no	—
331	C₂×Q₈	—	86	2	no	—
332	C₂×Q₈	—	172	2	no	—
333	C₂×Q₈	—	172	2	no	—
334	C₂×Q₈	—	172	1	no	—
335	C₂×Q₈	C₂×D₁₇₂	1	2	yes	—
336	C₂×D₄	—	86	1	no	—
337	C₂×D₄	—	86	1	no	—
338	C₂×D₄	—	86	1	no	—
339	C₂×D₄	—	172	1	no	—
340	C₂²×C₄	—	172	1	no	—
341	C₂²×C₄	—	172	1	no	—
342	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
343	C₂²×C₄	#10621898	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
345	Q₁₆	—	172	4	no	—
346	Q₁₆	—	172	4	no	—
347	SD₁₆	—	344	2	no	—
348	SD₁₆	—	172	4	no	—
349	SD₁₆	—	172	4	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	#10621884	1	4	yes	complemented
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	86	1	no	—
356	C₂×C₈	—	86	1	no	—
357	C₂×C₈	—	86	2	no	—
358	C₂×C₈	—	344	1	no	—
359	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
360	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	86	2	no	—
367	C₄⋊C₄	—	86	1	no	—
368	C₄⋊C₄	—	86	2	no	—
369	C₄⋊C₄	—	86	1	no	—
370	C₄⋊C₄	—	172	1	no	—
371	C₄⋊C₄	—	172	1	no	—
372	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	172	1	no	—
375	C₂²⋊C₄	—	172	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
378	C₄²	#10621898	1	1	yes	characteristic
379	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
380	C₄²	C₂³×D₄₃	1	1	yes	characteristic
381	C₂³	—	172	1	no	—
382	C₂³	#13063299	1	1	yes	characteristic
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	8	1	no	—
386	Q₈	—	344	2	no	—
387	Q₈	—	172	2	no	—
388	Q₈	—	172	1	no	—
389	Q₈	—	172	2	no	—
390	Q₈	—	172	1	no	—
391	D₄	—	344	1	no	—
392	D₄	—	344	2	no	—
393	D₄	—	172	1	no	—
394	D₄	—	172	1	no	—
395	D₄	—	172	1	no	—
396	D₄	—	172	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	344	2	no	—
403	C₂×C₄	—	344	2	no	—
404	C₂×C₄	—	172	1	no	—
405	C₂×C₄	—	172	2	no	—
406	C₂×C₄	#13063299	1	1	yes	characteristic
407	C₂×C₄	#13063299	1	1	yes	characteristic
408	C₂×C₄	#13063299	1	1	yes	characteristic
409	C₂×C₄	C₂×#10621884	1	2	yes	—
410	C₂×C₄	#13063350	1	2	yes	—
411	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
413	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₈	—	172	2	no	—
418	C₈	—	172	1	no	—
419	C₈	—	172	1	no	—
420	C₈	C₂×#10621884	1	4	yes	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	344	1	no	—
424	C₂²	—	344	1	no	—
425	C₂²	—	344	1	no	—
426	C₂²	#14583099	1	2	yes	—
427	C₂²	C₂×#13063299	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	344	1	no	—
434	C₄	—	344	2	no	—
435	C₄	#14583099	1	2	yes	—
436	C₄	C₂²×#10621884	1	1	yes	characteristic
437	C₄	C₂×#13063350	1	1	yes	characteristic
438	C₄	#14583711	1	1	yes	characteristic
439	C₄	#14583716	1	1	yes	characteristic
440	C₂	—	2	2	no	—
441	C₂	—	688	1	no	—
442	C₂	C₂×#14583099	1	1	yes	characteristic
443	C₂	#19144286	1	1	yes	characteristic
444	C₂	#19144332	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063299
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2962	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	#2962	D₄₃
hypocenter	C₄₃	#19239
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2962

Complements

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

N	H ≅ G/N	type
2. #19145736	C₂	semidirect
4. #19134089	C₂	semidirect
5. #19134067	C₂	semidirect
6. #19133965	C₂	semidirect
7. #19133943	C₂	semidirect
8. #19133347	C₂	semidirect
10. C₂×#14582646	C₂	semidirect
11. C₄₃×#2962	C₂	semidirect
123. M₁₆×C₄₃	SD₁₆	semidirect
221. #2962	D₄₃	semidirect
269. C₄₃	#19239	semidirect
351. M₁₆	#10621884	semidirect

Maximal subgroups

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

subgroup	index
#19145907	2
#19145736	2
#19145054	2
#19134089	2
#19134067	2
#19133965	2
#19133943	2
#19133347	2
#19133245	2
C₂×#14582646	2
C₄₃×#2962	2
#19239	43