Subgroups — #25000413

Order 11008.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583101	C₂	1	1	yes	maximal, characteristic
2	#19135557	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135388	C₂	1	1	yes	maximal, characteristic
4	#19134596	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582651	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621884	—	2	1	no	—
9	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
10	#14583101	—	2	2	no	—
11	#14583101	—	2	2	no	—
12	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#13063249	—	2	1	no	—
14	C₂×#13063247	—	2	1	no	—
15	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
16	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
17	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	#14582769	C₂²	1	1	yes	characteristic
19	#14582662	—	2	1	no	—
20	#14582661	—	2	1	no	—
21	#14582661	—	2	1	no	—
22	#14582651	—	2	2	no	—
23	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#332	—	2	2	no	—
27	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
28	C₂²×C₄×D₄₃	—	2	1	no	—
29	C₂×#10621884	—	2	4	no	—
30	C₂×#10621884	—	4	2	no	—
31	C₂×#10621884	—	4	2	no	—
32	C₂²×C₄₃⋊C₈	—	2	1	no	—
33	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
34	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
35	C₄×D₁₇₂	—	2	1	no	—
36	C₄×D₁₇₂	—	2	1	no	—
37	C₄×D₁₇₂	—	2	1	no	—
38	C₄×D₁₇₂	—	2	1	no	—
39	C₂×C₄⋊Dic₄₃	—	2	1	no	—
40	C₂×C₄⋊Dic₄₃	—	2	1	no	—
41	C₂×C₄⋊Dic₄₃	—	2	1	no	—
42	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
43	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
44	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
45	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
46	#13063249	—	2	4	no	—
47	#13063247	—	4	2	no	—
48	(C₂×D₄₃)⋊C₈	—	4	2	no	—
49	(C₂×D₄₃)⋊C₈	—	4	2	no	—
50	C₄×C₄₃⋊C₈	—	2	1	no	—
51	C₄×C₄₃⋊C₈	—	2	1	no	—
52	C₂²×Q₈×C₄₃	—	2	1	no	—
53	C₂²×C₈×C₄₃	—	2	1	no	—
54	C₂²×C₈×C₄₃	—	2	1	no	—
55	C₄⋊Q₈×C₄₃	—	2	1	no	—
56	C₄⋊Q₈×C₄₃	—	2	1	no	—
57	C₄⋊Q₈×C₄₃	—	2	1	no	—
58	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₄₃	—	2	1	no	—
63	C₄⋊C₈×C₄₃	—	2	1	no	—
64	C₄⋊C₈×C₄₃	—	2	1	no	—
65	C₄⋊C₈×C₄₃	—	2	1	no	—
66	C₂³×D₄₃	—	2	1	no	—
67	C₂×Q₈×C₄₃	—	2	2	no	—
68	C₂×Q₈×C₄₃	—	4	1	no	—
69	C₂×Q₈×C₄₃	—	4	1	no	—
70	C₂×Q₈×C₄₃	—	4	1	no	—
71	C₂×Q₈×C₄₃	—	4	1	no	—
72	C₂×Q₈×C₄₃	—	4	1	no	—
73	C₂²×C₄×C₄₃	—	4	1	no	—
74	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
77	C₂²×Dic₄₃	—	2	1	no	—
78	C₂²×Dic₄₃	—	4	1	no	—
79	C₂×D₁₇₂	—	2	1	no	—
80	C₂×D₁₇₂	—	2	1	no	—
81	C₂×D₁₇₂	—	2	1	no	—
82	C₂×D₁₇₂	—	2	1	no	—
83	C₂×D₁₇₂	—	2	1	no	—
84	C₂×D₁₇₂	D₈	1	2	yes	—
85	C₂×C₄×D₄₃	—	4	1	no	—
86	C₂×C₄×D₄₃	—	4	1	no	—
87	C₂×C₄×D₄₃	—	4	1	no	—
88	C₂×C₄×D₄₃	—	4	1	no	—
89	C₂×C₄×D₄₃	—	4	1	no	—
90	C₂×C₄×D₄₃	—	4	1	no	—
91	C₂×C₈×C₄₃	—	4	1	no	—
92	C₂×C₈×C₄₃	—	4	1	no	—
93	C₂×C₈×C₄₃	—	4	1	no	—
94	C₂×C₈×C₄₃	—	4	1	no	—
95	C₂×C₈×C₄₃	—	4	1	no	—
96	C₂×C₈×C₄₃	—	4	1	no	—
97	C₄⋊C₄×C₄₃	—	2	2	no	—
98	C₄⋊C₄×C₄₃	—	2	2	no	—
99	C₄⋊C₄×C₄₃	—	4	1	no	—
100	C₄⋊C₄×C₄₃	—	4	1	no	—
101	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₄₃	#41	1	1	yes	characteristic
104	C₄²×C₄₃	#41	1	1	yes	characteristic
105	#10621884	—	4	8	no	—
106	(C₂×D₄₃)⋊C₄	—	4	1	no	—
107	(C₂×D₄₃)⋊C₄	—	4	1	no	—
108	C₄⋊Dic₄₃	—	2	1	no	—
109	C₄⋊Dic₄₃	—	2	1	no	—
110	C₄⋊Dic₄₃	—	4	1	no	—
111	C₄⋊Dic₄₃	—	4	1	no	—
112	C₄⋊Dic₄₃	—	4	1	no	—
113	C₄⋊Dic₄₃	—	4	1	no	—
114	C₄⋊Dic₄₃	—	8	1	no	—
115	C₂×C₄₃⋊C₈	—	2	1	no	—
116	C₂×C₄₃⋊C₈	—	2	1	no	—
117	C₂×C₄₃⋊C₈	—	2	2	no	—
118	C₂×C₄₃⋊C₈	—	2	1	no	—
119	C₂×C₄₃⋊C₈	—	2	1	no	—
120	C₂×C₄₃⋊C₈	—	2	1	no	—
121	C₂×C₄₃⋊C₈	—	4	1	no	—
122	C₂×C₄₃⋊C₈	—	4	1	no	—
123	C₂×C₄₃⋊C₈	SD₁₆	1	2	yes	complemented
124	C₂³×C₄₃	#121	1	1	yes	characteristic
125	C₂²×D₄₃	—	2	2	no	—
126	C₂²×D₄₃	—	4	1	no	—
127	C₂²×D₄₃	—	4	1	no	—
128	C₂²×D₄₃	—	4	1	no	—
129	C₂²×D₄₃	—	4	1	no	—
130	C₂²×D₄₃	—	4	1	no	—
131	C₂²×D₄₃	—	4	1	no	—
132	Q₈×C₄₃	—	4	2	no	—
133	Q₈×C₄₃	—	4	2	no	—
134	Q₈×C₄₃	—	8	1	no	—
135	Q₈×C₄₃	—	8	1	no	—
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	4	2	no	—
139	C₂×C₄×C₄₃	—	8	1	no	—
140	C₂×C₄×C₄₃	—	8	1	no	—
141	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
142	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
143	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
144	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
145	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
146	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
147	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
150	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
151	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
154	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
155	C₂×Dic₄₃	—	4	1	no	—
156	C₂×Dic₄₃	—	4	1	no	—
157	C₂×Dic₄₃	—	4	1	no	—
158	C₂×Dic₄₃	—	8	1	no	—
159	C₂×Dic₄₃	—	8	1	no	—
160	C₂×Dic₄₃	—	8	1	no	—
161	D₁₇₂	—	2	2	no	—
162	D₁₇₂	—	2	2	no	—
163	D₁₇₂	—	4	1	no	—
164	D₁₇₂	—	4	1	no	—
165	C₄×D₄₃	—	8	1	no	—
166	C₄×D₄₃	—	8	1	no	—
167	C₄×D₄₃	—	8	1	no	—
168	C₄×D₄₃	—	8	1	no	—
169	C₈×C₄₃	—	8	1	no	—
170	C₈×C₄₃	—	8	1	no	—
171	C₄₃⋊C₈	—	2	2	no	—
172	C₄₃⋊C₈	—	4	2	no	—
173	C₄₃⋊C₈	—	4	1	no	—
174	#10476	—	43	1	no	maximal, Sylow
175	C₂²×C₄₃	#394	1	1	yes	characteristic
176	C₂²×C₄₃	#461	1	1	yes	characteristic
177	C₂²×C₄₃	#463	1	1	yes	characteristic
178	C₂²×C₄₃	#466	1	1	yes	characteristic
179	C₂²×C₄₃	#468	1	1	yes	characteristic
180	C₂²×C₄₃	#471	1	1	yes	characteristic
181	C₂²×C₄₃	#473	1	1	yes	characteristic
182	C₂×D₄₃	—	4	2	no	—
183	C₂×D₄₃	—	4	2	no	—
184	C₂×D₄₃	—	4	2	no	—
185	C₂×D₄₃	—	8	1	no	—
186	C₂×D₄₃	—	8	1	no	—
187	C₂×D₄₃	—	8	1	no	—
188	C₂×D₄₃	—	8	1	no	—
189	C₄×C₄₃	—	2	1	no	—
190	C₄×C₄₃	—	2	1	no	—
191	C₄×C₄₃	—	8	2	no	—
192	C₄×C₄₃	#447	1	1	yes	characteristic
193	C₄×C₄₃	#452	1	1	yes	characteristic
194	C₄×C₄₃	#460	1	1	yes	characteristic
195	C₄×C₄₃	#464	1	1	yes	characteristic
196	C₄×C₄₃	#465	1	1	yes	characteristic
197	C₄×C₄₃	#468	1	1	yes	characteristic
198	C₄×C₄₃	#480	1	1	yes	characteristic
199	C₄×C₄₃	#482	1	1	yes	characteristic
200	Dic₄₃	—	8	1	no	—
201	Dic₄₃	—	16	1	no	—
202	C₂×#461	—	43	1	no	—
203	#1990	—	43	1	no	—
204	#1954	—	43	1	no	—
205	#1802	—	43	1	no	—
206	C₂×#335	—	43	1	no	—
207	C₂×#332	D₄₃	1	1	yes	characteristic, complemented
208	#1296	—	43	1	no	—
209	C₂×C₄₃	#1673	1	1	yes	characteristic
210	C₂×C₄₃	#1681	1	1	yes	characteristic
211	C₂×C₄₃	#1691	1	1	yes	characteristic
212	C₂×C₄₃	#1699	1	1	yes	characteristic
213	C₂×C₄₃	#2033	1	1	yes	characteristic
214	C₂×C₄₃	#2052	1	1	yes	characteristic
215	C₂×C₄₃	#2055	1	1	yes	characteristic
216	D₄₃	—	8	2	no	—
217	C₂²×SD₁₆	—	86	1	no	—
218	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
219	C₂×C₄×D₄	—	43	1	no	—
220	#461	—	86	2	no	—
221	#461	—	86	2	no	—
222	C₂×C₄⋊C₈	—	43	1	no	—
223	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
225	C₂×#103	—	86	1	no	—
226	C₂×#102	—	86	1	no	—
227	C₂×C₂²⋊C₈	—	86	1	no	—
228	C₂×C₂²⋊C₈	—	86	1	no	—
229	C₂×C₄×C₈	—	43	1	no	—
230	#384	—	43	1	no	—
231	#340	—	86	1	no	—
232	#340	—	86	1	no	—
233	#340	—	86	1	no	—
234	#335	—	86	2	no	—
235	#332	—	2	2	no	—
236	C₄₃	#10476	1	1	yes	characteristic, complemented, Sylow
237	C₂²×Q₈	—	2	1	no	—
238	C₂²×D₄	—	43	1	no	—
239	C₂³×C₄	—	86	1	no	—
240	C₂×SD₁₆	—	86	4	no	—
241	C₂×SD₁₆	—	172	2	no	—
242	C₂×SD₁₆	—	172	2	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	43	1	no	—
246	C₂²×C₈	—	43	1	no	—
247	C₂²×C₈	—	86	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	C₂²⋊D₄₃	1	2	yes	—
252	C₄×D₄	—	86	1	no	—
253	C₄×D₄	—	86	1	no	—
254	C₄×D₄	—	86	1	no	—
255	C₄×D₄	—	86	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	43	1	no	—
259	C₂×C₄⋊C₄	—	86	1	no	—
260	C₂×C₄⋊C₄	—	86	1	no	—
261	C₂×C₄⋊C₄	—	86	1	no	—
262	C₂×C₂²⋊C₄	—	86	1	no	—
263	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	43	2	no	—
269	C₄⋊C₈	—	86	1	no	—
270	#103	—	86	4	no	—
271	#102	—	172	2	no	—
272	C₂²⋊C₈	—	172	2	no	—
273	C₂²⋊C₈	—	172	2	no	—
274	C₄×C₈	—	86	1	no	—
275	C₄×C₈	—	86	1	no	—
276	C₂⁴	—	86	1	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×D₄	—	43	2	no	—
284	C₂×D₄	—	86	1	no	—
285	C₂×D₄	—	86	1	no	—
286	C₂×D₄	—	86	1	no	—
287	C₂×D₄	—	86	1	no	—
288	C₂×D₄	—	86	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	86	1	no	—
291	C₂²×C₄	—	172	1	no	—
292	C₂²×C₄	—	172	1	no	—
293	C₂²×C₄	—	172	1	no	—
294	C₂²×C₄	—	172	1	no	—
295	C₂²×C₄	—	172	1	no	—
296	C₂²×C₄	—	172	1	no	—
297	C₂²×C₄	—	172	1	no	—
298	C₂²×C₄	#10621898	1	1	yes	characteristic
299	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
301	SD₁₆	—	172	8	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	43	2	no	—
309	C₂×C₈	—	86	1	no	—
310	C₂×C₈	—	86	1	no	—
311	C₂×C₈	—	86	2	no	—
312	C₂×C₈	—	86	1	no	—
313	C₂×C₈	—	86	1	no	—
314	C₂×C₈	—	86	1	no	—
315	C₂×C₈	—	172	1	no	—
316	C₂×C₈	—	172	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	86	1	no	—
322	C₄⋊C₄	—	86	1	no	—
323	C₄⋊C₄	—	344	1	no	—
324	C₄⋊C₄	—	172	1	no	—
325	C₄⋊C₄	—	172	1	no	—
326	C₄⋊C₄	—	172	1	no	—
327	C₄⋊C₄	—	172	1	no	—
328	C₂²⋊C₄	—	172	1	no	—
329	C₂²⋊C₄	—	172	1	no	—
330	C₄²	#10621898	1	1	yes	characteristic
331	C₄²	D₄×D₄₃	1	1	yes	characteristic
332	C₄²	#10621900	1	1	yes	characteristic
333	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
334	C₂³	—	86	2	no	—
335	C₂³	—	172	1	no	—
336	C₂³	—	172	1	no	—
337	C₂³	—	172	1	no	—
338	C₂³	—	172	1	no	—
339	C₂³	—	172	1	no	—
340	C₂³	—	172	1	no	—
341	C₂³	#13063298	1	1	yes	characteristic
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	8	1	no	—
345	Q₈	—	8	1	no	—
346	D₄	—	86	2	no	—
347	D₄	—	86	2	no	—
348	D₄	—	172	1	no	—
349	D₄	—	172	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	8	1	no	—
354	C₂×C₄	—	8	1	no	—
355	C₂×C₄	—	344	1	no	—
356	C₂×C₄	—	344	1	no	—
357	C₂×C₄	—	344	1	no	—
358	C₂×C₄	—	344	1	no	—
359	C₂×C₄	—	344	1	no	—
360	C₂×C₄	—	344	1	no	—
361	C₂×C₄	—	344	1	no	—
362	C₂×C₄	—	172	1	no	—
363	C₂×C₄	—	172	1	no	—
364	C₂×C₄	—	172	1	no	—
365	C₂×C₄	#13063293	1	1	yes	characteristic
366	C₂×C₄	#13063297	1	1	yes	characteristic
367	C₂×C₄	#13063298	1	1	yes	characteristic
368	C₂×C₄	#13063307	1	1	yes	characteristic
369	C₂×C₄	#13063308	1	1	yes	characteristic
370	C₂×C₄	#13063311	1	1	yes	characteristic
371	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
372	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
373	C₂×C₄	#13063346	1	1	yes	characteristic
374	C₂×C₄	#13063348	1	1	yes	characteristic
375	C₂×C₄	#13063349	1	1	yes	characteristic
376	C₂×C₄	#13063352	1	1	yes	characteristic
377	C₂×C₄	#13063354	1	1	yes	characteristic
378	C₂×C₄	#13063357	1	1	yes	characteristic
379	C₈	—	8	1	no	—
380	C₈	—	8	1	no	—
381	C₈	—	86	2	no	—
382	C₈	—	172	1	no	—
383	C₈	—	172	2	no	—
384	C₂²	—	344	1	no	—
385	C₂²	—	344	1	no	—
386	C₂²	—	344	1	no	—
387	C₂²	—	344	1	no	—
388	C₂²	—	172	2	no	—
389	C₂²	—	172	2	no	—
390	C₂²	—	172	2	no	—
391	C₂²	#14582814	1	1	yes	characteristic
392	C₂²	#14583103	1	1	yes	characteristic
393	C₂²	#14583117	1	1	yes	characteristic
394	C₂²	#14583134	1	1	yes	characteristic
395	C₂²	#14583144	1	1	yes	characteristic
396	C₂²	#14583165	1	1	yes	characteristic
397	C₂²	#14583173	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	344	1	no	—
402	C₄	—	688	1	no	—
403	C₄	#14583031	1	1	yes	characteristic
404	C₄	#14583058	1	1	yes	characteristic
405	C₄	#14583097	1	1	yes	characteristic
406	C₄	#14583123	1	1	yes	characteristic
407	C₄	#14583131	1	1	yes	characteristic
408	C₄	#14583148	1	1	yes	characteristic
409	C₄	#14583211	1	1	yes	characteristic
410	C₄	#14583222	1	1	yes	characteristic
411	C₂	—	344	2	no	—
412	C₂	#19133983	1	1	yes	characteristic
413	C₂	#19134035	1	1	yes	characteristic
414	C₂	#19134093	1	1	yes	characteristic
415	C₂	#19134145	1	1	yes	characteristic
416	C₂	#19135775	1	1	yes	characteristic
417	C₂	#19135894	1	1	yes	characteristic
418	C₂	#19135909	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063298
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#332	C₂
socle	C₂³×C₄₃	#121
prime radical	C₂²×D₁₇₂	D₄
hypercenter	C₂×#332	D₄₃
hypocenter	C₄₃	#10476
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#332

Complements

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

N	H ≅ G/N	type
2. #19135557	C₂	semidirect
5. C₂×#14582651	C₂	semidirect
6. #19132479	C₂	semidirect
7. C₂×C₄₃×#332	C₂	semidirect
123. C₂×C₄₃⋊C₈	SD₁₆	semidirect
207. C₂×#332	D₄₃	semidirect
236. C₄₃	#10476	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583101	2
#19135557	2
#19135388	2
#19134596	2
C₂×#14582651	2
#19132479	2
C₂×C₄₃×#332	2
#10476	43