Subgroups — #25079283

Order 11008.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144920	C₂	1	1	yes	maximal, characteristic
2	#19144630	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144627	C₂	1	1	yes	maximal, characteristic
4	C₂×#14583026	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134180	C₂	1	2	yes	maximal, complemented
6	#19134166	C₂	1	2	yes	maximal, complemented
7	#19134152	C₂	1	2	yes	maximal, complemented
8	#19134138	C₂	1	2	yes	maximal, complemented
9	#19133341	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133245	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1542	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583449	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
14	#14583256	—	2	1	no	—
15	#14583256	—	2	1	no	—
16	#14583251	C₂²	1	1	yes	characteristic
17	#14583251	C₂²	1	1	yes	characteristic
18	#14583247	C₂²	1	1	yes	characteristic
19	#14583247	C₂²	1	1	yes	characteristic
20	#14583232	—	2	1	no	—
21	#14583218	—	2	1	no	—
22	#14583191	C₂²	1	2	yes	—
23	#14583185	C₂²	1	2	yes	—
24	#14583106	C₂²	1	2	yes	—
25	#14583100	C₂²	1	2	yes	—
26	#14583054	—	2	1	no	—
27	#14583040	—	2	1	no	—
28	#14583026	—	2	1	no	—
29	#14583026	—	2	1	no	—
30	#14583026	C₂²	1	2	yes	—
31	#14583026	C₂²	1	2	yes	—
32	C₄×#10621885	—	2	2	no	—
33	C₄×#10621873	—	2	2	no	—
34	#14582952	C₂²	1	1	yes	characteristic
35	C₂×Dic₄₃⋊C₈	—	2	1	no	—
36	#14582893	—	2	1	no	—
37	#14582893	—	2	1	no	—
38	C₂×#13063235	—	2	1	no	—
39	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
40	#14582651	C₂²	1	2	yes	—
41	#14582649	C₂²	1	2	yes	—
42	#14582646	C₂²	1	2	yes	—
43	#14582642	C₂²	1	2	yes	—
44	C₄₃×#533	C₂²	1	1	yes	characteristic
45	C₄₃×#431	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#333	C₂²	1	2	yes	—
48	C₄₃×#332	C₂²	1	2	yes	—
49	C₂×#10621898	—	2	1	no	—
50	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
51	C₂×#10621885	—	2	2	no	—
52	C₂×#10621873	—	2	2	no	—
53	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
54	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
55	#13063325	C₂³	1	1	yes	characteristic
56	#13063322	C₂³	1	1	yes	characteristic
57	#13063313	—	2	1	no	—
58	#13063299	—	2	1	no	—
59	#13063299	—	2	1	no	—
60	C₄×Dic₈₆	—	2	1	no	—
61	C₄×Dic₈₆	—	2	1	no	—
62	C₄×Dic₈₆	D₄	1	2	yes	—
63	C₄×Dic₈₆	C₂³	1	2	yes	—
64	C₄×D₁₇₂	—	2	1	no	—
65	C₄×D₁₇₂	—	2	1	no	—
66	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
67	C₂×Dic₄₃⋊C₄	—	2	1	no	—
68	C₂×C₄×Dic₄₃	—	2	1	no	—
69	#13063258	—	2	2	no	—
70	#13063257	—	2	2	no	—
71	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
72	Dic₄₃⋊C₈	—	2	2	no	—
73	Dic₄₃⋊C₈	—	2	2	no	—
74	#13063250	—	2	2	no	—
75	#13063249	—	2	2	no	—
76	#13063248	—	2	2	no	—
77	#13063248	—	2	1	no	—
78	#13063248	—	2	1	no	—
79	#13063248	—	2	1	no	—
80	#13063248	—	2	1	no	—
81	#13063247	—	2	2	no	—
82	#13063245	—	2	1	no	—
83	#13063245	—	2	1	no	—
84	#13063245	—	2	1	no	—
85	#13063245	—	2	1	no	—
86	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
87	#13063235	—	2	2	no	—
88	#13063235	—	2	2	no	—
89	C₄×C₄₃⋊C₈	—	2	1	no	—
90	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
91	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
92	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₄₃	—	2	1	no	—
95	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
97	#125×C₄₃	—	2	1	no	—
98	C₂²⋊Q₈×C₄₃	—	2	1	no	—
99	C₂²⋊Q₈×C₄₃	—	2	1	no	—
100	C₄×Q₈×C₄₃	—	2	1	no	—
101	C₄×Q₈×C₄₃	—	2	1	no	—
102	#117×C₄₃	—	2	1	no	—
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₄₃	—	2	1	no	—
105	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
106	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
107	C₂²⋊C₈×C₄₃	—	2	1	no	—
108	C₄×C₈×C₄₃	—	2	1	no	—
109	C₂×Q₈×C₄₃	—	2	1	no	—
110	C₂×Q₈×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₃	—	4	1	no	—
115	C₂²×Dic₄₃	—	2	1	no	—
116	C₂²×Dic₄₃	—	2	1	no	—
117	#10621898	—	4	2	no	—
118	#10621898	—	4	2	no	—
119	C₂×D₁₇₂	—	2	1	no	—
120	C₂×D₁₇₂	—	2	1	no	—
121	C₂×D₁₇₂	—	2	1	no	—
122	C₂×C₄×D₄₃	—	4	1	no	—
123	C₂×Dic₈₆	—	2	1	no	—
124	C₂×Dic₈₆	—	2	1	no	—
125	C₂×Dic₈₆	—	4	2	no	—
126	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	4	2	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	—	2	1	no	—
134	C₄⋊C₄×C₄₃	—	4	1	no	—
135	C₄⋊C₄×C₄₃	—	4	1	no	—
136	C₂²⋊C₄×C₄₃	—	4	1	no	—
137	C₄²×C₄₃	—	4	1	no	—
138	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₃	#41	1	1	yes	characteristic
141	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
142	#10621885	—	4	4	no	—
143	(C₂×D₄₃)⋊C₄	—	4	1	no	—
144	(C₂×D₄₃)⋊C₄	—	4	1	no	—
145	C₄⋊Dic₄₃	—	2	1	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	—	2	1	no	—
148	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
149	Dic₄₃⋊C₄	—	2	2	no	—
150	Dic₄₃⋊C₄	—	2	2	no	—
151	C₄×Dic₄₃	—	2	2	no	—
152	C₄×Dic₄₃	—	2	2	no	—
153	C₂×C₄₃⋊C₈	—	2	2	no	—
154	C₂×C₄₃⋊C₈	—	2	2	no	—
155	C₂×C₄₃⋊C₈	—	2	2	no	—
156	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
160	#10621873	—	4	4	no	—
161	C₂³×C₄₃	#121	1	1	yes	characteristic
162	C₂²×D₄₃	—	4	1	no	—
163	Q₈×C₄₃	—	4	2	no	—
164	Q₈×C₄₃	—	8	1	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₃	#135	1	2	yes	—
173	C₂×C₄×C₄₃	#137	1	2	yes	—
174	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
177	C₂²⋊D₄₃	—	8	2	no	—
178	C₂×Dic₄₃	—	2	2	no	—
179	C₂×Dic₄₃	—	2	2	no	—
180	C₂×Dic₄₃	—	4	2	no	—
181	C₂×Dic₄₃	—	4	2	no	—
182	C₂×Dic₄₃	—	4	1	no	—
183	D₁₇₂	—	4	1	no	—
184	D₁₇₂	—	4	1	no	—
185	D₁₇₂	—	4	2	no	—
186	D₁₇₂	—	8	1	no	—
187	C₄×D₄₃	—	8	2	no	—
188	Dic₈₆	—	2	2	no	—
189	Dic₈₆	—	2	2	no	—
190	Dic₈₆	—	4	2	no	—
191	Dic₈₆	—	4	1	no	—
192	Dic₈₆	—	4	1	no	—
193	C₈×C₄₃	—	4	2	no	—
194	C₈×C₄₃	—	4	2	no	—
195	C₄₃⋊C₈	—	2	1	no	—
196	C₄₃⋊C₈	—	2	1	no	—
197	C₄₃⋊C₈	—	2	1	no	—
198	C₄₃⋊C₈	—	2	1	no	—
199	C₄₃⋊C₈	—	4	2	no	—
200	#19155	—	43	1	no	maximal, Sylow
201	C₂²×C₄₃	—	2	1	no	—
202	C₂²×C₄₃	—	2	1	no	—
203	C₂²×C₄₃	#464	1	2	yes	—
204	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
205	C₂×D₄₃	—	8	1	no	—
206	C₂×D₄₃	—	8	1	no	—
207	C₂×D₄₃	—	8	1	no	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	—	2	1	no	—
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	8	1	no	—
212	C₄×C₄₃	—	8	1	no	—
213	C₄×C₄₃	#464	1	2	yes	—
214	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
215	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
216	C₄×C₄₃	#575	1	2	yes	—
217	Dic₄₃	—	4	2	no	—
218	Dic₄₃	—	4	2	no	—
219	Dic₄₃	—	8	1	no	—
220	#3131	—	43	1	no	—
221	#3104	—	43	1	no	—
222	#3103	—	43	1	no	—
223	C₂×#446	—	43	1	no	—
224	#1704	—	43	2	no	—
225	#1702	—	43	2	no	—
226	#1700	—	43	2	no	—
227	#1698	—	43	2	no	—
228	#1564	—	43	1	no	—
229	#1542	D₄₃	1	1	yes	characteristic, complemented
230	#1540	—	43	1	no	—
231	C₂×C₄₃	—	2	2	no	—
232	C₂×C₄₃	C₂×#464	1	1	yes	characteristic
233	C₂×C₄₃	#3054	1	1	yes	characteristic
234	C₂×C₄₃	#3067	1	1	yes	characteristic
235	D₄₃	—	16	1	no	—
236	#533	C₂×D₄₃	1	1	yes	characteristic
237	#532	—	43	1	no	—
238	C₂×C₄×Q₈	—	43	1	no	—
239	#488	—	86	1	no	—
240	#488	—	86	1	no	—
241	#487	—	43	1	no	—
242	#487	—	43	1	no	—
243	#486	—	43	1	no	—
244	#486	—	43	1	no	—
245	#484	—	86	1	no	—
246	#481	—	86	1	no	—
247	#477	—	43	2	no	—
248	#475	—	43	2	no	—
249	#462	—	43	2	no	—
250	#460	—	43	2	no	—
251	#451	—	86	1	no	—
252	#448	—	86	1	no	—
253	#446	—	43	2	no	—
254	#446	—	43	2	no	—
255	#446	—	86	1	no	—
256	#446	—	86	1	no	—
257	C₄×Q₁₆	—	86	2	no	—
258	C₄×SD₁₆	—	86	2	no	—
259	#431	—	43	1	no	—
260	#431	C₂×D₄₃	1	1	yes	characteristic
261	C₂×C₄⋊C₈	—	86	1	no	—
262	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
263	#416	—	86	1	no	—
264	#416	—	86	1	no	—
265	C₂×#97	—	86	1	no	—
266	C₂×C₄×C₈	—	43	1	no	—
267	#335	—	43	2	no	—
268	#334	—	43	2	no	—
269	#333	C₂×D₄₃	1	2	yes	—
270	#332	—	43	2	no	—
271	#332	C₂×D₄₃	1	2	yes	—
272	#331	—	43	2	no	—
273	C₄₃	#19155	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	86	1	no	—
275	C₂²×Q₈	—	43	1	no	—
276	C₂×Q₁₆	—	86	2	no	—
277	C₂×SD₁₆	—	86	2	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	43	1	no	—
280	C₂²×C₈	—	43	1	no	—
281	C₄⋊Q₈	—	43	1	no	—
282	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
283	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
284	#127	—	43	1	no	—
285	#125	—	2	1	no	—
286	#124	—	86	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	#121	—	86	1	no	—
290	#121	—	86	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	43	2	no	—
294	C₄×Q₈	—	43	2	no	—
295	C₄×Q₈	—	86	1	no	—
296	C₄×Q₈	—	86	1	no	—
297	C₄×D₄	—	86	1	no	—
298	C₄×D₄	—	86	1	no	—
299	#117	—	2	1	no	—
300	C₂×C₄⋊C₄	—	43	1	no	—
301	C₂×C₄⋊C₄	—	86	1	no	—
302	C₂×C₄²	—	86	1	no	—
303	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
304	#107	—	86	2	no	—
305	#106	—	86	2	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	43	2	no	—
308	C₄⋊C₈	—	86	2	no	—
309	C₄⋊C₈	—	86	2	no	—
310	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
311	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
312	#103	—	86	1	no	—
313	#103	—	86	1	no	—
314	#103	—	86	1	no	—
315	#103	—	86	1	no	—
316	#103	—	86	2	no	—
317	#103	—	86	2	no	—
318	#103	—	86	2	no	—
319	#102	—	86	1	no	—
320	#102	—	86	1	no	—
321	#102	—	86	1	no	—
322	#102	—	86	1	no	—
323	#102	—	86	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	86	1	no	—
326	#97	—	86	2	no	—
327	#97	—	86	2	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	—	43	1	no	—
330	C₄×C₈	—	43	1	no	—
331	C₄×C₈	—	43	1	no	—
332	C₄×C₈	—	43	1	no	—
333	C₄×C₈	—	86	1	no	—
334	#41	—	172	2	no	—
335	#41	—	172	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	43	2	no	—
339	C₂×Q₈	—	86	1	no	—
340	C₂×Q₈	—	86	1	no	—
341	C₂×Q₈	—	172	2	no	—
342	C₂×D₄	—	86	1	no	—
343	C₂×D₄	—	86	1	no	—
344	C₂×D₄	—	86	1	no	—
345	C₂×D₄	—	172	1	no	—
346	C₂²×C₄	—	86	1	no	—
347	C₂²×C₄	—	86	1	no	—
348	C₂²×C₄	—	172	1	no	—
349	C₂²×C₄	#10621898	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
352	Q₁₆	—	172	4	no	—
353	SD₁₆	—	172	4	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	—	43	1	no	—
358	C₂×C₈	—	43	1	no	—
359	C₂×C₈	—	43	1	no	—
360	C₂×C₈	—	43	1	no	—
361	C₂×C₈	—	86	2	no	—
362	C₂×C₈	—	86	2	no	—
363	C₂×C₈	—	86	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	43	2	no	—
371	C₄⋊C₄	—	86	1	no	—
372	C₄⋊C₄	—	86	2	no	—
373	C₄⋊C₄	—	86	2	no	—
374	C₄⋊C₄	—	86	1	no	—
375	C₄⋊C₄	—	86	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	172	1	no	—
378	C₂²⋊C₄	—	172	1	no	—
379	C₄²	—	4	1	no	—
380	C₄²	—	86	2	no	—
381	C₄²	—	86	2	no	—
382	C₄²	#10621898	1	1	yes	characteristic
383	C₄²	D₄×D₄₃	1	1	yes	characteristic
384	C₄²	D₄×D₄₃	1	1	yes	characteristic
385	C₄²	C₂³×D₄₃	1	1	yes	characteristic
386	C₂³	—	172	1	no	—
387	C₂³	#13063298	1	1	yes	characteristic
388	Q₈	—	4	2	no	—
389	Q₈	—	8	1	no	—
390	Q₈	—	86	2	no	—
391	Q₈	—	86	2	no	—
392	Q₈	—	172	2	no	—
393	Q₈	—	172	1	no	—
394	Q₈	—	172	1	no	—
395	D₄	—	344	1	no	—
396	D₄	—	344	2	no	—
397	D₄	—	172	1	no	—
398	D₄	—	172	1	no	—
399	D₄	—	172	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	86	2	no	—
405	C₂×C₄	—	86	2	no	—
406	C₂×C₄	—	344	2	no	—
407	C₂×C₄	—	172	1	no	—
408	C₂×C₄	—	172	2	no	—
409	C₂×C₄	—	172	2	no	—
410	C₂×C₄	#13063298	1	1	yes	characteristic
411	C₂×C₄	#13063298	1	1	yes	characteristic
412	C₂×C₄	#13063298	1	1	yes	characteristic
413	C₂×C₄	#13063346	1	2	yes	—
414	C₂×C₄	#13063357	1	2	yes	—
415	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
417	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	86	1	no	—
421	C₈	—	86	1	no	—
422	C₈	—	86	1	no	—
423	C₈	—	86	1	no	—
424	C₈	—	172	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	344	1	no	—
428	C₂²	—	344	1	no	—
429	C₂²	—	344	1	no	—
430	C₂²	#14583124	1	2	yes	—
431	C₂²	C₂×#13063298	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	1	no	—
437	C₄	—	344	1	no	—
438	C₄	—	172	2	no	—
439	C₄	—	172	2	no	—
440	C₄	#14583124	1	2	yes	—
441	C₄	C₂×#13063346	1	1	yes	characteristic
442	C₄	C₂×#13063357	1	1	yes	characteristic
443	C₄	#14583696	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	688	1	no	—
446	C₂	C₂×#14583124	1	1	yes	characteristic
447	C₂	#19144203	1	1	yes	characteristic
448	C₂	#19144314	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063298
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1542	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	#1542	D₄₃
hypocenter	C₄₃	#19155
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1542

Complements

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

N	H ≅ G/N	type
2. #19144630	C₂	semidirect
4. C₂×#14583026	C₂	semidirect
5. #19134180	C₂	semidirect
6. #19134166	C₂	semidirect
7. #19134152	C₂	semidirect
8. #19134138	C₂	semidirect
9. #19133341	C₂	semidirect
11. C₄₃×#1542	C₂	semidirect
229. #1542	D₄₃	semidirect
273. C₄₃	#19155	semidirect

Maximal subgroups

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

subgroup	index
#19144920	2
#19144630	2
#19144627	2
C₂×#14583026	2
#19134180	2
#19134166	2
#19134152	2
#19134138	2
#19133341	2
#19133245	2
C₄₃×#1542	2
#19155	43