Subgroups — #19145183

Order 5504.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583444	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583435	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583307	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583285	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583262	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583260	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583152	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583150	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583147	C₂	1	1	yes	maximal, characteristic, complemented
10	SD₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#14582984	C₂	1	1	yes	maximal, characteristic, complemented
12	#14582981	C₂	1	1	yes	maximal, characteristic, complemented
13	#14582979	C₂	1	1	yes	maximal, characteristic, complemented
14	M₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10621900	—	2	1	no	—
17	C₂×#10621884	C₂²	1	1	yes	characteristic
18	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
19	C₂×#10621882	C₂²	1	1	yes	characteristic
20	C₂×#10621877	C₂²	1	1	yes	characteristic
21	#13063324	C₂²	1	1	yes	characteristic
22	#13063321	C₂²	1	1	yes	characteristic
23	#13063320	—	2	1	no	—
24	#13063316	C₂²	1	1	yes	characteristic
25	#13063314	C₂²	1	1	yes	characteristic
26	#13063311	—	2	1	no	—
27	#13063309	—	2	1	no	—
28	#13063299	C₂²	1	1	yes	characteristic
29	#13063299	C₂²	1	1	yes	characteristic
30	#13063297	—	2	1	no	—
31	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
32	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
33	#13063287	C₂²	1	1	yes	characteristic
34	#13063287	C₂²	1	1	yes	characteristic
35	(C₂²⋊D₄₃)⋊C₄	—	2	1	no	—
36	(C₂²⋊D₄₃)⋊C₄	—	2	1	no	—
37	#13063283	—	2	1	no	—
38	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
39	#13063258	C₂²	1	1	yes	characteristic
40	#13063257	C₂²	1	1	yes	characteristic
41	#13063256	C₂²	1	1	yes	characteristic
42	#13063249	C₂²	1	1	yes	characteristic
43	#13063247	C₂²	1	1	yes	characteristic
44	#13063247	C₂²	1	1	yes	characteristic
45	#13063246	C₂²	1	1	yes	characteristic
46	#13063245	C₂²	1	1	yes	characteristic
47	#13063245	C₂²	1	1	yes	characteristic
48	#13063235	C₂²	1	1	yes	characteristic
49	#13063235	C₂²	1	1	yes	characteristic
50	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
51	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
52	C₂×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
54	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
55	#121×C₄₃	C₂²	1	1	yes	characteristic
56	#107×C₄₃	C₂²	1	1	yes	characteristic
57	#103×C₄₃	C₂²	1	1	yes	characteristic
58	#102×C₄₃	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
60	C₂×D₄×C₄₃	—	2	1	no	—
61	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂×C₂²⋊D₄₃	—	2	1	no	—
64	C₂×C₂²⋊D₄₃	—	2	1	no	—
65	C₂×C₂²⋊D₄₃	—	2	1	no	—
66	C₂×C₂²⋊D₄₃	—	2	1	no	—
67	C₂²×Dic₄₃	—	2	1	no	—
68	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
69	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
70	#10621900	—	4	4	no	—
71	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
72	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
73	C₂×C₄×D₄₃	—	2	1	no	—
74	C₂×C₄×D₄₃	—	2	1	no	—
75	C₂×Dic₈₆	—	2	1	no	—
76	SD₁₆×C₄₃	—	2	2	no	—
77	M₁₆×C₄₃	—	2	2	no	—
78	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₄⋊C₄×C₄₃	—	2	1	no	—
81	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
82	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
83	C₂²⋊C₄×C₄₃	—	2	1	no	—
84	C₂²⋊C₄×C₄₃	—	2	1	no	—
85	C₂²⋊Dic₄₃	—	2	1	no	—
86	#10621884	—	2	2	no	—
87	#10621882	—	2	2	no	—
88	(C₂×D₄₃)⋊C₄	—	2	1	no	—
89	(C₂×D₄₃)⋊C₄	—	2	1	no	—
90	(C₂×D₄₃)⋊C₄	—	2	1	no	—
91	(C₂×D₄₃)⋊C₄	—	2	1	no	—
92	(C₂×D₄₃)⋊C₄	—	2	1	no	—
93	(C₂×D₄₃)⋊C₄	—	2	1	no	—
94	C₄⋊Dic₄₃	—	2	1	no	—
95	C₄⋊Dic₄₃	—	2	1	no	—
96	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
98	Dic₄₃⋊C₄	—	2	1	no	—
99	Dic₄₃⋊C₄	—	2	1	no	—
100	C₄×Dic₄₃	—	2	1	no	—
101	C₄×Dic₄₃	D₄	1	1	yes	characteristic
102	C₄×Dic₄₃	D₄	1	1	yes	characteristic
103	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
104	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
105	#10621877	—	2	2	no	—
106	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
107	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
108	D₃₄₄	—	2	2	no	—
109	C₂³×C₄₃	—	2	1	no	—
110	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×D₄₃	—	2	1	no	—
112	C₂²×D₄₃	—	2	1	no	—
113	Q₈×C₄₃	—	2	1	no	—
114	Q₈×C₄₃	—	2	1	no	—
115	D₄×C₄₃	—	2	1	no	—
116	D₄×C₄₃	—	2	1	no	—
117	D₄×C₄₃	—	4	2	no	—
118	C₂×C₄×C₄₃	—	2	1	no	—
119	C₂×C₄×C₄₃	—	2	1	no	—
120	C₂×C₄×C₄₃	—	2	1	no	—
121	C₂×C₄×C₄₃	—	2	1	no	—
122	C₂×C₄×C₄₃	—	2	1	no	—
123	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
125	C₂²⋊D₄₃	—	4	2	no	—
126	C₂²⋊D₄₃	—	4	2	no	—
127	C₂²⋊D₄₃	—	4	2	no	—
128	C₂²⋊D₄₃	—	4	2	no	—
129	C₂×Dic₄₃	—	2	2	no	—
130	C₂×Dic₄₃	—	2	1	no	—
131	C₂×Dic₄₃	—	2	1	no	—
132	C₂×Dic₄₃	—	4	1	no	—
133	C₂×Dic₄₃	—	4	2	no	—
134	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
138	D₁₇₂	—	2	1	no	—
139	D₁₇₂	—	2	1	no	—
140	D₁₇₂	—	2	1	no	—
141	D₁₇₂	—	2	1	no	—
142	C₄×D₄₃	—	4	2	no	—
143	C₄×D₄₃	—	4	2	no	—
144	Dic₈₆	—	4	2	no	—
145	C₈×C₄₃	—	2	1	no	—
146	C₈×C₄₃	#41	1	2	yes	complemented
147	C₄₃⋊C₈	—	2	1	no	—
148	C₄₃⋊C₈	#41	1	2	yes	complemented
149	C₂²×C₄₃	—	2	1	no	—
150	C₂²×C₄₃	—	2	1	no	—
151	C₂²×C₄₃	—	2	1	no	—
152	C₂²×C₄₃	—	4	1	no	—
153	C₂²×C₄₃	—	4	1	no	—
154	C₂²×C₄₃	—	4	1	no	—
155	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
156	C₂×D₄₃	—	4	1	no	—
157	C₂×D₄₃	—	4	1	no	—
158	C₂×D₄₃	—	4	1	no	—
159	C₂×D₄₃	—	4	1	no	—
160	C₂×D₄₃	—	4	1	no	—
161	C₂×D₄₃	—	4	1	no	—
162	C₄×C₄₃	—	2	1	no	—
163	C₄×C₄₃	—	4	1	no	—
164	C₄×C₄₃	—	4	1	no	—
165	C₄×C₄₃	—	4	1	no	—
166	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
167	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
168	Dic₄₃	—	2	1	no	—
169	Dic₄₃	—	2	1	no	—
170	Dic₄₃	—	2	1	no	—
171	Dic₄₃	—	4	1	no	—
172	Dic₄₃	—	4	1	no	—
173	Dic₄₃	AGL(1,ℤ/8)	1	2	yes	—
174	#3171	—	43	1	no	maximal, Sylow
175	C₂×C₄₃	—	4	1	no	—
176	C₂×C₄₃	—	8	1	no	—
177	C₂×C₄₃	#532	1	1	yes	characteristic
178	C₂×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₂×C₄₃	#575	1	1	yes	characteristic
180	D₄₃	—	8	1	no	—
181	D₄₃	—	8	1	no	—
182	#532	—	43	1	no	—
183	#529	—	43	1	no	—
184	#501	—	43	1	no	—
185	#496	—	43	1	no	—
186	#490	—	43	1	no	—
187	#489	—	43	1	no	—
188	#469	—	43	1	no	—
189	#469	—	43	1	no	—
190	#468	—	43	1	no	—
191	#468	D₄₃	1	1	yes	characteristic, complemented
192	C₄×SD₁₆	—	43	1	no	—
193	C₄×SD₁₆	—	43	1	no	—
194	C₄×D₈	—	43	1	no	—
195	C₄×D₈	—	43	1	no	—
196	C₄×M₁₆	—	43	1	no	—
197	C₄₃	#3171	1	1	yes	characteristic, complemented, Sylow
198	C₂×#41	—	86	1	no	—
199	C₂×SD₁₆	—	43	1	no	—
200	C₂×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
201	C₂×D₈	—	43	1	no	—
202	C₂×D₈	—	43	1	no	—
203	C₂×M₁₆	—	43	1	no	—
204	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
205	C₄⋊Q₈	—	43	1	no	—
206	#127	—	43	1	no	—
207	#126	—	86	1	no	—
208	#125	—	43	1	no	—
209	#124	—	43	1	no	—
210	#124	—	86	1	no	—
211	#123	—	86	1	no	—
212	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
213	#121	—	43	1	no	—
214	#121	—	43	1	no	—
215	#121	—	86	1	no	—
216	#121	C₂×D₄₃	1	1	yes	characteristic
217	C₄×Q₈	—	43	1	no	—
218	C₄×D₄	—	43	1	no	—
219	C₄×D₄	—	43	1	no	—
220	C₄×D₄	—	43	1	no	—
221	C₄×D₄	—	86	1	no	—
222	C₄×D₄	—	86	1	no	—
223	#117	—	86	1	no	—
224	C₂×C₄²	—	43	1	no	—
225	#107	—	43	1	no	—
226	#107	C₂×D₄₃	1	1	yes	characteristic
227	#106	—	43	1	no	—
228	#106	—	43	1	no	—
229	#103	—	43	1	no	—
230	#103	C₂×D₄₃	1	1	yes	characteristic
231	#102	—	43	1	no	—
232	#102	—	43	1	no	—
233	#102	—	43	1	no	—
234	#102	—	43	1	no	—
235	#102	—	43	1	no	—
236	#102	C₂×D₄₃	1	1	yes	characteristic
237	#97	—	43	1	no	—
238	#97	—	43	1	no	—
239	C₄×C₈	—	43	1	no	—
240	C₄×C₈	—	43	1	no	—
241	#41	—	172	4	no	—
242	C₂×Q₈	—	86	1	no	—
243	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
244	C₂×D₄	—	2	1	no	—
245	C₂×D₄	—	43	1	no	—
246	C₂×D₄	—	43	1	no	—
247	C₂×D₄	—	86	1	no	—
248	C₂×D₄	—	86	1	no	—
249	C₂×D₄	—	86	1	no	—
250	C₂×D₄	—	86	1	no	—
251	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
252	C₂²×C₄	—	43	1	no	—
253	C₂²×C₄	—	43	1	no	—
254	C₂²×C₄	—	86	1	no	—
255	C₂²×C₄	—	86	1	no	—
256	C₂²×C₄	—	86	1	no	—
257	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
258	SD₁₆	—	2	2	no	—
259	SD₁₆	—	86	2	no	—
260	D₈	—	86	2	no	—
261	D₈	—	86	2	no	—
262	M₁₆	—	2	2	no	—
263	M₁₆	—	86	2	no	—
264	C₂×C₈	—	43	1	no	—
265	C₂×C₈	—	43	1	no	—
266	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
267	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
268	C₄⋊C₄	—	2	1	no	—
269	C₄⋊C₄	—	43	1	no	—
270	C₄⋊C₄	—	43	1	no	—
271	C₄⋊C₄	—	86	1	no	—
272	C₄⋊C₄	—	86	1	no	—
273	C₄⋊C₄	—	86	1	no	—
274	C₄⋊C₄	—	86	1	no	—
275	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
276	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
277	C₂²⋊C₄	—	2	1	no	—
278	C₂²⋊C₄	—	2	1	no	—
279	C₂²⋊C₄	—	86	1	no	—
280	C₂²⋊C₄	—	86	1	no	—
281	C₂²⋊C₄	—	86	1	no	—
282	C₂²⋊C₄	—	86	1	no	—
283	C₂²⋊C₄	—	86	1	no	—
284	C₂²⋊C₄	—	86	1	no	—
285	C₂²⋊C₄	—	86	1	no	—
286	C₄²	—	43	1	no	—
287	C₄²	—	43	1	no	—
288	C₄²	—	43	1	no	—
289	C₄²	—	43	1	no	—
290	C₄²	—	86	1	no	—
291	C₂³	—	2	1	no	—
292	C₂³	—	86	1	no	—
293	C₂³	—	86	1	no	—
294	C₂³	D₄×D₄₃	1	1	yes	characteristic
295	Q₈	—	2	1	no	—
296	Q₈	—	2	1	no	—
297	Q₈	—	172	2	no	—
298	D₄	—	2	1	no	—
299	D₄	—	2	1	no	—
300	D₄	—	4	2	no	—
301	D₄	—	86	1	no	—
302	D₄	—	86	1	no	—
303	D₄	—	86	1	no	—
304	D₄	—	86	1	no	—
305	D₄	—	172	2	no	—
306	D₄	—	172	2	no	—
307	D₄	—	172	2	no	—
308	D₄	—	172	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	43	1	no	—
315	C₂×C₄	—	43	1	no	—
316	C₂×C₄	—	43	1	no	—
317	C₂×C₄	—	43	1	no	—
318	C₂×C₄	—	86	2	no	—
319	C₂×C₄	—	86	1	no	—
320	C₂×C₄	—	86	1	no	—
321	C₂×C₄	—	172	2	no	—
322	C₂×C₄	—	172	2	no	—
323	C₂×C₄	—	172	2	no	—
324	C₂×C₄	—	172	1	no	—
325	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
326	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
327	C₈	—	2	1	no	—
328	C₈	—	43	2	no	—
329	C₈	—	86	1	no	—
330	C₈	#10621900	1	2	yes	complemented
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	172	1	no	—
338	C₂²	—	172	1	no	—
339	C₂²	—	172	1	no	—
340	C₂²	—	172	1	no	—
341	C₂²	—	172	1	no	—
342	C₂²	—	172	1	no	—
343	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	4	1	no	—
346	C₄	—	4	1	no	—
347	C₄	—	4	1	no	—
348	C₄	—	43	2	no	—
349	C₄	—	86	1	no	—
350	C₄	—	86	1	no	—
351	C₄	—	86	1	no	—
352	C₄	—	172	1	no	—
353	C₄	—	172	1	no	—
354	C₄	#41×D₄₃	1	1	yes	characteristic
355	C₄	C₂×#10621900	1	1	yes	characteristic
356	C₂	—	4	1	no	—
357	C₂	—	8	1	no	—
358	C₂	—	344	1	no	—
359	C₂	—	344	1	no	—
360	C₂	#14583444	1	1	yes	characteristic
361	C₂	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
362	C₂	#14583698	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#468	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#468	D₄₃
hypocenter	C₄₃	#3171
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #468

Complements

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

N	H ≅ G/N	type
1. #14583444	C₂	semidirect
2. #14583435	C₂	semidirect
3. #14583307	C₂	semidirect
4. #14583285	C₂	semidirect
5. #14583262	C₂	semidirect
6. #14583260	C₂	semidirect
7. #14583152	C₂	semidirect
8. #14583150	C₂	semidirect
9. #14583147	C₂	semidirect
10. SD₁₆×Dic₄₃	C₂	semidirect
11. #14582984	C₂	semidirect
12. #14582981	C₂	semidirect
13. #14582979	C₂	semidirect
14. M₁₆×Dic₄₃	C₂	semidirect
15. C₄₃×#468	C₂	semidirect
146. C₈×C₄₃	#41	semidirect
148. C₄₃⋊C₈	#41	semidirect
191. #468	D₄₃	semidirect
197. C₄₃	#3171	semidirect
330. C₈	#10621900	semidirect