Subgroups — #19147612

Order 5504.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583618	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583569	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583287	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583270	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583112	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583111	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583102	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583097	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583096	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583092	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583027	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583001	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583000	C₂	1	1	yes	maximal, characteristic, complemented
14	D₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10621900	—	2	1	no	—
17	C₂×#10621873	C₂²	1	1	yes	characteristic
18	C₂×#10621883	C₂²	1	1	yes	characteristic
19	C₂×#10621883	C₂²	1	1	yes	characteristic
20	C₂×#10621884	C₂²	1	1	yes	characteristic
21	C₂×#10621882	C₂²	1	1	yes	characteristic
22	#13063323	C₂²	1	1	yes	characteristic
23	#13063321	C₂²	1	1	yes	characteristic
24	#13063321	C₂²	1	1	yes	characteristic
25	#13063318	—	2	1	no	—
26	#13063318	—	2	1	no	—
27	#13063312	C₂²	1	1	yes	characteristic
28	#13063302	—	2	1	no	—
29	#13063297	—	2	1	no	—
30	#13063297	—	2	1	no	—
31	#13063296	—	2	1	no	—
32	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
33	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
34	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
35	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
36	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
37	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
38	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
39	#13063281	—	2	1	no	—
40	#13063259	C₂²	1	1	yes	characteristic
41	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
42	Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
43	Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
44	#13063250	C₂²	1	1	yes	characteristic
45	#13063249	C₂²	1	1	yes	characteristic
46	#13063247	C₂²	1	1	yes	characteristic
47	#13063246	C₂²	1	1	yes	characteristic
48	#13063246	C₂²	1	1	yes	characteristic
49	#13063246	C₂²	1	1	yes	characteristic
50	#13063235	C₂²	1	1	yes	characteristic
51	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
52	C₂×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
54	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
55	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
56	#127×C₄₃	C₂²	1	1	yes	characteristic
57	#124×C₄₃	C₂²	1	1	yes	characteristic
58	#97×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	—	2	1	no	—
62	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₄₃	—	2	1	no	—
66	C₂×C₂²⋊D₄₃	—	2	1	no	—
67	C₂×C₂²⋊D₄₃	—	2	1	no	—
68	C₂×C₂²⋊D₄₃	—	2	1	no	—
69	C₂²×Dic₄₃	—	2	1	no	—
70	C₂²×Dic₄₃	—	2	1	no	—
71	C₂²×Dic₄₃	—	2	1	no	—
72	#10621900	—	4	4	no	—
73	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
74	C₂×C₄×D₄₃	—	2	1	no	—
75	C₂×Dic₈₆	D₄	1	1	yes	characteristic
76	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
77	SD₁₆×C₄₃	—	2	2	no	—
78	SD₁₆×C₄₃	—	4	1	no	—
79	D₈×C₄₃	—	2	2	no	—
80	D₈×C₄₃	—	4	1	no	—
81	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
82	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
83	C₂²⋊C₄×C₄₃	—	2	1	no	—
84	C₂²⋊C₄×C₄₃	—	2	1	no	—
85	C₄²×C₄₃	C₂³	1	1	yes	characteristic
86	C₂²⋊Dic₄₃	—	2	1	no	—
87	C₂²⋊Dic₄₃	—	2	1	no	—
88	C₂²⋊Dic₄₃	—	2	1	no	—
89	C₂²⋊Dic₄₃	—	2	1	no	—
90	C₂²⋊Dic₄₃	—	2	1	no	—
91	#10621884	—	4	1	no	—
92	#10621883	—	4	1	no	—
93	#10621883	—	4	1	no	—
94	#10621882	—	4	1	no	—
95	(C₂×D₄₃)⋊C₄	—	2	1	no	—
96	C₄⋊Dic₄₃	—	2	1	no	—
97	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
98	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
100	Dic₄₃⋊C₄	—	2	1	no	—
101	Dic₄₃⋊C₄	—	2	1	no	—
102	Dic₄₃⋊C₄	—	2	1	no	—
103	Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
104	Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
105	C₄×Dic₄₃	—	2	1	no	—
106	C₄×Dic₄₃	—	2	1	no	—
107	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
108	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
109	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
111	#10621873	—	2	2	no	—
112	C₂³×C₄₃	—	2	1	no	—
113	C₂³×C₄₃	—	2	1	no	—
114	C₂³×C₄₃	—	2	1	no	—
115	C₂²×D₄₃	—	2	1	no	—
116	Q₈×C₄₃	—	2	1	no	—
117	Q₈×C₄₃	—	2	1	no	—
118	D₄×C₄₃	—	2	1	no	—
119	D₄×C₄₃	—	2	1	no	—
120	D₄×C₄₃	—	2	1	no	—
121	D₄×C₄₃	—	2	1	no	—
122	D₄×C₄₃	—	2	1	no	—
123	D₄×C₄₃	—	2	1	no	—
124	D₄×C₄₃	—	4	2	no	—
125	D₄×C₄₃	—	8	1	no	—
126	C₂×C₄×C₄₃	—	2	1	no	—
127	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
130	C₂²⋊D₄₃	—	4	2	no	—
131	C₂²⋊D₄₃	—	4	2	no	—
132	C₂²⋊D₄₃	—	8	1	no	—
133	C₂²⋊D₄₃	—	8	1	no	—
134	C₂×Dic₄₃	—	2	1	no	—
135	C₂×Dic₄₃	—	2	1	no	—
136	C₂×Dic₄₃	—	2	1	no	—
137	C₂×Dic₄₃	—	4	2	no	—
138	C₂×Dic₄₃	—	4	2	no	—
139	C₂×Dic₄₃	—	4	2	no	—
140	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
141	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
144	D₁₇₂	—	2	1	no	—
145	D₁₇₂	—	2	1	no	—
146	C₄×D₄₃	—	4	2	no	—
147	Dic₈₆	—	2	2	no	—
148	Dic₈₆	—	2	1	no	—
149	Dic₈₆	—	2	1	no	—
150	C₈×C₄₃	—	2	1	no	—
151	C₈×C₄₃	#41	1	2	yes	complemented
152	C₄₃⋊C₈	—	2	1	no	—
153	C₄₃⋊C₈	—	2	1	no	—
154	C₂²×C₄₃	—	4	1	no	—
155	C₂²×C₄₃	—	4	1	no	—
156	C₂²×C₄₃	—	4	1	no	—
157	C₂²×C₄₃	—	4	1	no	—
158	C₂²×C₄₃	—	4	1	no	—
159	C₂²×C₄₃	—	4	1	no	—
160	C₂²×C₄₃	—	4	1	no	—
161	C₂²×C₄₃	—	4	1	no	—
162	C₂²×C₄₃	—	4	1	no	—
163	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×D₄₃	—	4	1	no	—
165	C₂×D₄₃	—	4	1	no	—
166	C₂×D₄₃	—	4	1	no	—
167	C₄×C₄₃	—	2	1	no	—
168	C₄×C₄₃	—	2	1	no	—
169	C₄×C₄₃	—	4	1	no	—
170	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
171	C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
172	Dic₄₃	—	2	1	no	—
173	Dic₄₃	—	2	1	no	—
174	Dic₄₃	—	2	1	no	—
175	Dic₄₃	—	4	1	no	—
176	Dic₄₃	—	4	1	no	—
177	Dic₄₃	—	4	1	no	—
178	Dic₄₃	AGL(1,ℤ/8)	1	2	yes	—
179	#3397	—	43	1	no	maximal, Sylow
180	C₂×C₄₃	—	8	1	no	—
181	C₂×C₄₃	—	8	1	no	—
182	C₂×C₄₃	—	8	1	no	—
183	C₂×C₄₃	#550	1	1	yes	characteristic
184	C₂×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×C₄₃	#577	1	1	yes	characteristic
186	D₄₃	—	8	1	no	—
187	#556	—	43	1	no	—
188	#550	—	43	1	no	—
189	#496	—	43	1	no	—
190	#496	D₄₃	1	1	yes	characteristic, complemented
191	#492	—	43	1	no	—
192	#463	—	43	1	no	—
193	#463	—	43	1	no	—
194	#461	—	43	1	no	—
195	#460	—	43	1	no	—
196	#460	—	43	1	no	—
197	#459	—	43	1	no	—
198	#446	—	43	1	no	—
199	#440	—	43	1	no	—
200	#440	—	43	1	no	—
201	C₄×D₈	—	43	1	no	—
202	C₄₃	#3397	1	1	yes	characteristic, complemented, Sylow
203	C₂×#41	—	86	1	no	—
204	C₂×SD₁₆	—	43	1	no	—
205	C₂×SD₁₆	—	43	1	no	—
206	C₂×SD₁₆	—	43	1	no	—
207	C₂×SD₁₆	—	43	1	no	—
208	C₂×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
209	C₂×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
210	C₂×D₈	—	43	1	no	—
211	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
212	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
213	C₄⋊Q₈	—	43	1	no	—
214	#127	—	43	1	no	—
215	#127	—	43	1	no	—
216	#127	C₂×D₄₃	1	1	yes	characteristic
217	#126	—	86	1	no	—
218	#126	—	86	1	no	—
219	#124	—	43	1	no	—
220	#124	C₂×D₄₃	1	1	yes	characteristic
221	C₂²⋊Q₈	—	86	1	no	—
222	#121	—	86	1	no	—
223	#121	—	86	1	no	—
224	#121	—	86	1	no	—
225	C₄×Q₈	—	43	1	no	—
226	C₄×Q₈	—	43	1	no	—
227	C₄×Q₈	—	43	1	no	—
228	C₄×D₄	—	43	1	no	—
229	C₄×D₄	—	43	1	no	—
230	C₄×D₄	—	43	1	no	—
231	C₄×D₄	—	43	1	no	—
232	#117	—	86	1	no	—
233	#107	—	43	1	no	—
234	C₄⋊C₈	—	43	1	no	—
235	C₄⋊C₈	—	43	1	no	—
236	C₄⋊C₈	—	43	1	no	—
237	#103	—	43	1	no	—
238	#103	—	43	1	no	—
239	#102	—	43	1	no	—
240	#102	—	43	1	no	—
241	#102	—	43	1	no	—
242	#102	—	43	1	no	—
243	#97	—	43	1	no	—
244	#97	C₂×D₄₃	1	1	yes	characteristic
245	C₄×C₈	—	43	1	no	—
246	#41	—	172	4	no	—
247	C₂×Q₈	—	43	1	no	—
248	C₂×Q₈	—	43	1	no	—
249	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
250	C₂×D₄	—	2	1	no	—
251	C₂×D₄	—	2	1	no	—
252	C₂×D₄	—	43	1	no	—
253	C₂×D₄	—	86	1	no	—
254	C₂×D₄	—	86	1	no	—
255	C₂×D₄	—	86	1	no	—
256	C₂×D₄	—	86	1	no	—
257	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
258	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
259	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
260	C₂²×C₄	—	86	1	no	—
261	C₂²×C₄	—	86	1	no	—
262	C₂²×C₄	—	86	1	no	—
263	C₂²×C₄	—	86	1	no	—
264	SD₁₆	—	2	2	no	—
265	SD₁₆	—	4	1	no	—
266	SD₁₆	—	86	2	no	—
267	SD₁₆	—	172	1	no	—
268	SD₁₆	—	172	1	no	—
269	SD₁₆	—	172	1	no	—
270	D₈	—	2	2	no	—
271	D₈	—	4	1	no	—
272	D₈	—	172	1	no	—
273	C₂×C₈	—	43	1	no	—
274	C₂×C₈	—	43	1	no	—
275	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
276	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
277	C₄⋊C₄	—	43	1	no	—
278	C₄⋊C₄	—	43	1	no	—
279	C₄⋊C₄	—	43	1	no	—
280	C₄⋊C₄	—	43	1	no	—
281	C₄⋊C₄	—	43	1	no	—
282	C₄⋊C₄	—	86	1	no	—
283	C₄⋊C₄	—	86	1	no	—
284	C₄⋊C₄	—	86	1	no	—
285	C₄⋊C₄	—	86	1	no	—
286	C₂²⋊C₄	—	2	1	no	—
287	C₂²⋊C₄	—	2	1	no	—
288	C₂²⋊C₄	—	86	1	no	—
289	C₂²⋊C₄	—	86	1	no	—
290	C₂²⋊C₄	—	86	1	no	—
291	C₂²⋊C₄	—	86	1	no	—
292	C₂²⋊C₄	—	86	1	no	—
293	C₂²⋊C₄	—	86	1	no	—
294	C₄²	—	43	1	no	—
295	C₄²	—	43	1	no	—
296	C₄²	—	86	1	no	—
297	C₄²	—	86	1	no	—
298	C₄²	C₂²×D₄₃	1	1	yes	characteristic
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	86	1	no	—
303	Q₈	—	2	1	no	—
304	Q₈	—	2	1	no	—
305	Q₈	—	86	2	no	—
306	Q₈	—	86	1	no	—
307	Q₈	—	86	1	no	—
308	D₄	—	2	1	no	—
309	D₄	—	2	1	no	—
310	D₄	—	2	1	no	—
311	D₄	—	2	1	no	—
312	D₄	—	2	1	no	—
313	D₄	—	2	1	no	—
314	D₄	—	4	2	no	—
315	D₄	—	8	1	no	—
316	D₄	—	86	1	no	—
317	D₄	—	86	1	no	—
318	D₄	—	344	1	no	—
319	D₄	—	344	1	no	—
320	D₄	—	172	2	no	—
321	D₄	—	172	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	43	1	no	—
324	C₂×C₄	—	43	1	no	—
325	C₂×C₄	—	43	1	no	—
326	C₂×C₄	—	43	1	no	—
327	C₂×C₄	—	86	1	no	—
328	C₂×C₄	—	86	1	no	—
329	C₂×C₄	—	86	1	no	—
330	C₂×C₄	—	172	2	no	—
331	C₂×C₄	—	172	2	no	—
332	C₂×C₄	—	172	2	no	—
333	C₂×C₄	—	172	2	no	—
334	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
335	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
336	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
337	C₈	—	2	1	no	—
338	C₈	—	86	1	no	—
339	C₈	—	86	1	no	—
340	C₈	#10621900	1	2	yes	complemented
341	C₂²	—	4	1	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	4	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	4	1	no	—
350	C₂²	—	172	1	no	—
351	C₂²	—	172	1	no	—
352	C₂²	—	172	1	no	—
353	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	1	no	—
357	C₄	—	43	2	no	—
358	C₄	—	86	1	no	—
359	C₄	—	86	1	no	—
360	C₄	—	86	1	no	—
361	C₄	—	172	1	no	—
362	C₄	—	172	1	no	—
363	C₄	—	172	1	no	—
364	C₄	C₂×#10621900	1	1	yes	characteristic
365	C₄	#13063370	1	1	yes	characteristic
366	C₂	—	8	1	no	—
367	C₂	—	8	1	no	—
368	C₂	—	8	1	no	—
369	C₂	—	344	1	no	—
370	C₂	#14583569	1	1	yes	characteristic
371	C₂	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
372	C₂	#14583709	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#496	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#496	D₄₃
hypocenter	C₄₃	#3397
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #496

Complements

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

N	H ≅ G/N	type
1. #14583618	C₂	semidirect
2. #14583569	C₂	semidirect
3. #14583287	C₂	semidirect
4. #14583270	C₂	semidirect
5. #14583112	C₂	semidirect
6. #14583111	C₂	semidirect
7. #14583102	C₂	semidirect
8. #14583097	C₂	semidirect
9. #14583096	C₂	semidirect
10. #14583092	C₂	semidirect
11. #14583027	C₂	semidirect
12. #14583001	C₂	semidirect
13. #14583000	C₂	semidirect
14. D₈×Dic₄₃	C₂	semidirect
15. C₄₃×#496	C₂	semidirect
151. C₈×C₄₃	#41	semidirect
190. #496	D₄₃	semidirect
202. C₄₃	#3397	semidirect
340. C₈	#10621900	semidirect