Subgroups — #19146896

Order 5504.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583550	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583548	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583248	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583234	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583233	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583177	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583148	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583145	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583103	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583045	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583044	C₂	1	1	yes	maximal, characteristic, complemented
12	#14582979	C₂	1	1	yes	maximal, characteristic, complemented
13	#14582975	C₂	1	1	yes	maximal, characteristic, complemented
14	#14582897	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10621898	—	2	1	no	—
17	C₂×#10621900	C₂²	1	1	yes	characteristic
18	C₂×#10621873	C₂²	1	1	yes	characteristic
19	C₂×#10621884	C₂²	1	1	yes	characteristic
20	C₂×#10621882	C₂²	1	1	yes	characteristic
21	C₂×#10621872	C₂²	1	1	yes	characteristic
22	#13063324	C₂²	1	1	yes	characteristic
23	#13063323	C₂²	1	1	yes	characteristic
24	#13063310	—	2	1	no	—
25	#13063308	—	2	1	no	—
26	#13063308	—	2	1	no	—
27	#13063306	—	2	1	no	—
28	#13063304	C₂²	1	1	yes	characteristic
29	#13063303	—	2	1	no	—
30	#13063301	C₂²	1	1	yes	characteristic
31	#13063300	C₂²	1	1	yes	characteristic
32	#13063299	C₂²	1	1	yes	characteristic
33	#13063297	—	2	1	no	—
34	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
35	#13063287	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
37	C₂×Dic₄₃⋊C₄	—	2	1	no	—
38	C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic
39	#13063259	C₂²	1	1	yes	characteristic
40	#13063258	C₂²	1	1	yes	characteristic
41	#13063258	C₂²	1	1	yes	characteristic
42	Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
43	#13063250	C₂²	1	1	yes	characteristic
44	#13063249	C₂²	1	1	yes	characteristic
45	#13063248	C₂²	1	1	yes	characteristic
46	#13063248	C₂²	1	1	yes	characteristic
47	#13063247	C₂²	1	1	yes	characteristic
48	#13063246	C₂²	1	1	yes	characteristic
49	C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
50	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
51	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
52	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
55	#103×C₄₃	C₂²	1	1	yes	characteristic
56	#103×C₄₃	C₂²	1	1	yes	characteristic
57	#102×C₄₃	C₂²	1	1	yes	characteristic
58	#102×C₄₃	C₂²	1	1	yes	characteristic
59	#41×C₄₃	—	2	2	no	—
60	#41×C₄₃	—	4	1	no	—
61	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₄₃	—	2	1	no	—
63	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₄₃	—	2	1	no	—
65	C₂²×C₄×C₄₃	—	2	1	no	—
66	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊D₄₃	—	2	1	no	—
68	C₂×C₂²⋊D₄₃	—	2	1	no	—
69	C₂×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
70	C₂²×Dic₄₃	—	2	1	no	—
71	C₂²×Dic₄₃	—	2	1	no	—
72	#10621900	—	2	2	no	—
73	#10621900	—	4	1	no	—
74	#10621898	—	4	4	no	—
75	C₂×D₁₇₂	—	2	1	no	—
76	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₄₃	—	2	1	no	—
78	C₂×C₄×D₄₃	—	2	1	no	—
79	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
80	C₂×Dic₈₆	—	2	1	no	—
81	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
82	M₁₆×C₄₃	—	4	1	no	—
83	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
85	C₄⋊C₄×C₄₃	—	2	1	no	—
86	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²⋊Dic₄₃	—	2	1	no	—
89	C₂²⋊Dic₄₃	—	2	1	no	—
90	C₂²⋊Dic₄₃	D₄	1	1	yes	characteristic
91	#10621884	—	4	1	no	—
92	#10621882	—	2	2	no	—
93	(C₂×D₄₃)⋊C₄	—	2	1	no	—
94	(C₂×D₄₃)⋊C₄	—	2	1	no	—
95	(C₂×D₄₃)⋊C₄	—	2	1	no	—
96	(C₂×D₄₃)⋊C₄	—	2	1	no	—
97	(C₂×D₄₃)⋊C₄	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	—	2	1	no	—
104	Dic₄₃⋊C₄	—	2	1	no	—
105	Dic₄₃⋊C₄	—	2	1	no	—
106	Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
107	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
108	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
109	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
110	#10621873	—	4	1	no	—
111	#10621872	—	4	1	no	—
112	C₂³×C₄₃	—	2	1	no	—
113	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×D₄₃	—	2	1	no	—
115	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
116	Q₈×C₄₃	—	2	1	no	—
117	Q₈×C₄₃	—	2	1	no	—
118	D₄×C₄₃	—	2	1	no	—
119	D₄×C₄₃	—	4	2	no	—
120	D₄×C₄₃	#41	1	2	yes	complemented
121	C₂×C₄×C₄₃	—	2	1	no	—
122	C₂×C₄×C₄₃	—	2	1	no	—
123	C₂×C₄×C₄₃	—	2	1	no	—
124	C₂×C₄×C₄₃	—	2	1	no	—
125	C₂×C₄×C₄₃	—	2	1	no	—
126	C₂×C₄×C₄₃	—	4	2	no	—
127	C₂×C₄×C₄₃	—	4	2	no	—
128	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
130	C₂²⋊D₄₃	—	2	2	no	—
131	C₂²⋊D₄₃	—	4	2	no	—
132	C₂²⋊D₄₃	—	4	2	no	—
133	C₂×Dic₄₃	—	2	1	no	—
134	C₂×Dic₄₃	—	2	1	no	—
135	C₂×Dic₄₃	—	2	1	no	—
136	C₂×Dic₄₃	—	4	2	no	—
137	C₂×Dic₄₃	—	4	2	no	—
138	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
141	D₁₇₂	—	2	1	no	—
142	D₁₇₂	—	2	1	no	—
143	D₁₇₂	—	4	2	no	—
144	C₄×D₄₃	—	2	1	no	—
145	C₄×D₄₃	—	2	1	no	—
146	C₄×D₄₃	—	4	2	no	—
147	C₄×D₄₃	—	4	2	no	—
148	Dic₈₆	—	2	1	no	—
149	Dic₈₆	—	2	1	no	—
150	Dic₈₆	—	4	2	no	—
151	C₈×C₄₃	—	2	1	no	—
152	C₈×C₄₃	—	2	1	no	—
153	C₄₃⋊C₈	—	2	1	no	—
154	C₄₃⋊C₈	—	2	1	no	—
155	C₂²×C₄₃	—	2	2	no	—
156	C₂²×C₄₃	—	2	1	no	—
157	C₂²×C₄₃	—	2	1	no	—
158	C₂²×C₄₃	—	2	1	no	—
159	C₂²×C₄₃	—	4	1	no	—
160	C₂²×C₄₃	—	4	1	no	—
161	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×D₄₃	—	2	1	no	—
163	C₂×D₄₃	—	2	1	no	—
164	C₂×D₄₃	—	2	1	no	—
165	C₂×D₄₃	—	4	1	no	—
166	C₂×D₄₃	—	4	1	no	—
167	C₂×D₄₃	—	4	1	no	—
168	C₄×C₄₃	—	2	1	no	—
169	C₄×C₄₃	—	4	1	no	—
170	C₄×C₄₃	—	4	1	no	—
171	C₄×C₄₃	—	4	1	no	—
172	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
173	C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
174	Dic₄₃	—	2	1	no	—
175	Dic₄₃	—	2	1	no	—
176	Dic₄₃	—	4	1	no	—
177	Dic₄₃	—	4	1	no	—
178	Dic₄₃	—	4	1	no	—
179	Dic₄₃	AGL(1,ℤ/8)	1	2	yes	—
180	#3330	—	43	1	no	maximal, Sylow
181	C₂×C₄₃	—	4	1	no	—
182	C₂×C₄₃	—	4	2	no	—
183	C₂×C₄₃	#546	1	1	yes	characteristic
184	C₂×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×C₄₃	#578	1	1	yes	characteristic
186	D₄₃	—	4	1	no	—
187	D₄₃	—	8	1	no	—
188	#547	—	43	1	no	—
189	#547	—	43	1	no	—
190	#487	—	43	1	no	—
191	#484	—	43	1	no	—
192	#484	—	43	1	no	—
193	#474	—	43	1	no	—
194	#468	—	43	1	no	—
195	#468	—	43	1	no	—
196	#461	—	43	1	no	—
197	#449	—	43	1	no	—
198	#449	—	43	1	no	—
199	C₄×D₈	—	43	1	no	—
200	#436	—	43	1	no	—
201	#417	—	43	1	no	—
202	#417	D₄₃	1	1	yes	characteristic, complemented
203	C₄₃	#3330	1	1	yes	characteristic, complemented, Sylow
204	C₂×#41	—	43	1	no	—
205	C₂×#41	—	86	1	no	—
206	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
207	C₂×SD₁₆	—	43	1	no	—
208	C₂×SD₁₆	—	43	1	no	—
209	C₂×D₈	—	43	1	no	—
210	C₂×M₁₆	—	43	1	no	—
211	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
212	C₄⋊Q₈	—	43	1	no	—
213	C₄⋊Q₈	—	43	1	no	—
214	#123	—	86	1	no	—
215	#123	—	86	1	no	—
216	#123	—	86	1	no	—
217	#123	—	86	1	no	—
218	C₂²⋊Q₈	—	43	1	no	—
219	C₂²⋊Q₈	—	43	1	no	—
220	C₂²⋊Q₈	—	86	1	no	—
221	#121	—	43	1	no	—
222	#121	—	43	1	no	—
223	#121	—	86	1	no	—
224	C₄×D₄	—	43	1	no	—
225	C₄×D₄	—	43	1	no	—
226	C₄×D₄	—	43	1	no	—
227	C₂×C₄⋊C₄	—	43	1	no	—
228	C₂×C₄⋊C₄	—	86	1	no	—
229	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
230	#107	—	43	1	no	—
231	#107	—	43	1	no	—
232	#107	—	43	1	no	—
233	C₄⋊C₈	—	43	1	no	—
234	#103	—	43	1	no	—
235	#103	—	43	1	no	—
236	#103	—	43	1	no	—
237	#103	—	43	1	no	—
238	#103	C₂×D₄₃	1	1	yes	characteristic
239	#103	C₂×D₄₃	1	1	yes	characteristic
240	#102	—	43	1	no	—
241	#102	—	43	1	no	—
242	#102	C₂×D₄₃	1	1	yes	characteristic
243	#102	C₂×D₄₃	1	1	yes	characteristic
244	C₂²⋊C₈	—	43	1	no	—
245	C₂²⋊C₈	—	43	1	no	—
246	C₄×C₈	—	43	1	no	—
247	#41	—	2	2	no	—
248	#41	—	4	1	no	—
249	#41	—	86	2	no	—
250	#41	—	172	4	no	—
251	#41	—	172	1	no	—
252	C₂×Q₈	—	43	1	no	—
253	C₂×Q₈	—	86	1	no	—
254	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
255	C₂×D₄	—	2	1	no	—
256	C₂×D₄	—	43	1	no	—
257	C₂×D₄	—	43	1	no	—
258	C₂×D₄	—	86	1	no	—
259	C₂×D₄	—	86	1	no	—
260	C₂×D₄	—	86	1	no	—
261	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	43	1	no	—
265	C₂²×C₄	—	86	1	no	—
266	C₂²×C₄	—	86	1	no	—
267	C₂²×C₄	—	86	1	no	—
268	C₂²×C₄	—	86	1	no	—
269	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
270	SD₁₆	—	172	1	no	—
271	SD₁₆	—	172	1	no	—
272	D₈	—	86	2	no	—
273	M₁₆	—	4	1	no	—
274	M₁₆	—	172	1	no	—
275	C₂×C₈	—	43	1	no	—
276	C₂×C₈	—	43	1	no	—
277	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
278	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
279	C₄⋊C₄	—	2	1	no	—
280	C₄⋊C₄	—	43	1	no	—
281	C₄⋊C₄	—	43	1	no	—
282	C₄⋊C₄	—	43	1	no	—
283	C₄⋊C₄	—	86	1	no	—
284	C₄⋊C₄	—	86	1	no	—
285	C₄⋊C₄	—	86	1	no	—
286	C₄⋊C₄	—	86	1	no	—
287	C₄⋊C₄	—	86	1	no	—
288	C₄⋊C₄	—	86	1	no	—
289	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
290	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
291	C₂²⋊C₄	—	43	1	no	—
292	C₂²⋊C₄	—	43	1	no	—
293	C₂²⋊C₄	—	86	1	no	—
294	C₂²⋊C₄	—	86	1	no	—
295	C₂²⋊C₄	—	86	1	no	—
296	C₂²⋊C₄	—	86	1	no	—
297	C₂²⋊C₄	—	86	1	no	—
298	C₂²⋊C₄	—	86	1	no	—
299	C₄²	—	43	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	43	1	no	—
302	C₂³	—	86	1	no	—
303	C₂³	D₄×D₄₃	1	1	yes	characteristic
304	Q₈	—	2	1	no	—
305	Q₈	—	2	1	no	—
306	Q₈	—	86	1	no	—
307	Q₈	—	86	1	no	—
308	Q₈	—	172	2	no	—
309	D₄	—	2	1	no	—
310	D₄	—	4	2	no	—
311	D₄	—	86	2	no	—
312	D₄	—	86	1	no	—
313	D₄	—	86	1	no	—
314	D₄	—	172	2	no	—
315	D₄	—	172	2	no	—
316	D₄	—	172	2	no	—
317	D₄	#10621898	1	2	yes	complemented
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	43	1	no	—
326	C₂×C₄	—	43	1	no	—
327	C₂×C₄	—	43	1	no	—
328	C₂×C₄	—	86	1	no	—
329	C₂×C₄	—	86	1	no	—
330	C₂×C₄	—	86	1	no	—
331	C₂×C₄	—	86	1	no	—
332	C₂×C₄	—	86	1	no	—
333	C₂×C₄	—	172	2	no	—
334	C₂×C₄	—	172	2	no	—
335	C₂×C₄	—	172	2	no	—
336	C₂×C₄	—	172	2	no	—
337	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
338	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
339	C₈	—	2	1	no	—
340	C₈	—	2	1	no	—
341	C₈	—	86	1	no	—
342	C₈	—	86	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	86	1	no	—
350	C₂²	—	86	1	no	—
351	C₂²	—	86	1	no	—
352	C₂²	—	172	1	no	—
353	C₂²	—	172	1	no	—
354	C₂²	—	172	1	no	—
355	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	43	2	no	—
361	C₄	—	86	1	no	—
362	C₄	—	86	1	no	—
363	C₄	—	172	1	no	—
364	C₄	—	172	1	no	—
365	C₄	—	172	1	no	—
366	C₄	C₂×#10621898	1	1	yes	characteristic
367	C₄	#13063370	1	1	yes	characteristic
368	C₂	—	4	1	no	—
369	C₂	—	4	2	no	—
370	C₂	—	344	1	no	—
371	C₂	—	172	1	no	—
372	C₂	#14583539	1	1	yes	characteristic
373	C₂	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
374	C₂	#14583715	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#417	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#417	D₄₃
hypocenter	C₄₃	#3330
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #417

Complements

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

N	H ≅ G/N	type
1. #14583550	C₂	semidirect
2. #14583548	C₂	semidirect
3. #14583248	C₂	semidirect
4. #14583234	C₂	semidirect
5. #14583233	C₂	semidirect
6. #14583177	C₂	semidirect
7. #14583148	C₂	semidirect
8. #14583145	C₂	semidirect
9. #14583103	C₂	semidirect
10. #14583045	C₂	semidirect
11. #14583044	C₂	semidirect
12. #14582979	C₂	semidirect
13. #14582975	C₂	semidirect
14. #14582897	C₂	semidirect
15. C₄₃×#417	C₂	semidirect
120. D₄×C₄₃	#41	semidirect
202. #417	D₄₃	semidirect
203. C₄₃	#3330	semidirect
317. D₄	#10621898	semidirect