Finite Group Databasebeta

← #19146530

Subgroups — #19146530

Order 5504.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583617C211yesmaximal, characteristic, complemented
2#14583568C211yesmaximal, characteristic
3#14583244C211yesmaximal, characteristic, complemented
4#14583223C211yesmaximal, characteristic, complemented
5#14583222C211yesmaximal, characteristic, complemented
6#14583182C211yesmaximal, characteristic, complemented
7#14583128C211yesmaximal, characteristic, complemented
8#14583127C211yesmaximal, characteristic, complemented
9#14583098C211yesmaximal, characteristic, complemented
10#14583064C211yesmaximal, characteristic, complemented
11#14583061C211yesmaximal, characteristic, complemented
12#14582991C211yesmaximal, characteristic, complemented
13C8×C22⋊D43C211yesmaximal, characteristic, complemented
14#14582894C211yesmaximal, characteristic, complemented
15C43×#416C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063321—21no—
23#13063321C2211yescharacteristic
24#13063319—21no—
25#13063318—21no—
26#13063311—21no—
27#13063305C2211yescharacteristic
28#13063304C2211yescharacteristic
29#13063299—21no—
30#13063299C2211yescharacteristic
31#13063296—21no—
32#13063296C2211yescharacteristic
33Q8×Dic43C2211yescharacteristic
34C4×Dic86—21no—
35#13063290C2211yescharacteristic
36C4×C22⋊D43—21no—
37C4×C22⋊D43C2211yescharacteristic
38#13063283C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063257C2211yescharacteristic
41#13063256C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic
54#117×C43C2211yescharacteristic
55#103×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—41no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43D411yescharacteristic
71#10621902—22no—
72#10621902—41no—
73C2×D172—21no—
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43C2311yescharacteristic
77C2×Dic86—21no—
78C2×Dic86C2311yescharacteristic
79C2×C8×C43—41no—
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C22⋊C4×C43—21no—
85C42×C43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43D411yescharacteristic
89#10621885—22no—
90#10621883—41no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4D411yescharacteristic
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109#10621873—41no—
110C8×D43—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43C2×D411yescharacteristic
115Q8×C43—21no—
116Q8×C43#4112yes—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—42no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—42no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—22no—
129C22⋊D43—42no—
130C22⋊D43—81no—
131C22⋊D43—81no—
132C22⋊D43—81no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139D172—21no—
140D172—21no—
141D172—42no—
142C4×D43—21no—
143C4×D43—21no—
144C4×D43—42no—
145Dic86—21no—
146Dic86—21no—
147Dic86—42no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43C22×D411yescharacteristic
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C4×C43—22no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43C2×#4111yescharacteristic
170C4×C43H(5,𝔽2)11yescharacteristic
171Dic43—21no—
172Dic43—21no—
173Dic43—41no—
174Dic43—41no—
175Dic43—41no—
176Dic43#13512yes—
177#3304—431nomaximal, Sylow
178C2×C43—41no—
179C2×C43—81no—
180C2×C43#54611yescharacteristic
181C2×C43C2×#13511yescharacteristic
182C2×C43#57711yescharacteristic
183D43—41no—
184D43—81no—
185#556—431no—
186#550—431no—
187#486—431no—
188#482—431no—
189#482—431no—
190#475—431no—
191#465—431no—
192#465—431no—
193#460—431no—
194#452—431no—
195#452—431no—
196C4×Q16—431no—
197C8×D4—431no—
198#416—431no—
199#416D4311yescharacteristic, complemented
200C43#330411yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C2×#41C2×D4311yescharacteristic
203C2×Q16—431no—
204C2×SD16—431no—
205C2×SD16—431no—
206C22×C8—431no—
207C22×C8C2×D4311yescharacteristic
208C4⋊Q8—431no—
209#127—431no—
210#127—861no—
211#126—861no—
212#126—861no—
213#124—861no—
214C22⋊Q8—431no—
215C22⋊Q8—431no—
216#121—431no—
217#121—431no—
218#121—861no—
219#121—861no—
220C4×Q8—431no—
221C4×Q8—431no—
222C4×Q8—861no—
223C4×D4—431no—
224C4×D4—861no—
225#117—431no—
226#117C2×D4311yescharacteristic
227#107—431no—
228#106—431no—
229#106—431no—
230C4⋊C8—431no—
231#103—431no—
232#103—431no—
233#103C2×D4311yescharacteristic
234#103C2×D4311yescharacteristic
235#102—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102C2×D4311yescharacteristic
240#102C2×D4311yescharacteristic
241C22⋊C8—431no—
242C22⋊C8—431no—
243C4×C8—431no—
244#41—22no—
245#41—41no—
246#41—862no—
247#41—1721no—
248C2×Q8—431no—
249C2×Q8—861no—
250C2×Q8C22×D4311yescharacteristic
251C2×D4—21no—
252C2×D4—431no—
253C2×D4—431no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4C22×D4311yescharacteristic
260C22×C4—21no—
261C22×C4—431no—
262C22×C4—861no—
263C22×C4C22×D4311yescharacteristic
264Q16—862no—
265SD16—1721no—
266SD16—1721no—
267C2×C8—41no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8—1721no—
271C2×C8C22×D4311yescharacteristic
272C2×C8C22×D4311yescharacteristic
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4C22×D4311yescharacteristic
282C4⋊C4C22×D4311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—431no—
285C22⋊C4—431no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C42—21no—
292C42—431no—
293C42—861no—
294C42—861no—
295C42—861no—
296C23—21no—
297C23—431no—
298C23—861no—
299C23D4×D4311yescharacteristic
300Q8—21no—
301Q8—861no—
302Q8—861no—
303Q8—1722no—
304Q8#1062189812yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—862no—
309D4—861no—
310D4—861no—
311D4—3441no—
312D4—3441no—
313D4—3441no—
314D4—1722no—
315D4—1722no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—431no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—1722no—
331C2×C4D4×D4311yescharacteristic
332C2×C4C23×D4311yescharacteristic
333C8—21no—
334C8—21no—
335C8—861no—
336C8—861no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—861no—
344C22—861no—
345C22—861no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22C2×D4×D4311yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—432no—
355C4—861no—
356C4—861no—
357C4—1721no—
358C4—1721no—
359C4—1721no—
360C4C2×#1062189811yescharacteristic
361C4#1306337011yescharacteristic
362C2—41no—
363C2—81no—
364C2—3441no—
365C2—1721no—
366C2#1458353911yescharacteristic
367C2#135×D4311yescharacteristic
368C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#416C2
socleC22×C43C22×D4
hypercenter#416D43
hypocenterC43#3304
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #14583617C2semidirect
3. #14583244C2semidirect
4. #14583223C2semidirect
5. #14583222C2semidirect
6. #14583182C2semidirect
7. #14583128C2semidirect
8. #14583127C2semidirect
9. #14583098C2semidirect
10. #14583064C2semidirect
11. #14583061C2semidirect
12. #14582991C2semidirect
13. C8×C22⋊D43C2semidirect
14. #14582894C2semidirect
15. C43×#416C2semidirect
199. #416D43semidirect
200. C43#3304semidirect