Finite Group Databasebeta

← #19146718

Subgroups — #19146718

Order 5504.

392 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#14583587C211yesmaximal, characteristic, complemented
2#14583571C211yesmaximal, characteristic
3#14583265C211yesmaximal, characteristic, complemented
4#14583226C211yesmaximal, characteristic, complemented
5#14583219C211yesmaximal, characteristic, complemented
6#14583146C211yesmaximal, characteristic, complemented
7#14583129C211yesmaximal, characteristic, complemented
8#14583100C211yesmaximal, characteristic, complemented
9#14583064C211yesmaximal, characteristic, complemented
10#14583064C211yesmaximal, characteristic, complemented
11#14583004C211yesmaximal, characteristic, complemented
12#14582969C211yesmaximal, characteristic, complemented
13#14582899C211yesmaximal, characteristic, complemented
14#14582894C211yesmaximal, characteristic, complemented
15C43×#479C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621902C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×#10621872C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic
23#13063322—21no—
24#13063322C2211yescharacteristic
25#13063320—21no—
26#13063316—21no—
27#13063310—21no—
28#13063305C2211yescharacteristic
29#13063305C2211yescharacteristic
30#13063300—21no—
31#13063300—21no—
32#13063300C2211yescharacteristic
33#13063300C2211yescharacteristic
34C4×Dic86C2211yescharacteristic
35C4×D172—21no—
36C4×D172C2211yescharacteristic
37#13063283—21no—
38#13063283C2211yescharacteristic
39C4⋊C4×D43C2211yescharacteristic
40#13063256C2211yescharacteristic
41#13063249C2211yescharacteristic
42#13063248C2211yescharacteristic
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic
52#125×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60#10621902—22no—
61#10621902—22no—
62#10621902—41no—
63#10621902—41no—
64C2×D172—21no—
65C2×D172—21no—
66C2×D172—21no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172—21no—
70C2×D172D411yescharacteristic
71C2×D172C2311yescharacteristic
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43C2311yescharacteristic
77C2×C4×D43C2311yescharacteristic
78C2×Dic86C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C42×C43—21no—
88C42×C43C2311yescharacteristic
89#10621885—22no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4D411yescharacteristic
96(C2×D43)⋊C4D411yescharacteristic
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43D411yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107#10621873—41no—
108#10621873—41no—
109#10621872—41no—
110C8×D43—41no—
111C22×D43—21no—
112C22×D43—21no—
113C22×D43C2×D411yescharacteristic
114C22×D43C2×D411yescharacteristic
115Q8×C43—21no—
116Q8×C43#4112yes—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2411yescharacteristic
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128D172—21no—
129D172—21no—
130D172—21no—
131D172—21no—
132D172—41no—
133D172—42no—
134D172—42no—
135D172—42no—
136D172—81no—
137D172—81no—
138D172—81no—
139C4×D43—21no—
140C4×D43—21no—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—42no—
144C4×D43—42no—
145C4×D43—42no—
146Dic86—21no—
147Dic86—21no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43C22×D411yescharacteristic
153C2×D43—21no—
154C2×D43—21no—
155C2×D43—21no—
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C4×C43—22no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43H(5,𝔽2)11yescharacteristic
173Dic43—21no—
174Dic43—21no—
175Dic43—41no—
176Dic43—41no—
177#3317—431nomaximal, Sylow
178C2×C43#54611yescharacteristic
179C2×C43#57511yescharacteristic
180C2×C43#57711yescharacteristic
181D43—41no—
182D43—41no—
183D43—81no—
184D43—81no—
185#552—431no—
186#550—431no—
187#490—431no—
188#482—431no—
189#481—431no—
190#479D4311yescharacteristic, complemented
191#468—431no—
192#465—431no—
193#460—431no—
194#452—431no—
195#452—431no—
196#441—431no—
197#435—431no—
198#417—431no—
199#416—431no—
200C43#331711yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C2×#41—431no—
203C2×Q16—431no—
204C2×SD16—431no—
205C2×SD16—431no—
206C2×M16—431no—
207C22×C8—431no—
208#127—431no—
209#127—861no—
210#126—861no—
211#125—861no—
212#125C2×D4311yescharacteristic
213#123—861no—
214C22⋊Q8—431no—
215C22⋊Q8—431no—
216#121—431no—
217#121—431no—
218#121—861no—
219#121—861no—
220C4×Q8—431no—
221C4×Q8C2×D4311yescharacteristic
222C4×D4—431no—
223C4×D4—861no—
224#117—431no—
225#117—861no—
226C2×C4⋊C4—431no—
227#107C2×D4311yescharacteristic
228#106—431no—
229#106C2×D4311yescharacteristic
230C4⋊C8C2×D4311yescharacteristic
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#102—431no—
240#102—431no—
241C22⋊C8—431no—
242C22⋊C8—431no—
243#97—431no—
244#41—862no—
245#41—862no—
246#41—1721no—
247#41—1721no—
248C2×Q8—431no—
249C2×Q8C22×D4311yescharacteristic
250C2×D4—431no—
251C2×D4—431no—
252C2×D4—431no—
253C2×D4—861no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—861no—
259C22×C4—431no—
260C22×C4—431no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264Q16—862no—
265SD16—1721no—
266SD16—1721no—
267M16—1721no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8—1721no—
271C2×C8C22×D4311yescharacteristic
272C2×C8C22×D4311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—431no—
277C4⋊C4—431no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4C22×D4311yescharacteristic
283C4⋊C4C22×D4311yescharacteristic
284C4⋊C4C22×D4311yescharacteristic
285C22⋊C4—431no—
286C22⋊C4—431no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C42—21no—
293C42—861no—
294C42—861no—
295C42C22×D4311yescharacteristic
296C23—431no—
297C23—431no—
298C23—861no—
299C23—861no—
300Q8—21no—
301Q8—861no—
302Q8—861no—
303Q8#1062190212yes—
304D4—861no—
305D4—861no—
306D4—861no—
307D4—861no—
308D4—3441no—
309D4—3441no—
310D4—3441no—
311D4—1721no—
312D4—1722no—
313D4—1722no—
314D4—1722no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—431no—
320C2×C4—431no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—1722no—
328C2×C4—1722no—
329C2×C4—1722no—
330C2×C4D4×D4311yescharacteristic
331C2×C4D4×D4311yescharacteristic
332C2×C4C23×D4311yescharacteristic
333C8—21no—
334C8—21no—
335C8—861no—
336C8—861no—
337C22—861no—
338C22—861no—
339C22—861no—
340C22—861no—
341C22—861no—
342C22—861no—
343C22—1721no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22C2×D4×D4311yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—861no—
357C4—861no—
358C4—1721no—
359C4—1721no—
360C4C2×#1062190211yescharacteristic
361C4#1306337111yescharacteristic
362C2—3441no—
363C2—3441no—
364C2—1721no—
365C2—1721no—
366C2#1458354011yescharacteristic
367C2#1458369811yescharacteristic
368C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#479C2
socleC22×C43C22×D4
hypercenter#479D43
hypocenterC43#3317
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #14583587C2semidirect
3. #14583265C2semidirect
4. #14583226C2semidirect
5. #14583219C2semidirect
6. #14583146C2semidirect
7. #14583129C2semidirect
8. #14583100C2semidirect
9. #14583064C2semidirect
10. #14583064C2semidirect
11. #14583004C2semidirect
12. #14582969C2semidirect
13. #14582899C2semidirect
14. #14582894C2semidirect
15. C43×#479C2semidirect
190. #479D43semidirect
200. C43#3317semidirect