Finite Group Databasebeta

← #19144841

Subgroups — #19144841

Order 5504.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583509C211yesmaximal, characteristic, complemented
2#14583374C211yesmaximal, characteristic
3#14583241C211yesmaximal, characteristic, complemented
4#14583237C211yesmaximal, characteristic, complemented
5#14583201C211yesmaximal, characteristic, complemented
6#14583197C211yesmaximal, characteristic, complemented
7#14583102C211yesmaximal, characteristic, complemented
8#14583102C211yesmaximal, characteristic, complemented
9#14583050C211yesmaximal, characteristic
10#14583000C211yesmaximal, characteristic, complemented
11#14582996C211yesmaximal, characteristic, complemented
12#14582990C211yesmaximal, characteristic, complemented
13SD16×Dic43C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#450C211yesmaximal, characteristic
16C2×#10621883C2211yescharacteristic
17C2×#10621883C2211yescharacteristic
18#13063323C2211yescharacteristic, complemented
19#13063318—21no—
20#13063318—21no—
21#13063316—21no—
22#13063316C2211yescharacteristic, complemented
23#13063315—21no—
24#13063304C2211yescharacteristic
25Q8×Dic43C2211yescharacteristic, complemented
26#13063290C2211yescharacteristic, complemented
27D4×Dic43—21no—
28D4×Dic43—21no—
29D4×Dic43C2211yescharacteristic
30D4×Dic43C2211yescharacteristic
31D4×Dic43C2211yescharacteristic
32D4×Dic43C2211yescharacteristic
33#13063284C2211yescharacteristic
34#13063284C2211yescharacteristic
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37#13063259C2211yescharacteristic, complemented
38#13063258C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063249C2211yescharacteristic, complemented
46#13063249C2211yescharacteristic, complemented
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C24×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—22no—
62C2×D4×C43—22no—
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×Dic86C2311yescharacteristic
72SD16×C43—22no—
73SD16×C43—22no—
74C2×C8×C43C2311yescharacteristic
75C2×C8×C43C2311yescharacteristic
76C4⋊C4×C43—21no—
77C4⋊C4×C43C2311yescharacteristic
78C22⋊C4×C43—21no—
79C22⋊Dic43—21no—
80C22⋊Dic43—21no—
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43D411yescharacteristic
86C22⋊Dic43D411yescharacteristic
87#10621883—22no—
88#10621883—22no—
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43D411yescharacteristic
92C4⋊Dic43D411yescharacteristic
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—24no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—81no—
112C23×C43—81no—
113C23×C43C2×D411yescharacteristic
114Q8×C43—21no—
115Q8×C43—21no—
116D4×C43—24no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43#4112yes—
120D4×C43#4112yes—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—81no—
132C2×Dic43—81no—
133C2×Dic43—81no—
134C2×Dic43—81no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139Dic86—21no—
140Dic86—21no—
141C8×C43—21no—
142C8×C43—21no—
143C43⋊C8—21no—
144C43⋊C8—21no—
145C22×C43—21no—
146C22×C43—22no—
147C22×C43—22no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—84no—
155C22×C43C22×D411yescharacteristic
156C4×C43—21no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43C2×#4111yescharacteristic
160C4×C43C2×#4111yescharacteristic
161Dic43—21no—
162Dic43—21no—
163Dic43—21no—
164Dic43—21no—
165Dic43—41no—
166Dic43—41no—
167Dic43—41no—
168Dic43—41no—
169#3123—431nomaximal, Sylow
170C2×C43—41no—
171C2×C43—42no—
172C2×C43—42no—
173C2×C43#52511yescharacteristic
174C2×C43#57711yescharacteristic
175C2×C43#57711yescharacteristic
176#541—431no—
177#518—431no—
178#485—431no—
179#485—431no—
180#478—431no—
181#478—431no—
182#461—431no—
183#461—431no—
184#450—431no—
185#450D4311yescharacteristic
186#440—431no—
187#440—431no—
188C4×SD16—431no—
189C4×SD16—431no—
190#433—431no—
191C43#312311yescharacteristic, complemented, Sylow
192C22×D4C2×D4311yescharacteristic
193C2×SD16—431no—
194C2×SD16—431no—
195C2×SD16C2×D4311yescharacteristic
196C2×SD16C2×D4311yescharacteristic
197C4⋊Q8—431no—
198#126—861no—
199#126—861no—
200#125—431no—
201#125—861no—
202#125—861no—
203C22⋊Q8—431no—
204C22⋊Q8C2×D4311yescharacteristic
205C4×Q8—431no—
206C4×Q8—431no—
207C4×D4—431no—
208C4×D4—431no—
209C4×D4—431no—
210C4×D4—431no—
211C4×D4—861no—
212C4×D4—861no—
213#117—431no—
214#117—431no—
215C2×C22⋊C4—861no—
216C2×C22⋊C4—861no—
217#107—431no—
218#107—431no—
219#106—431no—
220#106—431no—
221C4⋊C8—431no—
222C4⋊C8—431no—
223#103—431no—
224#103—431no—
225#103—431no—
226#103—431no—
227#102—431no—
228#102—431no—
229#102C2×D4311yescharacteristic
230#102C2×D4311yescharacteristic
231C22⋊C8—431no—
232C22⋊C8C2×D4311yescharacteristic
233#97—431no—
234C4×C8—431no—
235C24—21no—
236C2×Q8—431no—
237C2×Q8C22×D4311yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4C22×D4311yescharacteristic
242C2×D4C22×D4311yescharacteristic
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4C22×D4311yescharacteristic
248SD16—22no—
249SD16—22no—
250SD16—862no—
251SD16—862no—
252C2×C8—431no—
253C2×C8—431no—
254C2×C8C22×D4311yescharacteristic
255C2×C8C22×D4311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—431no—
258C4⋊C4—431no—
259C4⋊C4—431no—
260C4⋊C4—431no—
261C4⋊C4—431no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4C22×D4311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—431no—
272C22⋊C4—431no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C42—431no—
280C42—431no—
281C42—861no—
282C42—861no—
283C42—861no—
284C23—24no—
285C23—21no—
286C23—21no—
287C23—81no—
288C23—81no—
289C23D4×D4311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—861no—
293Q8—861no—
294D4—24no—
295D4—21no—
296D4—21no—
297D4#1062190012yes—
298D4#1062190012yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—431no—
304C2×C4—431no—
305C2×C4—431no—
306C2×C4—431no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—3441no—
312C2×C4—3441no—
313C2×C4—3441no—
314C2×C4—3441no—
315C2×C4D4×D4311yescharacteristic
316C2×C4C23×D4311yescharacteristic
317C8—21no—
318C8—21no—
319C8—861no—
320C8—861no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—84no—
331C22C2×D4×D4311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—861no—
336C4—861no—
337C4—861no—
338C4—861no—
339C4—1721no—
340C4—1721no—
341C4—1721no—
342C4—1721no—
343C4C2×#1062190011yescharacteristic
344C4C2×#1062190011yescharacteristic
345C2—41no—
346C2—42no—
347C2—42no—
348C2#1458340511yescharacteristic
349C2#1458370511yescharacteristic
350C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#450C2
socleC22×C43C22×D4
hypercenter#450D43
hypocenterC43#3123
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14583509C2semidirect
3. #14583241C2semidirect
4. #14583237C2semidirect
5. #14583201C2semidirect
6. #14583197C2semidirect
7. #14583102C2semidirect
8. #14583102C2semidirect
10. #14583000C2semidirect
11. #14582996C2semidirect
12. #14582990C2semidirect
13. SD16×Dic43C2semidirect
14. #14582957C2semidirect
18. #13063323C22semidirect
22. #13063316C22semidirect
25. Q8×Dic43C22semidirect
26. #13063290C22semidirect
37. #13063259C22semidirect
38. #13063258C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. Dic43⋊C8C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063250C22semidirect
44. #13063250C22semidirect
45. #13063249C22semidirect
46. #13063249C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
191. C43#3123semidirect