Finite Group Databasebeta

← #15761308

Subgroups — #15761308

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115763C211yesmaximal, characteristic
2#13115641C211yesmaximal, characteristic
3#13114705C211yesmaximal, characteristic, complemented
4C2×#11718077C211yesmaximal, characteristic
5#13112719C211yesmaximal, characteristic, complemented
6#13112670C211yesmaximal, characteristic, complemented
7C13×#1948C211yesmaximal, characteristic, complemented
8C2×#88128C2211yescharacteristic
9C2×C13×#106—21no—
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88049—21no—
14C2×#88049—21no—
15C2×#88049—21no—
16C2×#88049—21no—
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C2×#88043—21no—
20C2×C4×#1055C2211yescharacteristic
21C13×#340—21no—
22#11718116—21no—
23#11718077C414yescomplemented
24C22×D52—21no—
25C22×D52—21no—
26C22×D52—21no—
27C22×C8×C13—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C42×C13—21no—
34C2×C42×C13C2311yescharacteristic
35C22×#1055—21no—
36C22×#1055—21no—
37C22×#1055D411yescharacteristic
38C22×#1055D411yescharacteristic
39#88128—21no—
40#88128—21no—
41#88128—21no—
42#88128C2×C412yes—
43C13×#106—42no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8C2×C412yes—
46C13×#95—21no—
47#88049—42no—
48#88049—42no—
49#88049—42no—
50#88049—42no—
51C4⋊#1055—21no—
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055C2×C412yes—
55#88043—42no—
56C4×#1055—21no—
57C4×#1055—21no—
58#9572—131nomaximal, Sylow
59C23×D13—41no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—41no—
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13#4111yescharacteristic
66C2×D52—22no—
67C2×D52—22no—
68C2×D52—22no—
69C2×D52—41no—
70C2×D52—41no—
71C2×D52—41no—
72C2×D52—41no—
73C2×D52—41no—
74C2×D52—41no—
75C2×D52—41no—
76C2×D52—41no—
77C2×D52—41no—
78C2×D52—41no—
79C2×D52—41no—
80C2×D52—81no—
81C2×D52—81no—
82C2×C8×C13—22no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—81no—
94C42×C13—41no—
95C42×C13—41no—
96C42×C13C22×C411yescharacteristic
97C42×C13#4111yescharacteristic
98C42×C13#4111yescharacteristic
99C42×C13#4111yescharacteristic
100C2×#1055—21no—
101C2×#1055—21no—
102C2×#1055—22no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—41no—
107C2×#1055—41no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055SD1612yes—
112#1982—131no—
113#1957—131no—
114#1948D1311yescharacteristic, complemented
115#1770—131no—
116C2×#331—131no—
117#1296—131no—
118#1277—131no—
119C23×C13#12111yescharacteristic
120C22×D13—42no—
121C22×D13—81no—
122C22×D13—81no—
123C22×D13—81no—
124C22×D13—81no—
125C22×D13—81no—
126C22×D13—81no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13#11711yescharacteristic
139C2×C4×C13C4×D411yescharacteristic
140C2×C4×C13C4×D411yescharacteristic
141C2×C4×C13#12311yescharacteristic
142C2×C4×C13#12411yescharacteristic
143C2×C4×C13#12611yescharacteristic
144C2×C4×C13C2×SD1611yescharacteristic
145C2×C4×C13#13511yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C13#13711yescharacteristic
152D52—42no—
153D52—42no—
154D52—42no—
155D52—42no—
156D52—82no—
157D52—82no—
158D52—81no—
159D52—81no—
160D52—81no—
161D52—81no—
162C8×C13—42no—
163#1055—22no—
164#1055—42no—
165#1055—41no—
166#1055—81no—
167C2×#127—131no—
168C2×#106—21no—
169C2×C4⋊C8—131no—
170C2×C4⋊C8—131no—
171C2×C4⋊C8C2×D1311yescharacteristic
172C2×#102—261no—
173C2×#102—261no—
174C2×#102—261no—
175C2×#102—261no—
176C2×#97—261no—
177C2×C4×C8—131no—
178#384C2×D1311yescharacteristic
179C4×C4⋊C4C2×D1311yescharacteristic
180#340—21no—
181#336—261no—
182#331—134no—
183C22×C13#38811yescharacteristic
184C22×C13#46011yescharacteristic
185C22×C13#46311yescharacteristic
186C22×C13#46811yescharacteristic
187C22×C13#46911yescharacteristic
188C22×C13#47111yescharacteristic
189C22×C13#47211yescharacteristic
190C2×D13—82no—
191C2×D13—82no—
192C2×D13—82no—
193C2×D13—161no—
194C2×D13—161no—
195C2×D13—161no—
196C2×D13—161no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—81no—
200C4×C13—81no—
201C4×C13—161no—
202C4×C13C4×SD1611yescharacteristic
203C4×C13#44011yescharacteristic
204C4×C13#44211yescharacteristic
205C4×C13#44211yescharacteristic
206C4×C13#48111yescharacteristic
207C4×C13#48211yescharacteristic
208C4×C13#48911yescharacteristic
209C4×C13#49011yescharacteristic
210C22×D4—261no—
211C22×D4—261no—
212C22×D4—261no—
213C22×C8—21no—
214C22×C8—131no—
215C22×C8—131no—
216C22×C8—261no—
217C22×C8—261no—
218#127—132no—
219#127—261no—
220#127—261no—
221#127—261no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C22⋊D1311yescharacteristic
226C2×C4⋊C4C22⋊D1311yescharacteristic
227C2×C42—21no—
228C2×C42C22×D1311yescharacteristic
229#106—42no—
230C4⋊C8—21no—
231C4⋊C8—132no—
232C4⋊C8—261no—
233C4⋊C8—261no—
234C4⋊C8—261no—
235C4⋊C8C4×D1312yes—
236#102—522no—
237#102—522no—
238#102—522no—
239#102—522no—
240#97—522no—
241C4×C8—261no—
242C4×C8—261no—
243#95—21no—
244C2×C13#168611yescharacteristic
245C2×C13#168811yescharacteristic
246C2×C13#169711yescharacteristic
247C2×C13#170111yescharacteristic
248C2×C13#192611yescharacteristic
249C2×C13#193111yescharacteristic
250C2×C13#193611yescharacteristic
251D13—162no—
252C24—521no—
253C2×D4—262no—
254C2×D4—262no—
255C2×D4—262no—
256C2×D4—521no—
257C2×D4—521no—
258C2×D4—521no—
259C2×D4—521no—
260C2×D4—521no—
261C2×D4—521no—
262C2×D4—521no—
263C2×D4—521no—
264C2×D4—521no—
265C2×D4—521no—
266C2×D4—521no—
267C2×D4—1041no—
268C2×D4—1041no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4D4×D1311yescharacteristic
273C22×C4#612911yescharacteristic
274C22×C4C2×C22⋊D1311yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—132no—
279C2×C8—261no—
280C2×C8—261no—
281C2×C8—262no—
282C2×C8—261no—
283C2×C8—261no—
284C2×C8—261no—
285C2×C8—521no—
286C2×C8—521no—
287C2×C8—521no—
288C2×C8—521no—
289C2×C8—521no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—81no—
299C42—41no—
300C42—41no—
301C42C2×C4×D1311yescharacteristic
302C42#612711yescharacteristic
303C42#613111yescharacteristic
304C42#613111yescharacteristic
305C13#957211yescharacteristic, complemented, Sylow
306C23—522no—
307C23—1041no—
308C23—1041no—
309C23—1041no—
310C23—1041no—
311C23—1041no—
312C23—1041no—
313C23#8819311yescharacteristic
314D4—522no—
315D4—522no—
316D4—522no—
317D4—522no—
318D4—1042no—
319D4—1042no—
320D4—1041no—
321D4—1041no—
322D4—1041no—
323D4—1041no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4#8814611yescharacteristic
336C2×C4#8814711yescharacteristic
337C2×C4#8814811yescharacteristic
338C2×C4#8815211yescharacteristic
339C2×C4SD16×D1311yescharacteristic
340C2×C4#8816811yescharacteristic
341C2×C4#8816811yescharacteristic
342C2×C4#8817011yescharacteristic
343C2×C4C4×C22⋊D1311yescharacteristic
344C2×C4#8818611yescharacteristic
345C2×C4#8819611yescharacteristic
346C2×C4#8820111yescharacteristic
347C2×C4#8820311yescharacteristic
348C2×C4#8820311yescharacteristic
349C8—42no—
350C8—262no—
351C8—521no—
352C8—522no—
353C8—1041no—
354C22—1042no—
355C22—1042no—
356C22—1042no—
357C22—2081no—
358C22—2081no—
359C22—2081no—
360C22—2081no—
361C22#1171865111yescharacteristic
362C22#1171870011yescharacteristic
363C22#1171871011yescharacteristic
364C22#1171882411yescharacteristic
365C22#1171882611yescharacteristic
366C22#1171886011yescharacteristic
367C22#1171886411yescharacteristic
368C4—21no—
369C4—21no—
370C4—81no—
371C4—81no—
372C4—161no—
373C4#1171851311yescharacteristic
374C4#1171852411yescharacteristic
375C4#1171852711yescharacteristic
376C4#1171853011yescharacteristic
377C4#1171867511yescharacteristic
378C4#1171868711yescharacteristic
379C4#1171872811yescharacteristic
380C4#1171875011yescharacteristic
381C2—2082no—
382C2#1311431011yescharacteristic
383C2#1311431811yescharacteristic
384C2#1311437111yescharacteristic
385C2#1311439911yescharacteristic
386C2#1311546211yescharacteristic
387C2#1311549711yescharacteristic
388C2#1311553211yescharacteristic
subgroupG/H
centerC23#88193
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1948C2
socleC23×C13#121
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#1948D13
hypocenterC13#9572
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #13114705C2semidirect
5. #13112719C2semidirect
6. #13112670C2semidirect
7. C13×#1948C2semidirect
23. #11718077C4semidirect
114. #1948D13semidirect
305. C13#9572semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131157632
#131156412
#131147052
C2×#117180772
#131127192
#131126702
C13×#19482
#957213