Finite Group Databasebeta

← #15761307

Subgroups — #15761307

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#13115762C211yesmaximal, characteristic
2#13115641C211yesmaximal, characteristic
3#13115597C211yesmaximal, characteristic, complemented
4#13114706C211yesmaximal, characteristic, complemented
5C2×#11718077C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic, complemented
7C13×#1296C211yesmaximal, characteristic, complemented
8C2×#88128C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C2×#88061—21no—
13C2×#88061—21no—
14C2×#88055—21no—
15C2×#88049—21no—
16C2×#88049—21no—
17C2×#88048—21no—
18C4×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21#11718142—21no—
22#11718121—21no—
23#11718077C414yescomplemented
24C22×D52—21no—
25C22×D52—21no—
26C22×D52—21no—
27C22×C8×C13—21no—
28C22×C8×C13—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13D411yescharacteristic
34C2×C4⋊Dic13D411yescharacteristic
35C2×C4×Dic13—21no—
36C22×#1055—21no—
37C22×#1055D411yescharacteristic
38C22×#1055D411yescharacteristic
39#88128—21no—
40#88128—21no—
41#88128—21no—
42#88128C2×C412yes—
43C13×C4⋊C8—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8C2×C412yes—
47#88071—21no—
48#88061—42no—
49#88061—42no—
50#88055—42no—
51#88049—42no—
52#88049—42no—
53#88048—42no—
54C4⋊#1055—21no—
55C4⋊#1055C2×C412yes—
56C4×#1055—21no—
57C4×#1055—21no—
58#9572—131nomaximal, Sylow
59C23×D13—41no—
60C22×C4×C13—41no—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13#4111yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
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—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—81no—
93C42×C13C22×C411yescharacteristic
94C42×C13#4111yescharacteristic
95C42×C13#4111yescharacteristic
96C42×C13#4111yescharacteristic
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4×Dic13—41no—
102C4×Dic13—41no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055—22no—
106C2×#1055—21no—
107C2×#1055—21no—
108C2×#1055—21no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055SD1612yes—
112#1982—131no—
113#1957—131no—
114#1948—131no—
115#1770—131no—
116C2×#331—131no—
117#1296D1311yescharacteristic, complemented
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—81no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13#11711yescharacteristic
133C2×C4×C13C4×D411yescharacteristic
134C2×C4×C13C4×D411yescharacteristic
135C2×C4×C13#12311yescharacteristic
136C2×C4×C13#12411yescharacteristic
137C2×C4×C13#12611yescharacteristic
138C2×C4×C13C2×SD1611yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C13#13711yescharacteristic
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152D52—42no—
153D52—42no—
154D52—42no—
155D52—42no—
156D52—82no—
157D52—82no—
158D52—81no—
159D52—81no—
160D52—81no—
161D52—81no—
162C8×C13—42no—
163C8×C13—81no—
164#1055—22no—
165#1055—42no—
166#1055—41no—
167C2×#127—131no—
168C2×#106—261no—
169C2×C4⋊C8—131no—
170C2×C4⋊C8C2×D1311yescharacteristic
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⋊C4—131no—
180#340—261no—
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—161no—
200C4×C13C4×SD1611yescharacteristic
201C4×C13#44011yescharacteristic
202C4×C13#44211yescharacteristic
203C4×C13#44211yescharacteristic
204C4×C13#48111yescharacteristic
205C4×C13#48211yescharacteristic
206C4×C13#48911yescharacteristic
207C4×C13#49011yescharacteristic
208Dic13—81no—
209Dic13—81no—
210C22×D4—261no—
211C22×D4—261no—
212C22×D4—261no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—131no—
216C22×C8—131no—
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⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C42—261no—
228C2×C42C22×D1311yescharacteristic
229#106—522no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—132no—
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—261no—
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—41no—
270C22×C4—261no—
271C22×C4—261no—
272C22×C4#612711yescharacteristic
273C22×C4D4×D1311yescharacteristic
274C22×C4D4×D1311yescharacteristic
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—132no—
282C2×C8—261no—
283C2×C8—261no—
284C2×C8—262no—
285C2×C8—261no—
286C2×C8—261no—
287C2×C8—261no—
288C2×C8—521no—
289C2×C8—521no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—81no—
295C4⋊C4—261no—
296C4⋊C4—261no—
297C4⋊C4—261no—
298C4⋊C4—261no—
299C42—521no—
300C42—521no—
301C42C2×C4×D1311yescharacteristic
302C42#612711yescharacteristic
303C42#612911yescharacteristic
304C42#613111yescharacteristic
305C13#957211yescharacteristic, complemented, Sylow
306C23—522no—
307C23—1041no—
308C23—1041no—
309C23—1041no—
310C23—1041no—
311C23—1041no—
312C23—1041no—
313C23#8813811yescharacteristic
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—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4#8812611yescharacteristic
336C2×C4#8813511yescharacteristic
337C2×C4#8813911yescharacteristic
338C2×C4#8814711yescharacteristic
339C2×C4#8814811yescharacteristic
340C2×C4#8815211yescharacteristic
341C2×C4#8816511yescharacteristic
342C2×C4#8816511yescharacteristic
343C2×C4SD16×D1311yescharacteristic
344C2×C4#8816811yescharacteristic
345C2×C4#8816811yescharacteristic
346C2×C4#8816811yescharacteristic
347C2×C4#8817211yescharacteristic
348C2×C4#8817311yescharacteristic
349C8—42no—
350C8—81no—
351C8—262no—
352C8—522no—
353C8—521no—
354C22—1042no—
355C22—1042no—
356C22—1042no—
357C22—2081no—
358C22—2081no—
359C22—2081no—
360C22—2081no—
361C22#1171833011yescharacteristic
362C22#1171841011yescharacteristic
363C22#1171841511yescharacteristic
364C22#1171842311yescharacteristic
365C22#1171844311yescharacteristic
366C22#1171847311yescharacteristic
367C22#1171848011yescharacteristic
368C4—21no—
369C4—21no—
370C4—161no—
371C4—1041no—
372C4—1041no—
373C4#1171842511yescharacteristic
374C4#1171844611yescharacteristic
375C4#1171844911yescharacteristic
376C4#1171845611yescharacteristic
377C4#1171852411yescharacteristic
378C4#1171853011yescharacteristic
379C4#1171854611yescharacteristic
380C4#1171855011yescharacteristic
381C2—2082no—
382C2#1311431111yescharacteristic
383C2#1311431911yescharacteristic
384C2#1311437211yescharacteristic
385C2#1311440011yescharacteristic
386C2#1311546111yescharacteristic
387C2#1311549611yescharacteristic
388C2#1311553111yescharacteristic
subgroupG/H
centerC23#88138
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socleC23×C13#121
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#1296D13
hypocenterC13#9572
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #13115597C2semidirect
4. #13114706C2semidirect
6. #13112670C2semidirect
7. C13×#1296C2semidirect
23. #11718077C4semidirect
117. #1296D13semidirect
305. C13#9572semidirect

Maximal subgroups

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

subgroupindex
#131157622
#131156412
#131155972
#131147062
C2×#117180772
#131126702
C13×#12962
#957213