Finite Group Databasebeta

← #15767674

Subgroups — #15767674

Order 3328.

402 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115630C211yesmaximal, characteristic
2#13114833C211yesmaximal, characteristic
3#13114833C211yesmaximal, characteristic
4#13112719C211yesmaximal, characteristic, complemented
5#13112719C211yesmaximal, characteristic, complemented
6#13112671C211yesmaximal, characteristic, complemented
7C13×#1834C211yesmaximal, characteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C2×C4×C8×C13C2211yescharacteristic
10C13×#384C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C2×#88060—21no—
13C2×#88060—21no—
14C2×#88049—21no—
15C2×#88049—21no—
16C2×C4⋊#1055C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C13×#340—21no—
20C13×#340—21no—
21#11718121—21no—
22#11718121—21no—
23C22×D52D411yescharacteristic
24C22×C4×D13—21no—
25C22×C8×C13D411yescharacteristic
26C22×C8×C13D411yescharacteristic
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C42×C13C2311yescharacteristic
34C2×#6103—21no—
35C2×C4⋊Dic13D411yescharacteristic
36C22×#1055—21no—
37C22×#1055—21no—
38C22×#1055—21no—
39C4×D52—21no—
40C4×D52—21no—
41C4×D52—21no—
42C4×D52—21no—
43C4×C8×C13—21no—
44C4×C8×C13—21no—
45#88060—42no—
46#88060—42no—
47#88049—42no—
48#88049—42no—
49C4⋊#1055—21no—
50C4⋊#1055—21no—
51C4⋊#1055—21no—
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55#10625—131nomaximal, Sylow
56C23×D13—21no—
57C22×C4×C13—41no—
58C22×C4×C13—41no—
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13#4111yescharacteristic
62C22×Dic13—21no—
63C2×D52—21no—
64C2×D52—21no—
65C2×D52—21no—
66C2×D52—21no—
67C2×D52—21no—
68C2×D52SD1612yes—
69C2×C4×D13—41no—
70C2×C4×D13—41no—
71C2×C4×D13—41no—
72C2×C4×D13—41no—
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C2×C8×C13—21no—
76C2×C8×C13—21no—
77C2×C8×C13—21no—
78C2×C8×C13—21no—
79C2×C8×C13—21no—
80C2×C8×C13—21no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—81no—
90C13×C4⋊C4—81no—
91C42×C13#4111yescharacteristic
92C42×C13#4111yescharacteristic
93C42×C13#4111yescharacteristic
94C42×C13#4111yescharacteristic
95#6103—41no—
96#6103—41no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055—41no—
108#1954—131no—
109#1834D1311yescharacteristic, complemented
110#1802—131no—
111#1802—131no—
112#1296—131no—
113#1296—131no—
114#1277—131no—
115C23×C13#12111yescharacteristic
116C22×D13—22no—
117C22×D13—41no—
118C22×D13—41no—
119C22×D13—41no—
120C22×D13—41no—
121C22×D13—41no—
122C22×D13—41no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—81no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13#12311yescharacteristic
132C2×C4×C13#12311yescharacteristic
133C2×C4×C13#12311yescharacteristic
134C2×C4×C13#12411yescharacteristic
135C2×C4×C13#12611yescharacteristic
136C2×C4×C13#12611yescharacteristic
137C2×C4×C13C2×SD1611yescharacteristic
138C2×C4×C13#13511yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13#13511yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C13#13711yescharacteristic
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148D52—22no—
149D52—22no—
150D52—41no—
151D52—41no—
152C4×D13—81no—
153C4×D13—81no—
154C4×D13—81no—
155C4×D13—81no—
156C8×C13—41no—
157C8×C13—41no—
158#1055—81no—
159#1055—81no—
160#1055—81no—
161C2×C4×D4—131no—
162C2×C4⋊C8—131no—
163C2×C4⋊C8—131no—
164C2×C4⋊C8—131no—
165C2×#102—261no—
166C2×#102—261no—
167C2×C22⋊C8—261no—
168C2×C22⋊C8—261no—
169C2×C4×C8C2×D1311yescharacteristic
170#384C2×D1311yescharacteristic
171#384C2×D1311yescharacteristic
172#340—21no—
173#340—21no—
174#340—261no—
175#340—261no—
176C22×C13#39711yescharacteristic
177C22×C13#46311yescharacteristic
178C22×C13#46311yescharacteristic
179C22×C13#46511yescharacteristic
180C22×C13#46811yescharacteristic
181C22×C13#47211yescharacteristic
182C22×C13#47311yescharacteristic
183C2×D13—42no—
184C2×D13—42no—
185C2×D13—42no—
186C2×D13—81no—
187C2×D13—81no—
188C2×D13—81no—
189C2×D13—81no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—161no—
193C4×C13—161no—
194C4×C13#48111yescharacteristic
195C4×C13#48211yescharacteristic
196C4×C13#48211yescharacteristic
197C4×C13#48211yescharacteristic
198C4×C13#48311yescharacteristic
199C4×C13#48511yescharacteristic
200C4×C13#48811yescharacteristic
201C4×C13#49011yescharacteristic
202Dic13—81no—
203C22×D4—131no—
204C23×C4—261no—
205C22×C8—261no—
206C22×C8—261no—
207C22×C8—261no—
208C22×C8C22⋊D1311yescharacteristic
209C22×C8C22⋊D1311yescharacteristic
210C4×D4—261no—
211C4×D4—261no—
212C4×D4—261no—
213C4×D4—261no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—131no—
221C2×C22⋊C4—261no—
222C2×C42C22×D1311yescharacteristic
223C4⋊C8—261no—
224C4⋊C8—261no—
225C4⋊C8—261no—
226C4⋊C8—261no—
227C4⋊C8—261no—
228C4⋊C8—261no—
229#102—522no—
230#102—522no—
231C22⋊C8—522no—
232C22⋊C8—522no—
233C4×C8—21no—
234C4×C8—21no—
235C2×C13#167711yescharacteristic
236C2×C13#167911yescharacteristic
237C2×C13#169711yescharacteristic
238C2×C13#169911yescharacteristic
239C2×C13#207311yescharacteristic
240C2×C13#207711yescharacteristic
241C2×C13#207811yescharacteristic
242D13—82no—
243C24—261no—
244C2×D4—132no—
245C2×D4—261no—
246C2×D4—261no—
247C2×D4—261no—
248C2×D4—261no—
249C2×D4—261no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—261no—
253C22×C4—521no—
254C22×C4—521no—
255C22×C4—521no—
256C22×C4—521no—
257C22×C4—521no—
258C22×C4—521no—
259C22×C4D4×D1311yescharacteristic
260C22×C4#612911yescharacteristic
261C22×C4C2×C22⋊D1311yescharacteristic
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—521no—
269C2×C8—521no—
270C2×C8—521no—
271C2×C8—521no—
272C2×C8—521no—
273C2×C8—521no—
274C2×C8—521no—
275C2×C8—521no—
276C2×C8—521no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C4⋊C4—261no—
288C4⋊C4—261no—
289C22⋊C4—521no—
290C22⋊C4—521no—
291C42#612711yescharacteristic
292C42#612711yescharacteristic
293C42#613111yescharacteristic
294C42#613111yescharacteristic
295C13#1062511yescharacteristic, complemented, Sylow
296C23—262no—
297C23—521no—
298C23—521no—
299C23—521no—
300C23—521no—
301C23—521no—
302C23—521no—
303C23#8819211yescharacteristic
304D4—262no—
305D4—262no—
306D4—521no—
307D4—521no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—1041no—
320C2×C4—1041no—
321C2×C4—1041no—
322C2×C4—1041no—
323C2×C4#8814811yescharacteristic
324C2×C4#8814811yescharacteristic
325C2×C4#8815211yescharacteristic
326C2×C4#8815211yescharacteristic
327C2×C4SD16×D1311yescharacteristic
328C2×C4#8816811yescharacteristic
329C2×C4#8816911yescharacteristic
330C2×C4#8817011yescharacteristic
331C2×C4#8818311yescharacteristic
332C2×C4#8820111yescharacteristic
333C2×C4#8820311yescharacteristic
334C2×C4#8820311yescharacteristic
335C2×C4#8820411yescharacteristic
336C2×C4#8820411yescharacteristic
337C8—41no—
338C8—41no—
339C8—1041no—
340C8—1041no—
341C8—1041no—
342C22—522no—
343C22—522no—
344C22—522no—
345C22—1041no—
346C22—1041no—
347C22—1041no—
348C22—1041no—
349C22#1171865411yescharacteristic
350C22#1171871811yescharacteristic
351C22#1171871811yescharacteristic
352C22#1171882111yescharacteristic
353C22#1171883211yescharacteristic
354C22#1171883511yescharacteristic
355C22#1171885311yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—161no—
360C4—1041no—
361C4#1171852311yescharacteristic
362C4#1171852411yescharacteristic
363C4#1171852711yescharacteristic
364C4#1171852811yescharacteristic
365C4#1171866411yescharacteristic
366C4#1171866411yescharacteristic
367C4#1171872811yescharacteristic
368C4#1171872911yescharacteristic
369C2—1042no—
370C2#1311424211yescharacteristic
371C2#1311425611yescharacteristic
372C2#1311436611yescharacteristic
373C2#1311438011yescharacteristic
374C2#1311625011yescharacteristic
375C2#1311627011yescharacteristic
376C2#1311627711yescharacteristic
subgroupG/H
centerC23#88192
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1834C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenter#1834D13
hypocenterC13#10625
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
4. #13112719C2semidirect
5. #13112719C2semidirect
6. #13112671C2semidirect
7. C13×#1834C2semidirect
109. #1834D13semidirect
295. C13#10625semidirect

Maximal subgroups

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

subgroupindex
#131156302
#131148332
#131127192
#131126712
C13×#18342
#1062513