Finite Group Databasebeta

← #15761449

Subgroups — #15761449

Order 3328.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115755C211yesmaximal, characteristic
2#13115611C211yesmaximal, characteristic, complemented
3#13113483C211yesmaximal, characteristic
4#13113288C211yesmaximal, characteristic
5#13112738C211yesmaximal, characteristic, complemented
6#13112676C211yesmaximal, characteristic, complemented
7C13×#1451C211yesmaximal, characteristic, complemented
8#11719182C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C4×C13×M16C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C2×#88065—21no—
13C2×#88065—21no—
14C2×#88062—21no—
15C4×C4⋊Dic13C2211yescharacteristic
16#11718585C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C13×#322—21no—
19C13×#322—21no—
20#11718150—21no—
21#11718078C411yescharacteristic, complemented
22#11718078C411yescharacteristic, complemented
23#11718077C411yescharacteristic, complemented
24#11718077C411yescharacteristic, complemented
25#11718051—21no—
26#11718051—21no—
27C2×#6127—21no—
28C2×C13×M16D411yescharacteristic
29C2×C13×M16D411yescharacteristic
30C22×C8×C13—21no—
31C2×C42×C13C2311yescharacteristic
32#88184—21no—
33#88184—21no—
34C2×C4⋊Dic13—21no—
35C2×C4×Dic13—21no—
36C2×#6099—21no—
37C22×#1055—21no—
38#88129—21no—
39#88128C2×C411yescharacteristic
40C4×D52—21no—
41C4×D52—21no—
42#88123C2×C411yescharacteristic
43C13×C4⋊C8C2×C411yescharacteristic
44C13×C4⋊C8C2×C411yescharacteristic
45C13×C22⋊C8—21no—
46C13×#97—21no—
47C4×C8×C13—21no—
48C4×C8×C13—21no—
49C4×C8×C13—21no—
50C4×C8×C13D411yescharacteristic
51C4×C8×C13D411yescharacteristic
52#88071—21no—
53#88065—42no—
54#88065—42no—
55#88062—42no—
56C4⋊#1055—21no—
57C4⋊#1055—21no—
58C4⋊#1055—21no—
59C4⋊#1055C2×C411yescharacteristic
60C4⋊#1055C2×C411yescharacteristic
61#9592—131nomaximal, Sylow
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13#4111yescharacteristic
64C22×C4×C13#4111yescharacteristic
65C2×C22⋊D13—41no—
66C22×Dic13—41no—
67#6127—41no—
68#6127—41no—
69#6127—41no—
70#6127—41no—
71C2×D52—21no—
72C2×D52—21no—
73C2×D52—21no—
74C2×C4×D13—41no—
75C2×Dic26—21no—
76C13×M16—21no—
77C13×M16—21no—
78C13×M16—21no—
79C13×M16—21no—
80C2×C8×C13—21no—
81C2×C8×C13—21no—
82C2×C8×C13—21no—
83C2×C8×C13—21no—
84C2×C8×C13—21no—
85C2×C8×C13—21no—
86C2×C8×C13—42no—
87C42×C13C22×C411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13#4111yescharacteristic
90C42×C13#4111yescharacteristic
91#6103—41no—
92#6103—41no—
93C4⋊Dic13—22no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—41no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99#6099—41no—
100#6099—41no—
101C2×#1055—21no—
102C2×#1055—21no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106#1980—131no—
107#1950—131no—
108#1540—131no—
109#1492—131no—
110#1451D1311yescharacteristic, complemented
111#1303—131no—
112#1279—131no—
113C23×C13#12411yescharacteristic
114C22×D13—41no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—41no—
118C2×C4×C13#11711yescharacteristic
119C2×C4×C13C4×D411yescharacteristic
120C2×C4×C13C4×D411yescharacteristic
121C2×C4×C13#12111yescharacteristic
122C2×C4×C13#12311yescharacteristic
123C2×C4×C13#12611yescharacteristic
124C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C13#13711yescharacteristic
128C22⋊D13—81no—
129C22⋊D13—81no—
130C2×Dic13—42no—
131C2×Dic13—41no—
132C2×Dic13—81no—
133C2×Dic13—81no—
134D52—41no—
135D52—41no—
136D52—41no—
137D52—41no—
138D52—81no—
139C4×D13—81no—
140C4×D13—81no—
141Dic26—41no—
142Dic26—41no—
143C8×C13—22no—
144C8×C13—41no—
145C8×C13—41no—
146C8×C13—41no—
147C8×C13—41no—
148C8×C13—41no—
149#1055—41no—
150#1055—41no—
151#1055—81no—
152#532—131no—
153#431C2×D1311yescharacteristic
154C2×#108—261no—
155#423—131no—
156C2×C4⋊C8—131no—
157C2×#104—261no—
158C2×#104—261no—
159C4×M16C2×D1311yescharacteristic
160C2×C4×C8C2×D1311yescharacteristic
161C4×C4⋊C4—131no—
162#341—261no—
163#332—131no—
164#332—131no—
165#331—131no—
166#331—131no—
167D4⋊C8—261no—
168D4⋊C8—261no—
169#322—21no—
170#322—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13#38811yescharacteristic
174C22×C13#48911yescharacteristic
175C22×C13#49011yescharacteristic
176C2×D13—81no—
177C2×D13—81no—
178C2×D13—81no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13#44011yescharacteristic
183C4×C13#44211yescharacteristic
184C4×C13#44311yescharacteristic
185C4×C13#44411yescharacteristic
186C4×C13#46811yescharacteristic
187C4×C13#46911yescharacteristic
188Dic13—82no—
189Dic13—81no—
190C2×#41—261no—
191C2×M16—261no—
192C2×M16D5211yescharacteristic
193C2×M16D5211yescharacteristic
194C22×C8—21no—
195C22×C8—261no—
196C4⋊Q8—131no—
197#127—131no—
198#124—261no—
199#121—261no—
200#121—261no—
201C4×D4—261no—
202C4×D4—261no—
203C2×C4⋊C4—261no—
204C2×C42—261no—
205C2×C42C22×D1311yescharacteristic
206#108—522no—
207C4⋊C8—131no—
208C4⋊C8—131no—
209C4⋊C8—261no—
210C4⋊C8—261no—
211C4⋊C8—261no—
212C4⋊C8C4×D1311yescharacteristic
213C4⋊C8C4×D1311yescharacteristic
214#104—522no—
215#104—522no—
216C22⋊C8—21no—
217#97—21no—
218C4×C8—21no—
219C4×C8—21no—
220C4×C8—21no—
221C4×C8C22⋊D1311yescharacteristic
222C4×C8C22⋊D1311yescharacteristic
223#95—261no—
224C2×C13—21no—
225C2×C13—21no—
226C2×C13#192911yescharacteristic
227C2×C13#193211yescharacteristic
228C2×C13#193611yescharacteristic
229D13—161no—
230#41—521no—
231#41—521no—
232#41—521no—
233#41—521no—
234C2×Q8—261no—
235C2×D4—261no—
236C2×D4—261no—
237C2×D4—261no—
238C2×D4—521no—
239C22×C4—521no—
240C22×C4—521no—
241C22×C4C2×D5211yescharacteristic
242C22×C4#612711yescharacteristic
243C22×C4#612711yescharacteristic
244M16—21no—
245M16—21no—
246M16—21no—
247M16—21no—
248M16—521no—
249M16—521no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—42no—
257C2×C8—261no—
258C2×C8—261no—
259C2×C8—521no—
260C2×C8—521no—
261C2×C8—521no—
262C4⋊C4—262no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—521no—
266C22⋊C4—521no—
267C22⋊C4—521no—
268C42—521no—
269C42—521no—
270C42C2×C4×D1311yescharacteristic
271C42#612711yescharacteristic
272C42#612711yescharacteristic
273C42C2×C22⋊D1311yescharacteristic
274C13#959211yescharacteristic, complemented, Sylow
275C23—521no—
276C23#8812911yescharacteristic
277Q8—521no—
278Q8—521no—
279D4—521no—
280D4—521no—
281D4—521no—
282D4—521no—
283D4—1041no—
284D4—1041no—
285D4—1041no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—522no—
290C2×C4—521no—
291C2×C4—1041no—
292C2×C4—1041no—
293C2×C4—1041no—
294C2×C4—1041no—
295C2×C4#8812611yescharacteristic
296C2×C4C4×D5211yescharacteristic
297C2×C4#8813011yescharacteristic
298C2×C4#8816211yescharacteristic
299C2×C4#8816211yescharacteristic
300C2×C4#8816211yescharacteristic
301C2×C4#8816311yescharacteristic
302C2×C4C4×C22⋊D1311yescharacteristic
303C2×C4#8818311yescharacteristic
304C2×C4#8818411yescharacteristic
305C8—22no—
306C8—41no—
307C8—41no—
308C8—41no—
309C8—41no—
310C8—41no—
311C8—521no—
312C8—521no—
313C8—1041no—
314C22—21no—
315C22—21no—
316C22—1041no—
317C22—1041no—
318C22—1041no—
319C22#1171837411yescharacteristic
320C22#1171837511yescharacteristic
321C22#1171860111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—1042no—
326C4—1041no—
327C4#1171837111yescharacteristic
328C4#1171837211yescharacteristic
329C4#1171879511yescharacteristic
330C4#1171879611yescharacteristic
331C4#1171880511yescharacteristic
332C4#1171880611yescharacteristic
333C2—21no—
334C2—21no—
335C2—2081no—
336C2#1311548411yescharacteristic
337C2#1311550511yescharacteristic
338C2#1311553311yescharacteristic
subgroupG/H
centerC2×C4#88184
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1451C2
socleC22×C13#388
prime radical#11719182C22
cosocleC2×C42×C13C23
hypercenter#1451D13
hypocenterC13#9592
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1451

Complements

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

NH ≅ G/Ntype
2. #13115611C2semidirect
5. #13112738C2semidirect
6. #13112676C2semidirect
7. C13×#1451C2semidirect
21. #11718078C4semidirect
22. #11718078C4semidirect
23. #11718077C4semidirect
24. #11718077C4semidirect
110. #1451D13semidirect
274. C13#9592semidirect

Maximal subgroups

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

subgroupindex
#131157552
#131156112
#131134832
#131132882
#131127382
#131126762
C13×#14512
#959213