Finite Group Databasebeta

← #15761452

Subgroups — #15761452

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#13115611C211yesmaximal, characteristic, complemented
2#13113485C211yesmaximal, characteristic
3#13113287C211yesmaximal, characteristic
4#13113123C211yesmaximal, characteristic, complemented
5#13112739C211yesmaximal, characteristic, complemented
6#13112677C211yesmaximal, characteristic, complemented
7C13×#1980C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C2×C13×#104—21no—
10C2×C13×#104—21no—
11C4×C13×M16C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88062—21no—
14#11718586C2211yescharacteristic
15#11718585C2211yescharacteristic
16C2×C4⋊#1055C2211yescharacteristic
17C2×C4×#1055C2211yescharacteristic
18#11718150—21no—
19#11718139C411yescharacteristic, complemented
20#11718139C411yescharacteristic, complemented
21#11718136C411yescharacteristic, complemented
22#11718136C411yescharacteristic, complemented
23D4⋊#1055—21no—
24D4⋊#1055—21no—
25#11718046—21no—
26#11718046—21no—
27C2×C13×#41—21no—
28C2×C13×M16D411yescharacteristic
29C2×C13×M16D411yescharacteristic
30C13×C4⋊Q8C2×C411yescharacteristic
31C13×#127C2×C411yescharacteristic
32C13×#124—21no—
33C13×#121—21no—
34C13×#121—21no—
35C4×D4×C13—21no—
36C4×D4×C13—21no—
37C2×C13×C4⋊C4—21no—
38C2×C42×C13—21no—
39C2×C42×C13C2311yescharacteristic
40C2×#6099—21no—
41C22×#1055—21no—
42C22×#1055—21no—
43C13×#104—42no—
44C13×#104—42no—
45C13×#97—21no—
46C4×C8×C13—21no—
47C13×#95—21no—
48C22⋊#1055—21no—
49#88062—42no—
50C4⋊#1055—21no—
51C4⋊#1055—21no—
52C4⋊#1055—21no—
53C4⋊#1055C2×C411yescharacteristic
54C4⋊#1055C2×C411yescharacteristic
55C4⋊#1055C2×C411yescharacteristic
56C4⋊#1055C2×C411yescharacteristic
57C4×#1055—21no—
58C4×#1055—21no—
59C4×#1055D411yescharacteristic
60C4×#1055D411yescharacteristic
61#9592—131nomaximal, Sylow
62C13×#41—41no—
63C13×#41—41no—
64C13×#41—41no—
65C13×#41—41no—
66C2×Q8×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13#4111yescharacteristic
75C22×C4×C13#4111yescharacteristic
76C13×M16—21no—
77C13×M16—21no—
78C13×M16—21no—
79C13×M16—21no—
80C2×C8×C13—21no—
81C2×C8×C13—21no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C42×C13—41no—
89C42×C13—41no—
90C42×C13C22×C411yescharacteristic
91C42×C13C2×D411yescharacteristic
92C42×C13#4111yescharacteristic
93C42×C13#4111yescharacteristic
94#6099—41no—
95#6099—41no—
96C2×#1055—21no—
97C2×#1055—21no—
98C2×#1055—21no—
99C2×#1055—21no—
100C2×#1055—21no—
101C2×#1055—21no—
102C2×#1055—42no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106#1980D1311yescharacteristic
107#1950—131no—
108#1540—131no—
109#1492—131no—
110#1451—131no—
111#1303—131no—
112#1279—131no—
113C23×C13—41no—
114C23×C13#12411yescharacteristic
115Q8×C13—41no—
116Q8×C13—41no—
117D4×C13—41no—
118D4×C13—41no—
119D4×C13—41no—
120D4×C13—41no—
121D4×C13—81no—
122D4×C13—81no—
123D4×C13—81no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13#11711yescharacteristic
134C2×C4×C13C4×D411yescharacteristic
135C2×C4×C13C4×D411yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12311yescharacteristic
138C2×C4×C13#12611yescharacteristic
139C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C13#13711yescharacteristic
143C8×C13—41no—
144C8×C13—41no—
145#1055—22no—
146#1055—41no—
147#1055—41no—
148#1055—41no—
149#1055—41no—
150#1055—41no—
151#1055—81no—
152#532C2×D1311yescharacteristic
153#431—131no—
154C2×#108—261no—
155#423—131no—
156C2×C4⋊C8—131no—
157C2×#104—21no—
158C2×#104—21no—
159C4×M16C2×D1311yescharacteristic
160C2×C4×C8—131no—
161C4×C4⋊C4C2×D1311yescharacteristic
162#341—261no—
163#332—131no—
164#332—131no—
165#331—131no—
166#331—131no—
167D4⋊C8—261no—
168D4⋊C8—261no—
169#322—261no—
170#322—261no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—81no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13#38811yescharacteristic
177C22×C13#48911yescharacteristic
178C22×C13#49011yescharacteristic
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—82no—
183C4×C13—81no—
184C4×C13#44011yescharacteristic
185C4×C13#44211yescharacteristic
186C4×C13#44311yescharacteristic
187C4×C13#44411yescharacteristic
188C4×C13#46811yescharacteristic
189C4×C13#46911yescharacteristic
190C2×#41—21no—
191C2×M16—261no—
192C2×M16C22⋊D1311yescharacteristic
193C2×M16C22⋊D1311yescharacteristic
194C22×C8—261no—
195C22×C8—261no—
196C4⋊Q8C4×D1311yescharacteristic
197#127C4×D1311yescharacteristic
198#124—21no—
199#121—21no—
200#121—21no—
201C4×D4—21no—
202C4×D4—21no—
203C2×C4⋊C4—21no—
204C2×C42—21no—
205C2×C42C22×D1311yescharacteristic
206#108—522no—
207C4⋊C8—131no—
208C4⋊C8—131no—
209C4⋊C8—131no—
210C4⋊C8—131no—
211C4⋊C8—261no—
212C4⋊C8—261no—
213C4⋊C8—261no—
214#104—42no—
215#104—42no—
216C22⋊C8—261no—
217#97—21no—
218C4×C8—21no—
219C4×C8—131no—
220C4×C8—131no—
221C4×C8—261no—
222C4×C8—261no—
223#95—21no—
224C2×C13—21no—
225C2×C13—21no—
226C2×C13—161no—
227C2×C13#192911yescharacteristic
228C2×C13#193211yescharacteristic
229C2×C13#193611yescharacteristic
230#41—41no—
231#41—41no—
232#41—41no—
233#41—41no—
234C2×Q8—21no—
235C2×D4—21no—
236C2×D4—21no—
237C2×D4—21no—
238C2×D4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4#612911yescharacteristic
242C22×C4#612911yescharacteristic
243C22×C4C2×C22⋊D1311yescharacteristic
244M16—21no—
245M16—21no—
246M16—21no—
247M16—21no—
248M16—521no—
249M16—521no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—261no—
253C2×C8—261no—
254C2×C8—261no—
255C2×C8—261no—
256C2×C8—261no—
257C2×C8—261no—
258C2×C8—522no—
259C2×C8—521no—
260C2×C8—521no—
261C2×C8—521no—
262C4⋊C4—22no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—41no—
269C42—41no—
270C42C2×C4×D1311yescharacteristic
271C42#612711yescharacteristic
272C42D4×D1311yescharacteristic
273C42#612911yescharacteristic
274C13#959211yescharacteristic, complemented, Sylow
275C23—41no—
276C23#8819011yescharacteristic
277Q8—41no—
278Q8—41no—
279D4—41no—
280D4—41no—
281D4—41no—
282D4—41no—
283D4—81no—
284D4—81no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4#8813111yescharacteristic
296C2×C4#8813311yescharacteristic
297C2×C4#8813511yescharacteristic
298C2×C4#8813711yescharacteristic
299C2×C4C4×C22⋊D1311yescharacteristic
300C2×C4#8818611yescharacteristic
301C2×C4#8818611yescharacteristic
302C2×C4#8819311yescharacteristic
303C2×C4#8820311yescharacteristic
304C2×C4#8820511yescharacteristic
305C8—41no—
306C8—41no—
307C8—262no—
308C8—521no—
309C8—521no—
310C8—521no—
311C8—521no—
312C8—521no—
313C8—1041no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#1171860611yescharacteristic
320C22#1171871611yescharacteristic
321C22#1171873211yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—82no—
326C4—81no—
327C4#1171848411yescharacteristic
328C4#1171848511yescharacteristic
329C4#1171867511yescharacteristic
330C4#1171867911yescharacteristic
331C4#1171870011yescharacteristic
332C4#1171870311yescharacteristic
333C2—21no—
334C2—21no—
335C2—161no—
336C2#1311548711yescharacteristic
337C2#1311550811yescharacteristic
338C2#1311553611yescharacteristic
subgroupG/H
centerC2×C4#88193
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1980C2
socleC22×C13#388
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#1980D13
hypocenterC13#9592
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
1. #13115611C2semidirect
4. #13113123C2semidirect
5. #13112739C2semidirect
6. #13112677C2semidirect
19. #11718139C4semidirect
20. #11718139C4semidirect
21. #11718136C4semidirect
22. #11718136C4semidirect
274. C13#9592semidirect

Maximal subgroups

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

subgroupindex
#131156112
#131134852
#131132872
#131131232
#131127392
#131126772
C13×#19802
#959213