Finite Group Databasebeta

← #15761451

Subgroups — #15761451

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#13115756C211yesmaximal, characteristic
2#13115612C211yesmaximal, characteristic, complemented
3#13113287C211yesmaximal, characteristic
4#13113126C211yesmaximal, characteristic, complemented
5#13112738C211yesmaximal, characteristic, complemented
6#13112675C211yesmaximal, characteristic, complemented
7C13×#1540C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×#88077—21no—
12C2×#88077—21no—
13C2×#88059—21no—
14C4×C4⋊Dic13C2211yescharacteristic
15#11718585C2211yescharacteristic
16C4×#6099C2211yescharacteristic
17C2×C4×#1055C2211yescharacteristic
18C13×#332C411yescharacteristic, complemented
19C13×#332C411yescharacteristic, complemented
20C13×#331C411yescharacteristic, complemented
21C13×#331C411yescharacteristic, complemented
22#11718144—21no—
23D4⋊#1055—21no—
24D4⋊#1055—21no—
25#11718047—21no—
26#11718046—21no—
27C2×C13×#41—21no—
28C22×C8×C13—21no—
29C13×C4⋊Q8C2×C411yescharacteristic
30C13×#127C2×C411yescharacteristic
31C13×#124—21no—
32C13×#121—21no—
33C13×#121—21no—
34C4×D4×C13—21no—
35C4×D4×C13—21no—
36C2×C42×C13C2311yescharacteristic
37C2×C4⋊Dic13—21no—
38C2×C4×Dic13—21no—
39C2×#6099—21no—
40C2×#6099D411yescharacteristic
41C2×#6099D411yescharacteristic
42C22×#1055—21no—
43C13×C4⋊C8—21no—
44C13×C4⋊C8C2×C411yescharacteristic
45C13×C4⋊C8C2×C411yescharacteristic
46C13×C4⋊C8C2×C411yescharacteristic
47C13×C4⋊C8C2×C411yescharacteristic
48C13×C22⋊C8—21no—
49C4×C8×C13—21no—
50#88077—42no—
51#88077—42no—
52#88071—21no—
53#88059—42no—
54C4⋊#1055—21no—
55C4⋊#1055—21no—
56#88043—21no—
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×C13C2×D411yescharacteristic
73C22×C4×C13#4111yescharacteristic
74C22×C4×C13#4111yescharacteristic
75C22×Dic13—41no—
76C2×C8×C13—21no—
77C2×C8×C13—21no—
78C2×C8×C13—21no—
79C2×C8×C13—21no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C42×C13C22×C411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C42×C13#4111yescharacteristic
89C42×C13#4111yescharacteristic
90C4⋊Dic13—22no—
91C4⋊Dic13—41no—
92C4×Dic13—41no—
93C4×Dic13—41no—
94#6099—21no—
95#6099—21no—
96#6099—21no—
97#6099—21no—
98#6099—41no—
99#6099—41no—
100C2×#1055—21no—
101C2×#1055—21no—
102C2×#1055—21no—
103C2×#1055—21no—
104C2×#1055—42no—
105C2×#1055—41no—
106#1980—131no—
107#1950—131no—
108#1540D1311yescharacteristic
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—41no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13#11711yescharacteristic
131C2×C4×C13C4×D411yescharacteristic
132C2×C4×C13C4×D411yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12311yescharacteristic
135C2×C4×C13#12611yescharacteristic
136C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C13#13711yescharacteristic
140C2×Dic13—42no—
141C2×Dic13—81no—
142C2×Dic13—81no—
143C8×C13—41no—
144C8×C13—41no—
145C8×C13—41no—
146C8×C13—41no—
147#1055—22no—
148#1055—41no—
149#1055—41no—
150#1055—41no—
151#1055—81no—
152#532C2×D1311yescharacteristic
153#431C2×D1311yescharacteristic
154C2×#108—261no—
155#423—131no—
156C2×C4⋊C8C2×D1311yescharacteristic
157C2×#104—261no—
158C2×#104—261no—
159C4×M16—131no—
160C2×C4×C8—131no—
161C4×C4⋊C4—131no—
162#341—261no—
163#332Dic1311yescharacteristic, complemented
164#332Dic1311yescharacteristic, complemented
165#331Dic1311yescharacteristic, complemented
166#331Dic1311yescharacteristic, complemented
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—81no—
183C4×C13#44011yescharacteristic
184C4×C13#44211yescharacteristic
185C4×C13#44311yescharacteristic
186C4×C13#44411yescharacteristic
187C4×C13#46811yescharacteristic
188C4×C13#46911yescharacteristic
189Dic13—82no—
190C2×#41—21no—
191C2×M16—131no—
192C2×M16—131no—
193C2×M16—261no—
194C22×C8—21no—
195C22×C8—261no—
196C4⋊Q8C2×Dic1311yescharacteristic
197#127C2×Dic1311yescharacteristic
198#124—21no—
199#121—21no—
200#121—21no—
201C4×D4—21no—
202C4×D4—21no—
203C2×C4⋊C4—261no—
204C2×C42—261no—
205C2×C42C22×D1311yescharacteristic
206#108—522no—
207C4⋊C8—21no—
208C4⋊C8—261no—
209C4⋊C8—261no—
210C4⋊C8C2×Dic1311yescharacteristic
211C4⋊C8C2×Dic1311yescharacteristic
212C4⋊C8C2×Dic1311yescharacteristic
213C4⋊C8C2×Dic1311yescharacteristic
214#104—522no—
215#104—522no—
216C22⋊C8—21no—
217#97—261no—
218C4×C8—21no—
219C4×C8—131no—
220C4×C8—131no—
221C4×C8—261no—
222C4×C8—261no—
223#95—261no—
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—521no—
241C22×C4#612711yescharacteristic
242C22×C4D4×D1311yescharacteristic
243C22×C4#612911yescharacteristic
244M16—261no—
245M16—261no—
246M16—261no—
247M16—261no—
248M16—521no—
249M16—521no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—261no—
257C2×C8—261no—
258C2×C8—261no—
259C2×C8—261no—
260C2×C8—522no—
261C2×C8—521no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—262no—
265C4⋊C4—521no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—521no—
269C42—521no—
270C42#612711yescharacteristic
271C42D4×D1311yescharacteristic
272C42#612911yescharacteristic
273C42C22×Dic1311yescharacteristic
274C13#959211yescharacteristic, complemented, Sylow
275C23—41no—
276C23#8813911yescharacteristic
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—41no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—522no—
293C2×C4—1041no—
294C2×C4—1041no—
295C2×C4#8813311yescharacteristic
296C2×C4#8813711yescharacteristic
297C2×C4#8813811yescharacteristic
298C2×C4#8816511yescharacteristic
299C2×C4#8816511yescharacteristic
300C2×C4#8816811yescharacteristic
301C2×C4#8816911yescharacteristic
302C2×C4#8818011yescharacteristic
303C2×C4D4×Dic1311yescharacteristic
304C2×C4D4×Dic1311yescharacteristic
305C8—41no—
306C8—41no—
307C8—41no—
308C8—41no—
309C8—262no—
310C8—521no—
311C8—521no—
312C8—521no—
313C8—1041no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#1171842511yescharacteristic
320C22#1171842611yescharacteristic
321C22#1171861211yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—81no—
326C4—1042no—
327C4#1171844111yescharacteristic
328C4#1171844311yescharacteristic
329C4#1171881311yescharacteristic
330C4#1171882511yescharacteristic
331C4#1171885711yescharacteristic
332C4#1171885811yescharacteristic
333C2—21no—
334C2—21no—
335C2—161no—
336C2#1311548611yescharacteristic
337C2#1311550711yescharacteristic
338C2#1311553511yescharacteristic
subgroupG/H
centerC2×C4#88138
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1540C2
socleC22×C13#388
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#1540D13
hypocenterC13#9592
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
2. #13115612C2semidirect
4. #13113126C2semidirect
5. #13112738C2semidirect
6. #13112675C2semidirect
18. C13×#332C4semidirect
19. C13×#332C4semidirect
20. C13×#331C4semidirect
21. C13×#331C4semidirect
163. #332Dic13semidirect
164. #332Dic13semidirect
165. #331Dic13semidirect
166. #331Dic13semidirect
274. C13#9592semidirect

Maximal subgroups

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

subgroupindex
#131157562
#131156122
#131132872
#131131262
#131127382
#131126752
C13×#15402
#959213