Finite Group Databasebeta

← #15757236

Subgroups — #15757236

Order 3328.

438 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123401C211yesmaximal, characteristic
2#13114857C211yesmaximal, characteristic
3#13113606C211yesmaximal, characteristic, complemented
4#13113592C211yesmaximal, characteristic, complemented
5#13113219C211yesmaximal, characteristic
6#13112739C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×#88155—21no—
9C4×#6127C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13#11718763—21no—
14C2×#88045—21no—
15#11718586C2211yescharacteristic
16#11718585C2211yescharacteristic
17#11718585C2211yescharacteristic
18#11718500—22no—
19#11718498—21no—
20D13×C4⋊C8—21no—
21#11718115—21no—
22#11718072—21no—
23#11718072—21no—
24#11718051C411yescharacteristic, complemented
25#11718051C411yescharacteristic, complemented
26#11718049—22no—
27#11718048C411yescharacteristic, complemented
28#11718048C411yescharacteristic, complemented
29C2×#6127D411yescharacteristic
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C2×C13×C4⋊C4—21no—
33C2×C42×C13—21no—
34C2×C42×C13C2311yescharacteristic
35C4×C22⋊D13—21no—
36C4×C22⋊D13—21no—
37#88180D411yescharacteristic
38C2×#6099—21no—
39C2×#6099—21no—
40#88155—42no—
41#88155—42no—
42C2×#6094—22no—
43C2×C8×D13—22no—
44C4×D52C2×C411yescharacteristic
45C4×D52Q811yescharacteristic
46#88126—21no—
47C42×D13—21no—
48C4×Dic26C2×C411yescharacteristic
49C4×Dic26Q811yescharacteristic
50C13×C4⋊C8—21no—
51C13×C4⋊C8D411yescharacteristic
52C13×C4⋊C8D411yescharacteristic
53C4×C8×C13—21no—
54C4×C8×C13C2×C411yescharacteristic
55C4×C8×C13C2×C411yescharacteristic
56C13×#95—21no—
57C22⋊#1055—21no—
58#88054—22no—
59#88054—22no—
60#88045—42no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055C2×C411yescharacteristic
65C4⋊#1055C2×C411yescharacteristic
66C4⋊#1055D412yes—
67C4×#1055—21no—
68#8904—131nomaximal, Sylow
69C22×C4×C13—41no—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13#4111yescharacteristic
72C22×C4×C13#4111yescharacteristic
73C2×C22⋊D13—21no—
74#6127—21no—
75#6127—21no—
76#6127SD1612yes—
77#6127SD1612yes—
78C2×D52C4⋊C411yescharacteristic
79C2×C4×D13—21no—
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×Dic26C4⋊C411yescharacteristic
83C2×C8×C13—21no—
84C2×C8×C13—21no—
85C2×C8×C13—21no—
86C2×C8×C13—21no—
87C2×C8×C13—42no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—41no—
92C42×C13—41no—
93C42×C13—41no—
94C42×C13C22×C411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13C2×Q811yescharacteristic
98C22⋊Dic13—21no—
99#6103—21no—
100#6103—21no—
101C4⋊Dic13C4⋊C411yescharacteristic
102C4⋊Dic13C4⋊C411yescharacteristic
103#6101—21no—
104#6101—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108#6099—41no—
109#6099—41no—
110#6099—41no—
111#6099—41no—
112C2×#1055—21no—
113C2×#1055—21no—
114C2×#1055—22no—
115C2×#1055—41no—
116#6094—44no—
117C8×D13—44no—
118#2906—131no—
119#1806—131no—
120#1570—131no—
121#1566—131no—
122#1476—131no—
123#1303—131no—
124#1279D1311yescharacteristic, complemented
125C23×C13#12311yescharacteristic
126C22×D13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13C2×C4⋊C411yescharacteristic
134C2×C4×C13C4×D411yescharacteristic
135C2×C4×C13C4×D411yescharacteristic
136C2×C4×C13#12011yescharacteristic
137C2×C4×C13C22⋊Q811yescharacteristic
138C2×C4×C13C22⋊Q811yescharacteristic
139C2×C4×C13C2×SD1611yescharacteristic
140C2×C4×C13C2×SD1611yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C13#13711yescharacteristic
143C22⋊D13—22no—
144C22⋊D13—22no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148D52—21no—
149D52#10612yes—
150C4×D13—22no—
151C4×D13—22no—
152C4×D13—41no—
153C4×D13—41no—
154C4×D13—81no—
155Dic26—21no—
156Dic26#10612yes—
157C8×C13—22no—
158C8×C13—41no—
159C8×C13—41no—
160C8×C13—41no—
161#1055—41no—
162#1055—41no—
163#1055—42no—
164#1055—81no—
165C2×#131—261no—
166C4×#41—131no—
167#431—131no—
168#424—262no—
169#424—261no—
170#423—131no—
171#423—131no—
172#423—261no—
173C2×C4⋊C8—261no—
174C2×C4⋊C8C2×D1311yescharacteristic
175C2×#104—261no—
176C2×C4×C8C2×D1311yescharacteristic
177C4×C4⋊C4C2×D1311yescharacteristic
178#339—261no—
179#334—262no—
180#334—261no—
181#334—261no—
182Q8⋊C8—131no—
183Q8⋊C8—131no—
184D4⋊C8—131no—
185D4⋊C8—131no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13#38511yescharacteristic
189C22×C13#48111yescharacteristic
190C22×C13#48311yescharacteristic
191C2×D13—22no—
192C2×D13—41no—
193C2×D13—41no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—82no—
198C4×C13C2×#10611yescharacteristic
199C4×C13#42811yescharacteristic
200C4×C13#44311yescharacteristic
201C4×C13#44411yescharacteristic
202C4×C13#44811yescharacteristic
203C4×C13#45011yescharacteristic
204Dic13—22no—
205Dic13—41no—
206Dic13—41no—
207C2×#41—131no—
208#131—522no—
209#131—522no—
210C2×M16—262no—
211C2×M16—261no—
212C2×M16—261no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—262no—
216C4×Q8—131no—
217C4×Q8—131no—
218C4×D4—131no—
219C4×D4—131no—
220C4×D4—261no—
221C4×D4—261no—
222#117—131no—
223#117—261no—
224C2×C4⋊C4—21no—
225C2×C42—21no—
226C2×C42—261no—
227C2×C42C22×D1311yescharacteristic
228C4⋊C8—21no—
229C4⋊C8—131no—
230C4⋊C8—131no—
231C4⋊C8—132no—
232C4⋊C8—262no—
233C4⋊C8—262no—
234C4⋊C8—261no—
235C4⋊C8—261no—
236C4⋊C8—261no—
237C4⋊C8D5211yescharacteristic
238C4⋊C8D5211yescharacteristic
239#104—522no—
240C22⋊C8—261no—
241C4×C8—21no—
242C4×C8—261no—
243C4×C8C4×D1311yescharacteristic
244C4×C8C4×D1311yescharacteristic
245#95—21no—
246C2×C13—21no—
247C2×C13—21no—
248C2×C13#185311yescharacteristic
249C2×C13#186111yescharacteristic
250C2×C13#186611yescharacteristic
251D13—42no—
252#41—132no—
253#41—132no—
254#41—261no—
255#41—261no—
256C2×Q8—131no—
257C2×D4—131no—
258C2×D4—261no—
259C22×C4—41no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4#612711yescharacteristic
264C22×C4D4×D1311yescharacteristic
265C22×C4#612911yescharacteristic
266M16—524no—
267M16—521no—
268M16—521no—
269M16—521no—
270M16—521no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—42no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—261no—
279C2×C8—261no—
280C2×C8—262no—
281C2×C8—524no—
282C2×C8—521no—
283C4⋊C4—22no—
284C4⋊C4—41no—
285C4⋊C4—131no—
286C4⋊C4—131no—
287C4⋊C4—261no—
288C4⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C42—41no—
293C42—41no—
294C42—261no—
295C42—261no—
296C42—261no—
297C42C2×C4×D1311yescharacteristic
298C42C2×D5211yescharacteristic
299C42D4×D1311yescharacteristic
300C42Q8×D1311yescharacteristic
301C13#890411yescharacteristic, complemented, Sylow
302C23—261no—
303C23#8813711yescharacteristic
304Q8—132no—
305Q8—261no—
306D4—132no—
307D4—262no—
308D4—262no—
309D4—261no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—261no—
317C2×C4—262no—
318C2×C4—262no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—1041no—
324C2×C4C4×D5211yescharacteristic
325C2×C4#8813511yescharacteristic
326C2×C4#8813611yescharacteristic
327C2×C4C4⋊C4×D1311yescharacteristic
328C2×C4#8815011yescharacteristic
329C2×C4#8815111yescharacteristic
330C2×C4#8816511yescharacteristic
331C2×C4SD16×D1311yescharacteristic
332C2×C4SD16×D1311yescharacteristic
333C2×C4#8817211yescharacteristic
334C8—22no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—522no—
339C8—521no—
340C8—521no—
341C8—1041no—
342C22—21no—
343C22—21no—
344C22—262no—
345C22—521no—
346C22—521no—
347C22#1171832911yescharacteristic
348C22#1171843811yescharacteristic
349C22#1171846611yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—82no—
354C4—262no—
355C4—521no—
356C4—521no—
357C4#1171836111yescharacteristic
358C4#1171837811yescharacteristic
359C4#1171843711yescharacteristic
360C4#1171846711yescharacteristic
361C4D13×#10611yescharacteristic
362C4#1171854211yescharacteristic
363C2—21no—
364C2—21no—
365C2—522no—
366C2#1311503011yescharacteristic
367C2#1311507711yescharacteristic
368C2#1311511411yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC22×C13#385
prime radicalC2×#6127D4
cosocleC2×C42×C13C23
hypercenter#1279D13
hypocenterC13#8904
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. #13113606C2semidirect
4. #13113592C2semidirect
6. #13112739C2semidirect
7. C13×#1279C2semidirect
24. #11718051C4semidirect
25. #11718051C4semidirect
27. #11718048C4semidirect
28. #11718048C4semidirect
124. #1279D13semidirect
301. C13#8904semidirect

Maximal subgroups

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

subgroupindex
#131234012
#131148572
#131136062
#131135922
#131132192
#131127392
C13×#12792
#890413