Finite Group Databasebeta

← #15757229

Subgroups — #15757229

Order 3328.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123501C211yesmaximal, characteristic
2#13114857C211yesmaximal, characteristic
3#13113606C211yesmaximal, characteristic, complemented
4#13113595C211yesmaximal, characteristic, complemented
5#13113219C211yesmaximal, characteristic
6#13112739C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C4×#6127C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C13C2211yescharacteristic
11C4×C13×C4⋊C4C2211yescharacteristic
12#11718771—21no—
13#11718762—21no—
14C2×#88045—21no—
15#11718586C2211yescharacteristic
16#11718585C2211yescharacteristic
17#11718585C2211yescharacteristic
18#11718501—22no—
19#11718496—21no—
20#11718494—21no—
21#11718115—21no—
22#11718072—21no—
23#11718072—21no—
24#11718051C411yescharacteristic, complemented
25#11718051C411yescharacteristic, complemented
26#11718050—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—
40C4×D52C2×C411yescharacteristic
41C4×D52Q811yescharacteristic
42#88126—21no—
43C42×D13—21no—
44C4×Dic26C2×C411yescharacteristic
45C4×Dic26Q811yescharacteristic
46C13×C4⋊C8—21no—
47C13×C4⋊C8D411yescharacteristic
48C13×C4⋊C8D411yescharacteristic
49C4×C8×C13—21no—
50C4×C8×C13C2×C411yescharacteristic
51C4×C8×C13C2×C411yescharacteristic
52C13×#95—21no—
53C22⋊#1055—21no—
54#88060—22no—
55#88060—22no—
56#88055—22no—
57C8×Dic13—22no—
58#88045—42no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055C2×C411yescharacteristic
63C4⋊#1055C2×C411yescharacteristic
64C4⋊#1055D412yes—
65C4×#1055—21no—
66#8903—131nomaximal, Sylow
67C22×C4×C13—41no—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13#4111yescharacteristic
70C22×C4×C13#4111yescharacteristic
71C2×C22⋊D13—21no—
72#6127—21no—
73#6127—21no—
74#6127—21no—
75#6127—21no—
76C2×D52C4⋊C411yescharacteristic
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×Dic26C4⋊C411yescharacteristic
81C2×C8×C13—21no—
82C2×C8×C13—21no—
83C2×C8×C13—21no—
84C2×C8×C13—21no—
85C2×C8×C13—42no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—41no—
90C42×C13—41no—
91C42×C13—41no—
92C42×C13C22×C411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13C2×Q811yescharacteristic
96C22⋊Dic13—21no—
97#6103—21no—
98#6103—21no—
99C4⋊Dic13C4⋊C411yescharacteristic
100C4⋊Dic13C4⋊C411yescharacteristic
101#6101—21no—
102#6101—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106#6099—41no—
107#6099—41no—
108#6099—41no—
109#6099—41no—
110C2×#1055—21no—
111C2×#1055—21no—
112C2×#1055—22no—
113C2×#1055—41no—
114#2925—131no—
115#1806—131no—
116#1570—131no—
117#1567—131no—
118#1476—131no—
119#1303—131no—
120#1279D1311yescharacteristic, complemented
121C23×C13#12311yescharacteristic
122C22×D13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—41no—
126C2×C4×C13—42no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13C2×C4⋊C411yescharacteristic
130C2×C4×C13C4×D411yescharacteristic
131C2×C4×C13C4×D411yescharacteristic
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13C22⋊Q811yescharacteristic
134C2×C4×C13C22⋊Q811yescharacteristic
135C2×C4×C13#13511yescharacteristic
136C2×C4×C13#13511yescharacteristic
137C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C22⋊D13—41no—
140C22⋊D13—41no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144D52—21no—
145D52—21no—
146C4×D13—41no—
147C4×D13—41no—
148C4×D13—41no—
149C4×D13—41no—
150C4×D13—81no—
151Dic26—21no—
152Dic26—21no—
153C8×C13—22no—
154C8×C13—41no—
155C8×C13—41no—
156C8×C13—41no—
157#1055—41no—
158#1055—41no—
159#1055—42no—
160#1055—81no—
161C4×#41—131no—
162#433—262no—
163#432—261no—
164#431—131no—
165#431—261no—
166#423—131no—
167#423—131no—
168C2×C4⋊C8C2×D1311yescharacteristic
169C2×#104—261no—
170#408—261no—
171#405—261no—
172C2×C4×C8C2×D1311yescharacteristic
173C4×C4⋊C4C2×D1311yescharacteristic
174#339—261no—
175#335—262no—
176#334—261no—
177#334—261no—
178Q8⋊C8—131no—
179Q8⋊C8—131no—
180D4⋊C8—131no—
181D4⋊C8—131no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13#38511yescharacteristic
185C22×C13#48211yescharacteristic
186C22×C13#48511yescharacteristic
187C2×D13—41no—
188C2×D13—41no—
189C2×D13—41no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—82no—
194C4×C13#42711yescharacteristic
195C4×C13#42811yescharacteristic
196C4×C13#44311yescharacteristic
197C4×C13#44411yescharacteristic
198C4×C13#44911yescharacteristic
199C4×C13#45211yescharacteristic
200Dic13—41no—
201Dic13—41no—
202Dic13—41no—
203C2×#41—131no—
204C2×M16—261no—
205C2×M16—261no—
206C22×C8—21no—
207C22×C8—21no—
208C4×Q8—131no—
209C4×Q8—131no—
210C4×D4—131no—
211C4×D4—131no—
212C4×D4—261no—
213C4×D4—261no—
214#117—131no—
215#117—261no—
216C2×C4⋊C4—21no—
217C2×C42—21no—
218C2×C42—261no—
219C2×C42C22×D1311yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—131no—
222C4⋊C8—131no—
223C4⋊C8—132no—
224C4⋊C8—261no—
225C4⋊C8—261no—
226C4⋊C8—261no—
227C4⋊C8D5211yescharacteristic
228C4⋊C8D5211yescharacteristic
229#104—522no—
230C22⋊C8—262no—
231C22⋊C8—262no—
232C22⋊C8—261no—
233#97—262no—
234C4×C8—21no—
235C4×C8—262no—
236C4×C8—261no—
237C4×C8C4×D1311yescharacteristic
238C4×C8C4×D1311yescharacteristic
239#95—21no—
240C2×C13—21no—
241C2×C13—21no—
242C2×C13#185411yescharacteristic
243C2×C13#186111yescharacteristic
244C2×C13#186611yescharacteristic
245D13—81no—
246#41—261no—
247#41—261no—
248#41—261no—
249#41—261no—
250C2×Q8—131no—
251C2×D4—131no—
252C2×D4—261no—
253C22×C4—41no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4#612711yescharacteristic
258C22×C4D4×D1311yescharacteristic
259C22×C4#612911yescharacteristic
260M16—521no—
261M16—521no—
262M16—521no—
263M16—521no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—42no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—261no—
272C2×C8—261no—
273C2×C8—262no—
274C2×C8—521no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—131no—
278C4⋊C4—131no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C42—41no—
285C42—41no—
286C42—261no—
287C42—261no—
288C42—261no—
289C42C2×C4×D1311yescharacteristic
290C42C2×D5211yescharacteristic
291C42D4×D1311yescharacteristic
292C42Q8×D1311yescharacteristic
293C13#890311yescharacteristic, complemented, Sylow
294C23—261no—
295C23#8813711yescharacteristic
296Q8—261no—
297Q8—261no—
298D4—261no—
299D4—261no—
300D4—521no—
301D4—521no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—1041no—
316C2×C4C4×D5211yescharacteristic
317C2×C4#8813511yescharacteristic
318C2×C4#8813611yescharacteristic
319C2×C4C4⋊C4×D1311yescharacteristic
320C2×C4#8815011yescharacteristic
321C2×C4#8815111yescharacteristic
322C2×C4#8816611yescharacteristic
323C2×C4#8816811yescharacteristic
324C2×C4#8816911yescharacteristic
325C2×C4#8817311yescharacteristic
326C8—22no—
327C8—41no—
328C8—41no—
329C8—41no—
330C8—522no—
331C8—521no—
332C8—521no—
333C8—1041no—
334C22—21no—
335C22—21no—
336C22—521no—
337C22—521no—
338C22—521no—
339C22#1171832911yescharacteristic
340C22#1171844511yescharacteristic
341C22#1171847511yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—82no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4#1171836111yescharacteristic
350C4#1171837811yescharacteristic
351C4#1171844411yescharacteristic
352C4#1171847211yescharacteristic
353C4#1171852211yescharacteristic
354C4#1171854111yescharacteristic
355C2—21no—
356C2—21no—
357C2—1041no—
358C2#1311503811yescharacteristic
359C2#1311507711yescharacteristic
360C2#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#8903
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. #13113595C2semidirect
6. #13112739C2semidirect
7. C13×#1279C2semidirect
24. #11718051C4semidirect
25. #11718051C4semidirect
27. #11718048C4semidirect
28. #11718048C4semidirect
120. #1279D13semidirect
293. C13#8903semidirect

Maximal subgroups

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

subgroupindex
#131235012
#131148572
#131136062
#131135952
#131132192
#131127392
C13×#12792
#890313