Finite Group Databasebeta

← #15757409

Subgroups — #15757409

Order 3328.

426 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115611C211yesmaximal, characteristic, complemented
2#13113606C211yesmaximal, characteristic, complemented
3#13113485C211yesmaximal, characteristic
4#13113287C211yesmaximal, characteristic
5#13112674C211yesmaximal, characteristic, complemented
6#13112670C211yesmaximal, characteristic, complemented
7C13×#2935C211yesmaximal, characteristic
8C2×C13×#131—21no—
9C13×#532C2211yescharacteristic
10C13×#436—21no—
11C13×#435—22no—
12C8×D4×C13—21no—
13C2×C13×C4⋊C8C2211yescharacteristic
14C13×#408—21no—
15C4×C13×M16C2211yescharacteristic
16C2×#88062—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21#11718150—21no—
22#11718139C411yescharacteristic
23#11718139C411yescharacteristic
24#11718136C411yescharacteristic
25#11718136C411yescharacteristic
26D4⋊#1055—22no—
27#11718072—21no—
28#11718072—21no—
29C2×C13×#41—21no—
30C13×#131—42no—
31C13×#131—42no—
32C2×C13×M16—22no—
33C2×C13×M16D411yescharacteristic
34C2×C13×M16D411yescharacteristic
35C22×C8×C13—22no—
36C22×C8×C13—21no—
37C13×C4⋊Q8C2×C411yescharacteristic
38C13×#127C2×C411yescharacteristic
39C13×#124—21no—
40C13×#121—21no—
41C13×#121Q812yes—
42C4×D4×C13—21no—
43C4×D4×C13D412yes—
44C2×C42×C13C2311yescharacteristic
45C2×#6099—21no—
46C22×#1055—21no—
47C22×#1055—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8D411yescharacteristic
50C13×C4⋊C8D411yescharacteristic
51C13×C22⋊C8—22no—
52C13×C22⋊C8—22no—
53C13×#97—21no—
54C4×C8×C13—21no—
55C22⋊#1055—21no—
56#88062—42no—
57C4⋊#1055—21no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055C2×C411yescharacteristic
61C4⋊#1055C2×C411yescharacteristic
62C4⋊#1055C2×C411yescharacteristic
63C4⋊#1055C2×C411yescharacteristic
64C4×#1055—21no—
65C4×#1055—21no—
66C4×#1055—21no—
67#8932—131nomaximal, Sylow
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—41no—
71C13×#41—41no—
72C2×Q8×C13—21no—
73C2×D4×C13—22no—
74C2×D4×C13—21no—
75C2×D4×C13—21no—
76C2×D4×C13C4⋊C412yes—
77C22×C4×C13—22no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×Q811yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C13×M16—21no—
82C13×M16—21no—
83C13×M16—21no—
84C13×M16—44no—
85C13×M16SD1612yes—
86C2×C8×C13—21no—
87C2×C8×C13—21no—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—44no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4C4⋊C412yes—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—22no—
97C42×C13C22×C411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13#4111yescharacteristic
101#6099—41no—
102#6099—41no—
103C2×#1055—22no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055—21no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055—41no—
113#2935D1311yescharacteristic
114#1950—131no—
115#1570—131no—
116#1540—131no—
117#1492—131no—
118#1278—131no—
119#1277—131no—
120C23×C13—22no—
121C23×C13C22⋊Q811yescharacteristic
122Q8×C13—41no—
123Q8×C13—41no—
124D4×C13—42no—
125D4×C13—42no—
126D4×C13—42no—
127D4×C13—41no—
128D4×C13—41no—
129D4×C13—41no—
130D4×C13—41no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—22no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13C2×C4⋊C411yescharacteristic
138C2×C4×C13C4×D411yescharacteristic
139C2×C4×C13C4×D411yescharacteristic
140C2×C4×C13#12011yescharacteristic
141C2×C4×C13C22⋊Q811yescharacteristic
142C2×C4×C13#12311yescharacteristic
143C2×C4×C13C2×SD1611yescharacteristic
144C2×C4×C13#13511yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
147C8×C13—22no—
148C8×C13—41no—
149C8×C13—41no—
150C8×C13—41no—
151#1055—42no—
152#1055—41no—
153#1055—41no—
154#1055—41no—
155#1055—41no—
156#1055—81no—
157C2×#131—21no—
158#532C2×D1311yescharacteristic
159#436—21no—
160#435—22no—
161C8×D4—21no—
162#431—131no—
163C2×#108—261no—
164#423—131no—
165C2×C4⋊C8—131no—
166C2×C4⋊C8C2×D1311yescharacteristic
167#408—21no—
168C4×M16C2×D1311yescharacteristic
169C2×C4×C8—131no—
170#341—261no—
171#334—261no—
172#334—261no—
173#332—131no—
174#332—131no—
175#331—131no—
176#331—131no—
177D4⋊C8—262no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—42no—
181C22×C13—42no—
182C22×C13—42no—
183C22×C13#38511yescharacteristic
184C22×C13#47611yescharacteristic
185C22×C13#47811yescharacteristic
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—42no—
190C4×C13C4×SD1611yescharacteristic
191C4×C13#44211yescharacteristic
192C4×C13#44311yescharacteristic
193C4×C13#44411yescharacteristic
194C4×C13#44911yescharacteristic
195C4×C13#45011yescharacteristic
196C2×#41—21no—
197#131—42no—
198#131—42no—
199C2×M16—22no—
200C2×M16—261no—
201C2×M16C22⋊D1311yescharacteristic
202C2×M16C22⋊D1311yescharacteristic
203C22×C8—22no—
204C22×C8—21no—
205C22×C8—261no—
206C22×C8—261no—
207C4⋊Q8C4×D1311yescharacteristic
208#127C4×D1311yescharacteristic
209#124—21no—
210#121—21no—
211#121Dic2612yes—
212C4×D4—21no—
213C4×D4C22⋊D1312yes—
214C2×C42C22×D1311yescharacteristic
215#108—522no—
216C4⋊C8—21no—
217C4⋊C8—131no—
218C4⋊C8—131no—
219C4⋊C8—131no—
220C4⋊C8—131no—
221C4⋊C8—261no—
222C4⋊C8—261no—
223C4⋊C8—261no—
224C4⋊C8C22⋊D1311yescharacteristic
225C4⋊C8C22⋊D1311yescharacteristic
226C22⋊C8—22no—
227C22⋊C8—22no—
228C22⋊C8—261no—
229#97—21no—
230C4×C8—21no—
231C4×C8—261no—
232C4×C8—261no—
233C4×C8—261no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—82no—
237C2×C13#185811yescharacteristic
238C2×C13#186411yescharacteristic
239C2×C13#186611yescharacteristic
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4#610112yes—
249C22×C4—22no—
250C22×C4C2×Dic2611yescharacteristic
251C22×C4#612711yescharacteristic
252C22×C4C2×C22⋊D1311yescharacteristic
253M16—21no—
254M16—21no—
255M16—21no—
256M16—44no—
257M16—521no—
258M16—521no—
259M16#610512yes—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—44no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—262no—
268C2×C8—261no—
269C2×C8—261no—
270C2×C8—261no—
271C2×C8—261no—
272C2×C8—521no—
273C2×C8—521no—
274C2×C8—521no—
275C2×C8—521no—
276C2×C8—521no—
277C4⋊C4—21no—
278C4⋊C4#610112yes—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C42C2×C4×D1311yescharacteristic
282C42#612711yescharacteristic
283C42C2×C22⋊D1311yescharacteristic
284C42C2×C22⋊D1311yescharacteristic
285C13#893211yescharacteristic, complemented, Sylow
286C23—22no—
287C23#8817811yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—42no—
291D4—42no—
292D4—42no—
293D4—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4C2×#610111yescharacteristic
304C2×C4#8817811yescharacteristic
305C2×C4C4×C22⋊D1311yescharacteristic
306C2×C4C4×C22⋊D1311yescharacteristic
307C2×C4#8818311yescharacteristic
308C2×C4#8818611yescharacteristic
309C2×C4C2×#610511yescharacteristic
310C2×C4#8820311yescharacteristic
311C2×C4#8820411yescharacteristic
312C2×C4#8820711yescharacteristic
313C8—22no—
314C8—41no—
315C8—41no—
316C8—41no—
317C8—522no—
318C8—521no—
319C8—521no—
320C8—521no—
321C8—521no—
322C8—1041no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22#1171866911yescharacteristic
329C22#1171867011yescharacteristic
330C22#1171887111yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4#1171867511yescharacteristic
336C4C4×#610511yescharacteristic
337C4#1171880511yescharacteristic
338C4#1171880611yescharacteristic
339C4#1171887911yescharacteristic
340C4#1171889911yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1311505611yescharacteristic
345C2#1311509711yescharacteristic
346C2#1311511111yescharacteristic
subgroupG/H
centerC2×C4#88207
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2935C2
socleC22×C13#385
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#2935D13
hypocenterC13#8932
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
1. #13115611C2semidirect
2. #13113606C2semidirect
5. #13112674C2semidirect
6. #13112670C2semidirect
285. C13#8932semidirect

Maximal subgroups

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

subgroupindex
#131156112
#131136062
#131134852
#131132872
#131126742
#131126702
C13×#29352
#893213