Finite Group Databasebeta

← #15767458

Subgroups — #15767458

Order 3328.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115796C211yesmaximal, characteristic
2#13115758C211yesmaximal, characteristic
3#13115592C211yesmaximal, characteristic
4#13115552C211yesmaximal, characteristic
5C2×#11718072C211yesmaximal, characteristic
6C2×#11718078C211yesmaximal, characteristic
7C13×#1296C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C2×#88056—21no—
13C2×#88056—21no—
14C2×#88054—21no—
15C2×#88047—21no—
16C4×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19#11718142—21no—
20#11718121—21no—
21#11718121—21no—
22#11718121—21no—
23#11718078—22no—
24#11718072—22no—
25C22×Dic26—21no—
26C22×C8×C13—21no—
27C22×C8×C13—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13D411yescharacteristic
35C2×C4⋊Dic13D411yescharacteristic
36C2×C4×Dic13—21no—
37C22×#1055—21no—
38C22×#1055D411yescharacteristic
39C22×#1055D411yescharacteristic
40#88123—21no—
41#88123—21no—
42#88123—21no—
43#88123Q812yes—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48#88071—21no—
49#88056—42no—
50#88056—42no—
51#88054—42no—
52#88047—42no—
53C4⋊#1055—21no—
54C4⋊#1055D412yes—
55C4×#1055—21no—
56C4×#1055—21no—
57#10590—131nomaximal, Sylow
58C22×C4×C13—41no—
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13#4111yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13—41no—
65C2×Dic26—22no—
66C2×Dic26—41no—
67C2×Dic26—41no—
68C2×Dic26—41no—
69C2×Dic26—41no—
70C2×Dic26—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—81no—
82C42×C13C2×D411yescharacteristic
83C42×C13C2×Q811yescharacteristic
84C42×C13#4111yescharacteristic
85C42×C13#4111yescharacteristic
86C4⋊Dic13—21no—
87C4⋊Dic13—22no—
88C4⋊Dic13—22no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93C4⋊Dic13SD1612yes—
94C4×Dic13—41no—
95C4×Dic13—41no—
96C2×#1055—21no—
97C2×#1055—21no—
98C2×#1055—22no—
99C2×#1055—21no—
100C2×#1055—21no—
101C2×#1055—21no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055Q1612yes—
105#1990—131no—
106#1981—131no—
107#1947—131no—
108#1939—131no—
109C2×#334—131no—
110C2×#332—131no—
111#1296D1311yescharacteristic
112C23×C13#12111yescharacteristic
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—81no—
116C2×C4×C13—81no—
117C2×C4×C13—81no—
118C2×C4×C13#12111yescharacteristic
119C2×C4×C13#12111yescharacteristic
120C2×C4×C13C22⋊Q811yescharacteristic
121C2×C4×C13C22⋊Q811yescharacteristic
122C2×C4×C13C22⋊Q811yescharacteristic
123C2×C4×C13#12611yescharacteristic
124C2×C4×C13C2×SD1611yescharacteristic
125C2×C4×C13C2×Q1611yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13#13511yescharacteristic
128C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C13#13711yescharacteristic
132C2×Dic13—22no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—42no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—81no—
140C2×Dic13—81no—
141Dic26—42no—
142Dic26—42no—
143Dic26—81no—
144Dic26—81no—
145C8×C13—81no—
146C8×C13—81no—
147#1055—22no—
148#1055—42no—
149#1055—41no—
150C2×C4⋊Q8—131no—
151C2×#107—261no—
152C2×C4⋊C8—131no—
153C2×C4⋊C8—261no—
154C2×C4⋊C8C2×D1311yescharacteristic
155C2×C4⋊C8C2×D1311yescharacteristic
156C2×#103—261no—
157C2×#103—261no—
158C2×C4×C8—131no—
159#384C2×D1311yescharacteristic
160C4×C4⋊C4—131no—
161#340—261no—
162#340—261no—
163#340—261no—
164#336—261no—
165#334—262no—
166#332—262no—
167C22×C13#39611yescharacteristic
168C22×C13#46211yescharacteristic
169C22×C13#46311yescharacteristic
170C22×C13#46511yescharacteristic
171C22×C13#46911yescharacteristic
172C22×C13#47111yescharacteristic
173C22×C13#47311yescharacteristic
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—161no—
177C4×C13#46011yescharacteristic
178C4×C13#46311yescharacteristic
179C4×C13#46711yescharacteristic
180C4×C13#46811yescharacteristic
181C4×C13#47611yescharacteristic
182C4×C13#47711yescharacteristic
183C4×C13#47811yescharacteristic
184C4×C13#47911yescharacteristic
185Dic13—42no—
186Dic13—82no—
187Dic13—81no—
188C22×Q8—261no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—131no—
192C22×C8—131no—
193C22×C8—261no—
194C4⋊Q8—132no—
195C4⋊Q8—261no—
196C4⋊Q8—261no—
197C4⋊Q8—261no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C42—261no—
206C2×C42C22×D1311yescharacteristic
207#107—522no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—132no—
213C4⋊C8—261no—
214C4⋊C8—522no—
215#103—522no—
216#103—522no—
217C4×C8—261no—
218C4×C8—261no—
219#95—261no—
220C2×C13#167211yescharacteristic
221C2×C13#167911yescharacteristic
222C2×C13#169411yescharacteristic
223C2×C13#170111yescharacteristic
224C2×C13#206411yescharacteristic
225C2×C13#206511yescharacteristic
226C2×C13#206811yescharacteristic
227C2×Q8—262no—
228C2×Q8—521no—
229C2×Q8—521no—
230C2×Q8—521no—
231C2×Q8—521no—
232C2×Q8—521no—
233C22×C4—41no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—521no—
237C22×C4#612711yescharacteristic
238C22×C4D4×D1311yescharacteristic
239C22×C4D4×D1311yescharacteristic
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—132no—
247C2×C8—261no—
248C2×C8—261no—
249C2×C8—261no—
250C2×C8—262no—
251C2×C8—261no—
252C2×C8—261no—
253C2×C8—521no—
254C2×C8—521no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—81no—
260C4⋊C4—132no—
261C4⋊C4—261no—
262C4⋊C4—262no—
263C4⋊C4—262no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C42—521no—
269C42—521no—
270C42#612711yescharacteristic
271C42#612711yescharacteristic
272C42D4×D1311yescharacteristic
273C42Q8×D1311yescharacteristic
274C13#1059011yescharacteristic, complemented, Sylow
275C23#8813811yescharacteristic
276Q8—522no—
277Q8—522no—
278Q8—1041no—
279Q8—1041no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—262no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—522no—
292C2×C4—1041no—
293C2×C4—1041no—
294C2×C4#8813011yescharacteristic
295C2×C4#8813811yescharacteristic
296C2×C4#8813811yescharacteristic
297C2×C4#8815011yescharacteristic
298C2×C4#8815011yescharacteristic
299C2×C4#8815011yescharacteristic
300C2×C4#8816511yescharacteristic
301C2×C4#8816511yescharacteristic
302C2×C4SD16×D1311yescharacteristic
303C2×C4#8816811yescharacteristic
304C2×C4#8816911yescharacteristic
305C2×C4#8817011yescharacteristic
306C2×C4Q16×D1311yescharacteristic
307C2×C4#8817311yescharacteristic
308C8—81no—
309C8—81no—
310C8—262no—
311C8—521no—
312C8—522no—
313C22#1171833711yescharacteristic
314C22#1171840911yescharacteristic
315C22#1171841611yescharacteristic
316C22#1171844311yescharacteristic
317C22#1171844811yescharacteristic
318C22#1171845411yescharacteristic
319C22#1171846811yescharacteristic
320C4—21no—
321C4—21no—
322C4—161no—
323C4—522no—
324C4—1041no—
325C4—1042no—
326C4#1171842311yescharacteristic
327C4#1171844111yescharacteristic
328C4#1171847411yescharacteristic
329C4#1171848011yescharacteristic
330C4#1171851811yescharacteristic
331C4#1171853111yescharacteristic
332C4#1171853611yescharacteristic
333C4#1171855211yescharacteristic
334C2#1311422111yescharacteristic
335C2#1311425811yescharacteristic
336C2#1311435311yescharacteristic
337C2#1311439611yescharacteristic
338C2#1311620411yescharacteristic
339C2#1311621111yescharacteristic
340C2#1311623211yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socle, prime radicalC23×C13#121
hypercenter#1296D13
hypocenterC13#10590
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
274. C13#10590semidirect

Maximal subgroups

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

subgroupindex
#131157962
#131157582
#131155922
#131155522
C2×#117180722
C2×#117180782
C13×#12962
#1059013