Finite Group Databasebeta

← #15765538

Subgroups — #15765538

Order 3328.

562 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718739C211yesmaximal, characteristic, complemented
2C2×#11718503C211yesmaximal, characteristic
3C2×#11718745C211yesmaximal, characteristic
4#13115629C211yesmaximal, characteristic
5C2×#11718073C211yesmaximal, characteristic, complemented
6#13112670C211yesmaximal, characteristic, complemented
7C2×C13×#333C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×#88061—21no—
14C2×#88060—22no—
15C2×#88057—21no—
16#11718745—22no—
17#11718745—22no—
18#11718739—22no—
19#11718739—22no—
20C2×#88049—21no—
21C2×#88048—21no—
22C2×#88047—22no—
23C2×C4⋊#1055C2211yescharacteristic
24C2×C4×#1055C2211yescharacteristic
25#11718503—22no—
26#11718503—22no—
27C13×#333—22no—
28#11718073—22no—
29C22×Q8×C13—21no—
30C22×D52D411yescharacteristic
31C22×C4×D13—21no—
32C22×Dic26—21no—
33C22×C8×C13—21no—
34C22×C8×C13—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8D412yes—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C42×C13C2311yescharacteristic
42C2×#6103—21no—
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13D411yescharacteristic
46C22×#1055—21no—
47C22×#1055D412yes—
48C4×D52—21no—
49C4×D52—21no—
50C4×D52—21no—
51C4×D52—21no—
52#88123—21no—
53#88123—21no—
54#88123—21no—
55#88123D412yes—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8D412yes—
60#88061—24no—
61#88060—44no—
62#88057—24no—
63#88049—24no—
64#88048—24no—
65#88047—28no—
66C4⋊#1055—21no—
67C4⋊#1055D412yes—
68C4×#1055—21no—
69C4×#1055—21no—
70#10278—131nomaximal, Sylow
71C23×D13—21no—
72C2×Q8×C13—22no—
73C2×Q8×C13—41no—
74C2×Q8×C13—82no—
75C22×C4×C13—41no—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C22×Dic13—21no—
80C22×Dic13—41no—
81C2×D52—21no—
82C2×D52—21no—
83C2×D52—21no—
84C2×D52—21no—
85C2×D52—21no—
86C2×D52Q1612yes—
87C2×C4×D13—41no—
88C2×C4×D13—41no—
89C2×C4×D13—42no—
90C2×C4×D13—42no—
91C2×Dic26—22no—
92C2×Dic26—41no—
93C2×Dic26—82no—
94C2×C8×C13—22no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—42no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C42×C13C2×D411yescharacteristic
104C42×C13C2×D411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13C2×D411yescharacteristic
107#6103—41no—
108#6103—41no—
109C4⋊Dic13—22no—
110C4⋊Dic13—22no—
111C4⋊Dic13—21no—
112C4⋊Dic13—21no—
113C4⋊Dic13—41no—
114C4⋊Dic13—41no—
115C2×#1055—22no—
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#1055SD1614yes—
121C2×#500—131no—
122C2×#476—131no—
123C2×#476—131no—
124#1954—131no—
125C2×#333—131no—
126C2×#333D1311yescharacteristic, complemented
127#1277—131no—
128C23×C13#12111yescharacteristic
129C22×D13—22no—
130C22×D13—41no—
131C22×D13—42no—
132C22×D13—41no—
133C22×D13—42no—
134Q8×C13—82no—
135Q8×C13—82no—
136C2×C4×C13—22no—
137C2×C4×C13—42no—
138C2×C4×C13—82no—
139C2×C4×C13#12011yescharacteristic
140C2×C4×C13#12011yescharacteristic
141C2×C4×C13#12011yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13#12711yescharacteristic
145C2×C4×C13C2×SD1612yes—
146C2×C4×C13C2×Q1611yescharacteristic
147C2×C4×C13#13511yescharacteristic
148C2×C4×C13#13712yes—
149C2×C4×C13#13711yescharacteristic
150C2×C4×C13#13711yescharacteristic
151C2×Dic13—42no—
152C2×Dic13—41no—
153C2×Dic13—42no—
154C2×Dic13—82no—
155D52—22no—
156D52—22no—
157D52—41no—
158D52—41no—
159C4×D13—82no—
160C4×D13—81no—
161C4×D13—81no—
162Dic26—82no—
163Dic26—82no—
164C8×C13—42no—
165C8×C13—81no—
166#1055—24no—
167#1055—42no—
168C2×C4⋊Q8—131no—
169C2×C4⋊Q8C2×D1311yescharacteristic
170C2×C4×D4—131no—
171#500—262no—
172#500—262no—
173#476—262no—
174#476—262no—
175#476—262no—
176#476—262no—
177C2×#107—262no—
178C2×#106—261no—
179C2×#106—261no—
180C2×C4⋊C8—131no—
181C2×C4⋊C8C2×D1311yescharacteristic
182C2×C4⋊C8C2×D1311yescharacteristic
183C2×#102—261no—
184C2×#102—261no—
185C2×C22⋊C8—262no—
186C2×C4×C8—131no—
187#333—22no—
188#333—262no—
189C22×C13#39211yescharacteristic
190C22×C13#46112yes—
191C22×C13#46711yescharacteristic
192C22×C13#47011yescharacteristic
193C22×C13#47212yes—
194C2×D13—44no—
195C2×D13—42no—
196C2×D13—82no—
197C2×D13—81no—
198C2×D13—81no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—82no—
202C4×C13#44812yes—
203C4×C13#45111yescharacteristic
204C4×C13#45111yescharacteristic
205C4×C13#45211yescharacteristic
206C4×C13#45211yescharacteristic
207C4×C13#49211yescharacteristic
208C4×C13#49711yescharacteristic
209Dic13—81no—
210Dic13—82no—
211C22×Q8—21no—
212C22×Q8—261no—
213C22×D4—131no—
214C23×C4—261no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—132no—
218C22×C8—261no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—132no—
223C4⋊Q8—261no—
224C4⋊Q8—261no—
225C4⋊Q8—261no—
226C4⋊Q8D5212yes—
227C4×D4—261no—
228C4×D4—261no—
229C4×D4—261no—
230C4×D4—261no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—131no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4—261no—
236C2×C22⋊C4—261no—
237C2×C42C22×D1311yescharacteristic
238#107—268no—
239#106—264no—
240#106—264no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—132no—
245C4⋊C8—261no—
246C4⋊C8C22⋊D1312yes—
247#102—264no—
248#102—264no—
249C22⋊C8—524no—
250C4×C8—261no—
251C4×C8—261no—
252C2×C13#167512yes—
253C2×C13#169512yes—
254C2×C13#200111yescharacteristic
255C2×C13#201311yescharacteristic
256C2×C13#201811yescharacteristic
257D13—82no—
258C24—261no—
259C2×Q8—22no—
260C2×Q8—41no—
261C2×Q8—82no—
262C2×Q8—262no—
263C2×Q8—521no—
264C2×Q8—1042no—
265C2×D4—132no—
266C2×D4—261no—
267C2×D4—261no—
268C2×D4—261no—
269C2×D4—261no—
270C2×D4—261no—
271C22×C4—41no—
272C22×C4—261no—
273C22×C4—521no—
274C22×C4—521no—
275C22×C4—522no—
276C22×C4—522no—
277C22×C4—521no—
278C22×C4#612711yescharacteristic
279C22×C4D4×D1311yescharacteristic
280C22×C4D4×D1311yescharacteristic
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—42no—
285C2×C8—41no—
286C2×C8—134no—
287C2×C8—262no—
288C2×C8—262no—
289C2×C8—262no—
290C2×C8—521no—
291C2×C8—521no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—261no—
297C4⋊C4—262no—
298C4⋊C4—262no—
299C4⋊C4—261no—
300C4⋊C4—521no—
301C4⋊C4—521no—
302C22⋊C4—521no—
303C22⋊C4—521no—
304C42C2×D5211yescharacteristic
305C42D4×D1311yescharacteristic
306C42D4×D1311yescharacteristic
307C42C2×C22⋊D1311yescharacteristic
308C13#1027811yescharacteristic, complemented, Sylow
309C23—262no—
310C23—522no—
311C23—521no—
312C23—522no—
313C23—521no—
314C23#8813811yescharacteristic
315Q8—82no—
316Q8—82no—
317Q8—1042no—
318Q8—1042no—
319D4—262no—
320D4—262no—
321D4—521no—
322D4—521no—
323C2×C4—22no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—522no—
327C2×C4—521no—
328C2×C4—522no—
329C2×C4—1042no—
330C2×C4—1042no—
331C2×C4—1041no—
332C2×C4—1041no—
333C2×C4#8813611yescharacteristic
334C2×C4#8813611yescharacteristic
335C2×C4#8813811yescharacteristic
336C2×C4SD16×D1312yes—
337C2×C4#8816911yescharacteristic
338C2×C4#8817011yescharacteristic
339C2×C4Q16×D1311yescharacteristic
340C2×C4#8817212yes—
341C2×C4#8817211yescharacteristic
342C2×C4#8818411yescharacteristic
343C2×C4#8819111yescharacteristic
344C2×C4#8819411yescharacteristic
345C8—42no—
346C8—81no—
347C8—264no—
348C8—522no—
349C22—524no—
350C22—522no—
351C22—1041no—
352C22—1041no—
353C22—1042no—
354C22#1171841012yes—
355C22#1171847411yescharacteristic
356C22#1171847711yescharacteristic
357C22#1171847912yes—
358C22#1171862111yescharacteristic
359C4—21no—
360C4—21no—
361C4—82no—
362C4—1041no—
363C4—1042no—
364C4#1171846712yes—
365C4#1171846911yescharacteristic
366C4#1171847111yescharacteristic
367C4#1171883411yescharacteristic
368C4#1171883611yescharacteristic
369C4#1171884711yescharacteristic
370C4#1171885111yescharacteristic
371C2—1042no—
372C2#1311423412yes—
373C2#1311435812yes—
374C2#1311584511yescharacteristic
375C2#1311592011yescharacteristic
376C2#1311594411yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#333C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenterC2×#333D13
hypocenterC13#10278
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
1. C2×#11718739C2semidirect
5. C2×#11718073C2semidirect
6. #13112670C2semidirect
7. C2×C13×#333C2semidirect
126. C2×#333D13semidirect
308. C13#10278semidirect

Maximal subgroups

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

subgroupindex
C2×#117187392
C2×#117185032
C2×#117187452
#131156292
C2×#117180732
#131126702
C2×C13×#3332
#1027813