Finite Group Databasebeta

← #15765496

Subgroups — #15765496

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718740C211yesmaximal, characteristic, complemented
2C2×#11718503C211yesmaximal, characteristic
3C2×#11718744C211yesmaximal, characteristic
4#13115629C211yesmaximal, characteristic
5C2×#11718073C211yesmaximal, characteristic, complemented
6#13112670C211yesmaximal, characteristic, complemented
7C2×C13×#332C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C22×#6106—21no—
10C2×C4×D52C2211yescharacteristic
11C2×#88123C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×#88075—21no—
15C2×#88061—21no—
16C2×#88060—22no—
17C2×#88057—21no—
18#11718744—22no—
19#11718744—22no—
20#11718740—22no—
21#11718740—22no—
22C2×#88048—22no—
23C2×C4⋊#1055C2211yescharacteristic
24C2×C4×#1055C2211yescharacteristic
25#11718503—22no—
26#11718503—22no—
27C13×#332—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×#6106—24no—
43C2×#6106—42no—
44C2×#6106—42no—
45C2×#6103—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13D411yescharacteristic
49C22×#1055—21no—
50C22×#1055D412yes—
51C4×D52—21no—
52C4×D52—21no—
53C4×D52—21no—
54C4×D52—21no—
55#88123—21no—
56#88123—21no—
57#88123—21no—
58#88123D412yes—
59C13×C4⋊C8—21no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8D412yes—
63#88075—24no—
64#88061—24no—
65#88060—44no—
66#88057—24no—
67#88048—28no—
68C4⋊#1055—21no—
69C4⋊#1055D412yes—
70C4×#1055—21no—
71C4×#1055—21no—
72#10271—131nomaximal, Sylow
73C23×D13—21no—
74C2×Q8×C13—22no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C22×Dic13—21no—
85C22×Dic13—41no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×D52—21no—
91C2×D52SD1612yes—
92C2×C4×D13—41no—
93C2×C4×D13—41no—
94C2×C4×D13—42no—
95C2×C4×D13—42no—
96C2×Dic26—22no—
97C2×Dic26—41no—
98C2×Dic26—82no—
99C2×C8×C13—22no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C2×C8×C13—42no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C42×C13C2×D411yescharacteristic
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112#6106—48no—
113#6103—41no—
114#6103—41no—
115C4⋊Dic13—21no—
116C4⋊Dic13—22no—
117C4⋊Dic13—22no—
118C4⋊Dic13—21no—
119C4⋊Dic13—41no—
120C4⋊Dic13—41no—
121C2×#1055—22no—
122C2×#1055—22no—
123C2×#1055—22no—
124C2×#1055—41no—
125C2×#1055—41no—
126C2×#1055SD1614yescomplemented
127C2×#498—131no—
128C2×#476—131no—
129C2×#461—131no—
130#1954—131no—
131C2×#333—131no—
132C2×#332D1311yescharacteristic, complemented
133#1277—131no—
134C23×C13#12111yescharacteristic
135C22×D13—22no—
136C22×D13—41no—
137C22×D13—42no—
138C22×D13—41no—
139C22×D13—42no—
140Q8×C13—42no—
141Q8×C13—42no—
142Q8×C13—81no—
143Q8×C13—81no—
144C2×C4×C13—22no—
145C2×C4×C13—42no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13#12011yescharacteristic
149C2×C4×C13#12011yescharacteristic
150C2×C4×C13#12011yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12711yescharacteristic
154C2×C4×C13C2×SD1611yescharacteristic
155C2×C4×C13C2×SD1612yes—
156C2×C4×C13#13511yescharacteristic
157C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C13#13711yescharacteristic
159C2×C4×C13#13712yes—
160C2×Dic13—42no—
161C2×Dic13—41no—
162C2×Dic13—42no—
163C2×Dic13—82no—
164D52—22no—
165D52—22no—
166D52—41no—
167D52—41no—
168C4×D13—82no—
169C4×D13—81no—
170C4×D13—81no—
171Dic26—82no—
172Dic26—82no—
173C8×C13—42no—
174C8×C13—81no—
175#1055—24no—
176#1055—42no—
177C22×SD16—261no—
178C2×C4⋊Q8—131no—
179C2×C4⋊Q8C2×D1311yescharacteristic
180C2×C4×D4—131no—
181#498—262no—
182#498—262no—
183#476—262no—
184#476—262no—
185#461—262no—
186#461—262no—
187C2×#106—262no—
188C2×#106—261no—
189C2×C4⋊C8—131no—
190C2×C4⋊C8C2×D1311yescharacteristic
191C2×C4⋊C8C2×D1311yescharacteristic
192C2×#103—261no—
193C2×#102—261no—
194C2×C22⋊C8—262no—
195C2×C4×C8—131no—
196#333—262no—
197#332—22no—
198C22×C13#39211yescharacteristic
199C22×C13#46112yes—
200C22×C13#46511yescharacteristic
201C22×C13#46811yescharacteristic
202C22×C13#47112yes—
203C2×D13—44no—
204C2×D13—42no—
205C2×D13—82no—
206C2×D13—81no—
207C2×D13—81no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—82no—
211C4×C13#44812yes—
212C4×C13#44811yescharacteristic
213C4×C13#44911yescharacteristic
214C4×C13#45011yescharacteristic
215C4×C13#45211yescharacteristic
216C4×C13#49211yescharacteristic
217C4×C13#49711yescharacteristic
218Dic13—81no—
219Dic13—82no—
220C22×Q8—21no—
221C22×Q8—261no—
222C22×D4—131no—
223C23×C4—261no—
224C2×SD16—264no—
225C2×SD16—522no—
226C2×SD16—522no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—132no—
230C22×C8—261no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—132no—
235C4⋊Q8—261no—
236C4⋊Q8—261no—
237C4⋊Q8—261no—
238C4⋊Q8D5212yes—
239C4×D4—261no—
240C4×D4—261no—
241C4×D4—261no—
242C4×D4—261no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—131no—
246C2×C4⋊C4—261no—
247C2×C4⋊C4—261no—
248C2×C22⋊C4—261no—
249C2×C42C22×D1311yescharacteristic
250#106—268no—
251#106—264no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—132no—
256C4⋊C8—261no—
257C4⋊C8C22⋊D1312yes—
258#103—264no—
259#102—264no—
260C22⋊C8—524no—
261C4×C8—261no—
262C4×C8—261no—
263C2×C13#167112yes—
264C2×C13#169112yes—
265C2×C13#200011yescharacteristic
266C2×C13#201311yescharacteristic
267C2×C13#201911yescharacteristic
268D13—82no—
269C24—261no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—262no—
277C2×Q8—521no—
278C2×Q8—1042no—
279C2×D4—132no—
280C2×D4—261no—
281C2×D4—261no—
282C2×D4—261no—
283C2×D4—261no—
284C2×D4—261no—
285C22×C4—41no—
286C22×C4—261no—
287C22×C4—521no—
288C22×C4—521no—
289C22×C4—522no—
290C22×C4—522no—
291C22×C4—521no—
292C22×C4#612711yescharacteristic
293C22×C4D4×D1311yescharacteristic
294C22×C4D4×D1311yescharacteristic
295SD16—528no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—42no—
300C2×C8—41no—
301C2×C8—134no—
302C2×C8—262no—
303C2×C8—262no—
304C2×C8—262no—
305C2×C8—521no—
306C2×C8—521no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—261no—
312C4⋊C4—262no—
313C4⋊C4—262no—
314C4⋊C4—261no—
315C4⋊C4—521no—
316C4⋊C4—521no—
317C22⋊C4—521no—
318C22⋊C4—521no—
319C42C2×D5211yescharacteristic
320C42D4×D1311yescharacteristic
321C42D4×D1311yescharacteristic
322C42C2×C22⋊D1311yescharacteristic
323C13#1027111yescharacteristic, complemented, Sylow
324C23—262no—
325C23—522no—
326C23—521no—
327C23—522no—
328C23—521no—
329C23#8813811yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—81no—
333Q8—81no—
334Q8—1042no—
335Q8—1042no—
336D4—262no—
337D4—262no—
338D4—521no—
339D4—521no—
340C2×C4—22no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—522no—
345C2×C4—521no—
346C2×C4—522no—
347C2×C4—1042no—
348C2×C4—1042no—
349C2×C4—1041no—
350C2×C4—1041no—
351C2×C4#8813611yescharacteristic
352C2×C4#8813611yescharacteristic
353C2×C4#8813811yescharacteristic
354C2×C4#8816511yescharacteristic
355C2×C4#8816611yescharacteristic
356C2×C4SD16×D1311yescharacteristic
357C2×C4SD16×D1312yes—
358C2×C4#8816911yescharacteristic
359C2×C4#8817212yes—
360C2×C4#8818411yescharacteristic
361C2×C4#8819111yescharacteristic
362C2×C4#8819411yescharacteristic
363C8—42no—
364C8—81no—
365C8—264no—
366C8—522no—
367C22—524no—
368C22—522no—
369C22—1041no—
370C22—1041no—
371C22—1042no—
372C22#1171841512yes—
373C22#1171843911yescharacteristic
374C22#1171844111yescharacteristic
375C22#1171847912yes—
376C22#1171862111yescharacteristic
377C4—21no—
378C4—21no—
379C4—82no—
380C4—1041no—
381C4—1042no—
382C4#1171843711yescharacteristic
383C4#1171844411yescharacteristic
384C4#1171846712yes—
385C4#1171881911yescharacteristic
386C4#1171883111yescharacteristic
387C4#1171883611yescharacteristic
388C4#1171885111yescharacteristic
389C2—1042no—
390C2#1311421012yes—
391C2#1311433412yes—
392C2#1311584011yescharacteristic
393C2#1311592011yescharacteristic
394C2#1311594911yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#332C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenterC2×#332D13
hypocenterC13#10271
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#11718740C2semidirect
5. C2×#11718073C2semidirect
6. #13112670C2semidirect
7. C2×C13×#332C2semidirect
126. C2×#1055SD16semidirect
132. C2×#332D13semidirect
323. C13#10271semidirect

Maximal subgroups

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

subgroupindex
C2×#117187402
C2×#117185032
C2×#117187442
#131156292
C2×#117180732
#131126702
C2×C13×#3322
#1027113