Finite Group Databasebeta

← #15764112

Subgroups — #15764112

Order 3328.

634 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718744C211yesmaximal, characteristic
2#13119832C211yesmaximal, characteristic
3#13115789C211yesmaximal, characteristic, complemented
4C2×#11718139C211yesmaximal, characteristic, complemented
5C2×#11718051C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic, complemented
7C2×C13×#500C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×#88201—21no—
11C22×#6106—21no—
12C2×C4×D52C2211yescharacteristic
13C13×#500—22no—
14C13×#500—22no—
15C2×C13×#107—22no—
16C2×C4×C8×C13C2211yescharacteristic
17#11718891—21no—
18C2×#88075—21no—
19#11718744—22no—
20#11718744—22no—
21#11718654—22no—
22#11718648—22no—
23C4×C4⋊Dic13C2211yescharacteristic
24C2×C4⋊#1055C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26#11718139—22no—
27#11718121—22no—
28#11718051—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13—21no—
31C22×D52D411yescharacteristic
32C22×C4×D13—21no—
33C22×C8×C13—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8D412yes—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4D412yes—
46C2×C42×C13C2311yescharacteristic
47#88201—42no—
48#88201—42no—
49C2×#6106—24no—
50C2×#6106—42no—
51C2×#6106—42no—
52C2×#6103—24no—
53C2×#6103—21no—
54C2×C4⋊Dic13D411yescharacteristic
55C2×C4⋊Dic13D412yes—
56C2×C4×Dic13—21no—
57C22×#1055—21no—
58C22×#1055—21no—
59C4×D52—21no—
60C4×D52—21no—
61C4×D52—21no—
62C4×D52—21no—
63C13×#107—28no—
64C4×C8×C13—21no—
65C4×C8×C13D412yes—
66#88075—24no—
67#88071—24no—
68#88071—21no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055—21no—
72C4⋊#1055D412yes—
73#10066—131nomaximal, Sylow
74C23×D13—21no—
75C2×Q8×C13—22no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13—41no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×Q8×C13—41no—
86C2×Q8×C13—41no—
87C22×C4×C13—22no—
88C22×C4×C13—41no—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×Dic13—21no—
93C22×Dic13—22no—
94C2×D52—21no—
95C2×D52—21no—
96C2×D52—21no—
97C2×D52—21no—
98C2×D52—21no—
99C2×D52D812yes—
100C2×C4×D13—41no—
101C2×C4×D13—41no—
102C2×C4×D13—42no—
103C2×C4×D13—42no—
104C2×C8×C13—24no—
105C2×C8×C13—22no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C42×C13C2×D411yescharacteristic
115C42×C13C2×D411yescharacteristic
116C42×C13C2×D411yescharacteristic
117C42×C13#4111yescharacteristic
118#6106—48no—
119#6103—48no—
120#6103—41no—
121#6103—41no—
122C4⋊Dic13—21no—
123C4⋊Dic13—21no—
124C4⋊Dic13—22no—
125C4⋊Dic13—22no—
126C4×Dic13—41no—
127C4×Dic13—41no—
128C2×#1055—22no—
129C2×#1055—41no—
130C2×#1055—41no—
131C2×#1055—41no—
132C2×#1055—42no—
133C2×#500D1311yescharacteristic, complemented
134C2×#461—131no—
135#2547—131no—
136#1988—131no—
137C2×#332—131no—
138C2×D4⋊C8—131no—
139#1279—131no—
140C23×C13#12011yescharacteristic
141C22×D13—22no—
142C22×D13—41no—
143C22×D13—41no—
144C22×D13—42no—
145C22×D13—42no—
146Q8×C13—42no—
147Q8×C13—42no—
148Q8×C13—81no—
149Q8×C13—81no—
150Q8×C13—81no—
151Q8×C13—81no—
152Q8×C13—81no—
153Q8×C13—81no—
154C2×C4×C13—22no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—81no—
160C2×C4×C13—81no—
161C2×C4×C13#12011yescharacteristic
162C2×C4×C13#12011yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12111yescharacteristic
165C2×C4×C13#12111yescharacteristic
166C2×C4×C13#12711yescharacteristic
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13#13511yescharacteristic
169C2×C4×C13#13512yes—
170C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C13#13712yes—
173C2×Dic13—41no—
174C2×Dic13—42no—
175C2×Dic13—42no—
176C2×Dic13—42no—
177C2×Dic13—42no—
178D52—22no—
179D52—22no—
180D52—41no—
181D52—41no—
182C4×D13—82no—
183C4×D13—81no—
184C4×D13—81no—
185C8×C13—24no—
186#1055—42no—
187#1055—81no—
188C22×SD16—261no—
189C2×C4⋊Q8C2×D1311yescharacteristic
190C2×C4⋊Q8C2×D1311yescharacteristic
191C2×#124—261no—
192C2×C4×D4—131no—
193#500—22no—
194#500—22no—
195#461—262no—
196#461—262no—
197C2×#107—22no—
198C2×C4⋊C8—131no—
199C2×C4⋊C8—131no—
200C2×#103—261no—
201C2×C4×C8C2×D1311yescharacteristic
202#397—262no—
203#391—261no—
204#380—262no—
205C4×C4⋊C4—131no—
206#340—262no—
207#332—262no—
208D4⋊C8—262no—
209C22×C13#39211yescharacteristic
210C22×C13#44711yescharacteristic
211C22×C13#44911yescharacteristic
212C22×C13#45212yes—
213C22×C13#45612yes—
214C2×D13—44no—
215C2×D13—42no—
216C2×D13—82no—
217C2×D13—81no—
218C2×D13—81no—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—82no—
222C4×C13—82no—
223C4×C13#44711yescharacteristic
224C4×C13#44911yescharacteristic
225C4×C13#46412yes—
226C4×C13#46611yescharacteristic
227C4×C13#46911yescharacteristic
228C4×C13#49511yescharacteristic
229C4×C13#49711yescharacteristic
230Dic13—82no—
231Dic13—81no—
232C22×Q8—21no—
233C22×Q8—21no—
234C22×D4—131no—
235C23×C4—261no—
236C2×SD16—264no—
237C2×SD16—522no—
238C2×SD16—522no—
239C22×C8—21no—
240C22×C8—261no—
241C22×C8—261no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8C22⋊D1312yes—
250#124—522no—
251#124—522no—
252C4×D4—261no—
253C4×D4—261no—
254C4×D4—261no—
255C4×D4—261no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—131no—
260C2×C4⋊C4—132no—
261C2×C4⋊C4C22⋊D1312yes—
262C2×C22⋊C4—264no—
263C2×C22⋊C4—261no—
264C2×C42—261no—
265C2×C42C22×D1311yescharacteristic
266#107—28no—
267C4⋊C8—132no—
268C4⋊C8—261no—
269C4⋊C8—261no—
270C4⋊C8—261no—
271#103—264no—
272C4×C8—21no—
273C4×C8C22⋊D1312yes—
274#95—264no—
275#95—261no—
276C2×C13#164712yes—
277C2×C13#165012yes—
278C2×C13#199911yescharacteristic
279C2×C13#200511yescharacteristic
280C2×C13#201511yescharacteristic
281D13—82no—
282C24—261no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×D4—132no—
296C2×D4—261no—
297C2×D4—261no—
298C2×D4—261no—
299C2×D4—261no—
300C2×D4—261no—
301C22×C4—22no—
302C22×C4—41no—
303C22×C4—261no—
304C22×C4—262no—
305C22×C4—522no—
306C22×C4—522no—
307C22×C4—521no—
308C22×C4—521no—
309C22×C4D4×D1311yescharacteristic
310C22×C4D4×D1311yescharacteristic
311C22×C4C2×C22⋊D1311yescharacteristic
312SD16—528no—
313C2×C8—24no—
314C2×C8—22no—
315C2×C8—262no—
316C2×C8—521no—
317C2×C8—521no—
318C2×C8—522no—
319C2×C8—521no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—262no—
329C4⋊C4—262no—
330C4⋊C4—261no—
331C4⋊C4—261no—
332C22⋊C4—528no—
333C22⋊C4—521no—
334C22⋊C4—521no—
335C42—521no—
336C42—521no—
337C42D4×D1311yescharacteristic
338C42#612911yescharacteristic
339C42C2×C22⋊D1311yescharacteristic
340C42C2×C22⋊D1311yescharacteristic
341C13#1006611yescharacteristic, complemented, Sylow
342C23—262no—
343C23—522no—
344C23—521no—
345C23—522no—
346C23—521no—
347C23#8819111yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352Q8—81no—
353Q8—81no—
354Q8—81no—
355Q8—81no—
356D4—262no—
357D4—262no—
358D4—521no—
359D4—521no—
360C2×C4—22no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—522no—
368C2×C4—522no—
369C2×C4—522no—
370C2×C4—522no—
371C2×C4—521no—
372C2×C4—1042no—
373C2×C4—1041no—
374C2×C4—1041no—
375C2×C4D8×D1311yescharacteristic
376C2×C4#8816511yescharacteristic
377C2×C4#8816511yescharacteristic
378C2×C4#8816611yescharacteristic
379C2×C4#8817212yes—
380C2×C4#8817312yes—
381C2×C4#8819111yescharacteristic
382C2×C4#8819211yescharacteristic
383C2×C4#8819311yescharacteristic
384C2×C4#8819311yescharacteristic
385C2×C4#8819411yescharacteristic
386C2×C4#8820711yescharacteristic
387C8—24no—
388C8—522no—
389C8—1041no—
390C22—522no—
391C22—524no—
392C22—1041no—
393C22—1041no—
394C22—1042no—
395C22#1171875612yes—
396C22#1171881711yescharacteristic
397C22#1171881911yescharacteristic
398C22#1171884812yes—
399C22#1171888411yescharacteristic
400C4—21no—
401C4—21no—
402C4—82no—
403C4—82no—
404C4—1041no—
405C4—1042no—
406C4#1171881711yescharacteristic
407C4#1171881811yescharacteristic
408C4#1171881911yescharacteristic
409C4#1171882011yescharacteristic
410C4#1171884612yes—
411C4#1171885111yescharacteristic
412C4#1171885211yescharacteristic
413C2—1042no—
414C2#1311406812yes—
415C2#1311408912yes—
416C2#1311583111yescharacteristic
417C2#1311587211yescharacteristic
418C2#1311592711yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#500C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenterC2×#500D13
hypocenterC13#10066
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
3. #13115789C2semidirect
4. C2×#11718139C2semidirect
6. #13112676C2semidirect
7. C2×C13×#500C2semidirect
133. C2×#500D13semidirect
341. C13#10066semidirect

Maximal subgroups

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

subgroupindex
C2×#117187442
#131198322
#131157892
C2×#117181392
C2×#117180512
#131126762
C2×C13×#5002
#1006613