Finite Group Databasebeta

← #15764168

Subgroups — #15764168

Order 3328.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic
2#13119832C211yesmaximal, characteristic
3#13115760C211yesmaximal, characteristic, complemented
4C2×#11718139C211yesmaximal, characteristic, complemented
5C2×#11718051C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic, complemented
7C2×C13×#498C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×#88201—21no—
11C2×C4×D52C2211yescharacteristic
12C13×#498—22no—
13C13×#498—22no—
14C2×C13×#106—22no—
15C2×C4×C8×C13C2211yescharacteristic
16#11718891—21no—
17C2×#88075—22no—
18#11718748—22no—
19#11718748—22no—
20#11718654—22no—
21#11718648—22no—
22C2×#88049—21no—
23C2×#88047—21no—
24C4×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27#11718139—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×#6103—24no—
50C2×#6103—21no—
51C2×C4⋊Dic13D411yescharacteristic
52C2×C4⋊Dic13D412yes—
53C2×C4×Dic13—21no—
54C22×#1055—21no—
55C22×#1055—21no—
56C4×D52—21no—
57C4×D52—21no—
58C4×D52—21no—
59C4×D52—21no—
60C13×#106—28no—
61C4×C8×C13—21no—
62C4×C8×C13D412yes—
63#88075—44no—
64#88071—24no—
65#88071—21no—
66#88049—24no—
67#88047—24no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055D412yes—
72#10074—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—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13—42no—
83C2×Q8×C13—42no—
84C22×C4×C13—22no—
85C22×C4×C13—41no—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×Dic13—21no—
90C22×Dic13—22no—
91C2×D52—21no—
92C2×D52—21no—
93C2×D52—21no—
94C2×D52—21no—
95C2×D52—21no—
96C2×D52SD1612yes—
97C2×C4×D13—41no—
98C2×C4×D13—41no—
99C2×C4×D13—42no—
100C2×C4×D13—42no—
101C2×C8×C13—24no—
102C2×C8×C13—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C42×C13C2×D411yescharacteristic
112C42×C13C2×D411yescharacteristic
113C42×C13C2×D411yescharacteristic
114C42×C13#4111yescharacteristic
115#6103—48no—
116#6103—41no—
117#6103—41no—
118C4⋊Dic13—21no—
119C4⋊Dic13—21no—
120C4⋊Dic13—22no—
121C4⋊Dic13—22no—
122C4×Dic13—41no—
123C4×Dic13—41no—
124C2×#1055—22no—
125C2×#1055—41no—
126C2×#1055—41no—
127C2×#1055—41no—
128C2×#1055—42no—
129C2×#498D1311yescharacteristic, complemented
130C2×#474—131no—
131#2547—131no—
132#1981—131no—
133C2×#332—131no—
134C2×D4⋊C8—131no—
135#1279—131no—
136C23×C13#12011yescharacteristic
137C22×D13—22no—
138C22×D13—41no—
139C22×D13—42no—
140C22×D13—41no—
141C22×D13—42no—
142Q8×C13—44no—
143Q8×C13—81no—
144Q8×C13—81no—
145Q8×C13—81no—
146Q8×C13—81no—
147Q8×C13—81no—
148Q8×C13—81no—
149C2×C4×C13—22no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—82no—
155C2×C4×C13#12011yescharacteristic
156C2×C4×C13#12011yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13#12111yescharacteristic
160C2×C4×C13#12711yescharacteristic
161C2×C4×C13C2×SD1611yescharacteristic
162C2×C4×C13#13511yescharacteristic
163C2×C4×C13#13512yes—
164C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C13AGL(1,ℤ/8)12yes—
166C2×C4×C13#13711yescharacteristic
167C2×Dic13—41no—
168C2×Dic13—42no—
169C2×Dic13—42no—
170C2×Dic13—42no—
171C2×Dic13—42no—
172D52—22no—
173D52—22no—
174D52—41no—
175D52—41no—
176C4×D13—82no—
177C4×D13—81no—
178C4×D13—81no—
179C8×C13—24no—
180#1055—42no—
181#1055—81no—
182C2×C4⋊Q8C2×D1311yescharacteristic
183C2×C4⋊Q8C2×D1311yescharacteristic
184C2×#124—261no—
185C2×C4×D4—131no—
186#498—22no—
187#498—22no—
188#474—262no—
189#474—262no—
190C2×#107—261no—
191C2×#106—22no—
192C2×C4⋊C8—131no—
193C2×C4⋊C8—131no—
194C2×#103—262no—
195C2×#102—261no—
196C2×C4×C8C2×D1311yescharacteristic
197#397—262no—
198#391—261no—
199#380—262no—
200C4×C4⋊C4—131no—
201#332—262no—
202D4⋊C8—262no—
203C22×C13#39211yescharacteristic
204C22×C13#44912yes—
205C22×C13#45011yescharacteristic
206C22×C13#45211yescharacteristic
207C22×C13#45612yes—
208C2×D13—44no—
209C2×D13—42no—
210C2×D13—82no—
211C2×D13—81no—
212C2×D13—81no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—82no—
216C4×C13—82no—
217C4×C13#44811yescharacteristic
218C4×C13#44911yescharacteristic
219C4×C13#46312yes—
220C4×C13#46511yescharacteristic
221C4×C13#46811yescharacteristic
222C4×C13#49511yescharacteristic
223C4×C13#49611yescharacteristic
224Dic13—82no—
225Dic13—81no—
226C22×Q8—21no—
227C22×Q8—21no—
228C22×D4—131no—
229C23×C4—261no—
230C22×C8—21no—
231C22×C8—261no—
232C22×C8—261no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8C22⋊D1312yes—
241#124—522no—
242#124—522no—
243C4×D4—261no—
244C4×D4—261no—
245C4×D4—261no—
246C4×D4—261no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—131no—
251C2×C4⋊C4—132no—
252C2×C4⋊C4C22⋊D1312yes—
253C2×C22⋊C4—264no—
254C2×C22⋊C4—261no—
255C2×C42—261no—
256C2×C42C22×D1311yescharacteristic
257#107—264no—
258#106—28no—
259C4⋊C8—132no—
260C4⋊C8—261no—
261C4⋊C8—261no—
262C4⋊C8—261no—
263#103—524no—
264#102—264no—
265C4×C8—21no—
266C4×C8C22⋊D1312yes—
267#95—264no—
268#95—261no—
269C2×C13#165212yes—
270C2×C13#165412yes—
271C2×C13#200011yescharacteristic
272C2×C13#200511yescharacteristic
273C2×C13#201211yescharacteristic
274D13—82no—
275C24—261no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×D4—132no—
287C2×D4—261no—
288C2×D4—261no—
289C2×D4—261no—
290C2×D4—261no—
291C2×D4—261no—
292C22×C4—22no—
293C22×C4—41no—
294C22×C4—261no—
295C22×C4—262no—
296C22×C4—522no—
297C22×C4—522no—
298C22×C4—521no—
299C22×C4—521no—
300C22×C4D4×D1311yescharacteristic
301C22×C4D4×D1311yescharacteristic
302C22×C4C2×C22⋊D1311yescharacteristic
303C2×C8—24no—
304C2×C8—22no—
305C2×C8—262no—
306C2×C8—521no—
307C2×C8—521no—
308C2×C8—522no—
309C2×C8—521no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—262no—
319C4⋊C4—262no—
320C4⋊C4—261no—
321C4⋊C4—261no—
322C22⋊C4—528no—
323C22⋊C4—521no—
324C22⋊C4—521no—
325C42—521no—
326C42—521no—
327C42D4×D1311yescharacteristic
328C42#612911yescharacteristic
329C42C2×C22⋊D1311yescharacteristic
330C42C2×C22⋊D1311yescharacteristic
331C13#1007411yescharacteristic, complemented, Sylow
332C23—262no—
333C23—522no—
334C23—522no—
335C23—521no—
336C23—521no—
337C23#8819111yescharacteristic
338Q8—44no—
339Q8—81no—
340Q8—81no—
341Q8—81no—
342Q8—81no—
343Q8—81no—
344Q8—81no—
345D4—262no—
346D4—262no—
347D4—521no—
348D4—521no—
349C2×C4—22no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—82no—
355C2×C4—522no—
356C2×C4—522no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—521no—
360C2×C4—1042no—
361C2×C4—1041no—
362C2×C4—1041no—
363C2×C4SD16×D1311yescharacteristic
364C2×C4#8816812yes—
365C2×C4#8816811yescharacteristic
366C2×C4#8816911yescharacteristic
367C2×C4#8817012yes—
368C2×C4#8817011yescharacteristic
369C2×C4#8819111yescharacteristic
370C2×C4#8819211yescharacteristic
371C2×C4#8819311yescharacteristic
372C2×C4#8819311yescharacteristic
373C2×C4#8819411yescharacteristic
374C2×C4#8820711yescharacteristic
375C8—24no—
376C8—522no—
377C8—1041no—
378C22—524no—
379C22—522no—
380C22—1041no—
381C22—1041no—
382C22—1042no—
383C22#1171875612yes—
384C22#1171883011yescharacteristic
385C22#1171883312yes—
386C22#1171883411yescharacteristic
387C22#1171888411yescharacteristic
388C4—21no—
389C4—21no—
390C4—82no—
391C4—82no—
392C4—1042no—
393C4—1041no—
394C4#1171882612yes—
395C4#1171882911yescharacteristic
396C4#1171883111yescharacteristic
397C4#1171883211yescharacteristic
398C4#1171883311yescharacteristic
399C4#1171883511yescharacteristic
400C4#1171883711yescharacteristic
401C2—1042no—
402C2#1311410312yes—
403C2#1311411712yes—
404C2#1311583611yescharacteristic
405C2#1311587211yescharacteristic
406C2#1311591011yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#498C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenterC2×#498D13
hypocenterC13#10074
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
3. #13115760C2semidirect
4. C2×#11718139C2semidirect
6. #13112676C2semidirect
7. C2×C13×#498C2semidirect
129. C2×#498D13semidirect
331. C13#10074semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
#131198322
#131157602
C2×#117181392
C2×#117180512
#131126762
C2×C13×#4982
#1007413