Finite Group Databasebeta

← #15872440

Subgroups — #15872440

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic
2C2×#11718496C211yesmaximal, characteristic
3#13117240C211yesmaximal, characteristic
4#13115803C214yesmaximal, complemented
5#13115788C211yesmaximal, characteristic, complemented
6#13115787C211yesmaximal, characteristic, complemented
7#13115785C211yesmaximal, characteristic, complemented
8#13114929C214yesmaximal
9C13×#1987C211yesmaximal, characteristic, complemented
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×#88200—21no—
12C2×Q8×Dic13—21no—
13#11719433—24no—
14#11719433C418yescomplemented
15C2×#88151—21no—
16C2×#88146C2212yes—
17C2×#88144C2212yes—
18C2×#88141—21no—
19C2×#88126—21no—
20C2×C42×D13C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C2×#88060C2212yes—
25C2×#88055C2212yes—
26#11718648C2212yes—
27#11718637C2212yes—
28C4×C4⋊Dic13C2211yescharacteristic
29C4×#6101—21no—
30C2×C4⋊#1055C2211yescharacteristic
31#11718496—24no—
32#11718328—21no—
33#11718311—21no—
34C13×#340C2214yes—
35#11718143C2214yes—
36#11718121C2214yes—
37#11718121C2214yes—
38C22×Q8×C13—21no—
39C22×C4×D13D411yescharacteristic
40C22×C4×D13D411yescharacteristic
41C22×C4×D13C2311yescharacteristic
42C22×Dic26—21no—
43C22×C8×C13C2312yes—
44C13×C4⋊Q8—22no—
45C13×C4⋊Q8C2×C414yes—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4C2312yes—
48C2×C13×C4⋊C4C2312yes—
49C2×C42×C13—21no—
50C2×C42×C13C2311yescharacteristic
51#88200—28no—
52Q8×Dic13—28no—
53C2×#6103—22no—
54C2×#6103—22no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13C2312yes—
58C2×C4⋊Dic13C2312yes—
59C2×#6101—22no—
60C2×#6101—22no—
61C2×#6101—22no—
62C2×C4×Dic13—22no—
63C2×C4×Dic13—21no—
64C2×C4×Dic13D411yescharacteristic
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13C2311yescharacteristic
67C22×#1055C2312yes—
68#88151—28no—
69#88146—24no—
70#88146C2×C418yes—
71#88144—24no—
72#88144C2×C418yes—
73#88141—28no—
74#88126—44no—
75C42×D13C2×C414yes—
76C42×D13D414yes—
77#88123—22no—
78#88123C2×C414yes—
79C13×C4⋊C8—22no—
80C13×#95—21no—
81#88071—21no—
82#88071—22no—
83#88060—24no—
84#88055—24no—
85C4⋊#1055—22no—
86#21839—131nomaximal, Sylow
87C23×D13C2×D411yescharacteristic
88C2×Q8×C13—24no—
89C2×Q8×C13—44no—
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2411yescharacteristic
95C22×Dic13—22no—
96C22×Dic13—22no—
97C22×Dic13C2×D411yescharacteristic
98C22×Dic13C2×D411yescharacteristic
99C22×Dic13C2×D411yescharacteristic
100C2×C4×D13—22no—
101C2×C4×D13—22no—
102C2×C4×D13—22no—
103C2×C4×D13—22no—
104C2×C4×D13—42no—
105C2×C4×D13C22⋊C414yes—
106C2×C4×D13C22⋊C414yes—
107C2×C4×D13C22×C412yes—
108C2×C4×D13C2×D412yes—
109C2×Dic26—24no—
110C2×Dic26—42no—
111C2×Dic26—42no—
112C2×C8×C13—22no—
113C2×C8×C13—24no—
114C13×C4⋊C4—24no—
115C13×C4⋊C4—22no—
116C13×C4⋊C4—22no—
117C13×C4⋊C4—22no—
118C13×C4⋊C4C22×C414yes—
119C42×C13—42no—
120C42×C13C22×C412yes—
121C42×C13C2×D412yes—
122#6103—28no—
123#6103—44no—
124C4⋊Dic13—24no—
125C4⋊Dic13—22no—
126C4⋊Dic13—28no—
127C4⋊Dic13—22no—
128C4⋊Dic13—22no—
129C4⋊Dic13C22×C414yes—
130#6101—28no—
131#6101—44no—
132#6101—44no—
133C4×Dic13—28no—
134C4×Dic13—42no—
135C4×Dic13C22⋊C414yes—
136C4×Dic13C22⋊C414yes—
137C4×Dic13C22×C412yes—
138C4×Dic13C2×D412yes—
139C2×#1055—22no—
140C2×#1055—24no—
141C2×#533—131no—
142C2×#432—131no—
143#2285—131no—
144#1992—134no—
145#1988—131no—
146#1988—131no—
147#1987—131no—
148#1987D1311yescharacteristic, complemented
149#1825—134no—
150C23×C13C22×D411yescharacteristic
151C22×D13—22no—
152C22×D13—21no—
153C22×D13—21no—
154C22×D13—22no—
155C22×D13C2×C22⋊C412yes—
156Q8×C13—48no—
157C2×C4×C13—22no—
158C2×C4×C13—24no—
159C2×C4×C13—44no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13C2×C22⋊C412yes—
164C2×C4×C13C2×C22⋊C412yes—
165C2×C4×C13AGL(1,ℤ/8)12yes—
166C2×C4×C13#13712yes—
167C2×C4×C13C23×C411yescharacteristic
168C2×C4×C13C22×D411yescharacteristic
169C2×C4×C132−1+412yes—
170C2×C4×C132−1+412yes—
171C2×Dic13—22no—
172C2×Dic13—21no—
173C2×Dic13—21no—
174C2×Dic13—22no—
175C2×Dic13—24no—
176C2×Dic13—42no—
177C2×Dic13—42no—
178C2×Dic13—42no—
179C2×Dic13—42no—
180C2×Dic13—42no—
181C2×Dic13C2×C22⋊C412yes—
182C2×Dic13C2×C22⋊C412yes—
183C2×Dic13C2×C22⋊C412yes—
184C4×D13—24no—
185C4×D13—22no—
186C4×D13—22no—
187C4×D13—28no—
188C4×D13—44no—
189Dic26—48no—
190C8×C13—42no—
191#1055—42no—
192#533—138no—
193#533—264no—
194C2×C4⋊Q8—131no—
195C2×C4⋊Q8C2×D1311yescharacteristic
196C2×#125—132no—
197C2×C22⋊Q8—261no—
198C2×C22⋊Q8—261no—
199C2×C4×Q8—261no—
200C2×C4×Q8—261no—
201C2×#117—132no—
202C2×#117—261no—
203C22×C42—131no—
204#432—264no—
205C2×C4⋊C8—131no—
206C2×C4⋊C8C2×D1311yescharacteristic
207C2×C22⋊C8—132no—
208C2×#97—132no—
209#384—132no—
210#382—261no—
211#380—132no—
212#380—261no—
213C4×C4⋊C4—131no—
214C4×C4⋊C4—261no—
215C4×C4⋊C4C2×D1311yescharacteristic
216#340—134no—
217#340—134no—
218#340—134no—
219#340C2×D1314yes—
220C22×C13C22×C22⋊C411yescharacteristic
221C22×C13#53612yes—
222C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
223C22×C13C2×#13711yescharacteristic
224C22×C13#57512yes—
225C2×D13—22no—
226C2×D13—22no—
227C2×D13—22no—
228C2×D13—42no—
229C2×D13—42no—
230C4×C13—22no—
231C4×C13—44no—
232C4×C13—82no—
233C4×C13#41714yes—
234C4×C13#51912yes—
235C4×C13#53611yescharacteristic
236C4×C13#53611yescharacteristic
237Dic13—22no—
238Dic13—22no—
239Dic13—22no—
240Dic13—44no—
241Dic13—82no—
242C22×Q8—21no—
243C22×Q8—261no—
244C23×C4—131no—
245C23×C4—131no—
246C23×C4—131no—
247C22×C8—132no—
248C22×C8C22×D1312yes—
249C4⋊Q8—22no—
250C4⋊Q8—134no—
251C4⋊Q8—262no—
252C4⋊Q8C4×D1314yes—
253#125—138no—
254#125—264no—
255C22⋊Q8—268no—
256C22⋊Q8—268no—
257C4×Q8—268no—
258C4×Q8—268no—
259#117—138no—
260#117—264no—
261#117—524no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—132no—
264C2×C4⋊C4—132no—
265C2×C4⋊C4—262no—
266C2×C4⋊C4—262no—
267C2×C4⋊C4—261no—
268C2×C4⋊C4—262no—
269C2×C4⋊C4—262no—
270C2×C4⋊C4C22×D1312yes—
271C2×C4⋊C4C22×D1312yes—
272C2×C22⋊C4—262no—
273C2×C22⋊C4—262no—
274C2×C42—21no—
275C2×C42—131no—
276C2×C42—131no—
277C2×C42—131no—
278C2×C42—134no—
279C2×C42—134no—
280C2×C42—262no—
281C2×C42—261no—
282C2×C42C22×D1311yescharacteristic
283C4⋊C8—22no—
284C4⋊C8—262no—
285C22⋊C8—264no—
286#97—264no—
287#95—21no—
288#95—262no—
289#95—261no—
290C2×C13#231011yescharacteristic
291C2×C13C2×#41711yescharacteristic
292C2×C13#289611yescharacteristic
293C2×C13#323512yes—
294C2×C13#323712yes—
295D13—42no—
296C24—131no—
297C2×Q8—24no—
298C2×Q8—44no—
299C2×Q8—264no—
300C2×Q8—522no—
301C2×Q8—522no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—131no—
305C22×C4—131no—
306C22×C4—131no—
307C22×C4—134no—
308C22×C4—132no—
309C22×C4—132no—
310C22×C4—134no—
311C22×C4—262no—
312C22×C4—262no—
313C22×C4—262no—
314C22×C4—262no—
315C22×C4—262no—
316C22×C4—262no—
317C22×C4—522no—
318C22×C4D4×D1311yescharacteristic
319C22×C4D4×D1311yescharacteristic
320C22×C4C23×D1311yescharacteristic
321C2×C8—22no—
322C2×C8—24no—
323C2×C8—262no—
324C2×C8—264no—
325C4⋊C4—24no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—134no—
330C4⋊C4—268no—
331C4⋊C4—268no—
332C4⋊C4—264no—
333C4⋊C4—262no—
334C4⋊C4—262no—
335C4⋊C4—262no—
336C4⋊C4—524no—
337C4⋊C4—524no—
338C4⋊C4C2×C4×D1314yes—
339C22⋊C4—268no—
340C22⋊C4—524no—
341C42—42no—
342C42—134no—
343C42—134no—
344C42—132no—
345C42—132no—
346C42—268no—
347C42—522no—
348C42C2×C4×D1312yes—
349C42D4×D1312yes—
350C13#2183911yescharacteristic, complemented, Sylow
351C23—132no—
352C23—261no—
353C23—261no—
354C23—262no—
355C23—262no—
356C23C2×D4×D1311yescharacteristic
357Q8—48no—
358Q8—528no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—132no—
366C2×C4—132no—
367C2×C4—132no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—262no—
371C2×C4—262no—
372C2×C4—262no—
373C2×C4—268no—
374C2×C4—264no—
375C2×C4—262no—
376C2×C4—264no—
377C2×C4—524no—
378C2×C4—522no—
379C2×C4—522no—
380C2×C4—522no—
381C2×C4—522no—
382C2×C4—522no—
383C2×C4C22⋊C4×D1312yes—
384C2×C4C22⋊C4×D1312yes—
385C2×C4#8816812yes—
386C2×C4#8817212yes—
387C2×C4C22×C4×D1311yescharacteristic
388C2×C4C2×D4×D1311yescharacteristic
389C2×C4#8825412yes—
390C2×C4#8825712yes—
391C8—42no—
392C8—522no—
393C22—262no—
394C22—262no—
395C22—262no—
396C22—522no—
397C22—522no—
398C22C2×C22⋊C4×D1311yescharacteristic
399C22#1171933312yes—
400C22C2×#8816811yescharacteristic
401C22C2×#8817211yescharacteristic
402C22#1171947812yes—
403C4—22no—
404C4—44no—
405C4—82no—
406C4—262no—
407C4—262no—
408C4—262no—
409C4—524no—
410C4—1042no—
411C4#1171846414yes—
412C4#1171927712yes—
413C4#1171938011yescharacteristic
414C4#1171942911yescharacteristic
415C2—522no—
416C2#1311741911yescharacteristic
417C2C2×#1171846411yescharacteristic
418C2#1312335011yescharacteristic
419C2#1312603212yes—
420C2#1312604812yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1987C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1987D13
hypocenterC13#21839
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
4. #13115803C2semidirect
5. #13115788C2semidirect
6. #13115787C2semidirect
7. #13115785C2semidirect
9. C13×#1987C2semidirect
14. #11719433C4semidirect
148. #1987D13semidirect
350. C13#21839semidirect

Maximal subgroups

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

subgroupindex
C2×#117194332
C2×#117184962
#131172402
#131158032
#131157882
#131157872
#131157852
#131149292
C13×#19872
#2183913