Finite Group Databasebeta

← #15872409

Subgroups — #15872409

Order 3328.

1074 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic
2C2×#11718346C211yesmaximal, characteristic
3#13117241C211yesmaximal, characteristic
4#13115798C211yesmaximal, characteristic, complemented
5#13115797C211yesmaximal, characteristic, complemented
6#13115796C211yesmaximal, characteristic, complemented
7#13115792C214yesmaximal, complemented
8#13114929C214yesmaximal
9C13×#1990C211yesmaximal, characteristic, complemented
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×#88200—21no—
12C2×Q8×Dic13—21no—
13#11719433—24no—
14#11719433C418yescomplemented
15C2×#88151—21no—
16C2×#88146—21no—
17C2×#88146C2212yes—
18C2×#88144C2212yes—
19C2×#88141—21no—
20C2×C42×D13C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C13×#384C2211yescharacteristic
24C2×#88060C2212yes—
25C2×#88054C2212yes—
26#11718648—21no—
27#11718648C2212yes—
28#11718638—21no—
29C4⋊C4×Dic13—21no—
30C4⋊C4×Dic13C2212yes—
31#11718596C2211yescharacteristic
32C2×C4×#1055C2211yescharacteristic
33#11718346—24no—
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⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4C2312yes—
50C2×C13×C4⋊C4C2312yes—
51C2×C42×C13C2311yescharacteristic
52#88200—28no—
53Q8×Dic13—28no—
54C2×#6103—22no—
55C2×#6103—22no—
56C2×C4⋊Dic13—21no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13C2312yes—
61C2×C4⋊Dic13C2312yes—
62C2×#6101—22no—
63C2×C4×Dic13—22no—
64C2×C4×Dic13—22no—
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13C2311yescharacteristic
68C22×#1055C2312yes—
69#88151—28no—
70#88146—24no—
71#88146—44no—
72#88146C2×C418yes—
73#88144—24no—
74#88144C2×C418yes—
75#88141—28no—
76C42×D13C2×C414yes—
77C42×D13D414yes—
78#88123—22no—
79#88123C2×C414yes—
80C4×C8×C13—22no—
81#88071—22no—
82#88071—22no—
83#88060—24no—
84#88054—24no—
85C4×#1055—22no—
86#21835—131nomaximal, Sylow
87C23×D13C2×D411yescharacteristic
88C2×Q8×C13—24no—
89C2×Q8×C13—42no—
90C2×Q8×C13—42no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2411yescharacteristic
96C22×Dic13—22no—
97C22×Dic13—22no—
98C22×Dic13C2×D411yescharacteristic
99C22×Dic13C2×D411yescharacteristic
100C22×Dic13C2×D411yescharacteristic
101C2×C4×D13—22no—
102C2×C4×D13—22no—
103C2×C4×D13—22no—
104C2×C4×D13—22no—
105C2×C4×D13—22no—
106C2×C4×D13—22no—
107C2×C4×D13C22⋊C414yes—
108C2×C4×D13C22⋊C414yes—
109C2×C4×D13C22×C412yes—
110C2×C4×D13C2×D412yes—
111C2×Dic26—24no—
112C2×Dic26—42no—
113C2×Dic26—42no—
114C2×C8×C13—22no—
115C2×C8×C13—22no—
116C2×C8×C13—22no—
117C13×C4⋊C4—24no—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—24no—
120C13×C4⋊C4—42no—
121C13×C4⋊C4—42no—
122C13×C4⋊C4C22×C414yes—
123C42×C13C22×C412yes—
124C42×C13C2×D412yes—
125#6103—28no—
126#6103—44no—
127C4⋊Dic13—24no—
128C4⋊Dic13—22no—
129C4⋊Dic13—28no—
130C4⋊Dic13—24no—
131C4⋊Dic13—42no—
132C4⋊Dic13—42no—
133C4⋊Dic13C22×C414yes—
134#6101—28no—
135C4×Dic13—28no—
136C4×Dic13—44no—
137C4×Dic13C22⋊C414yes—
138C4×Dic13C22⋊C414yes—
139C4×Dic13C22×C412yes—
140C4×Dic13C2×D412yes—
141C2×#1055—22no—
142C2×#1055—22no—
143C2×#1055—22no—
144C2×#533—131no—
145C2×#431—131no—
146#2285—131no—
147#1990—131no—
148#1990—131no—
149#1990—131no—
150#1990D1311yescharacteristic, complemented
151#1989—134no—
152#1825—134no—
153C23×C13C22×D411yescharacteristic
154C22×D13—21no—
155C22×D13—21no—
156C22×D13—21no—
157C22×D13—21no—
158C22×D13—21no—
159C22×D13—21no—
160C22×D13C2×C22⋊C412yes—
161Q8×C13—48no—
162C2×C4×C13—24no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13C2×C22⋊C412yes—
169C2×C4×C13C2×C22⋊C412yes—
170C2×C4×C13#13512yes—
171C2×C4×C13#13512yes—
172C2×C4×C13AGL(1,ℤ/8)12yes—
173C2×C4×C13#13712yes—
174C2×C4×C13C23×C411yescharacteristic
175C2×C4×C13C22×D411yescharacteristic
176C2×C4×C132−1+412yes—
177C2×C4×C132−1+412yes—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13—21no—
182C2×Dic13—21no—
183C2×Dic13—21no—
184C2×Dic13—24no—
185C2×Dic13—42no—
186C2×Dic13—42no—
187C2×Dic13—42no—
188C2×Dic13—42no—
189C2×Dic13—42no—
190C2×Dic13C2×C22⋊C412yes—
191C2×Dic13C2×C22⋊C412yes—
192C2×Dic13C2×C22⋊C412yes—
193C4×D13—24no—
194C4×D13—24no—
195C4×D13—28no—
196C4×D13—28no—
197Dic26—48no—
198C8×C13—42no—
199#1055—42no—
200#533—138no—
201#533—264no—
202C2×C4⋊Q8—131no—
203C2×C4⋊Q8C2×D1311yescharacteristic
204C2×#125—132no—
205C2×C22⋊Q8—261no—
206C2×C22⋊Q8—261no—
207C2×C4×Q8—261no—
208C2×C4×Q8—261no—
209C2×#117—132no—
210C2×#117—261no—
211C22×C42—131no—
212#431—264no—
213C2×C4⋊C8—132no—
214C2×C22⋊C8—132no—
215C2×C4×C8—131no—
216C2×C4×C8C2×D1311yescharacteristic
217#384—131no—
218#384C2×D1311yescharacteristic
219#382—261no—
220#380—132no—
221#380—261no—
222C4×C4⋊C4—132no—
223C4×C4⋊C4—261no—
224#340—134no—
225#340—134no—
226#340—134no—
227#340C2×D1314yes—
228C22×C13C22×C22⋊C411yescharacteristic
229C22×C13#53611yescharacteristic
230C22×C13#53611yescharacteristic
231C22×C13C2×#13511yescharacteristic
232C22×C13C2×#13511yescharacteristic
233C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
234C22×C13C2×#13711yescharacteristic
235C2×D13—22no—
236C2×D13—22no—
237C2×D13—22no—
238C2×D13—41no—
239C2×D13—41no—
240C2×D13—41no—
241C2×D13—41no—
242C4×C13—44no—
243C4×C13—82no—
244C4×C13#41614yes—
245C4×C13#41714yes—
246C4×C13#51912yes—
247C4×C13#53612yes—
248Dic13—22no—
249Dic13—22no—
250Dic13—22no—
251Dic13—44no—
252Dic13—82no—
253C22×Q8—21no—
254C22×Q8—261no—
255C23×C4—131no—
256C23×C4—131no—
257C23×C4—131no—
258C22×C8—132no—
259C22×C8C22×D1312yes—
260C4⋊Q8—22no—
261C4⋊Q8—134no—
262C4⋊Q8—262no—
263C4⋊Q8C4×D1314yes—
264#125—138no—
265#125—264no—
266C22⋊Q8—268no—
267C22⋊Q8—268no—
268C4×Q8—268no—
269C4×Q8—268no—
270#117—138no—
271#117—264no—
272#117—524no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—132no—
277C2×C4⋊C4—132no—
278C2×C4⋊C4—262no—
279C2×C4⋊C4—262no—
280C2×C4⋊C4—261no—
281C2×C4⋊C4—261no—
282C2×C4⋊C4—261no—
283C2×C4⋊C4C22×D1312yes—
284C2×C4⋊C4C22×D1312yes—
285C2×C22⋊C4—262no—
286C2×C22⋊C4—262no—
287C2×C42—131no—
288C2×C42—131no—
289C2×C42—131no—
290C2×C42—134no—
291C2×C42—134no—
292C2×C42—262no—
293C2×C42—262no—
294C2×C42C22×D1311yescharacteristic
295C4⋊C8—264no—
296C22⋊C8—264no—
297C4×C8—22no—
298C4×C8—262no—
299#95—262no—
300#95—262no—
301C2×C13#231011yescharacteristic
302C2×C13C2×#41611yescharacteristic
303C2×C13C2×#41711yescharacteristic
304C2×C13#322811yescharacteristic
305C2×C13#322811yescharacteristic
306C2×C13#323111yescharacteristic
307C2×C13#323111yescharacteristic
308D13—42no—
309C24—131no—
310C2×Q8—24no—
311C2×Q8—42no—
312C2×Q8—42no—
313C2×Q8—264no—
314C2×Q8—522no—
315C2×Q8—522no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—131no—
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—134no—
322C22×C4—134no—
323C22×C4—132no—
324C22×C4—132no—
325C22×C4—262no—
326C22×C4—262no—
327C22×C4—262no—
328C22×C4—262no—
329C22×C4—262no—
330C22×C4—262no—
331C22×C4—262no—
332C22×C4—262no—
333C22×C4D4×D1311yescharacteristic
334C22×C4D4×D1311yescharacteristic
335C22×C4C23×D1311yescharacteristic
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—262no—
340C2×C8—262no—
341C2×C8—262no—
342C4⋊C4—24no—
343C4⋊C4—22no—
344C4⋊C4—24no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—134no—
348C4⋊C4—268no—
349C4⋊C4—268no—
350C4⋊C4—264no—
351C4⋊C4—262no—
352C4⋊C4—264no—
353C4⋊C4—522no—
354C4⋊C4—522no—
355C4⋊C4C2×C4×D1314yes—
356C22⋊C4—268no—
357C22⋊C4—524no—
358C42—134no—
359C42—134no—
360C42—132no—
361C42—132no—
362C42—268no—
363C42—524no—
364C42C2×C4×D1312yes—
365C42D4×D1312yes—
366C13#2183511yescharacteristic, complemented, Sylow
367C23—132no—
368C23—261no—
369C23—261no—
370C23—261no—
371C23—261no—
372C23—261no—
373C23—261no—
374C23C2×D4×D1311yescharacteristic
375Q8—48no—
376Q8—528no—
377C2×C4—24no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—132no—
384C2×C4—132no—
385C2×C4—132no—
386C2×C4—261no—
387C2×C4—261no—
388C2×C4—261no—
389C2×C4—261no—
390C2×C4—261no—
391C2×C4—261no—
392C2×C4—268no—
393C2×C4—268no—
394C2×C4—264no—
395C2×C4—264no—
396C2×C4—264no—
397C2×C4—522no—
398C2×C4—522no—
399C2×C4—522no—
400C2×C4—522no—
401C2×C4—522no—
402C2×C4C22⋊C4×D1312yes—
403C2×C4C22⋊C4×D1312yes—
404C2×C4#8816612yes—
405C2×C4#8816812yes—
406C2×C4#8817012yes—
407C2×C4#8817212yes—
408C2×C4C22×C4×D1311yescharacteristic
409C2×C4C2×D4×D1311yescharacteristic
410C2×C4#8825412yes—
411C2×C4#8825712yes—
412C8—42no—
413C8—522no—
414C22—262no—
415C22—262no—
416C22—262no—
417C22—521no—
418C22—521no—
419C22—521no—
420C22—521no—
421C22C2×C22⋊C4×D1311yescharacteristic
422C22#1171938011yescharacteristic
423C22#1171942911yescharacteristic
424C22C2×#8816611yescharacteristic
425C22C2×#8816811yescharacteristic
426C22C2×#8817011yescharacteristic
427C22C2×#8817211yescharacteristic
428C4—44no—
429C4—82no—
430C4—262no—
431C4—262no—
432C4—262no—
433C4—524no—
434C4—1042no—
435C4#1171843314yes—
436C4#1171846414yes—
437C4#1171927712yes—
438C4#1171933312yes—
439C2—522no—
440C2#1311741911yescharacteristic
441C2C2×#1171843311yescharacteristic
442C2C2×#1171846411yescharacteristic
443C2#1312596711yescharacteristic
444C2#1312597311yescharacteristic
445C2#1312599011yescharacteristic
446C2#1312599611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1990C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1990D13
hypocenterC13#21835
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. #13115798C2semidirect
5. #13115797C2semidirect
6. #13115796C2semidirect
7. #13115792C2semidirect
9. C13×#1990C2semidirect
14. #11719433C4semidirect
150. #1990D13semidirect
366. C13#21835semidirect

Maximal subgroups

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

subgroupindex
C2×#117194332
C2×#117183462
#131172412
#131157982
#131157972
#131157962
#131157922
#131149292
C13×#19902
#2183513