Finite Group Databasebeta

← #15872400

Subgroups — #15872400

Order 3328.

1302 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊Q8C211yesmaximal, characteristic
2C2×#11718494C211yesmaximal, characteristic
3#13117240C211yesmaximal, characteristic
4#13115795C214yesmaximal, complemented
5#13115789C211yesmaximal, characteristic, complemented
6#13115788C211yesmaximal, characteristic, complemented
7#13115787C211yesmaximal, characteristic, complemented
8#13114921C214yesmaximal
9C13×#1988C211yesmaximal, characteristic, complemented
10C22×Q8×D13—21no—
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×#88198—21no—
13D13×C4⋊Q8—24no—
14D13×C4⋊Q8C418yescomplemented
15C2×C4⋊C4×D13—21no—
16C2×C4⋊C4×D13C2212yes—
17C2×#88142—21no—
18C2×#88142C2212yes—
19C2×#88126—21no—
20C2×C42×D13C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C2×#88060C2212yes—
25C2×C8×Dic13C2212yes—
26#11718648C2212yes—
27#11718637C2212yes—
28C4×C4⋊Dic13C2211yescharacteristic
29C4×#6101—21no—
30C2×C4⋊#1055C2211yescharacteristic
31#11718494—24no—
32#11718328—21no—
33#11718311—21no—
34C13×#340C2214yes—
35#11718143C2214yes—
36#11718121C2214yes—
37#11718121C2214yes—
38C22×Q8×C13—21no—
39C2×Q8×D13—28no—
40C2×Q8×D13—44no—
41C2×Q8×D13—44no—
42C22×C4×D13—22no—
43C22×C4×D13D411yescharacteristic
44C22×C4×D13D411yescharacteristic
45C22×C4×D13C2311yescharacteristic
46C22×Dic26—21no—
47C22×Dic26—22no—
48C22×C8×C13C2312yes—
49C13×C4⋊Q8—22no—
50C13×C4⋊Q8C2×C414yes—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4C2312yes—
53C2×C13×C4⋊C4C2312yes—
54C2×C42×C13—21no—
55C2×C42×C13C2311yescharacteristic
56#88198—28no—
57C2×#6103—22no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13C2312yes—
60C2×C4⋊Dic13C2312yes—
61C2×#6101—22no—
62C2×#6101—22no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×C4×Dic13—21no—
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13D411yescharacteristic
68C2×C4×Dic13C2311yescharacteristic
69C22×#1055C2312yes—
70C4⋊C4×D13—28no—
71C4⋊C4×D13—24no—
72C4⋊C4×D13C2×C418yes—
73#88142—28no—
74#88142—24no—
75#88142C2×C418yes—
76#88126—44no—
77C42×D13C2×C414yes—
78C42×D13D414yes—
79#88123—22no—
80#88123C2×C414yes—
81C13×C4⋊C8—22no—
82C13×#95—21no—
83#88071—21no—
84#88071—22no—
85#88060—24no—
86C8×Dic13—24no—
87C4⋊#1055—22no—
88#21833—131nomaximal, Sylow
89C23×D13C2×D411yescharacteristic
90C2×Q8×C13—24no—
91C2×Q8×C13—42no—
92C2×Q8×C13—42no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2411yescharacteristic
98C22×Dic13—22no—
99C22×Dic13—22no—
100C22×Dic13C2×D411yescharacteristic
101C22×Dic13C2×D411yescharacteristic
102C22×Dic13C2×D411yescharacteristic
103Q8×D13—432no—
104C2×C4×D13—22no—
105C2×C4×D13—22no—
106C2×C4×D13—24no—
107C2×C4×D13—28no—
108C2×C4×D13—44no—
109C2×C4×D13—44no—
110C2×C4×D13C22⋊C414yes—
111C2×C4×D13C22⋊C414yes—
112C2×C4×D13D814yes—
113C2×C4×D13SD1614yes—
114C2×C4×D13C22×C412yes—
115C2×C4×D13C2×D412yes—
116C2×Dic26—24no—
117C2×Dic26—28no—
118C2×Dic26—42no—
119C2×Dic26—42no—
120C2×Dic26—44no—
121C2×Dic26—44no—
122C2×C8×C13—22no—
123C2×C8×C13—24no—
124C13×C4⋊C4—24no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4C22×C414yes—
129C42×C13—42no—
130C42×C13C22×C412yes—
131C42×C13C2×D412yes—
132#6103—44no—
133C4⋊Dic13—24no—
134C4⋊Dic13—22no—
135C4⋊Dic13—22no—
136C4⋊Dic13—22no—
137C4⋊Dic13C22×C414yes—
138#6101—28no—
139#6101—28no—
140#6101—44no—
141#6101—44no—
142C4×Dic13—42no—
143C4×Dic13C22⋊C414yes—
144C4×Dic13C22⋊C414yes—
145C4×Dic13C22×C412yes—
146C4×Dic13C2×D412yes—
147C2×#1055—22no—
148C2×#1055—24no—
149C22×C4⋊Q8—131no—
150C2×#431—131no—
151#2285—131no—
152#1990—134no—
153#1988—131no—
154#1988—131no—
155#1988—131no—
156#1988D1311yescharacteristic, complemented
157#1823—134no—
158C23×C13C22×D411yescharacteristic
159C22×D13—22no—
160C22×D13—22no—
161C22×D13C2×C22⋊C412yes—
162C22×D13C2×D812yes—
163C22×D13C2×SD1612yes—
164Q8×C13—48no—
165C2×C4×C13—22no—
166C2×C4×C13—24no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—42no—
170C2×C4×C13—42no—
171C2×C4×C13—42no—
172C2×C4×C13C2×C22⋊C412yes—
173C2×C4×C13C2×C22⋊C412yes—
174C2×C4×C13C2×D812yes—
175C2×C4×C13C2×SD1612yes—
176C2×C4×C13C23×C411yescharacteristic
177C2×C4×C13C22×D411yescharacteristic
178C2×C4×C132−1+412yes—
179C2×C4×C132−1+412yes—
180C2×Dic13—22no—
181C2×Dic13—24no—
182C2×Dic13—42no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185C2×Dic13—42no—
186C2×Dic13—42no—
187C2×Dic13C2×C22⋊C412yes—
188C2×Dic13C2×C22⋊C412yes—
189C2×Dic13C2×C22⋊C412yes—
190C2×Dic13C2×D812yes—
191C2×Dic13C2×SD1612yes—
192C2×Dic13#13714yes—
193C4×D13—24no—
194C4×D13—22no—
195C4×D13—22no—
196C4×D13—28no—
197C4×D13—416no—
198C4×D13#102116yes—
199Dic26—48no—
200Dic26—416no—
201C8×C13—42no—
202#1055—42no—
203C23×Q8—261no—
204C2×C4⋊Q8—138no—
205C2×C4⋊Q8—132no—
206C2×C4⋊Q8—131no—
207C2×C4⋊Q8—261no—
208C2×C4⋊Q8—264no—
209C2×C4⋊Q8—261no—
210C2×C4⋊Q8C2×D1311yescharacteristic
211C2×#117—261no—
212C22×C4⋊C4—132no—
213C22×C4⋊C4—261no—
214C22×C42—131no—
215#431—264no—
216C2×C4⋊C8—131no—
217C2×C4⋊C8C2×D1311yescharacteristic
218C2×C22⋊C8—132no—
219C2×C4×C8—132no—
220#384—132no—
221#382—261no—
222#380—132no—
223#380—261no—
224C4×C4⋊C4—131no—
225C4×C4⋊C4—261no—
226C4×C4⋊C4C2×D1311yescharacteristic
227#340—134no—
228#340—134no—
229#340—134no—
230#340C2×D1314yes—
231C22×C13C22×C22⋊C411yescharacteristic
232C22×C13#53612yes—
233C22×C13C22×D811yescharacteristic
234C22×C13C22×SD1611yescharacteristic
235C22×C13C2×#13712yes—
236C2×D13—22no—
237C2×D13—22no—
238C2×D13—24no—
239C2×D13—24no—
240C2×D13C2×#10214yes—
241C4×C13—22no—
242C4×C13—44no—
243C4×C13—82no—
244C4×C13C2×#10214yes—
245C4×C13#51912yes—
246C4×C13#53611yescharacteristic
247C4×C13#53611yescharacteristic
248Dic13—22no—
249Dic13—44no—
250Dic13—82no—
251Dic13C2×#10214yes—
252Dic13#41914yes—
253C22×Q8—21no—
254C22×Q8—262no—
255C22×Q8—268no—
256C22×Q8—261no—
257C22×Q8—524no—
258C22×Q8—524no—
259C23×C4—131no—
260C23×C4—131no—
261C23×C4—131no—
262C23×C4—262no—
263C22×C8—132no—
264C22×C8C22×D1312yes—
265C4⋊Q8—22no—
266C4⋊Q8—138no—
267C4⋊Q8—134no—
268C4⋊Q8—268no—
269C4⋊Q8—264no—
270C4⋊Q8—268no—
271C4⋊Q8—262no—
272C4⋊Q8C4×D1314yes—
273#117—524no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—132no—
276C2×C4⋊C4—138no—
277C2×C4⋊C4—132no—
278C2×C4⋊C4—264no—
279C2×C4⋊C4—268no—
280C2×C4⋊C4—262no—
281C2×C4⋊C4—262no—
282C2×C4⋊C4—261no—
283C2×C4⋊C4—262no—
284C2×C4⋊C4—262no—
285C2×C4⋊C4C22×D1312yes—
286C2×C4⋊C4C22×D1312yes—
287C2×C22⋊C4—262no—
288C2×C42—21no—
289C2×C42—131no—
290C2×C42—131no—
291C2×C42—131no—
292C2×C42—134no—
293C2×C42—134no—
294C2×C42—261no—
295C2×C42C22×D1311yescharacteristic
296C4⋊C8—22no—
297C4⋊C8—262no—
298C22⋊C8—264no—
299C4×C8—264no—
300#95—21no—
301#95—262no—
302#95—261no—
303C2×C13#231011yescharacteristic
304C2×C13C22×#10211yescharacteristic
305C2×C13C2×#41911yescharacteristic
306C2×C13#322612yes—
307C2×C13#322912yes—
308D13—24no—
309C24—131no—
310C2×Q8—24no—
311C2×Q8—42no—
312C2×Q8—42no—
313C2×Q8—268no—
314C2×Q8—264no—
315C2×Q8—524no—
316C2×Q8—524no—
317C2×Q8—5232no—
318C2×Q8—522no—
319C2×Q8—522no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—131no—
323C22×C4—131no—
324C22×C4—134no—
325C22×C4—134no—
326C22×C4—134no—
327C22×C4—131no—
328C22×C4—134no—
329C22×C4—132no—
330C22×C4—132no—
331C22×C4—264no—
332C22×C4—268no—
333C22×C4—262no—
334C22×C4—262no—
335C22×C4—262no—
336C22×C4—262no—
337C22×C4—524no—
338C22×C4—524no—
339C22×C4D4×D1311yescharacteristic
340C22×C4D4×D1311yescharacteristic
341C22×C4C23×D1311yescharacteristic
342C2×C8—22no—
343C2×C8—24no—
344C2×C8—262no—
345C2×C8—264no—
346C4⋊C4—24no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—134no—
351C4⋊C4—268no—
352C4⋊C4—268no—
353C4⋊C4—264no—
354C4⋊C4—262no—
355C4⋊C4—262no—
356C4⋊C4—262no—
357C4⋊C4—524no—
358C4⋊C4—524no—
359C4⋊C4C2×C4×D1314yes—
360C22⋊C4—524no—
361C42—42no—
362C42—134no—
363C42—134no—
364C42—132no—
365C42—132no—
366C42—522no—
367C42C2×C4×D1312yes—
368C42D4×D1312yes—
369C13#2183311yescharacteristic, complemented, Sylow
370C23—132no—
371C23—132no—
372C23—132no—
373C23—262no—
374C23—262no—
375C23C2×D4×D1311yescharacteristic
376Q8—48no—
377Q8—5216no—
378Q8—528no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—132no—
387C2×C4—132no—
388C2×C4—132no—
389C2×C4—132no—
390C2×C4—134no—
391C2×C4—1316no—
392C2×C4—132no—
393C2×C4—268no—
394C2×C4—262no—
395C2×C4—262no—
396C2×C4—264no—
397C2×C4—262no—
398C2×C4—264no—
399C2×C4—5216no—
400C2×C4—522no—
401C2×C4—522no—
402C2×C4—522no—
403C2×C4—522no—
404C2×C4—522no—
405C2×C4C22⋊C4×D1312yes—
406C2×C4C22⋊C4×D1312yes—
407C2×C4D8×D1312yes—
408C2×C4SD16×D1312yes—
409C2×C4C22×C4×D1311yescharacteristic
410C2×C4C2×D4×D1311yescharacteristic
411C2×C4#8825412yes—
412C2×C4#8825712yes—
413C8—42no—
414C8—522no—
415C22—134no—
416C22—262no—
417C22—264no—
418C22—264no—
419C22—262no—
420C22C2×C22⋊C4×D1311yescharacteristic
421C22#1171933312yes—
422C22C2×D8×D1311yescharacteristic
423C22C2×SD16×D1311yescharacteristic
424C22D13×#13712yes—
425C4—22no—
426C4—44no—
427C4—82no—
428C4—134no—
429C4—134no—
430C4—262no—
431C4—524no—
432C4—1042no—
433C4D13×#10214yes—
434C4#1171927712yes—
435C4#1171938011yescharacteristic
436C4#1171942911yescharacteristic
437C2—264no—
438C2#1311741911yescharacteristic
439C2C2×D13×#10211yescharacteristic
440C2D13×#41911yescharacteristic
441C2#1312595612yes—
442C2#1312597912yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1988C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1988D13
hypocenterC13#21833
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
4. #13115795C2semidirect
5. #13115789C2semidirect
6. #13115788C2semidirect
7. #13115787C2semidirect
9. C13×#1988C2semidirect
14. D13×C4⋊Q8C4semidirect
156. #1988D13semidirect
369. C13#21833semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C4⋊Q82
C2×#117184942
#131172402
#131157952
#131157892
#131157882
#131157872
#131149212
C13×#19882
#2183313