Finite Group Databasebeta

← #15867439

Subgroups — #15867439

Order 3328.

1250 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719393C211yesmaximal, characteristic
2C2×#11718498C211yesmaximal, characteristic
3C4×C4⋊C4×D13C211yesmaximal, characteristic
4#13115794C211yesmaximal, characteristic, complemented
5#13115793C211yesmaximal, characteristic, complemented
6#13115791C211yesmaximal, characteristic, complemented
7#13115786C212yesmaximal, complemented
8#13115782C212yesmaximal, complemented
9#13114554C212yesmaximal
10#13114554C212yesmaximal
11C13×#1989C211yesmaximal, characteristic, complemented
12C2×C13×#125C2211yescharacteristic
13C22×#6094C2212yes—
14#11719393—24no—
15#11719393C418yescomplemented
16C2×#88150—21no—
17C2×#88150—21no—
18C2×#88146C2211yescharacteristic
19C2×#88146C2211yescharacteristic
20C2×C4⋊C4×D13C2212yes—
21C2×#88142C2211yescharacteristic
22C2×#88142C2211yescharacteristic
23C2×#88141—21no—
24C2×#88141—21no—
25C2×C42×D13—21no—
26C2×C42×D13C2211yescharacteristic
27C2×#88124C2211yescharacteristic
28C2×C13×C4⋊C8C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C2×#88054C2212yes—
31C4⋊C4×Dic13C2212yes—
32C4×C4⋊Dic13C2211yescharacteristic
33C4×#6101—21no—
34C2×C4⋊#1055C2211yescharacteristic
35#11718498—24no—
36D13×#95—21no—
37#11718310—21no—
38C13×#340C2212yes—
39C13×#340C2212yes—
40#11718143C2212yes—
41#11718143C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46C22×C4×D13—22no—
47C22×C4×D13D411yescharacteristic
48C22×C4×D13D411yescharacteristic
49C22×C4×D13C2311yescharacteristic
50C22×Dic26—21no—
51C22×Dic26—21no—
52C22×C8×C13C2312yes—
53C13×#125—22no—
54C13×#125C2×C414yescomplemented
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4C2311yescharacteristic
58C2×C13×C4⋊C4C2311yescharacteristic
59C2×C13×C4⋊C4C2312yes—
60C2×C42×C13—21no—
61C2×C42×C13C2311yescharacteristic
62C2×#6103—21no—
63C2×#6103—21no—
64C2×C4⋊Dic13C2311yescharacteristic
65C2×C4⋊Dic13C2311yescharacteristic
66C2×C4⋊Dic13C2312yes—
67C2×#6101—21no—
68C2×#6101—21no—
69C2×#6101—21no—
70C2×#6101—21no—
71C2×#6101—22no—
72C2×C4×Dic13—21no—
73C2×C4×Dic13—21no—
74C2×C4×Dic13—21no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13D411yescharacteristic
77C2×C4×Dic13D411yescharacteristic
78C2×C4×Dic13C2311yescharacteristic
79C22×#1055C2312yes—
80C2×#6094—24no—
81C2×#6094—28no—
82#88150—28no—
83#88150—28no—
84#88146—22no—
85#88146—22no—
86#88146C2×C414yes—
87#88146C2×C414yes—
88C4⋊C4×D13—24no—
89C4⋊C4×D13Q818yescomplemented
90#88142—22no—
91#88142—22no—
92#88142C2×C414yescomplemented
93#88142C2×C414yescomplemented
94#88141—28no—
95#88141—28no—
96C42×D13—44no—
97C42×D13C2×C414yes—
98C42×D13D414yes—
99#88124—22no—
100#88124C2×C414yescomplemented
101C13×C4⋊C8—22no—
102C13×#95—21no—
103#88071—21no—
104#88071—22no—
105#88054—24no—
106C4⋊#1055—22no—
107#21312—131nomaximal, Sylow
108C23×D13C2×D411yescharacteristic
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2411yescharacteristic
115C22×Dic13—22no—
116C22×Dic13—21no—
117C22×Dic13—21no—
118C22×Dic13C2×D411yescharacteristic
119C22×Dic13C2×D411yescharacteristic
120C22×Dic13C2×D411yescharacteristic
121C2×C4×D13—22no—
122C2×C4×D13—22no—
123C2×C4×D13—28no—
124C2×C4×D13—42no—
125C2×C4×D13—44no—
126C2×C4×D13—44no—
127C2×C4×D13C22⋊C414yes—
128C2×C4×D13C22⋊C414yes—
129C2×C4×D13C22×C412yes—
130C2×C4×D13C2×D412yes—
131C2×C4×D13C2×Q814yes—
132C2×C4×D13#4114yes—
133C2×Dic26—24no—
134C2×Dic26—24no—
135C2×Dic26—44no—
136C2×Dic26—42no—
137C2×Dic26—42no—
138C2×C8×C13—22no—
139C2×C8×C13—24no—
140C13×C4⋊C4—24no—
141C13×C4⋊C4—24no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—22no—
145C13×C4⋊C4C22×C412yes—
146C13×C4⋊C4C22×C412yes—
147C13×C4⋊C4C2×Q814yes—
148C42×C13—42no—
149C42×C13C22×C412yes—
150C42×C13C2×D412yes—
151#6103—24no—
152#6103—24no—
153C4⋊Dic13—21no—
154C4⋊Dic13—21no—
155C4⋊Dic13—22no—
156C4⋊Dic13C22×C412yes—
157C4⋊Dic13C22×C412yes—
158C4⋊Dic13C2×Q814yes—
159#6101—24no—
160#6101—24no—
161#6101—24no—
162#6101—24no—
163#6101—28no—
164C4×Dic13—24no—
165C4×Dic13—24no—
166C4×Dic13—42no—
167C4×Dic13—44no—
168C4×Dic13C22⋊C414yes—
169C4×Dic13C22⋊C414yes—
170C4×Dic13C22×C412yes—
171C4×Dic13C2×D412yes—
172C2×#1055—22no—
173C2×#1055—24no—
174#6094—48no—
175C2×#533—131no—
176C2×#423—131no—
177C2×C4×C4⋊C4—131no—
178#1989—131no—
179#1989—131no—
180#1989—131no—
181#1989D1311yescharacteristic, complemented
182#1988—132no—
183#1987—132no—
184#1736—132no—
185#1736—132no—
186C23×C13C22×D411yescharacteristic
187C22×D13—21no—
188C22×D13—21no—
189C22×D13—22no—
190C22×D13C2×C22⋊C412yes—
191C22×D13C22⋊Q814yes—
192C2×C4×C13—21no—
193C2×C4×C13—21no—
194C2×C4×C13—22no—
195C2×C4×C13—22no—
196C2×C4×C13—22no—
197C2×C4×C13—24no—
198C2×C4×C13—42no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13C2×C22⋊C412yes—
204C2×C4×C13C2×C22⋊C412yes—
205C2×C4×C13C23×C411yescharacteristic
206C2×C4×C13C22×D411yescharacteristic
207C2×C4×C13C22×Q812yes—
208C2×C4×C13C2×#4112yes—
209C2×Dic13—22no—
210C2×Dic13—22no—
211C2×Dic13—22no—
212C2×Dic13—24no—
213C2×Dic13—42no—
214C2×Dic13—41no—
215C2×Dic13—41no—
216C2×Dic13—42no—
217C2×Dic13—42no—
218C2×Dic13C2×C22⋊C412yes—
219C2×Dic13C2×C22⋊C412yes—
220C2×Dic13C2×C22⋊C412yes—
221C2×Dic13C22⋊Q814yes—
222C2×Dic13AGL(1,ℤ/8)12yes—
223C2×Dic13#13712yes—
224C4×D13—28no—
225C4×D13—44no—
226C4×D13—416no—
227C4×D13C4×Q818yes—
228C4×D13#12414yes—
229C4×D13C4⋊Q814yes—
230Dic26—48no—
231Dic26—48no—
232C8×C13—42no—
233#1055—42no—
234C22×M16—132no—
235#533—138no—
236#533—264no—
237C2×C4⋊Q8—131no—
238C2×C4⋊Q8—131no—
239C2×#125—131no—
240C2×#125C2×D1311yescharacteristic
241C2×C22⋊Q8—261no—
242C2×C22⋊Q8—261no—
243C2×C4×Q8—261no—
244C2×C4×Q8—261no—
245C2×#117—131no—
246C2×#117—131no—
247C22×C4⋊C4—132no—
248C22×C42—131no—
249C22×C42—261no—
250#423—264no—
251C2×C4⋊C8—132no—
252C2×C4⋊C8—131no—
253C2×C4⋊C8C2×D1311yescharacteristic
254C4×C4⋊C4—132no—
255C4×C4⋊C4—131no—
256C4×C4⋊C4—261no—
257C4×C4⋊C4—261no—
258C4×C4⋊C4C2×D1311yescharacteristic
259C2×#95—261no—
260#340—132no—
261#340—132no—
262#340—132no—
263#340—132no—
264#340—132no—
265#340—132no—
266#340C2×D1312yes—
267#340C2×D1312yes—
268C22×C13C22×C22⋊C411yescharacteristic
269C22×C13C2×C22⋊Q812yes—
270C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C13C2×#13711yescharacteristic
272C22×C13#57512yes—
273C2×D13—24no—
274C2×D13—24no—
275C2×D13—22no—
276C2×D13—22no—
277C2×D13#39114yes—
278C4×C13—22no—
279C4×C13—22no—
280C4×C13—44no—
281C4×C13—42no—
282C4×C13—42no—
283C4×C13C2×C4×Q812yes—
284C4×C13C2×#12411yescharacteristic
285C4×C13C2×C4⋊Q811yescharacteristic
286Dic13—22no—
287Dic13—44no—
288Dic13—42no—
289Dic13—42no—
290Dic13#39114yes—
291Dic13#41714yes—
292C22×Q8—261no—
293C22×Q8—261no—
294C23×C4—131no—
295C23×C4—131no—
296C23×C4—131no—
297C23×C4—262no—
298C2×M16—268no—
299C2×M16—264no—
300C22×C8—132no—
301C22×C8C22×D1312yes—
302C4⋊Q8—134no—
303C4⋊Q8—134no—
304C4⋊Q8—262no—
305C4⋊Q8—262no—
306#125—22no—
307#125—134no—
308#125—262no—
309#125C4×D1314yescomplemented
310C22⋊Q8—268no—
311C22⋊Q8—268no—
312C4×Q8—268no—
313C4×Q8—268no—
314#117—134no—
315#117—134no—
316#117—262no—
317#117—262no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—132no—
321C2×C4⋊C4—131no—
322C2×C4⋊C4—131no—
323C2×C4⋊C4—138no—
324C2×C4⋊C4—264no—
325C2×C4⋊C4—262no—
326C2×C4⋊C4—261no—
327C2×C4⋊C4—261no—
328C2×C4⋊C4—261no—
329C2×C4⋊C4—261no—
330C2×C4⋊C4C22×D1311yescharacteristic
331C2×C4⋊C4C22×D1311yescharacteristic
332C2×C4⋊C4C22×D1312yes—
333C2×C22⋊C4—261no—
334C2×C22⋊C4—261no—
335C2×C42—21no—
336C2×C42—131no—
337C2×C42—131no—
338C2×C42—131no—
339C2×C42—134no—
340C2×C42—134no—
341C2×C42—261no—
342C2×C42—261no—
343C2×C42—262no—
344C2×C42—261no—
345C2×C42—524no—
346C2×C42C22×D1311yescharacteristic
347C4⋊C8—22no—
348C4⋊C8—264no—
349C4⋊C8—262no—
350#95—21no—
351#95—262no—
352#95—261no—
353C2×C13C2×#39111yescharacteristic
354C2×C13C2×#41711yescharacteristic
355C2×C13#289611yescharacteristic
356C2×C13#307712yes—
357C2×C13#307812yes—
358D13—24no—
359C24—131no—
360C2×Q8—264no—
361C2×Q8—264no—
362C2×Q8—522no—
363C2×Q8—522no—
364C2×Q8—524no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—131no—
369C22×C4—131no—
370C22×C4—132no—
371C22×C4—132no—
372C22×C4—134no—
373C22×C4—134no—
374C22×C4—131no—
375C22×C4—134no—
376C22×C4—134no—
377C22×C4—262no—
378C22×C4—262no—
379C22×C4—268no—
380C22×C4—262no—
381C22×C4—261no—
382C22×C4—261no—
383C22×C4—522no—
384C22×C4—524no—
385C22×C4—524no—
386C22×C4D4×D1311yescharacteristic
387C22×C4D4×D1311yescharacteristic
388C22×C4C23×D1311yescharacteristic
389M16—528no—
390C2×C8—22no—
391C2×C8—24no—
392C2×C8—262no—
393C2×C8—264no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—132no—
400C4⋊C4—132no—
401C4⋊C4—134no—
402C4⋊C4—268no—
403C4⋊C4—264no—
404C4⋊C4—264no—
405C4⋊C4—264no—
406C4⋊C4—264no—
407C4⋊C4—261no—
408C4⋊C4—261no—
409C4⋊C4—262no—
410C4⋊C4C2×C4×D1312yes—
411C4⋊C4C2×C4×D1312yes—
412C4⋊C4Q8×D1314yes—
413C22⋊C4—264no—
414C22⋊C4—264no—
415C42—42no—
416C42—134no—
417C42—134no—
418C42—132no—
419C42—132no—
420C42—264no—
421C42—264no—
422C42—522no—
423C42—524no—
424C42C2×C4×D1312yes—
425C42D4×D1312yes—
426C13#2131211yescharacteristic, complemented, Sylow
427C23—132no—
428C23—134no—
429C23—262no—
430C23—261no—
431C23—261no—
432C23C2×D4×D1311yescharacteristic
433Q8—528no—
434Q8—528no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—132no—
447C2×C4—132no—
448C2×C4—132no—
449C2×C4—132no—
450C2×C4—134no—
451C2×C4—134no—
452C2×C4—138no—
453C2×C4—134no—
454C2×C4—132no—
455C2×C4—268no—
456C2×C4—262no—
457C2×C4—262no—
458C2×C4—262no—
459C2×C4—264no—
460C2×C4—524no—
461C2×C4—5216no—
462C2×C4—522no—
463C2×C4—522no—
464C2×C4—522no—
465C2×C4—521no—
466C2×C4—521no—
467C2×C4C22⋊C4×D1312yes—
468C2×C4C22⋊C4×D1312yes—
469C2×C4C22×C4×D1311yescharacteristic
470C2×C4C2×D4×D1311yescharacteristic
471C2×C4C2×Q8×D1312yes—
472C2×C4#41×D1312yes—
473C8—42no—
474C8—522no—
475C22—134no—
476C22—262no—
477C22—262no—
478C22—264no—
479C22—264no—
480C22C2×C22⋊C4×D1311yescharacteristic
481C22D13×C22⋊Q812yes—
482C22#1171947312yes—
483C22D13×AGL(1,ℤ/8)11yescharacteristic
484C22D13×#13711yescharacteristic
485C4—22no—
486C4—22no—
487C4—42no—
488C4—42no—
489C4—44no—
490C4—134no—
491C4—134no—
492C4—262no—
493C4—522no—
494C4—522no—
495C4—524no—
496C4C4×Q8×D1312yes—
497C4D13×#12411yescharacteristic
498C4D13×C4⋊Q811yescharacteristic
499C2—264no—
500C2D13×#39111yescharacteristic
501C2D13×#41711yescharacteristic
502C2#1312335111yescharacteristic
503C2#1312463112yes—
504C2#1312463912yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1989C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1989D13
hypocenterC13#21312
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
4. #13115794C2semidirect
5. #13115793C2semidirect
6. #13115791C2semidirect
7. #13115786C2semidirect
8. #13115782C2semidirect
11. C13×#1989C2semidirect
15. #11719393C4semidirect
54. C13×#125C2×C4semidirect
89. C4⋊C4×D13Q8semidirect
92. #88142C2×C4semidirect
93. #88142C2×C4semidirect
100. #88124C2×C4semidirect
181. #1989D13semidirect
309. #125C4×D13semidirect
426. C13#21312semidirect

Maximal subgroups

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

subgroupindex
C2×#117193932
C2×#117184982
C4×C4⋊C4×D132
#131157942
#131157932
#131157912
#131157862
#131157822
#131145542
C13×#19892
#2131213