Finite Group Databasebeta

← #15867432

Subgroups — #15867432

Order 3328.

1194 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719393C211yesmaximal, characteristic
2C2×D13×C4⋊C8C211yesmaximal, characteristic
3C4×#88146C211yesmaximal, characteristic
4#13115794C211yesmaximal, characteristic, complemented
5#13115793C211yesmaximal, characteristic, complemented
6#13115791C211yesmaximal, characteristic, complemented
7#13115786C212yesmaximal, complemented
8#13115782C212yesmaximal, complemented
9#13114551C212yesmaximal
10#13114551C212yesmaximal
11C13×#1989C211yesmaximal, characteristic, complemented
12C2×C13×#125C2211yescharacteristic
13C22×C8×D13C2212yes—
14#11719393—24no—
15#11719393C418yescomplemented
16C2×#88150—21no—
17C2×#88150—21no—
18C2×#88146C2211yescharacteristic
19C2×#88146C2211yescharacteristic
20C2×#88146C2212yes—
21C2×#88142C2211yescharacteristic
22C2×#88142C2211yescharacteristic
23C2×#88141—21no—
24C2×#88141—21no—
25C2×C42×D13C2211yescharacteristic
26C2×#88124C2211yescharacteristic
27C2×C13×C4⋊C8C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C2×#88054C2212yes—
30C4⋊C4×Dic13C2212yes—
31C4×#6103—21no—
32C4×C4⋊Dic13C2211yescharacteristic
33C42×Dic13—21no—
34C2×C4⋊#1055C2211yescharacteristic
35D13×C4⋊C8—24no—
36#11718327—21no—
37#11718309—21no—
38C13×#340C2212yes—
39C13×#340C2212yes—
40#11718143C2212yes—
41#11718143C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13C2311yescharacteristic
49C22×Dic26—21no—
50C22×Dic26—21no—
51C22×C8×C13C2312yes—
52C13×#125—22no—
53C13×#125C2×C414yes—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4C2311yescharacteristic
57C2×C13×C4⋊C4C2311yescharacteristic
58C2×C13×C4⋊C4C2312yes—
59C2×C42×C13—21no—
60C2×C42×C13C2311yescharacteristic
61C2×#6103—21no—
62C2×#6103—21no—
63C2×#6103—22no—
64C2×C4⋊Dic13C2311yescharacteristic
65C2×C4⋊Dic13C2311yescharacteristic
66C2×C4⋊Dic13C2312yes—
67C2×#6101—21no—
68C2×#6101—21no—
69C2×#6101—21no—
70C2×#6101—21no—
71C2×C4×Dic13—21no—
72C2×C4×Dic13—21no—
73C2×C4×Dic13—22no—
74C2×C4×Dic13—21no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13D411yescharacteristic
77C2×C4×Dic13D411yescharacteristic
78C2×C4×Dic13C2311yescharacteristic
79C22×#1055C2312yes—
80C2×C8×D13—24no—
81C2×C8×D13—28no—
82#88150—28no—
83#88150—28no—
84#88146—22no—
85#88146—22no—
86#88146—24no—
87#88146C2×C414yes—
88#88146C2×C414yes—
89#88146Q818yescomplemented
90#88142—22no—
91#88142—22no—
92#88142C2×C414yes—
93#88142C2×C414yes—
94#88141—28no—
95#88141—28no—
96C42×D13C2×C414yes—
97C42×D13D414yes—
98#88124—22no—
99#88124C2×C414yes—
100C13×C4⋊C8—22no—
101C13×#95—21no—
102#88071—21no—
103#88071—22no—
104#88054—24no—
105C4⋊#1055—22no—
106#21311—131nomaximal, Sylow
107C23×D13C2×D411yescharacteristic
108C22×C4×C13—22no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2411yescharacteristic
114C22×Dic13—22no—
115C22×Dic13—21no—
116C22×Dic13—21no—
117C22×Dic13C2×D411yescharacteristic
118C22×Dic13C2×D411yescharacteristic
119C22×Dic13C2×D411yescharacteristic
120C2×C4×D13—24no—
121C2×C4×D13—41no—
122C2×C4×D13—41no—
123C2×C4×D13C22⋊C414yes—
124C2×C4×D13C22⋊C414yes—
125C2×C4×D13C22×C412yes—
126C2×C4×D13C2×D412yes—
127C2×C4×D13C2×Q814yes—
128C2×C4×D13#4114yes—
129C2×Dic26—24no—
130C2×Dic26—24no—
131C2×Dic26—42no—
132C2×Dic26—42no—
133C2×Dic26—44no—
134C2×C8×C13—22no—
135C2×C8×C13—24no—
136C13×C4⋊C4—24no—
137C13×C4⋊C4—24no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4—22no—
141C13×C4⋊C4C22×C412yes—
142C13×C4⋊C4C22×C412yes—
143C13×C4⋊C4C2×Q814yes—
144C42×C13—42no—
145C42×C13C22×C412yes—
146C42×C13C2×D412yes—
147#6103—24no—
148#6103—24no—
149#6103—28no—
150C4⋊Dic13—21no—
151C4⋊Dic13—21no—
152C4⋊Dic13—22no—
153C4⋊Dic13C22×C412yes—
154C4⋊Dic13C22×C412yes—
155C4⋊Dic13C2×Q814yes—
156#6101—24no—
157#6101—24no—
158#6101—24no—
159#6101—24no—
160C4×Dic13—24no—
161C4×Dic13—24no—
162C4×Dic13—28no—
163C4×Dic13—42no—
164C4×Dic13—44no—
165C4×Dic13C22⋊C414yes—
166C4×Dic13C22⋊C414yes—
167C4×Dic13C22×C412yes—
168C4×Dic13C2×D412yes—
169C2×#1055—22no—
170C2×#1055—24no—
171C8×D13—48no—
172C2×#533—131no—
173C22×C4⋊C8—131no—
174C4×#117—131no—
175#1989—131no—
176#1989—131no—
177#1989—131no—
178#1989D1311yescharacteristic, complemented
179#1988—132no—
180#1987—132no—
181#1735—132no—
182#1735—132no—
183C23×C13C22×D411yescharacteristic
184C22×D13—22no—
185C22×D13—21no—
186C22×D13—21no—
187C22×D13C2×C22⋊C412yes—
188C22×D13C22⋊Q814yes—
189C2×C4×C13—22no—
190C2×C4×C13—21no—
191C2×C4×C13—21no—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—24no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13C2×C22⋊C412yes—
201C2×C4×C13C2×C22⋊C412yes—
202C2×C4×C13C23×C411yescharacteristic
203C2×C4×C13C22×D411yescharacteristic
204C2×C4×C13C22×Q812yes—
205C2×C4×C13C2×#4112yes—
206C2×Dic13—21no—
207C2×Dic13—21no—
208C2×Dic13—22no—
209C2×Dic13—22no—
210C2×Dic13—24no—
211C2×Dic13—42no—
212C2×Dic13—42no—
213C2×Dic13—42no—
214C2×Dic13—41no—
215C2×Dic13—41no—
216C2×Dic13C2×C22⋊C412yes—
217C2×Dic13C2×C22⋊C412yes—
218C2×Dic13C2×C22⋊C412yes—
219C2×Dic13C22⋊Q814yes—
220C2×Dic13#13514yes—
221C4×D13—28no—
222C4×D13—44no—
223C4×D13C4×Q818yes—
224C4×D13#12414yes—
225C4×D13C4⋊Q814yes—
226Dic26—48no—
227Dic26—48no—
228C8×C13—42no—
229#1055—42no—
230C23×C8—132no—
231#533—138no—
232#533—264no—
233C2×C4⋊Q8—131no—
234C2×C4⋊Q8—131no—
235C2×#125—131no—
236C2×#125C2×D1311yescharacteristic
237C2×C22⋊Q8—261no—
238C2×C22⋊Q8—261no—
239C2×C4×Q8—261no—
240C2×C4×Q8—261no—
241C2×#117—131no—
242C2×#117—131no—
243C2×#117—132no—
244C22×C42—131no—
245C2×C4⋊C8—132no—
246C2×C4⋊C8—131no—
247C2×C4⋊C8—264no—
248C2×C4⋊C8C2×D1311yescharacteristic
249C4×C4⋊C4—132no—
250C4×C4⋊C4—131no—
251C4×C4⋊C4C2×D1311yescharacteristic
252C4×C22⋊C4—261no—
253C4×C22⋊C4—261no—
254#376—261no—
255C43—261no—
256#340—132no—
257#340—132no—
258#340—132no—
259#340—132no—
260#340—132no—
261#340—132no—
262#340C2×D1312yes—
263#340C2×D1312yes—
264C22×C13C22×C22⋊C411yescharacteristic
265C22×C13C2×C22⋊Q812yes—
266C22×C13C2×#13512yes—
267C22×C13#57511yescharacteristic
268C22×C13#57511yescharacteristic
269C2×D13—24no—
270C2×D13—24no—
271C2×D13—22no—
272C2×D13—22no—
273C2×D13#39114yes—
274C4×C13—22no—
275C4×C13—22no—
276C4×C13—44no—
277C4×C13—42no—
278C4×C13—42no—
279C4×C13C2×C4×Q812yes—
280C4×C13C2×#12411yescharacteristic
281C4×C13C2×C4⋊Q811yescharacteristic
282Dic13—22no—
283Dic13—44no—
284Dic13—42no—
285Dic13—42no—
286Dic13#39114yes—
287Dic13#41614yes—
288C22×Q8—261no—
289C22×Q8—261no—
290C23×C4—131no—
291C23×C4—131no—
292C23×C4—131no—
293C22×C8—132no—
294C22×C8—268no—
295C22×C8—264no—
296C22×C8C22×D1312yes—
297C4⋊Q8—134no—
298C4⋊Q8—134no—
299C4⋊Q8—262no—
300C4⋊Q8—262no—
301#125—22no—
302#125—134no—
303#125—262no—
304#125C4×D1314yes—
305C22⋊Q8—268no—
306C22⋊Q8—268no—
307C4×Q8—268no—
308C4×Q8—268no—
309#117—134no—
310#117—134no—
311#117—138no—
312#117—262no—
313#117—262no—
314#117—264no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—131no—
318C2×C4⋊C4—131no—
319C2×C4⋊C4—132no—
320C2×C4⋊C4—261no—
321C2×C4⋊C4—261no—
322C2×C4⋊C4—261no—
323C2×C4⋊C4—261no—
324C2×C4⋊C4C22×D1311yescharacteristic
325C2×C4⋊C4C22×D1311yescharacteristic
326C2×C4⋊C4C22×D1312yes—
327C2×C22⋊C4—261no—
328C2×C22⋊C4—261no—
329C2×C22⋊C4—262no—
330C2×C42—21no—
331C2×C42—131no—
332C2×C42—131no—
333C2×C42—131no—
334C2×C42—134no—
335C2×C42—134no—
336C2×C42—261no—
337C2×C42—261no—
338C2×C42—262no—
339C2×C42—262no—
340C2×C42—261no—
341C2×C42C22×D1311yescharacteristic
342C4⋊C8—22no—
343C4⋊C8—264no—
344C4⋊C8—262no—
345#95—21no—
346#95—262no—
347#95—261no—
348C2×C13C2×#39111yescharacteristic
349C2×C13C2×#41611yescharacteristic
350C2×C13#289611yescharacteristic
351C2×C13#307612yes—
352C2×C13#307612yes—
353D13—24no—
354C24—131no—
355C2×Q8—264no—
356C2×Q8—264no—
357C2×Q8—524no—
358C2×Q8—522no—
359C2×Q8—522no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—131no—
364C22×C4—131no—
365C22×C4—132no—
366C22×C4—132no—
367C22×C4—134no—
368C22×C4—134no—
369C22×C4—131no—
370C22×C4—134no—
371C22×C4—134no—
372C22×C4—264no—
373C22×C4—262no—
374C22×C4—261no—
375C22×C4—261no—
376C22×C4—521no—
377C22×C4—521no—
378C22×C4D4×D1311yescharacteristic
379C22×C4D4×D1311yescharacteristic
380C22×C4C23×D1311yescharacteristic
381C2×C8—22no—
382C2×C8—24no—
383C2×C8—262no—
384C2×C8—264no—
385C2×C8—528no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—132no—
392C4⋊C4—132no—
393C4⋊C4—134no—
394C4⋊C4—264no—
395C4⋊C4—264no—
396C4⋊C4—264no—
397C4⋊C4—264no—
398C4⋊C4—261no—
399C4⋊C4—261no—
400C4⋊C4—262no—
401C4⋊C4C2×C4×D1312yes—
402C4⋊C4C2×C4×D1312yes—
403C4⋊C4Q8×D1314yes—
404C22⋊C4—264no—
405C22⋊C4—264no—
406C22⋊C4—268no—
407C42—42no—
408C42—134no—
409C42—134no—
410C42—132no—
411C42—132no—
412C42—264no—
413C42—264no—
414C42—268no—
415C42—522no—
416C42—524no—
417C42C2×C4×D1312yes—
418C42D4×D1312yes—
419C13#2131111yescharacteristic, complemented, Sylow
420C23—132no—
421C23—134no—
422C23—262no—
423C23—261no—
424C23—261no—
425C23C2×D4×D1311yescharacteristic
426Q8—528no—
427Q8—528no—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—132no—
440C2×C4—132no—
441C2×C4—134no—
442C2×C4—134no—
443C2×C4—134no—
444C2×C4—138no—
445C2×C4—134no—
446C2×C4—132no—
447C2×C4—268no—
448C2×C4—261no—
449C2×C4—261no—
450C2×C4—262no—
451C2×C4—262no—
452C2×C4—264no—
453C2×C4—524no—
454C2×C4—522no—
455C2×C4—522no—
456C2×C4—521no—
457C2×C4—522no—
458C2×C4—521no—
459C2×C4C22⋊C4×D1312yes—
460C2×C4C22⋊C4×D1312yes—
461C2×C4C22×C4×D1311yescharacteristic
462C2×C4C2×D4×D1311yescharacteristic
463C2×C4C2×Q8×D1312yes—
464C2×C4#41×D1312yes—
465C8—42no—
466C8—522no—
467C22—134no—
468C22—262no—
469C22—264no—
470C22—264no—
471C22—262no—
472C22C2×C22⋊C4×D1311yescharacteristic
473C22D13×C22⋊Q812yes—
474C22D13×#13512yes—
475C22#1171947811yescharacteristic
476C22#1171948211yescharacteristic
477C4—22no—
478C4—22no—
479C4—42no—
480C4—44no—
481C4—42no—
482C4—134no—
483C4—134no—
484C4—262no—
485C4—522no—
486C4—524no—
487C4—522no—
488C4C4×Q8×D1312yes—
489C4D13×#12411yescharacteristic
490C4D13×C4⋊Q811yescharacteristic
491C2—264no—
492C2D13×#39111yescharacteristic
493C2D13×#41611yescharacteristic
494C2#1312335211yescharacteristic
495C2#1312462112yes—
496C2#1312462312yes—
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#21311
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
89. #88146Q8semidirect
178. #1989D13semidirect
419. C13#21311semidirect

Maximal subgroups

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

subgroupindex
C2×#117193932
C2×D13×C4⋊C82
C4×#881462
#131157942
#131157932
#131157912
#131157862
#131157822
#131145512
C13×#19892
#2131113