Finite Group Databasebeta

← #15879365

Subgroups — #15879365

Order 3328.

1154 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719284C211yesmaximal, characteristic
2C2×#11718499C211yesmaximal, characteristic
3#13117787C211yesmaximal, characteristic
4#13115796C211yesmaximal, characteristic, complemented
5#13115783C211yesmaximal, characteristic, complemented
6#13115266C212yesmaximal, complemented
7#13115145C212yesmaximal, complemented
8#13114921C212yesmaximal, complemented
9C4×#88075C211yesmaximal, characteristic, complemented
10#13114554C212yesmaximal, complemented
11C13×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C13C2211yescharacteristic
13C2×#88200C2212yes—
14C22×#6094C2212yes—
15#11719284—24no—
16#11719284C418yescomplemented
17C2×#88150—22no—
18C2×#88146C2212yes—
19C2×C4⋊C4×D13C2212yes—
20C2×C4×D52—21no—
21C2×C4×D52C2211yescharacteristic
22C2×#88124—21no—
23C2×#88123C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#103C2212yes—
26C13×#384C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C2×#88060C2212yes—
30#11718651—22no—
31#11718649—21no—
32#11718648C2212yes—
33C4⋊C4×Dic13—21no—
34C4×C4⋊Dic13C2211yescharacteristic
35C2×C4×#1055C2211yescharacteristic
36#11718499—24no—
37C13×#340C2212yes—
38#11718143C2212yes—
39#11718143C2212yes—
40#11718121C2212yes—
41#11718121C2211yescharacteristic
42#11718121C2211yescharacteristic
43#11718121C2212yes—
44C22×Q8×C13C2311yescharacteristic
45C22×D52D411yescharacteristic
46C22×C4×D13—22no—
47C22×C4×D13C2312yes—
48C22×Dic26—21no—
49C22×C8×C13C2312yes—
50C4×Q8×C13—22no—
51C4×Q8×C13C2×C414yes—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4C2312yes—
56C2×C13×C4⋊C4C2311yescharacteristic
57C2×C42×C13—21no—
58C2×C42×C13C2311yescharacteristic
59#88200—24no—
60#88200C2×C418yes—
61C2×#6103—22no—
62C2×#6103—22no—
63C2×#6103—22no—
64C2×#6103D412yes—
65C2×C4⋊Dic13—21no—
66C2×C4⋊Dic13D411yescharacteristic
67C2×C4⋊Dic13C2311yescharacteristic
68C2×C4⋊Dic13C2312yes—
69C2×C4⋊Dic13C2311yescharacteristic
70C2×#6101—22no—
71C2×#6101—22no—
72C2×C4×Dic13—21no—
73C2×C4×Dic13—22no—
74C22×#1055C2311yescharacteristic
75C22×#1055C2311yescharacteristic
76C2×#6094—24no—
77C2×#6094—24no—
78C2×#6094—42no—
79#88150—216no—
80#88146—24no—
81#88146—42no—
82C4⋊C4×D13—24no—
83C4⋊C4×D13C2×C418yes—
84C4×D52—28no—
85C4×D52C2×C414yes—
86C4×D52D414yes—
87#88124—28no—
88#88123—22no—
89#88123C2×C414yes—
90C13×C4⋊C8—22no—
91C13×#103—42no—
92#88075—22no—
93#88075—22no—
94#88071—21no—
95#88071—22no—
96#88060—24no—
97C4×#1055—22no—
98#22502—131nomaximal, Sylow
99C23×D13C2×D412yes—
100C2×Q8×C13—21no—
101C2×Q8×C13—21no—
102C2×Q8×C13—21no—
103C2×Q8×C13—21no—
104C2×Q8×C13—21no—
105C2×Q8×C13C22×C412yes—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—22no—
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2411yescharacteristic
112C22×Dic13—21no—
113C22×Dic13—22no—
114C22×Dic13—21no—
115C22×Dic13C2×D412yes—
116C2×D52—22no—
117C2×D52—22no—
118C2×D52C22⋊C414yes—
119C2×C4×D13—22no—
120C2×C4×D13—22no—
121C2×C4×D13—22no—
122C2×C4×D13—22no—
123C2×C4×D13—28no—
124C2×C4×D13—82no—
125C2×C4×D13—82no—
126C2×C4×D13C22×C414yes—
127C2×C4×D13C2×D414yes—
128C2×Dic26—24no—
129C2×Dic26—81no—
130C2×Dic26—81no—
131C2×C8×C13—22no—
132C2×C8×C13—22no—
133C2×C8×C13—22no—
134C13×C4⋊C4—24no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—22no—
137C13×C4⋊C4—22no—
138C13×C4⋊C4—42no—
139C13×C4⋊C4—81no—
140C13×C4⋊C4C22×C412yes—
141C42×C13—24no—
142C42×C13C22×C412yes—
143C42×C13C2×D412yes—
144#6103—28no—
145#6103—44no—
146#6103—82no—
147#6103C22⋊C418yes—
148C4⋊Dic13—24no—
149C4⋊Dic13—22no—
150C4⋊Dic13—21no—
151C4⋊Dic13—21no—
152C4⋊Dic13—21no—
153C4⋊Dic13C22⋊C414yes—
154C4⋊Dic13C22×C414yes—
155C4⋊Dic13#4112yes—
156#6101—28no—
157#6101—28no—
158C4×Dic13—44no—
159C4×Dic13—42no—
160C2×#1055—21no—
161C2×#1055—21no—
162C2×#1055—21no—
163C2×#1055—21no—
164C2×#1055—21no—
165C2×#1055#4112yes—
166#6094—48no—
167C2×#554—131no—
168C2×#436—131no—
169#2354—131no—
170#1990—131no—
171#1987—131no—
172#1894—132no—
173#1873—132no—
174#1823—132no—
175#1803D1311yescharacteristic, complemented
176C4×#103—131no—
177#1736—132no—
178C23×C13C22×D411yescharacteristic
179C22×D13—22no—
180C22×D13—22no—
181C22×D13—22no—
182C22×D13—22no—
183C22×D13—22no—
184C22×D13—22no—
185C22×D13C2×C22⋊C414yes—
186Q8×C13—22no—
187Q8×C13—22no—
188Q8×C13—41no—
189Q8×C13—41no—
190C2×C4×C13—21no—
191C2×C4×C13—21no—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—42no—
199C2×C4×C13—42no—
200C2×C4×C13—42no—
201C2×C4×C13C2×C22⋊C412yes—
202C2×C4×C13C2×C22⋊C412yes—
203C2×C4×C13#13712yes—
204C2×C4×C13#13712yes—
205C2×C4×C13C23×C411yescharacteristic
206C2×C4×C13C22×D411yescharacteristic
207C2×C4×C13C2×#4111yescharacteristic
208C2×C4×C13C2×#4111yescharacteristic
209C2×C4×C13H(5,𝔽2)11yescharacteristic
210C2×C4×C132−1+411yescharacteristic
211C2×Dic13—22no—
212C2×Dic13—22no—
213C2×Dic13—24no—
214C2×Dic13—22no—
215C2×Dic13—41no—
216C2×Dic13—42no—
217C2×Dic13—42no—
218C2×Dic13—41no—
219C2×Dic13—41no—
220C2×Dic13—41no—
221C2×Dic13—41no—
222C2×Dic13C2×C22⋊C414yes—
223D52—28no—
224C4×D13—24no—
225C4×D13—24no—
226C4×D13—24no—
227C4×D13—24no—
228C4×D13—88no—
229Dic26—84no—
230C8×C13—42no—
231#1055—22no—
232#1055—41no—
233C22×M16—132no—
234#554—138no—
235#554—264no—
236C2×C4⋊Q8—131no—
237C2×#125—261no—
238C2×C22⋊Q8—132no—
239C2×C22⋊Q8—262no—
240C2×C4×Q8C2×D1311yescharacteristic
241C2×C4×D4—131no—
242C2×C4×D4—261no—
243C2×#117—132no—
244C22×C4⋊C4—132no—
245#436—264no—
246C2×C4⋊C8C2×D1311yescharacteristic
247C2×#103—131no—
248C2×#103—131no—
249C2×#103C2×D1312yes—
250C2×C22⋊C8—132no—
251C2×C4×C8—131no—
252#390—261no—
253#388—262no—
254#384C2×D1311yescharacteristic
255#380—132no—
256C4×C4⋊C4—131no—
257C4×C4⋊C4—261no—
258#340—132no—
259#340—132no—
260#340—131no—
261#340—132no—
262#340—132no—
263#340—131no—
264#340C2×D1312yes—
265C22×C13C22×C22⋊C411yescharacteristic
266C22×C13#54611yescharacteristic
267C22×C13#54711yescharacteristic
268C22×C13C2×#13711yescharacteristic
269C22×C13C2×#13711yescharacteristic
270C22×C13#57611yescharacteristic
271C22×C13#57711yescharacteristic
272C2×D13—24no—
273C2×D13—24no—
274C2×D13—24no—
275C2×D13—42no—
276C2×D13—42no—
277C2×D13—42no—
278C2×D13—42no—
279C4×C13—22no—
280C4×C13—42no—
281C4×C13—42no—
282C4×C13—82no—
283C4×C13#41914yes—
284C4×C13C4×#4111yescharacteristic
285C4×C13#52011yescharacteristic
286C4×C13#54611yescharacteristic
287C4×C13#54711yescharacteristic
288Dic13—24no—
289Dic13—42no—
290Dic13—44no—
291Dic13—81no—
292C22×Q8—261no—
293C22×Q8C22×D1311yescharacteristic
294C22×D4—131no—
295C23×C4—132no—
296C23×C4—262no—
297C2×M16—264no—
298C2×M16—264no—
299C2×M16—522no—
300C22×C8—131no—
301C22×C8—131no—
302C22×C8C22×D1312yes—
303C4⋊Q8—134no—
304C4⋊Q8—262no—
305#125—268no—
306C22⋊Q8—138no—
307C22⋊Q8—2616no—
308C22⋊Q8—264no—
309C4×Q8—22no—
310C4×Q8C4×D1314yes—
311C4×D4—134no—
312C4×D4—134no—
313C4×D4—268no—
314#117—264no—
315#117—522no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—131no—
320C2×C4⋊C4—132no—
321C2×C4⋊C4—131no—
322C2×C4⋊C4—138no—
323C2×C4⋊C4—131no—
324C2×C4⋊C4—264no—
325C2×C4⋊C4—262no—
326C2×C4⋊C4—262no—
327C2×C4⋊C4—261no—
328C2×C4⋊C4C22×D1312yes—
329C2×C4⋊C4C22×D1311yescharacteristic
330C2×C22⋊C4—132no—
331C2×C22⋊C4—262no—
332C2×C22⋊C4—262no—
333C2×C22⋊C4—262no—
334C2×C42—21no—
335C2×C42—262no—
336C2×C42—261no—
337C2×C42C22×D1311yescharacteristic
338C4⋊C8—22no—
339#103—42no—
340#103—262no—
341#103—262no—
342C22⋊C8—264no—
343C4×C8—262no—
344#95—262no—
345#95—261no—
346C2×C13#233911yescharacteristic
347C2×C13C2×#41911yescharacteristic
348C2×C13#289711yescharacteristic
349C2×C13#333111yescharacteristic
350C2×C13#333311yescharacteristic
351C2×C13#335611yescharacteristic
352C2×C13#335711yescharacteristic
353D13—44no—
354C24—132no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—264no—
361C2×Q8—1041no—
362C2×Q8—1041no—
363C2×Q8C2×C4×D1312yes—
364C2×D4—134no—
365C2×D4—262no—
366C2×D4—262no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—132no—
371C22×C4—134no—
372C22×C4—134no—
373C22×C4—268no—
374C22×C4—262no—
375C22×C4—262no—
376C22×C4—262no—
377C22×C4—262no—
378C22×C4—261no—
379C22×C4—262no—
380C22×C4—261no—
381C22×C4—1042no—
382C22×C4—1042no—
383C22×C4D4×D1311yescharacteristic
384C22×C4D4×D1311yescharacteristic
385C22×C4C23×D1311yescharacteristic
386M16—528no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—132no—
391C2×C8—261no—
392C2×C8—261no—
393C2×C8—261no—
394C2×C8—261no—
395C2×C8—261no—
396C4⋊C4—24no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—42no—
401C4⋊C4—81no—
402C4⋊C4—134no—
403C4⋊C4—134no—
404C4⋊C4—132no—
405C4⋊C4—268no—
406C4⋊C4—268no—
407C4⋊C4—264no—
408C4⋊C4—262no—
409C4⋊C4—261no—
410C4⋊C4—261no—
411C4⋊C4—261no—
412C4⋊C4C2×C4×D1312yes—
413C22⋊C4—138no—
414C22⋊C4—268no—
415C22⋊C4—524no—
416C22⋊C4—1042no—
417C42—24no—
418C42—524no—
419C42—522no—
420C42C2×C4×D1312yes—
421C42D4×D1312yes—
422C13#2250211yescharacteristic, complemented, Sylow
423C23—134no—
424C23—262no—
425C23—262no—
426C23—262no—
427C23—262no—
428C23—262no—
429C23—262no—
430C23C2×D4×D1311yescharacteristic
431Q8—22no—
432Q8—22no—
433Q8—41no—
434Q8—41no—
435Q8—1044no—
436D4—268no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—134no—
449C2×C4—262no—
450C2×C4—262no—
451C2×C4—264no—
452C2×C4—264no—
453C2×C4—264no—
454C2×C4—264no—
455C2×C4—264no—
456C2×C4—262no—
457C2×C4—521no—
458C2×C4—522no—
459C2×C4—521no—
460C2×C4—522no—
461C2×C4—521no—
462C2×C4—521no—
463C2×C4—521no—
464C2×C4—1048no—
465C2×C4C22⋊C4×D1312yes—
466C2×C4C22⋊C4×D1312yes—
467C2×C4#8816912yes—
468C2×C4#8817212yes—
469C2×C4C22×C4×D1311yescharacteristic
470C2×C4C2×D4×D1311yescharacteristic
471C2×C4#8825111yescharacteristic
472C2×C4#8825411yescharacteristic
473C2×C4#41×D1311yescharacteristic
474C2×C4#41×D1311yescharacteristic
475C8—42no—
476C8—262no—
477C8—521no—
478C22—264no—
479C22—264no—
480C22—264no—
481C22—522no—
482C22—522no—
483C22—522no—
484C22—522no—
485C22C2×C22⋊C4×D1311yescharacteristic
486C22#1171931711yescharacteristic
487C22#1171933611yescharacteristic
488C22C2×#8816911yescharacteristic
489C22C2×#8817211yescharacteristic
490C22#1171947911yescharacteristic
491C22#1171948311yescharacteristic
492C4—22no—
493C4—42no—
494C4—42no—
495C4—82no—
496C4—264no—
497C4—524no—
498C4—522no—
499C4—1041no—
500C4#1171846314yes—
501C4#1171920911yescharacteristic
502C4#1171922711yescharacteristic
503C4#1171931711yescharacteristic
504C4#1171933611yescharacteristic
505C2—524no—
506C2#1311766411yescharacteristic
507C2C2×#1171846311yescharacteristic
508C2#1312336011yescharacteristic
509C2#1312715511yescharacteristic
510C2#1312717711yescharacteristic
511C2#1312744811yescharacteristic
512C2#1312745911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1803C2
socleC23×C13C22×D4
prime radicalC22×D52D4
cosocleC22×C4×C13C24
hypercenter#1803D13
hypocenterC13#22502
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
4. #13115796C2semidirect
5. #13115783C2semidirect
6. #13115266C2semidirect
7. #13115145C2semidirect
8. #13114921C2semidirect
9. C4×#88075C2semidirect
10. #13114554C2semidirect
11. C13×#1803C2semidirect
16. #11719284C4semidirect
175. #1803D13semidirect
422. C13#22502semidirect

Maximal subgroups

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

subgroupindex
C2×#117192842
C2×#117184992
#131177872
#131157962
#131157832
#131152662
#131151452
#131149212
C4×#880752
#131145542
C13×#18032
#2250213