Finite Group Databasebeta

← #15879749

Subgroups — #15879749

Order 3328.

1098 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719437C211yesmaximal, characteristic
2C2×#11718340C211yesmaximal, characteristic, complemented
3#13117748C211yesmaximal, characteristic, complemented
4#13115765C212yesmaximal
5#13115760C211yesmaximal, characteristic, complemented
6#13115649C212yesmaximal
7#13114839C212yesmaximal, complemented
8#13114833C211yesmaximal, characteristic
9#13114668C212yesmaximal, complemented
10C4×#88061C211yesmaximal, characteristic
11C13×#1956C211yesmaximal, characteristic, complemented
12C2×C13×C4⋊Q8C2211yescharacteristic
13C2×#88201C2212yes—
14C2×Q8×Dic13C2212yes—
15#11719437—24no—
16#11719437C418yescomplemented
17C2×#88152—22no—
18C2×#88151—21no—
19C2×#88146—21no—
20C2×#88141—21no—
21C2×C4×D52C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C2×C13×#103C2212yes—
24C2×C13×#103C2212yes—
25C2×C4×C8×C13C2211yescharacteristic
26C13×#384C2211yescharacteristic
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29C2×#88061C2211yescharacteristic
30C2×#88061C2211yescharacteristic
31C2×#88055C2212yes—
32C2×#88054C2212yes—
33#11718637C2212yes—
34C4⋊C4×Dic13C2212yes—
35#11718634—21no—
36#11718633—22no—
37C2×#88049C2212yes—
38C4×C4⋊Dic13C2211yescharacteristic
39C2×C4⋊#1055C2211yescharacteristic
40#11718340—24no—
41#11718143C2211yescharacteristic
42#11718143C2211yescharacteristic
43#11718121C2212yes—
44C22×Q8×C13C2312yes—
45C22×D52C2311yescharacteristic
46C22×C4×D13—21no—
47C22×Dic26D411yescharacteristic
48C22×C8×C13C2311yescharacteristic
49C22×C8×C13C2311yescharacteristic
50C13×C4⋊Q8—22no—
51C13×C4⋊Q8C2×C414yes—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4C2312yes—
57C2×C42×C13C2311yescharacteristic
58#88201—24no—
59#88201C2×C418yes—
60Q8×Dic13—24no—
61Q8×Dic13C2×C418yes—
62C2×#6103—21no—
63C2×#6103—22no—
64C2×#6103—22no—
65C2×C4⋊Dic13—22no—
66C2×C4⋊Dic13D411yescharacteristic
67C2×C4⋊Dic13C2311yescharacteristic
68C2×C4⋊Dic13C2311yescharacteristic
69C2×C4⋊Dic13C2311yescharacteristic
70C2×#6101—22no—
71C2×#6101—22no—
72C2×#6101D412yes—
73C2×C4×Dic13—22no—
74C2×C4×Dic13—21no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13C2312yes—
77C22×#1055C2312yes—
78#88152—216no—
79#88151—28no—
80#88146—28no—
81#88141—44no—
82C4×D52—22no—
83C4×D52C2×C414yes—
84C4×Dic26C2×C414yes—
85C4×Dic26D414yes—
86C13×#103—24no—
87C13×#103—42no—
88C4×C8×C13—22no—
89#88075—24no—
90#88075—42no—
91#88071—21no—
92#88071—22no—
93#88061—22no—
94#88061—22no—
95#88055—24no—
96#88054—24no—
97#88049—42no—
98C4⋊#1055—22no—
99#22544—131nomaximal, Sylow
100C23×D13—21no—
101C2×Q8×C13—22no—
102C2×Q8×C13—22no—
103C2×Q8×C13—22no—
104C2×Q8×C13—22no—
105C2×Q8×C13—22no—
106C2×Q8×C13C22×C414yes—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2411yescharacteristic
112C22×Dic13—21no—
113C22×Dic13—21no—
114C22×Dic13—21no—
115C22×Dic13C2×D412yes—
116C22×Dic13C2×D412yes—
117C2×D52—21no—
118C2×D52—21no—
119C2×D52—21no—
120C2×D52—21no—
121C2×D52—21no—
122C2×D52C22×C412yes—
123C2×C4×D13—24no—
124C2×C4×D13—42no—
125C2×C4×D13—42no—
126C2×Dic26—22no—
127C2×Dic26—22no—
128C2×Dic26C22⋊C414yes—
129C2×C8×C13—21no—
130C2×C8×C13—21no—
131C2×C8×C13—21no—
132C2×C8×C13—21no—
133C2×C8×C13—21no—
134C2×C8×C13#4112yes—
135C13×C4⋊C4—24no—
136C13×C4⋊C4—24no—
137C13×C4⋊C4—22no—
138C13×C4⋊C4—22no—
139C13×C4⋊C4—42no—
140C13×C4⋊C4—81no—
141C42×C13C22×C412yes—
142C42×C13C2×D412yes—
143#6103—24no—
144#6103—28no—
145#6103—28no—
146C4⋊Dic13—21no—
147C4⋊Dic13—21no—
148C4⋊Dic13—28no—
149C4⋊Dic13—21no—
150C4⋊Dic13—21no—
151C4⋊Dic13C22⋊C414yes—
152C4⋊Dic13C22×C412yes—
153C4⋊Dic13#4112yes—
154#6101—44no—
155#6101—82no—
156#6101C22⋊C418yes—
157C4×Dic13—28no—
158C4×Dic13—44no—
159C4×Dic13—42no—
160C4×Dic13C22×C414yes—
161C4×Dic13C2×D414yes—
162C2×#1055—22no—
163C2×#1055—22no—
164C2×#1055—22no—
165C2×#556—131no—
166C2×#446—131no—
167Q8×C4⋊C4—131no—
168#1983—132no—
169#1981—131no—
170#1959—132no—
171#1956D1311yescharacteristic, complemented
172#1803—132no—
173#1802—131no—
174#1763—132no—
175C4×#102—131no—
176C23×C13C22×D411yescharacteristic
177C22×D13—22no—
178C22×D13—41no—
179C22×D13—41no—
180C22×D13—41no—
181C22×D13—41no—
182C22×D13—41no—
183C22×D13—41no—
184Q8×C13—24no—
185Q8×C13—24no—
186Q8×C13—42no—
187Q8×C13—42no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—24no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13C2×C22⋊C412yes—
197C2×C4×C13C2×C22⋊C412yes—
198C2×C4×C13AGL(1,ℤ/8)12yes—
199C2×C4×C13#13712yes—
200C2×C4×C13C23×C411yescharacteristic
201C2×C4×C13C22×D411yescharacteristic
202C2×C4×C13C2×#4111yescharacteristic
203C2×C4×C13C2×#4111yescharacteristic
204C2×C4×C13H(5,𝔽2)11yescharacteristic
205C2×C4×C132−1+411yescharacteristic
206C2×Dic13—22no—
207C2×Dic13—22no—
208C2×Dic13—22no—
209C2×Dic13—22no—
210C2×Dic13—22no—
211C2×Dic13—22no—
212C2×Dic13—41no—
213C2×Dic13—41no—
214C2×Dic13—41no—
215C2×Dic13—41no—
216C2×Dic13—41no—
217C2×Dic13—41no—
218C2×Dic13—41no—
219C2×Dic13C2×C22⋊C414yes—
220C2×Dic13C2×C22⋊C414yes—
221D52—22no—
222D52—22no—
223D52—41no—
224D52—41no—
225C4×D13—48no—
226Dic26—28no—
227C8×C13—22no—
228C8×C13—41no—
229#1055—42no—
230#556—138no—
231#556—264no—
232C2×C4⋊Q8C2×D1311yescharacteristic
233C2×#126—262no—
234C2×#124—132no—
235C2×C22⋊Q8—261no—
236C2×C4×Q8—131no—
237C2×C4×Q8—132no—
238C2×C4×Q8—261no—
239C2×C4×D4—131no—
240C2×#117—261no—
241#446—264no—
242C2×C4⋊C8—132no—
243C2×C4⋊C8—131no—
244C2×#103—132no—
245C2×#103—132no—
246C2×#103C2×D1312yes—
247C2×#103C2×D1312yes—
248C2×#102—131no—
249C2×#102—131no—
250C2×#102—132no—
251C2×#97—132no—
252C2×C4×C8C2×D1311yescharacteristic
253#389—262no—
254#389—261no—
255#384—132no—
256#384C2×D1311yescharacteristic
257C4×C4⋊C4—132no—
258C4×C4⋊C4—131no—
259#340—131no—
260#340—131no—
261#340—132no—
262C22×C13C22×C22⋊C411yescharacteristic
263C22×C13#54811yescharacteristic
264C22×C13#55011yescharacteristic
265C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C13C2×#13711yescharacteristic
267C22×C13#57711yescharacteristic
268C22×C13#57811yescharacteristic
269C2×D13—42no—
270C2×D13—42no—
271C2×D13—42no—
272C2×D13—81no—
273C2×D13—81no—
274C2×D13—81no—
275C2×D13—81no—
276C4×C13—22no—
277C4×C13—44no—
278C4×C13—82no—
279C4×C13#41714yes—
280C4×C13C4×#4111yescharacteristic
281C4×C13#52011yescharacteristic
282C4×C13#54811yescharacteristic
283C4×C13#55011yescharacteristic
284Dic13—24no—
285Dic13—24no—
286Dic13—42no—
287Dic13—42no—
288Dic13—81no—
289C22×Q8—131no—
290C22×Q8C22×D1312yes—
291C22×D4—131no—
292C23×C4—261no—
293C22×C8—132no—
294C22×C8C22×D1311yescharacteristic
295C22×C8C22×D1311yescharacteristic
296C4⋊Q8—22no—
297C4⋊Q8C4×D1314yes—
298#126—2616no—
299#124—138no—
300#124—264no—
301C22⋊Q8—268no—
302C4×Q8—134no—
303C4×Q8—134no—
304C4×Q8—138no—
305C4×Q8—264no—
306C4×Q8—524no—
307C4×D4—134no—
308C4×D4—262no—
309#117—268no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—131no—
315C2×C4⋊C4—132no—
316C2×C4⋊C4—131no—
317C2×C4⋊C4—131no—
318C2×C4⋊C4—131no—
319C2×C4⋊C4—262no—
320C2×C4⋊C4—262no—
321C2×C4⋊C4—262no—
322C2×C4⋊C4C22×D1312yes—
323C2×C22⋊C4—262no—
324C2×C22⋊C4—262no—
325C2×C22⋊C4—261no—
326C2×C42—132no—
327C2×C42—262no—
328C2×C42—262no—
329C2×C42—261no—
330C2×C42C22×D1311yescharacteristic
331C4⋊C8—264no—
332C4⋊C8—262no—
333#103—24no—
334#103—42no—
335#103—264no—
336#103—522no—
337#102—262no—
338#102—262no—
339#102—522no—
340#97—264no—
341C4×C8—22no—
342#95—262no—
343#95—261no—
344C2×C13#234111yescharacteristic
345C2×C13C2×#41711yescharacteristic
346C2×C13#289811yescharacteristic
347C2×C13#336711yescharacteristic
348C2×C13#336911yescharacteristic
349C2×C13#339711yescharacteristic
350C2×C13#339811yescharacteristic
351D13—82no—
352C24—261no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—134no—
359C2×Q8—262no—
360C2×Q8—262no—
361C2×Q8C2×C4×D1314yes—
362C2×D4—132no—
363C2×D4—261no—
364C2×D4—261no—
365C2×D4—261no—
366C2×D4—261no—
367C2×D4—261no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—132no—
371C22×C4—132no—
372C22×C4—261no—
373C22×C4—261no—
374C22×C4—264no—
375C22×C4—261no—
376C22×C4—522no—
377C22×C4—522no—
378C22×C4D4×D1311yescharacteristic
379C22×C4D4×D1311yescharacteristic
380C22×C4C23×D1311yescharacteristic
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—262no—
387C2×C8—262no—
388C2×C8—262no—
389C2×C8#612912yes—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—42no—
395C4⋊C4—81no—
396C4⋊C4—134no—
397C4⋊C4—138no—
398C4⋊C4—132no—
399C4⋊C4—132no—
400C4⋊C4—268no—
401C4⋊C4—261no—
402C4⋊C4—261no—
403C4⋊C4—261no—
404C4⋊C4—261no—
405C4⋊C4—524no—
406C4⋊C4—1042no—
407C22⋊C4—268no—
408C22⋊C4—268no—
409C22⋊C4—264no—
410C42—134no—
411C42—134no—
412C42—268no—
413C42—524no—
414C42—522no—
415C42C2×C4×D1312yes—
416C42D4×D1312yes—
417C13#2254411yescharacteristic, complemented, Sylow
418C23—262no—
419C23—521no—
420C23—521no—
421C23—521no—
422C23—521no—
423C23—521no—
424C23—521no—
425C23C2×D4×D1311yescharacteristic
426Q8—24no—
427Q8—24no—
428Q8—42no—
429Q8—42no—
430Q8—268no—
431D4—262no—
432D4—262no—
433D4—521no—
434D4—521no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—24no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—134no—
444C2×C4—134no—
445C2×C4—262no—
446C2×C4—262no—
447C2×C4—262no—
448C2×C4—262no—
449C2×C4—262no—
450C2×C4—262no—
451C2×C4—521no—
452C2×C4—521no—
453C2×C4—521no—
454C2×C4—521no—
455C2×C4—528no—
456C2×C4—521no—
457C2×C4—521no—
458C2×C4—521no—
459C2×C4C22⋊C4×D1312yes—
460C2×C4C22⋊C4×D1312yes—
461C2×C4#8816812yes—
462C2×C4#8817212yes—
463C2×C4C22×C4×D1311yescharacteristic
464C2×C4C2×D4×D1311yescharacteristic
465C2×C4C2×#612911yescharacteristic
466C2×C4#8825111yescharacteristic
467C2×C4#41×D1311yescharacteristic
468C2×C4#8825711yescharacteristic
469C8—22no—
470C8—41no—
471C8—522no—
472C22—522no—
473C22—522no—
474C22—522no—
475C22—1041no—
476C22—1041no—
477C22—1041no—
478C22—1041no—
479C22C2×C22⋊C4×D1311yescharacteristic
480C22#1171938211yescharacteristic
481C22#1171942311yescharacteristic
482C22C2×#8816811yescharacteristic
483C22#1171946711yescharacteristic
484C22C2×#8817211yescharacteristic
485C22#1171947111yescharacteristic
486C4—22no—
487C4—44no—
488C4—82no—
489C4—264no—
490C4—264no—
491C4—522no—
492C4—522no—
493C4—1041no—
494C4#1171846414yes—
495C4C4×#612911yescharacteristic
496C4#1171925111yescharacteristic
497C4#1171930311yescharacteristic
498C4#1171930411yescharacteristic
499C2—1042no—
500C2#1311767511yescharacteristic
501C2C2×#1171846411yescharacteristic
502C2#1312336411yescharacteristic
503C2#1312755911yescharacteristic
504C2#1312758111yescharacteristic
505C2#1312786111yescharacteristic
506C2#1312787211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1956C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1956D13
hypocenterC13#22544
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
2. C2×#11718340C2semidirect
3. #13117748C2semidirect
5. #13115760C2semidirect
7. #13114839C2semidirect
9. #13114668C2semidirect
11. C13×#1956C2semidirect
16. #11719437C4semidirect
171. #1956D13semidirect
417. C13#22544semidirect

Maximal subgroups

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

subgroupindex
C2×#117194372
C2×#117183402
#131177482
#131157652
#131157602
#131156492
#131148392
#131148332
#131146682
C4×#880612
C13×#19562
#2254413