Finite Group Databasebeta

← #15913059

Subgroups — #15913059

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718495C211yesmaximal, characteristic
2#13119832C211yesmaximal, characteristic
3#13119754C211yesmaximal, characteristic
4#13116270C212yesmaximal, complemented
5#13116031C212yesmaximal, complemented
6#13115798C211yesmaximal, characteristic, complemented
7#13115600C211yesmaximal, characteristic, complemented
8#13115256C212yesmaximal, complemented
9#13114858C212yesmaximal, complemented
10C4×#88075C211yesmaximal, characteristic, complemented
11C2×C13×#475C211yesmaximal, characteristic, complemented
12C2×C13×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C13C2211yescharacteristic
14C2×#88201—21no—
15C2×#88200C2212yes—
16C22×C8×D13C2212yes—
17C2×C4×D52C2211yescharacteristic
18C13×#475—24no—
19C2×C13×#106C2212yes—
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×#103C2212yes—
22#11718891—21no—
23C2×#88075C2211yescharacteristic
24C2×#88075C2211yescharacteristic
25C2×#88060C2212yes—
26C2×#88057C2212yes—
27#11718655—22no—
28#11718654—22no—
29#11718648C2212yes—
30#11718648C2212yes—
31#11718648C2212yes—
32#11718600—21no—
33#11718596C2211yescharacteristic
34C4×C4⋊Dic13C2211yescharacteristic
35#11718589—21no—
36C2×C4×#1055C2211yescharacteristic
37#11718495—24no—
38#11718143C2212yes—
39#11718121C2211yescharacteristic
40#11718121C2211yescharacteristic
41#11718121C2212yes—
42#11718121C2212yes—
43C22×Q8×C13—21no—
44C22×Q8×C13C2311yescharacteristic
45C22×D52D411yescharacteristic
46C22×C4×D13C2312yes—
47C22×C8×C13C2312yes—
48C13×C4⋊Q8—22no—
49C13×C4⋊Q8—22no—
50C4×Q8×C13—22no—
51C4×Q8×C13—22no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4C2312yes—
55C2×C13×C4⋊C4C2311yescharacteristic
56C2×C42×C13—21no—
57C2×C42×C13C2311yescharacteristic
58#88201—44no—
59#88200—24no—
60#88200—42no—
61C2×#6103—22no—
62C2×#6103—22no—
63C2×#6103—22no—
64C2×#6103—22no—
65C2×#6103D412yes—
66C2×C4⋊Dic13—21no—
67C2×C4⋊Dic13—21no—
68C2×C4⋊Dic13D411yescharacteristic
69C2×C4⋊Dic13C2312yes—
70C2×C4⋊Dic13C2311yescharacteristic
71C2×C4⋊Dic13C2311yescharacteristic
72C2×#6101—22no—
73C2×C4×Dic13—21no—
74C22×#1055C2311yescharacteristic
75C22×#1055C2311yescharacteristic
76C2×C8×D13—24no—
77C2×C8×D13—24no—
78C2×C8×D13—42no—
79C4×D52—22no—
80C4×D52—22no—
81C13×#106—24no—
82C13×C4⋊C8D414yes—
83C13×#103—24no—
84#88075—22no—
85#88075—22no—
86#88071—21no—
87#88071—22no—
88#88071—22no—
89#88071—22no—
90#88060—24no—
91#88057—42no—
92C4×#1055—22no—
93#25341—131nomaximal, Sylow
94C23×D13C2×D412yes—
95C2×Q8×C13—21no—
96C2×Q8×C13—21no—
97C2×Q8×C13—21no—
98C2×Q8×C13—21no—
99C2×Q8×C13—21no—
100C2×Q8×C13—42no—
101C2×Q8×C13—42no—
102C2×Q8×C13—42no—
103C2×Q8×C13#4112yes—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2411yescharacteristic
110C22×Dic13—21no—
111C22×Dic13—21no—
112C22×Dic13—22no—
113C22×Dic13C2×D412yes—
114C2×D52—22no—
115C2×D52—22no—
116C2×D52SD1614yes—
117C2×C4×D13—22no—
118C2×C4×D13—22no—
119C2×C4×D13—22no—
120C2×C4×D13—22no—
121C2×C4×D13—22no—
122C2×C4×D13—22no—
123C2×C8×C13—22no—
124C2×C8×C13—22no—
125C2×C8×C13C2×D414yes—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—22no—
130C13×C4⋊C4—42no—
131C13×C4⋊C4—42no—
132C42×C13—42no—
133C42×C13C2×D412yes—
134C42×C13#4112yes—
135#6103—24no—
136#6103—44no—
137#6103—44no—
138#6103—44no—
139#6103—82no—
140C4⋊Dic13—22no—
141C4⋊Dic13—21no—
142C4⋊Dic13—21no—
143C4⋊Dic13—22no—
144C4⋊Dic13—22no—
145C4⋊Dic13—21no—
146C4⋊Dic13—21no—
147C4⋊Dic13—42no—
148C4⋊Dic13—81no—
149#6101—44no—
150C4×Dic13—42no—
151C2×#1055—21no—
152C2×#1055—21no—
153C2×#1055—21no—
154C2×#1055—21no—
155C2×#1055—21no—
156C2×#1055#4112yes—
157C8×D13—48no—
158C2×#475D1311yescharacteristic, complemented
159C2×C8×D4—131no—
160#2547—131no—
161#2538—131no—
162#2077—132no—
163#2035—132no—
164#1990—131no—
165#1948—131no—
166#1892—132no—
167#1807—132no—
168C4×#103—131no—
169C23×C13C22×D411yescharacteristic
170C22×D13—22no—
171C22×D13—22no—
172C22×D13—22no—
173C22×D13—22no—
174C22×D13—22no—
175C22×D13—22no—
176C22×D13C2×SD1614yes—
177Q8×C13—22no—
178Q8×C13—22no—
179Q8×C13—41no—
180Q8×C13—41no—
181Q8×C13—84no—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—22no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13#12112yes—
194C2×C4×C13#12112yes—
195C2×C4×C13C2×SD1612yes—
196C2×C4×C13#13512yes—
197C2×C4×C13C22×D411yescharacteristic
198C2×C4×C13C2×#4111yescharacteristic
199C2×C4×C13C2×#4111yescharacteristic
200C2×C4×C13C2×#4111yescharacteristic
201C2×C4×C13H(5,𝔽2)11yescharacteristic
202C2×C4×C132−1+411yescharacteristic
203C2×Dic13—22no—
204C2×Dic13—22no—
205C2×Dic13—22no—
206C2×Dic13—42no—
207C2×Dic13—41no—
208C2×Dic13—41no—
209C2×Dic13—41no—
210C2×Dic13—41no—
211C2×Dic13—42no—
212C2×Dic13—42no—
213C2×Dic13—41no—
214C2×Dic13—41no—
215D52—28no—
216C4×D13—42no—
217C4×D13—42no—
218C4×D13—42no—
219C4×D13—42no—
220C8×C13—24no—
221#1055—22no—
222#1055—41no—
223C23×C8—132no—
224C2×C4⋊Q8C2×D1311yescharacteristic
225C2×#124—261no—
226C2×C22⋊Q8—132no—
227C2×C4×Q8C2×D1311yescharacteristic
228C2×C4×D4—131no—
229#475—24no—
230C8×D4—264no—
231C2×#106—132no—
232C2×#106C2×D1312yes—
233C2×C4⋊C8C2×D1311yescharacteristic
234C2×#103—131no—
235C2×#103—131no—
236C2×#103C2×D1312yes—
237C2×C22⋊C8—132no—
238C2×C4×C8—131no—
239#397—262no—
240#396—262no—
241#391—261no—
242#390—261no—
243#389—261no—
244#384—131no—
245#380—132no—
246#380—132no—
247#380—132no—
248C4×C4⋊C4—131no—
249#340—132no—
250#340—131no—
251#340—132no—
252#340—131no—
253#340—132no—
254C22×C13C2×#12111yescharacteristic
255C22×C13#54611yescharacteristic
256C22×C13#54711yescharacteristic
257C22×C13C22×SD1611yescharacteristic
258C22×C13C2×#13511yescharacteristic
259C22×C13#57711yescharacteristic
260C22×C13#57811yescharacteristic
261C2×D13—24no—
262C2×D13—24no—
263C2×D13—24no—
264C2×D13—42no—
265C2×D13—42no—
266C2×D13—42no—
267C2×D13—42no—
268C4×C13—22no—
269C4×C13—42no—
270C4×C13—82no—
271C4×C13—81no—
272C4×C13#46514yes—
273C4×C13#52911yescharacteristic
274C4×C13#54211yescharacteristic
275C4×C13#54611yescharacteristic
276C4×C13#54811yescharacteristic
277Dic13—42no—
278Dic13—81no—
279Dic13—81no—
280Dic13—82no—
281C22×Q8—21no—
282C22×Q8C22×D1311yescharacteristic
283C22×D4—131no—
284C23×C4—132no—
285C22×C8—131no—
286C22×C8—131no—
287C22×C8—264no—
288C22×C8—264no—
289C22×C8—522no—
290C22×C8C22×D1312yes—
291C4⋊Q8—22no—
292C4⋊Q8—22no—
293#124—524no—
294C22⋊Q8—264no—
295C22⋊Q8—522no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×D4—262no—
299C4×D4—262no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—131no—
303C2×C4⋊C4—132no—
304C2×C4⋊C4—131no—
305C2×C4⋊C4—131no—
306C2×C4⋊C4—262no—
307C2×C4⋊C4—261no—
308C2×C4⋊C4—261no—
309C2×C4⋊C4C22×D1311yescharacteristic
310C2×C4⋊C4C22×D1312yes—
311C2×C22⋊C4—132no—
312C2×C22⋊C4—262no—
313C2×C22⋊C4—262no—
314C2×C22⋊C4—262no—
315C2×C22⋊C4—262no—
316C2×C42—21no—
317C2×C42—261no—
318C2×C42C22×D1311yescharacteristic
319#106—24no—
320#106—522no—
321C4⋊C8C22⋊D1314yes—
322#103—24no—
323#103—262no—
324#103—262no—
325C22⋊C8—264no—
326C4×C8—262no—
327#95—262no—
328#95—262no—
329#95—262no—
330#95—261no—
331C2×C13#242711yescharacteristic
332C2×C13C2×#46511yescharacteristic
333C2×C13#306311yescharacteristic
334C2×C13#329811yescharacteristic
335C2×C13#330411yescharacteristic
336C2×C13#333511yescharacteristic
337C2×C13#334211yescharacteristic
338D13—44no—
339C24—132no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—42no—
346C2×Q8—42no—
347C2×Q8—42no—
348C2×Q8#613112yes—
349C2×D4—134no—
350C2×D4—262no—
351C2×D4—262no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—132no—
356C22×C4—262no—
357C22×C4—262no—
358C22×C4—262no—
359C22×C4—262no—
360C22×C4—262no—
361C22×C4—262no—
362C22×C4—261no—
363C22×C4—261no—
364C22×C4—262no—
365C22×C4D4×D1311yescharacteristic
366C22×C4D4×D1311yescharacteristic
367C22×C4C23×D1311yescharacteristic
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—132no—
371C2×C8—261no—
372C2×C8—261no—
373C2×C8—261no—
374C2×C8—261no—
375C2×C8—261no—
376C2×C8—528no—
377C2×C8C2×C22⋊D1314yes—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—262no—
385C4⋊C4—261no—
386C4⋊C4—262no—
387C4⋊C4—261no—
388C4⋊C4—261no—
389C4⋊C4—261no—
390C4⋊C4—262no—
391C4⋊C4—524no—
392C4⋊C4—522no—
393C4⋊C4—1041no—
394C22⋊C4—264no—
395C22⋊C4—524no—
396C22⋊C4—524no—
397C22⋊C4—524no—
398C22⋊C4—1042no—
399C42—42no—
400C42—522no—
401C42#612912yes—
402C42C2×C22⋊D1312yes—
403C13#2534111yescharacteristic, complemented, Sylow
404C23—134no—
405C23—262no—
406C23—262no—
407C23—262no—
408C23—262no—
409C23—262no—
410C23—262no—
411C23C2×D4×D1311yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—41no—
415Q8—41no—
416Q8—84no—
417D4—268no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—262no—
430C2×C4—262no—
431C2×C4—262no—
432C2×C4—522no—
433C2×C4—522no—
434C2×C4—522no—
435C2×C4—522no—
436C2×C4—521no—
437C2×C4—521no—
438C2×C4—522no—
439C2×C4—522no—
440C2×C4—521no—
441C2×C4—521no—
442C2×C4—522no—
443C2×C4—521no—
444C2×C4—521no—
445C2×C4SD16×D1312yes—
446C2×C4#8817012yes—
447C2×C4#8819212yes—
448C2×C4#8819212yes—
449C2×C4C2×#612911yescharacteristic
450C2×C4C2×#613111yescharacteristic
451C2×C4#8825411yescharacteristic
452C2×C4#41×D1311yescharacteristic
453C2×C4#8825611yescharacteristic
454C2×C4C22×C22⋊D1311yescharacteristic
455C8—24no—
456C8—262no—
457C8—521no—
458C22—264no—
459C22—264no—
460C22—264no—
461C22—522no—
462C22—522no—
463C22—522no—
464C22—522no—
465C22#1171933511yescharacteristic
466C22#1171933611yescharacteristic
467C22C2×SD16×D1311yescharacteristic
468C22C2×#8817011yescharacteristic
469C22#1171948311yescharacteristic
470C22#1171948411yescharacteristic
471C22C2×#8819211yescharacteristic
472C4—22no—
473C4—42no—
474C4—82no—
475C4—81no—
476C4—522no—
477C4—1041no—
478C4—1041no—
479C4—1042no—
480C4#1171883214yes—
481C4#1171932911yescharacteristic
482C4#1171934811yescharacteristic
483C4#1171952211yescharacteristic
484C4#1171953411yescharacteristic
485C2—524no—
486C2#1311840911yescharacteristic
487C2C2×#1171883211yescharacteristic
488C2#1312452111yescharacteristic
489C2#1312669811yescharacteristic
490C2#1312677211yescharacteristic
491C2#1312719611yescharacteristic
492C2#1312726511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#475C2
socleC23×C13C22×D4
prime radicalC22×D52D4
hypercenterC2×#475D13
hypocenterC13#25341
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
4. #13116270C2semidirect
5. #13116031C2semidirect
6. #13115798C2semidirect
7. #13115600C2semidirect
8. #13115256C2semidirect
9. #13114858C2semidirect
10. C4×#88075C2semidirect
11. C2×C13×#475C2semidirect
158. C2×#475D13semidirect
403. C13#25341semidirect

Maximal subgroups

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

subgroupindex
C2×#117184952
#131198322
#131197542
#131162702
#131160312
#131157982
#131156002
#131152562
#131148582
C4×#880752
C2×C13×#4752
#2534113