Finite Group Databasebeta

← #15919881

Subgroups — #15919881

Order 3328.

1022 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718750C211yesmaximal, characteristic
2C2×#11718689C211yesmaximal, characteristic
3#13120324C211yesmaximal, characteristic
4#13115984C212yesmaximal, complemented
5#13115979C212yesmaximal
6#13115785C211yesmaximal, characteristic, complemented
7#13115777C211yesmaximal, characteristic, complemented
8#13115191C212yesmaximal
9#13115177C212yesmaximal, complemented
10#13114666C211yesmaximal, characteristic, complemented
11C2×C13×#557C211yesmaximal, characteristic, complemented
12C13×#557—24no—
13C13×#557—24no—
14C2×C13×C4⋊Q8—21no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#125—22no—
17C2×C13×#125C2212yes—
18C2×C4×Q8×C13—21no—
19C2×C4×Q8×C13C2212yes—
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×Q8×C13C2211yescharacteristic
22C22×#6107C2211yescharacteristic
23C22×#6106C2211yescharacteristic
24C2×#88129C2211yescharacteristic
25#11718892—21no—
26C2×#88075C2212yes—
27#11718750—24no—
28#11718689—24no—
29#11718654—21no—
30#11718651—22no—
31C2×#88050C2212yes—
32C2×#88050C2211yescharacteristic
33C2×#88049C2212yes—
34C2×#88049C2211yescharacteristic
35#11718600C2212yes—
36C4×C4⋊Dic13C2211yescharacteristic
37#11718590C2212yes—
38C2×C4⋊#1055C2211yescharacteristic
39C2×#88043C2211yescharacteristic
40#11718121C2212yes—
41#11718121C2212yes—
42#11718121C2212yes—
43#11718116C2212yes—
44#11718116C2212yes—
45C22×Q8×C13—21no—
46C22×Q8×C13D411yescharacteristic
47C22×Q8×C13C2311yescharacteristic
48C22×D52C2311yescharacteristic
49C22×Dic26C2311yescharacteristic
50C13×C4⋊Q8—28no—
51C13×C4⋊Q8—22no—
52C13×C4⋊Q8D414yes—
53C13×#125—216no—
54C13×#125—24no—
55C13×#125—24no—
56C4×Q8×C13—28no—
57C4×Q8×C13—24no—
58C4×Q8×C13—24no—
59C4×Q8×C13—22no—
60C4×Q8×C13—22no—
61C4×Q8×C13—22no—
62C4×Q8×C13D414yes—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C4⋊C4D412yes—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2312yes—
72C2×C42×C13—22no—
73C2×C42×C13—21no—
74C2×C42×C13C2312yes—
75C2×C42×C13C2311yescharacteristic
76C2×#6107—22no—
77C2×#6107—24no—
78C2×#6106—22no—
79C2×#6106—24no—
80C2×#6103—21no—
81C2×#6103—21no—
82C2×#6103—22no—
83C2×#6103—22no—
84C2×C4⋊Dic13C2312yes—
85C2×C4×Dic13—21no—
86C22×#1055C2311yescharacteristic
87C22×#1055C2311yescharacteristic
88C22×#1055C2312yes—
89#88129—22no—
90#88129—22no—
91#88075—24no—
92#88071—22no—
93#88071—22no—
94#88071—21no—
95#88050—22no—
96#88050—24no—
97#88049—22no—
98#88049—24no—
99C4⋊#1055—22no—
100#88043—22no—
101#25941—131nomaximal, Sylow
102C23×D13—21no—
103C2×Q8×C13—22no—
104C2×Q8×C13—24no—
105C2×Q8×C13—21no—
106C2×Q8×C13—22no—
107C2×Q8×C13—42no—
108C2×Q8×C13—44no—
109C2×Q8×C13C2×D412yes—
110C2×Q8×C13#4114yes—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
114C22×C4×C13C2×D412yes—
115C22×C4×C13C2×D412yes—
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2411yescharacteristic
119C22×Dic13—21no—
120C22×Dic13—22no—
121C2×D52—21no—
122C2×D52—21no—
123C2×D52—22no—
124C2×D52—22no—
125C2×Dic26—21no—
126C2×Dic26—21no—
127C2×Dic26—22no—
128C2×Dic26—22no—
129C13×C4⋊C4—28no—
130C13×C4⋊C4—28no—
131C13×C4⋊C4—28no—
132C13×C4⋊C4—24no—
133C13×C4⋊C4—24no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—24no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—22no—
138C13×C4⋊C4C2×D414yes—
139C13×C4⋊C4C2×D412yes—
140C42×C13—28no—
141C42×C13—24no—
142C42×C13—22no—
143C42×C13—22no—
144C42×C13C2×D412yes—
145C42×C13C2×D412yes—
146#6107—44no—
147#6106—44no—
148#6103—44no—
149#6103—42no—
150#6103—42no—
151#6103—82no—
152C4⋊Dic13—22no—
153C4⋊Dic13—22no—
154C4×Dic13—81no—
155C2×#1055—21no—
156C2×#1055—21no—
157C2×#1055—22no—
158C2×#1055—22no—
159C2×#1055—22no—
160C2×#1055—22no—
161C2×#1055—22no—
162C2×#557D1311yescharacteristic, complemented
163C2×#489—131no—
164C2×#464—131no—
165#2592—131no—
166#2026—132no—
167#2025—132no—
168#1987—131no—
169#1985—131no—
170#1880—132no—
171#1878—132no—
172#1763—131no—
173C23×C13C22×D411yescharacteristic
174C22×D13—41no—
175C22×D13—42no—
176C22×D13—42no—
177C22×D13—41no—
178C22×D13—41no—
179Q8×C13—22no—
180Q8×C13—24no—
181Q8×C13—44no—
182Q8×C13—48no—
183Q8×C13#12414yes—
184C2×C4×C13—22no—
185C2×C4×C13—24no—
186C2×C4×C13—22no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—24no—
193C2×C4×C13—22no—
194C2×C4×C13—22no—
195C2×C4×C13—22no—
196C2×C4×C13—22no—
197C2×C4×C13—44no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13#12012yes—
201C2×C4×C13#12012yes—
202C2×C4×C13C22×D411yescharacteristic
203C2×C4×C13C22×D411yescharacteristic
204C2×C4×C13C2×#4112yes—
205C2×C4×C132−1+412yes—
206C2×Dic13—41no—
207C2×Dic13—42no—
208C2×Dic13—42no—
209C2×Dic13—42no—
210C2×Dic13—42no—
211D52—41no—
212D52—41no—
213D52—42no—
214Dic26—41no—
215Dic26—41no—
216Dic26—42no—
217#1055—41no—
218#1055—41no—
219#1055—42no—
220C22×Q16—131no—
221C22×SD16—131no—
222#557—24no—
223#557—24no—
224C2×C4⋊Q8—21no—
225C2×C4⋊Q8C2×D1311yescharacteristic
226C2×#125—22no—
227C2×#125C2×D1312yes—
228C2×#124—131no—
229C2×C4×Q8—21no—
230C2×C4×Q8C2×D1312yes—
231C2×C4×Q8C2×D1311yescharacteristic
232C2×C4×Q8C2×D1311yescharacteristic
233#489—264no—
234#464—264no—
235C2×C4⋊C8—131no—
236C2×#103—132no—
237C2×#103—132no—
238C2×#103—131no—
239C2×#102—132no—
240C2×#102—131no—
241C2×#97—131no—
242#397—261no—
243#393—261no—
244#391—132no—
245#390—132no—
246#388—262no—
247C4×C4⋊C4—131no—
248#340—132no—
249#340—132no—
250#340—132no—
251#336—132no—
252#336—132no—
253C22×C13C2×#12011yescharacteristic
254C22×C13#54812yes—
255C22×C13#57512yes—
256C22×C13#57711yescharacteristic
257C22×C13#57811yescharacteristic
258C2×D13—82no—
259C2×D13—82no—
260C2×D13—81no—
261C2×D13—81no—
262C2×D13—81no—
263C4×C13—24no—
264C4×C13—22no—
265C4×C13—22no—
266C4×C13—42no—
267C4×C13—44no—
268C4×C13—42no—
269C4×C13—42no—
270C4×C13C2×#12411yescharacteristic
271C4×C13#53611yescharacteristic
272C4×C13#54812yes—
273Dic13—82no—
274Dic13—81no—
275C22×Q8—21no—
276C22×Q8—131no—
277C22×Q8C22⋊D1311yescharacteristic
278C22×Q8C22×D1311yescharacteristic
279C22×D4—131no—
280C2×Q16—264no—
281C2×Q16—262no—
282C2×SD16—264no—
283C2×SD16—262no—
284C22×C8—131no—
285C22×C8—131no—
286C22×C8—132no—
287C4⋊Q8—28no—
288C4⋊Q8—22no—
289C4⋊Q8C22⋊D1314yes—
290#125—216no—
291#125—24no—
292#125—24no—
293#124—262no—
294#124—262no—
295C4×Q8—28no—
296C4×Q8—24no—
297C4×Q8—24no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×Q8C22⋊D1314yes—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—132no—
308C2×C4⋊C4C22⋊D1311yescharacteristic
309C2×C4⋊C4C22⋊D1312yes—
310C2×C4⋊C4C22×D1311yescharacteristic
311C2×C4⋊C4C22×D1312yes—
312C2×C22⋊C4—261no—
313C2×C22⋊C4—261no—
314C2×C22⋊C4—262no—
315C2×C22⋊C4—262no—
316C2×C42—22no—
317C2×C42—21no—
318C2×C42—261no—
319C2×C42C22×D1312yes—
320C2×C42C22×D1311yescharacteristic
321C4⋊C8—262no—
322#103—264no—
323#103—262no—
324#103—264no—
325#102—262no—
326#102—264no—
327#97—262no—
328#95—261no—
329#95—262no—
330#95—262no—
331C2×C13#243611yescharacteristic
332C2×C13#300511yescharacteristic
333C2×C13#301311yescharacteristic
334C2×C13#337112yes—
335C2×C13#337712yes—
336D13—161no—
337C24—261no—
338C2×Q8—22no—
339C2×Q8—24no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—42no—
343C2×Q8—44no—
344C2×Q8—262no—
345C2×Q8—262no—
346C2×Q8—261no—
347C2×Q8—261no—
348C2×Q8#613114yes—
349C2×Q8C2×C22⋊D1312yes—
350C2×D4—262no—
351C2×D4—262no—
352C2×D4—261no—
353C2×D4—261no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—261no—
358C22×C4—262no—
359C22×C4C2×C22⋊D1312yes—
360C22×C4C2×C22⋊D1312yes—
361C22×C4C2×C22⋊D1311yescharacteristic
362C22×C4C2×C22⋊D1311yescharacteristic
363C22×C4C23×D1311yescharacteristic
364Q16—524no—
365SD16—524no—
366C2×C8—262no—
367C2×C8—262no—
368C2×C8—262no—
369C2×C8—262no—
370C2×C8—262no—
371C2×C8—261no—
372C2×C8—261no—
373C4⋊C4—28no—
374C4⋊C4—28no—
375C4⋊C4—28no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—22no—
379C4⋊C4—24no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—262no—
383C4⋊C4—262no—
384C4⋊C4C2×C22⋊D1314yes—
385C4⋊C4C2×C22⋊D1312yes—
386C22⋊C4—524no—
387C22⋊C4—522no—
388C22⋊C4—522no—
389C22⋊C4—1042no—
390C42—28no—
391C42—24no—
392C42—22no—
393C42—22no—
394C42—1041no—
395C42C2×C22⋊D1312yes—
396C42C2×C22⋊D1312yes—
397C13#2594111yescharacteristic, complemented, Sylow
398C23—522no—
399C23—522no—
400C23—521no—
401C23—521no—
402C23—521no—
403C23C22×C22⋊D1311yescharacteristic
404Q8—22no—
405Q8—24no—
406Q8—44no—
407Q8—48no—
408Q8—521no—
409Q8—521no—
410Q8—522no—
411Q8#8820114yes—
412D4—521no—
413D4—521no—
414D4—522no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—44no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—522no—
432C2×C4—522no—
433C2×C4—522no—
434C2×C4—522no—
435C2×C4—521no—
436C2×C4#8820712yes—
437C2×C4#8820712yes—
438C2×C4C2×#613112yes—
439C2×C4#8825412yes—
440C2×C4C22×C22⋊D1311yescharacteristic
441C2×C4C22×C22⋊D1311yescharacteristic
442C8—521no—
443C8—521no—
444C8—522no—
445C22—1041no—
446C22—1041no—
447C22—1042no—
448C22—1041no—
449C22—1042no—
450C22#1171952212yes—
451C22#1171952712yes—
452C22#1171954211yescharacteristic
453C22#1171954311yescharacteristic
454C22C2×#8820711yescharacteristic
455C4—24no—
456C4—22no—
457C4—22no—
458C4—42no—
459C4—42no—
460C4—42no—
461C4—44no—
462C4—1041no—
463C4—1042no—
464C4C2×#8820111yescharacteristic
465C4#1171952111yescharacteristic
466C4#1171952212yes—
467C2—2081no—
468C2#1311849011yescharacteristic
469C2#1312407811yescharacteristic
470C2#1312415111yescharacteristic
471C2#1312760412yes—
472C2#1312767812yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#557C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenterC2×#557D13
hypocenterC13#25941
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
4. #13115984C2semidirect
6. #13115785C2semidirect
7. #13115777C2semidirect
9. #13115177C2semidirect
10. #13114666C2semidirect
11. C2×C13×#557C2semidirect
162. C2×#557D13semidirect
397. C13#25941semidirect

Maximal subgroups

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

subgroupindex
C2×#117187502
C2×#117186892
#131203242
#131159842
#131159792
#131157852
#131157772
#131151912
#131151772
#131146662
C2×C13×#5572
#2594113