Finite Group Databasebeta

← #15919892

Subgroups — #15919892

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 484 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#13115974C212yesmaximal, complemented
5#13115969C212yesmaximal
6#13115789C211yesmaximal, characteristic, complemented
7#13115777C211yesmaximal, characteristic, complemented
8#13115191C212yesmaximal
9#13115177C212yesmaximal, complemented
10#13114666C211yesmaximal, characteristic, complemented
11C2×Q82×C13C211yesmaximal, characteristic, complemented
12Q82×C13—24no—
13Q82×C13—24no—
14C2×C13×C4⋊Q8—22no—
15C2×C13×C4⋊Q8—21no—
16C2×C13×C4⋊Q8C2212yes—
17C2×C13×C4⋊Q8C2211yescharacteristic
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—22no—
46C22×Q8×C13—21no—
47C22×Q8×C13D411yescharacteristic
48C22×Q8×C13C2311yescharacteristic
49C22×D52C2311yescharacteristic
50C22×Dic26C2311yescharacteristic
51C13×C4⋊Q8—216no—
52C13×C4⋊Q8—28no—
53C13×C4⋊Q8—24no—
54C13×C4⋊Q8—24no—
55C13×C4⋊Q8—22no—
56C13×C4⋊Q8D414yes—
57C4×Q8×C13—28no—
58C4×Q8×C13—24no—
59C4×Q8×C13—24no—
60C4×Q8×C13—22no—
61C4×Q8×C13—22no—
62C4×Q8×C13—22no—
63C4×Q8×C13D414yes—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4D412yes—
69C2×C13×C4⋊C4D411yescharacteristic
70C2×C13×C4⋊C4C2312yes—
71C2×C13×C4⋊C4C2311yescharacteristic
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#25942—131nomaximal, Sylow
102C23×D13—21no—
103C2×Q8×C13—28no—
104C2×Q8×C13—22no—
105C2×Q8×C13—24no—
106C2×Q8×C13—24no—
107C2×Q8×C13—21no—
108C2×Q8×C13—22no—
109C2×Q8×C13—81no—
110C2×Q8×C13—81no—
111C2×Q8×C13—82no—
112C2×Q8×C13—82no—
113C2×Q8×C13C2×D412yes—
114C2×Q8×C13#4114yes—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13C2×D412yes—
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13C2×D412yes—
122C22×C4×C13C2411yescharacteristic
123C22×Dic13—21no—
124C22×Dic13—22no—
125C2×D52—21no—
126C2×D52—21no—
127C2×D52—22no—
128C2×D52—22no—
129C2×Dic26—21no—
130C2×Dic26—21no—
131C2×Dic26—22no—
132C2×Dic26—22no—
133C13×C4⋊C4—28no—
134C13×C4⋊C4—28no—
135C13×C4⋊C4—24no—
136C13×C4⋊C4—24no—
137C13×C4⋊C4—24no—
138C13×C4⋊C4—22no—
139C13×C4⋊C4—22no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4C2×D414yes—
142C13×C4⋊C4C2×D412yes—
143C42×C13—28no—
144C42×C13—24no—
145C42×C13—22no—
146C42×C13—22no—
147C42×C13C2×D412yes—
148C42×C13C2×D412yes—
149#6107—44no—
150#6106—44no—
151#6103—42no—
152#6103—42no—
153#6103—44no—
154#6103—82no—
155C4⋊Dic13—22no—
156C4⋊Dic13—22no—
157C4×Dic13—81no—
158C2×#1055—21no—
159C2×#1055—21no—
160C2×#1055—22no—
161C2×#1055—22no—
162C2×#1055—22no—
163C2×#1055—22no—
164C2×#1055—22no—
165C2×Q82D1311yescharacteristic, complemented
166C2×#489—131no—
167C2×#464—131no—
168#2592—131no—
169#2024—132no—
170#2023—132no—
171#1988—131no—
172#1985—131no—
173#1880—132no—
174#1878—132no—
175#1763—131no—
176C23×C13C22×D411yescharacteristic
177C22×D13—41no—
178C22×D13—42no—
179C22×D13—42no—
180C22×D13—41no—
181C22×D13—41no—
182Q8×C13—28no—
183Q8×C13—22no—
184Q8×C13—24no—
185Q8×C13—84no—
186Q8×C13—88no—
187Q8×C13#12414yes—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—24no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
195C2×C4×C13—22no—
196C2×C4×C13—24no—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—42no—
201C2×C4×C13—41no—
202C2×C4×C13—42no—
203C2×C4×C13—41no—
204C2×C4×C13#12012yes—
205C2×C4×C13#12012yes—
206C2×C4×C13#13714yes—
207C2×C4×C13C22×D411yescharacteristic
208C2×C4×C13C22×D411yescharacteristic
209C2×C4×C13C2×#4112yes—
210C2×C4×C132−1+412yes—
211C2×Dic13—41no—
212C2×Dic13—42no—
213C2×Dic13—42no—
214C2×Dic13—42no—
215C2×Dic13—42no—
216D52—41no—
217D52—41no—
218D52—42no—
219Dic26—41no—
220Dic26—41no—
221Dic26—42no—
222#1055—41no—
223#1055—41no—
224#1055—42no—
225C22×Q16—131no—
226C22×SD16—131no—
227Q82—24no—
228Q82—24no—
229C2×C4⋊Q8—22no—
230C2×C4⋊Q8—21no—
231C2×C4⋊Q8C2×D1312yes—
232C2×C4⋊Q8C2×D1311yescharacteristic
233C2×#124—131no—
234C2×C4×Q8—21no—
235C2×C4×Q8C2×D1312yes—
236C2×C4×Q8C2×D1311yescharacteristic
237C2×C4×Q8C2×D1311yescharacteristic
238#489—264no—
239#464—264no—
240C2×C4⋊C8—131no—
241C2×#103—132no—
242C2×#103—132no—
243C2×#103—131no—
244C2×#102—132no—
245C2×#102—131no—
246C2×#97—131no—
247#397—261no—
248#393—261no—
249#391—132no—
250#390—132no—
251#388—262no—
252C4×C4⋊C4—131no—
253#340—132no—
254#340—132no—
255#340—132no—
256#336—132no—
257#336—132no—
258C22×C13C2×#12011yescharacteristic
259C22×C13#54812yes—
260C22×C13C2×#13712yes—
261C22×C13#57611yescharacteristic
262C22×C13#57711yescharacteristic
263C2×D13—82no—
264C2×D13—82no—
265C2×D13—81no—
266C2×D13—81no—
267C2×D13—81no—
268C4×C13—24no—
269C4×C13—22no—
270C4×C13—24no—
271C4×C13—22no—
272C4×C13—42no—
273C4×C13—44no—
274C4×C13—42no—
275C4×C13C2×#12411yescharacteristic
276C4×C13#53611yescharacteristic
277C4×C13#54812yes—
278Dic13—82no—
279Dic13—81no—
280C22×Q8—22no—
281C22×Q8—21no—
282C22×Q8—131no—
283C22×Q8C22⋊D1311yescharacteristic
284C22×Q8C22×D1311yescharacteristic
285C22×D4—131no—
286C2×Q16—264no—
287C2×Q16—262no—
288C2×SD16—264no—
289C2×SD16—262no—
290C22×C8—131no—
291C22×C8—131no—
292C22×C8—132no—
293C4⋊Q8—216no—
294C4⋊Q8—28no—
295C4⋊Q8—24no—
296C4⋊Q8—24no—
297C4⋊Q8—22no—
298C4⋊Q8C22⋊D1314yes—
299#124—262no—
300#124—262no—
301C4×Q8—28no—
302C4×Q8—24no—
303C4×Q8—24no—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8C22⋊D1314yes—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—132no—
313C2×C4⋊C4C22⋊D1312yes—
314C2×C4⋊C4C22⋊D1311yescharacteristic
315C2×C4⋊C4C22×D1312yes—
316C2×C4⋊C4C22×D1311yescharacteristic
317C2×C22⋊C4—261no—
318C2×C22⋊C4—261no—
319C2×C22⋊C4—262no—
320C2×C22⋊C4—262no—
321C2×C42—22no—
322C2×C42—21no—
323C2×C42—261no—
324C2×C42C22×D1312yes—
325C2×C42C22×D1311yescharacteristic
326C4⋊C8—262no—
327#103—264no—
328#103—262no—
329#103—264no—
330#102—262no—
331#102—264no—
332#97—262no—
333#95—261no—
334#95—262no—
335#95—262no—
336C2×C13#243611yescharacteristic
337C2×C13#300411yescharacteristic
338C2×C13#301211yescharacteristic
339C2×C13#336912yes—
340C2×C13#337512yes—
341D13—161no—
342C24—261no—
343C2×Q8—28no—
344C2×Q8—24no—
345C2×Q8—22no—
346C2×Q8—24no—
347C2×Q8—22no—
348C2×Q8—21no—
349C2×Q8—81no—
350C2×Q8—81no—
351C2×Q8—82no—
352C2×Q8—82no—
353C2×Q8—262no—
354C2×Q8—262no—
355C2×Q8—261no—
356C2×Q8—261no—
357C2×Q8#613114yes—
358C2×Q8C2×C22⋊D1312yes—
359C2×D4—262no—
360C2×D4—262no—
361C2×D4—261no—
362C2×D4—261no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—261no—
367C22×C4—262no—
368C22×C4C2×C22⋊D1312yes—
369C22×C4C2×C22⋊D1312yes—
370C22×C4C2×C22⋊D1311yescharacteristic
371C22×C4C2×C22⋊D1311yescharacteristic
372C22×C4C23×D1311yescharacteristic
373Q16—524no—
374SD16—524no—
375C2×C8—262no—
376C2×C8—262no—
377C2×C8—262no—
378C2×C8—262no—
379C2×C8—262no—
380C2×C8—261no—
381C2×C8—261no—
382C4⋊C4—28no—
383C4⋊C4—28no—
384C4⋊C4—24no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—262no—
391C4⋊C4—262no—
392C4⋊C4C2×C22⋊D1314yes—
393C4⋊C4C2×C22⋊D1312yes—
394C22⋊C4—524no—
395C22⋊C4—522no—
396C22⋊C4—522no—
397C22⋊C4—1042no—
398C42—28no—
399C42—24no—
400C42—22no—
401C42—22no—
402C42—1041no—
403C42C2×C22⋊D1312yes—
404C42C2×C22⋊D1312yes—
405C13#2594211yescharacteristic, complemented, Sylow
406C23—522no—
407C23—522no—
408C23—521no—
409C23—521no—
410C23—521no—
411C23C22×C22⋊D1311yescharacteristic
412Q8—28no—
413Q8—22no—
414Q8—24no—
415Q8—84no—
416Q8—88no—
417Q8—521no—
418Q8—521no—
419Q8—522no—
420Q8#8820114yes—
421D4—521no—
422D4—521no—
423D4—522no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—522no—
441C2×C4—522no—
442C2×C4—522no—
443C2×C4—522no—
444C2×C4—521no—
445C2×C4#8819614yes—
446C2×C4#8820712yes—
447C2×C4#8820712yes—
448C2×C4C2×#613112yes—
449C2×C4#8825412yes—
450C2×C4C22×C22⋊D1311yescharacteristic
451C2×C4C22×C22⋊D1311yescharacteristic
452C8—521no—
453C8—521no—
454C8—522no—
455C22—1041no—
456C22—1041no—
457C22—1042no—
458C22—1042no—
459C22—1041no—
460C22C2×#8819612yes—
461C22#1171952212yes—
462C22#1171954011yescharacteristic
463C22#1171954111yescharacteristic
464C22C2×#8820711yescharacteristic
465C4—24no—
466C4—22no—
467C4—24no—
468C4—22no—
469C4—42no—
470C4—44no—
471C4—42no—
472C4—1041no—
473C4—1042no—
474C4C2×#8820111yescharacteristic
475C4#1171952111yescharacteristic
476C4#1171952212yes—
477C2—2081no—
478C2#1311849011yescharacteristic
479C2#1312407011yescharacteristic
480C2#1312414011yescharacteristic
481C2#1312757612yes—
482C2#1312765012yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×Q82×C13C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenterC2×Q82D13
hypocenterC13#25942
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
4. #13115974C2semidirect
6. #13115789C2semidirect
7. #13115777C2semidirect
9. #13115177C2semidirect
10. #13114666C2semidirect
11. C2×Q82×C13C2semidirect
165. C2×Q82D13semidirect
405. C13#25942semidirect

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
#131159742
#131159692
#131157892
#131157772
#131151912
#131151772
#131146662
C2×Q82×C132
#2594213