Finite Group Databasebeta

← #15841451

Subgroups — #15841451

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125784C211yesmaximal, characteristic, complemented
2#13124844C211yesmaximal, characteristic
3#13124641C211yesmaximal, characteristic, complemented
4#13114043C214yesmaximal, complemented
5#13113970C214yesmaximal, complemented
6#13113517C211yesmaximal, characteristic, complemented
7#13113261C211yesmaximal, characteristic
8#13113231C211yesmaximal, characteristic, complemented
9C2×C13×#554C211yesmaximal, characteristic
10C13×#554—22no—
11C13×#554—22no—
12C13×#554—22no—
13C13×#554C2214yes—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#125—21no—
16C2×C13×C22⋊Q8—21no—
17C2×C13×C22⋊Q8—22no—
18C2×C4×Q8×C13C2211yescharacteristic
19C2×C4×D4×C13—21no—
20C2×C4×D4×C13C2211yescharacteristic
21C22×C13×C4⋊C4—21no—
22#11719175C2211yescharacteristic
23#11718889—22no—
24#11718886—21no—
25#11718879—21no—
26#11718753C2212yescomplemented
27#11718751—22no—
28#11718742C2212yescomplemented
29#11718683—22no—
30#11718682C2212yescomplemented
31#11718681C2212yescomplemented
32#11718680C2212yes—
33C4×#6105—22no—
34#11718669C2212yes—
35#11718632—21no—
36#11718625—21no—
37#11718586C2211yescharacteristic
38#11718586C2211yescharacteristic
39#11718585C2211yescharacteristic
40#11718138C2214yescomplemented
41Q8⋊#1055C2214yescomplemented
42D4⋊#1055C2214yes—
43C22×Q8×C13D411yescharacteristic
44C22×Q8×C13D412yes—
45C22×D4×C13D411yescharacteristic
46C23×C4×C13—22no—
47C23×C4×C13—21no—
48C13×C4⋊Q8—21no—
49C13×C4⋊Q8—21no—
50C13×C4⋊Q8D412yes—
51C13×C4⋊Q8C2312yes—
52C13×#125—24no—
53C13×#125—24no—
54C13×C22⋊Q8—24no—
55C13×C22⋊Q8—28no—
56C13×C22⋊Q8—24no—
57C13×C22⋊Q8—28no—
58C4×Q8×C13—21no—
59C4×Q8×C13—21no—
60C4×Q8×C13D412yes—
61C4×Q8×C13C2312yes—
62C4×D4×C13—24no—
63C4×D4×C13—24no—
64C4×D4×C13—21no—
65C4×D4×C13—21no—
66C4×D4×C13D412yes—
67C4×D4×C13C2312yes—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—24no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—24no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—21no—
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81C2×#6107—24no—
82C2×#6105—22no—
83#88180—21no—
84#88178—21no—
85#88178—21no—
86C2×#6099—21no—
87#88124—21no—
88#88123C2311yescharacteristic
89#88123C2311yescharacteristic
90C4×Dic26—21no—
91C4×Dic26—21no—
92#88075—22no—
93#88075—22no—
94#88075—24no—
95#88072—22no—
96C22⋊#1055—21no—
97C22⋊#1055—21no—
98#88050—22no—
99#88048—22no—
100#88048—22no—
101#88047—22no—
102C4⋊#1055—21no—
103C4⋊#1055—21no—
104C4⋊#1055C2312yes—
105C4⋊#1055C2312yes—
106C4×#1055—21no—
107C4×#1055C2312yes—
108#18753—131nomaximal, Sylow
109C24×C13—21no—
110C2×Q8×C13—21no—
111C2×Q8×C13—22no—
112C2×Q8×C13—22no—
113C2×Q8×C13—22no—
114C2×Q8×C13—82no—
115C2×Q8×C13C2×D412yes—
116C2×Q8×C13C2×D414yes—
117C2×D4×C13—24no—
118C2×D4×C13—21no—
119C2×D4×C13C2×D412yes—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—22no—
124C22×C4×C13—28no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—42no—
128C22×C4×C13—42no—
129C22×C4×C13—84no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C2×Dic26—21no—
134C2×Dic26—21no—
135C13×C4⋊C4—28no—
136C13×C4⋊C4—28no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—22no—
139C13×C4⋊C4—22no—
140C13×C4⋊C4—22no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—22no—
143C13×C4⋊C4—22no—
144C13×C4⋊C4—22no—
145C13×C4⋊C4C2×D412yes—
146C13×C4⋊C4C2×D412yes—
147C13×C22⋊C4—28no—
148C13×C22⋊C4—22no—
149C13×C22⋊C4—22no—
150C42×C13—22no—
151C42×C13—22no—
152C42×C13C2×D411yescharacteristic
153C42×C13C2×D411yescharacteristic
154C42×C13C2×D411yescharacteristic
155C42×C13C2411yescharacteristic
156C22⋊Dic13—41no—
157#6107—84no—
158#6105—44no—
159C4⋊Dic13—21no—
160C4⋊Dic13—21no—
161C4⋊Dic13—21no—
162C4⋊Dic13—21no—
163#6101—41no—
164#6101—41no—
165C4×Dic13—41no—
166#6099—42no—
167C2×#1055—22no—
168C2×#1055—22no—
169C2×#1055—22no—
170C2×#554D1311yescharacteristic
171#3209—131no—
172#3101—131no—
173#3078—131no—
174#1643—134no—
175#1632—134no—
176#1548—131no—
177#1486—131no—
178#1479—131no—
179C23×C13—24no—
180C23×C13—22no—
181C23×C13—42no—
182C23×C13—42no—
183C23×C13#12011yescharacteristic
184Q8×C13—22no—
185Q8×C13—22no—
186Q8×C13—44no—
187Q8×C13—42no—
188Q8×C13—82no—
189D4×C13—24no—
190D4×C13—22no—
191D4×C13#13714yes—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—22no—
195C2×C4×C13—22no—
196C2×C4×C13—24no—
197C2×C4×C13—41no—
198C2×C4×C13—42no—
199C2×C4×C13—44no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—44no—
205C2×C4×C13—88no—
206C2×C4×C13#12011yescharacteristic
207C2×C4×C13#12011yescharacteristic
208C2×C4×C13#12011yescharacteristic
209C2×C4×C13#13512yes—
210C2×C4×C13#13712yes—
211C2×C4×C13C22×D411yescharacteristic
212C2×C4×C13C22×D411yescharacteristic
213C2×C4×C13C22×D411yescharacteristic
214C2×Dic13—41no—
215C2×Dic13—41no—
216Dic26—42no—
217Dic26—42no—
218#1055—42no—
219#1055—42no—
220#1055—42no—
221#554—22no—
222#554—22no—
223#554—22no—
224#554C2×D1314yes—
225#533—131no—
226C2×C4⋊Q8C2×D1311yescharacteristic
227C2×#125—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—22no—
230C2×C4×Q8C2×D1311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4C2×D1311yescharacteristic
233C22×C4⋊C4—21no—
234#494—132no—
235#487—132no—
236#483—261no—
237#479—262no—
238#477—132no—
239#476—132no—
240#475—132no—
241#462—262no—
242#461—132no—
243#451—262no—
244#450—261no—
245C4×SD16—262no—
246#431—131no—
247#431—131no—
248#428—261no—
249#423—131no—
250#419—261no—
251#333—134no—
252Q8⋊C8—134no—
253D4⋊C8—134no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13—24no—
257C22×C13—48no—
258C22×C13—42no—
259C22×C13—42no—
260C22×C13#45212yes—
261C22×C13C2×#12011yescharacteristic
262C4×C13—21no—
263C4×C13—21no—
264C4×C13—21no—
265C4×C13—42no—
266C4×C13—42no—
267C4×C13—42no—
268C4×C13—44no—
269C4×C13#45212yes—
270C4×C13C2×#13511yescharacteristic
271C4×C13C2×#13712yes—
272C4×C13C2×#13711yescharacteristic
273Dic13—81no—
274Dic13—81no—
275C22×Q8C22⋊D1311yescharacteristic
276C22×Q8C22⋊D1312yes—
277C22×D4C22⋊D1311yescharacteristic
278C23×C4—22no—
279C23×C4—21no—
280C2×Q16—264no—
281C2×SD16—262no—
282C2×M16—261no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—131no—
286C4⋊Q8—131no—
287C4⋊Q8C22⋊D1312yes—
288C4⋊Q8C22×D1312yes—
289#125—24no—
290#125—24no—
291#125—261no—
292C22⋊Q8—24no—
293C22⋊Q8—28no—
294C22⋊Q8—24no—
295C22⋊Q8—28no—
296C22⋊Q8—261no—
297C22⋊Q8—261no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8—261no—
301C4×Q8—261no—
302C4×Q8C22⋊D1312yes—
303C4×Q8C22×D1312yes—
304C4×D4—24no—
305C4×D4—24no—
306C4×D4—21no—
307C4×D4—21no—
308C4×D4C22⋊D1312yes—
309C4×D4C22×D1312yes—
310#117—261no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4C22⋊D1311yescharacteristic
319C2×C4⋊C4C22⋊D1311yescharacteristic
320C2×C22⋊C4—22no—
321C2×C22⋊C4—21no—
322C2×C42—21no—
323C2×C42C22×D1311yescharacteristic
324#107—262no—
325#106—262no—
326#106—262no—
327C4⋊C8—132no—
328C4⋊C8—132no—
329C4⋊C8—261no—
330C4⋊C8—261no—
331#103—262no—
332#103—262no—
333#103—264no—
334#103—262no—
335#102—262no—
336C22⋊C8—261no—
337C22⋊C8—261no—
338C4×C8—132no—
339C4×C8—261no—
340C2×C13—22no—
341C2×C13—44no—
342C2×C13C2×#45211yescharacteristic
343C2×C13#300411yescharacteristic
344C2×C13#301911yescharacteristic
345C24—21no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—82no—
351C2×Q8—261no—
352C2×Q8—261no—
353C2×Q8C2×C22⋊D1312yes—
354C2×Q8C2×C22⋊D1314yes—
355C2×D4—24no—
356C2×D4—21no—
357C2×D4C2×C22⋊D1312yes—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—28no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—84no—
368C22×C4C2×C22⋊D1311yescharacteristic
369C22×C4C2×C22⋊D1311yescharacteristic
370C22×C4C2×C22⋊D1311yescharacteristic
371Q16—1044no—
372SD16—524no—
373M16—522no—
374C2×C8—262no—
375C2×C8—262no—
376C2×C8—262no—
377C4⋊C4—28no—
378C4⋊C4—28no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—261no—
388C4⋊C4—261no—
389C4⋊C4—261no—
390C4⋊C4—261no—
391C4⋊C4—521no—
392C4⋊C4—521no—
393C4⋊C4C2×C22⋊D1312yes—
394C4⋊C4C2×C22⋊D1312yes—
395C22⋊C4—28no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—521no—
399C42—22no—
400C42—22no—
401C42—521no—
402C42C2×C22⋊D1311yescharacteristic
403C42C2×C22⋊D1311yescharacteristic
404C42C2×C22⋊D1311yescharacteristic
405C42C23×D1311yescharacteristic
406C13#1875311yescharacteristic, complemented, Sylow
407C23—24no—
408C23—22no—
409C23—42no—
410C23—42no—
411C23#8820711yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—44no—
415Q8—42no—
416Q8—82no—
417Q8—522no—
418Q8—522no—
419D4—24no—
420D4—22no—
421D4#8819614yes—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—88no—
436C2×C4—521no—
437C2×C4—521no—
438C2×C4#8820412yes—
439C2×C4#8820512yes—
440C2×C4#8820711yescharacteristic
441C2×C4#8820711yescharacteristic
442C2×C4#8820711yescharacteristic
443C2×C4C22×C22⋊D1311yescharacteristic
444C2×C4C22×C22⋊D1311yescharacteristic
445C2×C4C22×C22⋊D1311yescharacteristic
446C8—522no—
447C8—522no—
448C8—522no—
449C22—21no—
450C22—21no—
451C22—24no—
452C22—48no—
453C22—42no—
454C22—42no—
455C22#1171890012yes—
456C22C2×#8820711yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—42no—
461C4—44no—
462C4—42no—
463C4—42no—
464C4—1041no—
465C4—1041no—
466C4#1171890012yes—
467C4C2×#8819612yes—
468C4C2×#8820411yescharacteristic
469C4C2×#8820511yescharacteristic
470C2—22no—
471C2—44no—
472C2C2×#1171890011yescharacteristic
473C2#1312407011yescharacteristic
474C2#1312419311yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#554C2
socleC22×C13C2×#120
prime radicalC22×D4×C13D4
hypercenterC2×#554D13
hypocenterC13#18753
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13125784C2semidirect
3. #13124641C2semidirect
4. #13114043C2semidirect
5. #13113970C2semidirect
6. #13113517C2semidirect
8. #13113231C2semidirect
26. #11718753C22semidirect
28. #11718742C22semidirect
30. #11718682C22semidirect
31. #11718681C22semidirect
40. #11718138C22semidirect
41. Q8⋊#1055C22semidirect
406. C13#18753semidirect

Maximal subgroups

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

subgroupindex
#131257842
#131248442
#131246412
#131140432
#131139702
#131135172
#131132612
#131132312
C2×C13×#5542
#1875313