Finite Group Databasebeta

← #15841757

Subgroups — #15841757

Order 3328.

1170 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125987C211yesmaximal, characteristic, complemented
2#13124844C211yesmaximal, characteristic, complemented
3#13124633C211yesmaximal, characteristic, complemented
4#13114071C214yesmaximal, complemented
5#13113987C214yesmaximal, complemented
6#13113521C211yesmaximal, characteristic, complemented
7#13113261C211yesmaximal, characteristic, complemented
8#13113227C211yesmaximal, characteristic, complemented
9C2×C13×#547C211yesmaximal, characteristic
10C22×C13×#41—21no—
11C13×#547—22no—
12C13×#547—22no—
13C13×#547—22no—
14C13×#547C2214yes—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#123—22no—
17C2×C13×C22⋊Q8—21no—
18C2×C13×#121—21no—
19C2×C4×D4×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C22×C13×C4⋊C4—21no—
22#11719175C2211yescharacteristic
23#11718879—21no—
24#11718876—21no—
25#11718754C2212yescomplemented
26#11718752—22no—
27#11718739C2212yescomplemented
28#11718680C2212yescomplemented
29C4×#6105—22no—
30#11718670—22no—
31#11718669C2212yescomplemented
32#11718669C2212yescomplemented
33#11718668C2212yescomplemented
34#11718632—21no—
35#11718631—22no—
36#11718625—21no—
37#11718586C2211yescharacteristic
38#11718586C2211yescharacteristic
39#11718585C2211yescharacteristic
40#11718139C2214yescomplemented
41D4⋊#1055C2214yescomplemented
42D4⋊#1055C2214yescomplemented
43C2×C13×#41—24no—
44C2×C13×#41—24no—
45C2×C13×#41—48no—
46C22×Q8×C13—21no—
47C22×D4×C13—22no—
48C22×D4×C13D411yescharacteristic
49C22×D4×C13D411yescharacteristic
50C23×C4×C13—22no—
51C23×C4×C13—21no—
52C23×C4×C13—21no—
53C13×C4⋊Q8—21no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8D412yes—
56C13×C4⋊Q8C2312yes—
57C13×#123—28no—
58C13×#123—28no—
59C13×C22⋊Q8—24no—
60C13×C22⋊Q8—24no—
61C13×#121—24no—
62C13×#121—24no—
63C4×D4×C13—21no—
64C4×D4×C13—21no—
65C4×D4×C13—21no—
66C4×D4×C13—21no—
67C4×D4×C13D412yes—
68C4×D4×C13D412yes—
69C4×D4×C13C2312yes—
70C4×D4×C13C2312yes—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—24no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—24no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4D412yes—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C42×C13C2311yescharacteristic
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#88072—22no—
93#88072—22no—
94#88072—22no—
95C22⋊#1055—21no—
96C22⋊#1055—21no—
97#88050—22no—
98#88050—24no—
99#88048—22no—
100#88048—22no—
101#88047—22no—
102#88047—24no—
103C4⋊#1055—21no—
104C4⋊#1055—21no—
105C4⋊#1055C2312yes—
106C4⋊#1055C2312yes—
107C4×#1055—21no—
108C4×#1055C2312yes—
109#18783—131nomaximal, Sylow
110C24×C13—21no—
111C24×C13—21no—
112C13×#41—416no—
113C13×#41—48no—
114C13×#41—48no—
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13—44no—
118C2×D4×C13—24no—
119C2×D4×C13—28no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—22no—
123C2×D4×C13—22no—
124C2×D4×C13—48no—
125C2×D4×C13C2×D412yes—
126C2×D4×C13C2×D412yes—
127C22×C4×C13—28no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—44no—
136C22×C4×C13—48no—
137C22×C4×C13—42no—
138C22×C4×C13—42no—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C2×Dic26—21no—
143C2×Dic26—21no—
144C13×C4⋊C4—28no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4C2×D412yes—
151C13×C4⋊C4C2×D412yes—
152C13×C4⋊C4C2×D414yes—
153C13×C22⋊C4—28no—
154C13×C22⋊C4—22no—
155C13×C22⋊C4—22no—
156C13×C22⋊C4—22no—
157C13×C22⋊C4—22no—
158C42×C13C2×D411yescharacteristic
159C42×C13C2×D411yescharacteristic
160C42×C13C2×D411yescharacteristic
161C42×C13C2411yescharacteristic
162C22⋊Dic13—41no—
163#6105—44no—
164C4⋊Dic13—21no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168#6101—41no—
169#6101—41no—
170C4×Dic13—41no—
171#6099—42no—
172C2×#1055—22no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#547D1311yescharacteristic
176#3230—131no—
177#3101—131no—
178#3077—131no—
179#1647—134no—
180#1635—134no—
181#1549—131no—
182#1486—131no—
183#1478—131no—
184C23×C13—24no—
185C23×C13—22no—
186C23×C13—22no—
187C23×C13—42no—
188C23×C13—42no—
189C23×C13—42no—
190C23×C13—42no—
191C23×C13—42no—
192C23×C13#12011yescharacteristic
193Q8×C13—44no—
194Q8×C13—44no—
195D4×C13—24no—
196D4×C13—22no—
197D4×C13—22no—
198D4×C13—22no—
199D4×C13—416no—
200D4×C13—42no—
201D4×C13AGL(1,ℤ/8)14yes—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—24no—
206C2×C4×C13—41no—
207C2×C4×C13—44no—
208C2×C4×C13—42no—
209C2×C4×C13—44no—
210C2×C4×C13—416no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—44no—
214C2×C4×C13—42no—
215C2×C4×C13—44no—
216C2×C4×C13#12011yescharacteristic
217C2×C4×C13#12011yescharacteristic
218C2×C4×C13#12011yescharacteristic
219C2×C4×C13#13512yes—
220C2×C4×C13#13712yes—
221C2×C4×C13C22×D411yescharacteristic
222C2×C4×C13C22×D411yescharacteristic
223C2×C4×C13C22×D411yescharacteristic
224C2×Dic13—41no—
225C2×Dic13—41no—
226Dic26—42no—
227Dic26—42no—
228#1055—42no—
229#1055—42no—
230#1055—42no—
231C22×#41—21no—
232#547—22no—
233#547—22no—
234#547—22no—
235#547C2×D1314yes—
236#533—131no—
237C2×C4⋊Q8C2×D1311yescharacteristic
238C2×#123—22no—
239C2×C22⋊Q8—21no—
240C2×#121—21no—
241C2×C4×D4C2×D1311yescharacteristic
242C2×C4×D4C2×D1311yescharacteristic
243C22×C4⋊C4—21no—
244#500—132no—
245#487—132no—
246#484—262no—
247#483—261no—
248#478—262no—
249#477—262no—
250#476—132no—
251#476—132no—
252#474—132no—
253#461—132no—
254#450—261no—
255C4×SD16—262no—
256#431—131no—
257#431—131no—
258#428—261no—
259#423—131no—
260#418—261no—
261#332—134no—
262D4⋊C8—134no—
263D4⋊C8—134no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—24no—
267C22×C13—48no—
268C22×C13—42no—
269C22×C13—42no—
270C22×C13—42no—
271C22×C13—42no—
272C22×C13—42no—
273C22×C13—84no—
274C22×C13#45212yes—
275C22×C13C2×#12011yescharacteristic
276C4×C13—21no—
277C4×C13—21no—
278C4×C13—21no—
279C4×C13—42no—
280C4×C13—42no—
281C4×C13—44no—
282C4×C13#45212yes—
283C4×C13C2×#13511yescharacteristic
284C4×C13C2×AGL(1,ℤ/8)12yes—
285C4×C13C2×#13711yescharacteristic
286Dic13—81no—
287Dic13—81no—
288C2×#41—24no—
289C2×#41—24no—
290C2×#41—48no—
291C22×Q8—21no—
292C22×D4—22no—
293C22×D4C22⋊D1311yescharacteristic
294C22×D4C22⋊D1311yescharacteristic
295C23×C4—22no—
296C23×C4—21no—
297C23×C4—21no—
298C2×SD16—262no—
299C2×M16—261no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—131no—
303C4⋊Q8—131no—
304C4⋊Q8C22⋊D1312yes—
305C4⋊Q8C22×D1312yes—
306#125—261no—
307#123—28no—
308#123—28no—
309C22⋊Q8—24no—
310C22⋊Q8—24no—
311C22⋊Q8—261no—
312C22⋊Q8—261no—
313#121—24no—
314#121—24no—
315C4×Q8—261no—
316C4×Q8—261no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4C22⋊D1312yes—
322C4×D4C22⋊D1312yes—
323C4×D4C22×D1312yes—
324C4×D4C22×D1312yes—
325#117—261no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4C22⋊D1311yescharacteristic
331C2×C4⋊C4C22⋊D1311yescharacteristic
332C2×C4⋊C4C22⋊D1312yes—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C42C22×D1311yescharacteristic
337#107—262no—
338#107—264no—
339#106—262no—
340#106—262no—
341C4⋊C8—132no—
342C4⋊C8—132no—
343C4⋊C8—261no—
344C4⋊C8—261no—
345#103—262no—
346#103—264no—
347#102—262no—
348#102—262no—
349#102—262no—
350C22⋊C8—261no—
351C22⋊C8—261no—
352C4×C8—132no—
353C4×C8—261no—
354C2×C13—22no—
355C2×C13—44no—
356C2×C13—82no—
357C2×C13C2×#45211yescharacteristic
358C2×C13#300311yescharacteristic
359C2×C13#302011yescharacteristic
360C24—21no—
361C24—21no—
362#41—416no—
363#41—48no—
364#41—48no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—44no—
368C2×Q8—261no—
369C2×Q8—261no—
370C2×D4—24no—
371C2×D4—28no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—48no—
377C2×D4C2×C22⋊D1312yes—
378C2×D4C2×C22⋊D1312yes—
379C22×C4—28no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—44no—
388C22×C4—48no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4C2×C22⋊D1311yescharacteristic
392C22×C4C2×C22⋊D1311yescharacteristic
393C22×C4C2×C22⋊D1311yescharacteristic
394SD16—524no—
395M16—522no—
396C2×C8—262no—
397C2×C8—262no—
398C2×C8—262no—
399C4⋊C4—28no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—261no—
406C4⋊C4—261no—
407C4⋊C4—261no—
408C4⋊C4—261no—
409C4⋊C4—521no—
410C4⋊C4—521no—
411C4⋊C4C2×C22⋊D1312yes—
412C4⋊C4C2×C22⋊D1314yes—
413C4⋊C4C2×C22⋊D1312yes—
414C22⋊C4—28no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—521no—
420C42—521no—
421C42C2×C22⋊D1311yescharacteristic
422C42C2×C22⋊D1311yescharacteristic
423C42C2×C22⋊D1311yescharacteristic
424C42C23×D1311yescharacteristic
425C13#1878311yescharacteristic, complemented, Sylow
426C23—24no—
427C23—22no—
428C23—22no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23#8820711yescharacteristic
435Q8—44no—
436Q8—44no—
437Q8—522no—
438Q8—522no—
439D4—24no—
440D4—22no—
441D4—22no—
442D4—22no—
443D4—416no—
444D4—42no—
445D4#8818614yes—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—41no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—416no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—521no—
461C2×C4—521no—
462C2×C4#8820412yes—
463C2×C4#8820512yes—
464C2×C4#8820711yescharacteristic
465C2×C4#8820711yescharacteristic
466C2×C4#8820711yescharacteristic
467C2×C4C22×C22⋊D1311yescharacteristic
468C2×C4C22×C22⋊D1311yescharacteristic
469C2×C4C22×C22⋊D1311yescharacteristic
470C8—522no—
471C8—522no—
472C8—522no—
473C22—21no—
474C22—21no—
475C22—24no—
476C22—48no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—84no—
483C22#1171890012yes—
484C22C2×#8820711yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—42no—
489C4—42no—
490C4—44no—
491C4—1041no—
492C4—1041no—
493C4#1171890012yes—
494C4C2×#8818612yes—
495C4C2×#8820411yescharacteristic
496C4C2×#8820511yescharacteristic
497C2—22no—
498C2—44no—
499C2—82no—
500C2C2×#1171890011yescharacteristic
501C2#1312406311yescharacteristic
502C2#1312420011yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC2×C13×#547C2
socleC22×C13C2×#120
hypercenterC2×#547D13
hypocenterC13#18783
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13125987C2semidirect
2. #13124844C2semidirect
3. #13124633C2semidirect
4. #13114071C2semidirect
5. #13113987C2semidirect
6. #13113521C2semidirect
7. #13113261C2semidirect
8. #13113227C2semidirect
25. #11718754C22semidirect
27. #11718739C22semidirect
28. #11718680C22semidirect
31. #11718669C22semidirect
32. #11718669C22semidirect
33. #11718668C22semidirect
40. #11718139C22semidirect
41. D4⋊#1055C22semidirect
42. D4⋊#1055C22semidirect
425. C13#18783semidirect

Maximal subgroups

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

subgroupindex
#131259872
#131248442
#131246332
#131140712
#131139872
#131135212
#131132612
#131132272
C2×C13×#5472
#1878313