Finite Group Databasebeta

← #15845815

Subgroups — #15845815

Order 3328.

680 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125210C211yesmaximal, characteristic
2#13124875C211yesmaximal, characteristic, complemented
3Q8×#6099C211yesmaximal, characteristic, complemented
4#13114402C212yesmaximal, complemented
5#13114374C212yesmaximal, complemented
6#13114278C212yesmaximal, complemented
7#13114250C212yesmaximal, complemented
8#13113586C211yesmaximal, characteristic, complemented
9#13113524C211yesmaximal, characteristic, complemented
10#13113504C211yesmaximal, characteristic
11C2×C13×#460C211yesmaximal, characteristic
12C22×C13×SD16—21no—
13C2×C13×#127C2211yescharacteristic
14C2×C4×Q8×C13C2211yescharacteristic
15#11719175C2211yescharacteristic
16C13×#460—21no—
17C13×#460—21no—
18C13×#460C2212yes—
19C13×#460C2212yes—
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×#102—21no—
22#11718889—21no—
23#11718876—21no—
24#11718876—21no—
25#11718732—22no—
26#11718731C2212yes—
27#11718731C2212yes—
28#11718692C2211yescharacteristic, complemented
29#11718692C2211yescharacteristic, complemented
30C4×#6107—21no—
31C4×#6107—21no—
32#11718685—22no—
33#11718685C2212yescomplemented
34Q8×#1055C2212yescomplemented
35#11718682C2211yescharacteristic, complemented
36#11718682C2211yescharacteristic, complemented
37#11718631—21no—
38#11718586C2211yescharacteristic
39#11718585—21no—
40#11718585C2211yescharacteristic
41C4×#6099—21no—
42C4×#6099C2211yescharacteristic
43#11718136C2212yes—
44#11718136C2212yes—
45#11718074C2212yescomplemented
46#11718073C2212yescomplemented
47#11718072C2212yescomplemented
48#11718071C2212yescomplemented
49C22×Q8×C13D411yescharacteristic
50C22×D4×C13—21no—
51C22×D4×C13—21no—
52C22×D4×C13—21no—
53C2×C13×SD16—22no—
54C2×C13×SD16—22no—
55C2×C13×SD16—44no—
56C22×C8×C13—21no—
57C13×#127—21no—
58C13×#127—21no—
59C13×#127—21no—
60C13×#127C2312yes—
61C4×Q8×C13—21no—
62C4×Q8×C13—21no—
63C4×Q8×C13D411yescharacteristic
64C4×Q8×C13D411yescharacteristic
65C4×Q8×C13C2311yescharacteristic
66C4×Q8×C13C2311yescharacteristic
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C42×C13—21no—
70C2×C42×C13C2311yescharacteristic
71C2×#6107—21no—
72C2×#6107—21no—
73#88180—21no—
74#88178—21no—
75#88178—21no—
76C2×#6099—21no—
77C2×#6099D411yescharacteristic
78C2×#6099D411yescharacteristic
79#88124—21no—
80#88123C2311yescharacteristic
81#88123C2311yescharacteristic
82C4×Dic26—21no—
83C4×Dic26—21no—
84C13×C4⋊C8—21no—
85C13×C4⋊C8C2312yes—
86C13×#102—22no—
87C13×#102—22no—
88#88075—21no—
89#88075—21no—
90#88072—22no—
91#88072—22no—
92#88072—22no—
93#88072—22no—
94C22⋊#1055—21no—
95#88050—21no—
96#88050—21no—
97#88047—21no—
98#88047—21no—
99C4⋊#1055—21no—
100C4⋊#1055—22no—
101C4⋊#1055—22no—
102C4⋊#1055C2311yescharacteristic
103C4⋊#1055C2311yescharacteristic
104C4⋊#1055C2312yes—
105#88043—22no—
106#88043D412yes—
107C4×#1055—21no—
108C4×#1055—22no—
109C4×#1055C2312yes—
110#19174—131nomaximal, Sylow
111C24×C13—41no—
112C2×Q8×C13—21no—
113C2×Q8×C13—22no—
114C2×Q8×C13—41no—
115C2×Q8×C13C2×D411yescharacteristic
116C2×Q8×C13C2×D411yescharacteristic
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13—42no—
121C2×D4×C13—42no—
122C2×D4×C13—41no—
123C2×D4×C13—41no—
124C2×D4×C13—41no—
125C2×D4×C13—42no—
126C2×D4×C13—42no—
127C2×D4×C13—82no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13#4111yescharacteristic
133C2×Dic26—21no—
134C2×Dic26—21no—
135C13×SD16—44no—
136C13×SD16—44no—
137C2×C8×C13—22no—
138C2×C8×C13—42no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4—21no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4C2×D411yescharacteristic
145C13×C4⋊C4C2×D411yescharacteristic
146C42×C13—21no—
147C42×C13—21no—
148C42×C13—21no—
149C42×C13—21no—
150C42×C13C2×D411yescharacteristic
151C42×C13C2×D411yescharacteristic
152C42×C13#4111yescharacteristic
153C42×C13C2411yescharacteristic
154C22⋊Dic13—41no—
155#6107—42no—
156#6107—42no—
157C4⋊Dic13—21no—
158C4⋊Dic13—21no—
159C4⋊Dic13—21no—
160C4⋊Dic13—21no—
161#6101—41no—
162#6101—41no—
163C4×Dic13—41no—
164#6099—22no—
165#6099—22no—
166#6099—42no—
167C2×#1055—21no—
168C2×#1055—21no—
169C2×#1055—22no—
170C2×#1055C2×D412yes—
171C2×#1055C2×D412yes—
172#3138—131no—
173#3104—131no—
174C2×#460D1311yescharacteristic
175Q8×M16—131no—
176#1702—132no—
177#1698—132no—
178#1682—132no—
179#1678—132no—
180#1565—131no—
181#1550—131no—
182#1545—131no—
183C23×C13—42no—
184C23×C13—82no—
185C23×C13—82no—
186C23×C13—82no—
187C23×C13#12111yescharacteristic
188Q8×C13—21no—
189Q8×C13—21no—
190Q8×C13—21no—
191Q8×C13—42no—
192Q8×C13AGL(1,ℤ/8)12yes—
193D4×C13—42no—
194D4×C13—42no—
195D4×C13—42no—
196D4×C13—42no—
197D4×C13—82no—
198D4×C13—82no—
199D4×C13—82no—
200D4×C13—82no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—41no—
208C2×C4×C13—42no—
209C2×C4×C13—81no—
210C2×C4×C13#12111yescharacteristic
211C2×C4×C13#12111yescharacteristic
212C2×C4×C13#12111yescharacteristic
213C2×C4×C13#13512yes—
214C2×C4×C13#13712yes—
215C2×C4×C13C22×D411yescharacteristic
216C2×C4×C13C22×D411yescharacteristic
217C2×C4×C13C2×#4111yescharacteristic
218C2×Dic13—41no—
219C2×Dic13—41no—
220Dic26—41no—
221Dic26—41no—
222Dic26—81no—
223C8×C13—42no—
224#1055—22no—
225#1055—22no—
226#1055—42no—
227#1055—41no—
228#1055—41no—
229C22×SD16—21no—
230#533—131no—
231C2×#127C2×D1311yescharacteristic
232C2×C4×Q8C2×D1311yescharacteristic
233#490—262no—
234#486—132no—
235#486—132no—
236#484—261no—
237#477—131no—
238#477—131no—
239#462—131no—
240#462—131no—
241#460—21no—
242#460—21no—
243#460C2×D1312yes—
244#460C2×D1312yes—
245#451—261no—
246#446—132no—
247#446—262no—
248C8×Q8—132no—
249C4×Q16—261no—
250C4×Q16—261no—
251#431—131no—
252#423—131no—
253#423—261no—
254C2×C4⋊C8C2×D1311yescharacteristic
255#418—261no—
256#418—261no—
257C2×#102—21no—
258C4×M16—131no—
259C4×M16—261no—
260#335—132no—
261#334—132no—
262#333—132no—
263#332—132no—
264#331—132no—
265#331—132no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—82no—
269C22×C13—82no—
270C22×C13—82no—
271C22×C13—164no—
272C22×C13#46412yes—
273C22×C13C2×#12111yescharacteristic
274C4×C13—21no—
275C4×C13—22no—
276C4×C13—21no—
277C4×C13—21no—
278C4×C13—41no—
279C4×C13—41no—
280C4×C13—41no—
281C4×C13#46412yes—
282C4×C13C2×#13511yescharacteristic
283C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
284C4×C13C2×#13711yescharacteristic
285C4×C13#57511yescharacteristic
286Dic13—81no—
287Dic13—81no—
288C22×Q8C22⋊D1311yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C2×Q16—261no—
293C2×Q16—261no—
294C2×SD16—22no—
295C2×SD16—22no—
296C2×SD16—44no—
297C2×M16—131no—
298C2×M16—131no—
299C2×M16—261no—
300C22×C8—21no—
301C4⋊Q8—131no—
302C4⋊Q8—131no—
303#127—21no—
304#127—21no—
305#127—21no—
306#127C22×D1312yes—
307#125—261no—
308C22⋊Q8—261no—
309C22⋊Q8—261no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—261no—
313C4×Q8—261no—
314C4×Q8C22⋊D1311yescharacteristic
315C4×Q8C22⋊D1311yescharacteristic
316C4×Q8C22×D1311yescharacteristic
317C4×Q8C22×D1311yescharacteristic
318#117—261no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4C22⋊D1311yescharacteristic
321C2×C42—21no—
322C2×C42C22×D1311yescharacteristic
323#107—261no—
324#107—261no—
325C4⋊C8—21no—
326C4⋊C8—132no—
327C4⋊C8—131no—
328C4⋊C8—131no—
329C4⋊C8—262no—
330C4⋊C8—262no—
331C4⋊C8—261no—
332C4⋊C8C22×D1312yes—
333#103—261no—
334#103—261no—
335#103—261no—
336#103—261no—
337#102—22no—
338#102—22no—
339#102—262no—
340#102—262no—
341#102—262no—
342#102—262no—
343C22⋊C8—261no—
344#97—132no—
345#97—262no—
346C4×C8—132no—
347C4×C8—262no—
348C4×C8—261no—
349C2×C13—22no—
350C2×C13—162no—
351C2×C13C2×#46411yescharacteristic
352C2×C13#305511yescharacteristic
353C2×C13#306811yescharacteristic
354C24—41no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—41no—
358C2×Q8—261no—
359C2×Q8—261no—
360C2×Q8C2×C22⋊D1311yescharacteristic
361C2×Q8C2×C22⋊D1311yescharacteristic
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—82no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4D4×D1311yescharacteristic
376C22×C4#612911yescharacteristic
377C22×C4C2×C22⋊D1311yescharacteristic
378Q16—522no—
379Q16—522no—
380SD16—44no—
381SD16—44no—
382M16—262no—
383M16—262no—
384M16—522no—
385C2×C8—22no—
386C2×C8—42no—
387C2×C8—132no—
388C2×C8—132no—
389C2×C8—262no—
390C2×C8—261no—
391C2×C8—261no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—261no—
398C4⋊C4—261no—
399C4⋊C4—261no—
400C4⋊C4—261no—
401C4⋊C4—521no—
402C4⋊C4—521no—
403C4⋊C4C2×C22⋊D1311yescharacteristic
404C4⋊C4C2×C22⋊D1311yescharacteristic
405C22⋊C4—521no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42—521no—
411C42D4×D1311yescharacteristic
412C42#612911yescharacteristic
413C42C2×C22⋊D1311yescharacteristic
414C42C23×D1311yescharacteristic
415C13#1917411yescharacteristic, complemented, Sylow
416C23—42no—
417C23—82no—
418C23—82no—
419C23—82no—
420C23#8819311yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—21no—
424Q8—42no—
425Q8—521no—
426Q8—521no—
427Q8—1041no—
428Q8#8818612yes—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—42no—
433D4—82no—
434D4—82no—
435D4—82no—
436D4—82no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—81no—
446C2×C4—521no—
447C2×C4—521no—
448C2×C4#8816912yes—
449C2×C4#8817012yes—
450C2×C4#8819311yescharacteristic
451C2×C4#8819311yescharacteristic
452C2×C4#8819311yescharacteristic
453C2×C4C2×D4×D1311yescharacteristic
454C2×C4C2×#612911yescharacteristic
455C2×C4C22×C22⋊D1311yescharacteristic
456C8—42no—
457C8—262no—
458C8—262no—
459C8—522no—
460C8—521no—
461C8—521no—
462C22—21no—
463C22—21no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22#1171882712yes—
469C22C2×#8819311yescharacteristic
470C4—21no—
471C4—22no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—1041no—
478C4—1041no—
479C4#1171882712yes—
480C4C2×#8816911yescharacteristic
481C4C2×#8817011yescharacteristic
482C4C2×#8818611yescharacteristic
483C4#1171952711yescharacteristic
484C2—22no—
485C2—162no—
486C2C2×#1171882711yescharacteristic
487C2#1312445111yescharacteristic
488C2#1312456111yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#460C2
socleC22×C13C2×#121
prime radicalC2×C13×#127C22
hypercenterC2×#460D13
hypocenterC13#19174
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. #13124875C2semidirect
3. Q8×#6099C2semidirect
4. #13114402C2semidirect
5. #13114374C2semidirect
6. #13114278C2semidirect
7. #13114250C2semidirect
8. #13113586C2semidirect
9. #13113524C2semidirect
28. #11718692C22semidirect
29. #11718692C22semidirect
33. #11718685C22semidirect
34. Q8×#1055C22semidirect
35. #11718682C22semidirect
36. #11718682C22semidirect
45. #11718074C22semidirect
46. #11718073C22semidirect
47. #11718072C22semidirect
48. #11718071C22semidirect
415. C13#19174semidirect

Maximal subgroups

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

subgroupindex
#131252102
#131248752
Q8×#60992
#131144022
#131143742
#131142782
#131142502
#131135862
#131135242
#131135042
C2×C13×#4602
#1917413