Finite Group Databasebeta

← #15841712

Subgroups — #15841712

Order 3328.

932 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#13125964C211yesmaximal, characteristic
2#13124867C211yesmaximal, characteristic
3#13124308C211yesmaximal, characteristic
4#13114113C214yesmaximal, complemented
5#13113932C214yesmaximal, complemented
6#13113521C211yesmaximal, characteristic, complemented
7#13113265C211yesmaximal, characteristic, complemented
8#13113231C211yesmaximal, characteristic, complemented
9C2×C13×#557C211yesmaximal, characteristic, complemented
10C13×#557—22no—
11C13×#557—22no—
12C13×#557—22no—
13C13×#557C2214yes—
14C2×C13×C4⋊Q8—21no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#125—22no—
17C2×C13×#125—21no—
18C2×C4×Q8×C13—21no—
19C2×C4×Q8×C13—21no—
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×Q8×C13C2211yescharacteristic
22C2×#88196—21no—
23#11719182C2211yescharacteristic
24#11718888—21no—
25#11718749C2212yes—
26#11718745—22no—
27#11718740C2212yes—
28#11718692C2212yes—
29#11718689—22no—
30#11718688C2212yes—
31#11718688C2212yes—
32C4×#6106—22no—
33#11718681C2212yes—
34#11718629—21no—
35#11718629—22no—
36#11718627—21no—
37#11718586C2211yescharacteristic
38#11718586C2211yescharacteristic
39#11718585C2211yescharacteristic
40#11718139C2214yes—
41Q8⋊#1055C2214yes—
42Q8⋊#1055C2214yes—
43C22×Q8×C13—21no—
44C22×Q8×C13D411yescharacteristic
45C22×Q8×C13D411yescharacteristic
46C2×#6127—21no—
47C13×C4⋊Q8—24no—
48C13×C4⋊Q8—24no—
49C13×C4⋊Q8—21no—
50C13×C4⋊Q8—21no—
51C13×C4⋊Q8D412yes—
52C13×C4⋊Q8C2312yes—
53C13×#125—28no—
54C13×#125—24no—
55C13×#125—28no—
56C13×#125—24no—
57C4×Q8×C13—24no—
58C4×Q8×C13—24no—
59C4×Q8×C13—24no—
60C4×Q8×C13—24no—
61C4×Q8×C13—21no—
62C4×Q8×C13—21no—
63C4×Q8×C13—21no—
64C4×Q8×C13—21no—
65C4×Q8×C13D412yes—
66C4×Q8×C13D412yes—
67C4×Q8×C13C2312yes—
68C4×Q8×C13C2312yes—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4D412yes—
78C2×C42×C13—22no—
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82C2×#6107—22no—
83#88196—44no—
84C2×#6106—22no—
85C2×#6106—22no—
86#88184—21no—
87#88184—21no—
88C2×#6099—21no—
89#88129—21no—
90#88128C2311yescharacteristic
91C4×D52—21no—
92C4×D52—21no—
93#88123C2311yescharacteristic
94#88075—22no—
95C22⋊#1055—21no—
96C22⋊#1055—21no—
97#88050—22no—
98#88049—22no—
99#88049—22no—
100#88049—24no—
101#88048—22no—
102#88048—24no—
103C4⋊#1055—21no—
104C4⋊#1055—21no—
105C4⋊#1055C2312yes—
106C4⋊#1055C2312yes—
107C4×#1055—21no—
108C4×#1055C2312yes—
109#18778—131nomaximal, Sylow
110C2×Q8×C13—21no—
111C2×Q8×C13—21no—
112C2×Q8×C13—22no—
113C2×Q8×C13—22no—
114C2×Q8×C13—22no—
115C2×Q8×C13—42no—
116C2×Q8×C13—44no—
117C2×Q8×C13SD1614yescomplemented
118C2×Q8×C13C2×D412yes—
119C2×Q8×C13C2×D412yes—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—22no—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C2×C22⋊D13—41no—
129#6127—42no—
130#6127—42no—
131C2×D52—21no—
132C2×D52—21no—
133C2×D52—21no—
134C2×C4×D13—41no—
135C2×Dic26—21no—
136C13×C4⋊C4—28no—
137C13×C4⋊C4—28no—
138C13×C4⋊C4—28no—
139C13×C4⋊C4—22no—
140C13×C4⋊C4—22no—
141C13×C4⋊C4—22no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—22no—
145C13×C4⋊C4—22no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4C2×D412yes—
149C13×C4⋊C4C2×D412yes—
150C13×C4⋊C4C2×D414yes—
151C42×C13—28no—
152C42×C13—22no—
153C42×C13—22no—
154C42×C13—22no—
155C42×C13—22no—
156C42×C13C2×D411yescharacteristic
157C42×C13C2×D411yescharacteristic
158C42×C13C2×D411yescharacteristic
159C42×C13C2411yescharacteristic
160#6107—44no—
161#6106—44no—
162#6106—44no—
163#6103—41no—
164#6103—41no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167#6099—42no—
168C2×#1055—22no—
169C2×#1055—22no—
170C2×#1055—22no—
171C2×#557D1311yescharacteristic, complemented
172#3227—131no—
173#3103—131no—
174#3037—131no—
175#1653—134no—
176#1626—134no—
177#1549—131no—
178#1487—131no—
179#1479—131no—
180C23×C13#12011yescharacteristic
181C22×D13—41no—
182Q8×C13—22no—
183Q8×C13—24no—
184Q8×C13—22no—
185Q8×C13—22no—
186Q8×C13—42no—
187Q8×C13—44no—
188Q8×C13—44no—
189Q8×C13C2×SD1614yes—
190C2×C4×C13—22no—
191C2×C4×C13—24no—
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—42no—
200C2×C4×C13—42no—
201C2×C4×C13—44no—
202C2×C4×C13#12011yescharacteristic
203C2×C4×C13#12011yescharacteristic
204C2×C4×C13#12011yescharacteristic
205C2×C4×C13C2×SD1612yes—
206C2×C4×C13#13712yes—
207C2×C4×C13C22×D411yescharacteristic
208C2×C4×C13C22×D411yescharacteristic
209C2×C4×C13C22×D411yescharacteristic
210C22⋊D13—82no—
211C2×Dic13—41no—
212D52—42no—
213D52—41no—
214D52—41no—
215D52—42no—
216C4×D13—82no—
217Dic26—41no—
218Dic26—41no—
219#1055—42no—
220#1055—42no—
221#1055—42no—
222C2×#137—261no—
223#557—22no—
224#557—22no—
225#557—22no—
226#557C2×D1314yes—
227#532—131no—
228C2×C4⋊Q8—21no—
229C2×C4⋊Q8C2×D1311yescharacteristic
230C2×#125—22no—
231C2×#125—21no—
232C2×C4×Q8—21no—
233C2×C4×Q8—21no—
234C2×C4×Q8C2×D1311yescharacteristic
235C2×C4×Q8C2×D1311yescharacteristic
236#498—132no—
237#486—132no—
238#481—261no—
239#481—262no—
240#476—262no—
241#475—132no—
242#464—262no—
243#462—132no—
244#460—132no—
245#460—132no—
246#448—261no—
247C4×SD16—262no—
248#431—131no—
249#431—131no—
250#423—131no—
251#417—261no—
252#332—134no—
253Q8⋊C8—134no—
254Q8⋊C8—134no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13#44812yes—
258C22×C13C2×#12011yescharacteristic
259C2×D13—81no—
260C2×D13—81no—
261C2×D13—81no—
262C4×C13—24no—
263C4×C13—21no—
264C4×C13—21no—
265C4×C13—21no—
266C4×C13—42no—
267C4×C13—44no—
268C4×C13—42no—
269C4×C13—42no—
270C4×C13#44812yes—
271C4×C13C22×SD1611yescharacteristic
272C4×C13C2×#13711yescharacteristic
273C4×C13#57512yes—
274Dic13—81no—
275C2×#41—261no—
276C22×Q8—21no—
277C22×Q8C22⋊D1311yescharacteristic
278C22×Q8C22⋊D1311yescharacteristic
279#137—524no—
280C2×Q16—262no—
281C2×SD16—262no—
282C2×SD16—262no—
283C2×M16—261no—
284C4⋊Q8—24no—
285C4⋊Q8—24no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—131no—
289C4⋊Q8C22⋊D1312yes—
290C4⋊Q8C22×D1312yes—
291#127—131no—
292#125—28no—
293#125—24no—
294#125—28no—
295#125—24no—
296#124—261no—
297#121—261no—
298#121—261no—
299C4×Q8—24no—
300C4×Q8—24no—
301C4×Q8—24no—
302C4×Q8—24no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8C22⋊D1312yes—
308C4×Q8C22⋊D1312yes—
309C4×Q8C22×D1312yes—
310C4×Q8C22×D1312yes—
311C4×D4—261no—
312C4×D4—261no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4C22⋊D1311yescharacteristic
320C2×C4⋊C4C22⋊D1311yescharacteristic
321C2×C4⋊C4C22⋊D1312yes—
322C2×C42—22no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42C22×D1311yescharacteristic
326#106—262no—
327#106—264no—
328C4⋊C8—132no—
329C4⋊C8—132no—
330C4⋊C8—261no—
331C4⋊C8—261no—
332#103—262no—
333#103—262no—
334#102—262no—
335#102—262no—
336#102—264no—
337C22⋊C8—261no—
338C22⋊C8—261no—
339C4×C8—132no—
340C4×C8—261no—
341C2×C13—22no—
342C2×C13C2×#44811yescharacteristic
343C2×C13#300511yescharacteristic
344C2×C13#302011yescharacteristic
345D13—161no—
346#41—522no—
347#41—522no—
348C2×Q8—22no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—42no—
354C2×Q8—44no—
355C2×Q8—261no—
356C2×Q8#610614yescomplemented
357C2×Q8C2×C22⋊D1312yes—
358C2×Q8C2×C22⋊D1312yes—
359C2×D4—261no—
360C2×D4—261no—
361C2×D4—261no—
362C2×D4—521no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—521no—
369C22×C4C2×C22⋊D1311yescharacteristic
370C22×C4C2×C22⋊D1311yescharacteristic
371C22×C4C2×C22⋊D1311yescharacteristic
372Q16—524no—
373SD16—524no—
374SD16—524no—
375M16—522no—
376C2×C8—262no—
377C2×C8—262no—
378C2×C8—262no—
379C4⋊C4—28no—
380C4⋊C4—28no—
381C4⋊C4—28no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—261no—
392C4⋊C4—261no—
393C4⋊C4C2×C22⋊D1312yes—
394C4⋊C4C2×C22⋊D1312yes—
395C4⋊C4C2×C22⋊D1314yes—
396C22⋊C4—521no—
397C22⋊C4—521no—
398C42—28no—
399C42—22no—
400C42—22no—
401C42—22no—
402C42—22no—
403C42C2×C22⋊D1311yescharacteristic
404C42C2×C22⋊D1311yescharacteristic
405C42C2×C22⋊D1311yescharacteristic
406C42C23×D1311yescharacteristic
407C13#1877811yescharacteristic, complemented, Sylow
408C23—521no—
409C23#8820711yescharacteristic
410Q8—22no—
411Q8—24no—
412Q8—22no—
413Q8—22no—
414Q8—42no—
415Q8—44no—
416Q8—44no—
417Q8—521no—
418Q8—521no—
419Q8C2×#610614yes—
420D4—522no—
421D4—521no—
422D4—521no—
423D4—522no—
424D4—1042no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—521no—
438C2×C4—1042no—
439C2×C4C2×#610612yes—
440C2×C4#8819612yes—
441C2×C4#8820711yescharacteristic
442C2×C4#8820711yescharacteristic
443C2×C4#8820711yescharacteristic
444C2×C4C22×C22⋊D1311yescharacteristic
445C2×C4C22×C22⋊D1311yescharacteristic
446C2×C4C22×C22⋊D1311yescharacteristic
447C8—522no—
448C8—522no—
449C8—522no—
450C22—21no—
451C22—21no—
452C22—1041no—
453C22—1041no—
454C22—1041no—
455C22#1171888812yes—
456C22C2×#8820711yescharacteristic
457C4—21no—
458C4—21no—
459C4—24no—
460C4—21no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4—44no—
465C4—1041no—
466C4#1171888812yes—
467C4C22×#610611yescharacteristic
468C4C2×#8819611yescharacteristic
469C4#1171952712yes—
470C2—22no—
471C2—2081no—
472C2C2×#1171888811yescharacteristic
473C2#1312407811yescharacteristic
474C2#1312420011yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#557C2
socleC22×C13C2×#120
prime radical#11719182C22
hypercenterC2×#557D13
hypocenterC13#18778
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
4. #13114113C2semidirect
5. #13113932C2semidirect
6. #13113521C2semidirect
7. #13113265C2semidirect
8. #13113231C2semidirect
9. C2×C13×#557C2semidirect
117. C2×Q8×C13SD16semidirect
171. C2×#557D13semidirect
356. C2×Q8#6106semidirect
407. C13#18778semidirect

Maximal subgroups

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

subgroupindex
#131259642
#131248672
#131243082
#131141132
#131139322
#131135212
#131132652
#131132312
C2×C13×#5572
#1877813