Finite Group Databasebeta

← #15918681

Subgroups — #15918681

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic
2C2×#11718740C211yesmaximal, characteristic, complemented
3#13123183C211yesmaximal, characteristic
4#13116172C214yesmaximal, complemented
5#13115798C211yesmaximal, characteristic, complemented
6#13115797C211yesmaximal, characteristic, complemented
7#13115032C214yesmaximal
8C4×#88060C211yesmaximal, characteristic
9C2×C13×#500C211yesmaximal, characteristic, complemented
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×#88200—21no—
13C2×#88200—21no—
14C2×Q8×Dic13—21no—
15#11719433—24no—
16#11719433—24no—
17C2×#88151—21no—
18C2×#88146C2212yes—
19C2×#88144C2212yes—
20C2×#88141—21no—
21C2×C42×D13C2211yescharacteristic
22C2×#88123C2211yescharacteristic
23C13×#500—24no—
24C2×C13×#107C2214yes—
25C2×C4×C8×C13C2211yescharacteristic
26#11718891—21no—
27C2×#88060C2212yes—
28#11718740—24no—
29#11718648—21no—
30#11718648C2212yes—
31#11718634—21no—
32#11718634C2212yes—
33C2×#88048C2214yes—
34#11718596C2211yescharacteristic
35C2×C4×#1055C2211yescharacteristic
36#11718143C2214yes—
37#11718142C2212yes—
38#11718121C2214yes—
39C22×Q8×C13—21no—
40C22×Q8×C13—21no—
41C22×C4×D13D411yescharacteristic
42C22×C4×D13D411yescharacteristic
43C22×C4×D13C2311yescharacteristic
44C22×Dic26—21no—
45C22×C8×C13C2312yes—
46C13×C4⋊Q8—22no—
47C13×C4⋊Q8—22no—
48C13×C4⋊Q8—22no—
49C13×C4⋊Q8D414yes—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4C2312yes—
53C2×C13×C4⋊C4C2312yes—
54C2×C42×C13C2311yescharacteristic
55#88200—28no—
56#88200—44no—
57Q8×Dic13—28no—
58C2×#6103—22no—
59C2×#6103—22no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13—21no—
63C2×C4⋊Dic13—21no—
64C2×C4⋊Dic13C2312yes—
65C2×C4⋊Dic13C2312yes—
66C2×#6101—22no—
67C2×#6101—22no—
68C2×C4×Dic13—22no—
69C2×C4×Dic13D411yescharacteristic
70C2×C4×Dic13D411yescharacteristic
71C2×C4×Dic13C2311yescharacteristic
72C22×#1055C2312yes—
73#88151—28no—
74#88146—24no—
75#88146—24no—
76#88144—24no—
77#88144—24no—
78#88141—28no—
79C42×D13—22no—
80C42×D13—22no—
81#88123—22no—
82#88123D414yes—
83C13×#107—28no—
84C4×C8×C13—22no—
85#88071—22no—
86#88071—22no—
87#88060Q818yescomplemented
88#88048—28no—
89C4×#1055—22no—
90#25812—131nomaximal, Sylow
91C23×D13C2×D411yescharacteristic
92C2×Q8×C13—24no—
93C2×Q8×C13—42no—
94C2×Q8×C13—42no—
95C2×Q8×C13—42no—
96C2×Q8×C13—42no—
97C2×Q8×C13—42no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2411yescharacteristic
103C22×Dic13—22no—
104C22×Dic13—22no—
105C22×Dic13C2×D411yescharacteristic
106C22×Dic13C2×D411yescharacteristic
107C22×Dic13C2×D411yescharacteristic
108C2×C4×D13—21no—
109C2×C4×D13—21no—
110C2×C4×D13—22no—
111C2×C4×D13—22no—
112C2×C4×D13—22no—
113C2×C4×D13—22no—
114C2×C4×D13—22no—
115C2×C4×D13—22no—
116C2×C4×D13—22no—
117C2×C4×D13C2×Q814yes—
118C2×Dic26—24no—
119C2×Dic26—42no—
120C2×Dic26—42no—
121C2×C8×C13—22no—
122C2×C8×C13—22no—
123C2×C8×C13C2×Q814yes—
124C13×C4⋊C4—24no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—42no—
129C13×C4⋊C4C2×D414yes—
130C42×C13C2×D412yes—
131C42×C13C2×D412yes—
132#6103—28no—
133#6103—44no—
134C4⋊Dic13—28no—
135C4⋊Dic13—24no—
136C4⋊Dic13—22no—
137C4⋊Dic13—24no—
138C4⋊Dic13—42no—
139C4⋊Dic13—42no—
140C4⋊Dic13C2×D414yes—
141#6101—28no—
142#6101—44no—
143C4×Dic13—28no—
144C4×Dic13—22no—
145C4×Dic13—22no—
146C4×Dic13—21no—
147C4×Dic13—21no—
148C2×#1055—22no—
149C2×#1055—22no—
150C2×#1055C2×Q814yes—
151C2×#533—131no—
152C2×#500D1311yescharacteristic, complemented
153C2×#498—131no—
154#2857—131no—
155#2059—134no—
156#1990—131no—
157#1990—131no—
158#1854—134no—
159C4×C22⋊C8—131no—
160C23×C13C22×D411yescharacteristic
161C22×D13—21no—
162C22×D13—21no—
163C22×D13—21no—
164C22×D13—21no—
165C22×D13—21no—
166C22×D13—21no—
167C22×D13C4⋊Q812yes—
168Q8×C13—48no—
169Q8×C13—84no—
170C2×C4×C13—24no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13#12012yes—
177C2×C4×C13#12012yes—
178C2×C4×C13#13512yes—
179C2×C4×C13#13512yes—
180C2×C4×C13AGL(1,ℤ/8)12yes—
181C2×C4×C13#13712yes—
182C2×C4×C13C22×D411yescharacteristic
183C2×C4×C13C22×D411yescharacteristic
184C2×C4×C13C22×Q812yes—
185C2×C4×C132−1+412yes—
186C2×Dic13—21no—
187C2×Dic13—21no—
188C2×Dic13—21no—
189C2×Dic13—21no—
190C2×Dic13—24no—
191C2×Dic13—21no—
192C2×Dic13—21no—
193C2×Dic13—21no—
194C2×Dic13—21no—
195C2×Dic13—42no—
196C2×Dic13—42no—
197C2×Dic13—42no—
198C2×Dic13—42no—
199C2×Dic13—42no—
200C2×Dic13C4⋊Q812yes—
201C4×D13—24no—
202C4×D13—24no—
203C4×D13—44no—
204C4×D13—44no—
205Dic26—48no—
206C8×C13—24no—
207#1055—24no—
208#533—264no—
209#533—264no—
210C2×C4⋊Q8—131no—
211C2×C4⋊Q8C2×D1311yescharacteristic
212C2×C4⋊Q8C2×D1311yescharacteristic
213C2×#125—132no—
214C2×C22⋊Q8—261no—
215C2×C22⋊Q8—261no—
216C2×C22⋊Q8—261no—
217C2×C4×Q8—261no—
218C2×C4×Q8—261no—
219C2×#117—132no—
220C22×C42—131no—
221#500—24no—
222#498—264no—
223C2×#107C2×D1314yes—
224C2×#106—134no—
225C2×C22⋊C8—132no—
226C2×C4×C8—131no—
227C2×C4×C8C2×D1311yescharacteristic
228#391—261no—
229#389—132no—
230#389—261no—
231#384—131no—
232#380—132no—
233#380—261no—
234#340—134no—
235#340—134no—
236#336—132no—
237C22×C13C2×#12011yescharacteristic
238C22×C13C2×C4⋊Q811yescharacteristic
239C22×C13#53611yescharacteristic
240C22×C13C2×#13511yescharacteristic
241C22×C13C2×#13511yescharacteristic
242C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
243C22×C13C2×#13711yescharacteristic
244C2×D13—22no—
245C2×D13—22no—
246C2×D13—22no—
247C2×D13—41no—
248C2×D13—41no—
249C2×D13—41no—
250C2×D13—41no—
251C4×C13—44no—
252C4×C13—82no—
253C4×C13#44914yes—
254C4×C13#45214yes—
255C4×C13D4×Q812yes—
256C4×C13D4×Q812yes—
257Dic13—22no—
258Dic13—41no—
259Dic13—44no—
260Dic13—41no—
261Dic13—82no—
262C22×Q8—21no—
263C22×Q8—21no—
264C22×Q8—261no—
265C23×C4—131no—
266C23×C4—131no—
267C23×C4—131no—
268C22×C8—132no—
269C22×C8C22×D1312yes—
270C4⋊Q8—22no—
271C4⋊Q8—22no—
272C4⋊Q8—22no—
273C4⋊Q8—134no—
274C4⋊Q8—262no—
275C4⋊Q8C22⋊D1314yes—
276#125—264no—
277#125—264no—
278C22⋊Q8—268no—
279C22⋊Q8—268no—
280C22⋊Q8—524no—
281C4×Q8—268no—
282C4×Q8—268no—
283#117—264no—
284#117—264no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—132no—
288C2×C4⋊C4—132no—
289C2×C4⋊C4—262no—
290C2×C4⋊C4—262no—
291C2×C4⋊C4—261no—
292C2×C4⋊C4—262no—
293C2×C4⋊C4—261no—
294C2×C4⋊C4—261no—
295C2×C4⋊C4C22×D1312yes—
296C2×C4⋊C4C22×D1312yes—
297C2×C22⋊C4—262no—
298C2×C22⋊C4—262no—
299C2×C42—131no—
300C2×C42—131no—
301C2×C42—131no—
302C2×C42—262no—
303C2×C42—262no—
304C2×C42—262no—
305C2×C42C22×D1311yescharacteristic
306#107—28no—
307#106—268no—
308C22⋊C8—138no—
309C4×C8—22no—
310C4×C8—262no—
311#95—262no—
312#95—262no—
313C2×C13#243411yescharacteristic
314C2×C13C2×#44911yescharacteristic
315C2×C13C2×#45211yescharacteristic
316C2×C13#316011yescharacteristic
317C2×C13#316511yescharacteristic
318C2×C13#322811yescharacteristic
319C2×C13#323111yescharacteristic
320D13—42no—
321C24—131no—
322C2×Q8—24no—
323C2×Q8—42no—
324C2×Q8—42no—
325C2×Q8—42no—
326C2×Q8—42no—
327C2×Q8—42no—
328C2×Q8—264no—
329C2×Q8—522no—
330C2×Q8—522no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—131no—
334C22×C4—134no—
335C22×C4—131no—
336C22×C4—131no—
337C22×C4—261no—
338C22×C4—262no—
339C22×C4—261no—
340C22×C4—262no—
341C22×C4—262no—
342C22×C4—262no—
343C22×C4—262no—
344C22×C4—262no—
345C22×C4—262no—
346C22×C4—262no—
347C22×C4—262no—
348C22×C4D4×D1311yescharacteristic
349C22×C4D4×D1311yescharacteristic
350C22×C4C23×D1311yescharacteristic
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—134no—
354C2×C8—262no—
355C2×C8—262no—
356C2×C8Q8×D1314yes—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—42no—
362C4⋊C4—134no—
363C4⋊C4—268no—
364C4⋊C4—268no—
365C4⋊C4—264no—
366C4⋊C4—262no—
367C4⋊C4—264no—
368C4⋊C4—524no—
369C4⋊C4—522no—
370C4⋊C4—522no—
371C4⋊C4C2×C22⋊D1314yes—
372C22⋊C4—268no—
373C22⋊C4—524no—
374C42—268no—
375C42—262no—
376C42—262no—
377C42—261no—
378C42—261no—
379C42D4×D1312yes—
380C42C2×C22⋊D1312yes—
381C13#2581211yescharacteristic, complemented, Sylow
382C23—132no—
383C23—261no—
384C23—261no—
385C23—261no—
386C23—261no—
387C23—261no—
388C23—261no—
389C23C2×D4×D1311yescharacteristic
390Q8—48no—
391Q8—84no—
392Q8—528no—
393C2×C4—24no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—132no—
400C2×C4—261no—
401C2×C4—261no—
402C2×C4—264no—
403C2×C4—264no—
404C2×C4—261no—
405C2×C4—261no—
406C2×C4—261no—
407C2×C4—261no—
408C2×C4—261no—
409C2×C4—261no—
410C2×C4—264no—
411C2×C4—522no—
412C2×C4—522no—
413C2×C4—524no—
414C2×C4—524no—
415C2×C4—522no—
416C2×C4—522no—
417C2×C4—522no—
418C2×C4#8816512yes—
419C2×C4#8816612yes—
420C2×C4#8817212yes—
421C2×C4#8817312yes—
422C2×C4#8819112yes—
423C2×C4#8819112yes—
424C2×C4C2×D4×D1311yescharacteristic
425C2×C4C2×Q8×D1312yes—
426C2×C4#8825412yes—
427C2×C4C22×C22⋊D1311yescharacteristic
428C8—24no—
429C8—264no—
430C22—262no—
431C22—262no—
432C22—262no—
433C22—521no—
434C22—521no—
435C22—521no—
436C22—521no—
437C22D13×C4⋊Q811yescharacteristic
438C22#1171942911yescharacteristic
439C22C2×#8816511yescharacteristic
440C22C2×#8816611yescharacteristic
441C22C2×#8817211yescharacteristic
442C22C2×#8817311yescharacteristic
443C22C2×#8819111yescharacteristic
444C4—44no—
445C4—82no—
446C4—262no—
447C4—521no—
448C4—521no—
449C4—524no—
450C4—1042no—
451C4#1171881914yes—
452C4#1171884814yes—
453C4#1171943212yes—
454C4Q8×C22⋊D1312yes—
455C2—522no—
456C2#1311847711yescharacteristic
457C2C2×#1171881911yescharacteristic
458C2C2×#1171884811yescharacteristic
459C2#1312534711yescharacteristic
460C2#1312537911yescharacteristic
461C2#1312597511yescharacteristic
462C2#1312599611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#500C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#500D13
hypocenterC13#25812
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. C2×#11718740C2semidirect
4. #13116172C2semidirect
5. #13115798C2semidirect
6. #13115797C2semidirect
9. C2×C13×#500C2semidirect
87. #88060Q8semidirect
152. C2×#500D13semidirect
381. C13#25812semidirect

Maximal subgroups

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

subgroupindex
C2×#117194332
C2×#117187402
#131231832
#131161722
#131157982
#131157972
#131150322
C4×#880602
C2×C13×#5002
#2581213