Finite Group Databasebeta

← #15873488

Subgroups — #15873488

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718366C211yesmaximal, characteristic
2#13117242C211yesmaximal, characteristic
3#13117241C211yesmaximal, characteristic
4#13115596C212yesmaximal, complemented
5#13115591C212yesmaximal, complemented
6#13115034C212yesmaximal
7#13115032C212yesmaximal
8#13115002C211yesmaximal, characteristic, complemented
9#13114970C211yesmaximal, characteristic, complemented
10#13114969C211yesmaximal, characteristic, complemented
11C13×#1847C211yesmaximal, characteristic, complemented
12C2×#88146—21no—
13C2×#88146C2211yescharacteristic
14C2×#88146C2211yescharacteristic
15C2×C42×D13C2211yescharacteristic
16C2×C13×#107C2212yes—
17C2×C13×#106C2212yes—
18C2×C13×#97C2211yescharacteristic
19C13×#384C2211yescharacteristic
20C13×#382C2211yescharacteristic
21C2×#88060C2212yes—
22C2×#88054C2212yes—
23#11718648—21no—
24#11718648C2212yes—
25#11718638—21no—
26#11718637C2211yescharacteristic
27#11718637C2211yescharacteristic
28C4⋊C4×Dic13—21no—
29C4⋊C4×Dic13C2212yes—
30C2×#88048C2212yes—
31C2×#88047C2212yes—
32#11718597C2211yescharacteristic
33#11718596C2211yescharacteristic
34C2×#88043C2211yescharacteristic
35#11718366C418yescomplemented
36#11718328—21no—
37#11718328—21no—
38#11718310—21no—
39#11718310—21no—
40#11718143C2212yes—
41#11718143C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C22×C4×D13D411yescharacteristic
45C22×C4×D13D411yescharacteristic
46C22×C4×D13C2311yescharacteristic
47C22×C8×C13C2312yes—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4C2311yescharacteristic
51C2×C13×C4⋊C4C2311yescharacteristic
52C2×C13×C4⋊C4C2312yes—
53C2×C42×C13C2311yescharacteristic
54C2×#6103—22no—
55C2×#6103—21no—
56C2×#6103—21no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13C2311yescharacteristic
60C2×C4⋊Dic13C2311yescharacteristic
61C2×C4⋊Dic13C2312yes—
62C2×#6101—21no—
63C2×#6101—21no—
64C2×#6101—21no—
65C2×#6101—21no—
66C2×C4×Dic13—22no—
67C2×C4×Dic13—21no—
68C2×C4×Dic13—21no—
69C2×C4×Dic13D411yescharacteristic
70C2×C4×Dic13D411yescharacteristic
71C2×C4×Dic13C2311yescharacteristic
72C22×#1055C2312yes—
73#88146—42no—
74#88146—42no—
75#88146—44no—
76C42×D13C2×C414yes—
77C42×D13Q814yes—
78C13×#107—42no—
79C13×#106—42no—
80C13×#97C2×C414yes—
81C13×#95—21no—
82C13×#95—21no—
83#88071—21no—
84#88071—21no—
85#88071—22no—
86#88071—22no—
87#88060C2×C418yes—
88#88054C2×C418yes—
89#88048—42no—
90#88047—42no—
91#88043C2×C414yes—
92#21988—131nomaximal, Sylow
93C23×D13C2×D411yescharacteristic
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2411yescharacteristic
100C22×Dic13—21no—
101C22×Dic13—21no—
102C22×Dic13—22no—
103C22×Dic13C2×D411yescharacteristic
104C22×Dic13C2×D411yescharacteristic
105C22×Dic13C2×D411yescharacteristic
106C2×C4×D13—22no—
107C2×C4×D13—22no—
108C2×C4×D13—22no—
109C2×C4×D13—22no—
110C2×C4×D13—41no—
111C2×C4×D13—41no—
112C2×C4×D13C4⋊C414yes—
113C2×C4×D13C4⋊C414yes—
114C2×C4×D13C22×C412yes—
115C2×C4×D13C2×Q812yes—
116C2×C8×C13—22no—
117C2×C8×C13—22no—
118C2×C8×C13C22×C414yes—
119C13×C4⋊C4—22no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—42no—
124C13×C4⋊C4—42no—
125C42×C13C22×C412yes—
126C42×C13C2×Q812yes—
127#6103—42no—
128#6103—42no—
129#6103—44no—
130C4⋊Dic13—22no—
131C4⋊Dic13—22no—
132C4⋊Dic13—24no—
133C4⋊Dic13—42no—
134C4⋊Dic13—42no—
135#6101—42no—
136#6101—42no—
137#6101—42no—
138#6101—42no—
139C4×Dic13—42no—
140C4×Dic13—42no—
141C4×Dic13—44no—
142C4×Dic13C4⋊C414yes—
143C4×Dic13C4⋊C414yes—
144C4×Dic13C22×C412yes—
145C4×Dic13C2×Q812yes—
146C2×#1055—22no—
147C2×#1055—22no—
148C2×#1055C22×C414yes—
149C2×#432—131no—
150#2285—131no—
151#2285—131no—
152#1948—132no—
153#1947—132no—
154#1854—132no—
155#1854—132no—
156#1847—131no—
157#1847D1311yescharacteristic, complemented
158#1836—131no—
159#1836—131no—
160C23×C13C22×D411yescharacteristic
161C22×D13—21no—
162C22×D13—21no—
163C22×D13—21no—
164C22×D13—21no—
165C22×D13—21no—
166C22×D13—21no—
167C22×D13C2×C4⋊C412yes—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—42no—
181C2×C4×C13C2×C4⋊C412yes—
182C2×C4×C13C2×C4⋊C412yes—
183C2×C4×C13C23×C411yescharacteristic
184C2×C4×C13C22×Q811yescharacteristic
185C2×C4×C13H(5,𝔽2)12yes—
186C2×C4×C132−1+412yes—
187C2×Dic13—21no—
188C2×Dic13—21no—
189C2×Dic13—21no—
190C2×Dic13—21no—
191C2×Dic13—41no—
192C2×Dic13—41no—
193C2×Dic13—42no—
194C2×Dic13—42no—
195C2×Dic13—41no—
196C2×Dic13—41no—
197C2×Dic13—41no—
198C2×Dic13—41no—
199C2×Dic13—42no—
200C2×Dic13C2×C4⋊C412yes—
201C2×Dic13C2×C4⋊C412yes—
202C2×Dic13C2×C4⋊C412yes—
203C2×Dic13AGL(1,ℤ/8)12yes—
204C2×Dic13#13712yes—
205C4×D13—24no—
206C4×D13—24no—
207C4×D13—28no—
208C4×D13—44no—
209C8×C13—24no—
210#1055—24no—
211C2×#117—131no—
212C2×#117—131no—
213C2×#117—261no—
214C22×C42—131no—
215#432—138no—
216C2×#107—132no—
217C2×#107C2×D1312yes—
218C2×#106—132no—
219C2×#106C2×D1312yes—
220C2×C4⋊C8—132no—
221C2×C22⋊C8—132no—
222C2×#97—131no—
223C2×#97C2×D1311yescharacteristic
224#384—131no—
225#384—131no—
226#384—131no—
227#384C2×D1311yescharacteristic
228#382—131no—
229#382—261no—
230#382C2×D1311yescharacteristic
231#380—132no—
232#380—261no—
233#380—261no—
234#380—261no—
235C4×C4⋊C4—132no—
236C4×C4⋊C4—261no—
237C4×C4⋊C4—261no—
238C4×C4⋊C4—261no—
239#340—132no—
240#340—132no—
241#340—132no—
242#340—132no—
243C22×C13C22×C4⋊C411yescharacteristic
244C22×C13#53511yescharacteristic
245C22×C13#53611yescharacteristic
246C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
247C22×C13C2×#13711yescharacteristic
248C22×C13#57511yescharacteristic
249C22×C13#57511yescharacteristic
250C2×D13—22no—
251C2×D13—22no—
252C2×D13—22no—
253C2×D13—41no—
254C2×D13—41no—
255C2×D13—41no—
256C2×D13—41no—
257C4×C13—22no—
258C4×C13—22no—
259C4×C13—81no—
260C4×C13—82no—
261C4×C13—81no—
262C4×C13#52012yes—
263C4×C13#54412yes—
264Dic13—22no—
265Dic13—22no—
266Dic13—81no—
267Dic13—81no—
268Dic13—82no—
269Dic13#42814yes—
270C23×C4—131no—
271C23×C4—131no—
272C23×C4—131no—
273C22×C8—132no—
274C22×C8C22×D1312yes—
275#117—522no—
276#117—522no—
277#117—524no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—131no—
281C2×C4⋊C4—131no—
282C2×C4⋊C4—132no—
283C2×C4⋊C4—261no—
284C2×C4⋊C4—261no—
285C2×C4⋊C4—261no—
286C2×C4⋊C4—261no—
287C2×C4⋊C4—261no—
288C2×C4⋊C4—261no—
289C2×C4⋊C4C22×D1311yescharacteristic
290C2×C4⋊C4C22×D1311yescharacteristic
291C2×C4⋊C4C22×D1312yes—
292C2×C22⋊C4—261no—
293C2×C22⋊C4—261no—
294C2×C22⋊C4—262no—
295C2×C42—131no—
296C2×C42—131no—
297C2×C42—131no—
298C2×C42—134no—
299C2×C42—134no—
300C2×C42—261no—
301C2×C42—261no—
302C2×C42—262no—
303C2×C42C22×D1311yescharacteristic
304#107—42no—
305#107—522no—
306#106—42no—
307#106—522no—
308C4⋊C8—138no—
309C22⋊C8—138no—
310#97—134no—
311#97C4×D1314yes—
312#95—21no—
313#95—21no—
314#95—262no—
315#95—262no—
316#95—261no—
317#95—261no—
318C2×C13#231711yescharacteristic
319C2×C13C2×#42811yescharacteristic
320C2×C13#291111yescharacteristic
321C2×C13#321411yescharacteristic
322C2×C13#321611yescharacteristic
323C2×C13#323511yescharacteristic
324C2×C13#323711yescharacteristic
325D13—42no—
326C24—131no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—131no—
331C22×C4—131no—
332C22×C4—131no—
333C22×C4—134no—
334C22×C4—132no—
335C22×C4—132no—
336C22×C4—134no—
337C22×C4—262no—
338C22×C4—262no—
339C22×C4—262no—
340C22×C4—262no—
341C22×C4—262no—
342C22×C4—261no—
343C22×C4—261no—
344C22×C4—521no—
345C22×C4—521no—
346C22×C4D4×D1311yescharacteristic
347C22×C4D4×D1311yescharacteristic
348C22×C4C23×D1311yescharacteristic
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—134no—
352C2×C8—262no—
353C2×C8—262no—
354C2×C8C2×C4×D1314yes—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—262no—
362C4⋊C4—262no—
363C4⋊C4—264no—
364C4⋊C4—522no—
365C4⋊C4—522no—
366C4⋊C4—522no—
367C4⋊C4—522no—
368C4⋊C4—522no—
369C4⋊C4—522no—
370C22⋊C4—524no—
371C22⋊C4—522no—
372C22⋊C4—522no—
373C42—134no—
374C42—134no—
375C42—132no—
376C42—132no—
377C42—524no—
378C42—522no—
379C42—522no—
380C42C2×C4×D1312yes—
381C42Q8×D1312yes—
382C13#2198811yescharacteristic, complemented, Sylow
383C23—132no—
384C23—261no—
385C23—261no—
386C23—261no—
387C23—261no—
388C23—261no—
389C23—261no—
390C23C2×D4×D1311yescharacteristic
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—132no—
405C2×C4—132no—
406C2×C4—132no—
407C2×C4—132no—
408C2×C4—132no—
409C2×C4—268no—
410C2×C4—261no—
411C2×C4—261no—
412C2×C4—261no—
413C2×C4—261no—
414C2×C4—264no—
415C2×C4—264no—
416C2×C4—524no—
417C2×C4—522no—
418C2×C4—522no—
419C2×C4—521no—
420C2×C4—521no—
421C2×C4—521no—
422C2×C4—522no—
423C2×C4—521no—
424C2×C4—521no—
425C2×C4—521no—
426C2×C4C4⋊C4×D1312yes—
427C2×C4C4⋊C4×D1312yes—
428C2×C4C22×C4×D1311yescharacteristic
429C2×C4#8825112yes—
430C2×C4C2×Q8×D1311yescharacteristic
431C2×C4#8825412yes—
432C8—24no—
433C8—264no—
434C22—262no—
435C22—262no—
436C22—262no—
437C22—521no—
438C22—521no—
439C22—521no—
440C22—521no—
441C22C2×C4⋊C4×D1311yescharacteristic
442C22#1171942011yescharacteristic
443C22#1171942911yescharacteristic
444C22D13×AGL(1,ℤ/8)11yescharacteristic
445C22#1171947811yescharacteristic
446C22D13×#13711yescharacteristic
447C22#1171948211yescharacteristic
448C4—22no—
449C4—22no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4—134no—
454C4—262no—
455C4—262no—
456C4—1042no—
457C4—1041no—
458C4—1041no—
459C4#1171920912yes—
460C4#1171943412yes—
461C2—522no—
462C2#1311745711yescharacteristic
463C2D13×#42811yescharacteristic
464C2#1312342311yescharacteristic
465C2#1312582611yescharacteristic
466C2#1312584211yescharacteristic
467C2#1312603511yescharacteristic
468C2#1312605111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1847C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1847D13
hypocenterC13#21988
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
4. #13115596C2semidirect
5. #13115591C2semidirect
8. #13115002C2semidirect
9. #13114970C2semidirect
10. #13114969C2semidirect
11. C13×#1847C2semidirect
35. #11718366C4semidirect
157. #1847D13semidirect
382. C13#21988semidirect

Maximal subgroups

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

subgroupindex
C2×#117183662
#131172422
#131172412
#131155962
#131155912
#131150342
#131150322
#131150022
#131149702
#131149692
C13×#18472
#2198813