Finite Group Databasebeta

← #15863472

Subgroups — #15863472

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718368C211yesmaximal, characteristic
2#13117241C211yesmaximal, characteristic
3#13117229C211yesmaximal, characteristic
4#13115005C211yesmaximal, characteristic, complemented
5#13115002C211yesmaximal, characteristic, complemented
6#13114970C211yesmaximal, characteristic, complemented
7#13114868C212yesmaximal
8#13114868C212yesmaximal
9#13114728C212yesmaximal, complemented
10#13114724C212yesmaximal, complemented
11C13×#1836C211yesmaximal, characteristic, complemented
12C22×#6094C2212yes—
13C2×#88146—21no—
14C2×C42×D13C2211yescharacteristic
15C2×C13×#97C2211yescharacteristic
16C13×#384C2211yescharacteristic
17C13×#382C2211yescharacteristic
18C2×C8×Dic13C2212yes—
19#11718648—21no—
20#11718648C2211yescharacteristic
21#11718648C2211yescharacteristic
22#11718648C2212yes—
23#11718638—21no—
24C4⋊C4×Dic13—21no—
25C4⋊C4×Dic13C2211yescharacteristic
26C4⋊C4×Dic13C2211yescharacteristic
27C4⋊C4×Dic13C2212yes—
28C2×#88048C2212yes—
29C2×#88048C2212yes—
30C2×#88047C2212yes—
31C2×#88047C2212yes—
32#11718597C2211yescharacteristic
33#11718596C2211yescharacteristic
34C2×#88043C2211yescharacteristic
35#11718368C418yescomplemented
36#11718327—21no—
37#11718325—21no—
38#11718312—21no—
39#11718309—21no—
40C13×#340C2212yes—
41C13×#340C2212yes—
42#11718143C2212yes—
43#11718143C2212yes—
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⋊Dic13C2312yes—
60C2×C4⋊Dic13C2311yescharacteristic
61C2×C4⋊Dic13C2311yescharacteristic
62C2×C4×Dic13—22no—
63C2×C4×Dic13—21no—
64C2×C4×Dic13—21no—
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13C2311yescharacteristic
68C22×#1055C2312yes—
69C2×#6094—24no—
70C2×#6094—24no—
71C2×#6094C2×C418yes—
72#88146—44no—
73C42×D13C2×C414yes—
74C42×D13Q814yes—
75C13×#97C2×C414yes—
76C13×#95—21no—
77C13×#95—21no—
78#88071—21no—
79#88071—21no—
80#88071—21no—
81#88071—21no—
82#88071—21no—
83#88071—21no—
84#88071—22no—
85#88071—22no—
86C8×Dic13C2×C418yes—
87#88048—24no—
88#88048—24no—
89#88047—24no—
90#88047—24no—
91#88043C2×C414yes—
92#20819—131nomaximal, Sylow
93C23×D13C2×D411yescharacteristic
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
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—44no—
128#6103—42no—
129#6103—42no—
130C4⋊Dic13—22no—
131C4⋊Dic13—22no—
132C4⋊Dic13—22no—
133C4⋊Dic13—22no—
134C4⋊Dic13—42no—
135C4⋊Dic13—42no—
136C4×Dic13—44no—
137C4×Dic13—42no—
138C4×Dic13—42no—
139C4×Dic13C4⋊C414yes—
140C4×Dic13C4⋊C414yes—
141C4×Dic13C22×C412yes—
142C4×Dic13C2×Q812yes—
143C2×#1055C22×C414yes—
144C2×#1055#4114yes—
145C2×#1055#4114yes—
146#6094—216no—
147C2×C4×M16—131no—
148#2285—131no—
149#2283—131no—
150#1847—131no—
151#1847—131no—
152#1836—131no—
153#1836D1311yescharacteristic, complemented
154#1809—132no—
155#1809—132no—
156C4×#107—132no—
157C4×#106—132no—
158C23×C13C22×D411yescharacteristic
159C22×D13—21no—
160C22×D13—21no—
161C22×D13—21no—
162C22×D13—21no—
163C22×D13—21no—
164C22×D13—21no—
165C22×D13C2×C4⋊C412yes—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—41no—
171C2×C4×C13—42no—
172C2×C4×C13—41no—
173C2×C4×C13—42no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—42no—
179C2×C4×C13C2×C4⋊C412yes—
180C2×C4×C13C2×C4⋊C412yes—
181C2×C4×C13C23×C411yescharacteristic
182C2×C4×C13C22×Q811yescharacteristic
183C2×C4×C13C2×#4112yes—
184C2×C4×C13C2×#4112yes—
185C2×Dic13—21no—
186C2×Dic13—21no—
187C2×Dic13—21no—
188C2×Dic13—21no—
189C2×Dic13—41no—
190C2×Dic13—42no—
191C2×Dic13—41no—
192C2×Dic13—42no—
193C2×Dic13—41no—
194C2×Dic13—41no—
195C2×Dic13—42no—
196C2×Dic13—41no—
197C2×Dic13—41no—
198C2×Dic13C2×C4⋊C412yes—
199C2×Dic13C2×C4⋊C412yes—
200C2×Dic13C2×C4⋊C412yes—
201C2×Dic13AGL(1,ℤ/8)12yes—
202C2×Dic13#13712yes—
203C4×D13—24no—
204C4×D13—24no—
205C4×D13—28no—
206C4×D13—44no—
207C8×C13—24no—
208#1055#11718yescomplemented
209C22×M16—132no—
210C2×#117—261no—
211C22×C42—131no—
212C2×#107—132no—
213C2×#107—132no—
214C2×#106—132no—
215C2×#106—132no—
216C4×M16—138no—
217C2×#97—131no—
218C2×#97C2×D1311yescharacteristic
219C2×C4×C8—132no—
220#384—131no—
221#384C2×D1311yescharacteristic
222#383—261no—
223#382—131no—
224#382—261no—
225#382C2×D1311yescharacteristic
226#381—261no—
227#380—131no—
228#380—131no—
229#380—132no—
230#380—261no—
231C4×C4⋊C4—131no—
232C4×C4⋊C4—131no—
233C4×C4⋊C4—132no—
234C4×C4⋊C4—261no—
235C4×C22⋊C4—261no—
236#376—261no—
237#340—132no—
238#340—132no—
239#340C2×D1312yes—
240#340C2×D1312yes—
241C22×C13C22×C4⋊C411yescharacteristic
242C22×C13#53211yescharacteristic
243C22×C13#53211yescharacteristic
244C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
245C22×C13C2×#13711yescharacteristic
246C22×C13#57511yescharacteristic
247C22×C13#57511yescharacteristic
248C2×D13—22no—
249C2×D13—22no—
250C2×D13—22no—
251C2×D13—41no—
252C2×D13—41no—
253C2×D13—41no—
254C2×D13—41no—
255C4×C13—22no—
256C4×C13—22no—
257C4×C13—82no—
258C4×C13—81no—
259C4×C13—81no—
260C4×C13C2×#11712yes—
261C4×C13#53312yes—
262Dic13—22no—
263Dic13—22no—
264Dic13—81no—
265Dic13—82no—
266Dic13—81no—
267Dic13#42814yes—
268C23×C4—131no—
269C23×C4—131no—
270C23×C4—131no—
271C2×M16—138no—
272C2×M16—264no—
273C2×M16—264no—
274C22×C8—132no—
275C22×C8C22×D1312yes—
276#117—524no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—131no—
280C2×C4⋊C4—131no—
281C2×C4⋊C4—132no—
282C2×C4⋊C4—261no—
283C2×C4⋊C4—261no—
284C2×C4⋊C4C22×D1311yescharacteristic
285C2×C4⋊C4C22×D1311yescharacteristic
286C2×C4⋊C4C22×D1312yes—
287C2×C22⋊C4—262no—
288C2×C22⋊C4—261no—
289C2×C22⋊C4—261no—
290C2×C42—131no—
291C2×C42—131no—
292C2×C42—131no—
293C2×C42—134no—
294C2×C42—134no—
295C2×C42—262no—
296C2×C42—261no—
297C2×C42—261no—
298C2×C42C22×D1311yescharacteristic
299#107—264no—
300#107—264no—
301#106—264no—
302#106—264no—
303#97—134no—
304#97C4×D1314yes—
305C4×C8—138no—
306#95—21no—
307#95—21no—
308#95—261no—
309#95—261no—
310#95—262no—
311#95—261no—
312#95—261no—
313#95—262no—
314#95—261no—
315#95—261no—
316C2×C13#228511yescharacteristic
317C2×C13C2×#42811yescharacteristic
318C2×C13#291111yescharacteristic
319C2×C13#317111yescharacteristic
320C2×C13#317111yescharacteristic
321C2×C13#317211yescharacteristic
322C2×C13#317211yescharacteristic
323D13—42no—
324C24—131no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—131no—
329C22×C4—131no—
330C22×C4—131no—
331C22×C4—134no—
332C22×C4—132no—
333C22×C4—132no—
334C22×C4—134no—
335C22×C4—262no—
336C22×C4—262no—
337C22×C4—262no—
338C22×C4—262no—
339C22×C4—261no—
340C22×C4—261no—
341C22×C4—262no—
342C22×C4—521no—
343C22×C4—521no—
344C22×C4D4×D1311yescharacteristic
345C22×C4D4×D1311yescharacteristic
346C22×C4C23×D1311yescharacteristic
347M16—2616no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—134no—
351C2×C8—134no—
352C2×C8—134no—
353C2×C8C2×C4×D1314yes—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—42no—
359C4⋊C4—42no—
360C4⋊C4—262no—
361C4⋊C4—262no—
362C4⋊C4—262no—
363C4⋊C4—262no—
364C4⋊C4—522no—
365C4⋊C4—522no—
366C22⋊C4—524no—
367C22⋊C4—522no—
368C22⋊C4—522no—
369C42—134no—
370C42—134no—
371C42—132no—
372C42—132no—
373C42—524no—
374C42—522no—
375C42—522no—
376C42C2×C4×D1312yes—
377C42Q8×D1312yes—
378C13#2081911yescharacteristic, complemented, Sylow
379C23—132no—
380C23—261no—
381C23—261no—
382C23—261no—
383C23—261no—
384C23—261no—
385C23—261no—
386C23C2×D4×D1311yescharacteristic
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—132no—
401C2×C4—132no—
402C2×C4—132no—
403C2×C4—132no—
404C2×C4—132no—
405C2×C4—268no—
406C2×C4—261no—
407C2×C4—261no—
408C2×C4—261no—
409C2×C4—261no—
410C2×C4—264no—
411C2×C4—264no—
412C2×C4—524no—
413C2×C4—522no—
414C2×C4—521no—
415C2×C4—521no—
416C2×C4—521no—
417C2×C4—521no—
418C2×C4—522no—
419C2×C4—521no—
420C2×C4—522no—
421C2×C4—521no—
422C2×C4C4⋊C4×D1312yes—
423C2×C4C4⋊C4×D1312yes—
424C2×C4C22×C4×D1311yescharacteristic
425C2×C4C2×Q8×D1311yescharacteristic
426C2×C4#41×D1312yes—
427C2×C4#41×D1312yes—
428C8—24no—
429C8—138no—
430C22—262no—
431C22—262no—
432C22—262no—
433C22—521no—
434C22—521no—
435C22—521no—
436C22—521no—
437C22C2×C4⋊C4×D1311yescharacteristic
438C22#1171937311yescharacteristic
439C22#1171937311yescharacteristic
440C22D13×AGL(1,ℤ/8)11yescharacteristic
441C22#1171947811yescharacteristic
442C22D13×#13711yescharacteristic
443C22#1171948211yescharacteristic
444C4—22no—
445C4—22no—
446C4—82no—
447C4—81no—
448C4—81no—
449C4—134no—
450C4—262no—
451C4—262no—
452C4—1041no—
453C4—1042no—
454C4—1041no—
455C4D13×#11712yes—
456C4#1171939312yes—
457C2—522no—
458C2#1311724211yescharacteristic
459C2D13×#42811yescharacteristic
460C2#1312342311yescharacteristic
461C2#1312543011yescharacteristic
462C2#1312543411yescharacteristic
463C2#1312544111yescharacteristic
464C2#1312544511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1836C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1836D13
hypocenterC13#20819
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
4. #13115005C2semidirect
5. #13115002C2semidirect
6. #13114970C2semidirect
9. #13114728C2semidirect
10. #13114724C2semidirect
11. C13×#1836C2semidirect
35. #11718368C4semidirect
153. #1836D13semidirect
208. #1055#117semidirect
378. C13#20819semidirect

Maximal subgroups

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

subgroupindex
C2×#117183682
#131172412
#131172292
#131150052
#131150022
#131149702
#131148682
#131147282
#131147242
C13×#18362
#2081913