Finite Group Databasebeta

← #15873484

Subgroups — #15873484

Order 3328.

902 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
1C2×#11718366C211yesmaximal, characteristic
2D13×#384C211yesmaximal, characteristic
3#13117229C211yesmaximal, characteristic
4#13115598C212yesmaximal, complemented
5#13115593C212yesmaximal, complemented
6#13115030C212yesmaximal
7#13115025C212yesmaximal
8#13115004C211yesmaximal, characteristic, complemented
9#13115002C211yesmaximal, characteristic, complemented
10#13114969C211yesmaximal, characteristic, complemented
11C13×#1836C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×D13—21no—
13C2×C4⋊C4×D13—21no—
14C2×C4⋊C4×D13C2212yes—
15C2×C42×D13C2211yescharacteristic
16C2×C13×#97C2211yescharacteristic
17C13×#384C2211yescharacteristic
18C13×#382C2211yescharacteristic
19C2×#88060C2212yes—
20C2×#88058C2212yes—
21C2×#88057C2212yes—
22C2×#88054C2212yes—
23#11718648C2211yescharacteristic
24#11718648C2211yescharacteristic
25#11718637—21no—
26#11718637—21no—
27#11718637C2212yes—
28C4⋊C4×Dic13C2211yescharacteristic
29C4⋊C4×Dic13C2211yescharacteristic
30C2×#88048C2212yes—
31C2×#88047C2212yes—
32#11718597C2211yescharacteristic
33#11718596C2211yescharacteristic
34C2×#88043C2211yescharacteristic
35#11718366C418yescomplemented
36#11718327—21no—
37#11718325—21no—
38#11718312—21no—
39#11718309—21no—
40C13×#340C2212yes—
41C13×#340C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C22×C4×D13—22no—
45C22×C4×D13D411yescharacteristic
46C22×C4×D13D411yescharacteristic
47C22×C4×D13C2311yescharacteristic
48C22×C8×C13C2312yes—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4C2311yescharacteristic
52C2×C13×C4⋊C4C2311yescharacteristic
53C2×C13×C4⋊C4C2312yes—
54C2×C42×C13C2311yescharacteristic
55C2×#6103—21no—
56C2×#6103—21no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13C2312yes—
60C2×C4⋊Dic13C2311yescharacteristic
61C2×C4⋊Dic13C2311yescharacteristic
62C2×#6101—22no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×C4×Dic13—21no—
66C2×C4×Dic13—21no—
67C2×C4×Dic13D411yescharacteristic
68C2×C4×Dic13D411yescharacteristic
69C2×C4×Dic13C2311yescharacteristic
70C22×#1055C2312yes—
71C4⋊C4×D13—42no—
72C4⋊C4×D13—42no—
73C4⋊C4×D13—44no—
74C4⋊C4×D13—44no—
75C42×D13C2×C414yes—
76C42×D13Q814yes—
77C13×#97C2×C414yescomplemented
78C13×#95—21no—
79C13×#95—21no—
80#88071—21no—
81#88071—21no—
82#88071—21no—
83#88071—21no—
84#88071—21no—
85#88071—21no—
86#88060C2×C418yes—
87#88058—42no—
88#88057—42no—
89#88054C2×C418yescomplemented
90#88048—42no—
91#88047—42no—
92#88043C2×C414yescomplemented
93#21987—131nomaximal, Sylow
94C23×D13C2×D411yescharacteristic
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—22no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2411yescharacteristic
101C22×Dic13—21no—
102C22×Dic13—21no—
103C22×Dic13—22no—
104C22×Dic13C2×D411yescharacteristic
105C22×Dic13C2×D411yescharacteristic
106C22×Dic13C2×D411yescharacteristic
107C2×C4×D13—22no—
108C2×C4×D13—22no—
109C2×C4×D13—22no—
110C2×C4×D13—22no—
111C2×C4×D13—22no—
112C2×C4×D13—22no—
113C2×C4×D13—44no—
114C2×C4×D13—44no—
115C2×C4×D13—44no—
116C2×C4×D13C4⋊C414yes—
117C2×C4×D13C4⋊C414yes—
118C2×C4×D13C22×C412yes—
119C2×C4×D13C2×Q812yes—
120C2×C8×C13—22no—
121C2×C8×C13—22no—
122C2×C8×C13C22×C414yes—
123C13×C4⋊C4—22no—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—42no—
128C13×C4⋊C4—42no—
129C42×C13C22×C412yes—
130C42×C13C2×Q812yes—
131#6103—42no—
132#6103—42no—
133C4⋊Dic13—22no—
134C4⋊Dic13—22no—
135C4⋊Dic13—22no—
136C4⋊Dic13—22no—
137C4⋊Dic13—42no—
138C4⋊Dic13—42no—
139#6101—44no—
140#6101—44no—
141#6101—44no—
142C4×Dic13—42no—
143C4×Dic13—42no—
144C4×Dic13C4⋊C414yes—
145C4×Dic13C4⋊C414yes—
146C4×Dic13C22×C412yes—
147C4×Dic13C2×Q812yes—
148C2×#1055—22no—
149C2×#1055—22no—
150C2×#1055C22×C414yes—
151C2×#432—131no—
152C2×#384—131no—
153#2283—131no—
154#1948—132no—
155#1947—132no—
156#1853—132no—
157#1852—132no—
158#1847—131no—
159#1847—131no—
160#1836—131no—
161#1836D1311yescharacteristic, complemented
162C23×C13C22×D411yescharacteristic
163C22×D13—21no—
164C22×D13—21no—
165C22×D13—21no—
166C22×D13—21no—
167C22×D13C2×C4⋊C412yes—
168C22×D13AGL(1,ℤ/8)12yes—
169C22×D13#13712yes—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—42no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—42no—
179C2×C4×C13—42no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13C2×C4⋊C412yes—
184C2×C4×C13C2×C4⋊C412yes—
185C2×C4×C13C23×C411yescharacteristic
186C2×C4×C13C22×Q811yescharacteristic
187C2×C4×C13H(5,𝔽2)12yes—
188C2×C4×C132−1+412yes—
189C2×Dic13—21no—
190C2×Dic13—21no—
191C2×Dic13—21no—
192C2×Dic13—21no—
193C2×Dic13—42no—
194C2×Dic13—41no—
195C2×Dic13—41no—
196C2×Dic13—41no—
197C2×Dic13—42no—
198C2×Dic13—42no—
199C2×Dic13—41no—
200C2×Dic13—41no—
201C2×Dic13—41no—
202C2×Dic13C2×C4⋊C412yes—
203C2×Dic13C2×C4⋊C412yes—
204C2×Dic13C2×C4⋊C412yes—
205C2×Dic13AGL(1,ℤ/8)12yes—
206C2×Dic13#13712yes—
207C4×D13—28no—
208C4×D13—24no—
209C4×D13—24no—
210C4×D13—28no—
211C4×D13—88no—
212C8×C13—24no—
213#1055—24no—
214C22×C4⋊C4—132no—
215C22×C4⋊C4—261no—
216C22×C4⋊C4—261no—
217C22×C42—131no—
218#432—138no—
219C2×#107—132no—
220C2×#107—132no—
221C2×#106—132no—
222C2×#106—132no—
223C2×C4⋊C8—132no—
224C2×C22⋊C8—132no—
225C2×#97—131no—
226C2×#97C2×D1311yescharacteristic
227#384—132no—
228#384—131no—
229#384—261no—
230#384—261no—
231#384C2×D1311yescharacteristic
232#383—261no—
233#382—131no—
234#382C2×D1311yescharacteristic
235#381—261no—
236#380—131no—
237#380—131no—
238C4×C4⋊C4—131no—
239C4×C4⋊C4—131no—
240C4×C22⋊C4—261no—
241#376—261no—
242#340—132no—
243#340—132no—
244#340C2×D1312yes—
245#340C2×D1312yes—
246C22×C13C22×C4⋊C411yescharacteristic
247C22×C13#53511yescharacteristic
248C22×C13#53611yescharacteristic
249C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
250C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C13C2×#13711yescharacteristic
252C22×C13C2×#13711yescharacteristic
253C2×D13—22no—
254C2×D13—22no—
255C2×D13—22no—
256C2×D13—22no—
257C2×D13—22no—
258C2×D13—22no—
259C2×D13#42814yes—
260C4×C13—22no—
261C4×C13—22no—
262C4×C13—82no—
263C4×C13—81no—
264C4×C13—81no—
265C4×C13#52012yes—
266C4×C13#54412yes—
267Dic13—22no—
268Dic13—22no—
269Dic13—82no—
270Dic13—81no—
271Dic13—81no—
272Dic13#42814yes—
273C23×C4—131no—
274C23×C4—131no—
275C23×C4—131no—
276C23×C4—262no—
277C22×C8—132no—
278C22×C8C22×D1312yes—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—132no—
282C2×C4⋊C4—131no—
283C2×C4⋊C4—131no—
284C2×C4⋊C4—262no—
285C2×C4⋊C4—262no—
286C2×C4⋊C4—262no—
287C2×C4⋊C4—261no—
288C2×C4⋊C4—261no—
289C2×C4⋊C4—522no—
290C2×C4⋊C4—522no—
291C2×C4⋊C4—524no—
292C2×C4⋊C4—524no—
293C2×C4⋊C4C22×D1312yes—
294C2×C4⋊C4C22×D1311yescharacteristic
295C2×C4⋊C4C22×D1311yescharacteristic
296C2×C22⋊C4—261no—
297C2×C22⋊C4—261no—
298C2×C42—131no—
299C2×C42—131no—
300C2×C42—131no—
301C2×C42—134no—
302C2×C42—134no—
303C2×C42—261no—
304C2×C42—261no—
305C2×C42C22×D1311yescharacteristic
306#107—522no—
307#107—522no—
308#106—522no—
309#106—522no—
310C4⋊C8—138no—
311C22⋊C8—138no—
312#97—134no—
313#97C4×D1314yescomplemented
314#95—21no—
315#95—21no—
316#95—261no—
317#95—261no—
318#95—261no—
319#95—261no—
320#95—261no—
321#95—261no—
322C2×C13#231711yescharacteristic
323C2×C13C2×#42811yescharacteristic
324C2×C13C2×#42811yescharacteristic
325C2×C13#321711yescharacteristic
326C2×C13#321811yescharacteristic
327C2×C13#323811yescharacteristic
328C2×C13#323911yescharacteristic
329D13—24no—
330C24—131no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—131no—
335C22×C4—131no—
336C22×C4—131no—
337C22×C4—134no—
338C22×C4—134no—
339C22×C4—132no—
340C22×C4—132no—
341C22×C4—262no—
342C22×C4—262no—
343C22×C4—262no—
344C22×C4—262no—
345C22×C4—262no—
346C22×C4—262no—
347C22×C4—261no—
348C22×C4—261no—
349C22×C4—262no—
350C22×C4—524no—
351C22×C4—524no—
352C22×C4—524no—
353C22×C4D4×D1311yescharacteristic
354C22×C4D4×D1311yescharacteristic
355C22×C4C23×D1311yescharacteristic
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—134no—
359C2×C8—262no—
360C2×C8—262no—
361C2×C8C2×C4×D1314yes—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—262no—
369C4⋊C4—262no—
370C4⋊C4—262no—
371C4⋊C4—262no—
372C4⋊C4—522no—
373C4⋊C4—522no—
374C4⋊C4—524no—
375C4⋊C4—524no—
376C4⋊C4—524no—
377C22⋊C4—522no—
378C22⋊C4—522no—
379C42—134no—
380C42—134no—
381C42—132no—
382C42—132no—
383C42—522no—
384C42—522no—
385C42C2×C4×D1312yes—
386C42Q8×D1312yes—
387C13#2198711yescharacteristic, complemented, Sylow
388C23—132no—
389C23—132no—
390C23—132no—
391C23—261no—
392C23—261no—
393C23—261no—
394C23—261no—
395C23C2×D4×D1311yescharacteristic
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—132no—
410C2×C4—132no—
411C2×C4—132no—
412C2×C4—132no—
413C2×C4—132no—
414C2×C4—268no—
415C2×C4—268no—
416C2×C4—261no—
417C2×C4—261no—
418C2×C4—261no—
419C2×C4—261no—
420C2×C4—264no—
421C2×C4—264no—
422C2×C4—521no—
423C2×C4—521no—
424C2×C4—522no—
425C2×C4—522no—
426C2×C4—521no—
427C2×C4—521no—
428C2×C4—522no—
429C2×C4—521no—
430C2×C4—521no—
431C2×C4—1048no—
432C2×C4C4⋊C4×D1312yes—
433C2×C4C4⋊C4×D1312yes—
434C2×C4C22×C4×D1311yescharacteristic
435C2×C4C2×Q8×D1311yescharacteristic
436C2×C4#8825612yes—
437C2×C4#8825712yes—
438C8—24no—
439C8—264no—
440C22—134no—
441C22—262no—
442C22—262no—
443C22—262no—
444C22—262no—
445C22—262no—
446C22—262no—
447C22C2×C4⋊C4×D1311yescharacteristic
448C22#1171937911yescharacteristic
449C22#1171938011yescharacteristic
450C22D13×AGL(1,ℤ/8)11yescharacteristic
451C22D13×AGL(1,ℤ/8)11yescharacteristic
452C22D13×#13711yescharacteristic
453C22D13×#13711yescharacteristic
454C4—22no—
455C4—22no—
456C4—81no—
457C4—81no—
458C4—82no—
459C4—134no—
460C4—262no—
461C4—262no—
462C4—1041no—
463C4—1042no—
464C4—1041no—
465C4#1171922812yes—
466C4#1171939412yes—
467C2—264no—
468C2#1311746111yescharacteristic
469C2D13×#42811yescharacteristic
470C2D13×#42811yescharacteristic
471C2#1312585511yescharacteristic
472C2#1312586411yescharacteristic
473C2#1312605311yescharacteristic
474C2#1312606211yescharacteristic
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#21987
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. #13115598C2semidirect
5. #13115593C2semidirect
8. #13115004C2semidirect
9. #13115002C2semidirect
10. #13114969C2semidirect
11. C13×#1836C2semidirect
35. #11718366C4semidirect
77. C13×#97C2×C4semidirect
89. #88054C2×C4semidirect
92. #88043C2×C4semidirect
161. #1836D13semidirect
313. #97C4×D13semidirect
387. C13#21987semidirect

Maximal subgroups

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

subgroupindex
C2×#117183662
D13×#3842
#131172292
#131155982
#131155932
#131150302
#131150252
#131150042
#131150022
#131149692
C13×#18362
#2198713