Finite Group Databasebeta

← #15879714

Subgroups — #15879714

Order 3328.

1074 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719437C211yesmaximal, characteristic
2C2×#11718491C211yesmaximal, characteristic, complemented
3#13117791C211yesmaximal, characteristic, complemented
4#13115765C212yesmaximal
5#13115644C212yesmaximal
6#13115639C211yesmaximal, characteristic, complemented
7#13114849C212yesmaximal, complemented
8#13114837C211yesmaximal, characteristic
9#103×Dic13C212yesmaximal, complemented
10C4×#88049C211yesmaximal, characteristic
11C13×#1981C211yesmaximal, characteristic, complemented
12C2×C13×C4⋊Q8C2211yescharacteristic
13C2×#88201C2212yes—
14C2×Q8×Dic13C2212yes—
15#11719437—24no—
16#11719437C418yescomplemented
17C2×#88152—22no—
18C2×#88151—21no—
19C2×#88146—21no—
20C2×C4×D52C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×#103C2212yes—
24C2×C13×#103C2212yes—
25C4×C13×C4⋊C4C2211yescharacteristic
26C2×#88075C2212yes—
27C2×#88075C2212yes—
28C2×#88061C2212yes—
29C2×#88054C2212yes—
30C2×C8×Dic13C2212yes—
31#11718638C2212yes—
32C4⋊C4×Dic13C2212yes—
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35#11718596C2211yescharacteristic
36C4×C4⋊Dic13—21no—
37#11718590—21no—
38C2×C4×#1055C2211yescharacteristic
39#11718491—24no—
40#11718316—22no—
41#11718143C2212yes—
42#11718121C2211yescharacteristic
43#11718121C2211yescharacteristic
44C22×Q8×C13C2312yes—
45C22×D52C2311yescharacteristic
46C22×C4×D13—21no—
47C22×Dic26D411yescharacteristic
48C22×C8×C13C2312yes—
49C13×C4⋊Q8—22no—
50C13×C4⋊Q8C2×C414yes—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4C2311yescharacteristic
54C2×C13×C4⋊C4C2311yescharacteristic
55C2×C42×C13—21no—
56C2×C42×C13C2311yescharacteristic
57#88201—24no—
58#88201C2×C418yes—
59Q8×Dic13—24no—
60Q8×Dic13C2×C418yes—
61C2×#6103—21no—
62C2×#6103—22no—
63C2×#6103—22no—
64C2×C4⋊Dic13—22no—
65C2×C4⋊Dic13—21no—
66C2×C4⋊Dic13—21no—
67C2×C4⋊Dic13D411yescharacteristic
68C2×C4⋊Dic13C2312yes—
69C2×C4⋊Dic13C2311yescharacteristic
70C2×#6101D412yes—
71C2×C4×Dic13—22no—
72C2×C4×Dic13—22no—
73C2×C4×Dic13C2312yes—
74C22×#1055C2311yescharacteristic
75C22×#1055C2311yescharacteristic
76#88152—216no—
77#88151—28no—
78#88146—28no—
79C4×D52—22no—
80C4×D52C2×C414yes—
81C4×Dic26C2×C414yes—
82C4×Dic26D414yes—
83C13×C4⋊C8—22no—
84C13×#103—24no—
85C13×#103—42no—
86C13×#95—21no—
87#88075—24no—
88#88075—42no—
89#88071—22no—
90#88071—22no—
91#88071—22no—
92#88061—42no—
93#88054—24no—
94C8×Dic13—24no—
95#88049—22no—
96#88049—22no—
97C4×#1055—22no—
98#22541—131nomaximal, Sylow
99C23×D13—21no—
100C2×Q8×C13—22no—
101C2×Q8×C13—22no—
102C2×Q8×C13—22no—
103C2×Q8×C13—22no—
104C2×Q8×C13—22no—
105C2×Q8×C13C22×C414yes—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2411yescharacteristic
112C22×Dic13—21no—
113C22×Dic13—22no—
114C22×Dic13C2×D412yes—
115C22×Dic13C2×D412yes—
116C2×D52—21no—
117C2×D52—21no—
118C2×D52—21no—
119C2×D52—21no—
120C2×D52—21no—
121C2×D52C22×C412yes—
122C2×C4×D13—24no—
123C2×C4×D13—42no—
124C2×C4×D13—42no—
125C2×Dic26—22no—
126C2×Dic26—22no—
127C2×Dic26C22⋊C414yes—
128C2×C8×C13—22no—
129C2×C8×C13—22no—
130C2×C8×C13—22no—
131C13×C4⋊C4—24no—
132C13×C4⋊C4—24no—
133C13×C4⋊C4—21no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4#4112yes—
137C42×C13—42no—
138C42×C13C22×C412yes—
139C42×C13C2×D412yes—
140#6103—24no—
141#6103—28no—
142#6103—28no—
143C4⋊Dic13—21no—
144C4⋊Dic13—28no—
145C4⋊Dic13—22no—
146C4⋊Dic13—22no—
147C4⋊Dic13—42no—
148C4⋊Dic13—81no—
149C4⋊Dic13C22⋊C414yes—
150C4⋊Dic13C22×C412yes—
151#6101C22⋊C418yes—
152C4×Dic13—28no—
153C4×Dic13—82no—
154C4×Dic13C22×C414yes—
155C4×Dic13C2×D414yes—
156C2×#1055—21no—
157C2×#1055—21no—
158C2×#1055—21no—
159C2×#1055—21no—
160C2×#1055—21no—
161C2×#1055#4112yes—
162C2×#556—131no—
163C2×C8×Q8—131no—
164#2355—131no—
165#1983—132no—
166#1981D1311yescharacteristic, complemented
167#1958—132no—
168#1956—131no—
169#1805—132no—
170#1802—131no—
171C4×#103—132no—
172C4×#102—131no—
173C23×C13C22×D411yescharacteristic
174C22×D13—22no—
175C22×D13—41no—
176C22×D13—41no—
177C22×D13—41no—
178C22×D13—41no—
179C22×D13—41no—
180C22×D13—41no—
181Q8×C13—24no—
182Q8×C13—24no—
183Q8×C13—42no—
184Q8×C13—42no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—24no—
188C2×C4×C13—22no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13C2×C22⋊C412yes—
197C2×C4×C13C2×C22⋊C412yes—
198C2×C4×C13#13512yes—
199C2×C4×C13#13512yes—
200C2×C4×C13C23×C411yescharacteristic
201C2×C4×C13C22×D411yescharacteristic
202C2×C4×C13C2×#4111yescharacteristic
203C2×C4×C13C2×#4111yescharacteristic
204C2×C4×C13H(5,𝔽2)11yescharacteristic
205C2×C4×C132−1+411yescharacteristic
206C2×Dic13—22no—
207C2×Dic13—22no—
208C2×Dic13—22no—
209C2×Dic13—22no—
210C2×Dic13—22no—
211C2×Dic13—41no—
212C2×Dic13—41no—
213C2×Dic13—42no—
214C2×Dic13—42no—
215C2×Dic13—42no—
216C2×Dic13C2×C22⋊C414yes—
217C2×Dic13C2×C22⋊C414yes—
218D52—22no—
219D52—22no—
220D52—41no—
221D52—41no—
222C4×D13—48no—
223Dic26—28no—
224C8×C13—42no—
225#1055—22no—
226#1055—41no—
227#556—138no—
228#556—264no—
229C2×C4⋊Q8C2×D1311yescharacteristic
230C2×#126—262no—
231C2×#124—132no—
232C2×C22⋊Q8—261no—
233C2×C4×Q8—131no—
234C2×C4×Q8—132no—
235C2×C4×D4—131no—
236C2×#117—261no—
237C8×Q8—264no—
238C2×C4⋊C8—132no—
239C2×C4⋊C8C2×D1311yescharacteristic
240C2×#103—132no—
241C2×#103—132no—
242C2×#103C2×D1312yes—
243C2×#103C2×D1312yes—
244C2×#102—131no—
245C2×#102—131no—
246C2×#102—132no—
247C2×C4×C8—132no—
248C2×C4×C8—131no—
249#391—261no—
250#387—262no—
251#384—131no—
252#382—132no—
253C4×C4⋊C4—132no—
254C4×C4⋊C4—261no—
255C4×C4⋊C4C2×D1311yescharacteristic
256#340—132no—
257#340—131no—
258#340—131no—
259C22×C13C22×C22⋊C411yescharacteristic
260C22×C13#54811yescharacteristic
261C22×C13#55011yescharacteristic
262C22×C13C2×#13511yescharacteristic
263C22×C13C2×#13511yescharacteristic
264C22×C13#57711yescharacteristic
265C22×C13#57811yescharacteristic
266C2×D13—42no—
267C2×D13—42no—
268C2×D13—42no—
269C2×D13—81no—
270C2×D13—81no—
271C2×D13—81no—
272C2×D13—81no—
273C4×C13—22no—
274C4×C13—42no—
275C4×C13—44no—
276C4×C13—81no—
277C4×C13#41614yes—
278C4×C13C4×#4111yescharacteristic
279C4×C13#52011yescharacteristic
280C4×C13#54811yescharacteristic
281C4×C13#55011yescharacteristic
282Dic13—24no—
283Dic13—24no—
284Dic13—42no—
285Dic13—82no—
286C22×Q8—131no—
287C22×Q8C22×D1312yes—
288C22×D4—131no—
289C23×C4—261no—
290C22×C8—131no—
291C22×C8—131no—
292C22×C8C22×D1312yes—
293C4⋊Q8—22no—
294C4⋊Q8C4×D1314yes—
295#126—2616no—
296#124—138no—
297#124—264no—
298C22⋊Q8—268no—
299C4×Q8—134no—
300C4×Q8—134no—
301C4×Q8—138no—
302C4×Q8—264no—
303C4×D4—134no—
304C4×D4—262no—
305#117—268no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—131no—
309C2×C4⋊C4—132no—
310C2×C4⋊C4—131no—
311C2×C4⋊C4—132no—
312C2×C4⋊C4—262no—
313C2×C4⋊C4—261no—
314C2×C4⋊C4—261no—
315C2×C4⋊C4C22×D1311yescharacteristic
316C2×C4⋊C4C22×D1311yescharacteristic
317C2×C22⋊C4—262no—
318C2×C22⋊C4—262no—
319C2×C22⋊C4—261no—
320C2×C42—21no—
321C2×C42—132no—
322C2×C42—262no—
323C2×C42—262no—
324C2×C42C22×D1311yescharacteristic
325C4⋊C8—22no—
326C4⋊C8—264no—
327#103—24no—
328#103—42no—
329#103—264no—
330#103—522no—
331#102—262no—
332#102—262no—
333#102—522no—
334C4×C8—264no—
335C4×C8—262no—
336#95—21no—
337#95—262no—
338#95—262no—
339#95—262no—
340C2×C13#234111yescharacteristic
341C2×C13C2×#41611yescharacteristic
342C2×C13#289811yescharacteristic
343C2×C13#336011yescharacteristic
344C2×C13#336411yescharacteristic
345C2×C13#339311yescharacteristic
346C2×C13#339411yescharacteristic
347D13—82no—
348C24—261no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—134no—
355C2×Q8—262no—
356C2×Q8—262no—
357C2×Q8C2×C4×D1314yes—
358C2×D4—132no—
359C2×D4—261no—
360C2×D4—261no—
361C2×D4—261no—
362C2×D4—261no—
363C2×D4—261no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—132no—
368C22×C4—132no—
369C22×C4—261no—
370C22×C4—264no—
371C22×C4—262no—
372C22×C4—522no—
373C22×C4—522no—
374C22×C4D4×D1311yescharacteristic
375C22×C4D4×D1311yescharacteristic
376C22×C4C23×D1311yescharacteristic
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—132no—
381C2×C8—261no—
382C2×C8—261no—
383C2×C8—261no—
384C2×C8—261no—
385C2×C8—261no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—134no—
392C4⋊C4—138no—
393C4⋊C4—132no—
394C4⋊C4—268no—
395C4⋊C4—261no—
396C4⋊C4—262no—
397C4⋊C4—262no—
398C4⋊C4—522no—
399C4⋊C4—1041no—
400C4⋊C4#612912yes—
401C22⋊C4—268no—
402C22⋊C4—268no—
403C22⋊C4—264no—
404C42—42no—
405C42—134no—
406C42—134no—
407C42—268no—
408C42—1042no—
409C42C2×C4×D1312yes—
410C42D4×D1312yes—
411C13#2254111yescharacteristic, complemented, Sylow
412C23—262no—
413C23—521no—
414C23—521no—
415C23—521no—
416C23—521no—
417C23—521no—
418C23—521no—
419C23C2×D4×D1311yescharacteristic
420Q8—24no—
421Q8—24no—
422Q8—42no—
423Q8—42no—
424Q8—268no—
425D4—262no—
426D4—262no—
427D4—521no—
428D4—521no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—134no—
441C2×C4—134no—
442C2×C4—262no—
443C2×C4—262no—
444C2×C4—262no—
445C2×C4—262no—
446C2×C4—262no—
447C2×C4—521no—
448C2×C4—521no—
449C2×C4—528no—
450C2×C4—522no—
451C2×C4—522no—
452C2×C4—522no—
453C2×C4C22⋊C4×D1312yes—
454C2×C4C22⋊C4×D1312yes—
455C2×C4#8817012yes—
456C2×C4#8817312yes—
457C2×C4C22×C4×D1311yescharacteristic
458C2×C4C2×D4×D1311yescharacteristic
459C2×C4C2×#612911yescharacteristic
460C2×C4#8825111yescharacteristic
461C2×C4#41×D1311yescharacteristic
462C2×C4#8825711yescharacteristic
463C8—42no—
464C8—262no—
465C8—521no—
466C22—522no—
467C22—522no—
468C22—522no—
469C22—1041no—
470C22—1041no—
471C22—1041no—
472C22—1041no—
473C22C2×C22⋊C4×D1311yescharacteristic
474C22#1171930311yescharacteristic
475C22#1171930411yescharacteristic
476C22C2×#8817011yescharacteristic
477C22C2×#8817311yescharacteristic
478C22#1171948311yescharacteristic
479C22#1171948411yescharacteristic
480C4—22no—
481C4—42no—
482C4—44no—
483C4—81no—
484C4—264no—
485C4—264no—
486C4—522no—
487C4—1042no—
488C4#1171846514yes—
489C4C4×#612911yescharacteristic
490C4#1171925111yescharacteristic
491C4#1171938211yescharacteristic
492C4#1171942311yescharacteristic
493C2—1042no—
494C2#1311767511yescharacteristic
495C2C2×#1171846511yescharacteristic
496C2#1312336811yescharacteristic
497C2#1312748911yescharacteristic
498C2#1312752511yescharacteristic
499C2#1312782311yescharacteristic
500C2#1312783111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1981C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1981D13
hypocenterC13#22541
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
2. C2×#11718491C2semidirect
3. #13117791C2semidirect
6. #13115639C2semidirect
7. #13114849C2semidirect
9. #103×Dic13C2semidirect
11. C13×#1981C2semidirect
16. #11719437C4semidirect
166. #1981D13semidirect
411. C13#22541semidirect

Maximal subgroups

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

subgroupindex
C2×#117194372
C2×#117184912
#131177912
#131157652
#131156442
#131156392
#131148492
#131148372
#103×Dic132
C4×#880492
C13×#19812
#2254113