Finite Group Databasebeta

← #15901304

Subgroups — #15901304

Order 3328.

986 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718632C211yesmaximal, characteristic
2#13118476C211yesmaximal, characteristic
3#13117705C211yesmaximal, characteristic
4#13116213C212yesmaximal, complemented
5#13116081C212yesmaximal, complemented
6#13115757C212yesmaximal, complemented
7#13115473C212yesmaximal, complemented
8#13115259C211yesmaximal, characteristic
9#13115014C211yesmaximal, characteristic
10#13114771C211yesmaximal, characteristic
11C22×C13×#103C211yesmaximal, characteristic
12C23×Q8×C13C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C2×#88198C2212yes—
16C2×#88180—21no—
17C2×#88178C2211yescharacteristic
18C2×C13×#103—24no—
19C2×C13×#103C2212yes—
20C2×C13×#103C2212yes—
21#11718891C2212yes—
22#11718890—22no—
23C2×#88075C2212yes—
24C2×#88075C2212yes—
25#11718873C2211yescharacteristic
26#11718872—21no—
27#11718871—21no—
28#11718871—21no—
29C4×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×#88056C2212yes—
32C2×#88054C2212yes—
33#11718646C2212yes—
34#11718642—22no—
35C4⋊C4×Dic13C2212yes—
36#11718632—24no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41#11718143C2212yes—
42#11718142C2212yes—
43C22×Q8×C13—21no—
44C22×Q8×C13—24no—
45C22×Q8×C13—22no—
46C22×Q8×C13—22no—
47C22×Q8×C13—42no—
48C22×Q8×C13C2312yes—
49C23×C4×C13—21no—
50C23×C4×C13—21no—
51C23×C4×C13C2311yescharacteristic
52C22×Dic26C2311yescharacteristic
53C22×C8×C13—22no—
54C22×C8×C13—42no—
55C22×C8×C13C2312yes—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4D414yes—
59C2×C13×C4⋊C4C2311yescharacteristic
60C2×C13×C4⋊C4C2311yescharacteristic
61C2×C22⋊Dic13—21no—
62C2×C22⋊Dic13—21no—
63C2×C22⋊Dic13D411yescharacteristic
64C2×C22⋊Dic13D411yescharacteristic
65#88198—24no—
66#88198—42no—
67#88180—44no—
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13C2311yescharacteristic
70C2×C4⋊Dic13C2312yes—
71#88178—22no—
72#88178—22no—
73C2×#6101—21no—
74C2×#6101—22no—
75C2×#6101—22no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13C2312yes—
78C22×#1055C2311yescharacteristic
79C22×#1055C2311yescharacteristic
80C13×#103—24no—
81C13×#103—24no—
82#88075—24no—
83#88075—42no—
84#88071—21no—
85#88071—22no—
86#88071—22no—
87#88071—22no—
88#88071—22no—
89#88071D412yes—
90C22⋊#1055—22no—
91#88056—42no—
92#88054—42no—
93#88050—22no—
94#88050—22no—
95#88048—22no—
96#88048—22no—
97#24480—131nomaximal, Sylow
98C24×C13C2×D411yescharacteristic
99C2×Q8×C13—22no—
100C2×Q8×C13—28no—
101C2×Q8×C13—22no—
102C2×Q8×C13—22no—
103C2×Q8×C13—22no—
104C2×Q8×C13—22no—
105C2×Q8×C13—44no—
106C2×Q8×C13—48no—
107C2×Q8×C13—44no—
108C2×Q8×C13—42no—
109C2×Q8×C13#4114yes—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—24no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—21no—
116C22×C4×C13—44no—
117C22×C4×C13—42no—
118C22×C4×C13—42no—
119C22×C4×C13—42no—
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13C2×D412yes—
122C22×C4×C13#4112yes—
123C22×C4×C13C2411yescharacteristic
124C22×Dic13—21no—
125C22×Dic13—22no—
126C22×Dic13—21no—
127C22×Dic13C2×D412yes—
128C22×Dic13C2×D412yes—
129C2×Dic26—21no—
130C2×Dic26—21no—
131C2×Dic26—22no—
132C2×Dic26—22no—
133C2×C8×C13—22no—
134C2×C8×C13—22no—
135C2×C8×C13—22no—
136C2×C8×C13—44no—
137C13×C4⋊C4—24no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4C2×D412yes—
141C13×C4⋊C4C2×D412yes—
142C22⋊Dic13—22no—
143C22⋊Dic13—42no—
144C22⋊Dic13—42no—
145C22⋊Dic13SD1614yes—
146C4⋊Dic13—21no—
147C4⋊Dic13—22no—
148C4⋊Dic13—21no—
149C4⋊Dic13—22no—
150C4⋊Dic13—44no—
151#6101—44no—
152#6101—44no—
153#6101—42no—
154C4×Dic13—22no—
155C4×Dic13—22no—
156C4×Dic13—44no—
157C2×#1055—21no—
158C2×#1055—21no—
159C2×#1055—22no—
160C2×#1055—22no—
161C2×#483—131no—
162C22×#103D1311yescharacteristic
163#2434—131no—
164#2344—131no—
165#2066—132no—
166#2043—132no—
167#1981—132no—
168#1927—132no—
169#1892—131no—
170#1850—131no—
171#1787—131no—
172C23×C13—22no—
173C23×C13—22no—
174C23×C13#12112yes—
175C23×C13C2×SD1612yes—
176C23×C13#13712yes—
177C23×C13C22×D411yescharacteristic
178Q8×C13—24no—
179Q8×C13—24no—
180Q8×C13—48no—
181Q8×C13—42no—
182Q8×C13—42no—
183C2×C4×C13—22no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—24no—
187C2×C4×C13—22no—
188C2×C4×C13—22no—
189C2×C4×C13—24no—
190C2×C4×C13—48no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—48no—
198C2×C4×C13#12112yes—
199C2×C4×C13C22×D411yescharacteristic
200C2×C4×C13C2×#4112yes—
201C2×C4×C13C2×#4111yescharacteristic
202C2×C4×C13H(5,𝔽2)12yes—
203C2×Dic13—22no—
204C2×Dic13—22no—
205C2×Dic13—22no—
206C2×Dic13—22no—
207C2×Dic13—22no—
208C2×Dic13—41no—
209C2×Dic13—41no—
210C2×Dic13—42no—
211C2×Dic13—42no—
212C2×Dic13—42no—
213C2×Dic13—42no—
214C2×Dic13—42no—
215C2×Dic13C2×SD1614yes—
216Dic26—41no—
217Dic26—41no—
218Dic26—42no—
219C8×C13—42no—
220#1055—41no—
221#1055—41no—
222C23×Q8C2×D1311yescharacteristic
223C23×C8C2×D1311yescharacteristic
224C2×C4⋊Q8—132no—
225C2×C22⋊Q8—131no—
226C2×#117—261no—
227C22×C4⋊C4C2×D1311yescharacteristic
228#483—264no—
229C2×#106—131no—
230C2×#106—131no—
231C2×C4⋊C8—132no—
232C2×#103—24no—
233C2×#103—132no—
234C2×#103—131no—
235C2×#103—131no—
236C2×#103—132no—
237C2×#103—132no—
238C2×#103C2×D1312yes—
239C2×#103C2×D1312yes—
240C2×C22⋊C8—131no—
241#395—262no—
242#391—132no—
243#389—132no—
244#387—262no—
245#385—261no—
246#385—261no—
247#381—261no—
248#380—131no—
249C4×C4⋊C4—132no—
250C4×C22⋊C4—131no—
251#340—132no—
252#336—132no—
253C22×C13—22no—
254C22×C13—24no—
255C22×C13—22no—
256C22×C13—24no—
257C22×C13#46114yes—
258C22×C13C2×#12111yescharacteristic
259C22×C13#54612yes—
260C22×C13C22×SD1611yescharacteristic
261C22×C13C2×#13711yescharacteristic
262C22×C13#57812yes—
263C4×C13—22no—
264C4×C13—44no—
265C4×C13—42no—
266C4×C13—42no—
267C4×C13#52511yescharacteristic
268C4×C13#53511yescharacteristic
269C4×C13#55112yes—
270Dic13—24no—
271Dic13—42no—
272Dic13—81no—
273Dic13—82no—
274Dic13—81no—
275C22×Q8—21no—
276C22×Q8—24no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8—42no—
280C22×Q8—131no—
281C22×Q8C22×D1312yes—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4C22×D1311yescharacteristic
285C22×C8—22no—
286C22×C8—42no—
287C22×C8—131no—
288C22×C8—131no—
289C22×C8C22×D1312yes—
290C4⋊Q8—264no—
291C4⋊Q8—522no—
292C22⋊Q8—262no—
293C22⋊Q8—262no—
294#117—524no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—131no—
298C2×C4⋊C4—132no—
299C2×C4⋊C4—262no—
300C2×C4⋊C4—262no—
301C2×C4⋊C4—262no—
302C2×C4⋊C4—261no—
303C2×C4⋊C4C22⋊D1314yes—
304C2×C4⋊C4C22×D1311yescharacteristic
305C2×C4⋊C4C22×D1311yescharacteristic
306C2×C22⋊C4—131no—
307C2×C22⋊C4—131no—
308C2×C22⋊C4—261no—
309C2×C22⋊C4—261no—
310C2×C42—132no—
311C2×C42—262no—
312#106—262no—
313#106—262no—
314C4⋊C8—522no—
315#103—24no—
316#103—24no—
317#103—264no—
318#103—262no—
319#103—262no—
320#103—522no—
321#103—522no—
322C22⋊C8—262no—
323#95—132no—
324#95—262no—
325#95—262no—
326#95—262no—
327#95—262no—
328#95—261no—
329C2×C13—24no—
330C2×C13#241111yescharacteristic
331C2×C13C2×#46111yescharacteristic
332C2×C13#304411yescharacteristic
333C2×C13#329812yes—
334C2×C13#331212yes—
335C24D4×D1311yescharacteristic
336C2×Q8—22no—
337C2×Q8—28no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—44no—
343C2×Q8—48no—
344C2×Q8—44no—
345C2×Q8—42no—
346C2×Q8—262no—
347C2×Q8—261no—
348C2×Q8—262no—
349C2×Q8—261no—
350C2×Q8#612714yes—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—24no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—44no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—132no—
362C22×C4—132no—
363C22×C4—261no—
364C22×C4—262no—
365C22×C4—261no—
366C22×C4D4×D1311yescharacteristic
367C22×C4#612912yes—
368C22×C4C2×C22⋊D1312yes—
369C22×C4C23×D1311yescharacteristic
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—44no—
374C2×C8—262no—
375C2×C8—262no—
376C2×C8—261no—
377C2×C8—261no—
378C4⋊C4—24no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—262no—
382C4⋊C4—261no—
383C4⋊C4—262no—
384C4⋊C4—261no—
385C4⋊C4—524no—
386C4⋊C4—524no—
387C4⋊C4—524no—
388C4⋊C4—522no—
389C4⋊C4C2×C22⋊D1312yes—
390C4⋊C4C2×C22⋊D1312yes—
391C22⋊C4—134no—
392C22⋊C4—262no—
393C22⋊C4—522no—
394C22⋊C4—522no—
395C42—262no—
396C42—262no—
397C42—524no—
398C13#2448011yescharacteristic, complemented, Sylow
399C23—22no—
400C23—22no—
401C23SD16×D1312yes—
402C23#8816912yes—
403C23#8819312yes—
404C23C2×D4×D1311yescharacteristic
405Q8—24no—
406Q8—24no—
407Q8—48no—
408Q8—42no—
409Q8—42no—
410Q8—522no—
411Q8—521no—
412Q8—521no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—48no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—48no—
428C2×C4—134no—
429C2×C4—262no—
430C2×C4—262no—
431C2×C4—262no—
432C2×C4—262no—
433C2×C4—262no—
434C2×C4—522no—
435C2×C4—522no—
436C2×C4—522no—
437C2×C4—522no—
438C2×C4—522no—
439C2×C4—521no—
440C2×C4—521no—
441C2×C4#8819312yes—
442C2×C4C2×#612712yes—
443C2×C4C2×#612911yescharacteristic
444C2×C4#8825112yes—
445C2×C4C22×C22⋊D1311yescharacteristic
446C8—42no—
447C8—521no—
448C8—521no—
449C22—22no—
450C22—22no—
451C22—24no—
452C22—24no—
453C22#1171882314yes—
454C22#1171919512yes—
455C22C2×SD16×D1311yescharacteristic
456C22C2×#8816911yescharacteristic
457C22#1171947112yes—
458C22C2×#8819311yescharacteristic
459C4—22no—
460C4—44no—
461C4—42no—
462C4—42no—
463C4—264no—
464C4—522no—
465C4—1041no—
466C4—1041no—
467C4—1042no—
468C4#1171920012yes—
469C4#1171949611yescharacteristic
470C4#1171951011yescharacteristic
471C2—24no—
472C2#1311822111yescharacteristic
473C2C2×#1171882311yescharacteristic
474C2#1312436311yescharacteristic
475C2#1312669712yes—
476C2#1312688312yes—
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#103C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC22×#103D13
hypocenterC13#24480
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
4. #13116213C2semidirect
5. #13116081C2semidirect
6. #13115757C2semidirect
7. #13115473C2semidirect
398. C13#24480semidirect

Maximal subgroups

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

subgroupindex
C2×#117186322
#131184762
#131177052
#131162132
#131160812
#131157572
#131154732
#131152592
#131150142
#131147712
C22×C13×#1032
#2448013