Finite Group Databasebeta

← #15766359

Subgroups — #15766359

Order 3328.

556 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119790C211yesmaximal, characteristic
2#13115597C211yesmaximal, characteristic, complemented
3#13114833C211yesmaximal, characteristic
4C2×#11718139C211yesmaximal, characteristic, complemented
5C2×#11718051C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic, complemented
7C13×#1990C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88200—21no—
10C2×#88200—21no—
11C2×C4×D52C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C13×#384C2211yescharacteristic
14#11718653—22no—
15#11718649—21no—
16#11718637—21no—
17C2×#88049—21no—
18C2×#88048—21no—
19C4×C4⋊Dic13C2211yescharacteristic
20C2×C4⋊#1055C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22C13×#340—22no—
23#11718139—22no—
24#11718121—21no—
25#11718121—21no—
26#11718051—22no—
27C22×Q8×C13—21no—
28C22×D52D411yescharacteristic
29C22×C4×D13—21no—
30C22×C8×C13—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4D412yes—
40C2×C42×C13C2311yescharacteristic
41#88200—42no—
42#88200—42no—
43#88200—42no—
44#88200—42no—
45C2×#6103—22no—
46C2×#6103—22no—
47C2×#6103—21no—
48C2×C4⋊Dic13D411yescharacteristic
49C2×C4⋊Dic13D411yescharacteristic
50C2×C4⋊Dic13D411yescharacteristic
51C2×#6101—22no—
52C2×#6101—22no—
53C2×C4×Dic13—21no—
54C22×#1055—21no—
55C22×#1055—21no—
56C4×D52—21no—
57C4×D52—21no—
58C4×D52—21no—
59C4×D52—21no—
60C4×C8×C13—21no—
61C4×C8×C13—21no—
62#88071—21no—
63#88049—42no—
64#88048—42no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055D412yes—
69#10420—131nomaximal, Sylow
70C23×D13—21no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C22×C4×C13—22no—
78C22×C4×C13—41no—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×D52SD1612yes—
91C2×C4×D13—41no—
92C2×C4×D13—41no—
93C2×C4×D13—41no—
94C2×C4×D13—41no—
95C2×C4×D13—41no—
96C2×C4×D13—41no—
97C2×C8×C13—22no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—42no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C42×C13C2×D411yescharacteristic
110C42×C13#4111yescharacteristic
111C42×C13#4111yescharacteristic
112C42×C13#4111yescharacteristic
113#6103—44no—
114#6103—44no—
115#6103—41no—
116#6103—41no—
117C4⋊Dic13—21no—
118C4⋊Dic13—21no—
119C4⋊Dic13—21no—
120C4⋊Dic13—21no—
121C4⋊Dic13D812yes—
122C4⋊Dic13SD1612yes—
123#6101—44no—
124#6101—44no—
125C4×Dic13—41no—
126C4×Dic13—41no—
127C2×#1055—22no—
128C2×#1055—41no—
129C2×#1055—41no—
130C2×#1055—41no—
131C2×#1055—41no—
132C2×#1055—41no—
133#2542—131no—
134#1990D1311yescharacteristic, complemented
135#1948—131no—
136#1802—131no—
137C2×#332—131no—
138C2×D4⋊C8—131no—
139#1279—131no—
140C23×C13#12011yescharacteristic
141C22×D13—22no—
142C22×D13—41no—
143C22×D13—41no—
144C22×D13—41no—
145C22×D13—41no—
146C22×D13—41no—
147C22×D13—41no—
148Q8×C13—81no—
149Q8×C13—81no—
150Q8×C13—81no—
151Q8×C13—81no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13—81no—
160C2×C4×C13#12111yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12311yescharacteristic
164C2×C4×C13#12311yescharacteristic
165C2×C4×C13#12411yescharacteristic
166C2×C4×C13C2×D811yescharacteristic
167C2×C4×C13C2×SD1611yescharacteristic
168C2×C4×C13C2×SD1611yescharacteristic
169C2×C4×C13#13511yescharacteristic
170C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C13#13711yescharacteristic
173C2×C4×C13#13711yescharacteristic
174C2×Dic13—22no—
175C2×Dic13—22no—
176C2×Dic13—41no—
177C2×Dic13—41no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—41no—
183D52—22no—
184D52—22no—
185D52—41no—
186D52—41no—
187C4×D13—81no—
188C4×D13—81no—
189C4×D13—81no—
190C4×D13—81no—
191C8×C13—42no—
192#1055—42no—
193#1055—81no—
194C2×C4⋊Q8C2×D1311yescharacteristic
195C2×C22⋊Q8—261no—
196C2×C22⋊Q8—261no—
197C2×C4×D4—131no—
198C2×#106—261no—
199C2×C4⋊C8—131no—
200C2×C4⋊C8—131no—
201C2×#102—261no—
202C2×C4×C8C2×D1311yescharacteristic
203#399—262no—
204#390—261no—
205#384—261no—
206#384C2×D1311yescharacteristic
207C4×C4⋊C4—131no—
208#340—22no—
209#340—261no—
210#340—261no—
211#332—262no—
212D4⋊C8—262no—
213C22×C13#39411yescharacteristic
214C22×C13#44711yescharacteristic
215C22×C13#44811yescharacteristic
216C22×C13#45011yescharacteristic
217C22×C13#45211yescharacteristic
218C22×C13#45411yescharacteristic
219C22×C13#45611yescharacteristic
220C2×D13—42no—
221C2×D13—42no—
222C2×D13—42no—
223C2×D13—81no—
224C2×D13—81no—
225C2×D13—81no—
226C2×D13—81no—
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—82no—
230C4×C13—161no—
231C4×C13#45911yescharacteristic
232C4×C13#46011yescharacteristic
233C4×C13#46511yescharacteristic
234C4×C13#47011yescharacteristic
235C4×C13#48311yescharacteristic
236C4×C13#48511yescharacteristic
237C4×C13#48611yescharacteristic
238C4×C13#49011yescharacteristic
239Dic13—42no—
240Dic13—42no—
241Dic13—81no—
242C22×Q8—21no—
243C22×D4—131no—
244C23×C4—261no—
245C22×C8—21no—
246C22×C8—261no—
247C22×C8—261no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C22⋊Q8—522no—
253C22⋊Q8—522no—
254C22⋊Q8—522no—
255C22⋊Q8—522no—
256C4×D4—261no—
257C4×D4—261no—
258C4×D4—261no—
259C4×D4—261no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—131no—
265C2×C4⋊C4—131no—
266C2×C4⋊C4—131no—
267C2×C4⋊C4—262no—
268C2×C4⋊C4—262no—
269C2×C4⋊C4C22⋊D1312yes—
270C2×C22⋊C4—262no—
271C2×C22⋊C4—262no—
272C2×C22⋊C4—261no—
273C2×C42—261no—
274C2×C42C22×D1311yescharacteristic
275#106—522no—
276C4⋊C8—132no—
277C4⋊C8—261no—
278C4⋊C8—261no—
279C4⋊C8—261no—
280#102—522no—
281C4×C8—21no—
282C4×C8—21no—
283#95—261no—
284C2×C13#162711yescharacteristic
285C2×C13#163511yescharacteristic
286C2×C13#164711yescharacteristic
287C2×C13#165111yescharacteristic
288C2×C13#203511yescharacteristic
289C2×C13#203811yescharacteristic
290C2×C13#204111yescharacteristic
291D13—82no—
292C24—261no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×D4—132no—
300C2×D4—261no—
301C2×D4—261no—
302C2×D4—261no—
303C2×D4—261no—
304C2×D4—261no—
305C22×C4—22no—
306C22×C4—41no—
307C22×C4—261no—
308C22×C4—261no—
309C22×C4—261no—
310C22×C4—521no—
311C22×C4—521no—
312C22×C4—521no—
313C22×C4—521no—
314C22×C4—521no—
315C22×C4—521no—
316C22×C4D4×D1311yescharacteristic
317C22×C4D4×D1311yescharacteristic
318C22×C4C2×C22⋊D1311yescharacteristic
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—262no—
323C2×C8—521no—
324C2×C8—521no—
325C2×C8—521no—
326C2×C8—521no—
327C2×C8—521no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—42no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—132no—
338C4⋊C4—132no—
339C4⋊C4—261no—
340C4⋊C4—261no—
341C4⋊C4—261no—
342C4⋊C4—261no—
343C4⋊C4—524no—
344C4⋊C4—524no—
345C22⋊C4—524no—
346C22⋊C4—524no—
347C22⋊C4—521no—
348C22⋊C4—521no—
349C42—521no—
350C42—521no—
351C42#612711yescharacteristic
352C42#612711yescharacteristic
353C42D4×D1311yescharacteristic
354C42#612911yescharacteristic
355C13#1042011yescharacteristic, complemented, Sylow
356C23—262no—
357C23—521no—
358C23—521no—
359C23—521no—
360C23—521no—
361C23—521no—
362C23—521no—
363C23#8819111yescharacteristic
364Q8—81no—
365Q8—81no—
366Q8—81no—
367Q8—81no—
368D4—262no—
369D4—262no—
370D4—521no—
371D4—521no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—262no—
381C2×C4—262no—
382C2×C4—521no—
383C2×C4—521no—
384C2×C4—521no—
385C2×C4—521no—
386C2×C4—521no—
387C2×C4—521no—
388C2×C4—521no—
389C2×C4—1041no—
390C2×C4—1041no—
391C2×C4—1041no—
392C2×C4—1041no—
393C2×C4#8813711yescharacteristic
394C2×C4#8813811yescharacteristic
395C2×C4#8813811yescharacteristic
396C2×C4#8813911yescharacteristic
397C2×C4D8×D1311yescharacteristic
398C2×C4#8816511yescharacteristic
399C2×C4SD16×D1311yescharacteristic
400C2×C4SD16×D1311yescharacteristic
401C2×C4#8816811yescharacteristic
402C2×C4#8816911yescharacteristic
403C2×C4#8817211yescharacteristic
404C2×C4#8817311yescharacteristic
405C2×C4#8818311yescharacteristic
406C2×C4#8819311yescharacteristic
407C8—42no—
408C8—522no—
409C8—1041no—
410C22—522no—
411C22—522no—
412C22—522no—
413C22—1041no—
414C22—1041no—
415C22—1041no—
416C22—1041no—
417C22#1171862011yescharacteristic
418C22#1171872311yescharacteristic
419C22#1171875611yescharacteristic
420C22#1171881711yescharacteristic
421C22#1171883011yescharacteristic
422C22#1171883111yescharacteristic
423C22#1171884811yescharacteristic
424C4—21no—
425C4—21no—
426C4—82no—
427C4—161no—
428C4—522no—
429C4—522no—
430C4—1041no—
431C4#1171842111yescharacteristic
432C4#1171842311yescharacteristic
433C4#1171842511yescharacteristic
434C4#1171844711yescharacteristic
435C4#1171846611yescharacteristic
436C4#1171846811yescharacteristic
437C4#1171847511yescharacteristic
438C4#1171847711yescharacteristic
439C2—1042no—
440C2#1311393611yescharacteristic
441C2#1311398411yescharacteristic
442C2#1311406811yescharacteristic
443C2#1311409611yescharacteristic
444C2#1311603011yescharacteristic
445C2#1311605311yescharacteristic
446C2#1311606811yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1990C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenter#1990D13
hypocenterC13#10420
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. #13115597C2semidirect
4. C2×#11718139C2semidirect
6. #13112676C2semidirect
7. C13×#1990C2semidirect
134. #1990D13semidirect
355. C13#10420semidirect

Maximal subgroups

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

subgroupindex
#131197902
#131155972
#131148332
C2×#117181392
C2×#117180512
#131126762
C13×#19902
#1042013