Finite Group Databasebeta

← #15766360

Subgroups — #15766360

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#13115798C211yesmaximal, characteristic, complemented
3#13115600C211yesmaximal, characteristic, complemented
4#13114837C211yesmaximal, characteristic
5C2×#11718075C211yesmaximal, characteristic
6#13112675C211yesmaximal, characteristic, complemented
7C2×C13×#332C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88200—21no—
10C2×#88200—21no—
11C2×C4×D52C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×#88061—21no—
15C2×#88057—21no—
16#11718653—22no—
17#11718649—21no—
18#11718637—21no—
19#11718596C2211yescharacteristic
20C4×C4⋊Dic13C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22C13×#332—22no—
23#11718143—21no—
24#11718143—21no—
25#11718121—22no—
26#11718075—22no—
27C22×Q8×C13—21no—
28C22×D52D411yescharacteristic
29C22×C4×D13—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4D412yes—
38C2×C42×C13C2311yescharacteristic
39#88200—42no—
40#88200—42no—
41#88200—42no—
42#88200—42no—
43C2×#6103—22no—
44C2×#6103—22no—
45C2×#6103—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13D411yescharacteristic
50C2×C4⋊Dic13D411yescharacteristic
51C2×C4⋊Dic13D411yescharacteristic
52C2×#6101—22no—
53C2×#6101—22no—
54C2×C4×Dic13—21no—
55C22×#1055—21no—
56C4×D52—21no—
57C4×D52—21no—
58C4×D52—21no—
59C4×D52—21no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8D412yes—
64#88071—21no—
65#88061—42no—
66#88057—42no—
67C4×#1055—21no—
68C4×#1055—21no—
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×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—41no—
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—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C42×C13C2×D411yescharacteristic
108C42×C13#4111yescharacteristic
109C42×C13#4111yescharacteristic
110C42×C13#4111yescharacteristic
111#6103—44no—
112#6103—44no—
113#6103—41no—
114#6103—41no—
115C4⋊Dic13—21no—
116C4⋊Dic13—21no—
117C4⋊Dic13—21no—
118C4⋊Dic13—21no—
119C4⋊Dic13—42no—
120C4⋊Dic13—41no—
121C4⋊Dic13—41no—
122C4⋊Dic13—41no—
123C4⋊Dic13—41no—
124C4⋊Dic13D812yes—
125C4⋊Dic13SD1612yes—
126#6101—44no—
127#6101—44no—
128C4×Dic13—41no—
129C4×Dic13—41no—
130C2×#1055—22no—
131C2×#1055—41no—
132C2×#1055—41no—
133#2542—131no—
134#1990—131no—
135#1948—131no—
136#1802—131no—
137C2×#332D1311yescharacteristic, complemented
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#12111yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13#12111yescharacteristic
160C2×C4×C13#12311yescharacteristic
161C2×C4×C13#12311yescharacteristic
162C2×C4×C13#12411yescharacteristic
163C2×C4×C13C2×D811yescharacteristic
164C2×C4×C13C2×SD1611yescharacteristic
165C2×C4×C13C2×SD1611yescharacteristic
166C2×C4×C13#13511yescharacteristic
167C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C13#13711yescharacteristic
170C2×C4×C13#13711yescharacteristic
171C2×Dic13—22no—
172C2×Dic13—22no—
173C2×Dic13—41no—
174C2×Dic13—41no—
175C2×Dic13—41no—
176C2×Dic13—41no—
177C2×Dic13—41no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—81no—
181C2×Dic13—81no—
182C2×Dic13—81no—
183D52—22no—
184D52—22no—
185D52—41no—
186D52—41no—
187C4×D13—81no—
188C4×D13—81no—
189C4×D13—81no—
190C4×D13—81no—
191C8×C13—42no—
192C8×C13—81no—
193#1055—42no—
194C2×C4⋊Q8C2×D1311yescharacteristic
195C2×C22⋊Q8—261no—
196C2×C22⋊Q8—261no—
197C2×C4×D4—131no—
198C2×#106—261no—
199C2×C4⋊C8C2×D1311yescharacteristic
200C2×C4⋊C8C2×D1311yescharacteristic
201C2×#102—261no—
202C2×C4×C8—131no—
203#399—262no—
204#390—261no—
205#384—131no—
206#384—261no—
207C4×C4⋊C4—131no—
208#340—261no—
209#340—261no—
210#340—262no—
211#332—22no—
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#45911yescharacteristic
231C4×C13#46011yescharacteristic
232C4×C13#46511yescharacteristic
233C4×C13#47011yescharacteristic
234C4×C13#48311yescharacteristic
235C4×C13#48511yescharacteristic
236C4×C13#48611yescharacteristic
237C4×C13#49011yescharacteristic
238Dic13—42no—
239Dic13—42no—
240Dic13—81no—
241Dic13—161no—
242C22×Q8—21no—
243C22×D4—131no—
244C23×C4—261no—
245C22×C8—21no—
246C22×C8—21no—
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—131no—
262C2×C4⋊C4—131no—
263C2×C4⋊C4—131no—
264C2×C4⋊C4—262no—
265C2×C4⋊C4—262no—
266C2×C4⋊C4—261no—
267C2×C4⋊C4—261no—
268C2×C4⋊C4—261no—
269C2×C4⋊C4D5212yes—
270C2×C22⋊C4—262no—
271C2×C22⋊C4—262no—
272C2×C22⋊C4—261no—
273C2×C42—261no—
274C2×C42C22×D1311yescharacteristic
275#106—522no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8C22⋊D1312yes—
280#102—522no—
281C4×C8—261no—
282C4×C8—261no—
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—261no—
307C22×C4—261no—
308C22×C4—261no—
309C22×C4—521no—
310C22×C4—521no—
311C22×C4—521no—
312C22×C4—521no—
313C22×C4—521no—
314C22×C4—521no—
315C22×C4—521no—
316C22×C4C2×D5211yescharacteristic
317C22×C4D4×D1311yescharacteristic
318C22×C4D4×D1311yescharacteristic
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—262no—
326C2×C8—521no—
327C2×C8—521no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—132no—
333C4⋊C4—132no—
334C4⋊C4—261no—
335C4⋊C4—261no—
336C4⋊C4—261no—
337C4⋊C4—261no—
338C4⋊C4—522no—
339C4⋊C4—524no—
340C4⋊C4—524no—
341C4⋊C4—521no—
342C4⋊C4—521no—
343C4⋊C4—521no—
344C4⋊C4—521no—
345C22⋊C4—524no—
346C22⋊C4—524no—
347C22⋊C4—521no—
348C22⋊C4—521no—
349C42—521no—
350C42—521no—
351C42#612711yescharacteristic
352C42#612911yescharacteristic
353C42#612911yescharacteristic
354C42C2×C22⋊D1311yescharacteristic
355C13#1042011yescharacteristic, complemented, Sylow
356C23—262no—
357C23—521no—
358C23—521no—
359C23—521no—
360C23—521no—
361C23—521no—
362C23—521no—
363C23#8813611yescharacteristic
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—262no—
378C2×C4—262no—
379C2×C4—521no—
380C2×C4—521no—
381C2×C4—521no—
382C2×C4—521no—
383C2×C4—521no—
384C2×C4—521no—
385C2×C4—521no—
386C2×C4—1041no—
387C2×C4—1041no—
388C2×C4—1041no—
389C2×C4—1041no—
390C2×C4—1041no—
391C2×C4—1041no—
392C2×C4—1041no—
393C2×C4#8813711yescharacteristic
394C2×C4#8813911yescharacteristic
395C2×C4#8814011yescharacteristic
396C2×C4D8×D1311yescharacteristic
397C2×C4#8816511yescharacteristic
398C2×C4SD16×D1311yescharacteristic
399C2×C4SD16×D1311yescharacteristic
400C2×C4#8816811yescharacteristic
401C2×C4#8817011yescharacteristic
402C2×C4#8817211yescharacteristic
403C2×C4#8817211yescharacteristic
404C2×C4#8818411yescharacteristic
405C2×C4#8819211yescharacteristic
406C2×C4#8819311yescharacteristic
407C8—42no—
408C8—81no—
409C8—522no—
410C22—522no—
411C22—522no—
412C22—522no—
413C22—1041no—
414C22—1041no—
415C22—1041no—
416C22—1041no—
417C22#1171841311yescharacteristic
418C22#1171841411yescharacteristic
419C22#1171843411yescharacteristic
420C22#1171843711yescharacteristic
421C22#1171846711yescharacteristic
422C22#1171847111yescharacteristic
423C22#1171862211yescharacteristic
424C4—21no—
425C4—21no—
426C4—82no—
427C4—522no—
428C4—522no—
429C4—1041no—
430C4—2081no—
431C4#1171842111yescharacteristic
432C4#1171842511yescharacteristic
433C4#1171846611yescharacteristic
434C4#1171847611yescharacteristic
435C4#1171881111yescharacteristic
436C4#1171882411yescharacteristic
437C4#1171883211yescharacteristic
438C4#1171885011yescharacteristic
439C2—1042no—
440C2#1311394011yescharacteristic
441C2#1311398811yescharacteristic
442C2#1311407211yescharacteristic
443C2#1311410011yescharacteristic
444C2#1311603111yescharacteristic
445C2#1311605411yescharacteristic
446C2#1311606911yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#332C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenterC2×#332D13
hypocenterC13#10420
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #13115798C2semidirect
3. #13115600C2semidirect
6. #13112675C2semidirect
7. C2×C13×#332C2semidirect
137. C2×#332D13semidirect
355. C13#10420semidirect

Maximal subgroups

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

subgroupindex
#131197902
#131157982
#131156002
#131148372
C2×#117180752
#131126752
C2×C13×#3322
#1042013