Finite Group Databasebeta

← #15766792

Subgroups — #15766792

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic
2#13115630C211yesmaximal, characteristic
3#13114833C211yesmaximal, characteristic
4C2×#11718049C211yesmaximal, characteristic, complemented
5C2×#11718139C211yesmaximal, characteristic, complemented
6#13112719C211yesmaximal, characteristic, complemented
7C13×#1956C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C2×C13×#103—21no—
11C2×C13×#103—21no—
12C2×C4×C8×C13C2211yescharacteristic
13C13×#384C2211yescharacteristic
14C2×#88060—21no—
15C2×#88060—21no—
16#11718748—22no—
17#11718748—22no—
18C2×#88049—21no—
19C2×#88049—21no—
20C2×#88047—21no—
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24#11718139—22no—
25#11718121—21no—
26#11718049—22no—
27C22×Q8×C13—21no—
28C22×D52D411yescharacteristic
29C22×C4×D13—21no—
30C22×C8×C13D411yescharacteristic
31C22×C8×C13D411yescharacteristic
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8D412yes—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C42×C13C2311yescharacteristic
42C2×#6103—21no—
43C2×C4⋊Dic13D411yescharacteristic
44C22×#1055—21no—
45C22×#1055—21no—
46C22×#1055—21no—
47C4×D52—21no—
48C4×D52—21no—
49C4×D52—21no—
50C4×D52—21no—
51C13×#103—42no—
52C13×#103—42no—
53C4×C8×C13—21no—
54C4×C8×C13—21no—
55#88060—42no—
56#88060—42no—
57#88049—24no—
58#88049—42no—
59#88047—24no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055D412yes—
66#10484—131nomaximal, Sylow
67C23×D13—21no—
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C22×Dic13—21no—
80C2×D52—21no—
81C2×D52—21no—
82C2×D52—21no—
83C2×D52—21no—
84C2×D52—21no—
85C2×D52SD1612yes—
86C2×C4×D13—41no—
87C2×C4×D13—41no—
88C2×C4×D13—41no—
89C2×C4×D13—41no—
90C2×C4×D13—41no—
91C2×C4×D13—41no—
92C2×C8×C13—21no—
93C2×C8×C13—21no—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13—21no—
97C2×C8×C13D812yes—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—81no—
107C42×C13C2×D411yescharacteristic
108C42×C13C2×D411yescharacteristic
109C42×C13#4111yescharacteristic
110C42×C13#4111yescharacteristic
111#6103—41no—
112#6103—41no—
113C4⋊Dic13—21no—
114C4⋊Dic13—21no—
115C2×#1055—22no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#1055—41no—
121C2×#1055—41no—
122C2×#1055—41no—
123C2×#1055—41no—
124C2×#474—131no—
125#1956D1311yescharacteristic, complemented
126#1954—131no—
127#1802—131no—
128C2×#334—131no—
129C2×#332—131no—
130#1296—131no—
131C23×C13#12111yescharacteristic
132C22×D13—22no—
133C22×D13—41no—
134C22×D13—41no—
135C22×D13—41no—
136C22×D13—41no—
137C22×D13—41no—
138C22×D13—41no—
139Q8×C13—42no—
140Q8×C13—42no—
141Q8×C13—81no—
142Q8×C13—81no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—42no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C2×C4×C13#12011yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12111yescharacteristic
154C2×C4×C13#12311yescharacteristic
155C2×C4×C13#12311yescharacteristic
156C2×C4×C13#12411yescharacteristic
157C2×C4×C13C2×D811yescharacteristic
158C2×C4×C13C2×SD1611yescharacteristic
159C2×C4×C13#13511yescharacteristic
160C2×C4×C13#13511yescharacteristic
161C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C13#13711yescharacteristic
164C2×C4×C13#13711yescharacteristic
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168D52—22no—
169D52—22no—
170D52—41no—
171D52—41no—
172C4×D13—81no—
173C4×D13—81no—
174C4×D13—81no—
175C4×D13—81no—
176C8×C13—22no—
177C8×C13—41no—
178#1055—42no—
179#1055—81no—
180#1055—81no—
181C2×C4⋊Q8C2×D1311yescharacteristic
182C2×C4×D4—131no—
183#474—262no—
184#474—262no—
185C2×#107—261no—
186C2×C4⋊C8—131no—
187C2×C4⋊C8—131no—
188C2×C4⋊C8—131no—
189C2×#103—21no—
190C2×#103—21no—
191C2×#102—261no—
192C2×#102—261no—
193C2×C22⋊C8—261no—
194C2×C22⋊C8—261no—
195C2×C4×C8C2×D1311yescharacteristic
196#384C2×D1311yescharacteristic
197#340—261no—
198#334—262no—
199#332—262no—
200C22×C13#39411yescharacteristic
201C22×C13#45911yescharacteristic
202C22×C13#46311yescharacteristic
203C22×C13#46511yescharacteristic
204C22×C13#47011yescharacteristic
205C22×C13#47111yescharacteristic
206C22×C13#47311yescharacteristic
207C2×D13—42no—
208C2×D13—42no—
209C2×D13—42no—
210C2×D13—81no—
211C2×D13—81no—
212C2×D13—81no—
213C2×D13—81no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—82no—
217C4×C13—161no—
218C4×C13#44811yescharacteristic
219C4×C13#45211yescharacteristic
220C4×C13#45911yescharacteristic
221C4×C13#46311yescharacteristic
222C4×C13#46611yescharacteristic
223C4×C13#46911yescharacteristic
224C4×C13#48311yescharacteristic
225C4×C13#48511yescharacteristic
226Dic13—81no—
227C22×Q8—21no—
228C22×D4—131no—
229C23×C4—261no—
230C22×C8—261no—
231C22×C8—261no—
232C22×C8—261no—
233C22×C8C22⋊D1311yescharacteristic
234C22×C8C22⋊D1311yescharacteristic
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8D5212yes—
239C4×D4—261no—
240C4×D4—261no—
241C4×D4—261no—
242C4×D4—261no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—131no—
249C2×C22⋊C4—261no—
250C2×C42C22×D1311yescharacteristic
251#107—264no—
252C4⋊C8—132no—
253C4⋊C8—261no—
254C4⋊C8—261no—
255C4⋊C8—261no—
256C4⋊C8—261no—
257C4⋊C8—261no—
258#103—42no—
259#103—42no—
260#102—264no—
261#102—522no—
262C22⋊C8—522no—
263C22⋊C8—522no—
264C4×C8—21no—
265C4×C8—21no—
266C2×C13#166511yescharacteristic
267C2×C13#167911yescharacteristic
268C2×C13#168911yescharacteristic
269C2×C13#170311yescharacteristic
270C2×C13#203511yescharacteristic
271C2×C13#205211yescharacteristic
272C2×C13#205411yescharacteristic
273D13—82no—
274C24—261no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×D4—132no—
282C2×D4—261no—
283C2×D4—261no—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—261no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—261no—
290C22×C4—521no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4—521no—
296C22×C4D4×D1311yescharacteristic
297C22×C4#612911yescharacteristic
298C22×C4C2×C22⋊D1311yescharacteristic
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—262no—
305C2×C8—521no—
306C2×C8—521no—
307C2×C8—521no—
308C2×C8—521no—
309C2×C8—521no—
310C2×C8—521no—
311C2×C8—521no—
312C2×C8—521no—
313C2×C8#610412yes—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—81no—
323C4⋊C4—261no—
324C4⋊C4—261no—
325C22⋊C4—521no—
326C22⋊C4—521no—
327C42C2×D5211yescharacteristic
328C42#612711yescharacteristic
329C42D4×D1311yescharacteristic
330C42#612911yescharacteristic
331C13#1048411yescharacteristic, complemented, Sylow
332C23—262no—
333C23—521no—
334C23—521no—
335C23—521no—
336C23—521no—
337C23—521no—
338C23—521no—
339C23#8819211yescharacteristic
340Q8—42no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344D4—262no—
345D4—262no—
346D4—521no—
347D4—521no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—1041no—
360C2×C4—1041no—
361C2×C4—1041no—
362C2×C4—1041no—
363C2×C4#8813611yescharacteristic
364C2×C4#8813711yescharacteristic
365C2×C4#8813911yescharacteristic
366C2×C4#8814011yescharacteristic
367C2×C4SD16×D1311yescharacteristic
368C2×C4#8817011yescharacteristic
369C2×C4#8817211yescharacteristic
370C2×C4#8817211yescharacteristic
371C2×C4#8818411yescharacteristic
372C2×C4C2×#610411yescharacteristic
373C2×C4#8818611yescharacteristic
374C2×C4#8819311yescharacteristic
375C2×C4#8820311yescharacteristic
376C2×C4#8820411yescharacteristic
377C8—22no—
378C8—41no—
379C8—522no—
380C8—1041no—
381C8—1041no—
382C22—522no—
383C22—522no—
384C22—522no—
385C22—1041no—
386C22—1041no—
387C22—1041no—
388C22—1041no—
389C22#1171862211yescharacteristic
390C22#1171871811yescharacteristic
391C22#1171873311yescharacteristic
392C22#1171883211yescharacteristic
393C22#1171883811yescharacteristic
394C22#1171885011yescharacteristic
395C22#1171885311yescharacteristic
396C4—21no—
397C4—21no—
398C4—82no—
399C4—161no—
400C4—1041no—
401C4#1171846611yescharacteristic
402C4#1171846711yescharacteristic
403C4#1171847111yescharacteristic
404C4#1171847611yescharacteristic
405C4#1171867611yescharacteristic
406C4#1171867711yescharacteristic
407C4#1171869911yescharacteristic
408C4#1171870011yescharacteristic
409C2—1042no—
410C2#1311417411yescharacteristic
411C2#1311425611yescharacteristic
412C2#1311432211yescharacteristic
413C2#1311440811yescharacteristic
414C2#1311603111yescharacteristic
415C2#1311613611yescharacteristic
416C2#1311614611yescharacteristic
subgroupG/H
centerC23#88192
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1956C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenter#1956D13
hypocenterC13#10484
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
4. C2×#11718049C2semidirect
5. C2×#11718139C2semidirect
6. #13112719C2semidirect
7. C13×#1956C2semidirect
125. #1956D13semidirect
331. C13#10484semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
#131156302
#131148332
C2×#117180492
C2×#117181392
#131127192
C13×#19562
#1048413