Finite Group Databasebeta

← #15756358

Subgroups — #15756358

Order 3328.

514 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117241C211yesmaximal, characteristic
2#13114813C211yesmaximal, characteristic
3#13114813C211yesmaximal, characteristic
4#13112720C211yesmaximal, characteristic, complemented
5#13112720C211yesmaximal, characteristic, complemented
6#13112719C211yesmaximal, characteristic, complemented
7C13×#1296C211yesmaximal, characteristic, complemented
8C2×#88146C412yes—
9C2×C42×D13C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C13×#384C2211yescharacteristic
13C2×#88060—21no—
14C2×#88060—21no—
15#11718648—21no—
16#11718648—21no—
17#11718638C412yes—
18C4⋊C4×Dic13—21no—
19C4⋊C4×Dic13—21no—
20#11718596C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23#11718142—21no—
24#11718142—21no—
25C22×C4×D13C2×C411yescharacteristic
26C22×C4×D13D411yescharacteristic
27C22×C4×D13D411yescharacteristic
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C42×C13C2311yescharacteristic
34C2×#6103—22no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C412yes—
38C2×C4×Dic13—22no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C22×#1055—21no—
43C22×#1055—21no—
44#88146—44no—
45C42×D13—21no—
46C42×D13—21no—
47C42×D13—21no—
48C42×D13—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53#88071—22no—
54#88071—22no—
55#88060—42no—
56#88060—42no—
57C4⋊#1055—21no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61#8729—131nomaximal, Sylow
62C23×D13C22⋊C411yescharacteristic
63C22×C4×C13—22no—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×Dic13—22no—
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C22⋊C411yescharacteristic
71C2×C4×D13—22no—
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13—22no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13—21no—
83C2×C4×D13—21no—
84C2×C4×D13—21no—
85C2×C4×D13—21no—
86C2×C4×D13—21no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C2×C8×C13—41no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C42×C13#4111yescharacteristic
99C42×C13#4111yescharacteristic
100C42×C13#4111yescharacteristic
101C42×C13#4111yescharacteristic
102#6103—44no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107C4⋊Dic13—42no—
108C4×Dic13—21no—
109C4×Dic13—21no—
110C4×Dic13—21no—
111C4×Dic13—21no—
112C4×Dic13—21no—
113C4×Dic13—21no—
114C4×Dic13—44no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#1055—41no—
121#2285—131no—
122#1797—131no—
123#1797—131no—
124#1296—131no—
125#1296—131no—
126#1296—131no—
127#1296D1311yescharacteristic, complemented
128C23×C13C2×C22⋊C411yescharacteristic
129C22×D13—21no—
130C22×D13—21no—
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—21no—
135C22×D13#10012yes—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13#11711yescharacteristic
142C2×C4×C13#11711yescharacteristic
143C2×C4×C13#12311yescharacteristic
144C2×C4×C13#12311yescharacteristic
145C2×C4×C13#12311yescharacteristic
146C2×C4×C13#12311yescharacteristic
147C2×C4×C13#13511yescharacteristic
148C2×C4×C13#13511yescharacteristic
149C2×C4×C13#13511yescharacteristic
150C2×C4×C13#13511yescharacteristic
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13#13711yescharacteristic
154C2×C4×C13#13711yescharacteristic
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13—42no—
166C2×Dic13#10112yes—
167C4×D13—24no—
168C4×D13—24no—
169C4×D13—41no—
170C4×D13—41no—
171C4×D13—41no—
172C4×D13—41no—
173C4×D13—41no—
174C4×D13—41no—
175C4×D13—41no—
176C4×D13—41no—
177C8×C13—81no—
178C8×C13—81no—
179#1055—81no—
180#1055—81no—
181C2×#117—132no—
182C22×C42—131no—
183C2×C4⋊C8—131no—
184C2×C4⋊C8—131no—
185C2×C4⋊C8C2×D1311yescharacteristic
186C2×C4⋊C8C2×D1311yescharacteristic
187C2×C22⋊C8—261no—
188C2×C22⋊C8—261no—
189#384—131no—
190#384C2×D1311yescharacteristic
191#382—132no—
192#380—261no—
193#380—261no—
194C4×C4⋊C4—261no—
195C4×C4⋊C4—261no—
196#336—261no—
197#336—261no—
198C22×C13#38111yescharacteristic
199C22×C13C2×#10011yescharacteristic
200C22×C13C2×#10111yescharacteristic
201C22×C13#41611yescharacteristic
202C22×C13#41611yescharacteristic
203C22×C13#41711yescharacteristic
204C22×C13#41711yescharacteristic
205C2×D13—22no—
206C2×D13—22no—
207C2×D13—22no—
208C2×D13—41no—
209C2×D13—41no—
210C2×D13—41no—
211C2×D13—41no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—82no—
215C4×C13#48211yescharacteristic
216C4×C13#48211yescharacteristic
217C4×C13#48211yescharacteristic
218C4×C13#48211yescharacteristic
219C4×C13#48511yescharacteristic
220C4×C13#48511yescharacteristic
221C4×C13#48511yescharacteristic
222C4×C13#48511yescharacteristic
223Dic13—22no—
224Dic13—41no—
225Dic13—41no—
226Dic13—82no—
227C23×C4—131no—
228C23×C4—131no—
229C23×C4—131no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—261no—
233C22×C8—261no—
234#117—524no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—132no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—261no—
240C2×C4⋊C4C4×D1312yes—
241C2×C22⋊C4—262no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—261no—
246C2×C42—261no—
247C2×C42—261no—
248C2×C42—261no—
249C2×C42—262no—
250C2×C42C22×D1311yescharacteristic
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—261no—
256C4⋊C8—261no—
257C4⋊C8—261no—
258C4⋊C8—261no—
259C22⋊C8—522no—
260C22⋊C8—522no—
261#95—262no—
262#95—262no—
263C2×C13#154411yescharacteristic
264C2×C13#155111yescharacteristic
265C2×C13#155111yescharacteristic
266C2×C13#156111yescharacteristic
267C2×C13#182111yescharacteristic
268C2×C13#182511yescharacteristic
269C2×C13#182511yescharacteristic
270D13—42no—
271C24—131no—
272C22×C4—22no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—262no—
277C22×C4—262no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—261no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4—261no—
291C22×C4—261no—
292C22×C4—262no—
293C22×C4C2×C4×D1311yescharacteristic
294C22×C4D4×D1311yescharacteristic
295C22×C4D4×D1311yescharacteristic
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—521no—
303C2×C8—521no—
304C2×C8—521no—
305C2×C8—521no—
306C2×C8—521no—
307C2×C8—521no—
308C4⋊C4—42no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—522no—
314C4⋊C4—521no—
315C4⋊C4—521no—
316C4⋊C4—521no—
317C4⋊C4—521no—
318C22⋊C4—524no—
319C42—261no—
320C42—261no—
321C42—261no—
322C42—261no—
323C42—261no—
324C42—261no—
325C42—524no—
326C42#612711yescharacteristic
327C42#612711yescharacteristic
328C42#612911yescharacteristic
329C42#613111yescharacteristic
330C13#872911yescharacteristic, complemented, Sylow
331C23—132no—
332C23—261no—
333C23—261no—
334C23—261no—
335C23—261no—
336C23—261no—
337C23—261no—
338C23C22⋊C4×D1311yescharacteristic
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—132no—
345C2×C4—264no—
346C2×C4—264no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—522no—
364C2×C4—522no—
365C2×C4—522no—
366C2×C4#8812611yescharacteristic
367C2×C4#8813711yescharacteristic
368C2×C4#8813711yescharacteristic
369C2×C4#8814611yescharacteristic
370C2×C4#8814811yescharacteristic
371C2×C4#8814811yescharacteristic
372C2×C4#8816511yescharacteristic
373C2×C4#8816611yescharacteristic
374C2×C4#8816811yescharacteristic
375C2×C4#8816911yescharacteristic
376C2×C4#8817011yescharacteristic
377C2×C4#8817011yescharacteristic
378C2×C4#8817211yescharacteristic
379C2×C4#8817311yescharacteristic
380C8—81no—
381C8—81no—
382C8—1041no—
383C8—1041no—
384C22—262no—
385C22—262no—
386C22—262no—
387C22—521no—
388C22—521no—
389C22—521no—
390C22—521no—
391C22#1171832511yescharacteristic
392C22D13×#10011yescharacteristic
393C22D13×#10111yescharacteristic
394C22#1171843211yescharacteristic
395C22#1171843311yescharacteristic
396C22#1171846411yescharacteristic
397C22#1171846511yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—262no—
402C4—521no—
403C4—521no—
404C4—1042no—
405C4#1171844011yescharacteristic
406C4#1171844511yescharacteristic
407C4#1171847511yescharacteristic
408C4#1171847611yescharacteristic
409C4#1171852711yescharacteristic
410C4#1171852811yescharacteristic
411C4#1171854611yescharacteristic
412C4#1171854911yescharacteristic
413C2—522no—
414C2#1311349911yescharacteristic
415C2#1311352811yescharacteristic
416C2#1311353011yescharacteristic
417C2#1311357211yescharacteristic
418C2#1311491511yescharacteristic
419C2#1311492911yescharacteristic
420C2#1311493011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1296D13
hypocenterC13#8729
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
4. #13112720C2semidirect
5. #13112720C2semidirect
6. #13112719C2semidirect
7. C13×#1296C2semidirect
127. #1296D13semidirect
330. C13#8729semidirect

Maximal subgroups

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

subgroupindex
#131172412
#131148132
#131127202
#131127192
C13×#12962
#872913