Finite Group Databasebeta

← #15757187

Subgroups — #15757187

Order 3328.

530 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117783C211yesmaximal, characteristic
2#13115594C211yesmaximal, characteristic, complemented
3#13114964C211yesmaximal, characteristic, complemented
4#13114837C211yesmaximal, characteristic
5C2×#11718051C211yesmaximal, characteristic
6#13112720C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×#88146—21no—
9C2×C4×D52C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88061—21no—
14#11718648—21no—
15C2×#88047—21no—
16#11718600—21no—
17#11718596C2211yescharacteristic
18#11718596C2211yescharacteristic
19C4×C4⋊Dic13—21no—
20C2×C4⋊#1055C2211yescharacteristic
21#11718331—22no—
22#11718143—22no—
23#11718143—21no—
24#11718121—21no—
25#11718051C414yescomplemented
26C22×D52D411yescharacteristic
27C22×C4×D13—21no—
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13—21no—
33C2×C42×C13C2311yescharacteristic
34C2×#6103—21no—
35C2×#6103—22no—
36C2×#6103—22no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13D412yes—
44C2×C4×Dic13—22no—
45C22×#1055—21no—
46#88146—42no—
47#88146—42no—
48C4×D52—21no—
49C4×D52—21no—
50C4×D52C2×C412yes—
51C4×D52Q812yes—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C4×C8×C13—21no—
55C4×C8×C13C2×C412yes—
56C13×#95—21no—
57#88071—22no—
58#88061—42no—
59#88047—42no—
60C4⋊#1055—21no—
61C4⋊#1055C2×C412yes—
62#8897—131nomaximal, Sylow
63C23×D13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—22no—
71C22×Dic13—41no—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52C4⋊C412yes—
78C2×C4×D13—22no—
79C2×C4×D13—22no—
80C2×C4×D13—41no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C8×C13—22no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4D812yes—
94C42×C13—41no—
95C42×C13—41no—
96C42×C13C22×C411yescharacteristic
97C42×C13C2×Q811yescharacteristic
98C42×C13#4111yescharacteristic
99C42×C13#4111yescharacteristic
100#6103—22no—
101#6103—22no—
102#6103—44no—
103#6103—82no—
104C4⋊Dic13—21no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107C4⋊Dic13—41no—
108C4⋊Dic13—41no—
109C4⋊Dic13—42no—
110C4⋊Dic13—42no—
111C4⋊Dic13—41no—
112C4⋊Dic13—41no—
113C4⋊Dic13—41no—
114C4⋊Dic13—41no—
115C4⋊Dic13C4⋊C412yes—
116C4×Dic13—44no—
117C2×#1055—22no—
118C2×#1055—41no—
119C2×#1055—41no—
120#2354—131no—
121#1947—131no—
122#1834—131no—
123#1802—131no—
124C2×D4⋊C8—131no—
125#1296—131no—
126#1279D1311yescharacteristic, complemented
127C23×C13#12011yescharacteristic
128C22×D13—22no—
129C22×D13—41no—
130C22×D13—41no—
131C22×D13—41no—
132C22×D13—41no—
133C22×D13—41no—
134C22×D13—41no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—22no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13C2×C4⋊C411yescharacteristic
144C2×C4×C13C4×D411yescharacteristic
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13C22⋊Q811yescharacteristic
147C2×C4×C13C22⋊Q811yescharacteristic
148C2×C4×C13#12311yescharacteristic
149C2×C4×C13C2×D811yescharacteristic
150C2×C4×C13#13511yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13#13511yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C13#13711yescharacteristic
156C2×C4×C13#13711yescharacteristic
157C2×Dic13—22no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—81no—
164C2×Dic13—81no—
165C2×Dic13—81no—
166D52—22no—
167D52—22no—
168D52—41no—
169D52—41no—
170C4×D13—42no—
171C4×D13—42no—
172C4×D13—42no—
173C4×D13—42no—
174C8×C13—42no—
175C8×C13—81no—
176#1055—42no—
177C2×C4×D4—131no—
178C2×#117—261no—
179C2×#107—261no—
180C2×C4⋊C8—131no—
181C2×C4⋊C8C2×D1311yescharacteristic
182C2×#102—261no—
183C2×C4×C8C2×D1311yescharacteristic
184#390—261no—
185#388—262no—
186#384—131no—
187#384—131no—
188#380—261no—
189C4×C4⋊C4—261no—
190C4×C4⋊C4C2×D1311yescharacteristic
191#340—261no—
192#340—262no—
193#340—261no—
194D4⋊C8—134no—
195C22×C13#38511yescharacteristic
196C22×C13#44711yescharacteristic
197C22×C13#44911yescharacteristic
198C22×C13#45211yescharacteristic
199C22×C13#45211yescharacteristic
200C22×C13#45411yescharacteristic
201C22×C13#45511yescharacteristic
202C2×D13—42no—
203C2×D13—42no—
204C2×D13—42no—
205C2×D13—81no—
206C2×D13—81no—
207C2×D13—81no—
208C2×D13—81no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—42no—
212C4×C13—81no—
213C4×C13#42711yescharacteristic
214C4×C13#42811yescharacteristic
215C4×C13C4×D811yescharacteristic
216C4×C13#44011yescharacteristic
217C4×C13#47411yescharacteristic
218C4×C13#47811yescharacteristic
219C4×C13#48211yescharacteristic
220C4×C13#48511yescharacteristic
221Dic13—42no—
222Dic13—82no—
223Dic13—161no—
224C22×D4—131no—
225C23×C4—261no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—261no—
229C4×D4—132no—
230C4×D4—132no—
231C4×D4—261no—
232C4×D4—261no—
233#117—522no—
234#117—522no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—132no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—261no—
240C2×C4⋊C4—261no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4D5211yescharacteristic
243C2×C4⋊C4D5211yescharacteristic
244C2×C22⋊C4—261no—
245C2×C22⋊C4—262no—
246C2×C22⋊C4—262no—
247C2×C42—21no—
248C2×C42—262no—
249C2×C42C22×D1311yescharacteristic
250#107—522no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—132no—
254C4⋊C8—261no—
255#102—522no—
256C4×C8—21no—
257C4×C8C4×D1312yes—
258#95—21no—
259#95—262no—
260C2×C13#162511yescharacteristic
261C2×C13#163811yescharacteristic
262C2×C13#164111yescharacteristic
263C2×C13#164611yescharacteristic
264C2×C13#185411yescharacteristic
265C2×C13#186011yescharacteristic
266C2×C13#186211yescharacteristic
267D13—82no—
268C24—261no—
269C2×D4—132no—
270C2×D4—261no—
271C2×D4—261no—
272C2×D4—261no—
273C2×D4—261no—
274C2×D4—261no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—261no—
278C22×C4—262no—
279C22×C4—262no—
280C22×C4—262no—
281C22×C4—521no—
282C22×C4—521no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4C2×D5211yescharacteristic
287C22×C4D4×D1311yescharacteristic
288C22×C4D4×D1311yescharacteristic
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—262no—
296C2×C8—521no—
297C2×C8—521no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—132no—
302C4⋊C4—261no—
303C4⋊C4—522no—
304C4⋊C4—522no—
305C4⋊C4—521no—
306C4⋊C4—521no—
307C4⋊C4—521no—
308C4⋊C4—521no—
309C4⋊C4—521no—
310C4⋊C4—521no—
311C4⋊C4—521no—
312C4⋊C4—521no—
313C4⋊C4D10412yes—
314C22⋊C4—262no—
315C22⋊C4—262no—
316C22⋊C4—524no—
317C22⋊C4—1042no—
318C42—41no—
319C42—41no—
320C42—524no—
321C42C2×C4×D1311yescharacteristic
322C42#612711yescharacteristic
323C42#612911yescharacteristic
324C42Q8×D1311yescharacteristic
325C13#889711yescharacteristic, complemented, Sylow
326C23—262no—
327C23—521no—
328C23—521no—
329C23—521no—
330C23—521no—
331C23—521no—
332C23—521no—
333C23#8813611yescharacteristic
334D4—262no—
335D4—262no—
336D4—521no—
337D4—521no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—262no—
347C2×C4—521no—
348C2×C4—521no—
349C2×C4—522no—
350C2×C4—522no—
351C2×C4—522no—
352C2×C4—522no—
353C2×C4—522no—
354C2×C4—522no—
355C2×C4—522no—
356C2×C4—1041no—
357C2×C4—1041no—
358C2×C4—1041no—
359C2×C4C4×D5211yescharacteristic
360C2×C4#8813511yescharacteristic
361C2×C4#8813711yescharacteristic
362C2×C4C4⋊C4×D1311yescharacteristic
363C2×C4#8815011yescharacteristic
364C2×C4#8815111yescharacteristic
365C2×C4C2×D10411yescharacteristic
366C2×C4#8815811yescharacteristic
367C2×C4#8816211yescharacteristic
368C2×C4#8816311yescharacteristic
369C2×C4#8816511yescharacteristic
370C2×C4#8817011yescharacteristic
371C2×C4#8817011yescharacteristic
372C2×C4#8817211yescharacteristic
373C8—42no—
374C8—81no—
375C8—522no—
376C22—522no—
377C22—522no—
378C22—522no—
379C22—1041no—
380C22—1041no—
381C22—1041no—
382C22—1041no—
383C22#1171832911yescharacteristic
384C22#1171839311yescharacteristic
385C22#1171839411yescharacteristic
386C22#1171844211yescharacteristic
387C22#1171847111yescharacteristic
388C22#1171848611yescharacteristic
389C22#1171848811yescharacteristic
390C4—21no—
391C4—21no—
392C4—42no—
393C4—81no—
394C4—522no—
395C4—1042no—
396C4—2081no—
397C4C4×D10411yescharacteristic
398C4#1171837111yescharacteristic
399C4#1171844011yescharacteristic
400C4#1171847611yescharacteristic
401C4#1171850711yescharacteristic
402C4#1171850811yescharacteristic
403C4#1171852111yescharacteristic
404C4#1171854211yescharacteristic
405C2—1042no—
406C2#1311392711yescharacteristic
407C2#1311401111yescharacteristic
408C2#1311403111yescharacteristic
409C2#1311406711yescharacteristic
410C2#1311503611yescharacteristic
411C2#1311507011yescharacteristic
412C2#1311508611yescharacteristic
subgroupG/H
centerC23#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13#120
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1279D13
hypocenterC13#8897
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #13115594C2semidirect
3. #13114964C2semidirect
6. #13112720C2semidirect
7. C13×#1279C2semidirect
25. #11718051C4semidirect
126. #1279D13semidirect
325. C13#8897semidirect

Maximal subgroups

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

subgroupindex
#131177832
#131155942
#131149642
#131148372
C2×#117180512
#131127202
C13×#12792
#889713