Finite Group Databasebeta

← #15757185

Subgroups — #15757185

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#13117787C211yesmaximal, characteristic
2#13115595C211yesmaximal, characteristic, complemented
3#13114963C211yesmaximal, characteristic, complemented
4#13114837C211yesmaximal, characteristic
5C2×#11718075C211yesmaximal, characteristic
6#13112675C211yesmaximal, characteristic, complemented
7C13×#1296C211yesmaximal, characteristic, complemented
8C2×#88146—21no—
9C2×C4×D52C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C13×#384C2211yescharacteristic
13C2×#88061—21no—
14C2×#88058—21no—
15#11718651—22no—
16#11718649—21no—
17#11718648—21no—
18C4⋊C4×Dic13—21no—
19#11718596C2211yescharacteristic
20C4×C4⋊Dic13C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718143—21no—
23#11718143—21no—
24#11718121—22no—
25#11718075C414yescomplemented
26C22×D52D411yescharacteristic
27C22×C4×D13—21no—
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D412yes—
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⋊Dic13D411yescharacteristic
41C2×C4⋊Dic13D411yescharacteristic
42C2×C4⋊Dic13D411yescharacteristic
43C2×C4×Dic13—22no—
44C2×C4×Dic13—21no—
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—
54C13×C4⋊C8—21no—
55C13×C4⋊C8C2×C412yes—
56#88071—22no—
57#88071—21no—
58#88061—42no—
59#88058—42no—
60C4×#1055—21no—
61C4×#1055C2×C412yes—
62#8897—131nomaximal, Sylow
63C23×D13—21no—
64C22×C4×C13—22no—
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
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—42no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C42×C13C22×C411yescharacteristic
96C42×C13C2×Q811yescharacteristic
97C42×C13#4111yescharacteristic
98C42×C13#4111yescharacteristic
99#6103—22no—
100#6103—22no—
101#6103—44no—
102#6103—82no—
103C4⋊Dic13—21no—
104C4⋊Dic13—21no—
105C4⋊Dic13—21no—
106C4⋊Dic13—21no—
107C4⋊Dic13—42no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4⋊Dic13C4⋊C412yes—
113C4⋊Dic13D812yes—
114C4×Dic13—44no—
115C4×Dic13—41no—
116C4×Dic13—41no—
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#1296D1311yescharacteristic, complemented
126#1279—131no—
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—42no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13C2×C4⋊C411yescharacteristic
141C2×C4×C13C4×D411yescharacteristic
142C2×C4×C13C4×D411yescharacteristic
143C2×C4×C13C22⋊Q811yescharacteristic
144C2×C4×C13C22⋊Q811yescharacteristic
145C2×C4×C13#12311yescharacteristic
146C2×C4×C13C2×D811yescharacteristic
147C2×C4×C13#13511yescharacteristic
148C2×C4×C13#13511yescharacteristic
149C2×C4×C13#13511yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C13#13711yescharacteristic
153C2×C4×C13#13711yescharacteristic
154C2×Dic13—22no—
155C2×Dic13—22no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
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⋊C8C2×D1311yescharacteristic
181C2×C4⋊C8C2×D1311yescharacteristic
182C2×#102—261no—
183C2×C4×C8—131no—
184#390—261no—
185#388—262no—
186#384—131no—
187#384C2×D1311yescharacteristic
188#380—261no—
189C4×C4⋊C4—131no—
190C4×C4⋊C4—261no—
191#340—261no—
192#340—261no—
193#340—262no—
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—82no—
212C4×C13#42711yescharacteristic
213C4×C13#42811yescharacteristic
214C4×C13C4×D811yescharacteristic
215C4×C13#44011yescharacteristic
216C4×C13#47411yescharacteristic
217C4×C13#47811yescharacteristic
218C4×C13#48211yescharacteristic
219C4×C13#48511yescharacteristic
220Dic13—42no—
221Dic13—42no—
222Dic13—81no—
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—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—131no—
238C2×C4⋊C4—131no—
239C2×C4⋊C4—131no—
240C2×C4⋊C4—261no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4D5212yes—
244C2×C22⋊C4—261no—
245C2×C22⋊C4—262no—
246C2×C22⋊C4—262no—
247C2×C42—262no—
248C2×C42—261no—
249C2×C42C22×D1311yescharacteristic
250#107—522no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8C4×D1312yes—
255#102—522no—
256C4×C8—132no—
257C4×C8—261no—
258#95—262no—
259#95—261no—
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—22no—
276C22×C4—261no—
277C22×C4—261no—
278C22×C4—262no—
279C22×C4—262no—
280C22×C4—261no—
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—42no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—132no—
304C4⋊C4—132no—
305C4⋊C4—261no—
306C4⋊C4—261no—
307C4⋊C4—261no—
308C4⋊C4—261no—
309C4⋊C4—522no—
310C4⋊C4—521no—
311C4⋊C4—521no—
312C4⋊C4—521no—
313C4⋊C4—521no—
314C22⋊C4—262no—
315C22⋊C4—262no—
316C22⋊C4—524no—
317C22⋊C4—1042no—
318C42—524no—
319C42—521no—
320C42—521no—
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—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—262no—
344C2×C4—262no—
345C2×C4—521no—
346C2×C4—521no—
347C2×C4—521no—
348C2×C4—521no—
349C2×C4—522no—
350C2×C4—522no—
351C2×C4—522no—
352C2×C4—522no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
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×C4D8×D1311yescharacteristic
366C2×C4#8816611yescharacteristic
367C2×C4#8816811yescharacteristic
368C2×C4#8816811yescharacteristic
369C2×C4#8816911yescharacteristic
370C2×C4#8817011yescharacteristic
371C2×C4#8817211yescharacteristic
372C2×C4#8817311yescharacteristic
373C8—42no—
374C8—81no—
375C8—522no—
376C22—522no—
377C22—522no—
378C22—522no—
379C22—1041no—
380C22—1041no—
381C22—1041no—
382C22—1041no—
383C22#1171832911yescharacteristic
384C22#1171840711yescharacteristic
385C22#1171841411yescharacteristic
386C22#1171843411yescharacteristic
387C22#1171844411yescharacteristic
388C22#1171847111yescharacteristic
389C22#1171847211yescharacteristic
390C4—21no—
391C4—21no—
392C4—82no—
393C4—522no—
394C4—522no—
395C4—1041no—
396C4—2081no—
397C4#1171841711yescharacteristic
398C4#1171844511yescharacteristic
399C4#1171847511yescharacteristic
400C4#1171847811yescharacteristic
401C4#1171852211yescharacteristic
402C4#1171853211yescharacteristic
403C4#1171854111yescharacteristic
404C4#1171855111yescharacteristic
405C2—1042no—
406C2#1311392611yescharacteristic
407C2#1311400911yescharacteristic
408C2#1311403011yescharacteristic
409C2#1311406511yescharacteristic
410C2#1311503811yescharacteristic
411C2#1311507211yescharacteristic
412C2#1311508411yescharacteristic
subgroupG/H
centerC23#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socleC23×C13#120
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1296D13
hypocenterC13#8897
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #13115595C2semidirect
3. #13114963C2semidirect
6. #13112675C2semidirect
7. C13×#1296C2semidirect
25. #11718075C4semidirect
125. #1296D13semidirect
325. C13#8897semidirect

Maximal subgroups

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

subgroupindex
#131177872
#131155952
#131149632
#131148372
C2×#117180752
#131126752
C13×#12962
#889713