Finite Group Databasebeta

← #15757099

Subgroups — #15757099

Order 3328.

546 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117783C211yesmaximal, characteristic
2#13114995C211yesmaximal, characteristic, complemented
3#13114833C211yesmaximal, characteristic
4C2×#11718075C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic, complemented
6#13112677C211yesmaximal, characteristic, complemented
7C13×#1948C211yesmaximal, characteristic, complemented
8C2×#88146—21no—
9C2×C4×D52C2211yescharacteristic
10C2×C13×#106—21no—
11C2×C13×C4⋊C8C2211yescharacteristic
12C13×#384C2211yescharacteristic
13C4×C13×C4⋊C4C2211yescharacteristic
14#11718648—21no—
15C2×#88049—21no—
16C2×#88047—22no—
17#11718600—21no—
18#11718596C2211yescharacteristic
19C4×C4⋊Dic13—21no—
20C2×C4⋊#1055C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718331—22no—
23C13×#340—21no—
24#11718121—21no—
25#11718075C414yescomplemented
26C22×D52D411yescharacteristic
27C22×C4×D13—21no—
28C22×C8×C13—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C42×C13—21no—
35C2×C42×C13C2311yescharacteristic
36C2×#6103—21no—
37C2×#6103—22no—
38C2×#6103—22no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13D411yescharacteristic
42C2×C4⋊Dic13D412yes—
43C2×C4×Dic13—22no—
44C22×#1055—21no—
45C22×#1055—21no—
46#88146—42no—
47#88146—42no—
48C4×D52—21no—
49C4×D52—21no—
50C4×D52C2×C412yes—
51C4×D52Q812yes—
52C13×#106—42no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8C2×C412yes—
55C13×#95—21no—
56#88071—22no—
57#88049—42no—
58#88047—44no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4×#1055—21no—
62C4×#1055C2×C412yes—
63#8885—131nomaximal, Sylow
64C23×D13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—41no—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—22no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52C4⋊C412yes—
79C2×C4×D13—22no—
80C2×C4×D13—22no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C8×C13—22no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4D812yes—
97C42×C13—41no—
98C42×C13—41no—
99C42×C13C22×C411yescharacteristic
100C42×C13C2×Q811yescharacteristic
101C42×C13#4111yescharacteristic
102C42×C13#4111yescharacteristic
103#6103—22no—
104#6103—22no—
105#6103—44no—
106#6103—82no—
107C4⋊Dic13—21no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4⋊Dic13—42no—
113C4⋊Dic13C4⋊C412yes—
114C4×Dic13—44no—
115C2×#1055—22no—
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#1055—41no—
121#2354—131no—
122#1948D1311yescharacteristic, complemented
123#1845—131no—
124#1802—131no—
125C2×D4⋊C8—131no—
126#1296—131no—
127#1279—131no—
128C23×C13#12011yescharacteristic
129C22×D13—22no—
130C22×D13—41no—
131C22×D13—41no—
132C22×D13—41no—
133C22×D13—41no—
134C22×D13—41no—
135C22×D13—41no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—22no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13C2×C4⋊C411yescharacteristic
148C2×C4×C13C4×D411yescharacteristic
149C2×C4×C13C4×D411yescharacteristic
150C2×C4×C13C22⋊Q811yescharacteristic
151C2×C4×C13C22⋊Q811yescharacteristic
152C2×C4×C13#12311yescharacteristic
153C2×C4×C13C2×D811yescharacteristic
154C2×C4×C13#13511yescharacteristic
155C2×C4×C13#13511yescharacteristic
156C2×C4×C13#13511yescharacteristic
157C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C13#13711yescharacteristic
160C2×C4×C13#13711yescharacteristic
161C2×Dic13—22no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—42no—
165C2×Dic13—42no—
166C2×Dic13—42no—
167D52—22no—
168D52—22no—
169D52—41no—
170D52—41no—
171C4×D13—42no—
172C4×D13—42no—
173C4×D13—42no—
174C4×D13—42no—
175C8×C13—42no—
176#1055—24no—
177#1055—81no—
178C2×C4×D4—131no—
179C2×#117—261no—
180C2×#107—262no—
181C2×#106—21no—
182C2×C4⋊C8—131no—
183C2×C4⋊C8C2×D1311yescharacteristic
184C2×#102—261no—
185C2×C4×C8—131no—
186#390—261no—
187#388—262no—
188#384—131no—
189#384C2×D1311yescharacteristic
190#380—261no—
191C4×C4⋊C4—261no—
192C4×C4⋊C4C2×D1311yescharacteristic
193#340—21no—
194#340—261no—
195D4⋊C8—134no—
196C22×C13#38511yescharacteristic
197C22×C13#44711yescharacteristic
198C22×C13#44911yescharacteristic
199C22×C13#45211yescharacteristic
200C22×C13#45211yescharacteristic
201C22×C13#45311yescharacteristic
202C22×C13#45611yescharacteristic
203C2×D13—42no—
204C2×D13—42no—
205C2×D13—42no—
206C2×D13—81no—
207C2×D13—81no—
208C2×D13—81no—
209C2×D13—81no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—42no—
213C4×C13—81no—
214C4×C13—161no—
215C4×C13#42711yescharacteristic
216C4×C13#42811yescharacteristic
217C4×C13C4×D811yescharacteristic
218C4×C13#44011yescharacteristic
219C4×C13#47411yescharacteristic
220C4×C13#47811yescharacteristic
221C4×C13#48211yescharacteristic
222C4×C13#48511yescharacteristic
223Dic13—42no—
224Dic13—82no—
225C22×D4—131no—
226C23×C4—261no—
227C22×C8—21no—
228C22×C8—261no—
229C22×C8—261no—
230C4×D4—132no—
231C4×D4—132no—
232C4×D4—261no—
233C4×D4—261no—
234#117—522no—
235#117—522no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—131no—
240C2×C4⋊C4—132no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4C22⋊D1311yescharacteristic
244C2×C4⋊C4C22⋊D1311yescharacteristic
245C2×C22⋊C4—261no—
246C2×C22⋊C4—262no—
247C2×C22⋊C4—262no—
248C2×C42—21no—
249C2×C42—262no—
250C2×C42C22×D1311yescharacteristic
251#107—524no—
252#106—42no—
253C4⋊C8—21no—
254C4⋊C8—261no—
255C4⋊C8—261no—
256C4⋊C8C4×D1312yes—
257#102—522no—
258C4×C8—132no—
259C4×C8—261no—
260#95—21no—
261#95—262no—
262C2×C13#162111yescharacteristic
263C2×C13#163411yescharacteristic
264C2×C13#164711yescharacteristic
265C2×C13#165011yescharacteristic
266C2×C13#185411yescharacteristic
267C2×C13#185911yescharacteristic
268C2×C13#186211yescharacteristic
269D13—82no—
270C24—261no—
271C2×D4—132no—
272C2×D4—261no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—261no—
276C2×D4—261no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—261no—
281C22×C4—262no—
282C22×C4—262no—
283C22×C4—262no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4—521no—
287C22×C4—521no—
288C22×C4D4×D1311yescharacteristic
289C22×C4D4×D1311yescharacteristic
290C22×C4C2×C22⋊D1311yescharacteristic
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—262no—
295C2×C8—262no—
296C2×C8—262no—
297C2×C8—521no—
298C2×C8—521no—
299C2×C8—521no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—42no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—132no—
309C4⋊C4—261no—
310C4⋊C4—522no—
311C4⋊C4—521no—
312C4⋊C4—521no—
313C4⋊C4—521no—
314C4⋊C4—521no—
315C4⋊C4#610412yes—
316C22⋊C4—262no—
317C22⋊C4—262no—
318C22⋊C4—524no—
319C22⋊C4—1042no—
320C42—41no—
321C42—41no—
322C42—524no—
323C42C2×C4×D1311yescharacteristic
324C42#612711yescharacteristic
325C42Q8×D1311yescharacteristic
326C42#613111yescharacteristic
327C13#888511yescharacteristic, complemented, Sylow
328C23—262no—
329C23—521no—
330C23—521no—
331C23—521no—
332C23—521no—
333C23—521no—
334C23—521no—
335C23#8819111yescharacteristic
336D4—262no—
337D4—262no—
338D4—521no—
339D4—521no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—262no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—522no—
355C2×C4—522no—
356C2×C4—522no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—522no—
360C2×C4—522no—
361C2×C4C4⋊C4×D1311yescharacteristic
362C2×C4#8814711yescharacteristic
363C2×C4#8814811yescharacteristic
364C2×C4#8815011yescharacteristic
365C2×C4#8816811yescharacteristic
366C2×C4#8816911yescharacteristic
367C2×C4#8817011yescharacteristic
368C2×C4#8817011yescharacteristic
369C2×C4C4×C22⋊D1311yescharacteristic
370C2×C4C2×#610411yescharacteristic
371C2×C4#8819611yescharacteristic
372C2×C4#8820011yescharacteristic
373C2×C4#8820311yescharacteristic
374C2×C4#8820411yescharacteristic
375C8—42no—
376C8—264no—
377C8—1041no—
378C22—522no—
379C22—522no—
380C22—522no—
381C22—1041no—
382C22—1041no—
383C22—1041no—
384C22—1041no—
385C22#1171865011yescharacteristic
386C22#1171869711yescharacteristic
387C22#1171870811yescharacteristic
388C22#1171883311yescharacteristic
389C22#1171883411yescharacteristic
390C22#1171885911yescharacteristic
391C22#1171886611yescharacteristic
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—161no—
397C4—522no—
398C4—1042no—
399C4#1171852111yescharacteristic
400C4#1171852211yescharacteristic
401C4#1171852711yescharacteristic
402C4#1171852811yescharacteristic
403C4C4×#610411yescharacteristic
404C4#1171868711yescharacteristic
405C4#1171872711yescharacteristic
406C4#1171874811yescharacteristic
407C2—1042no—
408C2#1311389911yescharacteristic
409C2#1311398011yescharacteristic
410C2#1311406911yescharacteristic
411C2#1311409111yescharacteristic
412C2#1311503411yescharacteristic
413C2#1311505911yescharacteristic
414C2#1311508211yescharacteristic
subgroupG/H
centerC23#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1948C2
socleC23×C13#120
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1948D13
hypocenterC13#8885
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. #13114995C2semidirect
5. #13112720C2semidirect
6. #13112677C2semidirect
7. C13×#1948C2semidirect
25. #11718075C4semidirect
122. #1948D13semidirect
327. C13#8885semidirect

Maximal subgroups

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

subgroupindex
#131177832
#131149952
#131148332
C2×#117180752
#131127202
#131126772
C13×#19482
#888513