Finite Group Databasebeta

← #15758659

Subgroups — #15758659

Order 3328.

800 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123167C211yesmaximal, characteristic
2#13114904C211yesmaximal, characteristic, complemented
3C2×#11718043C212yesmaximal
4#13112715C212yesmaximal, complemented
5C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4—21no—
7C22×C42×C13—21no—
8C22×C42×C13C2211yescharacteristic
9C2×#88184C2211yescharacteristic
10C2×#88183—21no—
11C4×C13×C4⋊C4—24no—
12C2×C13×#95C2212yes—
13#11718874—21no—
14#11718873C2211yescharacteristic
15C2×C22⋊#1055C2212yes—
16#11718601—22no—
17#11718600C412yescomplemented
18#11718589C412yescomplemented
19#11718116—22no—
20#11718043—24no—
21C23×C4×C13—22no—
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C22×C22⋊D13—21no—
26C22×D52C2×C411yescharacteristic
27C2×C13×C4⋊C4—24no—
28C2×C13×C4⋊C4—28no—
29C2×C42×C13—22no—
30C2×C42×C13—22no—
31C2×C42×C13—24no—
32C2×C42×C13—42no—
33C2×C42×C13—42no—
34C2×C42×C13C2×C412yes—
35C2×C42×C13D412yes—
36C2×C22⋊Dic13—21no—
37#88184—22no—
38#88184—22no—
39#88183—42no—
40#88183—42no—
41C2×#6103—22no—
42C2×#6103—22no—
43C2×#6103—21no—
44C2×C4⋊Dic13C2×C411yescharacteristic
45C2×C4⋊Dic13C2×C412yes—
46C2×#6101—22no—
47C22×#1055—22no—
48C13×#95—22no—
49C13×#95D414yes—
50#88071—22no—
51#88071—21no—
52C22⋊#1055—22no—
53C22⋊#1055—22no—
54#9148—131nomaximal, Sylow
55C24×C13C2×D411yescharacteristic
56C23×D13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—24no—
64C22×C4×C13—28no—
65C22×C4×C13—24no—
66C22×C4×C13—42no—
67C22×C4×C13—44no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13C22⋊C412yes—
71C22×C4×C13C22⋊C412yes—
72C22×C4×C13D812yes—
73C22×C4×C13SD1612yes—
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D412yes—
77C22×C4×C13#4112yes—
78C2×C22⋊D13—41no—
79C2×C22⋊D13—41no—
80C2×C22⋊D13—41no—
81C2×C22⋊D13—41no—
82C2×C22⋊D13—41no—
83C2×C22⋊D13—41no—
84C22×Dic13—21no—
85C22×Dic13—22no—
86C2×D52—22no—
87C2×D52—42no—
88C13×C4⋊C4—216no—
89C42×C13—24no—
90C42×C13—24no—
91C42×C13—48no—
92C22⋊Dic13—41no—
93C22⋊Dic13—41no—
94#6103—44no—
95#6103—44no—
96#6103—42no—
97C4⋊Dic13—22no—
98C4⋊Dic13—42no—
99#6101—44no—
100C2×#1055—44no—
101C2×#1055—42no—
102#2854—131no—
103C2×C4×C4⋊C4D1311yescharacteristic, complemented
104#1817—131no—
105C2×#327—132no—
106#1294—132no—
107C23×C13—22no—
108C23×C13—22no—
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13#12011yescharacteristic
111C23×C13#12311yescharacteristic
112C23×C13C2×D811yescharacteristic
113C23×C13C2×SD1611yescharacteristic
114C23×C13AGL(1,ℤ/8)11yescharacteristic
115C23×C13#13711yescharacteristic
116C22×D13—41no—
117C22×D13—42no—
118C22×D13—41no—
119C22×D13—41no—
120C22×D13—42no—
121C2×C4×C13—24no—
122C2×C4×C13—24no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—28no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—44no—
137C2×C4×C13—48no—
138C2×C4×C13—48no—
139C2×C4×C13—44no—
140C2×C4×C13#10214yes—
141C2×C4×C13#10414yes—
142C2×C4×C13C4×D412yes—
143C2×C4×C13#12112yes—
144C22⋊D13—81no—
145C22⋊D13—81no—
146C22⋊D13—81no—
147C22⋊D13—81no—
148C2×Dic13—41no—
149C2×Dic13—42no—
150C2×Dic13—41no—
151C2×Dic13—42no—
152C2×Dic13—41no—
153C2×Dic13—42no—
154D52—82no—
155#1055—82no—
156C2×#123—261no—
157C2×#121—131no—
158C22×C4⋊C4—21no—
159C22×C42—21no—
160C22×C42C2×D1311yescharacteristic
161C2×C22⋊C8—132no—
162#390—132no—
163#389—132no—
164#388—262no—
165#386—261no—
166#380—131no—
167C4×C4⋊C4—24no—
168C2×#95C2×D1312yes—
169#336—262no—
170#327—264no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13#38611yescharacteristic
180C22×C13#41012yes—
181C22×C13C2×#10211yescharacteristic
182C22×C13#41711yescharacteristic
183C22×C13C2×#10412yes—
184C22×C13#44711yescharacteristic
185C22×C13#44811yescharacteristic
186C22×C13#48011yescharacteristic
187C22×C13#48111yescharacteristic
188C2×D13—81no—
189C2×D13—81no—
190C2×D13—81no—
191C2×D13—82no—
192C2×D13—82no—
193C4×C13—24no—
194C4×C13—24no—
195C4×C13—22no—
196C4×C13—22no—
197C4×C13—48no—
198Dic13—81no—
199Dic13—82no—
200C22×D4—131no—
201C22×D4—261no—
202C23×C4—22no—
203C23×C4C22⋊D1311yescharacteristic
204C23×C4C22⋊D1311yescharacteristic
205C23×C4C22×D1311yescharacteristic
206C22×C8—262no—
207#123—522no—
208#123—522no—
209#121—262no—
210#121—262no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—28no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—132no—
215C2×C4⋊C4—262no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4—262no—
218C2×C22⋊C4—262no—
219C2×C22⋊C4—261no—
220C2×C42—22no—
221C2×C42—22no—
222C2×C42—24no—
223C2×C42—42no—
224C2×C42—42no—
225C2×C42C4×D1312yes—
226C2×C42D5212yes—
227C22⋊C8—262no—
228C22⋊C8—262no—
229#95—22no—
230#95—262no—
231#95—261no—
232#95C22⋊D1314yes—
233C2×C13—21no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13#150212yes—
238C2×C13#150912yes—
239C2×C13#187411yescharacteristic
240C2×C13#189611yescharacteristic
241C2×C13#189911yescharacteristic
242D13—161no—
243C24—261no—
244C24C2×C22⋊D1311yescharacteristic
245C2×D4—262no—
246C2×D4—522no—
247C2×D4—521no—
248C2×D4—521no—
249C2×D4—521no—
250C2×D4—521no—
251C2×D4—521no—
252C2×D4—521no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—24no—
260C22×C4—28no—
261C22×C4—24no—
262C22×C4—42no—
263C22×C4—44no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—262no—
267C22×C4—261no—
268C22×C4#610312yes—
269C22×C4#610312yes—
270C22×C4#610412yes—
271C22×C4#610612yes—
272C22×C4C2×C4×D1311yescharacteristic
273C22×C4C2×D5211yescharacteristic
274C22×C4#612712yes—
275C22×C4C2×C22⋊D1312yes—
276C2×C8—524no—
277C2×C8—522no—
278C4⋊C4—216no—
279C4⋊C4—262no—
280C4⋊C4—522no—
281C4⋊C4—524no—
282C22⋊C4—521no—
283C22⋊C4—521no—
284C22⋊C4—522no—
285C22⋊C4—524no—
286C22⋊C4—524no—
287C42—24no—
288C42—24no—
289C42—48no—
290C13#914811yescharacteristic, complemented, Sylow
291C23—22no—
292C23—22no—
293C23—522no—
294C23—522no—
295C23—521no—
296C23—521no—
297C23—521no—
298C23C2×#610311yescharacteristic
299C23#8818311yescharacteristic
300C23C2×#610411yescharacteristic
301C23#8818611yescharacteristic
302C23C2×#610611yescharacteristic
303C23#8819611yescharacteristic
304C23#8820711yescharacteristic
305D4—1042no—
306D4—1041no—
307D4—1041no—
308D4—1041no—
309D4—1041no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—28no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—48no—
326C2×C4—44no—
327C2×C4—48no—
328C2×C4—44no—
329C2×C4—522no—
330C2×C4—522no—
331C2×C4—521no—
332C2×C4—522no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4#8804514yes—
336C2×C4#8804914yes—
337C2×C4C4×C22⋊D1312yes—
338C2×C4#8818412yes—
339C8—1042no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—1042no—
349C22—1041no—
350C22—1041no—
351C22—1041no—
352C22—1042no—
353C22C2×#8804512yes—
354C22C2×#8804911yescharacteristic
355C22#1171862711yescharacteristic
356C22#1171862811yescharacteristic
357C22#1171862911yescharacteristic
358C22#1171866712yes—
359C22#1171887411yescharacteristic
360C22#1171887811yescharacteristic
361C22#1171888811yescharacteristic
362C4—24no—
363C4—24no—
364C4—22no—
365C4—22no—
366C4—48no—
367C4—1041no—
368C4—1042no—
369C2—21no—
370C2—21no—
371C2—21no—
372C2—21no—
373C2—2081no—
374C2#1311333012yes—
375C2#1311335912yes—
376C2#1311515311yescharacteristic
377C2#1311527911yescharacteristic
378C2#1311529411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C4×C13×C4⋊C4C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#9148
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13114904C2semidirect
4. #13112715C2semidirect
5. C2×C4×C13×C4⋊C4C2semidirect
17. #11718600C4semidirect
18. #11718589C4semidirect
103. C2×C4×C4⋊C4D13semidirect
290. C13#9148semidirect

Maximal subgroups

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

subgroupindex
#131231672
#131149042
C2×#117180432
#131127152
C2×C4×C13×C4⋊C42
#914813