Finite Group Databasebeta

← #15844245

Subgroups — #15844245

Order 3328.

938 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125839C212yesmaximal, complemented
2#13125385C211yesmaximal, characteristic, complemented
3#13114153C218yesmaximal, complemented
4#13113463C211yesmaximal, characteristic, complemented
5#13113434C212yesmaximal, complemented
6C2×C13×#562C211yesmaximal, characteristic
7C13×#562—22no—
8C13×#562—24no—
9C13×#562C2214yes—
10C2×C13×#125C2211yescharacteristic
11C2×C13×#124C2212yes—
12C2×C13×#123—22no—
13C2×C13×C22⋊Q8—22no—
14C2×C13×#121—22no—
15#11719175C2211yescharacteristic
16#11718889—22no—
17#11718879—22no—
18#11718726C2214yescomplemented
19#11718725—22no—
20#11718721C2214yescomplemented
21#11718716C2214yescomplemented
22#11718715—24no—
23#11718625—22no—
24#11718587C2212yes—
25C4×#6099C2211yescharacteristic
26#11718135C2214yescomplemented
27#11718132C2218yescomplemented
28C22×Q8×C13D412yes—
29C22×D4×C13—22no—
30C22×D4×C13D412yes—
31C23×C4×C13—22no—
32C13×#125—22no—
33C13×#125D412yes—
34C13×#125C2312yes—
35C13×#124—22no—
36C13×#124—22no—
37C13×#124D414yes—
38C13×#124C2314yes—
39C13×#123—28no—
40C13×#123—28no—
41C13×C22⋊Q8—28no—
42C13×C22⋊Q8—28no—
43C13×#121—28no—
44C13×#121—28no—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4—22no—
47C2×C13×C4⋊C4D412yes—
48C2×C13×C22⋊C4—22no—
49C2×C13×C22⋊C4—22no—
50C2×C13×C22⋊C4—22no—
51C2×C42×C13C2311yescharacteristic
52C2×#6107—24no—
53C2×#6105—24no—
54#88180—21no—
55#88178—22no—
56C2×#6099—21no—
57#88124—21no—
58#88123C2312yes—
59C4×Dic26—22no—
60#88075—24no—
61#88072—24no—
62C22⋊#1055—22no—
63#88048—24no—
64#88047—24no—
65C4⋊#1055—22no—
66#88043C2314yes—
67#88043C2312yes—
68C4×#1055—21no—
69#19006—131nomaximal, Sylow
70C24×C13—22no—
71C2×Q8×C13—22no—
72C2×Q8×C13—82no—
73C2×Q8×C13C2×D414yes—
74C2×D4×C13—28no—
75C2×D4×C13—22no—
76C2×D4×C13—82no—
77C2×D4×C13—84no—
78C2×D4×C13C2×D414yes—
79C22×C4×C13—22no—
80C22×C4×C13—22no—
81C22×C4×C13—28no—
82C22×C4×C13—84no—
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D412yes—
85C2×Dic26—22no—
86C13×C4⋊C4—28no—
87C13×C4⋊C4—24no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—24no—
90C13×C4⋊C4C2×D414yes—
91C13×C22⋊C4—28no—
92C13×C22⋊C4—24no—
93C13×C22⋊C4—24no—
94C13×C22⋊C4—24no—
95C13×C22⋊C4—24no—
96C42×C13C2×D412yes—
97C42×C13C2×D411yescharacteristic
98C42×C13C2411yescharacteristic
99C22⋊Dic13—41no—
100#6107—84no—
101#6105—84no—
102C4⋊Dic13—22no—
103C4⋊Dic13—22no—
104#6101—42no—
105C4×Dic13—41no—
106#6099—24no—
107C2×#1055—22no—
108C2×#1055—24no—
109C2×#562D1311yescharacteristic
110#3215—132no—
111#3166—131no—
112#1661—138no—
113#1534—131no—
114#1527—132no—
115C23×C13—24no—
116C23×C13—44no—
117C23×C13—44no—
118C23×C13—44no—
119C23×C13#12011yescharacteristic
120Q8×C13—44no—
121Q8×C13—82no—
122D4×C13—44no—
123D4×C13—82no—
124D4×C13—88no—
125C2×C4×C13—22no—
126C2×C4×C13—24no—
127C2×C4×C13—24no—
128C2×C4×C13—42no—
129C2×C4×C13—44no—
130C2×C4×C13—44no—
131C2×C4×C13—88no—
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12012yes—
134C2×C4×C13C22×D411yescharacteristic
135C2×C4×C13C22×D412yes—
136C2×Dic13—42no—
137Dic26—44no—
138#1055—24no—
139#1055—44no—
140#562—22no—
141#562—24no—
142#562C2×D1314yes—
143#533—131no—
144C2×#125C2×D1311yescharacteristic
145C2×#124C2×D1312yes—
146C2×#123—22no—
147C2×C22⋊Q8—22no—
148C2×#121—22no—
149#501—134no—
150#499—262no—
151#497—134no—
152#489—134no—
153#464—264no—
154#451—262no—
155#450—262no—
156#432—132no—
157#428—262no—
158C4×M16—131no—
159#330—134no—
160#329—138no—
161C22×C13—22no—
162C22×C13—44no—
163C22×C13—44no—
164C22×C13—44no—
165C22×C13—88no—
166C22×C13#45612yes—
167C22×C13C2×#12011yescharacteristic
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—44no—
173C4×C13—44no—
174Dic13—82no—
175C22×Q8C22⋊D1312yes—
176C22×D4—22no—
177C22×D4C22⋊D1312yes—
178C23×C4—22no—
179C2×Q16—264no—
180C2×SD16—264no—
181C2×M16—261no—
182C4⋊Q8—132no—
183#125—22no—
184#125—261no—
185#125C22⋊D1312yes—
186#125C22×D1312yes—
187#124—22no—
188#124—22no—
189#124C22⋊D1314yes—
190#124C22×D1314yes—
191#123—28no—
192#123—28no—
193C22⋊Q8—28no—
194C22⋊Q8—28no—
195C22⋊Q8—262no—
196#121—28no—
197#121—28no—
198C4×Q8—262no—
199#117—261no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4C22⋊D1312yes—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C42C22×D1311yescharacteristic
207#107—264no—
208#106—264no—
209C4⋊C8—262no—
210#103—264no—
211#102—264no—
212C22⋊C8—262no—
213#97—132no—
214#97—134no—
215C4×C8—261no—
216C2×C13—22no—
217C2×C13—84no—
218C2×C13C2×#45611yescharacteristic
219C2×C13#301912yes—
220C24—22no—
221C2×Q8—22no—
222C2×Q8—82no—
223C2×Q8—262no—
224C2×Q8C2×C22⋊D1314yes—
225C2×D4—28no—
226C2×D4—22no—
227C2×D4—82no—
228C2×D4—84no—
229C2×D4C2×C22⋊D1314yes—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—28no—
233C22×C4—84no—
234C22×C4C2×C22⋊D1311yescharacteristic
235C22×C4C2×C22⋊D1312yes—
236Q16—1044no—
237SD16—1044no—
238M16—264no—
239C2×C8—262no—
240C2×C8—264no—
241C4⋊C4—28no—
242C4⋊C4—24no—
243C4⋊C4—22no—
244C4⋊C4—24no—
245C4⋊C4—262no—
246C4⋊C4—262no—
247C4⋊C4—522no—
248C4⋊C4C2×C22⋊D1314yes—
249C22⋊C4—28no—
250C22⋊C4—24no—
251C22⋊C4—24no—
252C22⋊C4—24no—
253C22⋊C4—24no—
254C22⋊C4—521no—
255C42—521no—
256C42C2×C22⋊D1311yescharacteristic
257C42C2×C22⋊D1312yes—
258C42C23×D1311yescharacteristic
259C13#1900611yescharacteristic, complemented, Sylow
260C23—24no—
261C23—44no—
262C23—44no—
263C23—44no—
264C23#8820711yescharacteristic
265Q8—44no—
266Q8—82no—
267Q8—524no—
268D4—44no—
269D4—82no—
270D4—88no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—42no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—88no—
278C2×C4—522no—
279C2×C4#8820711yescharacteristic
280C2×C4#8820712yes—
281C2×C4C22×C22⋊D1311yescharacteristic
282C2×C4C22×C22⋊D1312yes—
283C8—264no—
284C8—524no—
285C22—22no—
286C22—44no—
287C22—44no—
288C22—44no—
289C22—88no—
290C22#1171890712yes—
291C22C2×#8820711yescharacteristic
292C4—21no—
293C4—21no—
294C4—22no—
295C4—22no—
296C4—44no—
297C4—44no—
298C4—1042no—
299C2—22no—
300C2—84no—
301C2C2×#1171890711yescharacteristic
302C2#1312419312yes—
subgroupG/H
centerC22C2×#88207
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC2×C13×#562C2
socleC22×C13C2×#120
hypercenterC2×#562D13
hypocenterC13#19006
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #13125839C2semidirect
2. #13125385C2semidirect
3. #13114153C2semidirect
4. #13113463C2semidirect
5. #13113434C2semidirect
18. #11718726C22semidirect
20. #11718721C22semidirect
21. #11718716C22semidirect
26. #11718135C22semidirect
27. #11718132C22semidirect
259. C13#19006semidirect

Maximal subgroups

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

subgroupindex
#131258392
#131253852
#131141532
#131134632
#131134342
C2×C13×#5622
#1900613