Finite Group Databasebeta

← #15755082

Subgroups — #15755082

Order 3328.

658 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 143 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#13115777C211yesmaximal, characteristic
2#13113536C212yesmaximal
3#13113451C212yesmaximal
4#13113180C211yesmaximal, characteristic
5C13×#3502C211yesmaximal, characteristic
6Q82×C13—22no—
7C13×#557—22no—
8C13×#557—24no—
9C13×#544—22no—
10C13×#544C412yes—
11C13×#533—22no—
12C13×#533C2212yes—
13C13×#519C412yes—
14C2×C4×Q8×C13C2211yescharacteristic
15#11718587C2212yes—
16C2×C4⋊#1055C2211yescharacteristic
17C2×#88043C2211yescharacteristic
18#11718139—22no—
19#11718139—22no—
20#11718135—24no—
21#11718120—22no—
22#11718116—22no—
23C22×Q8×C13C2×C411yescharacteristic
24C13×C4⋊Q8—22no—
25C13×C4⋊Q8—22no—
26C13×C4⋊Q8—28no—
27C13×C4⋊Q8—24no—
28C13×C4⋊Q8D412yes—
29C13×C4⋊Q8D412yes—
30C13×#125—24no—
31C13×#125—28no—
32C13×#125—24no—
33C13×#125D414yes—
34C13×C22⋊Q8—24no—
35C13×C22⋊Q8—22no—
36C13×C22⋊Q8—22no—
37C4×Q8×C13—24no—
38C4×Q8×C13—24no—
39C4×Q8×C13—24no—
40C4×Q8×C13—24no—
41C4×Q8×C13—22no—
42C4×Q8×C13—22no—
43C4×Q8×C13—22no—
44C4×Q8×C13—22no—
45C13×#117—24no—
46C13×#117C2×C414yes—
47C2×C13×C4⋊C4C2×C411yescharacteristic
48C2×C13×C4⋊C4D412yes—
49C2×C42×C13D412yes—
50C2×C42×C13C2311yescharacteristic
51C22×#1055—21no—
52C22×#1055—21no—
53C22⋊#1055—22no—
54C4⋊#1055—22no—
55C4⋊#1055—22no—
56#88043—22no—
57#88043—22no—
58#8460—131nomaximal, Sylow
59C2×Q8×C13—24no—
60C2×Q8×C13—24no—
61C2×Q8×C13—22no—
62C2×Q8×C13—22no—
63C2×Q8×C13—22no—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22⋊C412yes—
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C13×C4⋊C4—24no—
70C13×C4⋊C4—24no—
71C13×C4⋊C4—24no—
72C13×C4⋊C4—28no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—24no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—24no—
79C13×C4⋊C4C22⋊C414yes—
80C13×C4⋊C4C22⋊C414yes—
81C13×C22⋊C4—24no—
82C42×C13—28no—
83C42×C13—24no—
84C42×C13—22no—
85C42×C13—22no—
86C42×C13C2×D412yes—
87C42×C13C2×D412yes—
88C2×#1055—22no—
89C2×#1055—41no—
90C2×#1055—41no—
91C2×#1055—42no—
92C2×#1055—42no—
93C2×#1055—41no—
94#3502D1311yescharacteristic
95#1985—131no—
96#1552—132no—
97#1531—132no—
98#1467—131no—
99C23×C13C2×C22⋊C411yescharacteristic
100Q8×C13—28no—
101Q8×C13—42no—
102Q8×C13—42no—
103Q8×C13—82no—
104Q8×C13—84no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—24no—
111C2×C4×C13—24no—
112C2×C4×C13—22no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13#10114yes—
116C2×C4×C13C2×C22⋊C412yes—
117C2×C4×C13#12011yescharacteristic
118C2×C4×C13#12012yes—
119C2×C4×C13#12011yescharacteristic
120#1055—42no—
121#1055—82no—
122#1055—81no—
123Q82—22no—
124#557—22no—
125#557—24no—
126#544—22no—
127#544Dic1312yes—
128#533—22no—
129#533C2×D1312yes—
130#519Dic1312yes—
131C2×C4×Q8C2×D1311yescharacteristic
132#432—132no—
133C2×C4⋊C8—131no—
134C2×#97—131no—
135#336—262no—
136#332—262no—
137#332—262no—
138#330—264no—
139#324—262no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13#37911yescharacteristic
143C22×C13C2×#10112yes—
144C4×C13—21no—
145C4×C13—22no—
146C4×C13—24no—
147C4×C13—22no—
148C4×C13—44no—
149C4×C13—42no—
150C4×C13—44no—
151C4×C13#45411yescharacteristic
152C4×C13#45611yescharacteristic
153C22×Q8C2×Dic1311yescharacteristic
154C22×C8—261no—
155C22×C8—261no—
156C4⋊Q8—22no—
157C4⋊Q8—22no—
158C4⋊Q8—28no—
159C4⋊Q8—24no—
160C4⋊Q8C22⋊D1312yes—
161C4⋊Q8C22⋊D1312yes—
162#125—24no—
163#125—28no—
164#125—24no—
165#125C22⋊D1314yes—
166C22⋊Q8—24no—
167C22⋊Q8—22no—
168C22⋊Q8—22no—
169C4×Q8—24no—
170C4×Q8—24no—
171C4×Q8—24no—
172C4×Q8—24no—
173C4×Q8—22no—
174C4×Q8—22no—
175C4×Q8—22no—
176C4×Q8—22no—
177#117—24no—
178#117C2×Dic1314yes—
179C2×C4⋊C4C2×Dic1311yescharacteristic
180C2×C4⋊C4C22⋊D1312yes—
181C2×C42C22⋊D1312yes—
182C2×C42C22×D1311yescharacteristic
183C4⋊C8—262no—
184C4⋊C8—262no—
185C22⋊C8—262no—
186#97—262no—
187#97—262no—
188C2×C13—22no—
189C2×C13#178411yescharacteristic
190C2×C13#179311yescharacteristic
191C2×C13#179411yescharacteristic
192C2×Q8—24no—
193C2×Q8—24no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—22no—
197C22×C4C22⋊Dic1312yes—
198C22×C4C22⋊Dic1312yes—
199C22×C4C22×Dic1311yescharacteristic
200C22×C4C2×C22⋊D1311yescharacteristic
201C22×C4C2×C22⋊D1311yescharacteristic
202C2×C8—262no—
203C2×C8—521no—
204C2×C8—521no—
205C2×C8—522no—
206C2×C8—522no—
207C2×C8—521no—
208C4⋊C4—24no—
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—28no—
212C4⋊C4—22no—
213C4⋊C4—24no—
214C4⋊C4—24no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—24no—
218C4⋊C4C22⋊Dic1314yes—
219C4⋊C4C22⋊Dic1314yes—
220C22⋊C4—24no—
221C42—28no—
222C42—24no—
223C42—22no—
224C42—22no—
225C42C2×C22⋊D1312yes—
226C42C2×C22⋊D1312yes—
227C13#846011yescharacteristic, complemented, Sylow
228C23C2×C22⋊Dic1311yescharacteristic
229Q8—28no—
230Q8—42no—
231Q8—42no—
232Q8—82no—
233Q8—84no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—24no—
240C2×C4—24no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4#8807614yes—
245C2×C4C2×C22⋊Dic1312yes—
246C2×C4#8820711yescharacteristic
247C2×C4#8820712yes—
248C2×C4#8820711yescharacteristic
249C8—522no—
250C8—1042no—
251C8—1041no—
252C22—21no—
253C22—21no—
254C22C2×#8807612yes—
255C22#1171890811yescharacteristic
256C4—24no—
257C4—22no—
258C4—21no—
259C4—22no—
260C4—44no—
261C4—42no—
262C4—44no—
263C4#1171890611yescharacteristic
264C4#1171890711yescharacteristic
265C2—22no—
266C2#1311476011yescharacteristic
267C2#1311479511yescharacteristic
268C2#1311480011yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3502C2
socleC22×C13#379
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#3502D13
hypocenterC13#8460
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
227. C13#8460semidirect

Maximal subgroups

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

subgroupindex
#131157772
#131135362
#131134512
#131131802
C13×#35022
#846013