Finite Group Databasebeta

← #15755295

Subgroups — #15755295

Order 3328.

620 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 131 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#13115818C211yesmaximal, characteristic
2#13113566C212yesmaximal
3#13113474C211yesmaximal, characteristic
4#13113348C212yesmaximal
5C13×#3556C211yesmaximal, characteristic
6C13×#564—22no—
7C13×#557—22no—
8C13×#557—22no—
9C13×#557C414yescomplemented
10C13×#541—24no—
11C13×#541—22no—
12C13×#533C2212yes—
13C13×#533C2211yescharacteristic
14#11718593C2211yescharacteristic
15#11718587C2212yes—
16#11718585C2211yescharacteristic
17#11718139—22no—
18#11718138—22no—
19#11718135—22no—
20#11718130—24no—
21#11718124—22no—
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—24no—
24C13×C4⋊Q8C2×C412yes—
25C13×C4⋊Q8D412yes—
26C13×C4⋊Q8D412yes—
27C13×#126—28no—
28C13×#125—22no—
29C13×#125—28no—
30C13×#125—28no—
31C13×#125—24no—
32C13×#125—28no—
33C13×#125—22no—
34C13×#125D412yes—
35C13×C22⋊Q8—22no—
36C13×C22⋊Q8—22no—
37C13×C22⋊Q8D414yes—
38C4×Q8×C13—24no—
39C4×Q8×C13—24no—
40C4×Q8×C13—24no—
41C4×Q8×C13—22no—
42C4×Q8×C13—22no—
43C4×Q8×C13C2×C414yes—
44C13×#117—22no—
45C13×#117D412yes—
46C2×C42×C13C2311yescharacteristic
47C2×C4×Dic13—21no—
48C2×#6099—21no—
49#88071—22no—
50C22⋊#1055—22no—
51C4⋊#1055—22no—
52C4⋊#1055—22no—
53#88043—22no—
54#8495—131nomaximal, Sylow
55C2×Q8×C13—22no—
56C2×Q8×C13—22no—
57C2×Q8×C13C22⋊C414yes—
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D412yes—
60C22×Dic13—41no—
61C13×C4⋊C4—28no—
62C13×C4⋊C4—28no—
63C13×C4⋊C4—28no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—24no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—24no—
70C13×C4⋊C4—24no—
71C13×C4⋊C4C22⋊C414yes—
72C13×C4⋊C4C22⋊C414yes—
73C13×C22⋊C4—24no—
74C13×C22⋊C4—22no—
75C42×C13—28no—
76C42×C13—24no—
77C42×C13—22no—
78C42×C13C22×C411yescharacteristic
79C42×C13C2×D412yes—
80C42×C13C2×D411yescharacteristic
81C4×Dic13—22no—
82C4×Dic13—41no—
83#6099—42no—
84C2×#1055—42no—
85C2×#1055—41no—
86#3556D1311yescharacteristic
87#1995—131no—
88#1559—132no—
89#1537—131no—
90#1506—132no—
91C23×C13#12011yescharacteristic
92Q8×C13—44no—
93Q8×C13—44no—
94Q8×C13—42no—
95Q8×C13—42no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—24no—
99C2×C4×C13—24no—
100C2×C4×C13—24no—
101C2×C4×C13—42no—
102C2×C4×C13C2×C22⋊C412yes—
103C2×C4×C13C2×C22⋊C411yescharacteristic
104C2×C4×C13#12012yes—
105C2×C4×C13#12011yescharacteristic
106C2×Dic13—42no—
107C2×Dic13—82no—
108#1055—82no—
109#1055—81no—
110#564—22no—
111#557—22no—
112#557—22no—
113#557Dic1314yescomplemented
114#541—24no—
115#541—22no—
116#533C2×D1312yes—
117#533C2×D1311yescharacteristic
118#432—132no—
119#423—131no—
120#376—131no—
121#339—262no—
122#333—262no—
123#332—262no—
124#330—262no—
125#328—264no—
126C22×C13—21no—
127C22×C13—22no—
128C22×C13#37911yescharacteristic
129C4×C13—21no—
130C4×C13—22no—
131C4×C13—22no—
132C4×C13—44no—
133C4×C13—44no—
134C4×C13—44no—
135C4×C13#45411yescharacteristic
136C4×C13#45611yescharacteristic
137Dic13—82no—
138C2×M16—261no—
139C4⋊Q8—22no—
140C4⋊Q8—24no—
141C4⋊Q8C2×Dic1312yes—
142C4⋊Q8C22⋊D1312yes—
143C4⋊Q8C22⋊D1312yes—
144#126—28no—
145#125—22no—
146#125—28no—
147#125—28no—
148#125—24no—
149#125—28no—
150#125—22no—
151#125C22⋊D1312yes—
152C22⋊Q8—22no—
153C22⋊Q8—22no—
154C22⋊Q8C22⋊D1314yes—
155C4×Q8—24no—
156C4×Q8—24no—
157C4×Q8—24no—
158C4×Q8—22no—
159C4×Q8—22no—
160C4×Q8C2×Dic1314yes—
161#117—22no—
162#117C22⋊D1312yes—
163C2×C42—261no—
164C2×C42C22×D1311yescharacteristic
165C4⋊C8—262no—
166C4⋊C8—262no—
167C22⋊C8—262no—
168#97—262no—
169#95—262no—
170C2×C13—41no—
171C2×C13#179311yescharacteristic
172C2×C13#179612yes—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8C22⋊Dic1314yes—
176C22×C4—521no—
177C22×C4C2×C22⋊D1311yescharacteristic
178C22×C4C2×C22⋊D1312yes—
179M16—522no—
180C2×C8—522no—
181C2×C8—521no—
182C4⋊C4—28no—
183C4⋊C4—28no—
184C4⋊C4—28no—
185C4⋊C4—22no—
186C4⋊C4—24no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—24no—
191C4⋊C4—24no—
192C4⋊C4C22⋊Dic1314yes—
193C4⋊C4C22⋊Dic1314yes—
194C22⋊C4—24no—
195C22⋊C4—22no—
196C42—28no—
197C42—24no—
198C42—22no—
199C42—262no—
200C42—521no—
201C42C22×Dic1311yescharacteristic
202C42C2×C22⋊D1311yescharacteristic
203C42C2×C22⋊D1312yes—
204C13#849511yescharacteristic, complemented, Sylow
205C23#8820711yescharacteristic
206Q8—44no—
207Q8—44no—
208Q8—42no—
209Q8—42no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—24no—
214C2×C4—24no—
215C2×C4—42no—
216C2×C4—522no—
217C2×C4—1042no—
218C2×C4C2×C22⋊Dic1312yes—
219C2×C4C2×C22⋊Dic1311yescharacteristic
220C2×C4#8820712yes—
221C2×C4#8820711yescharacteristic
222C8—1042no—
223C8—1041no—
224C22—21no—
225C22—22no—
226C22#1171890811yescharacteristic
227C4—21no—
228C4—22no—
229C4—22no—
230C4—44no—
231C4—44no—
232C4—44no—
233C4—1042no—
234C4#1171890611yescharacteristic
235C4#1171890711yescharacteristic
236C2—41no—
237C2#1311479511yescharacteristic
238C2#1311481112yes—
subgroupG/H
centerC22#11718908
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3556C2
socleC22×C13#379
prime radicalC23×C13#120
cosocleC2×C42×C13C23
hypercenter#3556D13
hypocenterC13#8495
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3556

Complements

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

NH ≅ G/Ntype
9. C13×#557C4semidirect
113. #557Dic13semidirect
204. C13#8495semidirect

Maximal subgroups

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

subgroupindex
#131158182
#131135662
#131134742
#131133482
C13×#35562
#849513