Finite Group Databasebeta

← #13131088

Subgroups — #13131088

Order 1664.

264 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 52 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#11719291C211yesmaximal, characteristic
2#11719148C211yesmaximal, characteristic, complemented
3#11719142C211yesmaximal, characteristic, complemented
4#11718306C212yesmaximal, complemented
5#11718237C212yesmaximal, complemented
6C23×Dic13C411yescharacteristic, complemented
7C2×#6129C2211yescharacteristic
8C2×#6122—21no—
9#88237—21no—
10C13×#120C411yescharacteristic, complemented
11#88207C2211yescharacteristic
12#88193—21no—
13#88189C411yescharacteristic, complemented
14D4×Dic13—21no—
15#88140C2211yescharacteristic
16#88135—21no—
17#88132—21no—
18#88131C411yescharacteristic, complemented
19#88121C2212yes—
20#88119—21no—
21#88119C2212yes—
22#88113—21no—
23C24×C13C2×C411yescharacteristic
24C2×D4×C13—21no—
25C2×D4×C13C2×C411yescharacteristic
26C2×C22⋊D13—21no—
27C2×C22⋊D13D411yescharacteristic
28C2×C22⋊D13C2311yescharacteristic
29C22×Dic13—21no—
30C22×Dic13—21no—
31C22×Dic13—41no—
32C22×Dic13—41no—
33C22×Dic13C2×C411yescharacteristic
34C22×Dic13C2×C411yescharacteristic
35C22×Dic13D411yescharacteristic
36#6129—41no—
37#6129—41no—
38C2×C4×D13D411yescharacteristic
39C2×Dic26D411yescharacteristic
40C22⋊#261—22no—
41#6122—22no—
42#6122—41no—
43C2×#1057—41no—
44C4⋊#261—41no—
45C4×#261—41no—
46C13×C22⋊C4—21no—
47C13×C22⋊C4C2×C411yescharacteristic
48C22⋊Dic13—21no—
49C22⋊Dic13—21no—
50C22⋊Dic13C2×C411yescharacteristic
51#6103—21no—
52C4⋊Dic13—21no—
53#6101—21no—
54#6101—21no—
55C4×Dic13—21no—
56#2120—131nomaximal, Sylow
57C23×C13—21no—
58C23×C13—41no—
59C23×C13—42no—
60C23×C13C22⋊C411yescharacteristic
61C23×C13C22×C411yescharacteristic
62C22×D13C2×D411yescharacteristic
63C2×#261—42no—
64D4×C13—41no—
65D4×C13—42no—
66C2×C4×C13—21no—
67C2×C4×C13C22⋊C411yescharacteristic
68C22⋊D13—41no—
69C22⋊D13—41no—
70C22⋊D13—42no—
71C2×Dic13—21no—
72C2×Dic13—21no—
73C2×Dic13—21no—
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—21no—
77C2×Dic13—42no—
78C2×Dic13—41no—
79C2×Dic13—41no—
80C2×Dic13—41no—
81C2×Dic13C22⋊C411yescharacteristic
82C2×Dic13C22⋊C411yescharacteristic
83C2×Dic13C2×D411yescharacteristic
84C4×D13—21no—
85C4×D13—21no—
86Dic26—41no—
87#1057—42no—
88#525—131no—
89#413—131no—
90#410—131no—
91#352—132no—
92AΣL(1,𝔽16)—132no—
93C22×C13—22no—
94C22×C13—21no—
95C22×C13—21no—
96C22×C13—41no—
97C22×C13—41no—
98C22×C13—41no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—41no—
102C22×C13C2×C22⋊C411yescharacteristic
103C2×D13—21no—
104C2×D13—41no—
105#261—82no—
106C4×C13—21no—
107C4×C13—41no—
108Dic13—21no—
109Dic13—21no—
110Dic13—41no—
111Dic13—41no—
112Dic13#9911yescharacteristic
113Dic13#9911yescharacteristic
114C2×#41—131no—
115C23×C4—131no—
116C2×M16—261no—
117#123—131no—
118#123—131no—
119C22⋊Q8—261no—
120#121—261no—
121#120—131no—
122#120#26111yescharacteristic, complemented
123C4×D4—261no—
124C4×D4—261no—
125#117—131no—
126#117—261no—
127#101—261no—
128#100—132no—
129#99—132no—
130#99—261no—
131C2×C13—21no—
132C2×C13—41no—
133C2×C13—42no—
134C2×C13—41no—
135C2×C13C2×#9911yescharacteristic
136D13—41no—
137C24C2×#26111yescharacteristic
138#41—521no—
139#41—521no—
140C2×Q8—131no—
141C2×D4—21no—
142C2×D4—131no—
143C2×D4—131no—
144C2×D4—261no—
145C2×D4C2×#26111yescharacteristic
146C22×C4—131no—
147C22×C4—131no—
148C22×C4—131no—
149C22×C4—131no—
150C22×C4—261no—
151C22×C4—261no—
152C22×C4—521no—
153C22×C4—521no—
154M16—262no—
155M16—521no—
156C2×C8—521no—
157C4⋊C4—261no—
158C4⋊C4—261no—
159C4⋊C4—261no—
160C4⋊C4—521no—
161C22⋊C4—21no—
162C22⋊C4—131no—
163C22⋊C4—261no—
164C22⋊C4—261no—
165C22⋊C4—261no—
166C22⋊C4—262no—
167C22⋊C4C2×#26111yescharacteristic
168C42—261no—
169C42—521no—
170C13#212011yescharacteristic, complemented, Sylow
171C23—21no—
172C23—41no—
173C23—42no—
174C23—131no—
175C23C22⋊#26111yescharacteristic
176C23C22×#26111yescharacteristic
177Q8—521no—
178D4—41no—
179D4—42no—
180D4—521no—
181D4—521no—
182D4—522no—
183C2×C4—21no—
184C2×C4—131no—
185C2×C4—131no—
186C2×C4—131no—
187C2×C4—261no—
188C2×C4—261no—
189C2×C4—261no—
190C2×C4—261no—
191C2×C4—261no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—261no—
195C2×C4—521no—
196C2×C4—521no—
197C2×C4—522no—
198C2×C4—521no—
199C2×C4—522no—
200C2×C4C22⋊#26111yescharacteristic
201C8—522no—
202C22—22no—
203C22—21no—
204C22—21no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—42no—
210C22—41no—
211C22—261no—
212C22—521no—
213C22C2×C22⋊#26111yescharacteristic
214C4—21no—
215C4—41no—
216C4—131no—
217C4—131no—
218C4—261no—
219C4—261no—
220C4—521no—
221C4—521no—
222C4—1042no—
223C2—21no—
224C2—42no—
225C2—41no—
226C2—41no—
227C2—521no—
228C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC13×#120C4
socleC2×C13C2×#99
prime radical#11719291C2
cosocleC2×C22⋊D13C23
hypercenter#120#261
hypocenterC13#2120
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #120

Complements

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

NH ≅ G/Ntype
2. #11719148C2semidirect
3. #11719142C2semidirect
4. #11718306C2semidirect
5. #11718237C2semidirect
6. C23×Dic13C4semidirect
10. C13×#120C4semidirect
13. #88189C4semidirect
18. #88131C4semidirect
122. #120#261semidirect
170. C13#2120semidirect

Maximal subgroups

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

subgroupindex
#117192912
#117191482
#117191422
#117183062
#117182372
#212013