Finite Group Databasebeta

← #13131087

Subgroups — #13131087

Order 1664.

264 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 54 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#11719496C211yesmaximal, characteristic
2#11719132C211yesmaximal, characteristic, complemented
3#11719116C211yesmaximal, characteristic, complemented
4#11718306C212yesmaximal, complemented
5#11718288C212yesmaximal, complemented
6C23×C4×C13C411yescharacteristic, complemented
7C2×#6127C2211yescharacteristic
8#88237—21no—
9D13⋊M16—21no—
10#88207C411yescharacteristic, complemented
11#88207C2211yescharacteristic
12#88184—21no—
13#88183C411yescharacteristic, complemented
14#88183C2211yescharacteristic
15C4×C22⋊D13—21no—
16C4×C22⋊D13—21no—
17#88180C411yescharacteristic, complemented
18#88178—21no—
19#88121C2212yes—
20#88119C2212yes—
21#88113—21no—
22#88107—21no—
23C24×C13C2×C411yescharacteristic
24C22×C4×C13—21no—
25C22×C4×C13—21no—
26C22×C4×C13—41no—
27C22×C4×C13—41no—
28C22×C4×C13C2×C411yescharacteristic
29C22×C4×C13C2×C411yescharacteristic
30C2×C22⋊D13—21no—
31C2×C22⋊D13—21no—
32C2×C22⋊D13C2×C411yescharacteristic
33C2×C22⋊D13C2311yescharacteristic
34#6127—41no—
35#6127—41no—
36C2×D52D411yescharacteristic
37C2×C4×D13D411yescharacteristic
38C2×C4×D13D411yescharacteristic
39C2×Dic26D411yescharacteristic
40C22⋊#261—22no—
41#6122—22no—
42C4⋊#261—41no—
43C4×#261—41no—
44#6118—41no—
45D13⋊C8—41no—
46C22⋊Dic13—21no—
47C22⋊Dic13—21no—
48C22⋊Dic13C2×C411yescharacteristic
49C22⋊Dic13C2×C411yescharacteristic
50#6103—21no—
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
61C22×D13C22⋊C411yescharacteristic
62C22×D13C2×D411yescharacteristic
63C2×#261—42no—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—42no—
68C2×C4×C13—41no—
69C2×C4×C13—41no—
70C2×C4×C13—41no—
71C2×C4×C13C22⋊C411yescharacteristic
72C2×C4×C13C22⋊C411yescharacteristic
73C22⋊D13—41no—
74C22⋊D13—41no—
75C22⋊D13—42no—
76C22⋊D13—42no—
77C2×Dic13—21no—
78C2×Dic13—21no—
79C2×Dic13C22⋊C411yescharacteristic
80C2×Dic13C2×D411yescharacteristic
81D52—41no—
82C4×D13—21no—
83C4×D13—21no—
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—41no—
96C22×C13—41no—
97C22×C13—42no—
98C22×C13—42no—
99C22×C13—41no—
100C22×C13C2×C22⋊C411yescharacteristic
101C2×D13—21no—
102C2×D13—21no—
103C2×D13—41no—
104C2×D13—41no—
105#261—82no—
106C4×C13—21no—
107C4×C13—41no—
108C4×C13#9911yescharacteristic
109C4×C13#9911yescharacteristic
110Dic13—21no—
111Dic13—21no—
112Dic13—41no—
113Dic13—41no—
114C2×#41—131no—
115C23×C4#26111yescharacteristic, complemented
116C2×M16—261no—
117#123—131no—
118#123—131no—
119C22⋊Q8—261no—
120#121—261no—
121#120—131no—
122#120—131no—
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—42no—
133C2×C13—41no—
134C2×C13C2×#9911yescharacteristic
135D13—41no—
136D13—41no—
137C24C2×#26111yescharacteristic
138#41—521no—
139#41—521no—
140C2×Q8—131no—
141C2×D4—131no—
142C2×D4—131no—
143C2×D4—131no—
144C2×D4—261no—
145C2×D4—261no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—131no—
151C22×C4—131no—
152C22×C4C2×#26111yescharacteristic
153C22×C4C2×#26111yescharacteristic
154M16—262no—
155M16—521no—
156C2×C8—521no—
157C4⋊C4—261no—
158C4⋊C4—261no—
159C4⋊C4—261no—
160C4⋊C4—521no—
161C22⋊C4—131no—
162C22⋊C4—131no—
163C22⋊C4—261no—
164C22⋊C4—261no—
165C22⋊C4—261no—
166C22⋊C4—261no—
167C22⋊C4—262no—
168C42—261no—
169C42—521no—
170C13#212011yescharacteristic, complemented, Sylow
171C23—21no—
172C23—41no—
173C23—42no—
174C23—131no—
175C23—131no—
176C23C22×#26111yescharacteristic
177Q8—521no—
178D4—521no—
179D4—521no—
180D4—521no—
181D4—522no—
182D4—522no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—42no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—131no—
191C2×C4—131no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—522no—
199C2×C4C22⋊#26111yescharacteristic
200C2×C4C22⋊#26111yescharacteristic
201C8—522no—
202C22—22no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—42no—
207C22—42no—
208C22—41no—
209C22—261no—
210C22—261no—
211C22—521no—
212C22—521no—
213C22C2×C22⋊#26111yescharacteristic
214C4—21no—
215C4—41no—
216C4—261no—
217C4—261no—
218C4—521no—
219C4—521no—
220C4—1042no—
221C4#8811911yescharacteristic
222C4#8811911yescharacteristic
223C2—21no—
224C2—42no—
225C2—41no—
226C2—521no—
227C2—521no—
228C2C2×#8811911yescharacteristic
subgroupG/H
centerC4#88119
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC23×C4×C13C4
socleC2×C13C2×#99
prime radical#11719496C2
cosocleC2×C22⋊D13C23
hypercenterC23×C4#261
hypocenterC13#2120
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11719132C2semidirect
3. #11719116C2semidirect
4. #11718306C2semidirect
5. #11718288C2semidirect
6. C23×C4×C13C4semidirect
10. #88207C4semidirect
13. #88183C4semidirect
17. #88180C4semidirect
115. C23×C4#261semidirect
170. C13#2120semidirect

Maximal subgroups

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

subgroupindex
#117194962
#117191322
#117191162
#117183062
#117182882
#212013