Finite Group Databasebeta

← #13131097

Subgroups — #13131097

Order 1664.

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

normal subgroups only

This group has 266 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#11719230C211yesmaximal, characteristic
2#11719132C211yesmaximal, characteristic, complemented
3#11719116C211yesmaximal, characteristic, complemented
4#11718236C214yesmaximal, complemented
5C2×#6127C2211yescharacteristic
6C22×D52C411yescharacteristic, complemented
7#88237—21no—
8D13⋊M16—21no—
9C13×#117C411yescharacteristic, complemented
10#88149—21no—
11#88149—21no—
12#88136C412yescomplemented
13#88136C2212yes—
14#88129—21no—
15#88128—21no—
16#88121C2212yes—
17#88119C2212yes—
18#88113—21no—
19#88107—21no—
20C23×D13C2×C412yes—
21C22×C4×C13C2×C411yescharacteristic
22C2×C22⋊D13C2×C411yescharacteristic
23C2×C22⋊D13C2311yescharacteristic
24#6127—41no—
25#6127—41no—
26C2×D52—21no—
27C2×D52—21no—
28C2×D52—22no—
29C2×D52—22no—
30C2×D52—41no—
31C2×D52—41no—
32C2×D52D411yescharacteristic
33C2×C4×D13D411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C2×Dic26D411yescharacteristic
36C22⋊#261—22no—
37#6122—22no—
38C4⋊#261—41no—
39C4×#261—41no—
40#6118—41no—
41D13⋊C8—41no—
42C13×C4⋊C4—21no—
43C13×C22⋊C4C2×C412yes—
44C42×C13—21no—
45#6103—22no—
46#6103—22no—
47#2122—131nomaximal, Sylow
48C23×C13C22×C411yescharacteristic
49C22×D13—22no—
50C22×D13—42no—
51C22×D13—82no—
52C22×D13C22⋊C411yescharacteristic
53C22×D13C2×D411yescharacteristic
54C2×#261—42no—
55C2×C4×C13—21no—
56C2×C4×C13—21no—
57C2×C4×C13—22no—
58C2×C4×C13C22⋊C411yescharacteristic
59C2×C4×C13C22⋊C411yescharacteristic
60C22⋊D13—41no—
61C22⋊D13—41no—
62C2×Dic13C22⋊C411yescharacteristic
63C2×Dic13C2×D411yescharacteristic
64D52—41no—
65D52—42no—
66D52—41no—
67D52—41no—
68D52—82no—
69D52—82no—
70C4×D13—21no—
71C4×D13—21no—
72C4×D13—21no—
73C4×D13—21no—
74Dic26—41no—
75#1057—42no—
76#535—131no—
77#413—131no—
78#410—131no—
79AΣL(1,𝔽16)—134no—
80C22×C13—21no—
81C22×C13—41no—
82C22×C13C2×C22⋊C411yescharacteristic
83C2×D13—21no—
84C2×D13—21no—
85C2×D13—41no—
86C2×D13—41no—
87C2×D13—42no—
88C2×D13—42no—
89C2×D13—42no—
90C2×D13—84no—
91#261—82no—
92C4×C13—21no—
93C4×C13—42no—
94C4×C13#9911yescharacteristic
95C4×C13#9911yescharacteristic
96Dic13—21no—
97Dic13—21no—
98C2×#41—131no—
99C22×D4—131no—
100C2×M16—261no—
101#127—261no—
102#124—261no—
103#121—261no—
104#121—261no—
105#120—132no—
106#120—132no—
107#117—261no—
108#117#26111yescharacteristic, complemented
109#101—261no—
110#100—132no—
111#99—132no—
112#99—261no—
113C2×C13—21no—
114C2×C13—41no—
115C2×C13C2×#9911yescharacteristic
116D13—41no—
117D13—41no—
118D13—82no—
119C24—132no—
120#41—521no—
121#41—521no—
122C2×Q8—131no—
123C2×D4—131no—
124C2×D4—131no—
125C2×D4—131no—
126C2×D4—262no—
127C2×D4—262no—
128C2×D4—261no—
129C2×D4—261no—
130C2×D4—521no—
131C2×D4—521no—
132C22×C4—131no—
133C22×C4—131no—
134C22×C4C2×#26111yescharacteristic
135M16—262no—
136M16—521no—
137C2×C8—521no—
138C4⋊C4—21no—
139C4⋊C4—521no—
140C22⋊C4—262no—
141C22⋊C4—262no—
142C22⋊C4—262no—
143C22⋊C4C2×#26112yes—
144C42—21no—
145C42—521no—
146C13#212211yescharacteristic, complemented, Sylow
147C23—131no—
148C23—131no—
149C23—262no—
150C23—522no—
151C23—1042no—
152C23C22×#26111yescharacteristic
153Q8—521no—
154D4—521no—
155D4—522no—
156D4—521no—
157D4—521no—
158D4—521no—
159D4—521no—
160D4—1042no—
161D4—1042no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—131no—
166C2×C4—131no—
167C2×C4—261no—
168C2×C4—261no—
169C2×C4—261no—
170C2×C4—261no—
171C2×C4—522no—
172C2×C4C22⋊#26111yescharacteristic
173C2×C4C22⋊#26111yescharacteristic
174C8—522no—
175C22—21no—
176C22—41no—
177C22—261no—
178C22—261no—
179C22—521no—
180C22—521no—
181C22—522no—
182C22—522no—
183C22—522no—
184C22—1044no—
185C22C2×C22⋊#26111yescharacteristic
186C4—21no—
187C4—42no—
188C4—261no—
189C4—261no—
190C4—1042no—
191C4#8810711yescharacteristic
192C4#8810711yescharacteristic
193C2—21no—
194C2—41no—
195C2—521no—
196C2—521no—
197C2—1042no—
198C2C2×#8810711yescharacteristic
subgroupG/H
centerC2C2×#88107
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC13×#117C4
socleC2×C13C2×#99
prime radical#11719230C2
cosocleC2×C22⋊D13C23
hypercenter#117#261
hypocenterC13#2122
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11719132C2semidirect
3. #11719116C2semidirect
4. #11718236C2semidirect
6. C22×D52C4semidirect
9. C13×#117C4semidirect
12. #88136C4semidirect
108. #117#261semidirect
146. C13#2122semidirect

Maximal subgroups

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

subgroupindex
#117192302
#117191322
#117191162
#117182362
#212213