Finite Group Databasebeta

← #13130348

Subgroups — #13130348

Order 1664.

260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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#11719301C211yesmaximal, characteristic
2#11719129C211yesmaximal, characteristic, complemented
3C2×#88112C211yesmaximal, characteristic, complemented
4#11718297C212yesmaximal, complemented
5#11718245C212yesmaximal, complemented
6C2×#6129—21no—
7C2×#6122—21no—
8C22×#1057—21no—
9C13×#121C411yescharacteristic
10#88194C2211yescharacteristic
11#88193—21no—
12D4×Dic13C411yescharacteristic
13#88184C411yescharacteristic
14C2×C4×Dic13C2211yescharacteristic
15#88147C411yescharacteristic
16#88142C2211yescharacteristic
17#88139—21no—
18#88135—21no—
19#88112—21no—
20#88112C2212yes—
21#88112C2212yes—
22C4⋊#1057—21no—
23C2×D4×C13—21no—
24C2×D4×C13C2×C411yescharacteristic
25C22×C4×C13C2×C411yescharacteristic
26C2×C22⋊D13—21no—
27C2×C22⋊D13—21no—
28C2×C22⋊D13—21no—
29C22×Dic13—21no—
30C22×Dic13D411yescharacteristic
31C22×Dic13D411yescharacteristic
32#6129—42no—
33#6129—42no—
34C2×D52C2×C411yescharacteristic
35C2×C4×D13—21no—
36C2×Dic26—21no—
37#6122—42no—
38C2×#1057—22no—
39C2×#1057—22no—
40C2×#1057—42no—
41C13×C4⋊C4C2×C411yescharacteristic
42C13×C22⋊C4—21no—
43C22⋊Dic13—21no—
44#6103—21no—
45#6103—21no—
46C4⋊Dic13C2×C411yescharacteristic
47#6101—21no—
48C4×Dic13C2×C411yescharacteristic
49C4×Dic13D411yescharacteristic
50C4×Dic13D411yescharacteristic
51C4×Dic13C2311yescharacteristic
52#1547—131nomaximal, Sylow
53C23×C13—21no—
54C23×C13C22⋊C411yescharacteristic
55C22×D13—21no—
56D4×C13—41no—
57D4×C13—42no—
58C2×C4×C13—21no—
59C2×C4×C13—41no—
60C2×C4×C13C22⋊C411yescharacteristic
61C2×C4×C13C22×C411yescharacteristic
62C22⋊D13—42no—
63C22⋊D13—41no—
64C22⋊D13—41no—
65C22⋊D13—41no—
66C22⋊D13—41no—
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—21no—
70C2×Dic13—42no—
71C2×Dic13C22⋊C411yescharacteristic
72C2×Dic13C22⋊C411yescharacteristic
73C2×Dic13D812yes—
74C2×Dic13SD1612yes—
75C2×Dic13C2×D411yescharacteristic
76C2×Dic13C2×D411yescharacteristic
77D52—41no—
78C4×D13—42no—
79Dic26—41no—
80Dic26—41no—
81#1057—42no—
82#1057—42no—
83#532—131no—
84#423—131no—
85C2×C4⋊C8—131no—
86#332—132no—
87#331—132no—
88C22×C13—21no—
89C22×C13—21no—
90C22×C13—41no—
91C22×C13—41no—
92C22×C13—41no—
93C22×C13#10212yes—
94C22×C13C2×C22⋊C411yescharacteristic
95C2×D13—41no—
96C2×D13—41no—
97C2×D13—41no—
98C4×C13—21no—
99C4×C13—21no—
100C4×C13—41no—
101Dic13—21no—
102Dic13—41no—
103Dic13#10212yes—
104Dic13C2×D811yescharacteristic
105Dic13C2×SD1611yescharacteristic
106Dic13AGL(1,ℤ/8)11yescharacteristic
107Dic13#13711yescharacteristic
108C2×#41—261no—
109C2×M16—261no—
110C22×C8—261no—
111C4⋊Q8—131no—
112#127—131no—
113#124—261no—
114#121—131no—
115#121—261no—
116#121#26111yescharacteristic
117C4×D4—131no—
118C4×D4—131no—
119C4×D4—261no—
120C2×C42—131no—
121C4⋊C8—132no—
122C4⋊C8—132no—
123C4⋊C8—261no—
124C4⋊C8—261no—
125C2×C13—22no—
126C2×C13—81no—
127C2×C13#41311yescharacteristic
128C2×C13C2×#10211yescharacteristic
129C2×C13#41711yescharacteristic
130D13—81no—
131#41—522no—
132#41—522no—
133C2×Q8—261no—
134C2×D4—21no—
135C2×D4—131no—
136C2×D4—261no—
137C2×D4—261no—
138C2×D4—261no—
139C2×D4C2×#26111yescharacteristic
140C22×C4—131no—
141C22×C4—131no—
142C22×C4—261no—
143C22×C4—261no—
144C22×C4C2×#26111yescharacteristic
145M16—522no—
146C2×C8—262no—
147C2×C8—262no—
148C2×C8—522no—
149C4⋊C4—131no—
150C4⋊C4—261no—
151C4⋊C4C2×#26111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—261no—
154C22⋊C4—261no—
155C22⋊C4—261no—
156C42—131no—
157C42—131no—
158C42—131no—
159C42—131no—
160C13#154711yescharacteristic, complemented, Sylow
161C23—21no—
162C23—261no—
163C23C22⋊#26111yescharacteristic
164Q8—521no—
165Q8—521no—
166D4—41no—
167D4—42no—
168D4—521no—
169D4—521no—
170D4—521no—
171D4—521no—
172D4—521no—
173D4—522no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—132no—
177C2×C4—132no—
178C2×C4—131no—
179C2×C4—131no—
180C2×C4—131no—
181C2×C4—131no—
182C2×C4—261no—
183C2×C4—261no—
184C2×C4—261no—
185C2×C4—522no—
186C2×C4—522no—
187C2×C4C22⋊#26111yescharacteristic
188C2×C4C22×#26111yescharacteristic
189C8—522no—
190C8—522no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—41no—
196C22—521no—
197C22—521no—
198C22—521no—
199C22#8811512yes—
200C22C2×C22⋊#26111yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—132no—
205C4—131no—
206C4—131no—
207C4—131no—
208C4—131no—
209C4—261no—
210C4—521no—
211C2—22no—
212C2—81no—
213C2—1041no—
214C2C2×#8811511yescharacteristic
215C2#1171914811yescharacteristic
216C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#121C4
socleC22×C13C2×C22⋊C4
prime radical#11719301C2
cosocleC4×Dic13C23
hypercenter#121#261
hypocenterC13#1547
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11719129C2semidirect
3. C2×#88112C2semidirect
4. #11718297C2semidirect
5. #11718245C2semidirect
160. C13#1547semidirect

Maximal subgroups

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

subgroupindex
#117193012
#117191292
C2×#881122
#117182972
#117182452
#154713