Finite Group Databasebeta

← #16777678

Subgroups — #16777678

Order 3328.

244 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 50 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#13130087C211yesmaximal, characteristic
2#13130087C211yesmaximal, characteristic
3#13114905C211yesmaximal, characteristic
4C2×#88180C2211yescharacteristic
5#11719128—21no—
6#11719128—21no—
7C2×C13×C22⋊C8C411yescharacteristic
8C2×C22⋊#1055C411yescharacteristic
9#11718305—21no—
10#11718305—21no—
11#11718285C412yes—
12#11718285C412yes—
13#11718142—21no—
14#11718142—21no—
15C23×C4×C13C2×C411yescharacteristic
16C22×C8×C13—21no—
17C2×C22⋊Dic13D411yescharacteristic
18C2×C22⋊Dic13Q811yescharacteristic
19#88180—41no—
20#88180—41no—
21C2×C4⋊Dic13C2×C411yescharacteristic
22C2×C4⋊Dic13C2×C411yescharacteristic
23C2×C4×Dic13D411yescharacteristic
24C2×C4×Dic13D411yescharacteristic
25C22×#1055—21no—
26C22⋊#1057—22no—
27C22⋊#1057—22no—
28#88112—41no—
29#88112—41no—
30#88110—41no—
31#88110—41no—
32C13×C22⋊C8—41no—
33C22⋊#1055—41no—
34#7327—131nomaximal, Sylow
35C24×C13C4⋊C411yescharacteristic
36C22×C4×C13—21no—
37C22×C4×C13—21no—
38C22×C4×C13—42no—
39C22×C4×C13C4211yescharacteristic
40C22×C4×C13C22⋊C411yescharacteristic
41C22×Dic13C22⋊C411yescharacteristic
42C22×Dic13C22⋊C411yescharacteristic
43C22×Dic13C4⋊C411yescharacteristic
44C22×Dic13C4⋊C411yescharacteristic
45C2×#1057—42no—
46C2×#1057—42no—
47C2×C8×C13—42no—
48C2×C8×C13—41no—
49C22⋊Dic13—41no—
50C22⋊Dic13—41no—
51C4⋊Dic13—41no—
52C4⋊Dic13—41no—
53C4×Dic13—21no—
54C4×Dic13—21no—
55C4×Dic13—21no—
56C4×Dic13—21no—
57C2×#1055—42no—
58C2×#1055—41no—
59#1818—131no—
60#1464—131no—
61#1464—131no—
62C23×C13—21no—
63C23×C13—22no—
64C23×C13—41no—
65C23×C13—41no—
66C23×C13#9511yescharacteristic
67C2×C4×C13—22no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13#9911yescharacteristic
73C2×C4×C13#9911yescharacteristic
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—21no—
77C2×Dic13—21no—
78C2×Dic13—41no—
79C2×Dic13—41no—
80C2×Dic13—41no—
81C2×Dic13—41no—
82#1057—82no—
83#1057—82no—
84C8×C13—81no—
85#1055—81no—
86C2×#117—131no—
87#432—261no—
88#432—261no—
89C2×C22⋊C8—131no—
90C2×C22⋊C8#26111yescharacteristic
91#336—261no—
92#336—261no—
93#324—132no—
94#324—132no—
95#323—261no—
96#323—261no—
97C22×C13—21no—
98C22×C13—21no—
99C22×C13—41no—
100C22×C13—41no—
101C22×C13—41no—
102C22×C13—82no—
103C22×C13#34211yescharacteristic
104C22×C13#34412yes—
105C4×C13—21no—
106C4×C13—21no—
107C4×C13—41no—
108Dic13—41no—
109Dic13—41no—
110Dic13—41no—
111Dic13—41no—
112C23×C4C2×#26111yescharacteristic
113C22×C8—21no—
114C22×C8—261no—
115#117—521no—
116#117—521no—
117C2×C4⋊C4—131no—
118C2×C4⋊C4—131no—
119C2×C22⋊C4—131no—
120C2×C22⋊C4—131no—
121C2×C42—131no—
122C2×C42—131no—
123C4⋊C8—521no—
124C4⋊C8—521no—
125C22⋊C8—41no—
126C22⋊C8—262no—
127C22⋊C8—262no—
128C22⋊C8—521no—
129#97—521no—
130#97—521no—
131C2×C13—22no—
132C2×C13—81no—
133C2×C13#130611yescharacteristic
134C2×C13#139511yescharacteristic
135C2×C13#139511yescharacteristic
136C24C4⋊#26111yescharacteristic
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—42no—
140C22×C4—131no—
141C22×C4—131no—
142C22×C4—131no—
143C22×C4—131no—
144C22×C4C4×#26111yescharacteristic
145C22×C4C22⋊#26111yescharacteristic
146C2×C8—42no—
147C2×C8—41no—
148C2×C8—522no—
149C2×C8—522no—
150C2×C8—522no—
151C2×C8—521no—
152C4⋊C4—521no—
153C4⋊C4—521no—
154C22⋊C4—521no—
155C22⋊C4—521no—
156C42—261no—
157C42—261no—
158C42—261no—
159C42—261no—
160C13#732711yescharacteristic, complemented, Sylow
161C23—21no—
162C23—22no—
163C23—41no—
164C23—41no—
165C23(C2×#261)⋊C411yescharacteristic
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—261no—
172C2×C4—261no—
173C2×C4—261no—
174C2×C4—261no—
175C2×C4—521no—
176C2×C4—521no—
177C2×C4—521no—
178C2×C4—521no—
179C2×C4#8810711yescharacteristic
180C2×C4#8811911yescharacteristic
181C8—81no—
182C8—1041no—
183C8—1042no—
184C8—1042no—
185C22—21no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—82no—
191C22#1171823912yes—
192C22#1171828911yescharacteristic
193C4—21no—
194C4—21no—
195C4—41no—
196C4—521no—
197C4—521no—
198C4—521no—
199C4—521no—
200C2—22no—
201C2—81no—
202C2#1312973911yescharacteristic
203C2#1312993611yescharacteristic
204C2#1312993711yescharacteristic
subgroupG/H
centerC22#11718289
commutatorC22×C4×C13C42
FrattiniC23×C4C2×#261
FittingC2×C13×C22⋊C8C4
socleC22×C13#342
prime radicalC24×C13C4⋊C4
cosocleC2×#88180C22
hypercenterC2×C22⋊C8#261
hypocenterC13#7327
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
160. C13#7327semidirect

Maximal subgroups

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

subgroupindex
#131300872
#131149052
#732713