Finite Group Databasebeta

← #16777677

Subgroups — #16777677

Order 3328.

374 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 58 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#13130084C212yesmaximal
2#13113105C211yesmaximal, characteristic
3C22×C4⋊Dic13C2211yescharacteristic
4#11719169—22no—
5C2×C13×#95C411yescharacteristic
6C2×#88071—22no—
7C2×#88071C411yescharacteristic
8#11718285—22no—
9#11718285C414yescomplemented
10C23×C4×C13—21no—
11C23×C4×C13C2×C411yescharacteristic
12C23×Dic13—21no—
13C23×Dic13D412yes—
14C2×#6122—42no—
15C2×C4⋊Dic13—41no—
16C2×C4⋊Dic13—41no—
17C2×C4⋊Dic13C2×C412yes—
18C2×C4⋊Dic13D411yescharacteristic
19C2×C4⋊Dic13Q811yescharacteristic
20C22⋊#1057—24no—
21C22⋊#1057—42no—
22C13×#95—41no—
23#88071—44no—
24#88071—41no—
25#7326—131nomaximal, Sylow
26C24×C13C22⋊C411yescharacteristic
27C22×C4×C13—21no—
28C22×C4×C13—21no—
29C22×C4×C13—22no—
30C22×C4×C13—42no—
31C22×C4×C13—42no—
32C22×C4×C13—42no—
33C22×C4×C13—41no—
34C22×C4×C13—41no—
35C22×C4×C13C4211yescharacteristic
36C22×C4×C13C4⋊C411yescharacteristic
37C22×Dic13—22no—
38C22×Dic13—22no—
39C22×Dic13—22no—
40C22×Dic13—42no—
41C22×Dic13—42no—
42C22×Dic13—42no—
43C22×Dic13—41no—
44C22×Dic13—42no—
45C22×Dic13—41no—
46C22×Dic13C22⋊C412yes—
47C22×Dic13C4⋊C412yes—
48#6122—82no—
49#6122—82no—
50C2×#1057—44no—
51C4⋊Dic13—42no—
52C4⋊Dic13—41no—
53C4⋊Dic13—41no—
54#1463—132no—
55#1445—131no—
56C23×C13—22no—
57C23×C13—21no—
58C23×C13—21no—
59C23×C13—21no—
60C23×C13—21no—
61C23×C13#9511yescharacteristic
62C23×C13#9911yescharacteristic
63C23×C13#9911yescharacteristic
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—42no—
69C2×C4×C13—42no—
70C2×C4×C13—44no—
71C2×C4×C13—42no—
72C2×C4×C13—82no—
73C2×C4×C13—81no—
74C2×C4×C13—81no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—42no—
78C2×Dic13—42no—
79C2×Dic13—42no—
80C2×Dic13—42no—
81C2×Dic13—44no—
82C2×Dic13—42no—
83C2×Dic13—82no—
84C2×Dic13—82no—
85C2×Dic13—81no—
86C2×Dic13—81no—
87#1057—84no—
88C22×C4⋊C4—131no—
89#407—262no—
90C2×#95—131no—
91C2×#95—262no—
92C2×#95#26111yescharacteristic
93#324—134no—
94#324—262no—
95C22×C13—22no—
96C22×C13—22no—
97C22×C13—22no—
98C22×C13—22no—
99C22×C13—21no—
100C22×C13—21no—
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—21no—
104C22×C13—21no—
105C22×C13#34211yescharacteristic
106C22×C13#34412yes—
107C22×C13#35311yescharacteristic
108C22×C13#35411yescharacteristic
109C22×C13#35511yescharacteristic
110C22×C13#35611yescharacteristic
111C4×C13—41no—
112C4×C13—41no—
113C4×C13—82no—
114Dic13—42no—
115Dic13—42no—
116Dic13—82no—
117C23×C4—21no—
118C23×C4—132no—
119C23×C4—261no—
120C23×C4C2×#26111yescharacteristic
121C2×M16—522no—
122C2×C4⋊C4—132no—
123C2×C4⋊C4—131no—
124C2×C4⋊C4—131no—
125C2×C4⋊C4—521no—
126C2×C4⋊C4—521no—
127C22⋊C8—264no—
128C22⋊C8—522no—
129#95—41no—
130#95—521no—
131#95—524no—
132C2×C13—21no—
133C2×C13—21no—
134C2×C13—22no—
135C2×C13—21no—
136C2×C13—21no—
137C2×C13#130611yescharacteristic
138C2×C13#139311yescharacteristic
139C2×C13#139411yescharacteristic
140C24C22⋊#26111yescharacteristic
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—42no—
146C22×C4—41no—
147C22×C4—42no—
148C22×C4—41no—
149C22×C4—132no—
150C22×C4—132no—
151C22×C4—262no—
152C22×C4—262no—
153C22×C4—262no—
154C22×C4—522no—
155C22×C4—522no—
156C22×C4—522no—
157C22×C4—521no—
158C22×C4—522no—
159C22×C4—521no—
160C22×C4C4×#26111yescharacteristic
161C22×C4C4⋊#26111yescharacteristic
162M16—1042no—
163M16—1042no—
164C2×C8—524no—
165C4⋊C4—522no—
166C4⋊C4—521no—
167C4⋊C4—521no—
168C13#732611yescharacteristic, complemented, Sylow
169C23—21no—
170C23—21no—
171C23—22no—
172C23—21no—
173C23—21no—
174C23#8810711yescharacteristic
175C23(C2×#261)⋊C411yescharacteristic
176C23#8811911yescharacteristic
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—44no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—522no—
191C2×C4—522no—
192C2×C4—522no—
193C2×C4—522no—
194C2×C4—524no—
195C2×C4—522no—
196C2×C4—1042no—
197C2×C4—1042no—
198C2×C4—1041no—
199C2×C4—1041no—
200C8—1044no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1171822711yescharacteristic
212C22#1171822811yescharacteristic
213C22#1171823912yes—
214C22#1171828911yescharacteristic
215C22#1171829411yescharacteristic
216C22#1171830011yescharacteristic
217C4—41no—
218C4—41no—
219C4—82no—
220C4—522no—
221C4—522no—
222C4—1042no—
223C2—21no—
224C2—21no—
225C2—21no—
226C2—22no—
227C2—21no—
228C2#1312973911yescharacteristic
229C2#1312993111yescharacteristic
230C2#1312993311yescharacteristic
subgroupG/H
centerC22#11718289
commutatorC22×C4×C13C42
FrattiniC23×C4C2×#261
FittingC2×C13×#95C4
socleC22×C13#342
prime radicalC24×C13C22⋊C4
cosocleC22×C4⋊Dic13C22
hypercenterC2×#95#261
hypocenterC13#7326
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
9. #11718285C4semidirect
168. C13#7326semidirect

Maximal subgroups

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

subgroupindex
#131300842
#131131052
#732613