Finite Group Databasebeta

← #16781936

Subgroups — #16781936

Order 3328.

362 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 94 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#13130398C212yesmaximal
2#13130098C212yesmaximal
3#13129701C212yesmaximal
4C2×#11718491C211yesmaximal, characteristic
5C2×C4×Dic26C2211yescharacteristic
6#11719130C2214yes—
7C2×C13×C4⋊C8C411yescharacteristic
8C2×#88054C411yescharacteristic
9C2×#88054C2211yescharacteristic
10C2×C8×Dic13C411yescharacteristic
11C2×C8×Dic13C2211yescharacteristic
12C2×C4×#1055C411yescharacteristic
13#11718491—22no—
14#11718491—22no—
15#11718286—22no—
16#11718285—22no—
17#11718255—22no—
18#11718254—22no—
19C22×Dic26Q811yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21C22×C8×C13C2×C411yescharacteristic
22C2×C42×C13C2×C411yescharacteristic
23C2×C4⋊Dic13D411yescharacteristic
24C2×#6101D411yescharacteristic
25C2×#6101Q811yescharacteristic
26C2×C4×Dic13C2×C411yescharacteristic
27C2×C4×Dic13C2311yescharacteristic
28C22×#1055C2×C411yescharacteristic
29C22×#1055C2×C411yescharacteristic
30C4×Dic26—22no—
31C4×Dic26—22no—
32C22⋊#1057—24no—
33#88110—24no—
34C4⋊#1057—24no—
35C13×C4⋊C8—22no—
36#88054—22no—
37#88054—22no—
38C8×Dic13—21no—
39C8×Dic13—21no—
40C8×Dic13D412yes—
41C8×Dic13D412yes—
42C4×#1055—21no—
43C4×#1055—21no—
44#8621—131nomaximal, Sylow
45C22×C4×C13C4⋊C411yescharacteristic
46C22×C4×C13C4⋊C411yescharacteristic
47C22×C4×C13C22×C411yescharacteristic
48C22×Dic13C4⋊C411yescharacteristic
49C22×Dic13C4⋊C411yescharacteristic
50C22×Dic13C2×D411yescharacteristic
51C22×Dic13C2×Q811yescharacteristic
52C2×Dic26—22no—
53C2×Dic26—22no—
54C2×Dic26—22no—
55C2×#1057—44no—
56C2×C8×C13—21no—
57C2×C8×C13—41no—
58C2×C8×C13—41no—
59C2×C8×C13C22⋊C412yes—
60C42×C13—21no—
61C42×C13—21no—
62C4⋊Dic13—22no—
63#6101—22no—
64#6101—22no—
65C4×Dic13—21no—
66C4×Dic13—21no—
67C4×Dic13C2×D412yes—
68C4×Dic13#4112yes—
69C2×#1055—22no—
70C2×#1055—21no—
71C2×#1055—41no—
72C2×#1055C22⋊C411yescharacteristic
73C2×#1055C22⋊C411yescharacteristic
74C2×C8×Q8—131no—
75#1568—132no—
76#1467—132no—
77#1290—132no—
78C23×C13C2×C4⋊C411yescharacteristic
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—41no—
85C2×C4×C13#10812yes—
86C2×C4×C13C2×C22⋊C411yescharacteristic
87C2×C4×C13#11711yescharacteristic
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—21no—
93C2×Dic13—41no—
94C2×Dic13—41no—
95C2×Dic13#10812yes—
96C2×Dic13#12112yes—
97C2×Dic13C22⋊Q812yes—
98Dic26—28no—
99#1057—84no—
100C8×C13—22no—
101C8×C13—41no—
102#1055—21no—
103#1055—41no—
104#1055#10112yes—
105C2×C4×Q8—131no—
106C8×Q8—262no—
107C8×Q8—262no—
108#432—134no—
109C2×C4⋊C8—131no—
110C2×C4⋊C8—131no—
111C2×C4⋊C8#26111yescharacteristic
112C2×C4×C8—131no—
113C2×C4×C8—131no—
114C2×C4×C8—131no—
115#335—262no—
116#334—262no—
117#324—262no—
118#324—262no—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13#38011yescharacteristic
122C22×C13C2×#10811yescharacteristic
123C22×C13C2×#10811yescharacteristic
124C4×C13—21no—
125C4×C13—22no—
126C4×C13—41no—
127C4×C13C2×#10111yescharacteristic
128C4×C13#41311yescharacteristic
129Dic13—22no—
130Dic13—22no—
131Dic13—22no—
132Dic13—41no—
133C22×Q8—131no—
134C22×C8—131no—
135C22×C8—131no—
136C22×C8C2×#26111yescharacteristic
137C22×C8C2×#26111yescharacteristic
138C4×Q8—262no—
139C4×Q8—262no—
140C2×C4⋊C4—131no—
141C2×C4⋊C4—131no—
142C2×C4⋊C4—131no—
143C2×C42—131no—
144C2×C42—131no—
145C2×C42C2×#26111yescharacteristic
146C4⋊C8—22no—
147C4⋊C8—262no—
148C4⋊C8—264no—
149C4⋊C8—262no—
150C22⋊C8—264no—
151#97—264no—
152C4×C8—132no—
153C4×C8—132no—
154C4×C8—261no—
155C4×C8—261no—
156C4×C8—261no—
157C4×C8—261no—
158C2×C13—21no—
159C2×C13—21no—
160C2×C13#180111yescharacteristic
161C2×C13#181011yescharacteristic
162C2×C13#181211yescharacteristic
163C2×Q8—262no—
164C2×Q8—262no—
165C2×Q8—262no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4C4⋊#26111yescharacteristic
171C22×C4C4⋊#26111yescharacteristic
172C22×C4C22×#26111yescharacteristic
173C2×C8—21no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—131no—
177C2×C8—131no—
178C2×C8—262no—
179C2×C8—261no—
180C2×C8—521no—
181C2×C8—524no—
182C2×C8C22⋊#26112yes—
183C4⋊C4—262no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C42—21no—
187C42—21no—
188C42—132no—
189C42—132no—
190C42—261no—
191C42—261no—
192C13#862111yescharacteristic, complemented, Sylow
193C23C2×C4⋊#26111yescharacteristic
194Q8—268no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—132no—
202C2×C4—132no—
203C2×C4—132no—
204C2×C4—261no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—261no—
209C2×C4—521no—
210C2×C4—521no—
211C2×C4#8810412yes—
212C2×C4#8823711yescharacteristic
213C2×C4C2×C22⋊#26111yescharacteristic
214C8—22no—
215C8—41no—
216C8—132no—
217C8—261no—
218C8—521no—
219C8—1044no—
220C22—21no—
221C22—21no—
222C22C2×#8810411yescharacteristic
223C22D13⋊#10811yescharacteristic
224C22#1171913611yescharacteristic
225C4—21no—
226C4—22no—
227C4—41no—
228C4—262no—
229C4—262no—
230C4—262no—
231C4—521no—
232C4#1171914811yescharacteristic
233C4D13⋊#10111yescharacteristic
234C2—21no—
235C2—21no—
236C2#1313070311yescharacteristic
237C2#1313071611yescharacteristic
238C2#1313071911yescharacteristic
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊C8C4
socleC22×C13#380
prime radicalC23×C13C2×C4⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4⋊C8#261
hypocenterC13#8621
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
192. C13#8621semidirect

Maximal subgroups

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

subgroupindex
#131303982
#131300982
#131297012
C2×#117184912
#862113