Finite Group Databasebeta

← #16778481

Subgroups — #16778481

Order 3328.

658 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 116 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#13130562C212yesmaximal
2#13129656C214yesmaximal, complemented
3C2×#11718891C211yesmaximal, characteristic
4C23×Q8×C13C411yescharacteristic
5C22×C4⋊Dic13C411yescharacteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×C22⋊#1057—22no—
8C2×#88110—22no—
9#11718891—22no—
10#11718891C412yes—
11#11718891C2212yes—
12C2×#88071—22no—
13#11718290C2214yes—
14C22×Q8×C13—24no—
15C22×Q8×C13—21no—
16C22×Q8×C13—42no—
17C22×Q8×C13—42no—
18C22×Q8×C13C2×C412yes—
19C23×C4×C13—21no—
20C23×C4×C13C2×C411yescharacteristic
21C23×Dic13—21no—
22C23×Dic13D412yes—
23C22×#1057—24no—
24C2×C4⋊Dic13—21no—
25C2×C4⋊Dic13—42no—
26C2×C4⋊Dic13C2×C412yes—
27C2×C4×Dic13—42no—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×C4×Dic13D412yes—
30C2×C4×Dic13C2311yescharacteristic
31C22⋊#1057—28no—
32#88110—44no—
33#88071—24no—
34#88071—24no—
35#7629—131nomaximal, Sylow
36C24×C13C22⋊C411yescharacteristic
37C2×Q8×C13—24no—
38C2×Q8×C13—22no—
39C2×Q8×C13—416no—
40C2×Q8×C13—42no—
41C2×Q8×C13—42no—
42C2×Q8×C13—42no—
43C2×Q8×C13—42no—
44C2×Q8×C13M1614yes—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—24no—
49C22×C4×C13—22no—
50C22×C4×C13—42no—
51C22×C4×C13—42no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—24no—
55C22×Dic13—24no—
56C22×Dic13—22no—
57C22×Dic13—42no—
58C22×Dic13—42no—
59C22×Dic13—44no—
60C22×Dic13C22⋊C412yes—
61C22×Dic13C2×D412yes—
62C2×#1057—28no—
63C2×#1057—44no—
64C2×#1057—44no—
65C4⋊Dic13—42no—
66C4⋊Dic13—42no—
67C4×Dic13—24no—
68C4×Dic13—41no—
69C4×Dic13—41no—
70C2×#391—131no—
71#1749—132no—
72#1272—134no—
73C23×C13—21no—
74C23×C13—21no—
75C23×C13—22no—
76C23×C13#10012yes—
77C23×C13#10414yes—
78C23×C13C2×C22⋊C411yescharacteristic
79Q8×C13—48no—
80Q8×C13—44no—
81Q8×C13—44no—
82C2×C4×C13—28no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—24no—
88C2×C4×C13—48no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13#9912yes—
92C2×C4×C13C2×M1612yes—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—48no—
99C2×Dic13—42no—
100C2×Dic13—44no—
101C2×Dic13—84no—
102C2×Dic13#13714yes—
103#1057—48no—
104C23×Q8#26111yescharacteristic
105C22×C4⋊C4—131no—
106C22×C42—131no—
107C2×C22⋊C8—262no—
108C2×#97—262no—
109#391—132no—
110#391—132no—
111#391—262no—
112C2×#95—262no—
113#336—134no—
114C22×C13—22no—
115C22×C13—22no—
116C22×C13—24no—
117C22×C13—24no—
118C22×C13#32914yes—
119C22×C13#40711yescharacteristic
120C22×C13C2×#9911yescharacteristic
121C22×C13C2×#10011yescharacteristic
122C22×C13#41912yes—
123C22×C13C2×#10412yes—
124C4×C13—22no—
125C4×C13—22no—
126C4×C13—44no—
127Dic13—24no—
128Dic13—42no—
129Dic13—82no—
130C22×Q8—24no—
131C22×Q8—21no—
132C22×Q8—42no—
133C22×Q8—42no—
134C22×Q8C2×#26112yes—
135C23×C4—21no—
136C23×C4—132no—
137C23×C4—261no—
138C23×C4C2×#26111yescharacteristic
139C22×C8—264no—
140C2×C4⋊C4—132no—
141C2×C4⋊C4—261no—
142C2×C4⋊C4—522no—
143C2×C42—132no—
144C2×C42—131no—
145C2×C42—131no—
146C2×C42—522no—
147C22⋊C8—268no—
148#97—524no—
149#95—264no—
150#95—264no—
151C2×C13—24no—
152C2×C13#146211yescharacteristic
153C2×C13#149112yes—
154C2×C13#150812yes—
155C2×C13C2×#32911yescharacteristic
156C2×C13#155811yescharacteristic
157C24C22⋊#26111yescharacteristic
158C2×Q8—24no—
159C2×Q8—22no—
160C2×Q8—416no—
161C2×Q8—42no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8#612214yes—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—22no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—132no—
174C22×C4—132no—
175C22×C4—264no—
176C22×C4—264no—
177C22×C4—262no—
178C22×C4—522no—
179C22×C4—524no—
180C22×C4—522no—
181C22×C4C22⋊#26111yescharacteristic
182C22×C4C22×#26111yescharacteristic
183C2×C8—268no—
184C2×C8—524no—
185C2×C8—524no—
186C4⋊C4—522no—
187C4⋊C4—522no—
188C42—264no—
189C42—521no—
190C42—521no—
191C13#762911yescharacteristic, complemented, Sylow
192C23—21no—
193C23—22no—
194C23—21no—
195C23#8811814yes—
196C23#8812112yes—
197C23C2×C22⋊#26111yescharacteristic
198Q8—44no—
199Q8—48no—
200Q8—44no—
201C2×C4—28no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—48no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—134no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—528no—
217C2×C4—522no—
218C2×C4—524no—
219C2×C4—1044no—
220C2×C4#8811912yes—
221C2×C4C2×#612212yes—
222C8—528no—
223C22—22no—
224C22—22no—
225C22—24no—
226C22—24no—
227C22#1171829914yes—
228C22#1171915312yes—
229C22C2×#8811812yes—
230C22C2×#8811911yescharacteristic
231C22#1171916911yescharacteristic
232C22C2×#8812111yescharacteristic
233C4—22no—
234C4—22no—
235C4—44no—
236C4—264no—
237C4—522no—
238C4—1042no—
239C2—24no—
240C2#1313008111yescharacteristic
241C2#1313017812yes—
242C2#1313023612yes—
243C2C2×#1171829911yescharacteristic
244C2#1313036911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC23×Q8×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC23×Q8#261
hypocenterC13#7629
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
2. #13129656C2semidirect
191. C13#7629semidirect

Maximal subgroups

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

subgroupindex
#131305622
#131296562
C2×#117188912
#762913