Finite Group Databasebeta

← #16778564

Subgroups — #16778564

Order 3328.

456 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 122 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#13130753C212yesmaximal
2#13129657C212yesmaximal
3#13129656C212yesmaximal
4C4×#88198C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic
6C2×#88198C411yescharacteristic
7C2×C4×Dic26C411yescharacteristic
8C2×C4⋊#1057—22no—
9#11718891C2211yescharacteristic
10#11718637C411yescharacteristic
11#11718635C2211yescharacteristic
12#11718633—22no—
13C4×#6101—22no—
14C42×Dic13C2211yescharacteristic
15#11718290—22no—
16#11718290C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×Dic26C2×C411yescharacteristic
19C22×#1057—24no—
20C4×Q8×C13—42no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C42×C13—21no—
24C2×C42×C13C2×C411yescharacteristic
25#88198—22no—
26#88198—22no—
27C2×C4⋊Dic13C2×C411yescharacteristic
28C2×#6101—22no—
29C2×#6101—21no—
30C2×#6101—22no—
31C2×C4×Dic13—21no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D412yes—
34C2×C4×Dic13D412yes—
35C2×C4×Dic13C2311yescharacteristic
36C4×Dic26—42no—
37C4⋊#1057—44no—
38#88071—22no—
39#88071—22no—
40#7653—131nomaximal, Sylow
41C2×Q8×C13—21no—
42C2×Q8×C13—41no—
43C2×Q8×C13—41no—
44C2×Q8×C13M1612yes—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13C22×C411yescharacteristic
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13C22⋊C412yes—
53C22×Dic13C2×D412yes—
54C2×Dic26—21no—
55C2×Dic26—41no—
56C2×Dic26—41no—
57C2×Dic26M1612yes—
58C2×#1057—44no—
59C2×#1057—44no—
60C2×#1057—44no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—42no—
63C42×C13—22no—
64C42×C13—42no—
65C4⋊Dic13—41no—
66#6101—28no—
67#6101—44no—
68#6101—42no—
69C4×Dic13—21no—
70C4×Dic13—21no—
71C4×Dic13—42no—
72C4×Dic13—41no—
73C4×Dic13—42no—
74C4×Dic13SD1614yes—
75C4×Dic13Q1614yes—
76C4×C4⋊Q8—131no—
77#1831—132no—
78#1272—132no—
79#1272—132no—
80C23×C13C2×C22⋊C411yescharacteristic
81Q8×C13—42no—
82Q8×C13—42no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13#10012yes—
93C2×C4×C13#10314yes—
94C2×C4×C13C2×M1611yescharacteristic
95C2×C4×C13C2×M1611yescharacteristic
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—41no—
102C2×Dic13—41no—
103C2×Dic13—41no—
104C2×Dic13—42no—
105C2×Dic13#10314yes—
106C2×Dic13C2×SD1612yes—
107C2×Dic13C2×Q1612yes—
108Dic26—42no—
109Dic26—42no—
110#1057—84no—
111C2×C4⋊Q8—131no—
112C2×C4×Q8—131no—
113C2×C4×Q8#26111yescharacteristic
114C2×C4⋊C8—262no—
115#391—131no—
116#391—131no—
117#389—262no—
118#384—131no—
119C4×C4⋊C4—262no—
120C43—131no—
121#336—134no—
122#336—262no—
123C22×C13#40711yescharacteristic
124C22×C13#41011yescharacteristic
125C22×C13C2×#10011yescharacteristic
126C22×C13C2×#10312yes—
127C22×C13#42112yes—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—41no—
131C4×C13—42no—
132C4×C13—81no—
133C4×C13#33314yes—
134Dic13—24no—
135Dic13—22no—
136Dic13—22no—
137Dic13—42no—
138Dic13—81no—
139C22×Q8—131no—
140C22×Q8C2×#26111yescharacteristic
141C22×C8—264no—
142C4⋊Q8—262no—
143C4⋊Q8—262no—
144C4×Q8—42no—
145C4×Q8—522no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—131no—
148C2×C4⋊C4—262no—
149C2×C4⋊C4—262no—
150C2×C4⋊C4—261no—
151C2×C4⋊C4C2×#26111yescharacteristic
152C2×C42—21no—
153C2×C42—132no—
154C2×C42—131no—
155C2×C42—132no—
156C2×C42—131no—
157C2×C42—261no—
158C2×C42C2×#26111yescharacteristic
159C4⋊C8—524no—
160#95—262no—
161#95—262no—
162C2×C13#146611yescharacteristic
163C2×C13#148712yes—
164C2×C13#151812yes—
165C2×C13#153611yescharacteristic
166C2×C13C2×#33311yescharacteristic
167C2×Q8—21no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8—132no—
171C2×Q8—261no—
172C2×Q8—521no—
173C2×Q8—521no—
174C2×Q8#611812yes—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—132no—
178C22×C4—132no—
179C22×C4—261no—
180C22×C4—261no—
181C22×C4C22⋊#26111yescharacteristic
182C22×C4C22⋊#26111yescharacteristic
183C22×C4C22×#26111yescharacteristic
184C2×C8—524no—
185C2×C8—524no—
186C2×C8—524no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—268no—
190C4⋊C4—521no—
191C4⋊C4—522no—
192C4⋊C4—524no—
193C42—22no—
194C42—42no—
195C42—134no—
196C42—134no—
197C42—261no—
198C42—261no—
199C42—521no—
200C42—522no—
201C42—522no—
202C13#765311yescharacteristic, complemented, Sylow
203C23C2×C22⋊#26111yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—522no—
207Q8—522no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—132no—
218C2×C4—134no—
219C2×C4—132no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4—521no—
228C2×C4—522no—
229C2×C4#8811714yes—
230C2×C4#8812112yes—
231C2×C4C2×#611811yescharacteristic
232C2×C4D13⋊M1611yescharacteristic
233C8—1044no—
234C22#1171911611yescharacteristic
235C22#1171912711yescharacteristic
236C22C2×#8811712yes—
237C22#1171916612yes—
238C22C2×#8812111yescharacteristic
239C4—21no—
240C4—21no—
241C4—41no—
242C4—42no—
243C4—81no—
244C4—262no—
245C4—262no—
246C4—264no—
247C4—522no—
248C4—1041no—
249C4#1171830314yes—
250C2#1313009511yescharacteristic
251C2#1313016512yes—
252C2#1313026912yes—
253C2#1313032411yescharacteristic
254C2C2×#1171830311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×Q8#261
hypocenterC13#7653
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
202. C13#7653semidirect

Maximal subgroups

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

subgroupindex
#131307532
#131296572
#131296562
C4×#881982
#765313