Finite Group Databasebeta

← #16778467

Subgroups — #16778467

Order 3328.

462 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 104 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#13130764C211yesmaximal, characteristic
2#13130621C211yesmaximal, characteristic
3#13129657C214yesmaximal
4#13117403C211yesmaximal, characteristic
5C2×#88141C412yes—
6C2×#88123C411yescharacteristic
7C2×#88112—21no—
8C2×#88110—21no—
9C13×#384C411yescharacteristic
10C4⋊C4×Dic13—21no—
11C4⋊C4×Dic13—21no—
12#11718635C2212yes—
13#11718634—21no—
14#11718634—21no—
15C42×Dic13C2211yescharacteristic
16#11718290—21no—
17#11718290—21no—
18#11718290C2212yes—
19#11718290C2212yes—
20C22×Dic26C2×C412yes—
21C22×#1057—22no—
22C22×#1057—22no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C42×C13C2×C411yescharacteristic
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13—21no—
29C2×#6101—22no—
30C2×C4×Dic13—22no—
31C2×C4×Dic13C2×C411yescharacteristic
32C2×C4×Dic13D411yescharacteristic
33C2×C4×Dic13D411yescharacteristic
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13C2311yescharacteristic
37#88141—44no—
38#88123—24no—
39#88112—24no—
40#88110—42no—
41#88071—22no—
42#88071—22no—
43#7624—131nomaximal, Sylow
44C22×C4×C13—22no—
45C22×C4×C13C22⋊C411yescharacteristic
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C22×C411yescharacteristic
48C22×Dic13—22no—
49C22×Dic13C22⋊C411yescharacteristic
50C22×Dic13C22⋊C411yescharacteristic
51C22×Dic13C2×D411yescharacteristic
52C22×Dic13C2×D411yescharacteristic
53C2×Dic26—22no—
54C2×Dic26—42no—
55C2×Dic26—42no—
56C2×Dic26M1614yes—
57C2×#1057—24no—
58C2×#1057—42no—
59C2×#1057—42no—
60C2×#1057—42no—
61C2×#1057—42no—
62C2×#1057—42no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—42no—
66C42×C13—22no—
67C4⋊Dic13—24no—
68C4⋊Dic13—24no—
69#6101—44no—
70C4×Dic13—22no—
71C4×Dic13—22no—
72C4×Dic13—22no—
73C4×Dic13—41no—
74C4×Dic13—41no—
75C4×Dic13—44no—
76C4×Dic13SD1612yes—
77C4×Dic13Q1612yes—
78C4×C4⋊Q8—131no—
79#1839—131no—
80#1767—131no—
81#1272—134no—
82C23×C13C2×C22⋊C411yescharacteristic
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13#10312yes—
93C2×C4×C13#10412yes—
94C2×C4×C13C2×M1612yes—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—24no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13#10012yes—
107C2×Dic13#10312yes—
108C2×Dic13C2×SD1611yescharacteristic
109C2×Dic13C2×Q1611yescharacteristic
110C2×Dic13#13712yes—
111Dic26—44no—
112Dic26—44no—
113#1057—44no—
114#1057—82no—
115C2×C4⋊Q8—131no—
116C2×C4×Q8—132no—
117C2×C4⋊C8—261no—
118C2×#97—261no—
119#391—132no—
120#389—261no—
121#389—261no—
122#384#26111yescharacteristic
123C4×C4⋊C4—261no—
124C4×C4⋊C4—261no—
125C43—131no—
126#336—132no—
127#336—132no—
128#336—261no—
129#336—261no—
130C22×C13#40711yescharacteristic
131C22×C13#41011yescharacteristic
132C22×C13C2×#10011yescharacteristic
133C22×C13C2×#10311yescharacteristic
134C22×C13#41911yescharacteristic
135C22×C13C2×#10411yescharacteristic
136C22×C13#42111yescharacteristic
137C4×C13—22no—
138C4×C13—22no—
139C4×C13—22no—
140C4×C13—82no—
141Dic13—22no—
142Dic13—21no—
143Dic13—21no—
144Dic13—22no—
145Dic13—22no—
146Dic13—44no—
147C22×Q8—132no—
148C22×C8—262no—
149C22×C8—262no—
150C4⋊Q8—264no—
151C4×Q8—524no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—261no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4—262no—
157C2×C4⋊C4C2×#26112yes—
158C2×C42—131no—
159C2×C42—131no—
160C2×C42—131no—
161C2×C42—131no—
162C2×C42—131no—
163C2×C42—131no—
164C2×C42—262no—
165C2×C42C2×#26111yescharacteristic
166C4⋊C8—264no—
167#97—522no—
168#95—262no—
169#95—262no—
170C2×C13#146611yescharacteristic
171C2×C13#148711yescharacteristic
172C2×C13#149111yescharacteristic
173C2×C13#150311yescharacteristic
174C2×C13#151511yescharacteristic
175C2×C13#153011yescharacteristic
176C2×C13#154811yescharacteristic
177C2×Q8—134no—
178C2×Q8—262no—
179C2×Q8—522no—
180C2×Q8—522no—
181C22×C4—22no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—131no—
186C22×C4—262no—
187C22×C4C22⋊#26111yescharacteristic
188C22×C4C22⋊#26111yescharacteristic
189C22×C4C22×#26111yescharacteristic
190C2×C8—264no—
191C2×C8—522no—
192C2×C8—522no—
193C2×C8—522no—
194C2×C8—522no—
195C2×C8—522no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—264no—
200C4⋊C4—264no—
201C4⋊C4—524no—
202C42—22no—
203C42—132no—
204C42—132no—
205C42—262no—
206C42—262no—
207C42—262no—
208C42—521no—
209C42—521no—
210C42—524no—
211C13#762411yescharacteristic, complemented, Sylow
212C23C2×C22⋊#26111yescharacteristic
213Q8—524no—
214Q8—524no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—132no—
225C2×C4—131no—
226C2×C4—132no—
227C2×C4—131no—
228C2×C4—132no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—261no—
237C2×C4—264no—
238C2×C4—522no—
239C2×C4—522no—
240C2×C4#8811612yes—
241C2×C4#8811712yes—
242C2×C4D13⋊M1612yes—
243C8—524no—
244C8—1042no—
245C22#1171912611yescharacteristic
246C22C2×#8811611yescharacteristic
247C22#1171914011yescharacteristic
248C22D13⋊#10011yescharacteristic
249C22C2×#8811711yescharacteristic
250C22#1171915311yescharacteristic
251C22#1171915611yescharacteristic
252C4—22no—
253C4—22no—
254C4—22no—
255C4—82no—
256C4—262no—
257C4—262no—
258C4—262no—
259C4—261no—
260C4—261no—
261C4—524no—
262C2#1313009711yescharacteristic
263C2#1313016611yescharacteristic
264C2#1313018011yescharacteristic
265C2#1313021911yescharacteristic
266C2#1313025911yescharacteristic
267C2#1313030611yescharacteristic
268C2#1313035011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#7624
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
211. C13#7624semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131306212
#131296572
#131174032
#762413