Finite Group Databasebeta

← #16786046

Subgroups — #16786046

Order 3328.

1318 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 184 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
1C22×#88113C214yesmaximal
2#13130499C212yesmaximal
3C22×#88142C211yesmaximal, characteristic
4C23×Dic26C2212yes—
5C22×#6122C2214yes—
6C22×C13×C4⋊C4C411yescharacteristic
7C22×C4⋊Dic13C411yescharacteristic
8C22×#6101C412yes—
9C22×C4×Dic13C2211yescharacteristic
10C2×#88142—28no—
11C2×#88142—24no—
12C2×#88113—28no—
13C2×#88113—216no—
14#11718290—24no—
15C23×C4×C13C2×C412yes—
16C23×C4×C13C2×C411yescharacteristic
17C23×Dic13C2×C411yescharacteristic
18C23×Dic13C2×C412yes—
19C23×Dic13C2311yescharacteristic
20C22×Dic26—24no—
21C22×Dic26—24no—
22C22×Dic26—28no—
23C22×Dic26—28no—
24C22×Dic26D418yes—
25C2×#6122—24no—
26C2×#6122—28no—
27C2×#6122—28no—
28C2×#6122D418yes—
29C22×#1057—24no—
30C2×C13×C4⋊C4—24no—
31C2×C13×C4⋊C4—22no—
32C2×C4⋊Dic13—22no—
33C2×C4⋊Dic13—24no—
34C2×#6101—24no—
35C2×#6101—24no—
36C2×#6101—24no—
37C2×C4×Dic13—24no—
38C2×C4×Dic13D414yes—
39#88142—232no—
40#88113—232no—
41#10983—131nomaximal, Sylow
42C24×C13C22×C411yescharacteristic
43C22×C4×C13—22no—
44C22×C4×C13—24no—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—28no—
48C22×C4×C13C22⋊C414yes—
49C22×C4×C13C22⋊C412yes—
50C22×Dic13—22no—
51C22×Dic13—24no—
52C22×Dic13—22no—
53C22×Dic13—22no—
54C22×Dic13—28no—
55C22×Dic13C22⋊C414yes—
56C22×Dic13C22⋊C412yes—
57C22×Dic13C2×D414yes—
58C22×Dic13C2×D414yes—
59C22×Dic13C2×D412yes—
60C22×Dic13#4114yes—
61C2×Dic26—28no—
62C2×Dic26—216no—
63C2×Dic26—216no—
64C2×Dic26—28no—
65C2×Dic26—44no—
66C2×Dic26—48no—
67C2×Dic26—48no—
68C2×Dic26—44no—
69C2×Dic26—44no—
70C2×Dic26—44no—
71#6122—216no—
72#6122—48no—
73C2×#1057—28no—
74C2×#1057—44no—
75C2×#1057—44no—
76C13×C4⋊C4—28no—
77C4⋊Dic13—28no—
78#6101—216no—
79C4×Dic13—28no—
80C22×C4⋊Q8—131no—
81C22×#101—134no—
82#1728—132no—
83C23×C13—22no—
84C23×C13—22no—
85C23×C13C2×C22⋊C412yes—
86C23×C13C2×C22⋊C411yescharacteristic
87C23×C13C4×D414yes—
88C2×C4×C13—28no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—24no—
92C2×C4×C13—28no—
93C2×C4×C13—44no—
94C2×C4×C13—44no—
95C2×C4×C13#10114yescomplemented
96C2×Dic13—28no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—24no—
100C2×Dic13—28no—
101C2×Dic13—44no—
102C2×Dic13—44no—
103C2×Dic13#10114yescomplemented
104C2×Dic13#12014yes—
105C2×Dic13#12014yes—
106C2×Dic13#12118yes—
107C2×Dic13#12114yes—
108C2×Dic13#12314yes—
109C2×Dic13#12412yes—
110C2×Dic13#12712yes—
111Dic26—416no—
112Dic26—416no—
113#1057—48no—
114C23×Q8—132no—
115C22×M16—134no—
116C2×C4⋊Q8—264no—
117C2×C4⋊Q8—268no—
118C22×C4⋊C4—132no—
119C22×C4⋊C4—131no—
120C22×C4⋊C4#26111yescharacteristic
121C22×C42—131no—
122C2×#101—2616no—
123C2×#101—268no—
124#336—264no—
125C22×C13—28no—
126C22×C13—22no—
127C22×C13—22no—
128C22×C13#37911yescharacteristic
129C22×C13#38614yes—
130C22×C13#39012yes—
131C22×C13C2×#10112yes—
132C22×C13C2×#10112yes—
133C4×C13—24no—
134C4×C13—44no—
135Dic13—24no—
136Dic13—44no—
137Dic13#39214yes—
138Dic13#39414yes—
139C22×Q8—138no—
140C22×Q8—264no—
141C22×Q8—264no—
142C22×Q8—268no—
143C22×Q8—268no—
144C23×C4—131no—
145C23×C4—132no—
146C23×C4—131no—
147C23×C4C2×#26112yes—
148C23×C4C2×#26111yescharacteristic
149C2×M16—138no—
150C2×M16—264no—
151C2×M16—268no—
152C2×M16—268no—
153C22×C8—264no—
154C4⋊Q8—2632no—
155C2×C4⋊C4—24no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—264no—
158C2×C4⋊C4—264no—
159C2×C4⋊C4—264no—
160C2×C4⋊C4—264no—
161C2×C4⋊C4—262no—
162C2×C42—134no—
163C2×C42—264no—
164#101—2632no—
165C2×C13—24no—
166C2×C13#143811yescharacteristic
167C2×C13#178411yescharacteristic
168C2×C13#178411yescharacteristic
169C2×C13#196614yes—
170C24C22×#26111yescharacteristic
171C2×Q8—268no—
172C2×Q8—2616no—
173C2×Q8—2616no—
174C2×Q8—268no—
175C2×Q8—524no—
176C2×Q8—528no—
177C2×Q8—524no—
178C2×Q8—528no—
179C2×Q8—524no—
180C2×Q8—524no—
181C22×C4—22no—
182C22×C4—24no—
183C22×C4—28no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—134no—
187C22×C4—134no—
188C22×C4—134no—
189C22×C4—132no—
190C22×C4—132no—
191C22×C4—134no—
192C22×C4—264no—
193C22×C4—262no—
194C22×C4—268no—
195C22×C4—262no—
196C22×C4—262no—
197C22×C4C22⋊#26114yes—
198C22×C4C22⋊#26112yes—
199M16—2616no—
200M16—528no—
201C2×C8—268no—
202C2×C8—524no—
203C2×C8—524no—
204C4⋊C4—28no—
205C4⋊C4—2616no—
206C4⋊C4—268no—
207C42—268no—
208C13#1098311yescharacteristic, complemented, Sylow
209C23—22no—
210C23—22no—
211C23D4×#26114yes—
212C23C2×C22⋊#26112yes—
213C23C2×C22⋊#26111yescharacteristic
214Q8—5216no—
215Q8—5216no—
216C2×C4—28no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—24no—
220C2×C4—28no—
221C2×C4—44no—
222C2×C4—44no—
223C2×C4—134no—
224C2×C4—134no—
225C2×C4—138no—
226C2×C4—134no—
227C2×C4—134no—
228C2×C4—132no—
229C2×C4—132no—
230C2×C4—134no—
231C2×C4—268no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—264no—
235C2×C4—268no—
236C2×C4—524no—
237C2×C4—524no—
238C2×C4#8811314yescomplemented
239C8—528no—
240C22—22no—
241C22—22no—
242C22—28no—
243C22C2×#8811312yes—
244C22#1171915014yes—
245C22#1171915112yes—
246C22D13⋊#10112yes—
247C22#1171917111yescharacteristic
248C4—24no—
249C4—44no—
250C4—134no—
251C4—134no—
252C4—264no—
253C4—524no—
254C2—24no—
255C2#1313001811yescharacteristic
256C2#1313067011yescharacteristic
257C2#1313067111yescharacteristic
258C2#1313097914yes—
subgroupG/H
centerC23C2×C22⋊#261
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
cosocleC23×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#10983
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
95. C2×C4×C13#101semidirect
103. C2×Dic13#101semidirect
208. C13#10983semidirect
238. C2×C4#88113semidirect

Maximal subgroups

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

subgroupindex
C22×#881132
#131304992
C22×#881422
#1098313