Finite Group Databasebeta

← C2×#11719146 #13131416

Subgroups — C2×#11719146 #13131416

Order 1664.

792 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 218 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×#6129C211yesmaximal, characteristic
2C22×#6122C211yesmaximal, characteristic, complemented
3C23×#1057C211yesmaximal, characteristic, complemented
4C2×C22⋊#1057C212yesmaximal, complemented
5#11719146C218yesmaximal, direct product factor
6C2×#88111C212yesmaximal, complemented
7C22×D4×C13C411yescharacteristic
8C22×C22⋊D13C411yescharacteristic
9C22×C22⋊D13C411yescharacteristic
10C23×Dic13C2211yescharacteristic
11C23×Dic13C2211yescharacteristic
12C2×#6129—24no—
13C2×#6129—24no—
14C2×#6129C414yes—
15C2×#6129C2214yes—
16C22×C4×D13C2211yescharacteristic
17C22×Dic26C411yescharacteristic
18C2×#6122—24no—
19C2×#6122C2214yescomplemented
20C22×#1057—24no—
21C22×#1057C2212yes—
22C22×#1057C2212yes—
23C22×#1057C2214yescomplemented
24C22⋊#1057C2218yescomplemented
25#88111C2218yescomplemented
26C24×C13C2×C411yescharacteristic
27C24×C13C2×C411yescharacteristic
28C23×D13C2×C411yescharacteristic
29C2×D4×C13—24no—
30C2×D4×C13C2×C414yes—
31C22×C4×C13C2×C411yescharacteristic
32C2×C22⋊D13—24no—
33C2×C22⋊D13—24no—
34C2×C22⋊D13C2×C414yes—
35C2×C22⋊D13C2×C414yes—
36C22×Dic13—22no—
37C22×Dic13—22no—
38C22×Dic13C2×C411yescharacteristic
39C22×Dic13C2×C412yes—
40C22×Dic13C2×C411yescharacteristic
41C22×Dic13C2×C412yes—
42C22×Dic13D414yes—
43C22×Dic13D414yes—
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2312yes—
47#6129—216no—
48#6129—28no—
49#6129—28no—
50C2×C4×D13—22no—
51C2×C4×D13—22no—
52C2×C4×D13C2×C412yes—
53C2×C4×D13C2312yes—
54C2×Dic26—24no—
55C2×Dic26C2×C414yes—
56#6122—28no—
57C2×#1057—24no—
58C2×#1057—28no—
59C2×#1057—24no—
60C2×#1057C2314yes—
61C2×#1057C2314yes—
62C2×#408—131nomaximal, Sylow
63C23×C13—24no—
64C23×C13—22no—
65C23×C13—24no—
66C23×C13C22⋊C414yes—
67C23×C13C22×C412yes—
68C23×C13C22×C412yes—
69C23×C13C22×C411yescharacteristic
70C22×D13—22no—
71C22×D13—24no—
72C22×D13C22×C412yes—
73D4×C13—28no—
74C2×C4×C13—22no—
75C2×C4×C13C22×C412yes—
76C22⋊D13—28no—
77C22⋊D13—28no—
78C2×Dic13—22no—
79C2×Dic13—24no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13C22⋊C414yes—
83C2×Dic13C22⋊C418yes—
84C2×Dic13C22×C412yes—
85C2×Dic13C22×C412yes—
86C2×Dic13C22×C411yescharacteristic
87C2×Dic13C2×D412yes—
88C2×Dic13C2×D412yes—
89C2×Dic13C2×D414yes—
90C2×Dic13C2×D414yes—
91C2×Dic13C2411yescharacteristic
92C4×D13—24no—
93C4×D13—22no—
94C4×D13—22no—
95Dic26—28no—
96#1057—24no—
97#1057—24no—
98C22×#41—131no—
99C22×M16—131no—
100C23×C8—131no—
101#408—138no—
102C2×C22⋊C8—132no—
103C2×C22⋊C8—132no—
104C22×C13—24no—
105C22×C13—28no—
106C22×C13—22no—
107C22×C13—24no—
108C22×C13—44no—
109C22×C13C2×C22⋊C414yes—
110C22×C13C2×C22⋊C412yes—
111C22×C13#13114yes—
112C22×C13C23×C411yescharacteristic
113C2×D13—22no—
114C2×D13—24no—
115C2×D13—44no—
116C4×C13—22no—
117Dic13—22no—
118Dic13C2×C22⋊C414yes—
119Dic13C2×C22⋊C412yes—
120Dic13C22×D411yescharacteristic
121Dic13C22×D411yescharacteristic
122C2×#41—134no—
123C2×#41—134no—
124C2×#41—264no—
125C2×#41—264no—
126C22×Q8—131no—
127C22×D4—131no—
128C22×D4—131no—
129C22×D4#26111yescharacteristic
130C23×C4—131no—
131C23×C4—131no—
132C23×C4—131no—
133C2×M16—134no—
134C2×M16—264no—
135C22×C8—132no—
136C22×C8—134no—
137C22×C8—132no—
138C22×C8—264no—
139C22⋊C8—138no—
140C22⋊C8—138no—
141C2×C13—24no—
142C2×C13—42no—
143C2×C13#40814yescomplemented
144C2×C13C22×C22⋊C411yescharacteristic
145C2×C13C2×#13112yes—
146D13—42no—
147C24—131no—
148C24C2×#26111yescharacteristic
149C24C2×#26111yescharacteristic
150#41—268no—
151#41—268no—
152#41—2616no—
153C2×Q8—134no—
154C2×Q8—264no—
155C2×D4—24no—
156C2×D4—134no—
157C2×D4—134no—
158C2×D4—264no—
159C2×D4—264no—
160C2×D4C2×#26114yes—
161C22×C4—134no—
162C22×C4—134no—
163C22×C4—132no—
164C22×C4—132no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—132no—
168C22×C4—132no—
169C22×C4—131no—
170C22×C4—132no—
171C22×C4—132no—
172C22×C4—262no—
173C22×C4—262no—
174C22×C4—262no—
175C22×C4—262no—
176C22×C4C2×#26111yescharacteristic
177M16—268no—
178C2×C8—134no—
179C2×C8—134no—
180C2×C8—264no—
181C2×C8—268no—
182C2×C8—264no—
183C13C2×#40811yescharacteristic, complemented, Sylow
184C23—24no—
185C23—24no—
186C23—22no—
187C23—132no—
188C23—264no—
189C23—262no—
190C23C22⋊#26114yes—
191C23C22×#26112yes—
192C23C22×#26112yes—
193C23C22×#26111yescharacteristic
194Q8—268no—
195D4—28no—
196D4—268no—
197D4—268no—
198C2×C4—22no—
199C2×C4—132no—
200C2×C4—132no—
201C2×C4—134no—
202C2×C4—134no—
203C2×C4—134no—
204C2×C4—138no—
205C2×C4—131no—
206C2×C4—131no—
207C2×C4—132no—
208C2×C4—132no—
209C2×C4—264no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—264no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4C22×#26112yes—
217C8—264no—
218C8—264no—
219C22—24no—
220C22—28no—
221C22—24no—
222C22—22no—
223C22—44no—
224C22—264no—
225C22—262no—
226C22—524no—
227C22#8823814yes—
228C22C2×C22⋊#26114yes—
229C22C2×C22⋊#26112yes—
230C22C23×#26111yescharacteristic
231C4—22no—
232C4—132no—
233C4—134no—
234C4—131no—
235C4—131no—
236C4—262no—
237C2—24no—
238C2—42no—
239C2—522no—
240C2#1171914614yesdirect product factor
241C2C2×#8823812yes—
242C2C22×C22⋊#26111yescharacteristic
subgroupG/H
centerC23C22×#261
commutatorC22×C13C23×C4
FrattiniC22C23×#261
FittingC22×D4×C13C4
socleC23×C13C22×C4
prime radicalC22×#6129C2
cosocleC2×Dic13C24
hypercenterC22×D4#261
hypocenterC13C2×#408
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×#6122C2semidirect
3. C23×#1057C2semidirect
4. C2×C22⋊#1057C2semidirect
5. #11719146C2direct (N × H)
6. C2×#88111C2semidirect
19. C2×#6122C22semidirect
23. C22×#1057C22semidirect
24. C22⋊#1057C22semidirect
25. #88111C22semidirect
143. C2×C13#408semidirect
183. C13C2×#408semidirect
240. C2#11719146direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#61292
C22×#61222
C23×#10572
C2×C22⋊#10572
#117191462
C2×#881112
C2×#40813