Finite Group Databasebeta

← C2×#13129777 #16786788

Subgroups — C2×#13129777 #16786788

Order 3328.

510 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C2×#11718285C212yesmaximal
2#13129777C214yesmaximal, direct product factor
3C2×#11718638C211yesmaximal, characteristic
4C22×C13×C4⋊C4C411yescharacteristic
5C22×C4⋊Dic13C2211yescharacteristic
6C22×C4×Dic13C411yescharacteristic
7C2×C22⋊#1057—22no—
8C2×#88071—22no—
9#11718638—22no—
10#11718638C412yes—
11#11718638C2212yes—
12#11718285—22no—
13#11718285C2214yes—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13—21no—
17C23×Dic13D412yes—
18C22×#1057—42no—
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4—41no—
21C2×C13×C4⋊C4—41no—
22C2×C13×C4⋊C4C2×C412yes—
23C2×C4⋊Dic13—41no—
24C2×C4⋊Dic13—41no—
25C2×C4⋊Dic13C2×C411yescharacteristic
26C2×C4⋊Dic13D412yes—
27C2×C4⋊Dic13C2311yescharacteristic
28C2×C4×Dic13—21no—
29C2×C4×Dic13—22no—
30C2×C4×Dic13C814yescomplemented
31C2×C4×Dic13C2×C412yes—
32C22⋊#1057—24no—
33C22⋊#1057—42no—
34#88071—24no—
35#88071—24no—
36C2×#1324—131nomaximal, Sylow
37C24×C13C22⋊C411yescharacteristic
38C22×C4×C13—21no—
39C22×C4×C13—21no—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13—44no—
43C22×C4×C13—41no—
44C22×C4×C13—41no—
45C22×C4×C13C22⋊C411yescharacteristic
46C22×C4×C13C2×C812yes—
47C22×C4×C13M1612yes—
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—24no—
50C22×Dic13—22no—
51C22×Dic13—22no—
52C22×Dic13—22no—
53C22×Dic13—42no—
54C22×Dic13—42no—
55C22×Dic13—44no—
56C22×Dic13C22⋊C412yes—
57C22×Dic13C2×D412yes—
58C2×#1057—44no—
59C2×#1057—84no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—42no—
62C4⋊Dic13—41no—
63C4⋊Dic13—42no—
64C4⋊Dic13—41no—
65C4×Dic13—24no—
66C4×Dic13—22no—
67C4×Dic13C2×C814yescomplemented
68C2×#382—131no—
69C2×#324—132no—
70#1324—134no—
71C23×C13—22no—
72C23×C13—22no—
73C23×C13C22⋊C812yes—
74C23×C13#9911yescharacteristic
75C23×C13#9911yescharacteristic
76C23×C13#10112yes—
77C23×C13C2×C22⋊C411yescharacteristic
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—44no—
87C2×C4×C13—42no—
88C2×C4×C13—82no—
89C2×C4×C13—82no—
90C2×C4×C13C22⋊C812yes—
91C2×C4×C13C22×C811yescharacteristic
92C2×C4×C13C2×M1611yescharacteristic
93C2×Dic13—24no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—48no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—44no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—82no—
103#1057—84no—
104C22×C4⋊C4—131no—
105C22×C4⋊C4#26111yescharacteristic
106C22×C42—131no—
107C2×C22⋊C8—262no—
108#382—132no—
109#382—132no—
110#382—262no—
111C2×#95—262no—
112#324—134no—
113#324—262no—
114C22×C13—24no—
115C22×C13—24no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13#32412yes—
121C22×C13#32412yes—
122C22×C13#35412yes—
123C22×C13#35512yes—
124C22×C13C2×C22⋊C811yescharacteristic
125C22×C13C2×#9911yescharacteristic
126C22×C13C2×#10111yescharacteristic
127C4×C13—22no—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—82no—
131Dic13—44no—
132Dic13—42no—
133Dic13—42no—
134C23×C4—21no—
135C23×C4—132no—
136C23×C4—261no—
137C23×C4C2×#26111yescharacteristic
138C22×C8—522no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4—131no—
144C2×C4⋊C4—131no—
145C2×C4⋊C4—521no—
146C2×C4⋊C4—521no—
147C2×C4⋊C4C2×#26112yes—
148C2×C42—134no—
149C2×C42—132no—
150C2×C42—262no—
151C2×C42—261no—
152C22⋊C8—264no—
153C22⋊C8—522no—
154#95—264no—
155#95—264no—
156C2×C13—21no—
157C2×C13—22no—
158C2×C13—21no—
159C2×C13#132414yescomplemented
160C2×C13C2×#32411yescharacteristic
161C2×C13C2×#35411yescharacteristic
162C2×C13C2×#35511yescharacteristic
163C24C22⋊#26111yescharacteristic
164C22×C4—22no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—44no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—132no—
172C22×C4—132no—
173C22×C4—264no—
174C22×C4—262no—
175C22×C4—262no—
176C22×C4—262no—
177C22×C4—522no—
178C22×C4—522no—
179C22×C4—524no—
180C22×C4D13⋊C812yes—
181C22×C4#611812yes—
182C22×C4C22⋊#26111yescharacteristic
183C22×C4C22×#26111yescharacteristic
184C2×C8—524no—
185C2×C8—1044no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—522no—
189C4⋊C4—521no—
190C4⋊C4—521no—
191C42—134no—
192C42—264no—
193C42—262no—
194C13C2×#132411yescharacteristic, complemented, Sylow
195C23—22no—
196C23—22no—
197C23#8811112yes—
198C23#8811312yes—
199C23#8811911yescharacteristic
200C23#8811911yescharacteristic
201C23C2×C22⋊#26111yescharacteristic
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4—82no—
213C2×C4—82no—
214C2×C4—264no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—528no—
218C2×C4—522no—
219C2×C4—522no—
220C2×C4—524no—
221C2×C4—522no—
222C2×C4—522no—
223C2×C4—1042no—
224C2×C4#8811112yes—
225C2×C4C2×D13⋊C811yescharacteristic
226C2×C4C2×#611811yescharacteristic
227C8—1044no—
228C22—24no—
229C22—24no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22#1171828612yes—
235C22#1171828612yes—
236C22#1171829512yes—
237C22#1171830012yes—
238C22C2×#8811111yescharacteristic
239C22C2×#8811311yescharacteristic
240C22C2×#8811911yescharacteristic
241C4—22no—
242C4—21no—
243C4—21no—
244C4—82no—
245C4—524no—
246C4—522no—
247C4—522no—
248C2—21no—
249C2—22no—
250C2—21no—
251C2#1312977714yesdirect product factor
252C2C2×#1171828611yescharacteristic
253C2C2×#1171830011yescharacteristic
254C2C2×#1171829511yescharacteristic
subgroupG/H
centerC23#88119
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13#99
prime radicalC24×C13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#1324
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13129777C2direct (N × H)
30. C2×C4×Dic13C8semidirect
67. C4×Dic13C2×C8semidirect
159. C2×C13#1324semidirect
194. C13C2×#1324semidirect
251. C2#13129777direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117182852
#131297772
C2×#117186382
C2×#132413