Finite Group Databasebeta

← C2×#13129778 #16786789

Subgroups — C2×#13129778 #16786789

Order 3328.

598 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 128 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#13129778C214yesmaximal, direct product factor
3C2×#11718596C211yesmaximal, characteristic
4C22×C42×C13C411yescharacteristic
5C22×C4⋊Dic13—22no—
6C22×C4⋊Dic13C411yescharacteristic
7C22×C4⋊Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9#11718596—22no—
10#11718596C412yes—
11#11718596C2212yes—
12#11718285—22no—
13#11718285C2214yes—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C23×Dic13—21no—
17C23×Dic13D412yes—
18C22×#1057—42no—
19C2×C42×C13—21no—
20C2×C42×C13—22no—
21C2×C42×C13C814yescomplemented
22C2×C42×C13C2×C412yes—
23C2×C4⋊Dic13—21no—
24C2×C4⋊Dic13—24no—
25C2×C4⋊Dic13—24no—
26C2×C4⋊Dic13—41no—
27C2×C4⋊Dic13—41no—
28C2×C4⋊Dic13—48no—
29C2×C4⋊Dic13—41no—
30C2×C4⋊Dic13—41no—
31C2×C4⋊Dic13C2×C412yes—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13D412yes—
34C2×C4⋊Dic13C2311yescharacteristic
35C22⋊#1057—24no—
36C22⋊#1057—42no—
37C2×#1325—131nomaximal, Sylow
38C24×C13C22⋊C411yescharacteristic
39C22×C4×C13—24no—
40C22×C4×C13—24no—
41C22×C4×C13—24no—
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13—22no—
45C22×C4×C13—22no—
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C2×C812yes—
48C22×C4×C13M1612yes—
49C22×C4×C13C22×C411yescharacteristic
50C22×Dic13—22no—
51C22×Dic13—22no—
52C22×Dic13—22no—
53C22×Dic13—44no—
54C22×Dic13—44no—
55C22×Dic13—41no—
56C22×Dic13—41no—
57C22×Dic13C22⋊C412yes—
58C22×Dic13C2×D412yes—
59C2×#1057—44no—
60C2×#1057—84no—
61C42×C13—24no—
62C42×C13—22no—
63C42×C13C2×C814yescomplemented
64C4⋊Dic13—41no—
65C4⋊Dic13—42no—
66C4⋊Dic13—41no—
67C4⋊Dic13—48no—
68C4⋊Dic13—48no—
69C4⋊Dic13—42no—
70C4⋊Dic13—42no—
71C2×#384—131no—
72C2×#324—132no—
73#1325—134no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13C22⋊C812yes—
77C23×C13#9911yescharacteristic
78C23×C13#9911yescharacteristic
79C23×C13#10112yes—
80C23×C13C2×C22⋊C411yescharacteristic
81C2×C4×C13—24no—
82C2×C4×C13—216no—
83C2×C4×C13—24no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—24no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13C22⋊C812yes—
94C2×C4×C13C22×C811yescharacteristic
95C2×C4×C13C2×M1611yescharacteristic
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—44no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—44no—
102C2×Dic13—42no—
103C2×Dic13—82no—
104C2×Dic13—82no—
105C2×Dic13—82no—
106#1057—84no—
107C22×C4⋊C4—131no—
108C22×C4⋊C4—131no—
109C22×C4⋊C4—262no—
110C22×C42#26111yescharacteristic
111C2×C22⋊C8—262no—
112#384—132no—
113#384—132no—
114#384—262no—
115#324—134no—
116#324—262no—
117C22×C13—24no—
118C22×C13—24no—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#32412yes—
124C22×C13#32412yes—
125C22×C13#35312yes—
126C22×C13#35612yes—
127C22×C13C2×C22⋊C811yescharacteristic
128C22×C13C2×#9911yescharacteristic
129C22×C13C2×#10111yescharacteristic
130C4×C13—28no—
131C4×C13—22no—
132C4×C13—21no—
133C4×C13—21no—
134Dic13—42no—
135Dic13—42no—
136Dic13—82no—
137C23×C4—21no—
138C23×C4—132no—
139C23×C4—261no—
140C23×C4C2×#26111yescharacteristic
141C22×C8—522no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4—131no—
144C2×C4⋊C4—131no—
145C2×C4⋊C4—132no—
146C2×C4⋊C4—264no—
147C2×C4⋊C4—264no—
148C2×C4⋊C4—261no—
149C2×C4⋊C4—521no—
150C2×C4⋊C4—521no—
151C2×C4⋊C4—521no—
152C2×C4⋊C4—521no—
153C2×C4⋊C4—528no—
154C2×C42—22no—
155C2×C42—21no—
156C2×C42#105714yescomplemented
157C2×C42C2×#26112yes—
158C22⋊C8—264no—
159C22⋊C8—522no—
160C2×C13—21no—
161C2×C13—22no—
162C2×C13—21no—
163C2×C13#132514yescomplemented
164C2×C13C2×#32411yescharacteristic
165C2×C13C2×#35311yescharacteristic
166C2×C13C2×#35611yescharacteristic
167C24C22⋊#26111yescharacteristic
168C22×C4—24no—
169C22×C4—24no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—132no—
176C22×C4—132no—
177C22×C4—262no—
178C22×C4—262no—
179C22×C4—262no—
180C22×C4—524no—
181C22×C4—524no—
182C22×C4—521no—
183C22×C4—521no—
184C22×C4C2×#105712yes—
185C22×C4#612212yes—
186C22×C4C22⋊#26111yescharacteristic
187C22×C4C22×#26111yescharacteristic
188C2×C8—524no—
189C2×C8—1044no—
190C4⋊C4—522no—
191C4⋊C4—521no—
192C4⋊C4—521no—
193C4⋊C4—522no—
194C4⋊C4—528no—
195C4⋊C4—528no—
196C4⋊C4—522no—
197C42—24no—
198C42—22no—
199C42C2×#105714yescomplemented
200C13C2×#132511yescharacteristic, complemented, Sylow
201C23—22no—
202C23—22no—
203C23#8810711yescharacteristic
204C23#8810711yescharacteristic
205C23#8811312yes—
206C23C22⋊#105712yes—
207C23C2×C22⋊#26111yescharacteristic
208C2×C4—24no—
209C2×C4—216no—
210C2×C4—24no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—524no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4—524no—
226C2×C4—522no—
227C2×C4—1042no—
228C2×C4—1042no—
229C2×C4—1042no—
230C2×C4C22⋊#105712yes—
231C2×C4C22×#105711yescharacteristic
232C2×C4C2×#612211yescharacteristic
233C8—1044no—
234C22—24no—
235C22—24no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—21no—
240C22#1171822512yes—
241C22#1171822712yes—
242C22#1171828512yes—
243C22#1171828512yes—
244C22C2×#8810711yescharacteristic
245C22C2×#8811311yescharacteristic
246C22C2×C22⋊#105711yescharacteristic
247C4—28no—
248C4—22no—
249C4—21no—
250C4—21no—
251C4—522no—
252C4—522no—
253C4—1042no—
254C2—21no—
255C2—22no—
256C2—21no—
257C2#1312977814yesdirect product factor
258C2C2×#1171828511yescharacteristic
259C2C2×#1171822511yescharacteristic
260C2C2×#1171822711yescharacteristic
subgroupG/H
centerC23#88107
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC22×C42×C13C4
socleC23×C13#99
prime radicalC24×C13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC22×C42#261
hypocenterC13C2×#1325
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #13129778C2direct (N × H)
21. C2×C42×C13C8semidirect
63. C42×C13C2×C8semidirect
156. C2×C42#1057semidirect
163. C2×C13#1325semidirect
199. C42C2×#1057semidirect
200. C13C2×#1325semidirect
257. C2#13129778direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117182852
#131297782
C2×#117185962
C2×#132513