Finite Group Databasebeta

← C2×#13129969 #16791253

Subgroups — C2×#13129969 #16791253

Order 3328.

474 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 64 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×#11718225C212yesmaximal
2#13129969C214yesmaximal, direct product factor
3C2×#11718746C211yesmaximal, characteristic
4C2×C13×C4⋊Q8C411yescharacteristic, complemented
5C22×#6106—22no—
6C2×#88128C2211yescharacteristic
7C2×#88107—22no—
8#11718746—22no—
9#11718746C412yescomplemented
10#11718746C2212yes—
11C2×C4×#1055C411yescharacteristic, complemented
12#11718225—22no—
13#11718225C2214yes—
14C22×Q8×C13—21no—
15C22×D52—41no—
16C22×D52D412yes—
17C2×C22⋊#261—42no—
18C13×C4⋊Q8—21no—
19C13×C4⋊Q8—41no—
20C13×C4⋊Q8C2×C412yescomplemented
21C2×C13×C4⋊C4—41no—
22C2×C42×C13C2×C411yescharacteristic
23C2×#6106—24no—
24C2×#6106—24no—
25C2×#6106—44no—
26C2×#6106—44no—
27C22×#1055—21no—
28#88128—41no—
29#88128C2×C411yescharacteristic
30#88128D412yes—
31#88128C2311yescharacteristic
32#88107—24no—
33#88107—42no—
34C4×#1055—21no—
35C4×#1055C2×C412yescomplemented
36C2×#1409—131nomaximal, Sylow
37C23×D13—22no—
38C22×#261—82no—
39C2×Q8×C13—22no—
40C2×Q8×C13—42no—
41C2×Q8×C13—42no—
42C2×Q8×C13—41no—
43C22×C4×C13—21no—
44C22×C4×C13—41no—
45C22×C4×C13C22⋊C411yescharacteristic
46C2×D52—22no—
47C2×D52—42no—
48C2×D52—42no—
49C2×D52—41no—
50C2×D52—42no—
51C2×D52—41no—
52C2×D52—84no—
53C2×D52C22⋊C412yes—
54C2×D52C2×D412yes—
55C22⋊#261—44no—
56C22⋊#261—82no—
57C13×C4⋊C4—42no—
58C13×C4⋊C4—42no—
59C42×C13—21no—
60C42×C13C22⋊C411yescharacteristic
61C42×C13C22×C411yescharacteristic
62#6106—48no—
63#6106—48no—
64C2×#1055—22no—
65C2×#1055—22no—
66C2×#1055—22no—
67C2×#492—131no—
68C2×#353—132no—
69#1409—134no—
70C23×C13#9911yescharacteristic
71C22×D13—22no—
72C22×D13—22no—
73C22×D13—42no—
74C22×D13—42no—
75C22×D13—84no—
76C2×#261—84no—
77C2×#261—164no—
78Q8×C13—44no—
79Q8×C13—82no—
80C2×C4×C13—24no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—42no—
86C2×C4×C13—81no—
87C2×C4×C13—81no—
88C2×C4×C13#9911yescharacteristic
89C2×C4×C13C2×C22⋊C411yescharacteristic
90D52—42no—
91D52—42no—
92D52—82no—
93D52—82no—
94D52—84no—
95D52—82no—
96#1055—24no—
97C22×SD16—262no—
98C2×C4⋊Q8#26111yescharacteristic, complemented
99C2×#127—131no—
100#492—132no—
101#492—132no—
102#492—262no—
103C2×#99—262no—
104C2×C4×C8—131no—
105#353—134no—
106#353—262no—
107C22×C13—22no—
108C22×C13#35311yescharacteristic
109C22×C13#35311yescharacteristic
110C22×C13C2×#9911yescharacteristic
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—84no—
114C2×D13—82no—
115C2×D13—82no—
116C2×D13—162no—
117#261—164no—
118C4×C13—22no—
119C4×C13—22no—
120C4×C13—21no—
121C4×C13—21no—
122C4×C13—82no—
123C22×Q8—21no—
124C22×D4—132no—
125C22×D4—521no—
126C2×SD16—264no—
127C2×SD16—264no—
128C2×SD16—524no—
129C2×SD16—524no—
130C22×C8—261no—
131C4⋊Q8—21no—
132C4⋊Q8—41no—
133C4⋊Q8C2×#26112yescomplemented
134#127—132no—
135#127—131no—
136#127—131no—
137#127—521no—
138C2×C4⋊C4—41no—
139C2×C22⋊C4—522no—
140C2×C42C2×#26111yescharacteristic
141#99—264no—
142#99—522no—
143C4×C8—132no—
144C4×C8—261no—
145C2×C13—21no—
146C2×C13—21no—
147C2×C13#140912yescomplemented
148C2×C13C2×#35311yescharacteristic
149D13—82no—
150D13—82no—
151C24—262no—
152C2×Q8—22no—
153C2×Q8—42no—
154C2×Q8—42no—
155C2×Q8—41no—
156C2×D4—132no—
157C2×D4—132no—
158C2×D4—262no—
159C2×D4—522no—
160C2×D4—522no—
161C2×D4—522no—
162C2×D4—521no—
163C2×D4—521no—
164C2×D4—1044no—
165C22×C4—21no—
166C22×C4—41no—
167C22×C4—1042no—
168C22×C4C22⋊#26111yescharacteristic
169SD16—528no—
170SD16—528no—
171C2×C8—262no—
172C2×C8—262no—
173C2×C8—262no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C22⋊C4—524no—
177C22⋊C4—1042no—
178C42—21no—
179C42C22⋊#26111yescharacteristic
180C42C22×#26111yescharacteristic
181C13C2×#140911yescharacteristic, complemented, Sylow
182C23—262no—
183C23—262no—
184C23—522no—
185C23—522no—
186C23—1044no—
187C23#8811911yescharacteristic
188Q8—44no—
189Q8—82no—
190D4—522no—
191D4—522no—
192D4—1042no—
193D4—1044no—
194D4—1042no—
195D4—1042no—
196C2×C4—24no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—1044no—
205C2×C4—2084no—
206C2×C4#8811911yescharacteristic
207C2×C4C2×C22⋊#26111yescharacteristic
208C8—264no—
209C22—22no—
210C22—522no—
211C22—522no—
212C22—1042no—
213C22—1042no—
214C22—1044no—
215C22—2082no—
216C22#1171829411yescharacteristic
217C22#1171829411yescharacteristic
218C22C2×#8811911yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—2084no—
225C2—21no—
226C2—21no—
227C2—1042no—
228C2—1042no—
229C2#1312996912yesdirect product factor
230C2C2×#1171829411yescharacteristic
subgroupG/H
centerC22#11718294
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13#353
prime radicalC2×#88128C22
cosocle#88128C23
hypercenterC2×C4⋊Q8#261
hypocenterC13C2×#1409
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13129969C2direct (N × H)
4. C2×C13×C4⋊Q8C4semidirect
9. #11718746C4semidirect
11. C2×C4×#1055C4semidirect
20. C13×C4⋊Q8C2×C4semidirect
35. C4×#1055C2×C4semidirect
98. C2×C4⋊Q8#261semidirect
133. C4⋊Q8C2×#261semidirect
147. C2×C13#1409semidirect
181. C13C2×#1409semidirect
229. C2#13129969direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117182252
#131299692
C2×#117187462
C2×#140913