Finite Group Databasebeta

← C2×#13129971 #16791270

Subgroups — C2×#13129971 #16791270

Order 3328.

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

normal subgroups only

This group has 450 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×#11718227C212yesmaximal, complemented
2#13129971C214yesmaximal, direct product factor
3C2×#11718737C211yesmaximal, characteristic
4C2×C13×#127C411yescharacteristic
5C22×#6105—22no—
6C2×#88123C2211yescharacteristic
7C2×#88113—22no—
8#11718737—22no—
9#11718737C412yes—
10#11718737C2212yes—
11C2×C4×#1055C411yescharacteristic
12#11718227—22no—
13#11718227C2214yescomplemented
14C22×D4×C13—21no—
15C22×D4×C13—41no—
16C22×Dic26D412yes—
17C2×#6122—42no—
18C13×#127—21no—
19C13×#127—41no—
20C13×#127C2×C412yes—
21C2×C42×C13C2×C411yescharacteristic
22C2×#6105—24no—
23C2×#6105—24no—
24C2×#6105—44no—
25C2×#6105—44no—
26C2×C4⋊Dic13—41no—
27C22×#1055—21no—
28#88123—41no—
29#88123C2×C411yescharacteristic
30#88123D412yes—
31#88123C2311yescharacteristic
32#88113—24no—
33#88113—42no—
34C4×#1055—21no—
35C4×#1055C2×C412yes—
36C2×#1410—131nomaximal, Sylow
37C24×C13—41no—
38C2×D4×C13—22no—
39C2×D4×C13—42no—
40C2×D4×C13—42no—
41C2×D4×C13—42no—
42C2×D4×C13—42no—
43C2×D4×C13—41no—
44C2×D4×C13—84no—
45C22×C4×C13—21no—
46C22×C4×C13C22⋊C411yescharacteristic
47C22×Dic13—22no—
48C2×Dic26—22no—
49C2×Dic26—42no—
50C2×Dic26—42no—
51C2×Dic26C22⋊C412yes—
52C2×Dic26C2×D412yes—
53#6122—44no—
54#6122—82no—
55C2×#1057—82no—
56C42×C13—21no—
57C42×C13C22⋊C411yescharacteristic
58C42×C13C22×C411yescharacteristic
59#6105—48no—
60#6105—48no—
61C4⋊Dic13—41no—
62C4⋊Dic13—42no—
63C4⋊Dic13—41no—
64C2×#1055—22no—
65C2×#1055—22no—
66C2×#1055—22no—
67C2×#492—131no—
68C2×#356—132no—
69#1410—134no—
70C23×C13—42no—
71C23×C13—84no—
72C23×C13—81no—
73C23×C13—81no—
74C23×C13#9911yescharacteristic
75D4×C13—44no—
76D4×C13—82no—
77D4×C13—84no—
78D4×C13—84no—
79C2×C4×C13—24no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13#9911yescharacteristic
85C2×C4×C13C2×C22⋊C411yescharacteristic
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—42no—
89C2×Dic13—42no—
90Dic26—42no—
91Dic26—42no—
92Dic26—82no—
93#1057—84no—
94#1055—24no—
95C22×SD16—262no—
96C2×C4⋊Q8—131no—
97C2×#127#26111yescharacteristic
98#492—132no—
99#492—132no—
100#492—262no—
101C2×#101—262no—
102C2×C4×C8—131no—
103#356—134no—
104#356—262no—
105C22×C13—22no—
106C22×C13—84no—
107C22×C13—82no—
108C22×C13—162no—
109C22×C13—162no—
110C22×C13#35311yescharacteristic
111C22×C13#35311yescharacteristic
112C22×C13C2×#9911yescharacteristic
113C4×C13—22no—
114C4×C13—22no—
115C4×C13—21no—
116C4×C13—21no—
117Dic13—42no—
118Dic13—42no—
119C22×Q8—132no—
120C22×D4—21no—
121C22×D4—41no—
122C2×SD16—264no—
123C2×SD16—264no—
124C2×SD16—524no—
125C2×SD16—524no—
126C2×M16—522no—
127C22×C8—261no—
128C4⋊Q8—132no—
129C4⋊Q8—131no—
130C4⋊Q8—131no—
131C4⋊Q8—521no—
132#127—21no—
133#127—41no—
134#127C2×#26112yes—
135C2×C4⋊C4—521no—
136C2×C42C2×#26111yescharacteristic
137#101—264no—
138#101—522no—
139C4×C8—132no—
140C4×C8—261no—
141C2×C13—21no—
142C2×C13—21no—
143C2×C13—162no—
144C2×C13#141012yescomplemented
145C2×C13C2×#35311yescharacteristic
146C24—41no—
147C2×Q8—132no—
148C2×Q8—132no—
149C2×Q8—262no—
150C2×Q8—522no—
151C2×Q8—522no—
152C2×D4—22no—
153C2×D4—42no—
154C2×D4—42no—
155C2×D4—42no—
156C2×D4—42no—
157C2×D4—41no—
158C2×D4—84no—
159C22×C4—21no—
160C22×C4—262no—
161C22×C4C22⋊#26111yescharacteristic
162SD16—528no—
163SD16—528no—
164M16—524no—
165M16—1042no—
166C2×C8—262no—
167C2×C8—262no—
168C2×C8—262no—
169C2×C8—1042no—
170C4⋊C4—522no—
171C4⋊C4—521no—
172C4⋊C4—521no—
173C42—21no—
174C42C22⋊#26111yescharacteristic
175C42C22×#26111yescharacteristic
176C13C2×#141011yescharacteristic, complemented, Sylow
177C23—42no—
178C23—84no—
179C23—81no—
180C23—81no—
181C23#8811911yescharacteristic
182Q8—522no—
183Q8—522no—
184Q8—1042no—
185D4—44no—
186D4—82no—
187D4—84no—
188D4—84no—
189C2×C4—24no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4#8811911yescharacteristic
199C2×C4C2×C22⋊#26111yescharacteristic
200C8—264no—
201C8—1044no—
202C22—22no—
203C22—84no—
204C22—82no—
205C22—162no—
206C22—162no—
207C22#1171829411yescharacteristic
208C22#1171829411yescharacteristic
209C22C2×#8811911yescharacteristic
210C4—22no—
211C4—22no—
212C4—21no—
213C4—21no—
214C4—522no—
215C4—522no—
216C2—21no—
217C2—21no—
218C2—162no—
219C2#1312997112yesdirect product factor
220C2C2×#1171829411yescharacteristic
subgroupG/H
centerC22#11718294
commutatorC42×C13C22×C4
FrattiniC42C22×#261
Fitting, prime radicalC2×C13×#127C4
socleC22×C13#353
cosocle#88123C23
hypercenterC2×#127#261
hypocenterC13C2×#1410
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#11718227C2semidirect
2. #13129971C2direct (N × H)
13. #11718227C22semidirect
144. C2×C13#1410semidirect
176. C13C2×#1410semidirect
219. C2#13129971direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117182272
#131299712
C2×#117187372
C2×#141013