Finite Group Databasebeta

← C2×#13129973 #16791273

Subgroups — C2×#13129973 #16791273

Order 3328.

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

normal subgroups only

This group has 398 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
2#13129973C214yesmaximal, direct product factor
3C2×#11718753C211yesmaximal, characteristic
4C2×C13×C4⋊Q8C411yescharacteristic
5C22×#6107—22no—
6C2×#88123C2211yescharacteristic
7C2×#88113—22no—
8#11718753—22no—
9#11718753C412yes—
10#11718753C2212yes—
11C2×C4×#1055C411yescharacteristic
12#11718227—22no—
13#11718227C2214yes—
14C22×Q8×C13—21no—
15C22×Dic26D412yes—
16C2×#6122—42no—
17C13×C4⋊Q8—21no—
18C13×C4⋊Q8—41no—
19C13×C4⋊Q8C2×C412yes—
20C2×C13×C4⋊C4—41no—
21C2×C42×C13C2×C411yescharacteristic
22C2×#6107—24no—
23C2×#6107—24no—
24C2×#6107—44no—
25C2×#6107—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×#1411—131nomaximal, Sylow
37C2×Q8×C13—22no—
38C2×Q8×C13—42no—
39C2×Q8×C13—42no—
40C2×Q8×C13—41no—
41C22×C4×C13—21no—
42C22×C4×C13—41no—
43C22×C4×C13C22⋊C411yescharacteristic
44C22×Dic13—22no—
45C2×Dic26—22no—
46C2×Dic26—42no—
47C2×Dic26—42no—
48C2×Dic26C22⋊C412yes—
49C2×Dic26C2×D412yes—
50#6122—44no—
51#6122—82no—
52C2×#1057—82no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—42no—
55C42×C13—21no—
56C42×C13C22⋊C411yescharacteristic
57C42×C13C22×C411yescharacteristic
58#6107—48no—
59#6107—48no—
60C4⋊Dic13—41no—
61C4⋊Dic13—42no—
62C4⋊Dic13—41no—
63C2×#1055—22no—
64C2×#1055—22no—
65C2×#1055—22no—
66C2×#494—131no—
67C2×#356—132no—
68#1411—134no—
69C23×C13#9911yescharacteristic
70Q8×C13—44no—
71Q8×C13—82no—
72C2×C4×C13—24no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—42no—
78C2×C4×C13—81no—
79C2×C4×C13—81no—
80C2×C4×C13#9911yescharacteristic
81C2×C4×C13C2×C22⋊C411yescharacteristic
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—42no—
85C2×Dic13—42no—
86Dic26—42no—
87Dic26—42no—
88Dic26—82no—
89#1057—84no—
90#1055—24no—
91C22×Q16—262no—
92C2×C4⋊Q8—131no—
93C2×C4⋊Q8#26111yescharacteristic
94#494—132no—
95#494—132no—
96#494—262no—
97C2×#101—262no—
98C2×C4×C8—131no—
99#356—134no—
100#356—262no—
101C22×C13—22no—
102C22×C13#35311yescharacteristic
103C22×C13#35311yescharacteristic
104C22×C13C2×#9911yescharacteristic
105C4×C13—22no—
106C4×C13—22no—
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—82no—
110Dic13—42no—
111Dic13—42no—
112C22×Q8—21no—
113C22×Q8—132no—
114C2×Q16—264no—
115C2×Q16—264no—
116C2×Q16—524no—
117C2×Q16—524no—
118C2×M16—522no—
119C22×C8—261no—
120C4⋊Q8—21no—
121C4⋊Q8—41no—
122C4⋊Q8—132no—
123C4⋊Q8—131no—
124C4⋊Q8—131no—
125C4⋊Q8—521no—
126C4⋊Q8C2×#26112yes—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—521no—
129C2×C42C2×#26111yescharacteristic
130#101—264no—
131#101—522no—
132C4×C8—132no—
133C4×C8—261no—
134C2×C13—21no—
135C2×C13—21no—
136C2×C13#141112yescomplemented
137C2×C13C2×#35311yescharacteristic
138C2×Q8—22no—
139C2×Q8—42no—
140C2×Q8—42no—
141C2×Q8—41no—
142C2×Q8—132no—
143C2×Q8—132no—
144C2×Q8—262no—
145C2×Q8—522no—
146C2×Q8—522no—
147C22×C4—21no—
148C22×C4—41no—
149C22×C4—262no—
150C22×C4C22⋊#26111yescharacteristic
151Q16—528no—
152Q16—528no—
153M16—524no—
154M16—1042no—
155C2×C8—262no—
156C2×C8—262no—
157C2×C8—262no—
158C2×C8—1042no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—522no—
162C4⋊C4—521no—
163C4⋊C4—521no—
164C42—21no—
165C42C22⋊#26111yescharacteristic
166C42C22×#26111yescharacteristic
167C13C2×#141111yescharacteristic, complemented, Sylow
168C23#8811911yescharacteristic
169Q8—44no—
170Q8—82no—
171Q8—522no—
172Q8—522no—
173Q8—1042no—
174C2×C4—24no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—42no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—522no—
185C2×C4—522no—
186C2×C4#8811911yescharacteristic
187C2×C4C2×C22⋊#26111yescharacteristic
188C8—264no—
189C8—1044no—
190C22—22no—
191C22#1171829411yescharacteristic
192C22#1171829411yescharacteristic
193C22C2×#8811911yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—21no—
198C4—82no—
199C4—522no—
200C4—522no—
201C2—21no—
202C2—21no—
203C2#1312997312yesdirect product factor
204C2C2×#1171829411yescharacteristic
subgroupG/H
centerC22#11718294
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13#353
prime radicalC23×C13#99
cosocle#88123C23
hypercenterC2×C4⋊Q8#261
hypocenterC13C2×#1411
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. #13129973C2direct (N × H)
136. C2×C13#1411semidirect
167. C13C2×#1411semidirect
203. C2#13129973direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117182272
#131299732
C2×#117187532
C2×#141113