Finite Group Databasebeta

← #15777180

Subgroups — #15777180

Order 3328.

216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#13117088C211yesmaximal, characteristic
2#13116738C211yesmaximal, characteristic
3#13114207C211yesmaximal, characteristic
4#13114203C211yesmaximal, characteristic
5#13112907C211yesmaximal, characteristic
6#13112886C211yesmaximal, characteristic
7C13×#1362C211yesmaximal, characteristic
8C13×#494C2211yescharacteristic
9C2×#88069—21no—
10C2×#88069—21no—
11#11718755—21no—
12#11718512—21no—
13#11718360C2211yescharacteristic
14C8×Dic26C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17#11718139—21no—
18#11718093—21no—
19C16×Dic13—21no—
20#11718078—21no—
21C4×#6090C2211yescharacteristic
22#11718050C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C13×C4⋊Q8—21no—
26C2×Dic52—21no—
27C2×Dic52—21no—
28#88123—21no—
29C4×Dic26D411yescharacteristic
30C2×C13×C16—21no—
31C13×C4⋊C8—21no—
32C4×C8×C13C2311yescharacteristic
33#88069—42no—
34#88069—42no—
35#88057—41no—
36#88056—41no—
37#88054—21no—
38C8×Dic13—21no—
39C2×#6090D411yescharacteristic
40C2×#6090D411yescharacteristic
41#88050—41no—
42#88048—41no—
43C4⋊#1055—21no—
44C4⋊#1055D411yescharacteristic
45#12440—131nomaximal, Sylow
46C2×Q8×C13—41no—
47C2×Dic26—41no—
48C2×Dic26D811yescharacteristic
49C13×Q16—41no—
50C13×Q16—41no—
51C13×Q16—81no—
52C2×C8×C13—41no—
53C2×C8×C13C2×D411yescharacteristic
54C2×C8×C13#4111yescharacteristic
55C13×C4⋊C4—41no—
56C13×C4⋊C4—41no—
57C42×C13C2×D411yescharacteristic
58C4⋊Dic13—41no—
59C4⋊Dic13—41no—
60C4⋊Dic13D811yescharacteristic
61#6101—21no—
62C4×Dic13—21no—
63C2×#1055—21no—
64C2×#1055—41no—
65Dic52—41no—
66Dic52—41no—
67Dic52—81no—
68C13×C16—41no—
69#6090—21no—
70#6090SD1612yes—
71#2247—131no—
72Q8×C16—131no—
73#1670—131no—
74#1670—131no—
75#1371—131no—
76#1362—131no—
77#1362D1311yescharacteristic
78Q8×C13—81no—
79Q8×C13—81no—
80C2×C4×C13—81no—
81C2×C4×C13#12111yescharacteristic
82C2×C4×C13C2×D811yescharacteristic
83C2×C4×C13#13511yescharacteristic
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—81no—
87Dic26—21no—
88Dic26—81no—
89Dic26—81no—
90Dic26Q3212yescomplemented
91C8×C13—21no—
92C8×C13—81no—
93C8×C13C2×SD1611yescharacteristic
94C8×C13AGL(1,ℤ/8)11yescharacteristic
95#1055—41no—
96#1055—81no—
97C2×Q32—261no—
98C2×Q32—261no—
99#494—131no—
100#494C2×D1311yescharacteristic
101#475—261no—
102#475—261no—
103C8×Q8—131no—
104C4⋊C16—261no—
105C4⋊C16C2×D1311yescharacteristic
106C4×C16—131no—
107C4×C16—261no—
108#335—131no—
109#335C2×D1311yescharacteristic
110#332—261no—
111#332—261no—
112C22×C13#46611yescharacteristic
113C4×C13—21no—
114C4×C13—161no—
115C4×C13#46011yescharacteristic
116C4×C13#47211yescharacteristic
117C4×C13C2×Q3211yescharacteristic
118C4×C13#50811yescharacteristic
119Dic13—22no—
120Dic13—41no—
121Dic13—161no—
122C2×Q16—21no—
123C2×Q16—21no—
124C2×Q16—261no—
125C2×Q16—261no—
126C4⋊Q8—21no—
127C4⋊Q8—261no—
128C4×Q8—131no—
129Q32—522no—
130Q32—522no—
131C2×C16—21no—
132C2×C16—131no—
133C2×C16—131no—
134#106—521no—
135#106—521no—
136C4⋊C8—21no—
137C4⋊C8—131no—
138C4⋊C8—261no—
139C4⋊C8—261no—
140#103—521no—
141#103—521no—
142C4×C8—261no—
143C4×C8C22×D1311yescharacteristic
144C2×C13#166811yescharacteristic
145C2×C13#221611yescharacteristic
146C2×C13#222211yescharacteristic
147C2×Q8—41no—
148C2×Q8—131no—
149C2×Q8—521no—
150Q16—41no—
151Q16—41no—
152Q16—81no—
153Q16—521no—
154Q16—521no—
155Q16—1041no—
156C2×C8—41no—
157C2×C8—261no—
158C2×C8—521no—
159C2×C8#612711yescharacteristic
160C2×C8D4×D1311yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—131no—
164C4⋊C4—261no—
165C4⋊C4—521no—
166C4⋊C4—521no—
167C42—261no—
168C42D4×D1311yescharacteristic
169C16—41no—
170C16—132no—
171C16—261no—
172C13#1244011yescharacteristic, complemented, Sylow
173Q8—81no—
174Q8—81no—
175Q8—132no—
176Q8—261no—
177Q8—1041no—
178Q8—1041no—
179C2×C4—81no—
180C2×C4—261no—
181C2×C4—261no—
182C2×C4—1041no—
183C2×C4#8813811yescharacteristic
184C2×C4D8×D1311yescharacteristic
185C2×C4#8817011yescharacteristic
186C8—21no—
187C8—81no—
188C8—521no—
189C8—1041no—
190C8#8816511yescharacteristic
191C8SD16×D1311yescharacteristic
192C22#1171843611yescharacteristic
193C4—21no—
194C4—161no—
195C4—262no—
196C4—521no—
197C4—2081no—
198C4#1171841011yescharacteristic
199C4#1171842311yescharacteristic
200C4#1171857711yescharacteristic
201C4D13×Q3211yescharacteristic
202C2#1311419511yescharacteristic
203C2#1311692611yescharacteristic
204C2#1311696011yescharacteristic
subgroupG/H
centerC22#11718436
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1362C2
socle, prime radicalC22×C13#466
hypercenter#1362D13
hypocenterC13#12440
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
90. Dic26Q32semidirect
172. C13#12440semidirect

Maximal subgroups

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

subgroupindex
#131170882
#131167382
#131142072
#131142032
#131129072
#131128862
C13×#13622
#1244013