Finite Group Databasebeta

← #15767078

Subgroups — #15767078

Order 3328.

342 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 77 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#13115010C211yesmaximal, characteristic
2#13113566C212yesmaximal
3#13113451C212yesmaximal
4#13112747C211yesmaximal, characteristic
5C13×#3255C211yesmaximal, characteristic
6C13×#533C2212yes—
7C13×#475—22no—
8C13×#470—22no—
9C13×#462—22no—
10C13×#423C2211yescharacteristic
11C2×#88062—22no—
12#11718587C2212yes—
13#11718585C2211yescharacteristic
14C2×#88043C2211yescharacteristic
15#11718139—22no—
16#11718138—22no—
17#11718135—24no—
18C2×C13×Q16—22no—
19C2×C13×M16D412yes—
20C13×C4⋊Q8D412yes—
21C13×C4⋊Q8D412yes—
22C13×#125—22no—
23C13×C22⋊Q8—22no—
24C13×C22⋊Q8—22no—
25C4×Q8×C13—22no—
26C4×Q8×C13—22no—
27C13×#117—22no—
28C2×C42×C13C2311yescharacteristic
29C2×#6099—21no—
30C22×#1055—21no—
31C13×#106—22no—
32C13×C4⋊C8—22no—
33C13×#103—24no—
34C22⋊#1055—22no—
35#88062—44no—
36C4⋊#1055—22no—
37C4⋊#1055—22no—
38#88043—21no—
39#88043—22no—
40#88043D412yes—
41#10528—131nomaximal, Sylow
42C2×Q8×C13—22no—
43C2×Q8×C13—22no—
44C22×C4×C13C2×D411yescharacteristic
45C22×C4×C13#4112yes—
46C13×Q16—82no—
47C13×M16—42no—
48C2×C8×C13—22no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—42no—
55C13×C22⋊C4—42no—
56C42×C13—42no—
57C42×C13C2×D411yescharacteristic
58C42×C13C2×D412yes—
59C42×C13#4111yescharacteristic
60#6099—42no—
61C2×#1055—22no—
62C2×#1055—22no—
63C2×#1055—22no—
64C2×#1055—41no—
65C2×#1055—42no—
66#3255D1311yescharacteristic
67#1849—131no—
68#1559—132no—
69#1531—132no—
70#1307—131no—
71C23×C13#12411yescharacteristic
72Q8×C13—42no—
73Q8×C13—42no—
74Q8×C13—82no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13#12011yescharacteristic
81C2×C4×C13#12111yescharacteristic
82C2×C4×C13#12112yes—
83C2×C4×C13#12312yes—
84C8×C13—42no—
85#1055—24no—
86#1055—82no—
87#1055—81no—
88#533C2×D1312yes—
89#475—22no—
90#470—22no—
91#462—22no—
92#432—132no—
93C2×#108—262no—
94#423—131no—
95#423C2×D1311yescharacteristic
96C2×#97—131no—
97#333—262no—
98#332—262no—
99#330—264no—
100C22×C13—22no—
101C22×C13—21no—
102C22×C13#39411yescharacteristic
103C4×C13—22no—
104C4×C13—22no—
105C4×C13—21no—
106C4×C13—82no—
107C4×C13—82no—
108C4×C13#45311yescharacteristic
109C4×C13#45611yescharacteristic
110C2×Q16—22no—
111C2×M16—261no—
112C2×M16C22⋊D1312yes—
113C22×C8—261no—
114C4⋊Q8C22⋊D1312yes—
115C4⋊Q8C22⋊D1312yes—
116#125—22no—
117C22⋊Q8—22no—
118C22⋊Q8—22no—
119C4×Q8—22no—
120C4×Q8—22no—
121#117—22no—
122C2×C42C22×D1311yescharacteristic
123#108—524no—
124#106—22no—
125C4⋊C8—22no—
126C4⋊C8—262no—
127C4⋊C8—262no—
128#103—24no—
129C22⋊C8—262no—
130#97—132no—
131#97—262no—
132#97—261no—
133C2×C13—41no—
134C2×C13#203911yescharacteristic
135C2×C13#204912yes—
136C2×Q8—22no—
137C2×Q8—22no—
138C22×C4#612912yes—
139C22×C4C2×C22⋊D1311yescharacteristic
140Q16—82no—
141M16—42no—
142M16—522no—
143C2×C8—22no—
144C2×C8—262no—
145C2×C8—262no—
146C2×C8—262no—
147C2×C8—522no—
148C2×C8—521no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C22⋊C4—42no—
156C42—42no—
157C42D4×D1311yescharacteristic
158C42#612911yescharacteristic
159C42C2×C22⋊D1312yes—
160C13#1052811yescharacteristic, complemented, Sylow
161C23#8819011yescharacteristic
162Q8—42no—
163Q8—42no—
164Q8—82no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4#8818912yes—
171C2×C4#8819211yescharacteristic
172C2×C4#8819312yes—
173C2×C4#8820711yescharacteristic
174C8—42no—
175C8—264no—
176C8—1042no—
177C8—1041no—
178C22—21no—
179C22—22no—
180C22#1171888311yescharacteristic
181C4—21no—
182C4—22no—
183C4—22no—
184C4—82no—
185C4—82no—
186C4#1171890211yescharacteristic
187C4#1171890711yescharacteristic
188C2—41no—
189C2#1311605711yescharacteristic
190C2#1311611312yes—
subgroupG/H
centerC22#11718883
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3255C2
socleC22×C13#394
prime radicalC23×C13#124
hypercenter#3255D13
hypocenterC13#10528
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
160. C13#10528semidirect

Maximal subgroups

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

subgroupindex
#131150102
#131135662
#131134512
#131127472
C13×#32552
#1052813