Finite Group Databasebeta

← #15777562

Subgroups — #15777562

Order 3328.

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

normal subgroups only

This group has 200 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#13116985C211yesmaximal, characteristic
2#13116975C211yesmaximal, characteristic
3#13113734C211yesmaximal, characteristic
4#13112900C211yesmaximal, characteristic
5#13112894C211yesmaximal, characteristic
6#13112891C211yesmaximal, characteristic
7C13×#1710C211yesmaximal, characteristic
8C13×#500C2211yescharacteristic
9C13×#500C2211yescharacteristic
10C13×#487—21no—
11C13×#487—21no—
12C4×Dic52C2211yescharacteristic
13#11718340—21no—
14C82×C13C2211yescharacteristic
15#11718084—21no—
16#11718084—21no—
17#11718082—21no—
18#11718081—21no—
19C4⋊#6090C2211yescharacteristic
20C4⋊#6090C2211yescharacteristic
21#11718050C2211yescharacteristic
22#11718048—21no—
23C13×C4⋊Q8—21no—
24C13×C4⋊Q8—21no—
25C2×Dic52D411yescharacteristic
26C4×Dic26—21no—
27C13×#107—21no—
28C13×#107—21no—
29C13×#107—21no—
30C13×#107—21no—
31C13×#103—42no—
32C13×#103—41no—
33C13×#103—41no—
34C4×C8×C13D411yescharacteristic
35C4×C8×C13D411yescharacteristic
36C4×C8×C13C2311yescharacteristic
37#88058D411yescharacteristic
38#88056—21no—
39#88055—41no—
40#88054—41no—
41C2×#6090—21no—
42C2×#6090—21no—
43C4⋊#1055—21no—
44#12502—131nomaximal, Sylow
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Dic26—21no—
48C2×C8×C13—21no—
49C2×C8×C13D811yescharacteristic
50C2×C8×C13D811yescharacteristic
51C2×C8×C13C2×D411yescharacteristic
52C2×C8×C13#4111yescharacteristic
53C13×C4⋊C4—41no—
54C13×C4⋊C4—41no—
55C13×C4⋊C4—41no—
56C13×C4⋊C4—41no—
57C42×C13C2×D411yescharacteristic
58C4⋊Dic13—21no—
59#6101—41no—
60C4×Dic13—41no—
61C2×#1055—41no—
62Dic52—21no—
63Dic52—21no—
64#6090—41no—
65#6090—41no—
66#2227—131no—
67#2225—131no—
68#1710D1311yescharacteristic
69#1591—131no—
70#1367—131no—
71#1365—131no—
72#1364—131no—
73Q8×C13—82no—
74Q8×C13—81no—
75Q8×C13—81no—
76C2×C4×C13—81no—
77C2×C4×C13—81no—
78C2×C4×C13#12111yescharacteristic
79C2×C4×C13C2×D811yescharacteristic
80C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
81C2×Dic13—41no—
82C2×Dic13—41no—
83Dic26—41no—
84Dic26—41no—
85C8×C13—21no—
86C8×C13—21no—
87C8×C13—21no—
88C8×C13—41no—
89C8×C13#13711yescharacteristic
90C8×C13#13711yescharacteristic
91#1055—81no—
92#500C2×D1311yescharacteristic
93#500C2×D1311yescharacteristic
94#487—21no—
95#487—21no—
96#446—261no—
97C4×Q16—131no—
98#367—261no—
99#366—261no—
100C4⋊C16—131no—
101C4⋊C16—131no—
102#358—261no—
103#358—261no—
104#335—131no—
105Q8⋊C8—261no—
106C82C2×D1311yescharacteristic
107C22×C13#45911yescharacteristic
108C4×C13—21no—
109C4×C13—161no—
110C4×C13—161no—
111C4×C13#47011yescharacteristic
112C4×C13#47311yescharacteristic
113C4×C13#50811yescharacteristic
114C4×C13#51011yescharacteristic
115Dic13—81no—
116Dic13—81no—
117C2×Q16—131no—
118C4⋊Q8—21no—
119C4⋊Q8—21no—
120C4×Q8—261no—
121C2×C16—261no—
122C2×C16—261no—
123#107—21no—
124#107—21no—
125#107—21no—
126#107—21no—
127#107—131no—
128C4⋊C8—261no—
129C4⋊C8—521no—
130#103—42no—
131#103—41no—
132#103—41no—
133#103—261no—
134#97—521no—
135C4×C8C22⋊D1311yescharacteristic
136C4×C8C22⋊D1311yescharacteristic
137C4×C8C22×D1311yescharacteristic
138C2×C13#168911yescharacteristic
139C2×C13#221111yescharacteristic
140C2×C13#221211yescharacteristic
141C2×Q8—41no—
142C2×Q8—41no—
143C2×Q8—261no—
144Q16—261no—
145Q16—261no—
146C2×C8—21no—
147C2×C8—521no—
148C2×C8#610411yescharacteristic
149C2×C8#610411yescharacteristic
150C2×C8D4×D1311yescharacteristic
151C2×C8#612911yescharacteristic
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—261no—
157C4⋊C4—521no—
158C42—521no—
159C42C2×C22⋊D1311yescharacteristic
160C16—521no—
161C16—521no—
162C13#1250211yescharacteristic, complemented, Sylow
163Q8—82no—
164Q8—81no—
165Q8—81no—
166Q8—521no—
167Q8—521no—
168C2×C4—81no—
169C2×C4—81no—
170C2×C4—521no—
171C2×C4—521no—
172C2×C4C2×#610411yescharacteristic
173C2×C4#8818611yescharacteristic
174C2×C4#8819211yescharacteristic
175C8—21no—
176C8—21no—
177C8—21no—
178C8—41no—
179C8—1041no—
180C8#8817211yescharacteristic
181C8#8817211yescharacteristic
182C22#1171873311yescharacteristic
183C4—21no—
184C4—161no—
185C4—161no—
186C4—1041no—
187C4—1041no—
188C4#1171885011yescharacteristic
189C4#1171885311yescharacteristic
190C4#1171885511yescharacteristic
191C4#1171885611yescharacteristic
192C2#1311432211yescharacteristic
193C2#1311689511yescharacteristic
194C2#1311690211yescharacteristic
subgroupG/H
centerC22#11718733
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1710C2
socle, prime radicalC22×C13#459
hypercenter#1710D13
hypocenterC13#12502
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1710

Complements

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

NH ≅ G/Ntype
162. C13#12502semidirect

Maximal subgroups

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

subgroupindex
#131169852
#131169752
#131137342
#131129002
#131128942
#131128912
C13×#17102
#1250213