Finite Group Databasebeta

← #15777185

Subgroups — #15777185

Order 3328.

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

normal subgroups only

This group has 232 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#13117091C211yesmaximal, characteristic
2#13116738C211yesmaximal, characteristic, complemented
3#13114207C211yesmaximal, characteristic, complemented
4#13114193C211yesmaximal, characteristic
5#13112909C211yesmaximal, characteristic, complemented
6#13112886C211yesmaximal, characteristic, complemented
7C13×#1361C211yesmaximal, characteristic
8C13×#493C2211yescharacteristic
9C2×#88067—21no—
10C2×#88067—21no—
11#11718736—21no—
12#11718512—21no—
13#11718360C2211yescharacteristic
14C8×Dic26C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17#11718136—21no—
18#11718093—21no—
19C16×Dic13—21no—
20#11718078—21no—
21C4×#6090C2211yescharacteristic
22#11718050C2211yescharacteristic
23C2×C13×D8—21no—
24C2×C13×D8—21no—
25C13×#127—21no—
26C2×#6105—41no—
27C2×Dic52—21no—
28C2×Dic52—21no—
29#88123—21no—
30C4×Dic26D411yescharacteristic
31C2×C13×C16—21no—
32C13×C4⋊C8—21no—
33C4×C8×C13C2311yescharacteristic
34#88072—41no—
35#88067—42no—
36#88067—42no—
37#88057—41no—
38#88056—41no—
39#88054—21no—
40C8×Dic13—21no—
41C2×#6090D411yescharacteristic
42C2×#6090D411yescharacteristic
43C4⋊#1055—21no—
44C4⋊#1055D411yescharacteristic
45#12441—131nomaximal, Sylow
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×Dic26—41no—
50C2×Dic26D811yescharacteristic
51C13×D8—41no—
52C13×D8—41no—
53C13×D8—81no—
54C2×C8×C13—41no—
55C2×C8×C13C2×D411yescharacteristic
56C2×C8×C13#4111yescharacteristic
57C42×C13C2×D411yescharacteristic
58#6105—82no—
59C4⋊Dic13—41no—
60C4⋊Dic13—41no—
61C4⋊Dic13D811yescharacteristic
62#6101—21no—
63C4×Dic13—21no—
64C2×#1055—21no—
65C2×#1055—41no—
66Dic52—41no—
67Dic52—41no—
68Dic52—81no—
69C13×C16—41no—
70#6090—21no—
71#6090SD1612yescomplemented
72#2248—131no—
73Q8×C16—131no—
74#1670—131no—
75#1668—131no—
76#1372—131no—
77#1362—131no—
78#1361D1311yescharacteristic
79C23×C13—81no—
80D4×C13—81no—
81D4×C13—81no—
82D4×C13—81no—
83D4×C13—81no—
84D4×C13—161no—
85C2×C4×C13#12111yescharacteristic
86C2×C4×C13C2×D811yescharacteristic
87C2×C4×C13#13511yescharacteristic
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—81no—
91Dic26—21no—
92Dic26—81no—
93Dic26—81no—
94Dic26SD3212yescomplemented
95C8×C13—21no—
96C8×C13—81no—
97C8×C13C2×SD1611yescharacteristic
98C8×C13AGL(1,ℤ/8)11yescharacteristic
99#1055—41no—
100#1055—81no—
101C2×SD32—261no—
102C2×SD32—261no—
103#494—131no—
104#493C2×D1311yescharacteristic
105#475—261no—
106#460—261no—
107C8×Q8—131no—
108C4⋊C16—261no—
109C4⋊C16C2×D1311yescharacteristic
110C4×C16—131no—
111C4×C16—261no—
112#335—131no—
113#335C2×D1311yescharacteristic
114#332—261no—
115#331—261no—
116C22×C13—161no—
117C22×C13—161no—
118C22×C13—161no—
119C22×C13#46611yescharacteristic
120C4×C13—21no—
121C4×C13#46011yescharacteristic
122C4×C13#47211yescharacteristic
123C4×C13C2×SD3211yescharacteristic
124C4×C13#50811yescharacteristic
125Dic13—22no—
126Dic13—41no—
127Dic13—161no—
128C2×Q16—261no—
129C2×Q16—261no—
130C2×SD16—521no—
131C2×D8—21no—
132C2×D8—21no—
133C4⋊Q8—261no—
134#127—21no—
135C4×Q8—131no—
136SD32—522no—
137SD32—522no—
138C2×C16—21no—
139C2×C16—131no—
140C2×C16—131no—
141#106—521no—
142C4⋊C8—21no—
143C4⋊C8—131no—
144C4⋊C8—261no—
145C4⋊C8—261no—
146#103—521no—
147#102—521no—
148C4×C8—261no—
149C4×C8C22×D1311yescharacteristic
150C2×C13—321no—
151C2×C13#166811yescharacteristic
152C2×C13#221711yescharacteristic
153C2×C13#222311yescharacteristic
154C2×Q8—131no—
155C2×Q8—521no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159Q16—521no—
160Q16—521no—
161Q16—1041no—
162SD16—1042no—
163D8—41no—
164D8—41no—
165D8—81no—
166C2×C8—41no—
167C2×C8—261no—
168C2×C8—521no—
169C2×C8#612711yescharacteristic
170C2×C8D4×D1311yescharacteristic
171C4⋊C4—131no—
172C4⋊C4—261no—
173C4⋊C4—521no—
174C4⋊C4—521no—
175C42—261no—
176C42D4×D1311yescharacteristic
177C16—41no—
178C16—132no—
179C16—261no—
180C13#1244111yescharacteristic, complemented, Sylow
181C23—81no—
182Q8—132no—
183Q8—261no—
184Q8—1041no—
185Q8—1041no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—261no—
192C2×C4—261no—
193C2×C4—1041no—
194C2×C4#8813811yescharacteristic
195C2×C4D8×D1311yescharacteristic
196C2×C4#8817011yescharacteristic
197C8—21no—
198C8—81no—
199C8—521no—
200C8—1041no—
201C8#8816511yescharacteristic
202C8SD16×D1311yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1171843611yescharacteristic
207C4—21no—
208C4—262no—
209C4—521no—
210C4—2081no—
211C4#1171841011yescharacteristic
212C4#1171842311yescharacteristic
213C4#1171857311yescharacteristic
214C4D13×SD3211yescharacteristic
215C2—321no—
216C2#1311419511yescharacteristic
217C2#1311693111yescharacteristic
218C2#1311696511yescharacteristic
subgroupG/H
centerC22#11718436
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1361C2
socleC22×C13#466
prime radicalC13×#493C22
hypercenter#1361D13
hypocenterC13#12441
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #13116738C2semidirect
3. #13114207C2semidirect
5. #13112909C2semidirect
6. #13112886C2semidirect
71. #6090SD16semidirect
94. Dic26SD32semidirect
180. C13#12441semidirect

Maximal subgroups

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

subgroupindex
#131170912
#131167382
#131142072
#131141932
#131129092
#131128862
C13×#13612
#1244113