Finite Group Databasebeta

← #15777183

Subgroups — #15777183

Order 3328.

232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C16×Dic26C211yesmaximal, characteristic, complemented
2#13114203C211yesmaximal, characteristic, complemented
3#13114193C211yesmaximal, characteristic
4#13112910C211yesmaximal, characteristic, complemented
5#13112885C211yesmaximal, characteristic, complemented
6#13112882C211yesmaximal, characteristic
7C13×#2248C211yesmaximal, characteristic
8C2×C13×SD32—21no—
9C2×C13×SD32—21no—
10C13×#494C2211yescharacteristic
11C13×#493C2211yescharacteristic
12#11718755—21no—
13#11718736—21no—
14C8×Dic26C2211yescharacteristic
15C4×C13×C16C2211yescharacteristic
16#11718139—21no—
17#11718136—21no—
18#11718093—21no—
19C16×Dic13—21no—
20C4⋊#6090C2211yescharacteristic
21#11718050C2211yescharacteristic
22#11718050C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C2×C13×D8—21no—
26C2×C13×D8—21no—
27C13×C4⋊Q8—21no—
28C13×#127—21no—
29C2×#6105—41no—
30C4×Dic26D411yescharacteristic
31C13×SD32—42no—
32C13×SD32—42no—
33C2×C13×C16D411yescharacteristic
34C2×C13×C16D411yescharacteristic
35C4×C8×C13C2311yescharacteristic
36#88072—41no—
37#88054—21no—
38C8×Dic13—21no—
39C2×#6090—21no—
40#88050—41no—
41#88048—41no—
42C4⋊#1055—21no—
43C4⋊#1055—21no—
44C4⋊#1055D411yescharacteristic
45#12441—131nomaximal, Sylow
46C2×Q8×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×Dic26D811yescharacteristic
51C13×Q16—41no—
52C13×Q16—41no—
53C13×Q16—81no—
54C13×D8—41no—
55C13×D8—41no—
56C13×D8—81no—
57C2×C8×C13C2×D411yescharacteristic
58C2×C8×C13#4111yescharacteristic
59C13×C4⋊C4—41no—
60C13×C4⋊C4—41no—
61C42×C13C2×D411yescharacteristic
62#6105—82no—
63C4⋊Dic13D811yescharacteristic
64#6101—21no—
65C4×Dic13—21no—
66C2×#1055—21no—
67C2×#1055—41no—
68C2×#1055—41no—
69C13×C16—21no—
70C13×C16SD1612yescomplemented
71#6090—41no—
72#2248D1311yescharacteristic
73Q8×C16—131no—
74#1670—131no—
75#1668—131no—
76#1372—131no—
77#1362—131no—
78#1361—131no—
79C23×C13—81no—
80Q8×C13—81no—
81Q8×C13—81no—
82D4×C13—81no—
83D4×C13—81no—
84D4×C13—81no—
85D4×C13—81no—
86D4×C13—161no—
87C2×C4×C13—81no—
88C2×C4×C13#12111yescharacteristic
89C2×C4×C13C2×D811yescharacteristic
90C2×C4×C13#13511yescharacteristic
91C2×Dic13—21no—
92C2×Dic13—21no—
93Dic26—21no—
94Dic26SD3212yescomplemented
95C8×C13—21no—
96C8×C13C2×SD1611yescharacteristic
97C8×C13AGL(1,ℤ/8)11yescharacteristic
98#1055—41no—
99#1055—81no—
100#1055—81no—
101C2×SD32—21no—
102C2×SD32—21no—
103#494C2×D1311yescharacteristic
104#493C2×D1311yescharacteristic
105#475—261no—
106#460—261no—
107C8×Q8—131no—
108C4⋊C16—131no—
109C4⋊C16—261no—
110C4×C16—261no—
111C4×C16C2×D1311yescharacteristic
112#335—131no—
113#335—131no—
114#332—261no—
115#331—261no—
116C22×C13—161no—
117C22×C13—161no—
118C22×C13—161no—
119C22×C13#46611yescharacteristic
120C4×C13—21no—
121C4×C13—161no—
122C4×C13#46011yescharacteristic
123C4×C13#47211yescharacteristic
124C4×C13C2×SD3211yescharacteristic
125C4×C13#50811yescharacteristic
126Dic13—22no—
127Dic13—41no—
128C2×Q16—21no—
129C2×Q16—21no—
130C2×SD16—521no—
131C2×D8—21no—
132C2×D8—21no—
133C4⋊Q8—21no—
134#127—21no—
135C4×Q8—131no—
136SD32—42no—
137SD32—42no—
138C2×C16—261no—
139C2×C16C22⋊D1311yescharacteristic
140C2×C16C22⋊D1311yescharacteristic
141#106—521no—
142C4⋊C8—131no—
143C4⋊C8—261no—
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—41no—
155C2×Q8—131no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159Q16—41no—
160Q16—41no—
161Q16—81no—
162SD16—1042no—
163D8—41no—
164D8—41no—
165D8—81no—
166C2×C8—261no—
167C2×C8—521no—
168C2×C8—521no—
169C2×C8#612911yescharacteristic
170C2×C8C2×C22⋊D1311yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—131no—
174C4⋊C4—261no—
175C42—261no—
176C42D4×D1311yescharacteristic
177C16—21no—
178C16—521no—
179C16#610512yescomplemented
180C13#1244111yescharacteristic, complemented, Sylow
181C23—81no—
182Q8—81no—
183Q8—81no—
184Q8—132no—
185Q8—261no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—81no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4D8×D1311yescharacteristic
195C2×C4#8816611yescharacteristic
196C2×C4#8819211yescharacteristic
197C8—21no—
198C8—521no—
199C8—1041no—
200C8—1041no—
201C8#8818611yescharacteristic
202C8C2×#610511yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1171881811yescharacteristic
207C4—21no—
208C4—161no—
209C4—262no—
210C4—521no—
211C4D13×SD3211yescharacteristic
212C4#1171857711yescharacteristic
213C4#1171873611yescharacteristic
214C4#1171882111yescharacteristic
215C2—321no—
216C2#1311419311yescharacteristic
217C2#1311692911yescharacteristic
218C2#1311696311yescharacteristic
subgroupG/H
centerC22#11718818
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2248C2
socleC22×C13#466
prime radicalC13×#493C22
hypercenter#2248D13
hypocenterC13#12441
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. C16×Dic26C2semidirect
2. #13114203C2semidirect
4. #13112910C2semidirect
5. #13112885C2semidirect
70. C13×C16SD16semidirect
94. Dic26SD32semidirect
179. C16#6105semidirect
180. C13#12441semidirect

Maximal subgroups

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

subgroupindex
C16×Dic262
#131142032
#131141932
#131129102
#131128852
#131128822
C13×#22482
#1244113