Finite Group Databasebeta

← #15777342

Subgroups — #15777342

Order 3328.

234 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 63 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#13117059C211yesmaximal, characteristic, complemented
2#13116655C211yesmaximal, characteristic, complemented
3#13114236C211yesmaximal, characteristic, complemented
4#13114188C211yesmaximal, characteristic
5#13112909C211yesmaximal, characteristic, complemented
6#13112893C211yesmaximal, characteristic, complemented
7C13×#1361C211yesmaximal, characteristic, complemented
8C13×#493C2211yescharacteristic
9#11718733—21no—
10C2×C16×D13—21no—
11#11718503—21no—
12C8×D52C2211yescharacteristic
13#11718343C2211yescharacteristic
14C13×C4⋊C16C2211yescharacteristic
15C13×#335C2211yescharacteristic
16#11718154—21no—
17#11718154—21no—
18#11718136—21no—
19#11718099—21no—
20#11718073—21no—
21C4×#6090C2211yescharacteristic
22#11718050C2211yescharacteristic
23C2×C13×D8—21no—
24C2×C13×D8—21no—
25C13×#127—21no—
26C2×#6104—41no—
27C2×C8×D13—21no—
28C4×D52D411yescharacteristic
29#88123—21no—
30C2×C13×C16—21no—
31C13×C4⋊C8—21no—
32C4×C8×C13C2311yescharacteristic
33#88072—41no—
34#88061—41no—
35#88060—21no—
36#88058—21no—
37#88058—21no—
38#88057—41no—
39C2×#6090D411yescharacteristic
40C2×#6090D411yescharacteristic
41C4⋊#1055—21no—
42C4⋊#1055D411yescharacteristic
43C16×D13—42no—
44#12468—131nomaximal, Sylow
45C2×D4×C13—41no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D52D811yescharacteristic
49C2×C4×D13—21no—
50C2×Dic26—41no—
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#6104—82no—
59#6103—21no—
60C4⋊Dic13—41no—
61C4⋊Dic13—41no—
62C4⋊Dic13D811yescharacteristic
63C2×#1055—21no—
64C2×#1055—41no—
65C8×D13—41no—
66C8×D13—41no—
67C13×C16—41no—
68#6090—21no—
69#6090—21no—
70#2240—131no—
71D4×C16—131no—
72#1675—131no—
73#1667—131no—
74#1372—131no—
75#1365—131no—
76#1361D1311yescharacteristic, complemented
77C23×C13—81no—
78C22×D13—21no—
79D4×C13—81no—
80D4×C13—81no—
81D4×C13—81no—
82D4×C13—81no—
83D4×C13—161no—
84C2×C4×C13#12111yescharacteristic
85C2×C4×C13C2×D811yescharacteristic
86C2×C4×C13#13511yescharacteristic
87C2×Dic13—21no—
88C2×Dic13—81no—
89D52—21no—
90D52SD3212yes—
91C4×D13—41no—
92C4×D13—41no—
93Dic26—161no—
94C8×C13—21no—
95C8×C13—81no—
96C8×C13#13511yescharacteristic
97C8×C13AGL(1,ℤ/8)11yescharacteristic
98#1055—41no—
99#1055—81no—
100C22×C16—261no—
101#500—131no—
102#493C2×D1311yescharacteristic
103#476—261no—
104#459—261no—
105C8×D4—131no—
106C4⋊C16C2×D1311yescharacteristic
107#357—261no—
108#357—261no—
109C22⋊C16—261no—
110C4×C16—131no—
111#335—131no—
112#335C2×D1311yescharacteristic
113#333—261no—
114#331—261no—
115C22×C13—161no—
116C22×C13—161no—
117C22×C13—161no—
118C22×C13#46611yescharacteristic
119C2×D13—22no—
120C2×D13—41no—
121C2×D13—41no—
122C4×C13—21no—
123C4×C13#46311yescharacteristic
124C4×C13#47111yescharacteristic
125C4×C13C2×SD3211yescharacteristic
126C4×C13#50811yescharacteristic
127Dic13—41no—
128Dic13—161no—
129C2×D8—21no—
130C2×D8—21no—
131C2×D8—521no—
132C22×C8—261no—
133C4⋊Q8—261no—
134#127—21no—
135C4×D4—131no—
136C2×C16—21no—
137C2×C16—131no—
138C2×C16—131no—
139C2×C16—522no—
140#107—261no—
141#107—261no—
142#106—521no—
143C4⋊C8—21no—
144C4⋊C8—131no—
145C4⋊C8—261no—
146#102—521no—
147#102—521no—
148C22⋊C8—261no—
149C4×C8C22×D1311yescharacteristic
150C2×C13—321no—
151C2×C13#168111yescharacteristic
152C2×C13#221711yescharacteristic
153C2×C13#222111yescharacteristic
154D13—42no—
155C2×Q8—521no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—131no—
160C22×C4—261no—
161D8—41no—
162D8—41no—
163D8—81no—
164D8—1042no—
165C2×C8—41no—
166C2×C8—261no—
167C2×C8—521no—
168C2×C8—521no—
169C2×C8—521no—
170C2×C8#612711yescharacteristic
171C2×C8D4×D1311yescharacteristic
172C4⋊C4—131no—
173C4⋊C4—521no—
174C4⋊C4—521no—
175C22⋊C4—261no—
176C42D4×D1311yescharacteristic
177C16—41no—
178C16—261no—
179C16—261no—
180C13#1246811yescharacteristic, complemented, Sylow
181C23—81no—
182C23—261no—
183Q8—2081no—
184D4—81no—
185D4—81no—
186D4—81no—
187D4—81no—
188D4—132no—
189D4—161no—
190D4—261no—
191C2×C4—261no—
192C2×C4—521no—
193C2×C4—521no—
194C2×C4—1041no—
195C2×C4#8813811yescharacteristic
196C2×C4D8×D1311yescharacteristic
197C2×C4#8817011yescharacteristic
198C8—21no—
199C8—81no—
200C8—521no—
201C8—1041no—
202C8#8816511yescharacteristic
203C8#8817011yescharacteristic
204C22—161no—
205C22—161no—
206C22—161no—
207C22—262no—
208C22—521no—
209C22—521no—
210C22#1171843611yescharacteristic
211C4—21no—
212C4—521no—
213C4—2081no—
214C4#1171840911yescharacteristic
215C4#1171844811yescharacteristic
216C4#1171857311yescharacteristic
217C4D13×SD3211yescharacteristic
218C2—321no—
219C2—522no—
220C2#1311427211yescharacteristic
221C2#1311693111yescharacteristic
222C2#1311695511yescharacteristic
subgroupG/H
centerC22#11718436
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1361C2
socleC22×C13#466
prime radical#13114188C2
hypercenter#1361D13
hypocenterC13#12468
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
1. #13117059C2semidirect
2. #13116655C2semidirect
3. #13114236C2semidirect
5. #13112909C2semidirect
6. #13112893C2semidirect
7. C13×#1361C2semidirect
76. #1361D13semidirect
180. C13#12468semidirect

Maximal subgroups

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

subgroupindex
#131170592
#131166552
#131142362
#131141882
#131129092
#131128932
C13×#13612
#1246813