Finite Group Databasebeta

← #15777339

Subgroups — #15777339

Order 3328.

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

normal subgroups only

This group has 240 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#13117061C211yesmaximal, characteristic, complemented
2#13116655C211yesmaximal, characteristic, complemented
3#13114222C211yesmaximal, characteristic, complemented
4#13114192C211yesmaximal, characteristic
5#13112907C211yesmaximal, characteristic, complemented
6#13112883C211yesmaximal, characteristic, complemented
7C13×#1364C211yesmaximal, characteristic, complemented
8C13×#500C2211yescharacteristic
9#11718744—21no—
10C2×C16×D13—21no—
11#11718504—21no—
12#11718356C2211yescharacteristic
13C8×D52C2211yescharacteristic
14C13×C4⋊C16C2211yescharacteristic
15C13×#335C2211yescharacteristic
16#11718139—21no—
17#11718099—21no—
18#11718083—21no—
19#11718083—21no—
20#11718077—21no—
21C4×#6090C2211yescharacteristic
22#11718050C2211yescharacteristic
23C13×C4⋊Q8—21no—
24C2×#6106—41no—
25C2×D104—21no—
26C2×D104—21no—
27C2×D104—41no—
28C2×C8×D13—21no—
29#88128—21no—
30C4×D52D411yescharacteristic
31C2×C13×C16—21no—
32C13×#107—21no—
33C13×#107—21no—
34C13×C4⋊C8—21no—
35C4×C8×C13C2311yescharacteristic
36#88075—41no—
37#88061—41no—
38#88060—21no—
39C2×#6090D411yescharacteristic
40C2×#6090D411yescharacteristic
41C4⋊#1055—21no—
42C4⋊#1055D411yescharacteristic
43C16×D13—42no—
44#12467—131nomaximal, Sylow
45C2×Q8×C13—41no—
46C2×D52—41no—
47C2×D52—41no—
48C2×D52—41no—
49C2×D52D811yescharacteristic
50C2×C4×D13—21no—
51C2×C8×C13—41no—
52C2×C8×C13C2×D411yescharacteristic
53C2×C8×C13#4111yescharacteristic
54C13×C4⋊C4—41no—
55C13×C4⋊C4—41no—
56C42×C13C2×D411yescharacteristic
57#6106—82no—
58#6103—21no—
59C4⋊Dic13D811yescharacteristic
60C2×#1055—21no—
61C2×#1055—41no—
62D104—41no—
63D104—41no—
64D104—81no—
65D104—82no—
66C8×D13—41no—
67C8×D13—41no—
68C13×C16—41no—
69#6090—21no—
70#6090—21no—
71#2240—131no—
72D4×C16—131no—
73#1673—131no—
74#1667—131no—
75#1371—131no—
76#1364D1311yescharacteristic, complemented
77#1361—131no—
78C22×D13—21no—
79C22×D13—81no—
80Q8×C13—81no—
81Q8×C13—81no—
82C2×C4×C13—81no—
83C2×C4×C13#12111yescharacteristic
84C2×C4×C13C2×D811yescharacteristic
85C2×C4×C13#13511yescharacteristic
86C2×Dic13—21no—
87D52—21no—
88D52—81no—
89D52—81no—
90D52—81no—
91D52—81no—
92D52—161no—
93D52D1612yes—
94C4×D13—41no—
95C4×D13—41no—
96C8×C13—21no—
97C8×C13—81no—
98C8×C13#13511yescharacteristic
99C8×C13AGL(1,ℤ/8)11yescharacteristic
100#1055—41no—
101#1055—81no—
102C22×C16—261no—
103#500C2×D1311yescharacteristic
104#493—131no—
105#461—261no—
106#459—261no—
107C8×D4—131no—
108C4⋊C16C2×D1311yescharacteristic
109#357—261no—
110#357—261no—
111C22⋊C16—261no—
112C4×C16—131no—
113#335—131no—
114#335C2×D1311yescharacteristic
115#332—261no—
116#331—261no—
117C22×C13#46611yescharacteristic
118C2×D13—22no—
119C2×D13—41no—
120C2×D13—41no—
121C2×D13—161no—
122C2×D13—161no—
123C2×D13—161no—
124C4×C13—21no—
125C4×C13—161no—
126C4×C13#46311yescharacteristic
127C4×C13#47111yescharacteristic
128C4×C13C2×D1611yescharacteristic
129C4×C13#50811yescharacteristic
130Dic13—41no—
131C2×SD16—521no—
132C2×D8—261no—
133C2×D8—261no—
134C2×D8—521no—
135C22×C8—261no—
136C4⋊Q8—21no—
137#127—261no—
138C4×D4—131no—
139C2×C16—21no—
140C2×C16—131no—
141C2×C16—131no—
142C2×C16—522no—
143#107—21no—
144#107—21no—
145C4⋊C8—21no—
146C4⋊C8—131no—
147C4⋊C8—261no—
148#103—521no—
149#102—521no—
150C22⋊C8—261no—
151C4×C8C22×D1311yescharacteristic
152C2×C13#168111yescharacteristic
153C2×C13#221511yescharacteristic
154C2×C13#222311yescharacteristic
155D13—42no—
156D13—321no—
157C2×Q8—41no—
158C2×D4—131no—
159C2×D4—521no—
160C2×D4—521no—
161C2×D4—521no—
162C22×C4—261no—
163SD16—1042no—
164D8—521no—
165D8—521no—
166D8—1041no—
167D8—1042no—
168C2×C8—41no—
169C2×C8—261no—
170C2×C8—521no—
171C2×C8—521no—
172C2×C8—521no—
173C2×C8#612711yescharacteristic
174C2×C8D4×D1311yescharacteristic
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—131no—
178C22⋊C4—261no—
179C42D4×D1311yescharacteristic
180C16—41no—
181C16—261no—
182C16—261no—
183C13#1246711yescharacteristic, complemented, Sylow
184C23—261no—
185C23—1041no—
186Q8—81no—
187Q8—81no—
188D4—132no—
189D4—261no—
190D4—1041no—
191D4—1041no—
192D4—1041no—
193D4—1041no—
194D4—2081no—
195C2×C4—81no—
196C2×C4—261no—
197C2×C4—521no—
198C2×C4—521no—
199C2×C4#8813811yescharacteristic
200C2×C4D8×D1311yescharacteristic
201C2×C4#8817011yescharacteristic
202C8—21no—
203C8—81no—
204C8—521no—
205C8—1041no—
206C8#8816811yescharacteristic
207C8#8817311yescharacteristic
208C22—262no—
209C22—521no—
210C22—521no—
211C22—2081no—
212C22—2081no—
213C22—2081no—
214C22#1171843611yescharacteristic
215C4—21no—
216C4—161no—
217C4—521no—
218C4#1171841511yescharacteristic
219C4#1171848011yescharacteristic
220C4D13×D1611yescharacteristic
221C4#1171857711yescharacteristic
222C2—522no—
223C2—4161no—
224C2#1311427611yescharacteristic
225C2#1311692111yescharacteristic
226C2#1311696911yescharacteristic
subgroupG/H
centerC22#11718436
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1364C2
socleC22×C13#466
prime radical#13114192C2
hypercenter#1364D13
hypocenterC13#12467
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
1. #13117061C2semidirect
2. #13116655C2semidirect
3. #13114222C2semidirect
5. #13112907C2semidirect
6. #13112883C2semidirect
7. C13×#1364C2semidirect
76. #1364D13semidirect
183. C13#12467semidirect

Maximal subgroups

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

subgroupindex
#131170612
#131166552
#131142222
#131141922
#131129072
#131128832
C13×#13642
#1246713