Finite Group Databasebeta

← #15766028

Subgroups — #15766028

Order 3328.

402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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#13123223C211yesmaximal, characteristic, complemented
2#13115664C211yesmaximal, characteristic
3#13113397C212yesmaximal
4#13112695C212yesmaximal, complemented
5C13×#1276C211yesmaximal, characteristic, complemented
6#11719182C2211yescharacteristic
7C13×#431C2212yes—
8C43×C13C2211yescharacteristic
9#11718597C2212yes—
10#11718594—24no—
11#11718589—22no—
12C2×#88045—22no—
13#11718585C2211yescharacteristic
14#11718062—24no—
15C2×#6127—21no—
16C2×C42×C13—22no—
17C2×C42×C13D412yes—
18C2×C42×C13C2311yescharacteristic
19#88184—22no—
20C2×C4⋊Dic13—22no—
21C2×#6101—24no—
22C2×#6099—21no—
23#88129—21no—
24#88128Q811yescharacteristic
25C4×D52—22no—
26#88123Q811yescharacteristic
27C13×C4⋊C8—22no—
28C13×C22⋊C8—22no—
29C4×C8×C13—22no—
30#88071—24no—
31#88071—22no—
32#88071D414yes—
33#88045—44no—
34C4⋊#1055—22no—
35#10366—131nomaximal, Sylow
36C22×C4×C13—22no—
37C22×C4×C13C2×D411yescharacteristic
38C22×C4×C13C2×D412yes—
39C2×C22⋊D13—41no—
40C22×Dic13—24no—
41#6127—42no—
42#6127—42no—
43C2×D52—21no—
44C2×D52—22no—
45C2×C4×D13—41no—
46C2×Dic26—21no—
47C2×C8×C13—42no—
48C42×C13—22no—
49C42×C13—22no—
50C42×C13—44no—
51C42×C13C2×Q811yescharacteristic
52C42×C13#4112yes—
53C42×C13#4111yescharacteristic
54#6103—42no—
55C4⋊Dic13—22no—
56C4⋊Dic13—42no—
57C4⋊Dic13—42no—
58#6101—48no—
59#6099—42no—
60C2×#1055—41no—
61#2864—131no—
62#1962—131no—
63#1517—132no—
64#1286—132no—
65#1276D1311yescharacteristic, complemented
66C23×C13#12011yescharacteristic
67C22×D13—41no—
68C2×C4×C13—24no—
69C2×C4×C13—42no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13C22⋊Q812yes—
73C2×C4×C13C22⋊Q811yescharacteristic
74C2×C4×C13#12412yes—
75C2×C4×C13#12411yescharacteristic
76C2×C4×C13#13512yes—
77C2×C4×C13AGL(1,ℤ/8)12yes—
78C22⋊D13—82no—
79C2×Dic13—48no—
80C2×Dic13—41no—
81C2×Dic13—44no—
82D52—42no—
83D52—82no—
84C4×D13—81no—
85C4×D13—81no—
86Dic26—42no—
87C8×C13—82no—
88#1055—81no—
89#532—131no—
90#431C2×D1312yes—
91#423—131no—
92C2×#104—262no—
93#389—262no—
94#387—264no—
95#382—132no—
96C43C2×D1311yescharacteristic
97#327—264no—
98C22×C13—22no—
99C22×C13#39311yescharacteristic
100C22×C13#44912yes—
101C2×D13—81no—
102C2×D13—82no—
103C4×C13—22no—
104C4×C13—22no—
105C4×C13—44no—
106C4×C13#47812yes—
107C4×C13#48811yescharacteristic
108C4×C13#49011yescharacteristic
109Dic13—84no—
110Dic13—81no—
111C2×#41—261no—
112C2×M16—261no—
113C4⋊Q8—131no—
114#127—131no—
115#124—261no—
116#121—262no—
117C4×D4—262no—
118C2×C4⋊C4—264no—
119C2×C4⋊C4—262no—
120C2×C42—22no—
121C2×C42D5212yes—
122C2×C42C22×D1311yescharacteristic
123C4⋊C8—22no—
124C4⋊C8—262no—
125#104—524no—
126C22⋊C8—22no—
127C4×C8—22no—
128#95—134no—
129#95—264no—
130#95—262no—
131C2×C13—22no—
132C2×C13#202511yescharacteristic
133C2×C13#203112yes—
134D13—161no—
135#41—522no—
136#41—522no—
137C2×Q8—261no—
138C2×D4—262no—
139C2×D4—261no—
140C2×D4—521no—
141C22×C4—22no—
142C22×C4—264no—
143C22×C4—521no—
144C22×C4C2×D5211yescharacteristic
145C22×C4D4×D1312yes—
146M16—522no—
147C2×C8—42no—
148C2×C8—521no—
149C4⋊C4—262no—
150C4⋊C4—528no—
151C4⋊C4—522no—
152C4⋊C4—522no—
153C22⋊C4—522no—
154C42—22no—
155C42—22no—
156C42—44no—
157C42#612712yes—
158C42#612911yescharacteristic
159C42Q8×D1311yescharacteristic
160C13#1036611yescharacteristic, complemented, Sylow
161C23—521no—
162C23#8813611yescharacteristic
163Q8—522no—
164D4—522no—
165D4—1042no—
166D4—1042no—
167C2×C4—24no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—528no—
172C2×C4—521no—
173C2×C4—524no—
174C2×C4—1041no—
175C2×C4—1041no—
176C2×C4#8812911yescharacteristic
177C2×C4#8813912yes—
178C2×C4#8815012yes—
179C2×C4#8815111yescharacteristic
180C2×C4#8815812yes—
181C2×C4#8816212yes—
182C8—82no—
183C8—1041no—
184C22—22no—
185C22—1041no—
186C22—1042no—
187C22#1171833411yescharacteristic
188C22#1171839512yes—
189C4—22no—
190C4—22no—
191C4—44no—
192C4—1044no—
193C4—1041no—
194C4#1171835811yescharacteristic
195C4#1171837411yescharacteristic
196C4#1171850812yes—
197C2—22no—
198C2—2081no—
199C2#1311598311yescharacteristic
200C2#1311600912yes—
subgroupG/H
centerC22#11718334
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#393
prime radical#11719182C22
hypercenter#1276D13
hypocenterC13#10366
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
1. #13123223C2semidirect
4. #13112695C2semidirect
5. C13×#1276C2semidirect
65. #1276D13semidirect
160. C13#10366semidirect

Maximal subgroups

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

subgroupindex
#131232232
#131156642
#131133972
#131126952
C13×#12762
#1036613