Finite Group Databasebeta

← #16777927

Subgroups — #16777927

Order 3328.

224 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 36 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#13129930C211yesmaximal, characteristic
2#13129765C211yesmaximal, characteristic
3#13116365C211yesmaximal, characteristic
4C2×#88107—21no—
5C13×#384C411yescharacteristic, complemented
6C2×#88049—21no—
7C2×#88047—21no—
8#11718600C2211yescharacteristic
9#11718285—21no—
10#11718116C411yescharacteristic, complemented
11C22×D52D411yescharacteristic
12C2×C22⋊#261—41no—
13C2×C13×C4⋊C4—21no—
14C2×C13×C4⋊C4—41no—
15C2×C42×C13C2×C411yescharacteristic
16C2×#6103—41no—
17C2×C4⋊Dic13D411yescharacteristic
18C22×#1055—21no—
19C22⋊#1057—41no—
20#88107—22no—
21#88107—41no—
22#88049—42no—
23#88047—42no—
24#7434—131nomaximal, Sylow
25C23×D13—21no—
26C22×#261—81no—
27C22×C4×C13—21no—
28C22×C4×C13—41no—
29C22×C4×C13C22⋊C411yescharacteristic
30C22×Dic13—21no—
31C2×D52—21no—
32C2×D52—41no—
33C2×D52—41no—
34C2×D52SD1611yescharacteristic
35C2×D52Q1611yescharacteristic
36C22⋊#261—42no—
37C22⋊#261—81no—
38C2×#1057—81no—
39C13×C4⋊C4—41no—
40C13×C4⋊C4—41no—
41C13×C4⋊C4—82no—
42C42×C13—41no—
43#6103—82no—
44C4⋊Dic13—41no—
45C2×#1055—22no—
46C2×#1055—41no—
47C2×#1055—41no—
48#2093—131no—
49#1393—131no—
50#1318—131no—
51C23×C13#9911yescharacteristic
52C22×D13—21no—
53C22×D13—21no—
54C22×D13—41no—
55C22×D13—41no—
56C22×D13—81no—
57C22×D13—81no—
58C2×#261—82no—
59C2×#261—161no—
60C2×#261—161no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—22no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13—82no—
67C2×C4×C13—81no—
68C2×C4×C13#10311yescharacteristic
69C2×C4×C13#10411yescharacteristic
70C2×Dic13—41no—
71C2×Dic13—81no—
72D52—41no—
73D52—41no—
74D52—81no—
75#1057—161no—
76#1055—42no—
77C2×#107—261no—
78C2×#102—261no—
79C2×#99—261no—
80#390—131no—
81#384#26111yescharacteristic, complemented
82#336—131no—
83#324—261no—
84C22×C13—21no—
85C22×C13—21no—
86C22×C13#32811yescharacteristic
87C22×C13#35211yescharacteristic
88C22×C13#35311yescharacteristic
89C2×D13—41no—
90C2×D13—41no—
91C2×D13—81no—
92C2×D13—81no—
93C2×D13—81no—
94C2×D13—81no—
95C2×D13—161no—
96#261—162no—
97C4×C13—21no—
98C4×C13—21no—
99C4×C13—42no—
100C4×C13—161no—
101Dic13—81no—
102C22×D4—131no—
103C22×C8—261no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—131no—
107C2×C22⋊C4—521no—
108C2×C22⋊C4—521no—
109C2×C42C2×#26111yescharacteristic
110#107—522no—
111#102—522no—
112#99—262no—
113#99—521no—
114C22⋊C8—521no—
115C2×C13—21no—
116C2×C13—21no—
117C2×C13#135211yescharacteristic
118C2×C13#140711yescharacteristic
119C2×C13#140811yescharacteristic
120D13—81no—
121D13—81no—
122C24—261no—
123C2×D4—131no—
124C2×D4—131no—
125C2×D4—261no—
126C2×D4—521no—
127C2×D4—521no—
128C22×C4—21no—
129C22×C4—41no—
130C22×C4—261no—
131C22×C4—1041no—
132C22×C4C22⋊#26111yescharacteristic
133C2×C8—262no—
134C2×C8—521no—
135C2×C8—521no—
136C2×C8—1041no—
137C4⋊C4—41no—
138C4⋊C4—41no—
139C4⋊C4—82no—
140C4⋊C4—521no—
141C22⋊C4—522no—
142C22⋊C4—1042no—
143C22⋊C4—1041no—
144C42—41no—
145C13#743411yescharacteristic, complemented, Sylow
146C23—261no—
147C23—261no—
148C23—521no—
149C23—521no—
150C23—1041no—
151C23—1041no—
152C23#8811911yescharacteristic
153D4—521no—
154D4—521no—
155D4—1041no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—82no—
162C2×C4—81no—
163C2×C4—521no—
164C2×C4—1041no—
165C2×C4—1042no—
166C2×C4—2081no—
167C2×C4—2081no—
168C2×C4#8811711yescharacteristic
169C2×C4#8811811yescharacteristic
170C8—522no—
171C8—2081no—
172C22—21no—
173C22—21no—
174C22—521no—
175C22—521no—
176C22—1041no—
177C22—1041no—
178C22—1041no—
179C22—1041no—
180C22—2081no—
181C22#1171828811yescharacteristic
182C22#1171829411yescharacteristic
183C22#1171829811yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—161no—
188C4—1041no—
189C4—2082no—
190C2—21no—
191C2—21no—
192C2—1041no—
193C2—1041no—
194C2#1312983311yescharacteristic
195C2#1312996511yescharacteristic
196C2#1312996711yescharacteristic
subgroupG/H
centerC22#11718294
commutatorC2×C42×C13C2×C4
FrattiniC2×C42C2×#261
FittingC13×#384C4
socleC22×C13#353
prime radicalC22×D52D4
cosocle#11718600C22
hypercenter#384#261
hypocenterC13#7434
LCSG ▷ C2×C42×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
5. C13×#384C4semidirect
10. #11718116C4semidirect
81. #384#261semidirect
145. C13#7434semidirect

Maximal subgroups

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

subgroupindex
#131299302
#131297652
#131163652
#743413