Finite Group Databasebeta

← #16778100

Subgroups — #16778100

Order 3328.

348 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C2×#11718225C212yesmaximal
2#13115642C211yesmaximal, characteristic
3C2×#88128C2211yescharacteristic
4C2×#88107—22no—
5C2×C4×C8×C13C411yescharacteristic, complemented
6C2×#88061—22no—
7#11718596C411yescharacteristic, complemented
8#11718225—22no—
9#11718225C414yescomplemented
10C22×D52—41no—
11C22×D52D412yes—
12C2×C22⋊#261—42no—
13C22×C8×C13—21no—
14C2×C42×C13C2×C411yescharacteristic
15C2×C4⋊Dic13—21no—
16C2×C4⋊Dic13—41no—
17#88128—41no—
18#88128C2×C412yes—
19#88128D411yescharacteristic
20#88128Q811yescharacteristic
21#88107—24no—
22#88107—42no—
23C4×C8×C13—41no—
24#88061—44no—
25#7498—131nomaximal, Sylow
26C23×D13—22no—
27C22×#261—82no—
28C22×C4×C13—21no—
29C22×C4×C13C22⋊C411yescharacteristic
30C22×Dic13—41no—
31C2×D52—22no—
32C2×D52—42no—
33C2×D52—42no—
34C2×D52—42no—
35C2×D52—41no—
36C2×D52—41no—
37C2×D52—82no—
38C2×D52—82no—
39C2×D52C22⋊C412yes—
40C2×D52C4⋊C412yes—
41C22⋊#261—44no—
42C22⋊#261—82no—
43C2×C8×C13—22no—
44C2×C8×C13—41no—
45C2×C8×C13—41no—
46C42×C13—21no—
47C42×C13C4211yescharacteristic
48C42×C13C4⋊C411yescharacteristic
49C4⋊Dic13—42no—
50C4⋊Dic13—82no—
51C2×#353—132no—
52#1957—131no—
53C23×C13#9911yescharacteristic
54C22×D13—22no—
55C22×D13—22no—
56C22×D13—42no—
57C22×D13—42no—
58C22×D13—82no—
59C22×D13—82no—
60C2×#261—84no—
61C2×#261—162no—
62C2×#261—162no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13#9511yescharacteristic
70C2×C4×C13#9911yescharacteristic
71C2×Dic13—82no—
72C2×Dic13—81no—
73D52—42no—
74D52—42no—
75D52—82no—
76D52—84no—
77D52—82no—
78D52—82no—
79C8×C13—42no—
80C2×#127—131no—
81C2×#102—262no—
82C2×#99—262no—
83C2×C4×C8#26111yescharacteristic, complemented
84#384—131no—
85#353—134no—
86#353—262no—
87C22×C13—21no—
88C22×C13—21no—
89C22×C13#34211yescharacteristic
90C22×C13#35311yescharacteristic
91C22×C13#35411yescharacteristic
92C2×D13—42no—
93C2×D13—42no—
94C2×D13—82no—
95C2×D13—82no—
96C2×D13—82no—
97C2×D13—82no—
98C2×D13—162no—
99#261—164no—
100C4×C13—22no—
101C4×C13—22no—
102C4×C13—21no—
103C4×C13—21no—
104Dic13—161no—
105C22×D4—132no—
106C22×D4—521no—
107C22×C8—21no—
108#127—132no—
109#127—131no—
110#127—131no—
111#127—521no—
112C2×C4⋊C4—261no—
113C2×C4⋊C4—521no—
114C2×C22⋊C4—522no—
115C2×C42C2×#26111yescharacteristic
116#102—524no—
117#99—264no—
118#99—522no—
119C4×C8—41no—
120C2×C13—21no—
121C2×C13—21no—
122C2×C13#139311yescharacteristic
123C2×C13#140811yescharacteristic
124C2×C13#140911yescharacteristic
125D13—82no—
126D13—82no—
127C24—262no—
128C2×D4—132no—
129C2×D4—132no—
130C2×D4—262no—
131C2×D4—522no—
132C2×D4—522no—
133C2×D4—522no—
134C2×D4—521no—
135C2×D4—521no—
136C2×D4—1042no—
137C2×D4—1042no—
138C22×C4—21no—
139C22×C4—521no—
140C22×C4—1042no—
141C22×C4C22⋊#26111yescharacteristic
142C2×C8—22no—
143C2×C8—41no—
144C2×C8—41no—
145C4⋊C4—522no—
146C4⋊C4—1042no—
147C22⋊C4—524no—
148C22⋊C4—1042no—
149C42—21no—
150C42C4×#26111yescharacteristic
151C42C4⋊#26111yescharacteristic
152C13#749811yescharacteristic, complemented, Sylow
153C23—262no—
154C23—262no—
155C23—522no—
156C23—522no—
157C23—1042no—
158C23—1042no—
159C23#8810711yescharacteristic
160D4—522no—
161D4—522no—
162D4—1042no—
163D4—1044no—
164D4—1042no—
165D4—1042no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—1042no—
173C2×C4—1044no—
174C2×C4—1041no—
175C2×C4—2082no—
176C2×C4—2082no—
177C2×C4(C2×#261)⋊C411yescharacteristic
178C2×C4#8811911yescharacteristic
179C8—42no—
180C22—21no—
181C22—21no—
182C22—522no—
183C22—522no—
184C22—1042no—
185C22—1042no—
186C22—1042no—
187C22—1042no—
188C22—2082no—
189C22#1171822511yescharacteristic
190C22#1171822611yescharacteristic
191C22#1171828911yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—2084no—
197C4—2081no—
198C2—21no—
199C2—21no—
200C2—1042no—
201C2—1042no—
202C2#1312993011yescharacteristic
203C2#1312996811yescharacteristic
204C2#1312997011yescharacteristic
subgroupG/H
centerC22#11718225
commutatorC42×C13C42
FrattiniC2×C42C2×#261
FittingC2×C4×C8×C13C4
socleC22×C13#353
prime radical, cosocleC2×#88128C22
hypercenterC2×C4×C8#261
hypocenterC13#7498
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
5. C2×C4×C8×C13C4semidirect
7. #11718596C4semidirect
9. #11718225C4semidirect
83. C2×C4×C8#261semidirect
152. C13#7498semidirect

Maximal subgroups

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

subgroupindex
C2×#117182252
#131156422
#749813