Finite Group Databasebeta

← #15783575

Subgroups — #15783575

Order 3328.

324 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 71 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×#11718112C212yesmaximal, complemented
2#13116927C211yesmaximal, characteristic, complemented
3#13113014C212yesmaximal, complemented
4C22⋊#88034C211yesmaximal, characteristic, complemented
5C22×C13×D16C211yesmaximal, characteristic
6C22×C13×D8—21no—
7C2×C13×D16—24no—
8C2×C13×D16—21no—
9C2×C13×D16C2212yes—
10C22×C13×C16C2211yescharacteristic
11#11718777—21no—
12C2×Dic104C2211yescharacteristic, complemented
13#11718112—24no—
14#11718096C2211yescharacteristic, complemented
15#11718095—21no—
16C2×#88034C2212yescomplemented
17C22×D4×C13—41no—
18C2×C13×D8—24no—
19C2×C13×D8—22no—
20C2×C13×D8—42no—
21C2×C13×D8—41no—
22C22×C8×C13D411yescharacteristic
23#88178—41no—
24C2×Dic52—21no—
25C13×D16—24no—
26C13×D16—22no—
27C13×D16D414yes—
28C2×C13×C16—22no—
29C2×C13×C16D411yescharacteristic
30C2×C13×C16C2311yescharacteristic
31#88058—21no—
32#88056—41no—
33Dic104—22no—
34#88034—22no—
35#13664—131nomaximal, Sylow
36C24×C13—81no—
37C2×D4×C13—44no—
38C2×D4×C13—42no—
39C2×D4×C13—82no—
40C2×D4×C13—81no—
41C22×C4×C13D811yescharacteristic
42C2×Dic26—41no—
43C13×D8—24no—
44C13×D8—44no—
45C13×D8—42no—
46C2×C8×C13—21no—
47C2×C8×C13—21no—
48C2×C8×C13D811yescharacteristic
49C2×C8×C13C2×D411yescharacteristic
50C22⋊Dic13—81no—
51C4⋊Dic13—41no—
52#6101—81no—
53Dic52—41no—
54Dic52—41no—
55C13×C16—21no—
56C13×C16C2×D412yes—
57C22×D16D1311yescharacteristic
58C2×SD64—132no—
59#2216—131no—
60#1415—132no—
61C22⋊C32—131no—
62C23×C13—84no—
63C23×C13—82no—
64C23×C13—162no—
65C23×C13—162no—
66C23×C13D1611yescharacteristic
67D4×C13—44no—
68D4×C13—84no—
69D4×C13—82no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13D1611yescharacteristic
73C2×C4×C13C2×D811yescharacteristic
74C2×Dic13—81no—
75C2×Dic13—81no—
76Dic26—81no—
77Dic26—81no—
78C8×C13—21no—
79C8×C13#12011yescharacteristic
80C8×C13AGL(1,ℤ/8)11yescharacteristic
81C22×D8—21no—
82C2×Q32—131no—
83C2×D16—24no—
84C2×D16—21no—
85C2×D16C2×D1312yes—
86C22×C16C2×D1311yescharacteristic
87#467—261no—
88SD64—264no—
89C2×C32—132no—
90#366—131no—
91#358—261no—
92C22×C13—21no—
93C22×C13—21no—
94C22×C13—84no—
95C22×C13—168no—
96C22×C13—162no—
97C22×C13—162no—
98C22×C13SD6412yescomplemented
99C22×C13C2×D1611yescharacteristic
100C4×C13—21no—
101C4×C13#44711yescharacteristic
102C4×C13#50911yescharacteristic
103Dic13—161no—
104Dic13—161no—
105C22×D4—41no—
106C2×Q16—261no—
107C2×D8—24no—
108C2×D8—22no—
109C2×D8—42no—
110C2×D8—41no—
111C22×C8C22⋊D1311yescharacteristic
112C22⋊Q8—521no—
113Q32—262no—
114D16—24no—
115D16—22no—
116D16C22⋊D1314yes—
117C2×C16—22no—
118C2×C16C22⋊D1311yescharacteristic
119C2×C16C22×D1311yescharacteristic
120#107—261no—
121#103—521no—
122C32—262no—
123C2×C13—22no—
124C2×C13—164no—
125C2×C13#218411yescharacteristic
126C2×C13C2×SD6411yescharacteristic
127C2×C13#226311yescharacteristic
128C24—81no—
129C2×Q8—521no—
130C2×D4—44no—
131C2×D4—42no—
132C2×D4—82no—
133C2×D4—81no—
134C22×C4#610411yescharacteristic
135Q16—521no—
136Q16—521no—
137D8—24no—
138D8—44no—
139D8—42no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8#610411yescharacteristic
143C2×C8C2×C22⋊D1311yescharacteristic
144C4⋊C4—521no—
145C4⋊C4—1041no—
146C22⋊C4—1041no—
147C16—21no—
148C16C2×C22⋊D1312yes—
149C13#1366411yescharacteristic, complemented, Sylow
150C23—84no—
151C23—82no—
152C23—162no—
153C23—162no—
154C23#8806611yescharacteristic
155Q8—1041no—
156Q8—1041no—
157D4—44no—
158D4—84no—
159D4—82no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—1041no—
163C2×C4—1041no—
164C2×C4#8806611yescharacteristic
165C2×C4C2×#610411yescharacteristic
166C8—21no—
167C8#8818611yescharacteristic
168C8#8820711yescharacteristic
169C22—21no—
170C22—21no—
171C22—84no—
172C22—168no—
173C22—162no—
174C22—162no—
175C22#1171811212yescomplemented
176C22C2×#8806611yescharacteristic
177C4—21no—
178C4—2081no—
179C4—2081no—
180C4#1171880811yescharacteristic
181C4#1171887811yescharacteristic
182C2—22no—
183C2—164no—
184C2#1311674811yescharacteristic
185C2C2×#1171811211yescharacteristic
186C2#1311714911yescharacteristic
subgroupG/H
centerC22C2×#88066
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
Fitting, prime radicalC22×C13×D16C2
socleC22×C13C2×D16
hypercenterC22×D16D13
hypocenterC13#13664
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22×D16

Complements

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

NH ≅ G/Ntype
1. C2×#11718112C2semidirect
2. #13116927C2semidirect
3. #13113014C2semidirect
4. C22⋊#88034C2semidirect
12. C2×Dic104C22semidirect
14. #11718096C22semidirect
16. C2×#88034C22semidirect
98. C22×C13SD64semidirect
149. C13#13664semidirect
175. C22#11718112semidirect

Maximal subgroups

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

subgroupindex
C2×#117181122
#131169272
#131130142
C22⋊#880342
C22×C13×D162
#1366413