Finite Group Databasebeta

← #11786143

Subgroups — #11786143

Order 1152.

481 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 481 conjugacy classes of subgroups — too many to draw. Only its 148 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#10592631C211yesmaximal, characteristic
2C3×#4524C212yesmaximal
3#10589156C212yesmaximal
4#10589156C212yesmaximal
5#68608—32nomaximal
6C2×C32×C42C2211yescharacteristic
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C22×C3×C3⋊C8C2214yes—
10#63658C414yes—
11#4932—32no—
12#4932—61no—
13C3×#336—32no—
14#4550—34no—
15#4550—34no—
16#4524D312yes—
17C22×C32×C4C2×C412yes—
18C22×C32×C4C2311yescharacteristic
19C22×C3⋊Dic3C2×C412yes—
20C22×C3⋊Dic3C2×C412yes—
21C32×C42—22no—
22C4×C3⋊Dic3—22no—
23C4×C3⋊Dic3—22no—
24C2×C3×C3⋊C8—24no—
25C2×C3×C3⋊C8—24no—
26C2×C3×C3⋊C8—24no—
27#1840—91noSylow
28C22×C3×C8—34no—
29C2×C3×C42—21no—
30C2×C3×C42C2×D312yes—
31C2×C4×Dic3—32no—
32C2×C4×Dic3—32no—
33C2×C4×Dic3—61no—
34C2×C4×Dic3—61no—
35C22×C3⋊C8C2×D314yes—
36C3⋊#95—34no—
37C3⋊#95—34no—
38C3⋊#95—64no—
39C23×C32C22×C411yescharacteristic
40C2×C32×C4—22no—
41C2×C32×C4—24no—
42C2×C32×C4#4112yes—
43C2×C32×C4#4112yes—
44C2×C32×C4#4112yes—
45C2×C3⋊Dic3—22no—
46C2×C3⋊Dic3—22no—
47C2×C3⋊Dic3—24no—
48C2×C3⋊Dic3—24no—
49C3×C3⋊C8—44no—
50#376—91no—
51#336—32no—
52#336—92no—
53#336—92no—
54C22×C3×C4—22no—
55C22×C3×C4—21no—
56C22×C3×C4C4×D314yes—
57C22×C3×C4C22×D312yes—
58C22×Dic3—32no—
59C22×Dic3—32no—
60C22×Dic3—34no—
61C22×Dic3—62no—
62C22×Dic3—62no—
63C2×C3×C8—64no—
64C2×C3×C8—64no—
65C2×C3×C8—64no—
66C3×C42—24no—
67C3×C42—24no—
68C4×Dic3—64no—
69C4×Dic3—64no—
70C4×Dic3—64no—
71C4×Dic3—62no—
72C4×Dic3—62no—
73C2×C3⋊C8—24no—
74C2×C3⋊C8—24no—
75C2×C3⋊C8—24no—
76C22×C32#11711yescharacteristic
77C22×C32#11711yescharacteristic
78C22×C32#11711yescharacteristic
79C22×C32#13114yes—
80C32×C4—42no—
81C32×C4#12614yes—
82C3⋊Dic3—42no—
83C3⋊Dic3—42no—
84C22×C8—34no—
85C2×C42—91no—
86C2×C42—91no—
87C2×C42D3211yescharacteristic
88#95—94no—
89C23×C3—21no—
90C23×C3C2×C4×D312yes—
91C2×C3×C4—24no—
92C2×C3×C4—24no—
93C2×C3×C4—24no—
94C2×C3×C4—24no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×C3×C4—44no—
99C2×C3×C4#23514yes—
100C2×C3×C4#23712yes—
101C2×C3×C4#23714yes—
102C2×C3×C4#23912yes—
103C2×Dic3—64no—
104C2×Dic3—64no—
105C2×Dic3—62no—
106C2×Dic3—62no—
107C2×Dic3—64no—
108C2×Dic3—64no—
109C2×Dic3—64no—
110C2×Dic3—64no—
111C2×Dic3—64no—
112C2×Dic3—124no—
113C2×Dic3—124no—
114C3×C8—124no—
115C3⋊C8—44no—
116C2×C32#38311yescharacteristic
117C2×C32#43312yes—
118C2×C32#43312yes—
119C2×C32#43312yes—
120C22×C4—92no—
121C22×C4—92no—
122C22×C4#62412yes—
123C22×C4C2×D3211yescharacteristic
124C2×C8—64no—
125C2×C8—64no—
126C2×C8—64no—
127C42—22no—
128C42—182no—
129C42—182no—
130C22×C3—24no—
131C22×C3—21no—
132C22×C3—21no—
133C22×C3—21no—
134C22×C3#87212yes—
135C22×C3#87712yes—
136C22×C3#89212yes—
137C22×C3#90114yes—
138C22×C3#90714yes—
139C3×C4—24no—
140C3×C4—44no—
141C3×C4—44no—
142C3×C4#87914yes—
143C3×C4#89814yes—
144Dic3—124no—
145Dic3—124no—
146Dic3—122no—
147Dic3—122no—
148Dic3—124no—
149C32#184011yescharacteristic, complemented, Sylow
150C23C2×#62411yescharacteristic
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—184no—
154C2×C4—184no—
155C2×C4—182no—
156C2×C4—182no—
157C2×C4#379612yes—
158C2×C4#379812yes—
159C2×C4#380512yes—
160C8—124no—
161C2×C3—22no—
162C2×C3—22no—
163C2×C3—22no—
164C2×C3—21no—
165C2×C3#465112yes—
166C2×C3#469012yes—
167C2×C3#470912yes—
168C2×C3#472014yes—
169C2×C3#484014yes—
170C22#6381714yes—
171C22#6384911yescharacteristic
172C22#6387411yescharacteristic
173C22#6395711yescharacteristic
174C4—42no—
175C4—362no—
176C4—362no—
177C4#6386214yes—
178C3—21no—
179C3#6860812yescomplemented
180C2#1059025712yes—
181C2#1059029812yes—
182C2#1059106212yes—
183C2#1059122911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutator, socle, prime radicalC23×C32C22×C4
FittingC2×C32×C42C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1840
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
149. C32#1840semidirect
179. C3#68608semidirect

Maximal subgroups

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

subgroupindex
#105926312
C3×#45242
#105891562
#686083