Finite Group Databasebeta

← #11785984

Subgroups — #11785984

Order 1152.

521 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 521 conjugacy classes of subgroups — too many to draw. Only its 156 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
2C2×#63572C212yesmaximal
3C3×#4524C212yesmaximal
4#10589156C212yesmaximal
5#68606—32nomaximal
6C2×C32×C42C2211yescharacteristic
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C22×C3×C3⋊C8C2214yes—
10#63658C414yes—
11#63572—24no—
12C2×Dic3⋊C8—34no—
13#4932—32no—
14#4932—61no—
15C3×#336—32no—
16#4550—34no—
17#4524D312yes—
18C22×C32×C4C2×C412yes—
19C22×C32×C4C2311yescharacteristic
20C22×C3⋊Dic3C2×C412yes—
21C22×C3⋊Dic3C2×C412yes—
22C32×C42—22no—
23C4×C3⋊Dic3—22no—
24C4×C3⋊Dic3D412yes—
25C4×C3⋊Dic3Q812yes—
26C2×C3×C3⋊C8—24no—
27C2×C3×C3⋊C8—24no—
28C2×C3×C3⋊C8—24no—
29#1832—91noSylow
30C22×C3×C8—34no—
31C2×C3×C42—21no—
32C2×C3×C42C2×D312yes—
33C2×C4×Dic3—32no—
34C2×C4×Dic3—32no—
35C2×C4×Dic3—61no—
36C2×C4×Dic3—61no—
37C22×C3⋊C8C2×D314yes—
38C3⋊#95—34no—
39C3⋊#95—34no—
40C3⋊#95—64no—
41Dic3⋊C8—68no—
42C23×C32C22×C411yescharacteristic
43C2×C32×C4—22no—
44C2×C32×C4—24no—
45C2×C32×C4C2×D411yescharacteristic
46C2×C32×C4C2×Q811yescharacteristic
47C2×C32×C4#4112yes—
48C2×C32×C4#4112yes—
49C2×C3⋊Dic3—22no—
50C2×C3⋊Dic3—24no—
51C2×C3⋊Dic3—24no—
52C2×C3⋊Dic3C4⋊C414yes—
53C3×C3⋊C8—44no—
54C2×C4⋊C8—92no—
55#376—91no—
56#336—32no—
57#336—92no—
58C22×C3×C4—22no—
59C22×C3×C4—21no—
60C22×C3×C4C4×D314yes—
61C22×C3×C4C22×D312yes—
62C22×Dic3—34no—
63C22×Dic3—32no—
64C22×Dic3—32no—
65C22×Dic3—62no—
66C22×Dic3—62no—
67C2×C3×C8—64no—
68C2×C3×C8—64no—
69C2×C3×C8—64no—
70C3×C42—24no—
71C3×C42—24no—
72C4×Dic3—34no—
73C4×Dic3—34no—
74C4×Dic3—62no—
75C4×Dic3—62no—
76C4×Dic3—64no—
77C4×Dic3—64no—
78C2×C3⋊C8—24no—
79C2×C3⋊C8—24no—
80C2×C3⋊C8—24no—
81C22×C32C2×C4⋊C411yescharacteristic
82C22×C32#11711yescharacteristic
83C22×C32#11711yescharacteristic
84C22×C32#13114yes—
85C32×C4—42no—
86C32×C4#12412yes—
87C32×C4#12512yes—
88C3⋊Dic3—24no—
89C3⋊Dic3—42no—
90C22×C8—34no—
91C2×C42—91no—
92C2×C42—91no—
93C2×C42D3211yescharacteristic
94C4⋊C8—184no—
95#95—94no—
96C23×C3—21no—
97C23×C3C2×C4×D312yes—
98C2×C3×C4—24no—
99C2×C3×C4—24no—
100C2×C3×C4—24no—
101C2×C3×C4—24no—
102C2×C3×C4—21no—
103C2×C3×C4—22no—
104C2×C3×C4—21no—
105C2×C3×C4—22no—
106C2×C3×C4—44no—
107C2×C3×C4#23514yes—
108C2×C3×C4D3×D412yes—
109C2×C3×C4#23714yes—
110C2×C3×C4D3×Q812yes—
111C2×Dic3—38no—
112C2×Dic3—64no—
113C2×Dic3—64no—
114C2×Dic3—64no—
115C2×Dic3—64no—
116C2×Dic3—62no—
117C2×Dic3—62no—
118C2×Dic3—64no—
119C2×Dic3—64no—
120C2×Dic3—124no—
121C2×Dic3—124no—
122C3×C8—124no—
123C3⋊C8—44no—
124C2×C32#38211yescharacteristic
125C2×C32#42412yes—
126C2×C32#43312yes—
127C2×C32#43312yes—
128C22×C4—92no—
129C22×C4—92no—
130C22×C4#62412yes—
131C22×C4C2×D3211yescharacteristic
132C2×C8—64no—
133C2×C8—64no—
134C2×C8—64no—
135C42—22no—
136C42—92no—
137C42—92no—
138C42—182no—
139C22×C3—24no—
140C22×C3—21no—
141C22×C3—21no—
142C22×C3—21no—
143C22×C3#87212yes—
144C22×C3#87712yes—
145C22×C3D3×C4⋊C412yes—
146C22×C3#90114yes—
147C22×C3#90714yes—
148C3×C4—22no—
149C3×C4—22no—
150C3×C4—44no—
151C3×C4—44no—
152C3×C4#88514yes—
153C3×C4#88914yes—
154Dic3—68no—
155Dic3—124no—
156Dic3—124no—
157Dic3—122no—
158Dic3—122no—
159C32#183211yescharacteristic, complemented, Sylow
160C23C2×#62411yescharacteristic
161C2×C4—24no—
162C2×C4—22no—
163C2×C4—94no—
164C2×C4—184no—
165C2×C4—184no—
166C2×C4—182no—
167C2×C4#379711yescharacteristic
168C2×C4#379812yes—
169C2×C4#380211yescharacteristic
170C2×C4#380512yes—
171C8—124no—
172C2×C3—22no—
173C2×C3—22no—
174C2×C3—22no—
175C2×C3—21no—
176C2×C3#465012yes—
177C2×C3#469012yes—
178C2×C3#470912yes—
179C2×C3#472014yes—
180C2×C3#483914yes—
181C22#6381714yes—
182C22#6387411yescharacteristic
183C22#6390011yescharacteristic
184C22#6395711yescharacteristic
185C4—42no—
186C4—184no—
187C4—362no—
188C4#6387012yes—
189C4#6391512yes—
190C3—21no—
191C3#6860612yescomplemented
192C2#1059029812yes—
193C2#1059033212yes—
194C2#1059106212yes—
195C2#1059136011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutator, socle, prime radicalC23×C32C22×C4
FittingC2×C32×C42C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1832
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
159. C32#1832semidirect
191. C3#68606semidirect

Maximal subgroups

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

subgroupindex
#105926312
C2×#635722
C3×#45242
#105891562
#686063