Finite Group Databasebeta

← #11785360

Subgroups — #11785360

Order 1152.

570 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C22×#3787C211yesmaximal, characteristic
2C2×#63742C212yesmaximal, complemented
3#10591355C212yesmaximal
4#10590075C212yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#622C2211yescharacteristic
7C22×#622C2211yescharacteristic
8C2×#3787—24no—
9C2×#3787C414yescomplemented
10C2×#3724C2214yes—
11C2×#3722—22no—
12#63742—24no—
13C3×C3⋊#95—22no—
14#4667—62no—
15C23×C3⋊D3D411yescharacteristic
16C22×C32×C4D411yescharacteristic
17C22×C3⋊Dic3C2311yescharacteristic
18C2×C4×C3⋊D3—22no—
19C2×C4×C3⋊D3—22no—
20C2×C4×C3⋊D3C2×C412yes—
21C2×C4×C3⋊D3Q812yes—
22C22×C3×Dic3—24no—
23C2×#622—22no—
24C2×#622C2×C412yes—
25C2×#622C2×C412yes—
26C2×#622D414yes—
27#3787—28no—
28#3724—24no—
29#3724—24no—
30#3722—44no—
31#1807—91nomaximal, Sylow
32C22×C4×D3—62no—
33C2×(C2×D3)⋊C4—64no—
34C2×Dic3⋊C4—64no—
35C3×#95—62no—
36C3⋊#95—22no—
37C23×C32C2×D411yescharacteristic
38C22×C3⋊D3—22no—
39C22×C3⋊D3—22no—
40C22×C3⋊D3C4⋊C412yes—
41C22×C3⋊D3SD1614yes—
42C2×C32×C4—22no—
43C2×C32×C4C4⋊C412yes—
44C2×C3⋊Dic3C22×C411yescharacteristic
45C2×C3⋊Dic3C2×D412yes—
46C2×C3⋊Dic3C2×Q811yescharacteristic
47C2×C3⋊Dic3#4112yes—
48C4×C3⋊D3—22no—
49C4×C3⋊D3—22no—
50C4×C3⋊D3—24no—
51C2×C3×Dic3—44no—
52C2×C3×Dic3—44no—
53C2×C3×Dic3—44no—
54#622—22no—
55#622C22⋊C414yescomplemented
56C23×C8—91no—
57C2×#106—92no—
58#380—92no—
59#340—92no—
60C23×D3—62no—
61C22×C3×C4—22no—
62C22×C3×C4—64no—
63C22×Dic3—24no—
64C22×Dic3—62no—
65C2×C4×D3—64no—
66C2×C4×D3—64no—
67C2×C4×D3—124no—
68C2×C4×D3—124no—
69(C2×D3)⋊C4—128no—
70Dic3⋊C4—124no—
71Dic3⋊C4—124no—
72C22×C32C2×C4⋊C411yescharacteristic
73C22×C32#12112yes—
74C22×C32C2×SD1612yes—
75C22×C32#13512yes—
76C2×C3⋊D3—22no—
77C2×C3⋊D3—22no—
78C2×C3⋊D3—28no—
79C2×C3⋊D3#10614yescomplemented
80C32×C4—22no—
81C3⋊Dic3C2×C22⋊C411yescharacteristic
82C3⋊Dic3#11711yescharacteristic
83C3⋊Dic3C22⋊Q812yes—
84C3×Dic3—84no—
85C23×C4—91no—
86C22×C8—91no—
87C22×C8—94no—
88C22×C8—91no—
89C22×C8—184no—
90C2×C4⋊C4—94no—
91C2×C22⋊C4—182no—
92#106—184no—
93#95—62no—
94C23×C3—22no—
95C22×D3—64no—
96C22×D3—64no—
97C22×D3—64no—
98C22×D3—124no—
99C22×D3—124no—
100C2×C3×C4—24no—
101C2×C3×C4—44no—
102C2×C3×C4—124no—
103C2×C3×C4—124no—
104C2×C3×C4—124no—
105C2×Dic3—44no—
106C2×Dic3—44no—
107C2×Dic3—44no—
108C2×Dic3—62no—
109C2×Dic3—64no—
110C2×Dic3—62no—
111C2×Dic3—64no—
112C4×D3—124no—
113C4×D3—124no—
114C4×D3—128no—
115C2×C32#38011yescharacteristic
116C2×C32C2×#10611yescharacteristic
117C2×C32#42711yescharacteristic
118C2×C32#46514yes—
119C3⋊D3—24no—
120C24—91no—
121C22×C4—64no—
122C22×C4—91no—
123C22×C4—92no—
124C22×C4—92no—
125C22×C4—182no—
126C22×C4—182no—
127C22×C4GO+(4,𝔽2)11yescharacteristic
128C2×C8—94no—
129C2×C8—92no—
130C2×C8—92no—
131C2×C8—188no—
132C2×C8—182no—
133C4⋊C4—184no—
134C4⋊C4—184no—
135C22⋊C4—364no—
136C22×C3—24no—
137C22×C3—22no—
138C22×C3—22no—
139C22×C3—22no—
140C22×C3—24no—
141C2×D3—68no—
142C2×D3—124no—
143C2×D3—124no—
144C2×D3—128no—
145C2×D3—128no—
146C3×C4—44no—
147C3×C4—244no—
148Dic3—62no—
149Dic3—62no—
150Dic3—64no—
151Dic3—84no—
152C32#180711yescharacteristic, complemented, Sylow
153C23—94no—
154C23—92no—
155C23—182no—
156C23—182no—
157C23C2×GO+(4,𝔽2)11yescharacteristic
158C2×C4—22no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—92no—
162C2×C4—92no—
163C2×C4—124no—
164C2×C4—124no—
165C2×C4—124no—
166C2×C4—182no—
167C2×C4—182no—
168C2×C4—184no—
169C2×C4#377312yes—
170C8—94no—
171C8—182no—
172C2×C3—22no—
173C2×C3—22no—
174C2×C3—24no—
175C2×C3—24no—
176C2×C3—22no—
177D3—128no—
178C22—94no—
179C22—182no—
180C22—188no—
181C22—182no—
182C22#6422312yes—
183C22#6422712yes—
184C22C2×#377311yescharacteristic
185C22#6424212yes—
186C4—22no—
187C4—91no—
188C4—91no—
189C4—92no—
190C4—244no—
191C3—22no—
192C2—184no—
193C2#1059338711yescharacteristic
194C2#1059338911yescharacteristic
195C2#1059343514yes—
196C2#1059351611yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1807
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63742C2semidirect
4. #10590075C2semidirect
9. C2×#3787C4semidirect
55. #622C22⋊C4semidirect
79. C2×C3⋊D3#106semidirect
152. C32#1807semidirect

Maximal subgroups

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

subgroupindex
C22×#37872
C2×#637422
#105913552
#105900752
#18079