Finite Group Databasebeta

← #11799752

Subgroups — #11799752

Order 1152.

293 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 293 conjugacy classes of subgroups — too many to draw. Only its 72 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#10592895C211yesmaximal, characteristic
2#10590874C211yesmaximal, characteristic, complemented
3C3×#4566C212yesmaximal
4#10589136C212yesmaximal, complemented
5#10589135C211yesmaximal, characteristic, complemented
6#69247—32nomaximal
7C32×#135C2211yescharacteristic
8#64157—21no—
9#63872—21no—
10#63664—21no—
11#63646C2211yescharacteristic
12C8×C3⋊Dic3C2211yescharacteristic
13C3×#817C2212yes—
14C3×#812C2212yes—
15#63576—21no—
16#5196—32no—
17#5196—61no—
18#4858—32no—
19C3×#360—32no—
20#4566D312yes—
21#4513—32no—
22#4511—32no—
23#4487—32no—
24C32×#41—21no—
25C32×Q16Q811yescharacteristic
26C32×SD16—21no—
27C32×D8Q811yescharacteristic
28C2×C32×C8C2311yescharacteristic
29C4×C3⋊Dic3D411yescharacteristic
30#3748—21no—
31#3748—41no—
32C2×C3⋊(C3⋊C8)—41no—
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C3×C4⋊Dic3—22no—
35Dic3⋊Dic3—42no—
36C3×C3⋊C16—22no—
37#2231—91noSylow
38C3×#135—21no—
39C3×#135C2×D312yes—
40#948—62no—
41#948—62no—
42#890—62no—
43C3×M32—32no—
44C3×#106—32no—
45#837—62no—
46#837—62no—
47#819—32no—
48#819—61no—
49#817C2×D312yes—
50C8×Dic3—32no—
51C8×Dic3—61no—
52#812C2×D312yes—
53#807—62no—
54C32×Q8—21no—
55C32×D4—21no—
56C32×D4—41no—
57C2×C32×C4—41no—
58C2×C32×C4C2×D411yescharacteristic
59C2×C3⋊Dic3—21no—
60C2×C3×Dic3—42no—
61C32×C8C2×Q811yescharacteristic
62C32×C8#4111yescharacteristic
63C3⋊(C3⋊C8)—41no—
64C3⋊(C3⋊C8)SD1611yescharacteristic
65C3⋊(C3⋊C8)SD1611yescharacteristic
66#499—91no—
67#443—91no—
68#365—92no—
69#364—91no—
70#360—32no—
71C3×#41—22no—
72C3×#41—22no—
73C3×Q16—21no—
74C3×Q16Dic612yes—
75C3×SD16—22no—
76C3×SD16—22no—
77C3×D8—21no—
78C3×D8Dic612yes—
79C2×C3×C8—21no—
80C2×C3×C8C22×D312yes—
81C3×C4⋊C4—62no—
82C4⋊Dic3—22no—
83C4⋊Dic3—122no—
84Dic3⋊C4—122no—
85C4×Dic3—32no—
86C4×Dic3—61no—
87#208—62no—
88#208—62no—
89#208—122no—
90#208—122no—
91C2×C3⋊C8—32no—
92C2×C3⋊C8—61no—
93C2×C3⋊C8—122no—
94C2×C3⋊C8—122no—
95C3×C16—62no—
96C3⋊C16—22no—
97C22×C32—41no—
98C22×C32AGL(1,ℤ/8)11yescharacteristic
99C32×C4—41no—
100C32×C4C22⋊Q811yescharacteristic
101C32×C4C2×SD1611yescharacteristic
102C3⋊Dic3—41no—
103C3×Dic3—82no—
104#135D3211yescharacteristic
105#131—181no—
106#125—181no—
107M32—32no—
108#108—91no—
109#107—181no—
110#106—32no—
111#104—181no—
112C4×C8—91no—
113C3×Q8—22no—
114C3×Q8—22no—
115C3×D4—22no—
116C3×D4—22no—
117C3×D4—42no—
118C3×D4—42no—
119C2×C3×C4—21no—
120C2×C3×C4—42no—
121C2×C3×C4—42no—
122C2×C3×C4—122no—
123C2×C3×C4D3×D412yes—
124C2×Dic3—42no—
125C2×Dic3—62no—
126C2×Dic3—121no—
127C3×C8—21no—
128C3×C8—21no—
129C3×C8C2×Dic612yes—
130C3×C8#23712yes—
131C3⋊C8—32no—
132C3⋊C8—32no—
133C3⋊C8—61no—
134C3⋊C8—61no—
135C3⋊C8—122no—
136C3⋊C8—122no—
137C2×C32—21no—
138C2×C32—81no—
139C2×C32#47611yescharacteristic
140#41—21no—
141Q16#62711yescharacteristic
142SD16—21no—
143D8#62711yescharacteristic
144M16—181no—
145M16—361no—
146C2×C8—91no—
147C2×C8—361no—
148C2×C8C2×D3211yescharacteristic
149C4⋊C4—62no—
150C4⋊C4—362no—
151C42—91no—
152C16—62no—
153C22×C3—21no—
154C22×C3—42no—
155C22×C3—42no—
156C22×C3#91112yes—
157C3×C4—21no—
158C3×C4—21no—
159C3×C4—42no—
160C3×C4—42no—
161C3×C4—242no—
162C3×C4#87812yes—
163C3×C4D3×SD1612yes—
164Dic3—82no—
165Dic3—122no—
166Dic3—122no—
167C32#223111yescharacteristic, complemented, Sylow
168Q8—21no—
169D4—21no—
170D4—41no—
171C2×C4—41no—
172C2×C4—122no—
173C2×C4—181no—
174C2×C4#381111yescharacteristic
175C8—91no—
176C8—91no—
177C8—361no—
178C8#380511yescharacteristic
179C8C2×#62711yescharacteristic
180C2×C3—22no—
181C2×C3—21no—
182C2×C3—41no—
183C2×C3—82no—
184C2×C3—82no—
185C2×C3#476112yes—
186C22—41no—
187C22#6392711yescharacteristic
188C4—41no—
189C4—242no—
190C4—361no—
191C4#6393011yescharacteristic
192C4#6398211yescharacteristic
193C3—21no—
194C3#6924712yescomplemented
195C2—21no—
196C2—81no—
197C2#1059149511yescharacteristic
subgroupG/H
centerC2#10591495
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
Fitting, prime radicalC32×#135C22
socleC2×C32#476
hypercenter#135D32
hypocenterC32#2231
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
2. #10590874C2semidirect
4. #10589136C2semidirect
5. #10589135C2semidirect
167. C32#2231semidirect
194. C3#69247semidirect

Maximal subgroups

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

subgroupindex
#105928952
#105908742
C3×#45662
#105891362
#105891352
#692473