Finite Group Databasebeta

← #11790783

Subgroups — #11790783

Order 1152.

670 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 78 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#10596196C211yesmaximal, characteristic
2C2×#63785C214yesmaximal, complemented
3C42×#157C211yesmaximal, characteristic, complemented
4#10593728C211yesmaximal, characteristic, complemented
5C2×#3832C2212yes—
6C2×C4×#157—22no—
7C2×C4×#157C2212yes—
8C2×#3788C2212yes—
9C32×C4⋊Q8C411yescharacteristic, complemented
10#64156C412yescomplemented
11#64104—22no—
12#64102—22no—
13#64083C411yescharacteristic, complemented
14C42×C3⋊D3C2211yescharacteristic
15#63785—28no—
16C4⋊#622—22no—
17#5725—62no—
18C22×#157—22no—
19C2×C32×Q8C2×C412yes—
20#3832—24no—
21#3832—24no—
22C2×C4⋊(C3⋊D3)—22no—
23C2×C4⋊(C3⋊D3)—22no—
24C2×C4⋊(C3⋊D3)C2×C412yes—
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3D412yes—
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×#622—22no—
29C4×#157—28no—
30C4×#157—22no—
31C4×#157D414yescomplemented
32#3788—24no—
33C32×C4⋊C4—22no—
34C32×C42C2×C411yescharacteristic
35#3752—24no—
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D412yes—
38#1962—91nomaximal, Sylow
39C2×#239—64no—
40C3×C4⋊Q8—22no—
41#947—64no—
42#895—68no—
43#893—68no—
44#874—62no—
45C42×D3—62no—
46C22×C3⋊D3—22no—
47C22×C3⋊D3C2×D411yescharacteristic
48C2×#157—28no—
49C2×#157—24no—
50C32×Q8—24no—
51C2×C32×C4—22no—
52C2×C32×C4C22⋊C412yes—
53C2×C32×C4C22×C411yescharacteristic
54C2×C3⋊Dic3C22⋊C412yes—
55C2×C3⋊Dic3C2×D411yescharacteristic
56C4⋊(C3⋊D3)—24no—
57C4⋊(C3⋊D3)—44no—
58C4⋊(C3⋊D3)—44no—
59C4×C3⋊D3—24no—
60C4×C3⋊D3—42no—
61C4×C3⋊D3—42no—
62C4×C3⋊D3C2×D412yes—
63C4×C3⋊D3#4112yes—
64#622—42no—
65#532—91no—
66#423—91no—
67C2×#104—94no—
68C43—91no—
69C2×C3×Q8—24no—
70#239—128no—
71#239—128no—
72C2×D12—64no—
73C2×D12—68no—
74C2×D12—68no—
75C2×C4×D3—62no—
76C2×C4×D3—64no—
77C2×C4×D3—68no—
78C3×C4⋊C4—28no—
79C3×C42—22no—
80(C2×D3)⋊C4—616no—
81C4×Dic3—64no—
82C4×Dic3—62no—
83C22×C32C2×C22⋊C411yescharacteristic
84C2×C3⋊D3—22no—
85C2×C3⋊D3—42no—
86C2×C3⋊D3—44no—
87C2×C3⋊D3#12112yes—
88#157—28no—
89C32×C4—42no—
90C32×C4#10414yescomplemented
91C32×C4C4×D412yes—
92C3⋊Dic3—22no—
93C3⋊Dic3#12411yescharacteristic
94C3⋊Dic3#12711yescharacteristic
95C2×#41—92no—
96C2×M16—92no—
97C4⋊Q8#15711yescharacteristic, complemented
98#127—91no—
99#124—92no—
100#121—182no—
101C4×D4—182no—
102C2×C42—91no—
103C2×C42—92no—
104C2×C42—182no—
105C4⋊C8—182no—
106#104—188no—
107C22×D3—62no—
108C22×D3—68no—
109C3×Q8—48no—
110C2×C3×C4—28no—
111C2×C3×C4—22no—
112C2×C3×C4—24no—
113C2×Dic3—62no—
114C2×Dic3—64no—
115D12—128no—
116D12—1216no—
117D12—1216no—
118C4×D3—64no—
119C4×D3—64no—
120C4×D3—128no—
121C4×D3—128no—
122C4×D3—128no—
123C2×C32#39011yescharacteristic
124C2×C32C2×#10412yes—
125C3⋊D3—22no—
126C3⋊D3—82no—
127#41—184no—
128#41—184no—
129C2×Q8C2×#15712yes—
130C2×D4—92no—
131C2×D4—182no—
132C2×D4—182no—
133C22×C4—91no—
134C22×C4—92no—
135C22×C4—182no—
136C22×C4—182no—
137M16—184no—
138C2×C8—182no—
139C4⋊C4—22no—
140C22⋊C4—184no—
141C42—91no—
142C42—92no—
143C42—94no—
144C42—182no—
145C42—188no—
146C42C2×#15711yescharacteristic
147C22×C3—22no—
148C2×D3—64no—
149C2×D3—124no—
150C2×D3—128no—
151C2×D3—1216no—
152C3×C4—24no—
153C3×C4—28no—
154C3×C4—48no—
155Dic3—62no—
156Dic3—62no—
157Dic3—124no—
158C32#196211yescharacteristic, complemented, Sylow
159C23—91no—
160C23—182no—
161Q8—24no—
162D4—184no—
163D4—364no—
164D4—364no—
165C2×C4—22no—
166C2×C4—91no—
167C2×C4—92no—
168C2×C4—92no—
169C2×C4—92no—
170C2×C4—184no—
171C2×C4—188no—
172C2×C4—184no—
173C2×C4—362no—
174C2×C4—362no—
175C2×C4C22⋊#15712yes—
176C2×C4C22×#15711yescharacteristic
177C8—362no—
178C2×C3—22no—
179C2×C3—24no—
180D3—124no—
181D3—248no—
182C22—92no—
183C22—182no—
184C22—362no—
185C22—364no—
186C22C2×C22⋊#15711yescharacteristic
187C4—42no—
188C4—91no—
189C4—91no—
190C4—188no—
191C4—182no—
192C4#6378514yescomplemented
193C4D4×#15712yes—
194C3—22no—
195C2—182no—
196C2—722no—
197C2#1059382711yescharacteristic
198C2C2×#6378512yes—
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radical#10596196C2
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊Q8#157
hypocenterC32#1962
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63785C2semidirect
3. C42×#157C2semidirect
4. #10593728C2semidirect
9. C32×C4⋊Q8C4semidirect
10. #64156C4semidirect
13. #64083C4semidirect
31. C4×#157D4semidirect
90. C32×C4#104semidirect
97. C4⋊Q8#157semidirect
158. C32#1962semidirect
192. C4#63785semidirect

Maximal subgroups

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

subgroupindex
#105961962
C2×#637852
C42×#1572
#105937282
#19629