Finite Group Databasebeta

← #11784409

Subgroups — #11784409

Order 1152.

338 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C2×#63771C211yesmaximal, characteristic
2C2×#63767C211yesmaximal, characteristic
3#10593748C212yesmaximal
4#10592559C211yesmaximal, characteristic
5#10590164C212yesmaximal
6C2×C4×#157C2211yescharacteristic
7C2×#3788C2212yes—
8C2×#3787C2211yescharacteristic
9C2×C8×C3⋊D3C2211yescharacteristic
10#64101C2212yes—
11#63777—22no—
12C4×#622—22no—
13#63771C414yescomplemented
14#63767C414yescomplemented
15C32×#106C411yescharacteristic, complemented
16#63644C411yescharacteristic, complemented
17#63634C412yescomplemented
18#4860—62no—
19C22×#157—21no—
20C2×C4×C3⋊D3C2311yescharacteristic
21C2×#622—22no—
22C2×#622D412yes—
23C4×#157—21no—
24C4×#157C2×C412yes—
25#3788—22no—
26#3788C2×C414yes—
27#3787C2×C412yes—
28#3787Q812yes—
29C2×C32×C8C2×C411yescharacteristic
30C32×C4⋊C4C2×C412yes—
31#3752—22no—
32C4⋊(C3⋊Dic3)C2×C412yes—
33C4×C3⋊Dic3—22no—
34C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
35C8×C3⋊D3C2×C412yes—
36C8×C3⋊D3C2×C412yes—
37#1773—91nomaximal, Sylow
38C2×D3×C8—62no—
39#892—64no—
40C3×#106—22no—
41#817—62no—
42#807—64no—
43C22×C3⋊D3#4111yescharacteristic
44C2×#157—22no—
45C2×#157—42no—
46C2×C32×C4—22no—
47C2×C32×C4C22×C411yescharacteristic
48C2×C3⋊Dic3—22no—
49C2×C3⋊Dic3C2×D411yescharacteristic
50C4×C3⋊D3C22×C411yescharacteristic
51C4×C3⋊D3C22×C411yescharacteristic
52C4×C3⋊D3C2×Q811yescharacteristic
53C4×C3⋊D3#4111yescharacteristic
54#622—24no—
55#622C4⋊C414yes—
56C32×C8C4212yes—
57C3⋊(C3⋊C8)C4212yes—
58C2×#108—91no—
59#427—91no—
60#405—92no—
61C2×#97—91no—
62#339—92no—
63C2×C4×D3—62no—
64C2×C3×C8—22no—
65C3×C4⋊C4—24no—
66(C2×D3)⋊C4—124no—
67C4⋊Dic3—64no—
68C4×Dic3—124no—
69C2×C3⋊C8—62no—
70D3×C8—64no—
71D3×C8—64no—
72C22×C32C4×D411yescharacteristic
73C2×C3⋊D3—22no—
74C2×C3⋊D3#11711yescharacteristic
75C2×C3⋊D3C4×Q811yescharacteristic
76#157—42no—
77C32×C4—42no—
78C32×C4C2×C4211yescharacteristic
79C32×C4C4×Q811yescharacteristic
80C3⋊Dic3—42no—
81C3⋊Dic3C2×C4⋊C411yescharacteristic
82C3⋊Dic3C4×D411yescharacteristic
83C2×M16—92no—
84C22×C8—91no—
85C22×C8—91no—
86#117—92no—
87C2×C42—91no—
88#108—94no—
89#107—92no—
90#106—91no—
91#106#15711yescharacteristic, complemented
92#97—94no—
93#97—182no—
94C4×C8—182no—
95C22×D3—62no—
96C2×C3×C4—22no—
97C2×C3×C4—44no—
98C2×Dic3—62no—
99C2×Dic3—124no—
100C4×D3—62no—
101C4×D3—62no—
102C4×D3—62no—
103C4×D3—62no—
104C3×C8—24no—
105C3⋊C8—64no—
106C2×C32C4×C4⋊C411yescharacteristic
107C2×C32#44412yes—
108C3⋊D3—21no—
109C3⋊D3—21no—
110C22×C4—91no—
111C22×C4—181no—
112M16—94no—
113M16—182no—
114C2×C8—92no—
115C2×C8—92no—
116C2×C8—92no—
117C2×C8—91no—
118C2×C8—92no—
119C2×C8—92no—
120C2×C8—182no—
121C2×C8C2×#15711yescharacteristic
122C4⋊C4—92no—
123C4⋊C4C2×#15712yes—
124C22⋊C4—182no—
125C42—92no—
126C42—182no—
127C42—181no—
128C22×C3—22no—
129C2×D3—62no—
130C2×D3—62no—
131C2×D3—124no—
132C3×C4—22no—
133C3×C4—22no—
134C3×C4—84no—
135Dic3—62no—
136Dic3—62no—
137Dic3—244no—
138C32#177311yescharacteristic, complemented, Sylow
139C23—91no—
140C2×C4—22no—
141C2×C4—91no—
142C2×C4—91no—
143C2×C4—91no—
144C2×C4—91no—
145C2×C4—91no—
146C2×C4—182no—
147C2×C4—182no—
148C2×C4—362no—
149C2×C4C22×#15711yescharacteristic
150C8—94no—
151C8—92no—
152C8—184no—
153C8C4×#15712yes—
154C2×C3—22no—
155C2×C3—24no—
156D3—122no—
157D3—122no—
158C22—91no—
159C22—91no—
160C22—182no—
161C22D4×#15711yescharacteristic
162C4—42no—
163C4—91no—
164C4—91no—
165C4—362no—
166C4—362no—
167C4C2×C4×#15711yescharacteristic
168C4Q8×#15711yescharacteristic
169C3—22no—
170C2—181no—
171C2—181no—
172C2C4⋊C4×#15711yescharacteristic
173C2#1059378412yes—
subgroupG/H
centerC22D4×#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×#106C4
socleC22×C32C4×D4
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenter#106#157
hypocenterC32#1773
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
13. #63771C4semidirect
14. #63767C4semidirect
15. C32×#106C4semidirect
16. #63644C4semidirect
17. #63634C4semidirect
91. #106#157semidirect
138. C32#1773semidirect

Maximal subgroups

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

subgroupindex
C2×#637712
C2×#637672
#105937482
#105925592
#105901642
#17739