Finite Group Databasebeta

← #11797374

Subgroups — #11797374

Order 1152.

176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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#10593748C211yesmaximal, characteristic
2#10593265C211yesmaximal, characteristic, complemented
3#10593264C211yesmaximal, characteristic
4#10593264C211yesmaximal, characteristic
5#10593263C211yesmaximal, characteristic, complemented
6C4⋊#3771C211yesmaximal, characteristic, complemented
7C4×#3771C211yesmaximal, characteristic, complemented
8C2×#3788C411yescharacteristic
9C2×#3787C2211yescharacteristic
10C2×#3771C2211yescharacteristic
11C2×#3771C2211yescharacteristic
12C2×#3771C2211yescharacteristic
13C2×#3771C2211yescharacteristic
14#64101C411yescharacteristic
15#63777C411yescharacteristic
16#63777C411yescharacteristic
17C4×#622C2211yescharacteristic
18C4×#622C2211yescharacteristic
19C2×C4×C3⋊D3C2×C411yescharacteristic
20C2×#622C2×C411yescharacteristic
21C2×#622C2×C411yescharacteristic
22C2×#622C2×C411yescharacteristic
23C2×#622C2311yescharacteristic
24#3788—22no—
25#3787—21no—
26#3787—21no—
27#3771—21no—
28#3771—21no—
29#3771—21no—
30#3771—21no—
31C32×C4⋊C4C811yescharacteristic
32#3752C811yescharacteristic
33#3752C811yescharacteristic
34C4⋊(C3⋊Dic3)C811yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37#2164—91nomaximal, Sylow
38#892—121no—
39C22×C3⋊D3C2×C811yescharacteristic
40C2×C32×C4C2×C811yescharacteristic
41C2×C32×C4C2×C811yescharacteristic
42C2×C32×C4C2×C811yescharacteristic
43C2×C3⋊Dic3C2×C811yescharacteristic
44C2×C3⋊Dic3C2×C811yescharacteristic
45C2×C3⋊Dic3C22×C411yescharacteristic
46C4×C3⋊D3—21no—
47C4×C3⋊D3—21no—
48#622—21no—
49#622—21no—
50#622M1612yes—
51#622#4111yescharacteristic
52#622#4111yescharacteristic
53#405—91no—
54C4⋊C16—91no—
55C4⋊C16—91no—
56C22⋊C16—91no—
57C22⋊C16—91no—
58#346—91no—
59C4×C16—91no—
60C2×C4×D3—121no—
61C3×C4⋊C4—41no—
62(C2×D3)⋊C4—121no—
63(C2×D3)⋊C4—121no—
64C4⋊Dic3—121no—
65C4×Dic3—121no—
66C4×Dic3—121no—
67C22×C32C22×C811yescharacteristic
68C2×C3⋊D3—21no—
69C2×C3⋊D3—21no—
70C2×C3⋊D3—21no—
71C32×C4—21no—
72C32×C4—21no—
73C32×C4—21no—
74C3⋊Dic3—21no—
75C3⋊Dic3—21no—
76C3⋊Dic3#11711yescharacteristic
77C3⋊Dic3C2×M1611yescharacteristic
78C2×M16—91no—
79C22×C8—91no—
80#117—91no—
81C2×C16—91no—
82C2×C16—91no—
83C2×C16—91no—
84C2×C16—91no—
85#97—91no—
86#97—91no—
87C4×C8—91no—
88C4×C8—91no—
89C22×D3—121no—
90C2×C3×C4—41no—
91C2×C3×C4—41no—
92C2×C3×C4—41no—
93C2×Dic3—121no—
94C2×Dic3—121no—
95C2×Dic3—121no—
96C4×D3—122no—
97C4×D3—122no—
98C2×C32#43111yescharacteristic
99C2×C32#50411yescharacteristic
100C2×C32#50411yescharacteristic
101C3⋊D3—41no—
102C22×C4—91no—
103M16—182no—
104C2×C8—91no—
105C2×C8—91no—
106C2×C8—91no—
107C2×C8—91no—
108C2×C8—181no—
109C2×C8—181no—
110C4⋊C4—91no—
111C4⋊C4AGL(1,𝔽9)11yescharacteristic
112C22⋊C4—91no—
113C22⋊C4—91no—
114C42—91no—
115C42—91no—
116C16—181no—
117C16—181no—
118C16—181no—
119C16—181no—
120C22×C3—41no—
121C2×D3—122no—
122C2×D3—241no—
123C2×D3—241no—
124C3×C4—42no—
125C3×C4—81no—
126C3×C4—81no—
127Dic3—121no—
128Dic3—121no—
129Dic3—241no—
130Dic3—241no—
131C32#216411yescharacteristic, complemented, Sylow
132C23—91no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—91no—
136C2×C4—181no—
137C2×C4—181no—
138C2×C4C2×AGL(1,𝔽9)11yescharacteristic
139C2×C4C2×AGL(1,𝔽9)11yescharacteristic
140C2×C4C2×AGL(1,𝔽9)11yescharacteristic
141C8—91no—
142C8—91no—
143C8—92no—
144C8—181no—
145C8—181no—
146C2×C3—41no—
147C2×C3—41no—
148C2×C3—41no—
149D3—242no—
150C22—181no—
151C22—181no—
152C22—181no—
153C22C22×AGL(1,𝔽9)11yescharacteristic
154C4—21no—
155C4—21no—
156C4—21no—
157C4—91no—
158C4—91no—
159C4—181no—
160C4—181no—
161C3—41no—
162C2—361no—
163C2#1059648411yescharacteristic
164C2#1059648511yescharacteristic
165C2#1059648711yescharacteristic
subgroupG/H
center, FrattiniC22C22×AGL(1,𝔽9)
commutator, socleC22×C32C22×C8
FittingC32×C4⋊C4C8
prime radicalC22×C3⋊D3C2×C8
cosocleC2×#622C23
hypercenterC4⋊C4AGL(1,𝔽9)
hypocenterC32#2164
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593265C2semidirect
5. #10593263C2semidirect
6. C4⋊#3771C2semidirect
7. C4×#3771C2semidirect
131. C32#2164semidirect

Maximal subgroups

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

subgroupindex
#105937482
#105932652
#105932642
#105932632
C4⋊#37712
C4×#37712
#21649