Finite Group Databasebeta

← #11790547

Subgroups — #11790547

Order 1152.

222 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 63 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#10593771C211yesmaximal, characteristic
2C2×#63771C211yesmaximal, characteristic
3#10593765C211yesmaximal, characteristic
4#10593547C212yesmaximal
5#10590095C212yesmaximal
6#64286C2211yescharacteristic
7#64283C2212yes—
8#64283C2211yescharacteristic
9C2×#3788C2212yes—
10C2×C8×C3⋊D3C2211yescharacteristic
11#63771—21no—
12#63771C412yescomplemented
13#63771C412yescomplemented
14#63770—21no—
15#63767—21no—
16C8×#157—21no—
17#63748—24no—
18C2×C4×C3⋊D3C2311yescharacteristic
19C22⋊#157Q812yes—
20#3792—22no—
21#3792D412yes—
22C2×#622—22no—
23C4⋊#157—21no—
24C4×#157—21no—
25#3788—22no—
26#3788—21no—
27#3788—22no—
28#3788C2×C414yes—
29#3787—21no—
30#3787—22no—
31C2×C32×C8Q811yescharacteristic
32C2×C3⋊(C3⋊C8)Q811yescharacteristic
33C8×C3⋊D3C2×C411yescharacteristic
34C8×C3⋊D3C2×C411yescharacteristic
35C8×C3⋊D3D411yescharacteristic
36C8×C3⋊D3D411yescharacteristic
37#1953—91nomaximal, Sylow
38C2×D3×C8—121no—
39C22×C3⋊D3C2×Q811yescharacteristic
40C2×#157—22no—
41C2×C32×C4C2×Q811yescharacteristic
42C2×C3⋊Dic3C2×D411yescharacteristic
43C4×C3⋊D3C22×C411yescharacteristic
44C4×C3⋊D3C2×D411yescharacteristic
45C4×C3⋊D3#4111yescharacteristic
46C4×C3⋊D3#4111yescharacteristic
47#622—24no—
48#622—22no—
49#622—42no—
50C32×C8C4⋊C411yescharacteristic
51C32×C8C4⋊C411yescharacteristic
52C3⋊(C3⋊C8)C4⋊C411yescharacteristic
53C3⋊(C3⋊C8)C4⋊C411yescharacteristic
54#430—92no—
55C2×#108—91no—
56C2×#108—91no—
57#405—91no—
58#344—92no—
59C2×C4×D3—121no—
60C2×C3×C8—41no—
61C2×C3⋊C8—121no—
62D3×C8—121no—
63D3×C8—121no—
64D3×C8—121no—
65D3×C8—121no—
66C22×C32C4⋊Q811yescharacteristic
67C2×C3⋊D3—41no—
68C2×C3⋊D3C4×Q811yescharacteristic
69C2×C3⋊D3C22⋊Q811yescharacteristic
70#157—42no—
71C32×C4C2×C4⋊C411yescharacteristic
72C32×C4#12511yescharacteristic
73C3⋊Dic3C4×D411yescharacteristic
74C3⋊Dic3#12111yescharacteristic
75C2×M16—92no—
76C2×M16—91no—
77C2×M16—92no—
78C22×C8—91no—
79#117—91no—
80#108—92no—
81#108—92no—
82#108—181no—
83#108—181no—
84#108—184no—
85#97—181no—
86C4×C8—181no—
87C22×D3—121no—
88C2×C3×C4—41no—
89C2×Dic3—121no—
90C4×D3—121no—
91C4×D3—121no—
92C4×D3—121no—
93C4×D3—121no—
94C3×C8—41no—
95C3×C8—41no—
96C3⋊C8—121no—
97C3⋊C8—121no—
98C2×C32—21no—
99C2×C32#38911yescharacteristic
100C3⋊D3—21no—
101C3⋊D3—21no—
102C22×C4—91no—
103M16—94no—
104M16—92no—
105M16—182no—
106M16—181no—
107M16—182no—
108M16—182no—
109C2×C8—91no—
110C2×C8—91no—
111C2×C8—91no—
112C2×C8—91no—
113C2×C8—91no—
114C2×C8—181no—
115C2×C8—182no—
116C2×C8—182no—
117C2×C8PSU(3,𝔽2)11yescharacteristic
118C4⋊C4—181no—
119C22⋊C4—92no—
120C42—181no—
121C22×C3—41no—
122C2×D3—121no—
123C2×D3—121no—
124C2×D3—124no—
125C3×C4—41no—
126C3×C4—41no—
127Dic3—121no—
128Dic3—121no—
129C32#195311yescharacteristic, complemented, Sylow
130C23—91no—
131C2×C4—91no—
132C2×C4—91no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—91no—
136C2×C4—182no—
137C2×C4C2×PSU(3,𝔽2)11yescharacteristic
138C8—91no—
139C8—91no—
140C8—184no—
141C8—182no—
142C8—362no—
143C8#377711yescharacteristic
144C8#377711yescharacteristic
145C2×C3—42no—
146C2×C3—41no—
147D3—122no—
148D3—122no—
149C22—91no—
150C22—91no—
151C22—361no—
152C22C4⋊PSU(3,𝔽2)11yescharacteristic
153C4—91no—
154C4—91no—
155C4—362no—
156C4#6424311yescharacteristic
157C4C2×#377711yescharacteristic
158C3—41no—
159C2—21no—
160C2—181no—
161C2—181no—
162C2#1059355411yescharacteristic
subgroupG/H
centerC2#10593554
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC2×C32×C8Q8
socleC2×C32#389
prime radicalC22×C3⋊D3C2×Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8PSU(3,𝔽2)
hypocenterC32#1953
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
12. #63771C4semidirect
13. #63771C4semidirect
129. C32#1953semidirect

Maximal subgroups

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

subgroupindex
#105937712
C2×#637712
#105937652
#105935472
#105900952
#19539