Finite Group Databasebeta

← #11786021

Subgroups — #11786021

Order 1152.

210 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 59 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×#63770C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic
3#10593765C211yesmaximal, characteristic
4#10590095C212yesmaximal
5#10590091C212yesmaximal
6#64286C2212yes—
7#64286C2211yescharacteristic
8#64283C2211yescharacteristic
9C2×#3788C2212yes—
10C2×C8×C3⋊D3C2211yescharacteristic
11#63770—21no—
12#63770—21no—
13#63769—21no—
14#63768—21no—
15#63767C412yescomplemented
16C8×#157C412yescomplemented
17C2×C4×C3⋊D3C2311yescharacteristic
18C22⋊#157—21no—
19C22⋊#157—22no—
20#3792—21no—
21C2×#622—22no—
22C4⋊#157—22no—
23C4⋊#157—21no—
24C4×#157—22no—
25C4×#157C2×C412yes—
26#3788—21no—
27#3788—22no—
28#3788—22no—
29#3787C2×C412yes—
30C2×C32×C8Q811yescharacteristic
31C2×C3⋊(C3⋊C8)Q811yescharacteristic
32C8×C3⋊D3C2×C411yescharacteristic
33C8×C3⋊D3C2×C411yescharacteristic
34C8×C3⋊D3D411yescharacteristic
35C8×C3⋊D3D411yescharacteristic
36#1833—91nomaximal, Sylow
37C2×D3×C8—121no—
38C22×C3⋊D3#4111yescharacteristic
39C2×#157—22no—
40C2×#157—42no—
41C2×C32×C4C2×Q811yescharacteristic
42C2×C3⋊Dic3#4111yescharacteristic
43C4×C3⋊D3C22×C411yescharacteristic
44C4×C3⋊D3C2×D411yescharacteristic
45C4×C3⋊D3#4111yescharacteristic
46C4×C3⋊D3#4111yescharacteristic
47#622—22no—
48#622—42no—
49C32×C8C4⋊C411yescharacteristic
50C32×C8C4⋊C411yescharacteristic
51C3⋊(C3⋊C8)C4⋊C411yescharacteristic
52C3⋊(C3⋊C8)C4⋊C411yescharacteristic
53C2×#108—91no—
54#427—91no—
55#405—91no—
56#344—92no—
57H(3,ℤ/4)—92no—
58C2×C4×D3—121no—
59C2×C3×C8—41no—
60C2×C3⋊C8—121no—
61D3×C8—121no—
62D3×C8—121no—
63D3×C8—121no—
64D3×C8—121no—
65C22×C32#12511yescharacteristic
66C2×C3⋊D3—41no—
67C2×C3⋊D3#11711yescharacteristic
68C2×C3⋊D3#12411yescharacteristic
69#157—42no—
70#157—82no—
71C32×C4C2×C4⋊C411yescharacteristic
72C32×C4#12511yescharacteristic
73C3⋊Dic3#11711yescharacteristic
74C3⋊Dic3#12411yescharacteristic
75C2×M16—91no—
76C2×M16—92no—
77C22×C8—91no—
78#117—91no—
79#117—92no—
80#108—181no—
81#108—181no—
82#107—181no—
83#106—181no—
84#97—92no—
85C4×C8—92no—
86C22×D3—121no—
87C2×C3×C4—41no—
88C2×Dic3—121no—
89C4×D3—121no—
90C4×D3—121no—
91C4×D3—121no—
92C4×D3—121no—
93C3×C8—41no—
94C3×C8—41no—
95C3⋊C8—121no—
96C3⋊C8—121no—
97C2×C32—21no—
98C2×C32#38211yescharacteristic
99C3⋊D3—21no—
100C3⋊D3—21no—
101C22×C4—91no—
102M16—181no—
103M16—181no—
104M16—182no—
105M16—182no—
106C2×C8—91no—
107C2×C8—91no—
108C2×C8—91no—
109C2×C8—91no—
110C2×C8—91no—
111C2×C8—92no—
112C2×C8—182no—
113C2×C8PSU(3,𝔽2)11yescharacteristic
114C4⋊C4—181no—
115C4⋊C4—182no—
116C22⋊C4—181no—
117C22⋊C4—182no—
118C42—92no—
119C42—182no—
120C22×C3—41no—
121C2×D3—121no—
122C2×D3—121no—
123C2×D3—124no—
124C3×C4—41no—
125C3×C4—41no—
126Dic3—121no—
127Dic3—121no—
128C32#183311yescharacteristic, complemented, Sylow
129C23—91no—
130C2×C4—91no—
131C2×C4—91no—
132C2×C4—91no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—182no—
136C2×C4—362no—
137C2×C4C2×PSU(3,𝔽2)11yescharacteristic
138C8—91no—
139C8—91no—
140C8—182no—
141C8—362no—
142C8#377711yescharacteristic
143C8#377711yescharacteristic
144C2×C3—42no—
145C2×C3—41no—
146D3—122no—
147D3—122no—
148C22—91no—
149C22—91no—
150C22—361no—
151C22#6424311yescharacteristic
152C4—91no—
153C4—91no—
154C4—362no—
155C4—722no—
156C4#6424311yescharacteristic
157C4C2×#377711yescharacteristic
158C3—41no—
159C2—21no—
160C2—181no—
161C2—181no—
162C2#1059354511yescharacteristic
subgroupG/H
centerC2#10593545
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC2×C32×C8Q8
socleC2×C32#382
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8PSU(3,𝔽2)
hypocenterC32#1833
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
15. #63767C4semidirect
16. C8×#157C4semidirect
128. C32#1833semidirect

Maximal subgroups

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

subgroupindex
C2×#637702
#105937682
#105937652
#105900952
#105900912
#18339