Finite Group Databasebeta

← #11797896

Subgroups — #11797896

Order 1152.

250 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593333C211yesmaximal, characteristic
2#10590389C212yesmaximal, complemented
3#10590148C211yesmaximal, characteristic, complemented
4#10590070C211yesmaximal, characteristic, complemented
5#10590063C212yesmaximal, complemented
6#63822C2212yes—
7#63815—22no—
8C2×#3708C2211yescharacteristic
9C2×#3708C2211yescharacteristic
10#63736C411yescharacteristic, complemented
11#63735C412yescomplemented
12#63734C411yescharacteristic, complemented
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#805—22no—
15#63578C2212yes—
16#4824—62no—
17C3×#235—22no—
18C32×C42D411yescharacteristic
19C2×C3⋊(C3⋊C8)D411yescharacteristic
20C2×C3⋊(C3⋊C8)C2311yescharacteristic
21C3×#208—22no—
22#3718C2×C412yes—
23#3715—22no—
24#3713C2×C412yes—
25#3711—42no—
26D3×C3⋊C8—42no—
27#3708—21no—
28#3708C2×C411yescharacteristic
29#3708C2×C411yescharacteristic
30#2179—91nomaximal, Sylow
31#950—62no—
32#948—62no—
33#907—62no—
34C3×#104—62no—
35#822—62no—
36#805—22no—
37C4×C3⋊C8—62no—
38C2×C32×C4—21no—
39C2×C32×C4C2×D411yescharacteristic
40C3×#67—42no—
41C3×D12—22no—
42C3×C4×D3—42no—
43C3×Dic6—22no—
44C3⋊(C3⋊C8)D812yes—
45C3⋊(C3⋊C8)C22×C411yescharacteristic
46C3⋊(C3⋊C8)#4111yescharacteristic
47C3×C3⋊C8—42no—
48#508—91no—
49#443—92no—
50#368—91no—
51#359—92no—
52#346—91no—
53C3×#41—62no—
54#235—22no—
55C3×M16—62no—
56C3×C42—22no—
57#216—62no—
58#215—62no—
59#214—62no—
60#213—62no—
61#208—22no—
62#208—122no—
63C2×C3⋊C8—62no—
64C2×C3⋊C8—62no—
65C2×C3⋊C8—122no—
66ΓL(1,𝔽25)—122no—
67D3×C8—122no—
68C22×C32#13511yescharacteristic
69C2×C3×D3—42no—
70C32×C4—41no—
71C32×C4C4×D411yescharacteristic
72C32×C4C2×D811yescharacteristic
73C3×Dic3—42no—
74#135—92no—
75#131—182no—
76Q32—91no—
77SD32—92no—
78D16—91no—
79C2×C16—91no—
80C2×C16—91no—
81#108—92no—
82#104—62no—
83C4×C8—91no—
84C3×Q8—62no—
85C3×D4—62no—
86C3×D4—122no—
87C2×C3×C4—22no—
88C2×C3×C4—42no—
89C2×C3×C4—122no—
90#67—42no—
91D12—22no—
92C4×D3—42no—
93Dic6—22no—
94C3×C8—122no—
95C3⋊C8—42no—
96C3⋊C8—62no—
97C3⋊C8—62no—
98C3⋊C8—62no—
99C3⋊C8—62no—
100C2×C32—21no—
101C2×C32C4×D811yescharacteristic
102C3×D3—82no—
103#41—62no—
104Q16—92no—
105SD16—182no—
106D8—92no—
107M16—62no—
108M16—362no—
109C2×C8—91no—
110C2×C8—91no—
111C2×C8—362no—
112C42GO+(4,𝔽2)11yescharacteristic
113C16—91no—
114C16—91no—
115C16—181no—
116C22×C3—22no—
117C22×C3—122no—
118C2×D3—42no—
119C3×C4—22no—
120C3×C4—22no—
121C3×C4—44no—
122C3×C4—122no—
123Dic3—42no—
124C32#217911yescharacteristic, complemented, Sylow
125Q8—62no—
126D4—62no—
127D4—122no—
128C2×C4—21no—
129C2×C4—122no—
130C2×C4C2×GO+(4,𝔽2)11yescharacteristic
131C8—92no—
132C8—91no—
133C8—91no—
134C8—122no—
135C2×C3—22no—
136C2×C3—42no—
137C2×C3—242no—
138D3—82no—
139C22—122no—
140C22#6423711yescharacteristic
141C4—41no—
142C4—122no—
143C4#6422511yescharacteristic
144C4C4×GO+(4,𝔽2)11yescharacteristic
145C3—22no—
146C2—21no—
147C2—242no—
148C2#1059342011yescharacteristic
subgroupG/H
centerC4#64225
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC2×C32C4×D8
prime radical#10593333C2
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2179
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10590389C2semidirect
3. #10590148C2semidirect
4. #10590070C2semidirect
5. #10590063C2semidirect
10. #63736C4semidirect
11. #63735C4semidirect
12. #63734C4semidirect
124. C32#2179semidirect

Maximal subgroups

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

subgroupindex
#105933332
#105903892
#105901482
#105900702
#105900632
#21799