Finite Group Databasebeta

← #11799403

Subgroups — #11799403

Order 1152.

256 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 37 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#10593772C211yesmaximal, characteristic, complemented
2C2×#63734C211yesmaximal, characteristic, complemented
3#10590988C212yesmaximal, complemented
4#10590070C211yesmaximal, characteristic, complemented
5#10590065C212yesmaximal, complemented
6#64116C2211yescharacteristic
7#63830—22no—
8C2×#3713C2212yes—
9#63773C2211yescharacteristic
10C2×#3708C2211yescharacteristic
11#63765—21no—
12#63764—21no—
13#63734—21no—
14#63734—21no—
15C3×#823—22no—
16#63578C2212yes—
17#4749—62no—
18#3828D411yescharacteristic
19C2×C3×D12—22no—
20C32×M16D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2311yescharacteristic
22#3743—21no—
23C8×C3⋊D3—21no—
24C3×#208—22no—
25#3716—42no—
26#3714—42no—
27#3713—22no—
28#3713—22no—
29#3708—21no—
30#3708D411yescharacteristic
31#3708D411yescharacteristic
32#2221—91nomaximal, Sylow
33#932—62no—
34C2×#213—62no—
35#908—62no—
36#907—62no—
37C3×#100—62no—
38#823—22no—
39#822—62no—
40C22×C3×D3—42no—
41C2×C32×C4C2×D411yescharacteristic
42#638—21no—
43C4⋊(C3⋊D3)D811yescharacteristic
44C4×C3⋊D3—21no—
45#634D811yescharacteristic
46C3×D12—42no—
47C3×D12—42no—
48C32×C8—21no—
49C3⋊(C3⋊C8)C2×D411yescharacteristic
50C3⋊(C3⋊C8)#4111yescharacteristic
51C3×C3⋊C8—42no—
52C2×D16—91no—
53#504—91no—
54#472—92no—
55#368—91no—
56#361—92no—
57C2×C3×D4—62no—
58#235—62no—
59C2×D12—22no—
60C3×M16—22no—
61C3×M16—62no—
62#214—122no—
63#213—122no—
64#213—122no—
65#213—122no—
66#208—22no—
67C2×C3⋊C8—62no—
68D24—122no—
69#204—122no—
70ΓL(1,𝔽25)—122no—
71D3×C8—122no—
72C22×C32#13511yescharacteristic
73C2×C3⋊D3—21no—
74C2×C3×D3—82no—
75C2×C3×D3—162no—
76C32×C4#12111yescharacteristic
77C32×C4C2×D811yescharacteristic
78C3⋊Dic3—21no—
79AGL(1,ℤ/8)—182no—
80C2×D8—92no—
81#131—91no—
82D16—181no—
83D16—181no—
84M32—91no—
85M32—181no—
86C2×C16—91no—
87C2×C16—181no—
88#108—92no—
89#100—62no—
90C23×C3—122no—
91C22×D3—42no—
92C3×D4—122no—
93C3×D4—122no—
94C2×C3×C4—22no—
95#67—122no—
96D12—42no—
97D12—42no—
98D12—62no—
99C4×D3—122no—
100Dic6—62no—
101C3×C8—42no—
102C3×C8—122no—
103C3⋊C8—42no—
104C3⋊C8—62no—
105C3⋊C8—62no—
106C2×C32—21no—
107C2×C32#46611yescharacteristic
108C3⋊D3—41no—
109C3×D3—162no—
110#41—91no—
111C2×D4—62no—
112SD16—362no—
113D8—182no—
114D8—182no—
115D8—362no—
116M16—62no—
117M16—181no—
118M16GO+(4,𝔽2)11yescharacteristic
119C2×C8—91no—
120C2×C8—181no—
121C16—91no—
122C16—91no—
123C16—181no—
124C22×C3—22no—
125C22×C3—242no—
126C22×C3—482no—
127C2×D3—82no—
128C2×D3—122no—
129C2×D3—162no—
130C3×C4—22no—
131C3×C4—22no—
132Dic3—122no—
133C32#222111yescharacteristic, complemented, Sylow
134C23—122no—
135Q8—91no—
136D4—91no—
137D4—122no—
138D4—122no—
139D4—181no—
140C2×C4—181no—
141C2×C4C2×GO+(4,𝔽2)11yescharacteristic
142C8—21no—
143C8—91no—
144C8—91no—
145C8—122no—
146C2×C3—22no—
147C2×C3—42no—
148C2×C3—482no—
149D3—162no—
150D3—242no—
151C22—181no—
152C22—242no—
153C22—482no—
154C22#6422311yescharacteristic
155C4—181no—
156C4#6422511yescharacteristic
157C4#6424211yescharacteristic
158C3—22no—
159C2—21no—
160C2—361no—
161C2—482no—
162C2#1059342311yescharacteristic
subgroupG/H
centerC2#10593423
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×M16D4
socleC2×C32#466
hypercenterM16GO+(4,𝔽2)
hypocenterC32#2221
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
1. #10593772C2semidirect
2. C2×#63734C2semidirect
3. #10590988C2semidirect
4. #10590070C2semidirect
5. #10590065C2semidirect
133. C32#2221semidirect

Maximal subgroups

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

subgroupindex
#105937722
C2×#637342
#105909882
#105900702
#105900652
#22219