Finite Group Databasebeta

← #11797225

Subgroups — #11797225

Order 1152.

246 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 64 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#10593768C211yesmaximal, characteristic
2C2×#63769C211yesmaximal, characteristic
3C3⋊D3×M32C211yesmaximal, characteristic
4#10590139C212yesmaximal, complemented
5#10590138C212yesmaximal, complemented
6#64286—21no—
7C2×C4⋊#157—21no—
8C2×C8×C3⋊D3C2211yescharacteristic
9#63769—21no—
10#63769C2211yescharacteristic
11#63769C2212yes—
12#63769C2211yescharacteristic
13#63768—21no—
14C32×M32C411yescharacteristic, complemented
15#63639C411yescharacteristic, complemented
16#63625C412yescomplemented
17C16×C3⋊D3C2212yes—
18D3×M32—62no—
19C22×#157—41no—
20C2×C4×C3⋊D3D411yescharacteristic
21C22⋊#157—41no—
22C4⋊#157—21no—
23C4⋊#157—21no—
24C4⋊#157—22no—
25C4⋊#157—41no—
26C4×#157—41no—
27C2×C32×C8C2×C411yescharacteristic
28C2×C3⋊(C3⋊C8)Q811yescharacteristic
29C8×C3⋊D3C2×C411yescharacteristic
30C8×C3⋊D3D411yescharacteristic
31C8×C3⋊D3Q811yescharacteristic
32C8×C3⋊D3C2311yescharacteristic
33C32×C16C2×C412yescomplemented
34C3⋊(C3⋊C16)C2×C412yescomplemented
35#2159—91nomaximal, Sylow
36C2×D3×C8—62no—
37C3×M32—22no—
38#812—62no—
39#798—64no—
40D3×C16—64no—
41C22×C3⋊D3D811yescharacteristic
42C2×#157—42no—
43C2×#157—41no—
44C2×#157—41no—
45C2×#157—82no—
46C2×C32×C4C4⋊C411yescharacteristic
47C2×C3⋊Dic3Q1611yescharacteristic
48C4×C3⋊D3C4⋊C411yescharacteristic
49C4×C3⋊D3D811yescharacteristic
50C4×C3⋊D3Q1611yescharacteristic
51C4×C3⋊D3C2×D411yescharacteristic
52C32×C8C4⋊C411yescharacteristic
53C32×C8C22×C411yescharacteristic
54C3⋊(C3⋊C8)C4⋊C411yescharacteristic
55C3⋊(C3⋊C8)C2×Q811yescharacteristic
56C2×M32—91no—
57#427—91no—
58C2×#107—91no—
59#367—92no—
60#366—92no—
61C2×C4×D3—62no—
62C2×C3×C8—22no—
63C2×C3⋊C8—62no—
64D3×C8—62no—
65D3×C8—62no—
66D3×C8—62no—
67D3×C8—62no—
68C3×C16—24no—
69C3⋊C16—64no—
70C22×C32#10711yescharacteristic
71C2×C3⋊D3—21no—
72C2×C3⋊D3—21no—
73C2×C3⋊D3#10711yescharacteristic
74C2×C3⋊D3C2×D811yescharacteristic
75#157—81no—
76#157—82no—
77#157—81no—
78C32×C4#10711yescharacteristic
79C32×C4C2×C4⋊C411yescharacteristic
80C3⋊Dic3#10711yescharacteristic
81C3⋊Dic3C2×Q1611yescharacteristic
82C22×C8—91no—
83#117—181no—
84C2×C4⋊C4—181no—
85M32—91no—
86M32—92no—
87M32#15711yescharacteristic, complemented
88C2×C16—92no—
89#107—91no—
90#107—92no—
91#107—91no—
92#107—181no—
93#106—181no—
94C22×D3—62no—
95C2×C3×C4—22no—
96C2×Dic3—62no—
97C4×D3—62no—
98C4×D3—62no—
99C4×D3—62no—
100C4×D3—62no—
101C3×C8—22no—
102C3×C8—22no—
103C3⋊C8—62no—
104C3⋊C8—62no—
105C2×C32—21no—
106C2×C32C2×#10711yescharacteristic
107C3⋊D3—21no—
108C3⋊D3#50911yescharacteristic
109C3⋊D3#51011yescharacteristic
110C22×C4—91no—
111C22×C4—361no—
112C2×C8—91no—
113C2×C8—91no—
114C2×C8—91no—
115C2×C8—91no—
116C2×C8—91no—
117C2×C8C2×#15711yescharacteristic
118C4⋊C4—181no—
119C4⋊C4—181no—
120C4⋊C4—182no—
121C4⋊C4—361no—
122C22⋊C4—361no—
123C42—361no—
124C16—92no—
125C16C2×#15712yescomplemented
126C22×C3—22no—
127C2×D3—62no—
128C2×D3—62no—
129C2×D3—122no—
130C2×D3—122no—
131C3×C4—22no—
132C3×C4—22no—
133Dic3—62no—
134Dic3—62no—
135C32#215911yescharacteristic, complemented, Sylow
136C23—91no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—91no—
141C2×C4—91no—
142C2×C4—361no—
143C2×C4—361no—
144C2×C4—362no—
145C2×C4—722no—
146C2×C4C4⋊#15711yescharacteristic
147C8—91no—
148C8—91no—
149C8C4⋊#15711yescharacteristic
150C8C22×#15711yescharacteristic
151C2×C3—22no—
152C2×C3—42no—
153D3—62no—
154D3—62no—
155D3—122no—
156C22—91no—
157C22—91no—
158C22—181no—
159C22—181no—
160C22#6376911yescharacteristic
161C4—91no—
162C4—91no—
163C4—722no—
164C4—721no—
165C4—721no—
166C4#6376911yescharacteristic
167C4C2×C4⋊#15711yescharacteristic
168C3—22no—
169C2—21no—
170C2—91no—
171C2—91no—
172C2—181no—
173C2C2×#6376911yescharacteristic
subgroupG/H
centerC2C2×#63769
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC32×M32C4
socleC2×C32C2×#107
prime radicalC22×C3⋊D3D8
cosocleC8×C3⋊D3C23
hypercenterM32#157
hypocenterC32#2159
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
4. #10590139C2semidirect
5. #10590138C2semidirect
14. C32×M32C4semidirect
15. #63639C4semidirect
16. #63625C4semidirect
33. C32×C16C2×C4semidirect
34. C3⋊(C3⋊C16)C2×C4semidirect
87. M32#157semidirect
125. C16C2×#157semidirect
135. C32#2159semidirect

Maximal subgroups

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

subgroupindex
#105937682
C2×#637692
C3⋊D3×M322
#105901392
#105901382
#21599