Finite Group Databasebeta

← #11797880

Subgroups — #11797880

Order 1152.

228 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 46 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#10593787C211yesmaximal, characteristic, complemented
2#10593779C211yesmaximal, characteristic, complemented
3#10592615C211yesmaximal, characteristic
4#10590198C211yesmaximal, characteristic, complemented
5#10590194C211yesmaximal, characteristic, complemented
6#10590140C211yesmaximal, characteristic, complemented
7#10590135C211yesmaximal, characteristic, complemented
8#64289—21no—
9#64287—21no—
10#64128C2211yescharacteristic
11#64121C2211yescharacteristic
12#63785—21no—
13#63783—21no—
14#63771C2211yescharacteristic
15#63771C2211yescharacteristic
16C8×#157C2211yescharacteristic
17#63764C2211yescharacteristic
18C32×SD32C411yescharacteristic, complemented
19#63656C411yescharacteristic, complemented
20#63653C411yescharacteristic, complemented
21#63627C411yescharacteristic, complemented
22C16×C3⋊D3C2211yescharacteristic
23#4916—62no—
24#3832—21no—
25#3830—21no—
26#3792—41no—
27C2×#622—41no—
28C4×#157D411yescharacteristic
29#3788—21no—
30#3788—21no—
31#3788—41no—
32#3787—41no—
33#3787D411yescharacteristic
34C32×Q16C2×C411yescharacteristic
35C32×D8C2×C411yescharacteristic
36#3755—21no—
37#3754—21no—
38#3746C2×C411yescharacteristic
39#3745C2×C411yescharacteristic
40C8×C3⋊D3C2311yescharacteristic
41#3708—21no—
42C32×C16C2×C411yescharacteristic
43C3⋊(C3⋊C16)C2×C411yescharacteristic
44#2179—91nomaximal, Sylow
45#919—62no—
46#912—62no—
47C3×SD32—22no—
48#829—62no—
49#826—62no—
50#800—62no—
51D3×C16—62no—
52C2×#157—21no—
53C32×Q8—21no—
54C32×D4—21no—
55#638—41no—
56C2×C3⋊Dic3—41no—
57C4⋊(C3⋊D3)—21no—
58C4⋊(C3⋊D3)—41no—
59C4×C3⋊D3—41no—
60C4×C3⋊D3C2×D411yescharacteristic
61#634—21no—
62#622—41no—
63#622—41no—
64#622D811yescharacteristic
65#622D811yescharacteristic
66C32×C8C22×C411yescharacteristic
67C3⋊(C3⋊C8)#4111yescharacteristic
68#508—91no—
69#443—91no—
70#443—91no—
71#368—91no—
72#359—91no—
73#359—91no—
74#346—91no—
75#239—122no—
76#237—122no—
77C3×Q16—22no—
78C3×D8—22no—
79#215—122no—
80#214—122no—
81Dic12—62no—
82D24—62no—
83D3×C8—62no—
84C3×C16—22no—
85C3⋊C16—62no—
86C22×C32—41no—
87C2×C3⋊D3—41no—
88C2×C3⋊D3#13511yescharacteristic
89#157—41no—
90C32×C4—41no—
91C32×C4C4×D411yescharacteristic
92C3⋊Dic3—41no—
93C3⋊Dic3C2×D811yescharacteristic
94#135—91no—
95#135—91no—
96#131—181no—
97#131—181no—
98Q32—91no—
99SD32—91no—
100SD32#15711yescharacteristic, complemented
101D16—91no—
102C2×C16—91no—
103C2×C16—91no—
104#108—91no—
105#108—91no—
106#104—181no—
107#104—181no—
108C4×C8—91no—
109C3×Q8—42no—
110C3×D4—42no—
111#67—242no—
112C2×Dic3—242no—
113D12—122no—
114D12—242no—
115C4×D3—62no—
116C4×D3—242no—
117Dic6—122no—
118C3×C8—22no—
119C3⋊C8—62no—
120C2×C32—81no—
121C2×C32C4×D811yescharacteristic
122C3⋊D3—21no—
123C3⋊D3—81no—
124#41—181no—
125#41—181no—
126Q16—91no—
127Q16C2×#15711yescharacteristic
128SD16—181no—
129SD16—181no—
130D8—91no—
131D8C2×#15711yescharacteristic
132M16—181no—
133M16—181no—
134M16—361no—
135M16—361no—
136C2×C8—91no—
137C2×C8—91no—
138C2×C8—361no—
139C2×C8—361no—
140C42—91no—
141C16—91no—
142C16—181no—
143C16C2×#15711yescharacteristic
144C22×C3—82no—
145C2×D3—62no—
146C2×D3—242no—
147C3×C4—22no—
148C3×C4—82no—
149Dic3—62no—
150Dic3—242no—
151C32#217911yescharacteristic, complemented, Sylow
152Q8—21no—
153Q8—181no—
154D4—21no—
155D4—181no—
156D4—361no—
157D4—361no—
158C2×C4—91no—
159C2×C4—181no—
160C2×C4—361no—
161C2×C4—361no—
162C8—91no—
163C8—91no—
164C8—91no—
165C8—361no—
166C8—361no—
167C8C22×#15711yescharacteristic
168C2×C3—22no—
169C2×C3—162no—
170D3—122no—
171D3—482no—
172C22—41no—
173C22—91no—
174C22—361no—
175C4—41no—
176C4—91no—
177C4—361no—
178C4—361no—
179C4D4×#15711yescharacteristic
180C3—22no—
181C2—81no—
182C2—181no—
183C2—721no—
184C2D8×#15711yescharacteristic
subgroupG/H
centerC2D8×#157
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC32×SD32C4
socleC2×C32C4×D8
prime radical#10592615C2
cosocleC8×C3⋊D3C23
hypercenterSD32#157
hypocenterC32#2179
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #10593787C2semidirect
2. #10593779C2semidirect
4. #10590198C2semidirect
5. #10590194C2semidirect
6. #10590140C2semidirect
7. #10590135C2semidirect
18. C32×SD32C4semidirect
19. #63656C4semidirect
20. #63653C4semidirect
21. #63627C4semidirect
100. SD32#157semidirect
151. C32#2179semidirect

Maximal subgroups

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

subgroupindex
#105937872
#105937792
#105926152
#105901982
#105901942
#105901402
#105901352
#21799