Finite Group Databasebeta

← #11799394

Subgroups — #11799394

Order 1152.

338 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 78 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#10592839C211yesmaximal, characteristic, complemented
2C3×#5142C212yesmaximal, complemented
3C2×#63545C211yesmaximal, characteristic, complemented
4#10589144C211yesmaximal, characteristic, complemented
5#10589126C212yesmaximal, complemented
6#71092—32nomaximal
7C32×#131C2211yescharacteristic
8C3×#949—22no—
9C2×C3×D24C2212yes—
10#63639—21no—
11#63639C2211yescharacteristic
12C2×C3⋊(C3⋊C16)—21no—
13C2×C3⋊(C3⋊C16)C2211yescharacteristic
14C3×#823—22no—
15C3×#819C2212yes—
16#63545—21no—
17#63545—21no—
18C3×#472—32no—
19C2×#826—32no—
20#5142D312yescomplemented
21#5140—32no—
22#5140—61no—
23#4563—32no—
24#4495—32no—
25#4493—32no—
26C32×#41D411yescharacteristic
27C2×C3×D12—22no—
28C32×M16—21no—
29C32×M16D411yescharacteristic
30C2×C32×C8—21no—
31C2×C32×C8C2311yescharacteristic
32C3×#215—42no—
33C3×#213—42no—
34C3×#208—22no—
35C3×D24—22no—
36C3×D24—22no—
37C3⋊(C3⋊C16)—21no—
38C3⋊(C3⋊C16)D411yescharacteristic
39C3⋊(C3⋊C16)D411yescharacteristic
40#2221—91noSylow
41C3×AGL(1,ℤ/8)—62no—
42C2×C3×D8—32no—
43C3×#131—21no—
44C3×#131C2×D312yes—
45#949—22no—
46C2×D24C2×D312yes—
47C3×#108—32no—
48C3×#100—62no—
49#826—62no—
50#826—62no—
51#823—22no—
52#819C2×D312yes—
53#812—32no—
54#812—61no—
55#812—62no—
56#812—62no—
57C2×C3⋊C16—32no—
58C2×C3⋊C16—61no—
59C2×C3⋊C16—62no—
60C2×C3⋊C16—62no—
61C22×C3×D3—42no—
62C32×Q8D811yescharacteristic
63C32×D4—21no—
64C32×D4D811yescharacteristic
65C2×C32×C4—21no—
66C2×C32×C4C2×D411yescharacteristic
67C3×D12—42no—
68C3×D12—42no—
69C32×C8—21no—
70C32×C8C2×D411yescharacteristic
71C32×C8#4111yescharacteristic
72C3×C3⋊C8—42no—
73C2×D16—91no—
74#504—91no—
75#472—32no—
76#368—91no—
77#361—92no—
78C3×#41—21no—
79C3×#41#6712yes—
80C2×C3×D4—62no—
81C2×D12—22no—
82C3×SD16—122no—
83C3×D8—62no—
84C3×D8—62no—
85C3×D8—122no—
86C3×M16—22no—
87C3×M16—22no—
88C3×M16—21no—
89C3×M16—62no—
90C3×M16#6712yes—
91C2×C3×C8—22no—
92C2×C3×C8—22no—
93C2×C3×C8—21no—
94C2×C3×C8C22×D312yes—
95#215—42no—
96#213—42no—
97#208—22no—
98D24—22no—
99D24—22no—
100C3⋊C16—32no—
101C3⋊C16—32no—
102C3⋊C16—61no—
103C3⋊C16—61no—
104C3⋊C16—62no—
105C3⋊C16—62no—
106C22×C32—21no—
107C22×C32#13511yescharacteristic
108C2×C3×D3—82no—
109C2×C3×D3—162no—
110C32×C4—21no—
111C32×C4#12111yescharacteristic
112C32×C4C2×D811yescharacteristic
113AGL(1,ℤ/8)—62no—
114C2×D8—32no—
115#131D3211yescharacteristic
116D16—181no—
117D16—181no—
118M32—91no—
119M32—181no—
120C2×C16—91no—
121C2×C16—181no—
122#108—32no—
123#100—62no—
124C23×C3—122no—
125C22×D3—42no—
126C3×Q8—21no—
127C3×Q8#21312yes—
128C3×D4—22no—
129C3×D4—22no—
130C3×D4—21no—
131C3×D4—122no—
132C3×D4—122no—
133C3×D4#21312yes—
134C2×C3×C4—22no—
135C2×C3×C4—22no—
136C2×C3×C4—21no—
137C2×C3×C4C2×#6712yes—
138D12—42no—
139D12—42no—
140C3×C8—22no—
141C3×C8—22no—
142C3×C8—21no—
143C3×C8—21no—
144C3×C8—122no—
145C3×C8D3×D412yes—
146C3×C8#23712yes—
147C3⋊C8—42no—
148C2×C32—21no—
149C2×C32—41no—
150C2×C32#46611yescharacteristic
151C3×D3—162no—
152#41#62511yescharacteristic
153C2×D4—62no—
154SD16—122no—
155D8—62no—
156D8—62no—
157D8—122no—
158M16—21no—
159M16—62no—
160M16#62511yescharacteristic
161C2×C8—21no—
162C2×C8C2×D3211yescharacteristic
163C16—91no—
164C16—91no—
165C16—181no—
166C22×C3—22no—
167C22×C3—22no—
168C22×C3—21no—
169C22×C3—242no—
170C22×C3—482no—
171C22×C3#95012yes—
172C2×D3—82no—
173C2×D3—162no—
174C3×C4—22no—
175C3×C4—22no—
176C3×C4—21no—
177C3×C4—21no—
178C3×C4C2×#21312yes—
179C3×C4#93912yes—
180C32#222111yescharacteristic, complemented, Sylow
181C23—122no—
182Q8#371311yescharacteristic
183D4—21no—
184D4—122no—
185D4—122no—
186D4#371311yescharacteristic
187C2×C4—21no—
188C2×C4C2×#62511yescharacteristic
189C8—21no—
190C8—122no—
191C8#380511yescharacteristic
192C8#381111yescharacteristic
193C2×C3—22no—
194C2×C3—21no—
195C2×C3—41no—
196C2×C3—42no—
197C2×C3—42no—
198C2×C3—482no—
199C2×C3#503812yes—
200D3—162no—
201C22—21no—
202C22—242no—
203C22—482no—
204C22#6382211yescharacteristic
205C4—21no—
206C4C2×#371311yescharacteristic
207C4#6398011yescharacteristic
208C3—21no—
209C3#7109212yescomplemented
210C2—21no—
211C2—41no—
212C2—482no—
213C2#1059116611yescharacteristic
subgroupG/H
centerC2#10591166
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#131C22
socleC2×C32#466
hypercenter#131D32
hypocenterC32#2221
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131

Complements

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

NH ≅ G/Ntype
1. #10592839C2semidirect
2. C3×#5142C2semidirect
3. C2×#63545C2semidirect
4. #10589144C2semidirect
5. #10589126C2semidirect
20. #5142D3semidirect
180. C32#2221semidirect
209. C3#71092semidirect

Maximal subgroups

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

subgroupindex
#105928392
C3×#51422
C2×#635452
#105891442
#105891262
#710923