Finite Group Databasebeta

← #11799987

Subgroups — #11799987

Order 1152.

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

normal subgroups only

This group has 333 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#10592858C211yesmaximal, characteristic
2#10590914C211yesmaximal, characteristic, complemented
3C3×#4563C212yesmaximal, complemented
4#10589137C212yesmaximal, complemented
5#10589110C211yesmaximal, characteristic, complemented
6#69257—32nomaximal
7C2×C32×D8C2211yescharacteristic
8#64147—21no—
9C2×#3743C2211yescharacteristic
10#63818—21no—
11#63659—21no—
12#63644C2211yescharacteristic
13C3×#819C2212yes—
14C3×#812C2212yes—
15#63578—21no—
16#5159—32no—
17#5159—61no—
18#4893—32no—
19C3×#361—32no—
20#4563D312yescomplemented
21#4514—32no—
22#4513—32no—
23#4494—32no—
24C2×C32×D4—21no—
25C2×#638—41no—
26C2×C4×C3⋊D3D411yescharacteristic
27C32×D8—22no—
28C2×C32×C8C2311yescharacteristic
29#3757—41no—
30C4⋊(C3⋊Dic3)—21no—
31C2×C3⋊(C3⋊C8)D411yescharacteristic
32#3743—22no—
33C3×#208—22no—
34#3712—41no—
35#3710—41no—
36C3×C3⋊C16—22no—
37#2238—91noSylow
38C2×C3×D8—21no—
39C2×C3×D8C2×D312yes—
40#938—62no—
41#938—62no—
42D3×M16—62no—
43C2×ΓL(1,𝔽25)—32no—
44C2×ΓL(1,𝔽25)—61no—
45C3×M32—32no—
46C3×#108—32no—
47#832—62no—
48#832—62no—
49#822—62no—
50#819C2×D312yes—
51#817—32no—
52#817—61no—
53#812C2×D312yes—
54C23×C32—41no—
55C22×C3⋊D3SD1611yescharacteristic
56C32×D4—41no—
57C32×D4—41no—
58C2×C32×C4C2×D411yescharacteristic
59#638—82no—
60C2×C3⋊Dic3—41no—
61C2×C3⋊Dic3SD1611yescharacteristic
62C4×C3⋊D3—21no—
63C4×C3⋊D3—21no—
64C32×C8#4112yes—
65C3⋊(C3⋊C8)—21no—
66C3×C3⋊C8—42no—
67#469—91no—
68#430—91no—
69#365—92no—
70#361—32no—
71#349—91no—
72C2×C3×D4—22no—
73C2×C3×D4—22no—
74C2×#67—122no—
75C2×#67—122no—
76C2×C4×D3—32no—
77C2×C4×D3—61no—
78C3×D8—22no—
79C3×D8—22no—
80C3×D8—42no—
81C3×M16—62no—
82C2×C3×C8—21no—
83C2×C3×C8C22×D312yes—
84#217—122no—
85#217—122no—
86C4⋊Dic3—62no—
87C4⋊Dic3—62no—
88#208—22no—
89C2×C3⋊C8—32no—
90C2×C3⋊C8—61no—
91ΓL(1,𝔽25)—62no—
92ΓL(1,𝔽25)—62no—
93ΓL(1,𝔽25)—122no—
94ΓL(1,𝔽25)—122no—
95D3×C8—122no—
96C3×C16—62no—
97C3⋊C16—22no—
98C22×C32—81no—
99C22×C32—81no—
100C22×C32—81no—
101C22×C32C2×SD1611yescharacteristic
102C2×C3⋊D3—21no—
103C2×C3⋊D3—41no—
104C32×C4#12311yescharacteristic
105C32×C4AGL(1,ℤ/8)11yescharacteristic
106C3⋊Dic3—21no—
107C3⋊Dic3—81no—
108C2×D8D3211yescharacteristic
109C2×M16—91no—
110C2×M16—181no—
111#121—181no—
112M32—32no—
113#108—32no—
114#108—181no—
115#106—91no—
116#102—181no—
117C23×C3—42no—
118C23×C3—42no—
119C22×D3—32no—
120C22×D3—61no—
121C3×D4—42no—
122C3×D4—42no—
123C3×D4—42no—
124C3×D4—42no—
125C2×C3×C4—21no—
126C2×C3×C4D3×D412yes—
127#67—244no—
128#67—244no—
129C2×Dic3—32no—
130C2×Dic3—61no—
131C2×Dic3—122no—
132C2×Dic3—122no—
133C4×D3—62no—
134C4×D3—62no—
135C4×D3—121no—
136C4×D3—121no—
137C3×C8—22no—
138C3×C8—122no—
139C3×C8#23512yes—
140C3×C8#23712yes—
141C3⋊C8—42no—
142C3⋊C8—62no—
143C3⋊C8—121no—
144C2×C32—21no—
145C2×C32—161no—
146C2×C32#48111yescharacteristic
147C3⋊D3—41no—
148C2×D4—21no—
149C2×D4—361no—
150C22×C4—91no—
151D8—22no—
152M16—62no—
153M16—182no—
154M16—361no—
155C2×C8—91no—
156C2×C8—361no—
157C2×C8C2×D3211yescharacteristic
158C4⋊C4—181no—
159C22⋊C4—361no—
160C16—62no—
161C22×C3—21no—
162C22×C3—82no—
163C22×C3—82no—
164C22×C3—82no—
165C22×C3—82no—
166C22×C3—82no—
167C22×C3—82no—
168C22×C3D3×SD1612yes—
169C2×D3—62no—
170C2×D3—121no—
171C2×D3—122no—
172C2×D3—122no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4#88312yes—
176C3×C4#91112yes—
177Dic3—62no—
178Dic3—121no—
179Dic3—242no—
180Dic3—242no—
181C32#223811yescharacteristic, complemented, Sylow
182C23—41no—
183C23—91no—
184D4—41no—
185D4—41no—
186D4—722no—
187C2×C4—91no—
188C2×C4—181no—
189C2×C4—181no—
190C2×C4—361no—
191C2×C4#381111yescharacteristic
192C8—122no—
193C8—181no—
194C8#380412yes—
195C2×C3—22no—
196C2×C3—22no—
197C2×C3—21no—
198C2×C3—162no—
199C2×C3—162no—
200C2×C3#477712yes—
201D3—122no—
202D3—241no—
203C22—81no—
204C22—81no—
205C22—81no—
206C22—181no—
207C22—361no—
208C22#6393011yescharacteristic
209C4—181no—
210C4—721no—
211C4#6392711yescharacteristic
212C4#6397511yescharacteristic
213C3—21no—
214C3#6925712yescomplemented
215C2—21no—
216C2—161no—
217C2—361no—
218C2#1059141911yescharacteristic
subgroupG/H
centerC2#10591419
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC2×C32#481
prime radical#10592858C2
hypercenterC2×D8D32
hypocenterC32#2238
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10590914C2semidirect
3. C3×#4563C2semidirect
4. #10589137C2semidirect
5. #10589110C2semidirect
20. #4563D3semidirect
181. C32#2238semidirect
214. C3#69257semidirect

Maximal subgroups

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

subgroupindex
#105928582
#105909142
C3×#45632
#105891372
#105891102
#692573