Finite Group Databasebeta

← #11799883

Subgroups — #11799883

Order 1152.

337 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 337 conjugacy classes of subgroups — too many to draw. Only its 74 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#10592887C211yesmaximal, characteristic
2#10590687C211yesmaximal, characteristic
3C3×#4564C212yesmaximal, complemented
4#10589141C212yesmaximal, complemented
5#10589108C211yesmaximal, characteristic
6#69231—32nomaximal
7C2×C32×Q16C2211yescharacteristic
8#64155—21no—
9C2×C8×C3⋊D3C2211yescharacteristic
10#63900—21no—
11#63662—21no—
12#63645C2211yescharacteristic
13C3×#818C2212yes—
14C2×C3×C3⋊C16C2212yes—
15#63576—21no—
16#5188—32no—
17#5188—61no—
18D3×#107—32no—
19C3×#358—32no—
20#4564D312yescomplemented
21(C2×D3)⋊C16—32no—
22#4505—32no—
23#4490—32no—
24C2×C32×Q8—21no—
25C2×C4×C3⋊D3D411yescharacteristic
26C2×#624—41no—
27C32×Q16—22no—
28C2×C32×C8C2311yescharacteristic
29#3752—41no—
30C4⋊(C3⋊Dic3)—21no—
31#3750—41no—
32C2×C3⋊(C3⋊C8)D411yescharacteristic
33C8×C3⋊D3—22no—
34C3×C4⋊Dic3—22no—
35#3724—41no—
36C3×C3⋊C16—22no—
37#2235—91noSylow
38C2×C3×Q16—21no—
39C2×C3×Q16C2×D312yes—
40#946—62no—
41#946—62no—
42C2×D3×C8—32no—
43C2×D3×C8—61no—
44D3×C4⋊C4—62no—
45C2×C3×C16—32no—
46C3×#107—32no—
47#835—62no—
48#835—62no—
49#818—32no—
50#818—61no—
51#818C2×D312yes—
52C2×C3⋊C16C2×D312yes—
53#807—62no—
54C22×C3⋊D3D811yescharacteristic
55C32×Q8—41no—
56C32×Q8—41no—
57C2×C32×C4—41no—
58C2×C32×C4C2×D411yescharacteristic
59C2×C3⋊Dic3—41no—
60C2×C3⋊Dic3D811yescharacteristic
61C4×C3⋊D3—21no—
62C4×C3⋊D3—21no—
63C2×C3×Dic3—42no—
64#624—82no—
65C32×C8#4112yes—
66C3⋊(C3⋊C8)—21no—
67#467—91no—
68C2×#107—91no—
69#367—92no—
70#358—32no—
71C22⋊C16—91no—
72C2×C3×Q8—22no—
73C2×C3×Q8—22no—
74C2×C4×D3—32no—
75C2×C4×D3—61no—
76C2×C4×D3—122no—
77C3×Q16—22no—
78C3×Q16—22no—
79C3×Q16—42no—
80C2×C3×C8—21no—
81C2×C3×C8C22×D312yes—
82C3×C4⋊C4—62no—
83(C2×D3)⋊C4—122no—
84(C2×D3)⋊C4—122no—
85C4⋊Dic3—22no—
86C4⋊Dic3—62no—
87C4⋊Dic3—62no—
88Dic3⋊C4—122no—
89Dic3⋊C4—122no—
90Dic3⋊C4—122no—
91C2×C3⋊C8—32no—
92C2×C3⋊C8—61no—
93D3×C8—62no—
94D3×C8—62no—
95D3×C8—122no—
96C3×C16—62no—
97C3⋊C16—22no—
98C22×C32C2×D811yescharacteristic
99C2×C3⋊D3—21no—
100C2×C3⋊D3—21no—
101C2×C3⋊D3SD3212yes—
102C32×C4—81no—
103C32×C4#12311yescharacteristic
104C32×C4#13711yescharacteristic
105C3⋊Dic3—21no—
106C3⋊Dic3—81no—
107C3×Dic3—82no—
108C2×Q16D3211yescharacteristic
109C22×C8—91no—
110C22⋊Q8—181no—
111C2×C4⋊C4—181no—
112C2×C16—32no—
113#107—32no—
114#107—91no—
115#107—181no—
116#103—181no—
117C22×D3—32no—
118C22×D3—61no—
119C3×Q8—42no—
120C3×Q8—42no—
121C3×Q8—42no—
122C3×Q8—42no—
123C2×C3×C4—21no—
124C2×C3×C4—42no—
125C2×C3×C4—42no—
126C2×C3×C4—122no—
127C2×C3×C4D3×D412yes—
128C2×Dic3—32no—
129C2×Dic3—42no—
130C2×Dic3—61no—
131C2×Dic3—122no—
132C2×Dic3—122no—
133C4×D3—62no—
134C4×D3—62no—
135C4×D3—121no—
136C4×D3—121no—
137C4×D3—244no—
138C3×C8—22no—
139C3×C8#23512yes—
140C3×C8#23712yes—
141C3⋊C8—62no—
142C3⋊C8—121no—
143C2×C32#48011yescharacteristic
144C2×C32C2×SD3211yescharacteristic
145C2×C32#51011yescharacteristic
146C3⋊D3—22no—
147C2×Q8—21no—
148C22×C4—91no—
149C22×C4—361no—
150Q16—22no—
151C2×C8—91no—
152C2×C8—182no—
153C2×C8C2×D3211yescharacteristic
154C4⋊C4—62no—
155C4⋊C4—181no—
156C4⋊C4—361no—
157C4⋊C4—361no—
158C22⋊C4—361no—
159C16—62no—
160C22×C3—21no—
161C22×C3D3×D812yes—
162C2×D3—34no—
163C2×D3—62no—
164C2×D3—62no—
165C2×D3—62no—
166C2×D3—121no—
167C2×D3—121no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—82no—
171C3×C4—82no—
172C3×C4—242no—
173C3×C4#88312yes—
174C3×C4#91512yes—
175Dic3—62no—
176Dic3—82no—
177Dic3—121no—
178Dic3—242no—
179Dic3—242no—
180C32#223511yescharacteristic, complemented, Sylow
181C23—91no—
182Q8—41no—
183Q8—41no—
184C2×C4—41no—
185C2×C4—91no—
186C2×C4—122no—
187C2×C4—181no—
188C2×C4—181no—
189C2×C4—361no—
190C2×C4—722no—
191C2×C4#381111yescharacteristic
192C8—181no—
193C8#380412yes—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3#477412yes—
198C2×C3D3×SD3212yes—
199C2×C3#491812yes—
200D3—64no—
201D3—122no—
202C22—92no—
203C22—181no—
204C22—181no—
205C22#6392611yescharacteristic
206C4—81no—
207C4—181no—
208C4—242no—
209C4—721no—
210C4#6393111yescharacteristic
211C4#6397511yescharacteristic
212C3—21no—
213C3#6923112yescomplemented
214C2—182no—
215C2#1059103911yescharacteristic
216C2#1059104411yescharacteristic
217C2#1059141711yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC22×C3⋊D3D8
hypercenterC2×Q16D32
hypocenterC32#2235
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. C3×#4564C2semidirect
4. #10589141C2semidirect
20. #4564D3semidirect
180. C32#2235semidirect
213. C3#69231semidirect

Maximal subgroups

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

subgroupindex
#105928872
#105906872
C3×#45642
#105891412
#105891082
#692313