Finite Group Databasebeta

← #11799509

Subgroups — #11799509

Order 1152.

351 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 76 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#10592571C211yesmaximal, characteristic
2#10590902C211yesmaximal, characteristic, complemented
3C3×#4489C212yesmaximal, complemented
4#10589133C211yesmaximal, characteristic, complemented
5#10589116C212yesmaximal
6#69333—32nomaximal
7C2×#3745C2211yescharacteristic
8#64102—21no—
9#63919—21no—
10C32×#107C2211yescharacteristic
11C8×C3⋊Dic3C2211yescharacteristic
12#63636—21no—
13C3×#818C2212yes—
14C2×C3×C3⋊C16C2212yes—
15#63576—21no—
16#4874—32no—
17#4872—32no—
18#4872—61no—
19C3×#366—32no—
20#4509—32no—
21Dic3⋊C16—32no—
22#4491—32no—
23#4489D312yescomplemented
24C2×C4⋊(C3⋊D3)—21no—
25C2×C4×C3⋊D3—41no—
26C2×#627—41no—
27C2×C32×C8C2311yescharacteristic
28C32×C4⋊C4—21no—
29#3752—41no—
30C4×C3⋊Dic3D411yescharacteristic
31C2×C3⋊(C3⋊C8)D411yescharacteristic
32#3745—21no—
33#3745Q812yescomplemented
34C3×C4⋊Dic3—22no—
35#3724—41no—
36C3×C3⋊C16—22no—
37#2224—91noSylow
38C2×D24—32no—
39C2×D24—61no—
40#893—62no—
41#893—62no—
42#888—62no—
43C2×C3×C16—32no—
44C3×#107—21no—
45C3×#107—32no—
46C3×#107C2×D312yes—
47#818C2×D312yes—
48C8×Dic3—32no—
49C8×Dic3—61no—
50C2×C3⋊C16C2×D312yes—
51#809—62no—
52#809—62no—
53#807—62no—
54C22×C3⋊D3—41no—
55C2×C32×C4—41no—
56C2×C32×C4C2×D411yescharacteristic
57C2×C3⋊Dic3D811yescharacteristic
58C2×C3⋊Dic3D811yescharacteristic
59C4⋊(C3⋊D3)—22no—
60C4⋊(C3⋊D3)—41no—
61C4×C3⋊D3—82no—
62C2×C3×Dic3—42no—
63#627—82no—
64C32×C8C2×Q811yescharacteristic
65C32×C8#4111yescharacteristic
66C3⋊(C3⋊C8)—21no—
67#500—91no—
68C4×D8—91no—
69#366—32no—
70C4⋊C16—91no—
71#357—92no—
72C2×D12—62no—
73C2×D12—62no—
74C2×C4×D3—122no—
75C2×C4×D3—122no—
76C2×Dic6—122no—
77C2×C3×C8—21no—
78C2×C3×C8C22×D312yes—
79C3×C4⋊C4—22no—
80C3×C4⋊C4—22no—
81C3×C4⋊C4—62no—
82(C2×D3)⋊C4—122no—
83(C2×D3)⋊C4—122no—
84C4⋊Dic3—22no—
85Dic3⋊C4—122no—
86C4×Dic3—32no—
87C4×Dic3—61no—
88C2×C3⋊C8—32no—
89C2×C3⋊C8—61no—
90D24—34no—
91D24—62no—
92D24—62no—
93D24—62no—
94C3×C16—62no—
95C3⋊C16—22no—
96C22×C32C2×D811yescharacteristic
97C2×C3⋊D3—42no—
98C2×C3⋊D3—81no—
99C2×C3⋊D3—81no—
100C32×C4—81no—
101C32×C4C22⋊Q811yescharacteristic
102C32×C4#13711yescharacteristic
103C3⋊Dic3—21no—
104C3⋊Dic3D1612yes—
105C3×Dic3—82no—
106C2×D8—91no—
107C4⋊Q8—181no—
108C4×D4—181no—
109C2×C16—32no—
110#107—32no—
111#107—181no—
112#107D3211yescharacteristic
113#102—181no—
114C4×C8—91no—
115C22×D3—122no—
116C22×D3—122no—
117C2×C3×C4—21no—
118C2×C3×C4—42no—
119C2×C3×C4—42no—
120C2×C3×C4—122no—
121C2×C3×C4D3×D412yes—
122C2×Dic3—32no—
123C2×Dic3—32no—
124C2×Dic3—42no—
125C2×Dic3—61no—
126C2×Dic3—61no—
127D12—64no—
128D12—64no—
129D12—122no—
130D12—122no—
131C4×D3—244no—
132C4×D3—244no—
133Dic6—244no—
134C3×C8—21no—
135C3×C8—21no—
136C3×C8#23512yes—
137C3×C8D3×Q812yes—
138C3⋊C8—62no—
139C3⋊C8—121no—
140C2×C32#47411yescharacteristic
141C2×C32C2×D1611yescharacteristic
142C2×C32#51011yescharacteristic
143C3⋊D3—82no—
144C2×Q8—361no—
145C2×D4—181no—
146C22×C4—361no—
147D8—92no—
148D8—181no—
149C2×C8—91no—
150C2×C8C2×D3211yescharacteristic
151C4⋊C4—21no—
152C4⋊C4—62no—
153C4⋊C4—361no—
154C22⋊C4—361no—
155C42—91no—
156C16—62no—
157C22×C3—21no—
158C22×C3D3×D812yes—
159C2×D3—124no—
160C2×D3—124no—
161C2×D3—242no—
162C2×D3—242no—
163C2×D3—242no—
164C2×D3—242no—
165C3×C4—21no—
166C3×C4—21no—
167C3×C4—82no—
168C3×C4—82no—
169C3×C4—242no—
170C3×C4#89612yes—
171C3×C4#91812yes—
172Dic3—34no—
173Dic3—62no—
174Dic3—62no—
175Dic3—82no—
176Dic3—121no—
177C32#222411yescharacteristic, complemented, Sylow
178C23—361no—
179Q8—722no—
180D4—182no—
181D4—361no—
182C2×C4—41no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—122no—
186C2×C4—722no—
187C2×C4#381111yescharacteristic
188C8—181no—
189C8#379711yescharacteristic
190C8#379811yescharacteristic
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—21no—
194C2×C3#489012yes—
195C2×C3D3×D1612yes—
196C2×C3#491812yes—
197D3—244no—
198D3—244no—
199C22—362no—
200C22—721no—
201C22—721no—
202C22#6392611yescharacteristic
203C4—81no—
204C4—92no—
205C4—181no—
206C4—242no—
207C4#6386511yescharacteristic
208C4#6394511yescharacteristic
209C3—21no—
210C3#6933312yescomplemented
211C2—722no—
212C2#1059043011yescharacteristic
213C2#1059102511yescharacteristic
214C2#1059104411yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenter#107D32
hypocenterC32#2224
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10590902C2semidirect
3. C3×#4489C2semidirect
4. #10589133C2semidirect
23. #4489D3semidirect
33. #3745Q8semidirect
177. C32#2224semidirect
210. C3#69333semidirect

Maximal subgroups

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

subgroupindex
#105925712
#105909022
C3×#44892
#105891332
#105891162
#693333