Finite Group Databasebeta

← #11781976

Subgroups — #11781976

Order 1152.

351 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 82 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#10592530C211yesmaximal, characteristic
2#10590388C212yesmaximal
3#10590312C211yesmaximal, characteristic
4C3×#4486C212yesmaximal
5#10589098C211yesmaximal, characteristic
6#68475—32nomaximal
7C4×#634C2211yescharacteristic
8C3×#869C2212yes—
9C2×#3719—22no—
10C32×C4⋊C8C2211yescharacteristic
11#63642—21no—
12#63641—21no—
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×C4⋊(C3⋊C8)C2212yes—
15#63576—21no—
16#63576—21no—
17#63566—22no—
18#5090—32no—
19#5078—32no—
20#4849—32no—
21#4831—32no—
22#4831—61no—
23C3×#332—32no—
24#4486D312yes—
25#4480—32no—
26C2×#634D411yescharacteristic
27C2×C3×Dic6—22no—
28C2×C32×C8—21no—
29C32×C42C2311yescharacteristic
30C4⋊(C3⋊Dic3)D411yescharacteristic
31#3750—21no—
32C4×C3⋊Dic3—21no—
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C3×C4⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C2×C3×C3⋊C8—22no—
38#3719—44no—
39#1694—91noSylow
40C3×C4⋊Q8—32no—
41C2×#216—62no—
42C2×Dic12—62no—
43#869C2×D312yes—
44C4×Dic6—32no—
45C4×Dic6—61no—
46C3×C4⋊C8—21no—
47C3×C4⋊C8—32no—
48C3×C4⋊C8C2×D312yes—
49#835—62no—
50#816—62no—
51#815—62no—
52#815—62no—
53Dic3⋊C8—62no—
54Dic3⋊C8—62no—
55#807—62no—
56#807—62no—
57C4⋊(C3⋊C8)C2×D312yes—
58C4×C3⋊C8—32no—
59C4×C3⋊C8—61no—
60C2×C32×C4C2×D411yescharacteristic
61C2×C32×C4C2×D411yescharacteristic
62C2×C32×C4#4111yescharacteristic
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3—21no—
65#634—22no—
66C2×C3×Dic3—42no—
67C3×Dic6—42no—
68C3×Dic6—42no—
69C32×C8—41no—
70C3⋊(C3⋊C8)—21no—
71C3⋊(C3⋊C8)Q1612yescomplemented
72C3×C3⋊C8—42no—
73#500—91no—
74#462—92no—
75#446—91no—
76#334—91no—
77#332—32no—
78C2×C3×Q8—62no—
79C2×Dic6—22no—
80C2×Dic6—32no—
81C2×Dic6—61no—
82C2×C3×C8—22no—
83C2×C3×C8—22no—
84C2×C3×C8—62no—
85C3×C4⋊C4—62no—
86C3×C4⋊C4—62no—
87C3×C42—21no—
88C3×C42C22×D312yes—
89#216—124no—
90C4⋊Dic3—22no—
91C4⋊Dic3—22no—
92C4⋊Dic3—32no—
93C4⋊Dic3—61no—
94Dic3⋊C4—62no—
95Dic3⋊C4—62no—
96C4×Dic3—62no—
97C4×Dic3—62no—
98C2×C3⋊C8—22no—
99C2×C3⋊C8—32no—
100C2×C3⋊C8—32no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—61no—
103Dic12—124no—
104C22×C32#12111yescharacteristic
105C32×C4—21no—
106C32×C4C2×Q1611yescharacteristic
107C32×C4AGL(1,ℤ/8)12yes—
108C32×C4#13711yescharacteristic
109C3⋊Dic3—41no—
110C3⋊Dic3—41no—
111C3×Dic3—82no—
112C2×Q16—182no—
113C4⋊Q8—32no—
114C4×Q8—91no—
115#107—181no—
116#107—181no—
117C4⋊C8—32no—
118C4⋊C8—181no—
119C4⋊C8D3211yescharacteristic
120#103—182no—
121#97—181no—
122C4×C8—91no—
123C3×Q8—122no—
124C3×Q8—122no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—122no—
129C2×C3×C4#23512yes—
130C2×C3×C4D3×D412yes—
131C2×C3×C4D3×D412yes—
132C2×Dic3—42no—
133C2×Dic3—62no—
134C2×Dic3—62no—
135C2×Dic3—62no—
136C2×Dic3—62no—
137Dic6—42no—
138Dic6—42no—
139Dic6—62no—
140Dic6—62no—
141Dic6—122no—
142C3×C8—42no—
143C3×C8—42no—
144C3×C8—122no—
145C3⋊C8—34no—
146C3⋊C8—42no—
147C3⋊C8—62no—
148C3⋊C8—62no—
149C3⋊C8—121no—
150C2×C32#46211yescharacteristic
151C2×C32#46911yescharacteristic
152C2×C32#47311yescharacteristic
153C2×Q8—62no—
154C2×Q8—91no—
155Q16—364no—
156C2×C8—21no—
157C2×C8—62no—
158C2×C8—91no—
159C2×C8—91no—
160C4⋊C4—62no—
161C4⋊C4—62no—
162C4⋊C4—91no—
163C4⋊C4—181no—
164C42—181no—
165C42C2×D3211yescharacteristic
166C22×C3—21no—
167C22×C3#88412yes—
168C3×C4—22no—
169C3×C4—22no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—41no—
173C3×C4—242no—
174C3×C4#91112yes—
175C3×C4#91412yes—
176C3×C4#91512yes—
177C3×C4D3×Q1612yes—
178Dic3—82no—
179Dic3—122no—
180Dic3—122no—
181Dic3—122no—
182Dic3—122no—
183C32#169411yescharacteristic, complemented, Sylow
184Q8—122no—
185Q8—122no—
186Q8—182no—
187C2×C4—122no—
188C2×C4—181no—
189C2×C4—181no—
190C2×C4#379811yescharacteristic
191C2×C4#380211yescharacteristic
192C2×C4#381111yescharacteristic
193C8—41no—
194C8—92no—
195C8—122no—
196C8—181no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3#475512yes—
201C2×C3#478212yes—
202C2×C3#479512yes—
203C22#6391211yescharacteristic
204C4—21no—
205C4—242no—
206C4—361no—
207C4—361no—
208C4#6379812yes—
209C4#6393111yescharacteristic
210C4#6394411yescharacteristic
211C3—21no—
212C3#6847512yescomplemented
213C2#1059056611yescharacteristic
214C2#1059084011yescharacteristic
215C2#1059099311yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1694
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
71. C3⋊(C3⋊C8)Q16semidirect
183. C32#1694semidirect
212. C3#68475semidirect

Maximal subgroups

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

subgroupindex
#105925302
#105903882
#105903122
C3×#44862
#105890982
#684753