Finite Group Databasebeta

← #11780722

Subgroups — #11780722

Order 1152.

389 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 389 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593868C211yesmaximal, characteristic
2#10592402C211yesmaximal, characteristic
3#10590306C212yesmaximal
4C3×#4465C212yesmaximal
5#10589089C211yesmaximal, characteristic
6#68376—32nomaximal
7#64079C2211yescharacteristic
8#64078C2211yescharacteristic
9C3×#870C2212yes—
10#63847—22no—
11#63846—22no—
12#63845—22no—
13C32×#97C2211yescharacteristic
14#63643—22no—
15C3×#803C2212yes—
16#63575—22no—
17#63573—22no—
18C3⋊#564—32no—
19#5064—32no—
20#4703—32no—
21#4703—61no—
22#4702—32no—
23C3×#330—32no—
24#4465—32no—
25#4465D312yes—
26C2×#634—21no—
27C2×C32×C8—21no—
28C32×C42C2311yescharacteristic
29C4⋊(C3⋊Dic3)—22no—
30C4⋊(C3⋊Dic3)D412yes—
31#3750—22no—
32C3×C4⋊Dic3D412yes—
33C3×C4⋊Dic3D412yes—
34C3×Dic3⋊C4—22no—
35C3×Dic3⋊C4—22no—
36C2×C3×C3⋊C8—22no—
37#3724—22no—
38Dic3⋊Dic3—22no—
39Dic3⋊Dic3—22no—
40Dic32—22no—
41#1663—91noSylow
42C3×#125—32no—
43#890—62no—
44#890—62no—
45#889—62no—
46#889—62no—
47#889—62no—
48#889—62no—
49#870—32no—
50#870—61no—
51#870C2×D312yes—
52#869—32no—
53#869—61no—
54C3×#97—21no—
55C3×#97—32no—
56C3×#97C2×D312yes—
57#818—62no—
58#817—62no—
59#816—62no—
60#816—62no—
61#816—64no—
62#808—62no—
63#807—62no—
64#803C2×D312yes—
65C2×C32×C4C2×D412yes—
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3—22no—
68C2×C3⋊Dic3—41no—
69#634—42no—
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72C32×C8—41no—
73C3×C3⋊C8—24no—
74#564—91no—
75#501—92no—
76#491—91no—
77#330—32no—
78#330—91no—
79C2×Dic6—62no—
80C2×Dic6—62no—
81C2×C3×C8—22no—
82C2×C3×C8—22no—
83C2×C3×C8—62no—
84C3×C4⋊C4—32no—
85C3×C4⋊C4—32no—
86C3×C4⋊C4—62no—
87C3×C4⋊C4—62no—
88C3×C42—21no—
89C3×C42C22×D312yes—
90C4⋊Dic3—32no—
91C4⋊Dic3—32no—
92C4⋊Dic3—62no—
93C4⋊Dic3—62no—
94C4⋊Dic3—62no—
95C4⋊Dic3—62no—
96C4⋊Dic3—62no—
97C4⋊Dic3—122no—
98C4⋊Dic3D1212yes—
99C4⋊Dic3D1212yes—
100Dic3⋊C4—22no—
101Dic3⋊C4—22no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104Dic3⋊C4—62no—
105Dic3⋊C4—62no—
106Dic3⋊C4—62no—
107Dic3⋊C4—62no—
108Dic3⋊C4—122no—
109C4×Dic3—62no—
110C4×Dic3—62no—
111C2×C3⋊C8—22no—
112C22×C32#12011yescharacteristic
113C32×C4—21no—
114C32×C4—22no—
115C3⋊Dic3—42no—
116C3⋊Dic3—81no—
117C3×Dic3—42no—
118C3×Dic3—42no—
119C4⋊Q8—91no—
120#125—32no—
121#125—91no—
122#125—182no—
123#125—182no—
124#125—182no—
125#107—182no—
126#106—182no—
127#103—182no—
128#97—32no—
129#97D3211yescharacteristic
130C2×C3×C4—22no—
131C2×C3×C4—21no—
132C2×C3×C4—62no—
133C2×C3×C4—62no—
134C2×C3×C4C2×D1212yes—
135C2×C3×C4D3×D412yes—
136C2×C3×C4D3×D412yes—
137C2×Dic3—22no—
138C2×Dic3—22no—
139C2×Dic3—62no—
140C2×Dic3—62no—
141C2×Dic3—122no—
142C2×Dic3—122no—
143C2×Dic3—122no—
144Dic6—124no—
145Dic6—124no—
146C3×C8—42no—
147C3×C8—42no—
148C3×C8—64no—
149C3⋊C8—24no—
150C2×C32#45411yescharacteristic
151C2×C32#45612yes—
152C2×Q8—181no—
153C2×C8—21no—
154C2×C8—62no—
155C4⋊C4—32no—
156C4⋊C4—32no—
157C4⋊C4—62no—
158C4⋊C4—62no—
159C4⋊C4—92no—
160C4⋊C4—182no—
161C4⋊C4—182no—
162C4⋊C4—182no—
163C4⋊C4—182no—
164C4⋊C4—182no—
165C42—182no—
166C42C2×D3211yescharacteristic
167C22×C3—21no—
168C22×C3#88212yes—
169C3×C4—22no—
170C3×C4—22no—
171C3×C4—22no—
172C3×C4—22no—
173C3×C4—42no—
174C3×C4—122no—
175C3×C4—122no—
176Dic3—42no—
177Dic3—42no—
178Dic3—122no—
179Dic3—122no—
180Dic3—242no—
181Dic3—242no—
182Dic3—242no—
183C32#166311yescharacteristic, complemented, Sylow
184Q8—362no—
185C2×C4—62no—
186C2×C4—62no—
187C2×C4—182no—
188C2×C4—361no—
189C2×C4D3×D1212yes—
190C2×C4#381111yescharacteristic
191C8—41no—
192C8—64no—
193C2×C3—22no—
194C2×C3—21no—
195C2×C3#475212yes—
196C2×C3#482612yes—
197C2×C3#482712yes—
198C22#6392311yescharacteristic
199C4—22no—
200C4—21no—
201C4—122no—
202C4—122no—
203C4—362no—
204C4—721no—
205C3—21no—
206C3#6837612yescomplemented
207C2#1059040211yescharacteristic
208C2#1059102112yes—
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socle, prime radicalC22×C32#120
hypercenter#97D32
hypocenterC32#1663
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
183. C32#1663semidirect
206. C3#68376semidirect

Maximal subgroups

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

subgroupindex
#105938682
#105924022
#105903062
C3×#44652
#105890892
#683763