Finite Group Databasebeta

← #11785480

Subgroups — #11785480

Order 1152.

780 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 213 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
1C2×#64157C211yesmaximal, characteristic
2C32×#410C211yesmaximal, characteristic
3#10592939C211yesmaximal, characteristic
4#10592697C212yesmaximal, complemented
5#10589397C212yesmaximal, complemented
6#70041—34nomaximal
7C2×C32×#41C2211yescharacteristic
8C32×#117C2212yes—
9#64157—22no—
10#64157—22no—
11#64135C2212yes—
12C2×#3748C412yescomplemented
13C2×#3748C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C412yescomplemented
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C32×#99—22no—
17#63661—22no—
18#63635—22no—
19#63634—22no—
20C2×#948—34no—
21C3×#410D314yes—
22#5240—34no—
23#4998—38no—
24#4531—38no—
25C32×#41—22no—
26C32×#41—22no—
27C2×C32×Q8Q811yescharacteristic
28C2×C32×D4D412yes—
29C2×C32×D4Q811yescharacteristic
30C22×C32×C4C2×C412yes—
31C22×C32×C4C2311yescharacteristic
32C32×C4⋊C4—22no—
33C32×C22⋊C4—22no—
34C32×C42—22no—
35#3757—22no—
36C4⋊(C3⋊Dic3)—22no—
37C4×C3⋊Dic3—22no—
38#3748—22no—
39#3748—24no—
40C2×C3⋊(C3⋊C8)—22no—
41C2×C3⋊(C3⋊C8)—22no—
42C2×C3⋊(C3⋊C8)C2×C412yes—
43C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
44C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
45C2×C3⋊(C3⋊C8)D412yes—
46C2×C3⋊(C3⋊C8)D412yes—
47#1812—91noSylow
48C2×C3×#41C2×D314yes—
49C3×#117C2×D318yes—
50#948—68no—
51#948—68no—
52#926—38no—
53C2×#208—38no—
54C2×#208—34no—
55C22×C3⋊C8—34no—
56C22×C3⋊C8—38no—
57C3×#99—28no—
58#834—68no—
59#808—68no—
60#807—68no—
61C23×C32C4⋊C412yes—
62C23×C32C2×D411yescharacteristic
63C32×Q8—22no—
64C32×D4—24no—
65C32×D4—22no—
66C2×C32×C4—22no—
67C2×C32×C4—22no—
68C2×C32×C4—42no—
69C2×C32×C4C4⋊C412yes—
70C2×C32×C4C22×C411yescharacteristic
71C2×C32×C4C2×D412yes—
72C2×C32×C4C2×Q811yescharacteristic
73C2×C32×C4#4112yes—
74C2×C3⋊Dic3—42no—
75C3⋊(C3⋊C8)—22no—
76C3⋊(C3⋊C8)C22⋊C411yescharacteristic
77C3⋊(C3⋊C8)C22⋊C411yescharacteristic
78C3⋊(C3⋊C8)C22⋊C412yes—
79C2×#131—91no—
80#427—92no—
81#410—91no—
82#410C3⋊D311yescharacteristic
83H(3,ℤ/4)—92no—
84C3×#41—28no—
85C3×#41—28no—
86C2×C3×Q8Dic614yes—
87C2×C3×D4Dic614yes—
88C2×C3×D4#6718yes—
89C22×C3×C4C4×D318yes—
90C22×C3×C4C22×D314yes—
91C3×C4⋊C4—28no—
92C3×C22⋊C4—28no—
93C3×C42—28no—
94#217—68no—
95C4⋊Dic3—68no—
96C4×Dic3—68no—
97#208—616no—
98#208—68no—
99C2×C3⋊C8—34no—
100C2×C3⋊C8—34no—
101C2×C3⋊C8—38no—
102C2×C3⋊C8—38no—
103C2×C3⋊C8—38no—
104C2×C3⋊C8—68no—
105C2×C3⋊C8—68no—
106C22×C32—22no—
107C22×C32—41no—
108C22×C32—42no—
109C22×C32C2×C4⋊C411yescharacteristic
110C22×C32#12112yes—
111C32×C4—22no—
112C32×C4—82no—
113C32×C4C2×C22⋊C411yescharacteristic
114C32×C4#11711yescharacteristic
115C32×C4C22⋊Q812yes—
116C3⋊Dic3—82no—
117C2×#41C2×C3⋊D311yescharacteristic
118#131—182no—
119#131—182no—
120C2×M16—92no—
121C2×M16—91no—
122C22×C8—91no—
123C22×C8—92no—
124#117—92no—
125#117C2×C3⋊D312yes—
126#107—182no—
127#106—182no—
128#99—22no—
129#99—182no—
130C23×C3Dic3⋊C418yes—
131C23×C3C2×#6714yes—
132C3×Q8—28no—
133C3×D4—216no—
134C3×D4—28no—
135C2×C3×C4—28no—
136C2×C3×C4—28no—
137C2×C3×C4—48no—
138C2×C3×C4Dic3⋊C418yes—
139C2×C3×C4C2×Dic614yes—
140C2×C3×C4C2×C4×D314yes—
141C2×C3×C4D3×D418yes—
142C2×C3×C4#23718yes—
143C2×Dic3—128no—
144C3⋊C8—34no—
145C3⋊C8—34no—
146C3⋊C8—38no—
147C3⋊C8—68no—
148C2×C32—22no—
149C2×C32—21no—
150C2×C32—42no—
151C2×C32#38011yescharacteristic
152#41—22no—
153#41—22no—
154C2×Q8#63411yescharacteristic
155C2×D4#63411yescharacteristic
156C2×D4#63812yes—
157C22×C4C4×C3⋊D312yes—
158C22×C4C22×C3⋊D311yescharacteristic
159M16—184no—
160M16—182no—
161C2×C8—91no—
162C2×C8—91no—
163C2×C8—92no—
164C2×C8—92no—
165C2×C8—92no—
166C2×C8—182no—
167C2×C8—182no—
168C4⋊C4—22no—
169C4⋊C4—182no—
170C22⋊C4—22no—
171C22⋊C4—182no—
172C42—22no—
173C42—182no—
174C22×C3—28no—
175C22×C3—44no—
176C22×C3—48no—
177C22×C3C2×Dic3⋊C414yes—
178C22×C3#93918yes—
179C3×C4—28no—
180C3×C4—88no—
181C3×C4#87714yes—
182C3×C4#87818yes—
183C3×C4D3×C22⋊C414yes—
184Dic3—248no—
185C32#181211yescharacteristic, complemented, Sylow
186C23#375012yes—
187C23C2×#63811yescharacteristic
188Q8—22no—
189D4—24no—
190D4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—42no—
194C2×C4—362no—
195C2×C4#375012yes—
196C2×C4C2×#63411yescharacteristic
197C2×C4C2×C4×C3⋊D311yescharacteristic
198C2×C4D4×C3⋊D312yes—
199C2×C4#383012yes—
200C8—91no—
201C8—91no—
202C8—92no—
203C8—182no—
204C2×C3—28no—
205C2×C3—24no—
206C2×C3—48no—
207C2×C3#494214yes—
208C22—22no—
209C22—41no—
210C22—42no—
211C22C2×#375011yescharacteristic
212C22#6414812yes—
213C4—22no—
214C4—82no—
215C4—722no—
216C4#6408611yescharacteristic
217C4#6408712yes—
218C4C22⋊C4×C3⋊D311yescharacteristic
219C3#7004114yescomplemented
220C2—22no—
221C2—21no—
222C2—42no—
223C2#1059264111yescharacteristic
subgroupG/H
centerC4#64086
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#410C2
socleC2×C32#380
prime radicalC2×C32×#41C22
cosocleC22×C32×C4C23
hypercenter#410C3⋊D3
hypocenterC32#1812
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
4. #10592697C2semidirect
5. #10589397C2semidirect
12. C2×#3748C4semidirect
14. C22×C3⋊(C3⋊C8)C4semidirect
185. C32#1812semidirect
219. C3#70041semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C32×#4102
#105929392
#105926972
#105893972
#700413