Finite Group Databasebeta

← #11783796

Subgroups — #11783796

Order 1152.

888 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 888 conjugacy classes of subgroups — too many to draw. Only its 223 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×#64096C211yesmaximal, characteristic
2C2×#63651C212yesmaximal
3M16×C3⋊Dic3C212yesmaximal
4C32×#343C211yesmaximal, characteristic
5#10589396C211yesmaximal, characteristic
6#68973—34nomaximal
7C22×#634C2211yescharacteristic
8C2×C32×M16C2212yes—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×#3750C412yes—
11C2×C4×C3⋊Dic3C412yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2212yes—
14#64096—22no—
15#64096—22no—
16#63651C418yescomplemented
17#63642—22no—
18C8×C3⋊Dic3—22no—
19C2×#887—34no—
20C2×#824—38no—
21Dic3×M16—38no—
22C3×#343D314yes—
23#4530—34no—
24C22×C32×C4C2×C412yes—
25C22×C32×C4C2311yescharacteristic
26C22×C3⋊Dic3C2×C412yes—
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C2×#634—22no—
30C2×#634—21no—
31C2×#634—21no—
32C2×#634C2×C414yes—
33C32×M16—22no—
34C32×M16C2×C414yes—
35C2×C32×C8—22no—
36C32×C4⋊C4—22no—
37#3750—24no—
38C4×C3⋊Dic3—22no—
39C4×C3⋊Dic3—22no—
40C4×C3⋊Dic3D412yes—
41C4×C3⋊Dic3D412yes—
42#3748—22no—
43#3748C2×C414yes—
44C2×C3⋊(C3⋊C8)—22no—
45C4×#101—91noSylow
46C22×Dic6—34no—
47C2×C3×M16C2×D318yes—
48C2×C3×C4⋊C4C2×D314yes—
49C2×Dic3⋊C4—38no—
50C2×C4×Dic3—34no—
51C2×C4×Dic3—38no—
52C2×#208—38no—
53#887—68no—
54#887—68no—
55#824—332no—
56#815—68no—
57C8×Dic3—68no—
58C23×C32C22×C411yescharacteristic
59C2×C32×C4—22no—
60C2×C32×C4—42no—
61C2×C32×C4C22×C412yes—
62C2×C32×C4C2×D412yes—
63C2×C32×C4#4111yescharacteristic
64C2×C32×C4#4111yescharacteristic
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3—22no—
68C2×C3⋊Dic3—41no—
69C2×C3⋊Dic3C4214yes—
70C2×C3⋊Dic3C22⋊C411yescharacteristic
71C2×C3⋊Dic3C22⋊C412yes—
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73#634—24no—
74#634—24no—
75C32×C8—24no—
76C3⋊(C3⋊C8)—24no—
77C2×C4×Q8—91no—
78C2×#101—92no—
79C4×M16—92no—
80#343—91no—
81#343C3⋊D311yescharacteristic
82C22×C3×C4C4×D318yes—
83C22×C3×C4C22×D314yes—
84C22×Dic3—34no—
85C22×Dic3—38no—
86C22×Dic3—34no—
87C2×Dic6—316no—
88C2×Dic6—68no—
89C2×Dic6—64no—
90C2×Dic6—64no—
91C3×M16—28no—
92C3×M16C4×D3116yes—
93C2×C3×C8—28no—
94C3×C4⋊C4—28no—
95Dic3⋊C4—616no—
96C4×Dic3—38no—
97C4×Dic3—38no—
98C4×Dic3—68no—
99C4×Dic3—68no—
100#208—316no—
101#208—68no—
102C2×C3⋊C8—68no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32C2×C4211yescharacteristic
106C22×C32C2×C22⋊C411yescharacteristic
107C22×C32#11711yescharacteristic
108C32×C4—42no—
109C32×C4C4×D412yes—
110C32×C4C4×D412yes—
111C3⋊Dic3—24no—
112C3⋊Dic3—21no—
113C3⋊Dic3—22no—
114C3⋊Dic3#10112yescomplemented
115C22×Q8—91no—
116C2×M16—92no—
117C2×M16C2×C3⋊D312yes—
118C4×Q8—182no—
119C4×Q8—182no—
120C2×C4⋊C4—92no—
121C2×C4⋊C4C2×C3⋊D311yescharacteristic
122C2×C42—91no—
123C2×C42—92no—
124#101—98no—
125#97—182no—
126C4×C8—182no—
127C23×C3C2×C4×D314yes—
128C2×C3×C4—28no—
129C2×C3×C4—48no—
130C2×C3×C4C2×C4×D318yes—
131C2×C3×C4D3×D418yes—
132C2×C3×C4#23714yes—
133C2×C3×C4#23914yes—
134C2×Dic3—34no—
135C2×Dic3—316no—
136C2×Dic3—34no—
137C2×Dic3—38no—
138C2×Dic3—68no—
139C2×Dic3—68no—
140C2×Dic3—68no—
141C2×Dic3—124no—
142Dic6—616no—
143Dic6—616no—
144C3×C8—216no—
145C3⋊C8—616no—
146C2×C32—21no—
147C2×C32—21no—
148C2×C32C4×C22⋊C411yescharacteristic
149C2×C32C2×#10111yescharacteristic
150C2×C32#41311yescharacteristic
151C2×Q8—94no—
152C2×Q8—182no—
153C2×Q8—181no—
154C2×Q8—181no—
155C22×C4—91no—
156C22×C4—92no—
157C22×C4—91no—
158C22×C4C4×C3⋊D312yes—
159C22×C4C22×C3⋊D311yescharacteristic
160M16—22no—
161M16—94no—
162M16—182no—
163M16C4×C3⋊D314yes—
164C2×C8—22no—
165C2×C8—182no—
166C4⋊C4—22no—
167C4⋊C4—184no—
168C42—92no—
169C42—92no—
170C42—182no—
171C42—182no—
172C22×C3—24no—
173C22×C3—24no—
174C22×C3C42×D314yes—
175C22×C3D3×C22⋊C414yes—
176C22×C3#89214yes—
177C3×C4—48no—
178C3×C4#67⋊C418yes—
179C3×C4#89318yes—
180Dic3—38no—
181Dic3—616no—
182Dic3—68no—
183Dic3—64no—
184C32C4×#10111yescharacteristic, complemented, Sylow
185C23C2×C4×C3⋊D311yescharacteristic
186Q8—184no—
187Q8—184no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—91no—
191C2×C4—94no—
192C2×C4—91no—
193C2×C4—92no—
194C2×C4—182no—
195C2×C4—182no—
196C2×C4—182no—
197C2×C4—361no—
198C2×C4C2×C4×C3⋊D312yes—
199C2×C4D4×C3⋊D312yes—
200C2×C4#383011yescharacteristic
201C2×C4#383211yescharacteristic
202C8—24no—
203C8—184no—
204C2×C3—24no—
205C2×C3—24no—
206C2×C3#466614yes—
207C2×C3#474514yes—
208C2×C3D3×#10114yes—
209C22—21no—
210C22—21no—
211C22C42×C3⋊D311yescharacteristic
212C22C22⋊C4×C3⋊D311yescharacteristic
213C22#6410111yescharacteristic
214C4—42no—
215C4—92no—
216C4—184no—
217C4—182no—
218C4—181no—
219C4#6409012yes—
220C4#6410212yes—
221C3#6897314yescomplemented
222C2—21no—
223C2—21no—
224C2#1059236511yescharacteristic
225C2#1059244411yescharacteristic
226C2C3⋊D3×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C2×C42
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenter#343C3⋊D3
hypocenterC32C4×#101
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
16. #63651C4semidirect
114. C3⋊Dic3#101semidirect
184. C32C4×#101semidirect
221. C3#68973semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#636512
M16×C3⋊Dic32
C32×#3432
#105893962
#689733