Finite Group Databasebeta

← #101×C3⋊Dic3 #11783805

Subgroups — #101×C3⋊Dic3 #11783805

Order 1152.

888 conjugacy classes of subgroups; only the 283 normal subgroups are shown.

normal subgroups only

This group has 888 conjugacy classes of subgroups — too many to draw. Only its 283 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×Q8×C3⋊Dic3C211yesmaximal, characteristic
2C2×C32×#101C211yesmaximal, characteristic
3C2×#63663C211yesmaximal, characteristic
4M16×C3⋊Dic3C212yesmaximal
5#10589420C212yesmaximal
6Dic3×#101—34nomaximal
7C22×C32×Q8C2211yescharacteristic
8C2×C32×M16C2212yes—
9Q8×C3⋊Dic3—22no—
10Q8×C3⋊Dic3—22no—
11C2×C4⋊(C3⋊Dic3)C412yes—
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4×C3⋊Dic3C412yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×#3748C2212yes—
16C32×#101C414yescomplemented
17#63663C414yescomplemented
18#63642—22no—
19C8×C3⋊Dic3—22no—
20C2×Q8×Dic3—34no—
21C2×C3×#101D314yes—
22C2×#836—34no—
23Dic3×M16—38no—
24#4554—38no—
25C2×C32×Q8—22no—
26C2×C32×Q8—22no—
27C2×C32×Q8C2×C412yes—
28C2×C32×Q8C2×C412yes—
29C22×C32×C4C2×C412yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C22×C3⋊Dic3C2×C412yes—
33C22×C3⋊Dic3C2×C411yescharacteristic
34C32×M16—22no—
35C32×M16C2×C414yes—
36C2×C32×C8—22no—
37C4⋊(C3⋊Dic3)—22no—
38C4⋊(C3⋊Dic3)—24no—
39C4×C3⋊Dic3—22no—
40C4×C3⋊Dic3—22no—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3D412yes—
43#3748—22no—
44#3748C2×C414yes—
45C2×C3⋊(C3⋊C8)—22no—
46C4×#101—91noSylow
47C22×C3×Q8C2×D314yes—
48C2×C3×M16C2×D318yes—
49Q8×Dic3—68no—
50Q8×Dic3—68no—
51C2×C4⋊Dic3—38no—
52C2×C4⋊Dic3—34no—
53C2×C4×Dic3—34no—
54C2×C4×Dic3—38no—
55C2×#208—38no—
56C3×#101Dic3116yescomplemented
57#836—316no—
58#815—68no—
59C8×Dic3—68no—
60C23×C32C22×C411yescharacteristic
61C32×Q8—24no—
62C32×Q8—24no—
63C2×C32×C4—22no—
64C2×C32×C4—22no—
65C2×C32×C4C4214yes—
66C2×C32×C4C22×C411yescharacteristic
67C2×C32×C4C22×C411yescharacteristic
68C2×C32×C4C2×D412yes—
69C2×C32×C4#4112yes—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3—42no—
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C22⋊C412yes—
76C2×C3⋊Dic3C22⋊C411yescharacteristic
77C32×C8—24no—
78C3⋊(C3⋊C8)—24no—
79C2×C4×Q8—91no—
80C2×#101—91no—
81C2×#101C3⋊D311yescharacteristic
82C4×M16—92no—
83#343—92no—
84C2×C3×Q8—28no—
85C2×C3×Q8—28no—
86C2×C3×Q8C4×D318yes—
87C2×C3×Q8C2×Dic318yes—
88C22×C3×C4C4×D318yes—
89C22×C3×C4C22×D314yes—
90C22×Dic3—34no—
91C22×Dic3—34no—
92C22×Dic3—38no—
93C3×M16—28no—
94C3×M16C2×Dic3116yes—
95C2×C3×C8—28no—
96C4⋊Dic3—616no—
97C4⋊Dic3—68no—
98C4×Dic3—38no—
99C4×Dic3—38no—
100C4×Dic3—68no—
101C4×Dic3—68no—
102#208—316no—
103#208—68no—
104C2×C3⋊C8—68no—
105C22×C32—21no—
106C22×C32—21no—
107C22×C32C2×C4211yescharacteristic
108C22×C32C2×C22⋊C411yescharacteristic
109C22×C32#11711yescharacteristic
110C32×C4—24no—
111C32×C4C4×D412yes—
112C32×C4C4×D412yes—
113C3⋊Dic3—21no—
114C3⋊Dic3—22no—
115C3⋊Dic3—42no—
116C3⋊Dic3#10112yesdirect product factor
117C22×Q8C2×C3⋊D311yescharacteristic
118C2×M16—92no—
119C2×M16C2×C3⋊D312yes—
120C4×Q8—182no—
121C4×Q8—182no—
122C2×C4⋊C4—92no—
123C2×C4⋊C4—91no—
124C2×C42—91no—
125C2×C42—92no—
126#101—94no—
127#101C3⋊Dic314yesdirect product factor
128#97—182no—
129C4×C8—182no—
130C23×C3C2×C4×D314yes—
131C3×Q8—216no—
132C3×Q8—216no—
133C2×C3×C4—28no—
134C2×C3×C4—28no—
135C2×C3×C4C4×Dic3116yes—
136C2×C3×C4C2×C4×D314yes—
137C2×C3×C4D3×D418yes—
138C2×C3×C4#23718yes—
139C2×C3×C4C22×Dic314yes—
140C2×Dic3—34no—
141C2×Dic3—34no—
142C2×Dic3—38no—
143C2×Dic3—68no—
144C2×Dic3—68no—
145C2×Dic3—124no—
146C2×Dic3—128no—
147C3×C8—216no—
148C3⋊C8—616no—
149C2×C32—21no—
150C2×C32—21no—
151C2×C32C4×C22⋊C411yescharacteristic
152C2×C32C2×#10111yescharacteristic
153C2×C32#41311yescharacteristic
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8C4×C3⋊D312yes—
157C2×Q8C2×C3⋊Dic312yes—
158C22×C4—91no—
159C22×C4—91no—
160C22×C4—92no—
161C22×C4C4×C3⋊D312yes—
162C22×C4C22×C3⋊D311yescharacteristic
163M16—22no—
164M16—94no—
165M16—182no—
166M16C2×C3⋊Dic314yes—
167C2×C8—22no—
168C2×C8—182no—
169C4⋊C4—184no—
170C4⋊C4—182no—
171C42—92no—
172C42—92no—
173C42—182no—
174C42—182no—
175C22×C3—24no—
176C22×C3—24no—
177C22×C3#87714yes—
178C22×C3D3×C22⋊C414yes—
179C22×C3C2×C4×Dic314yes—
180C3×C4—216no—
181C3×C4#67⋊C418yes—
182C3×C4D4×Dic318yes—
183Dic3—38no—
184Dic3—64no—
185Dic3—68no—
186Dic3—128no—
187C32C4×#10111yescharacteristic, complemented, Sylow
188C23C2×C4×C3⋊D311yescharacteristic
189Q8—24no—
190Q8—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—92no—
196C2×C4—182no—
197C2×C4—182no—
198C2×C4—361no—
199C2×C4—362no—
200C2×C4C4×C3⋊Dic314yes—
201C2×C4C2×C4×C3⋊D311yescharacteristic
202C2×C4D4×C3⋊D312yes—
203C2×C4#383012yes—
204C2×C4C22×C3⋊Dic311yescharacteristic
205C8—24no—
206C8—184no—
207C2×C3—24no—
208C2×C3—24no—
209C2×C3D3×#10114yes—
210C2×C3#475114yes—
211C2×C3Dic3×C22⋊C414yes—
212C22—21no—
213C22—21no—
214C22#6408611yescharacteristic
215C22C22⋊C4×C3⋊D311yescharacteristic
216C22C2×C4×C3⋊Dic311yescharacteristic
217C4—24no—
218C4—92no—
219C4—181no—
220C4—182no—
221C4—362no—
222C4#6409012yes—
223C4D4×C3⋊Dic312yes—
224C3Dic3×#10114yescomplemented
225C2—21no—
226C2—21no—
227C2C3⋊D3×#10111yescharacteristic
228C2#1059245011yescharacteristic
229C2C22⋊C4×C3⋊Dic311yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C2×C42
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#101C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC2×#101C3⋊D3
hypocenterC32C4×#101
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
16. C32×#101C4semidirect
17. #63663C4semidirect
56. C3×#101Dic3semidirect
116. C3⋊Dic3#101direct (N × H)
127. #101C3⋊Dic3direct (N × H)
187. C32C4×#101semidirect
224. C3Dic3×#101semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×C32×#1012
C2×#636632
M16×C3⋊Dic32
#105894202
Dic3×#1013