Finite Group Databasebeta

← #10593882

Subgroups — #10593882

Order 576.

498 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C42×C3⋊D3C211yesmaximal, characteristic
2C3×C4×Dic6C212yesmaximal, complemented
3#63919C211yesmaximal, characteristic, complemented
4C4×#627C212yesmaximal, complemented
5#63874C212yesmaximal
6#63873C211yesmaximal, characteristic, complemented
7#63871C212yesmaximal
8#63870C212yesmaximal, complemented
9#63865C212yesmaximal
10#5578—32nomaximal
11C2×C4×C3⋊D3C2211yescharacteristic
12C2×C4×C3⋊D3C2211yescharacteristic
13C2×C4×C3⋊D3C2211yescharacteristic
14C2×C3×Dic6C2212yes—
15C2×#627C2212yes—
16C32×C42C2211yescharacteristic
17C4×C3⋊Dic3C2211yescharacteristic
18C4×C3⋊Dic3C2211yescharacteristic
19C4×C3⋊Dic3C2211yescharacteristic
20C3×C4⋊Dic3C2212yes—
21C3×Dic3⋊C4C2214yes—
22C3×C4×Dic3C2214yes—
23#3724C2212yes—
24#3724C2212yes—
25#3724C2212yes—
26Dic3⋊Dic3C2214yes—
27#3722C2214yes—
28C3×C4×Q8—32no—
29#946—32no—
30#944—32no—
31#897—32no—
32#896—34no—
33#889—34no—
34#888—32no—
35#872—34no—
36C42×D3—32no—
37C42×D3—61no—
38C4×Dic6—34no—
39C4×Dic6D312yescomplemented
40C22×C3⋊D3C2311yescharacteristic
41C2×C32×C4C2311yescharacteristic
42C2×C32×C4C2311yescharacteristic
43C2×C32×C4C2311yescharacteristic
44C2×C3⋊Dic3C2311yescharacteristic
45C2×C3⋊Dic3C2311yescharacteristic
46C2×C3⋊Dic3C2311yescharacteristic
47C4×C3⋊D3—22no—
48C4×C3⋊D3—22no—
49C4×C3⋊D3Q814yescomplemented
50C2×C3×Dic3C2314yes—
51C2×C3×Dic3C2314yes—
52C3×Dic6—24no—
53#627—24no—
54#533—91noSylow
55C2×C3×Q8—32no—
56C2×C4×D3—32no—
57C2×C4×D3—32no—
58C2×C4×D3—32no—
59C2×C4×D3—61no—
60C2×C4×D3—61no—
61C2×C4×D3—61no—
62C2×Dic6—34no—
63C2×Dic6C2×D312yes—
64C3×C4⋊C4—32no—
65C3×C4⋊C4—34no—
66C3×C42—21no—
67C3×C42—34no—
68C3×C42C2×D312yes—
69(C2×D3)⋊C4—34no—
70(C2×D3)⋊C4—34no—
71C4⋊Dic3—34no—
72C4⋊Dic3C2×D312yes—
73Dic3⋊C4—34no—
74Dic3⋊C4—34no—
75Dic3⋊C4—34no—
76Dic3⋊C4—34no—
77Dic3⋊C4C2×D314yes—
78C4×Dic3—32no—
79C4×Dic3—32no—
80C4×Dic3—32no—
81C4×Dic3—61no—
82C4×Dic3—61no—
83C4×Dic3—61no—
84C4×Dic3C2×D314yes—
85C22×C32C2411yescharacteristic
86C2×C3⋊D3—21no—
87C2×C3⋊D3—21no—
88C2×C3⋊D3C2×Q812yes—
89C32×C4—21no—
90C32×C4C2×Q812yes—
91C32×C4#4112yes—
92C3⋊Dic3—21no—
93C3⋊Dic3C2×Q812yes—
94C3⋊Dic3#4112yes—
95C3×Dic3—24no—
96C3×Dic3—24no—
97C4⋊Q8—91no—
98C4⋊Q8—91no—
99#125—92no—
100C22⋊Q8—92no—
101C22⋊Q8—92no—
102C4×Q8—32no—
103C4×Q8—92no—
104#117—92no—
105C2×C42—91no—
106C22×D3—32no—
107C22×D3—61no—
108C3×Q8—64no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—34no—
113C2×C3×C4—34no—
114C2×C3×C4C22×D312yes—
115C2×C3×C4C22×D312yes—
116C2×C3×C4C22×D312yes—
117C2×Dic3—32no—
118C2×Dic3—32no—
119C2×Dic3—32no—
120C2×Dic3—61no—
121C2×Dic3—61no—
122C2×Dic3—61no—
123C2×Dic3C22×D314yes—
124C2×Dic3C22×D314yes—
125C4×D3—38no—
126C4×D3—64no—
127C4×D3—64no—
128C4×D3—64no—
129C4×D3—64no—
130C4×D3—64no—
131Dic6—24no—
132Dic6—68no—
133C2×C32C22×Q811yescharacteristic
134C2×C32C2×#4111yescharacteristic
135C2×C32C2×#4111yescharacteristic
136C3⋊D3—22no—
137C2×Q8—32no—
138C2×Q8—92no—
139C22×C4—91no—
140C22×C4—91no—
141C22×C4—91no—
142C4⋊C4—34no—
143C4⋊C4—32no—
144C4⋊C4—92no—
145C4⋊C4—92no—
146C4⋊C4—94no—
147C4⋊C4—92no—
148C22⋊C4—94no—
149C42—34no—
150C42—91no—
151C42—91no—
152C42—91no—
153C42D3211yescharacteristic
154C22×C3—21no—
155C22×C3C23×D312yes—
156C2×D3—34no—
157C2×D3—62no—
158C2×D3—62no—
159C2×D3—62no—
160C2×D3—62no—
161C2×D3—62no—
162C3×C4—22no—
163C3×C4—22no—
164C3×C4—22no—
165C3×C4—22no—
166C3×C4—64no—
167C3×C4—64no—
168C3×C4#23514yes—
169C3×C4D3×Q814yes—
170Dic3—24no—
171Dic3—24no—
172Dic3—34no—
173Dic3—34no—
174Dic3—62no—
175Dic3—62no—
176Dic3—62no—
177Dic3—62no—
178C32#53311yescharacteristic, complemented, Sylow
179C23—91no—
180Q8—64no—
181Q8—184no—
182C2×C4—34no—
183C2×C4—34no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—94no—
187C2×C4—91no—
188C2×C4—182no—
189C2×C4—182no—
190C2×C4C2×D3211yescharacteristic
191C2×C4C2×D3211yescharacteristic
192C2×C4C2×D3211yescharacteristic
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3C2×#23512yes—
197C2×C3C2×D3×Q812yes—
198C2×C3D3×#4112yes—
199D3—64no—
200D3—64no—
201C22—92no—
202C22—181no—
203C22—181no—
204C22C22×D3211yescharacteristic
205C4—21no—
206C4—64no—
207C4—64no—
208C4—92no—
209C4—92no—
210C4—181no—
211C4#379712yes—
212C4#379812yes—
213C3—21no—
214C3#557812yescomplemented
215C2—182no—
216C2C2×#379711yescharacteristic
217C2C2×#379811yescharacteristic
218C2#6430611yescharacteristic
subgroupG/H
centerC2×C4C2×D32
commutator, socle, cosocleC22×C32C24
FrattiniC22C22×D32
FittingC32×C42C22
prime radicalC22×C3⋊D3C23
hypercenterC42D32
hypocenterC32#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×Dic6C2semidirect
3. #63919C2semidirect
4. C4×#627C2semidirect
6. #63873C2semidirect
8. #63870C2semidirect
39. C4×Dic6D3semidirect
49. C4×C3⋊D3Q8semidirect
178. C32#533semidirect
214. C3#5578semidirect

Maximal subgroups

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

subgroupindex
C42×C3⋊D32
C3×C4×Dic62
#639192
C4×#6272
#638742
#638732
#638712
#638702
#638652
#55783