Finite Group Databasebeta

← #10594084

Subgroups — #10594084

Order 576.

578 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C22×#627C211yesmaximal, characteristic, complemented
2C2×#3805C211yesmaximal, characteristic
3#64086C211yesmaximal, characteristic, complemented
4C3×#886C212yesmaximal, complemented
5#63961C212yesmaximal, complemented
6#63919C212yesmaximal, complemented
7#63915C212yesmaximal, complemented
8#63899C214yesmaximal, complemented
9#5648—32nomaximal
10C22×C3⋊Dic3C2211yescharacteristic
11C2×C3×#67C2212yes—
12C22×C3×Dic3C2212yes—
13C2×#627—24no—
14C2×#627C2211yescharacteristic
15C2×#627C2212yes—
16C2×#627C2212yes—
17C2×#625C2211yescharacteristic
18#3805—24no—
19C2×D3×Dic3C2212yes—
20C32×C22⋊C4C2211yescharacteristic
21#3757C2211yescharacteristic
22#3750C2212yes—
23C4×C3⋊Dic3C2212yes—
24C3×(C2×D3)⋊C4C2214yes—
25C3×C4⋊Dic3C2214yes—
26#3724C2214yes—
27(C2×D3)⋊Dic3C2214yes—
28C2×#237—32no—
29C22×Dic6—32no—
30C3×#123—32no—
31#935—32no—
32#929—32no—
33#896—34no—
34#888—34no—
35#886D312yescomplemented
36#885—34no—
37#878—34no—
38#877—32no—
39#877—61no—
40C23×C32C2311yescharacteristic
41C22×C3×D3C2312yes—
42C2×C32×C4C2312yes—
43C2×C3⋊Dic3D414yes—
44C2×C3⋊Dic3C2312yes—
45C2×C3⋊Dic3C2311yescharacteristic
46C2×C3⋊Dic3C2311yescharacteristic
47C3×#67—24no—
48C2×C3×Dic3—24no—
49C2×C3×Dic3C2314yes—
50C2×C3×Dic3C2312yes—
51#627—22no—
52#627—24no—
53#627—24no—
54#625—22no—
55D3×Dic3—24no—
56#536—91noSylow
57C2×C3×D4—32no—
58C22×C3×C4—32no—
59C2×#67—32no—
60C2×#67C2×D312yes—
61C22×Dic3—32no—
62C22×Dic3—32no—
63C22×Dic3—61no—
64C22×Dic3C2×D312yes—
65#237—68no—
66C2×C4×D3—32no—
67C2×Dic6—34no—
68C2×Dic6—34no—
69C2×Dic6—32no—
70C2×Dic6—68no—
71C3×C4⋊C4—34no—
72C3×C22⋊C4—21no—
73C3×C22⋊C4—34no—
74C3×C22⋊C4C2×D312yes—
75#217—32no—
76#217—34no—
77#217—61no—
78(C2×D3)⋊C4—34no—
79(C2×D3)⋊C4C2×D314yes—
80C4⋊Dic3C2×D314yes—
81Dic3⋊C4—34no—
82Dic3⋊C4—34no—
83Dic3⋊C4—34no—
84Dic3⋊C4—62no—
85C4×Dic3—34no—
86C4×Dic3—62no—
87C22×C32—22no—
88C22×C32C2×D412yes—
89C22×C32C2411yescharacteristic
90C2×C3×D3—22no—
91C2×C3×D3—24no—
92C32×C4—22no—
93C3⋊Dic3—22no—
94C3⋊Dic3C2×D412yes—
95C3⋊Dic3C2×D412yes—
96C3×Dic3—22no—
97C3×Dic3—24no—
98C2×#41—91no—
99C22×Q8—91no—
100C4⋊Q8—92no—
101#124—92no—
102#123—32no—
103#123—92no—
104C22⋊Q8—94no—
105#117—91no—
106C23×C3—21no—
107C23×C3—32no—
108C23×C3C22×D312yes—
109C22×D3C22×D312yes—
110C3×D4—64no—
111C2×C3×C4—22no—
112C2×C3×C4—32no—
113C2×C3×C4—34no—
114C2×C3×C4—64no—
115C2×C3×C4C22×D314yes—
116#67—24no—
117#67—64no—
118C2×Dic3—24no—
119C2×Dic3—38no—
120C2×Dic3—32no—
121C2×Dic3—32no—
122C2×Dic3—34no—
123C2×Dic3—64no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C2×Dic3—62no—
127C2×Dic3—64no—
128C2×Dic3C22×D312yes—
129C2×Dic3C22×D314yes—
130C4×D3—64no—
131Dic6—68no—
132Dic6—68no—
133Dic6—64no—
134C2×C32—22no—
135C2×C32C22×D411yescharacteristic
136C2×C322−1+412yes—
137C3×D3—42no—
138#41—184no—
139C2×Q8—92no—
140C2×Q8—92no—
141C2×Q8—91no—
142C2×Q8—184no—
143C2×D4—32no—
144C2×D4—91no—
145C22×C4—32no—
146C22×C4—92no—
147C22×C4—91no—
148C4⋊C4—34no—
149C4⋊C4—94no—
150C4⋊C4—92no—
151C22⋊C4—34no—
152C22⋊C4—94no—
153C22⋊C4—91no—
154C22⋊C4D3211yescharacteristic
155C42—92no—
156C22×C3—24no—
157C22×C3—21no—
158C22×C3—22no—
159C22×C3—42no—
160C22×C3—62no—
161C22×C3—64no—
162C22×C3D3×D414yes—
163C22×C3C23×D312yes—
164C2×D3—22no—
165C2×D3—24no—
166C3×C4—24no—
167C3×C4—42no—
168C3×C4—64no—
169C3×C4—62no—
170Dic3—24no—
171Dic3—22no—
172Dic3—34no—
173Dic3—34no—
174Dic3—62no—
175Dic3—62no—
176Dic3—64no—
177Dic3—122no—
178C32#53611yescharacteristic, complemented, Sylow
179C23—32no—
180C23C2×D3211yescharacteristic
181Q8—184no—
182Q8—184no—
183Q8—182no—
184D4—64no—
185D4—182no—
186C2×C4—34no—
187C2×C4—32no—
188C2×C4—64no—
189C2×C4—91no—
190C2×C4—91no—
191C2×C4—94no—
192C2×C4—92no—
193C2×C4—184no—
194C2×C4C2×D3212yes—
195C2×C3—24no—
196C2×C3—21no—
197C2×C3—22no—
198C2×C3—42no—
199C2×C3—122no—
200C2×C3C2×D3×D412yes—
201C2×C3#101014yes—
202D3—42no—
203C22—22no—
204C22—62no—
205C22—64no—
206C22#380212yes—
207C22C22×D3211yescharacteristic
208C4—22no—
209C4—64no—
210C4—62no—
211C4—92no—
212C4—92no—
213C4—182no—
214C3—21no—
215C3#564812yescomplemented
216C2—22no—
217C2—122no—
218C2C2×#380211yescharacteristic
219C2#6430912yes—
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
prime radicalC2×#3805C2
hypercenterC22⋊C4D32
hypocenterC32#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#627C2semidirect
3. #64086C2semidirect
4. C3×#886C2semidirect
5. #63961C2semidirect
6. #63919C2semidirect
7. #63915C2semidirect
8. #63899C2semidirect
35. #886D3semidirect
178. C32#536semidirect
215. C3#5648semidirect

Maximal subgroups

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

subgroupindex
C22×#6272
C2×#38052
#640862
C3×#8862
#639612
#639192
#639152
#638992
#56483