Finite Group Databasebeta

← #10594245

Subgroups — #10594245

Order 576.

570 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 192 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
2#64086C211yesmaximal, characteristic
3C3×#877C212yesmaximal
4#63957C211yesmaximal, characteristic
5#63955C212yesmaximal
6C4×#627C212yesmaximal, complemented
7#63838C212yesmaximal, complemented
8#63837C214yesmaximal, complemented
9#5516—32nomaximal
10C22×C3⋊Dic3C2211yescharacteristic
11C22×C3×Dic3C2212yes—
12C2×#627C418yescomplemented
13C2×#627C2212yes—
14C2×#627C2211yescharacteristic
15C2×#627C2211yescharacteristic
16C32×C22⋊C4C2211yescharacteristic
17#3757C2211yescharacteristic
18#3750C2212yes—
19C4×C3⋊Dic3C2212yes—
20C3×#217C2212yes—
21C3×Dic3⋊C4C2214yes—
22C3×C4×Dic3C2214yes—
23#3724C2212yes—
24Dic3⋊Dic3C2214yes—
25Dic32C2212yes—
26Dic32C2214yes—
27C22×Dic6—32no—
28C3×#117—32no—
29#926—32no—
30#887—34no—
31#887—34no—
32#877—32no—
33#877—32no—
34#877—32no—
35#877—61no—
36#877D312yes—
37C4×Dic6—34no—
38C4×Dic6—34no—
39C23×C32C2311yescharacteristic
40C2×C32×C4C2312yes—
41C2×C3⋊Dic3C2×C414yes—
42C2×C3⋊Dic3C2312yes—
43C2×C3⋊Dic3C2311yescharacteristic
44C2×C3⋊Dic3C2311yescharacteristic
45C2×C3×Dic3C2×C418yes—
46C2×C3×Dic3C2314yes—
47C2×C3×Dic3C2312yes—
48C2×C3×Dic3C2312yes—
49#627C2×C418yes—
50#627C2×C414yes—
51#627C2×C414yes—
52#519—91noSylow
53C22×C3×C4—32no—
54C22×Dic3—32no—
55C22×Dic3—61no—
56C22×Dic3C2×D312yes—
57C2×Dic6—316no—
58C2×Dic6—32no—
59C2×Dic6—32no—
60C2×Dic6—32no—
61C2×Dic6—32no—
62C3×C4⋊C4—34no—
63C3×C22⋊C4—21no—
64C3×C22⋊C4—32no—
65C3×C22⋊C4C2×D312yes—
66C3×C42—34no—
67#217—32no—
68#217—61no—
69#217C2×D312yes—
70C4⋊Dic3—34no—
71Dic3⋊C4—34no—
72Dic3⋊C4—34no—
73Dic3⋊C4—34no—
74Dic3⋊C4—62no—
75Dic3⋊C4C2×D314yes—
76C4×Dic3—34no—
77C4×Dic3—34no—
78C4×Dic3—34no—
79C4×Dic3—34no—
80C4×Dic3—62no—
81C4×Dic3C2×D314yes—
82C22×C32—22no—
83C22×C32C22×C412yes—
84C22×C32C2411yescharacteristic
85C32×C4—22no—
86C3⋊Dic3—22no—
87C3⋊Dic3C22×C412yes—
88C3⋊Dic3C22×C412yes—
89C3×Dic3—24no—
90C3×Dic3C22×C414yes—
91C3×Dic3C22×C414yes—
92C22×Q8—91no—
93C4×Q8—92no—
94C4×Q8—94no—
95C4×Q8—92no—
96#117—32no—
97#117—91no—
98#117—92no—
99#117—91no—
100C23×C3—21no—
101C23×C3C22×D312yes—
102C2×C3×C4—22no—
103C2×C3×C4—38no—
104C2×C3×C4—32no—
105C2×C3×C4—32no—
106C2×C3×C4—34no—
107C2×C3×C4C22×D314yes—
108C2×Dic3—38no—
109C2×Dic3—32no—
110C2×Dic3—32no—
111C2×Dic3—34no—
112C2×Dic3—64no—
113C2×Dic3—61no—
114C2×Dic3—61no—
115C2×Dic3—62no—
116C2×Dic3C4×D318yes—
117C2×Dic3C22×D314yes—
118C2×Dic3C22×D312yes—
119C2×Dic3C22×D312yes—
120Dic6—38no—
121Dic6—38no—
122Dic6—38no—
123Dic6—38no—
124C2×C32—22no—
125C2×C32C23×C411yescharacteristic
126C2×C322−1+412yes—
127C2×Q8—91no—
128C2×Q8—92no—
129C2×Q8—91no—
130C2×Q8—98no—
131C22×C4—32no—
132C22×C4—91no—
133C4⋊C4—34no—
134C4⋊C4—92no—
135C4⋊C4—94no—
136C4⋊C4—92no—
137C22⋊C4—32no—
138C22⋊C4—91no—
139C22⋊C4D3211yescharacteristic
140C42—34no—
141C42—94no—
142C42—92no—
143C42—92no—
144C22×C3—24no—
145C22×C3—21no—
146C22×C3—22no—
147C22×C3—42no—
148C22×C3C2×C4×D314yes—
149C22×C3C23×D312yes—
150C3×C4—24no—
151C3×C4—34no—
152C3×C4—34no—
153C3×C4—42no—
154C3×C4—64no—
155Dic3—24no—
156Dic3—34no—
157Dic3—34no—
158Dic3—62no—
159Dic3—62no—
160Dic3—64no—
161Dic3—122no—
162Dic3C2×C4×D314yes—
163Dic3C2×C4×D314yes—
164C32#51911yescharacteristic, complemented, Sylow
165C23C2×D3211yescharacteristic
166Q8—94no—
167Q8—98no—
168Q8—94no—
169C2×C4—32no—
170C2×C4—32no—
171C2×C4—38no—
172C2×C4—34no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—94no—
176C2×C4—92no—
177C2×C4C2×D3212yes—
178C2×C3—24no—
179C2×C3—21no—
180C2×C3—22no—
181C2×C3—42no—
182C2×C3C22×C4×D312yes—
183C2×C3#101014yes—
184C22—22no—
185C22C4×D3212yes—
186C22C22×D3211yescharacteristic
187C4—22no—
188C4—34no—
189C4—34no—
190C4—64no—
191C4—92no—
192C4—92no—
193C4—182no—
194C3—21no—
195C3#551612yescomplemented
196C2—22no—
197C2C2×C4×D3211yescharacteristic
198C2#6430912yes—
subgroupG/H
center, FrattiniC22C22×D32
commutatorC2×C32C23×C4
FittingC32×C22⋊C4C22
socle, cosocleC22×C32C24
prime radicalC23×C32C23
hypercenterC22⋊C4D32
hypocenterC32#519
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
6. C4×#627C2semidirect
7. #63838C2semidirect
8. #63837C2semidirect
12. C2×#627C4semidirect
164. C32#519semidirect
195. C3#5516semidirect

Maximal subgroups

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

subgroupindex
C22×#6272
#640862
C3×#8772
#639572
#639552
C4×#6272
#638382
#638372
#55163