Finite Group Databasebeta

← C3×#4979 #10592076

Subgroups — C3×#4979 #10592076

Order 576.

410 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 134 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×C3×Dic6C211yesmaximal, characteristic
2C2×C32×C4⋊C4C211yesmaximal, characteristic
3C2×C3×Dic3⋊C4C212yesmaximal
4C3×C3⋊#95C212yesmaximal
5C3×C3⋊#95C211yesmaximal, characteristic
6C3×#395—31nomaximal
7#4979C311yesmaximal, characteristic, direct product factor
8C22×C32×C4C2211yescharacteristic
9C22×C32×C4C2211yescharacteristic
10C22×C32×C4C2211yescharacteristic
11C22×C3×Dic3C2212yes—
12C22×C3×Dic3C2212yes—
13C2×C3×Dic6—22no—
14C2×C3×Dic6—24no—
15C32×C4⋊C4—22no—
16C3×Dic3⋊C4—24no—
17C22×C3×Q8—31no—
18C22×Dic6C2×C311yescharacteristic
19C2×C3×C4⋊C4—21no—
20C2×C3×C4⋊C4—32no—
21C2×C3×C4⋊C4D311yescharacteristic
22C2×C3×C4⋊C4C2×C311yescharacteristic
23C2×Dic3⋊C4C2×C312yes—
24C3×#95—31no—
25C3×#95—32no—
26C3⋊#95C2×C312yes—
27C3⋊#95C2×C311yescharacteristic
28C23×C32C2311yescharacteristic
29C2×C32×C4—21no—
30C2×C32×C4—21no—
31C2×C32×C4—21no—
32C2×C32×C4—22no—
33C2×C32×C4—22no—
34C2×C32×C4D412yes—
35C2×C32×C4Q812yescomplemented
36C2×C3×Dic3—22no—
37C2×C3×Dic3—22no—
38C2×C3×Dic3—22no—
39C2×C3×Dic3—22no—
40C2×C3×Dic3D414yes—
41C2×C3×Dic3Q814yescomplemented
42C3×Dic6—28no—
43#395—31noSylow
44C2×C3×Q8—64no—
45C2×C3×Q8—62no—
46C22×C3×C4—21no—
47C22×C3×C4—21no—
48C22×C3×C4—21no—
49C22×C3×C4—32no—
50C22×C3×C4—32no—
51C22×C3×C4C2×D311yescharacteristic
52C22×C3×C4C2×D311yescharacteristic
53C22×C3×C4C2×D311yescharacteristic
54C22×C3×C4C22×C311yescharacteristic
55C22×C3×C4C22×C311yescharacteristic
56C22×C3×C4C22×C311yescharacteristic
57C22×Dic3C22×C312yes—
58C22×Dic3C22×C312yes—
59C2×Dic6—22no—
60C2×Dic6—24no—
61C3×C4⋊C4—24no—
62C3×C4⋊C4—22no—
63C3×C4⋊C4—22no—
64C3×C4⋊C4—64no—
65Dic3⋊C4—24no—
66C22×C32C2×D412yes—
67C22×C32C2×D411yescharacteristic
68C22×C32C2×Q811yescharacteristic
69C22×C32C2×Q812yes—
70C22×C32#4111yescharacteristic
71C32×C4—22no—
72C32×C4—22no—
73C32×C4—41no—
74C3×Dic3—24no—
75C3×Dic3—24no—
76C22×Q8—31no—
77C2×C4⋊C4—32no—
78C2×C4⋊C4C3×D311yescharacteristic
79#95—31no—
80#95—32no—
81C23×C3—21no—
82C23×C3C22×D311yescharacteristic
83C23×C3C23×C311yescharacteristic
84C3×Q8—68no—
85C2×C3×C4—22no—
86C2×C3×C4—22no—
87C2×C3×C4—21no—
88C2×C3×C4—22no—
89C2×C3×C4—21no—
90C2×C3×C4—21no—
91C2×C3×C4—22no—
92C2×C3×C4—21no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—21no—
96C2×C3×C4—22no—
97C2×C3×C4—21no—
98C2×C3×C4—22no—
99C2×C3×C4—22no—
100C2×C3×C4—34no—
101C2×C3×C4—34no—
102C2×C3×C4—42no—
103C2×C3×C4—42no—
104C2×C3×C4—62no—
105C2×C3×C4—62no—
106C2×C3×C4—62no—
107C2×C3×C4—62no—
108C2×C3×C4Dic612yescomplemented
109C2×C3×C4#6712yes—
110C2×C3×C4C3×D412yes—
111C2×C3×C4C3×Q812yescomplemented
112C2×Dic3—22no—
113C2×Dic3—22no—
114C2×Dic3—22no—
115C2×Dic3—22no—
116C2×Dic3C3×D414yes—
117C2×Dic3C3×Q814yescomplemented
118Dic6—28no—
119C2×C32#12011yescharacteristic
120C2×C32C22⋊Q812yes—
121C2×C32C22⋊Q811yescharacteristic
122C2×C32C4⋊Q812yes—
123C2×C32C4⋊Q811yescharacteristic
124C2×Q8—64no—
125C2×Q8—62no—
126C22×C4—32no—
127C22×C4—32no—
128C22×C4C2×C3×D311yescharacteristic
129C22×C4C2×C3×D311yescharacteristic
130C22×C4C2×C3×D311yescharacteristic
131C4⋊C4—22no—
132C4⋊C4—64no—
133C22×C3—21no—
134C22×C3—21no—
135C22×C3—22no—
136C22×C3—22no—
137C22×C3—21no—
138C22×C3C2×Dic611yescharacteristic
139C22×C3#23511yescharacteristic
140C22×C3D3×D412yes—
141C22×C3D3×Q812yes—
142C22×C3C2×#6711yescharacteristic
143C22×C3C2×C3×D412yes—
144C22×C3C2×C3×D411yescharacteristic
145C22×C3C2×C3×Q811yescharacteristic
146C22×C3C2×C3×Q812yes—
147C22×C3C3×#4111yescharacteristic
148C3×C4—24no—
149C3×C4—22no—
150C3×C4—22no—
151C3×C4—22no—
152C3×C4—22no—
153C3×C4—42no—
154C3×C4—42no—
155C3×C4—41no—
156C3×C4—41no—
157C3×C4—64no—
158C3×C4—64no—
159Dic3—24no—
160Dic3—24no—
161C32#39511yescharacteristic, complemented, Sylow
162C23C22×C3×D311yescharacteristic
163Q8—68no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—34no—
170C2×C4—34no—
171C2×C4—62no—
172C2×C4—62no—
173C2×C4—62no—
174C2×C4—62no—
175C2×C4C3×Dic612yescomplemented
176C2×C4C3×#6712yes—
177C2×C3—22no—
178C2×C3—22no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3#88812yes—
183C2×C3#89612yes—
184C2×C3#92411yescharacteristic
185C2×C3#93711yescharacteristic
186C2×C3#94411yescharacteristic
187C2×C3C3×#12011yescharacteristic
188C2×C3C3×C22⋊Q812yes—
189C2×C3C3×C22⋊Q811yescharacteristic
190C2×C3C3×C4⋊Q812yes—
191C2×C3C3×C4⋊Q811yescharacteristic
192C22C2×C3×Dic611yescharacteristic
193C22C3×#23511yescharacteristic
194C22C3×D3×D412yes—
195C22C3×D3×Q812yes—
196C22C2×C3×#6711yescharacteristic
197C4—22no—
198C4—22no—
199C4—41no—
200C4—64no—
201C4—64no—
202C3—21no—
203C3#497911yescharacteristic, direct product factor
204C3C3×#39511yescharacteristic, complemented
205C2C3×#88812yes—
206C2C3×#89612yes—
207C2C3×#92411yescharacteristic
208C2C3×#93711yescharacteristic
209C2C3×#94411yescharacteristic
subgroupG/H
centerC23×C3C22×D3
commutator, cosocleC23×C3C23×C3
FrattiniC23C22×C3×D3
FittingC2×C32×C4⋊C4C2
socle, prime radicalC23×C32C23
hypercenterC2×C3×C4⋊C4D3
hypocenterC3C3×#395
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. #4979C3direct (N × H)
35. C2×C32×C4Q8semidirect
41. C2×C3×Dic3Q8semidirect
108. C2×C3×C4Dic6semidirect
111. C2×C3×C4C3×Q8semidirect
117. C2×Dic3C3×Q8semidirect
161. C32#395semidirect
175. C2×C4C3×Dic6semidirect
203. C3#4979direct (N × H)
204. C3C3×#395semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic62
C2×C32×C4⋊C42
C2×C3×Dic3⋊C42
C3×C3⋊#952
C3×#3953
#49793