Finite Group Databasebeta

← #10591203

Subgroups — #10591203

Order 576.

438 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 100 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×#3752C211yesmaximal, characteristic
2C2×C3×Dic3⋊C4C212yesmaximal, complemented
3C2×#3724C211yesmaximal, characteristic, complemented
4C2×#3722C212yesmaximal
5#63579C211yesmaximal, characteristic, complemented
6#4993—32nomaximal
7C23×C3⋊D3C2211yescharacteristic
8C22×C32×C4C2211yescharacteristic
9C22×C3⋊Dic3C2211yescharacteristic
10C22×C3×Dic3C2212yes—
11C22×C3×Dic3C2212yes—
12#3752—22no—
13C3×Dic3⋊C4—24no—
14#3724—22no—
15#3722—24no—
16C2×C3×C4⋊C4—32no—
17C2×(C2×D3)⋊C4—32no—
18C2×(C2×D3)⋊C4—32no—
19C2×(C2×D3)⋊C4—32no—
20C2×(C2×D3)⋊C4—61no—
21C2×Dic3⋊C4—32no—
22C2×Dic3⋊C4D312yescomplemented
23C3⋊#95—32no—
24C23×C32C2311yescharacteristic
25C22×C3⋊D3—21no—
26C22×C3⋊D3—21no—
27C22×C3⋊D3—22no—
28C22×C3⋊D3—22no—
29C22×C3⋊D3Q812yes—
30C2×C32×C4—21no—
31C2×C32×C4—22no—
32C2×C3⋊Dic3—22no—
33C2×C3⋊Dic3D412yes—
34C2×C3×Dic3—22no—
35C2×C3×Dic3—22no—
36C2×C3×Dic3—22no—
37C2×C3×Dic3—22no—
38C2×C3×Dic3—22no—
39C2×C3×Dic3D414yes—
40#399—91noSylow
41C23×D3—32no—
42C23×D3—61no—
43C22×C3×C4—21no—
44C22×C3×C4—32no—
45C22×C3×C4—32no—
46C22×C3×C4C2×D312yes—
47C22×Dic3—32no—
48C22×Dic3—61no—
49C22×Dic3C2×D312yes—
50C22×Dic3C2×D312yes—
51C3×C4⋊C4—64no—
52(C2×D3)⋊C4—64no—
53(C2×D3)⋊C4—64no—
54(C2×D3)⋊C4—64no—
55(C2×D3)⋊C4—64no—
56Dic3⋊C4—24no—
57Dic3⋊C4—64no—
58C22×C32C2×D411yescharacteristic
59C22×C32C2×D412yes—
60C22×C32C2×Q811yescharacteristic
61C22×C32#4111yescharacteristic
62C22×C32#4112yes—
63C2×C3⋊D3—22no—
64C2×C3⋊D3—24no—
65C2×C3⋊D3—41no—
66C2×C3⋊D3—42no—
67C2×C3⋊D3—41no—
68C32×C4—41no—
69C3⋊Dic3—22no—
70C3×Dic3—24no—
71C3×Dic3—42no—
72C2×C4⋊C4—32no—
73C2×C4⋊C4—91no—
74C2×C22⋊C4—92no—
75C2×C22⋊C4—91no—
76#95—91no—
77C23×C3—21no—
78C23×C3C22×D312yes—
79C22×D3—34no—
80C22×D3—62no—
81C22×D3—62no—
82C22×D3—62no—
83C22×D3—62no—
84C22×D3—62no—
85C22×D3—62no—
86C22×D3—62no—
87C22×D3—62no—
88C22×D3—62no—
89C22×D3—122no—
90C22×D3—122no—
91C2×C3×C4—22no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—34no—
96C2×C3×C4—42no—
97C2×C3×C4—62no—
98C2×C3×C4—62no—
99C2×C3×C4—62no—
100C2×C3×C4—62no—
101C2×C3×C4—62no—
102C2×Dic3—22no—
103C2×Dic3—22no—
104C2×Dic3—22no—
105C2×Dic3—22no—
106C2×Dic3—22no—
107C2×Dic3—34no—
108C2×Dic3—62no—
109C2×Dic3—62no—
110C2×Dic3—62no—
111C2×Dic3—122no—
112C2×Dic3#6714yes—
113C2×C32C22⋊Q811yescharacteristic
114C2×C32C22⋊Q812yes—
115C2×C32#12311yescharacteristic
116C2×C32#12312yes—
117C2×C32#12711yescharacteristic
118C3⋊D3—42no—
119C24—91no—
120C22×C4—32no—
121C22×C4—32no—
122C22×C4—91no—
123C22×C4D3211yescharacteristic
124C4⋊C4—64no—
125C4⋊C4—182no—
126C22⋊C4—182no—
127C22⋊C4—184no—
128C22×C3—21no—
129C22×C3—21no—
130C22×C3—22no—
131C22×C3—22no—
132C22×C3—21no—
133C22×C3#23512yes—
134C22×C3#23512yes—
135C22×C3D3×D412yes—
136C22×C3D3×D412yes—
137C22×C3D3×Q812yes—
138C22×C3#23912yes—
139C22×C3C2×#6712yes—
140C2×D3—64no—
141C2×D3—64no—
142C2×D3—64no—
143C2×D3—64no—
144C2×D3—124no—
145C2×D3—124no—
146C2×D3—122no—
147C2×D3—122no—
148C2×D3—122no—
149C2×D3—122no—
150C2×D3—122no—
151C2×D3—122no—
152C3×C4—42no—
153C3×C4—42no—
154C3×C4—64no—
155C3×C4—122no—
156Dic3—24no—
157Dic3—42no—
158Dic3—64no—
159Dic3—122no—
160C32#39911yescharacteristic, complemented, Sylow
161C23—92no—
162C23—181no—
163C23—182no—
164C23—182no—
165C23—181no—
166C23C2×D3211yescharacteristic
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—34no—
170C2×C4—62no—
171C2×C4—62no—
172C2×C4—62no—
173C2×C4—62no—
174C2×C4—62no—
175C2×C4—92no—
176C2×C4—182no—
177C2×C3—22no—
178C2×C3—21no—
179C2×C3—22no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3#89412yes—
183C2×C3#89412yes—
184C2×C3#89612yes—
185C2×C3#89612yes—
186C2×C3#92912yes—
187C2×C3#94012yes—
188C2×C3#94612yes—
189D3—124no—
190D3—124no—
191C22—182no—
192C22—184no—
193C22—362no—
194C22—361no—
195C22—361no—
196C22#379711yescharacteristic
197C22#379811yescharacteristic
198C22#379912yes—
199C22D3×#6712yes—
200C22#381111yescharacteristic
201C4—41no—
202C4—64no—
203C4—122no—
204C4—182no—
205C3—21no—
206C3#499312yescomplemented
207C2—362no—
208C2#6385012yes—
209C2#6386511yescharacteristic
210C2#6388812yes—
211C2#6389711yescharacteristic
212C2#6397911yescharacteristic
subgroupG/H
center, FrattiniC23C2×D32
commutator, socle, cosocleC23×C32C23
FittingC22×C32×C4C22
prime radicalC23×C3⋊D3C22
hypercenterC22×C4D32
hypocenterC32#399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×Dic3⋊C4C2semidirect
3. C2×#3724C2semidirect
5. #63579C2semidirect
22. C2×Dic3⋊C4D3semidirect
160. C32#399semidirect
206. C3#4993semidirect

Maximal subgroups

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

subgroupindex
C2×#37522
C2×C3×Dic3⋊C42
C2×#37242
C2×#37222
#635792
#49933