Finite Group Databasebeta

← #10591715

Subgroups — #10591715

Order 576.

438 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3757C211yesmaximal, characteristic
2C2×C3×#217C212yesmaximal
3C2×#3724C211yesmaximal, characteristic, complemented
4C2×Dic3⋊Dic3C212yesmaximal, complemented
5#63579C211yesmaximal, characteristic, complemented
6#4949—32nomaximal
7C24×C32C2211yescharacteristic
8C22×C3⋊Dic3C2211yescharacteristic
9C22×C3⋊Dic3C2211yescharacteristic
10C22×C3×Dic3C2212yes—
11C22×C3×Dic3C2212yes—
12#3757—22no—
13C3×#217—24no—
14#3724—22no—
15Dic3⋊Dic3—24no—
16C2×C3×C22⋊C4—32no—
17C2×#217—32no—
18C2×#217—61no—
19C2×#217D312yes—
20C2×C4⋊Dic3—32no—
21C2×Dic3⋊C4—32no—
22C2×Dic3⋊C4—32no—
23C3⋊#95—32no—
24C23×C32—21no—
25C23×C32—21no—
26C23×C32—22no—
27C23×C32—22no—
28C23×C32Q812yes—
29C23×C32C2311yescharacteristic
30C2×C3⋊Dic3—21no—
31C2×C3⋊Dic3—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
41C24×C3—21no—
42C24×C3C2×D312yes—
43C22×C3×C4—32no—
44C22×C3×C4—32no—
45C22×Dic3—32no—
46C22×Dic3—32no—
47C22×Dic3—61no—
48C22×Dic3—61no—
49C22×Dic3C2×D312yes—
50C22×Dic3C2×D312yes—
51C3×C22⋊C4—64no—
52#217—24no—
53#217—64no—
54#217—64no—
55C4⋊Dic3—64no—
56Dic3⋊C4—64no—
57Dic3⋊C4—64no—
58C22×C32—22no—
59C22×C32—24no—
60C22×C32—41no—
61C22×C32—42no—
62C22×C32—41no—
63C22×C32C2×D411yescharacteristic
64C22×C32C2×D412yes—
65C22×C32C2×Q811yescharacteristic
66C22×C32#4112yes—
67C22×C32#4111yescharacteristic
68C3⋊Dic3—22no—
69C3⋊Dic3—41no—
70C3×Dic3—24no—
71C3×Dic3—42no—
72C2×C4⋊C4—91no—
73C2×C4⋊C4—92no—
74C2×C22⋊C4—32no—
75C2×C22⋊C4—91no—
76#95—91no—
77C23×C3—22no—
78C23×C3—22no—
79C23×C3—22no—
80C23×C3—22no—
81C23×C3—22no—
82C23×C3—22no—
83C23×C3—22no—
84C23×C3—22no—
85C23×C3—22no—
86C23×C3—21no—
87C23×C3—42no—
88C23×C3—42no—
89C23×C3Dic614yes—
90C23×C3C22×D312yes—
91C2×C3×C4—34no—
92C2×C3×C4—62no—
93C2×C3×C4—62no—
94C2×C3×C4—62no—
95C2×C3×C4—62no—
96C2×C3×C4—62no—
97C2×Dic3—22no—
98C2×Dic3—22no—
99C2×Dic3—22no—
100C2×Dic3—22no—
101C2×Dic3—22no—
102C2×Dic3—34no—
103C2×Dic3—62no—
104C2×Dic3—62no—
105C2×Dic3—62no—
106C2×Dic3—62no—
107C2×Dic3—62no—
108C2×Dic3—62no—
109C2×Dic3—62no—
110C2×Dic3—122no—
111C2×Dic3—122no—
112C2×Dic3#6714yes—
113C2×C32—42no—
114C2×C32C22⋊Q811yescharacteristic
115C2×C32C22⋊Q812yes—
116C2×C32#12311yescharacteristic
117C2×C32#12312yes—
118C2×C32#12711yescharacteristic
119C24D3211yescharacteristic
120C22×C4—32no—
121C22×C4—32no—
122C22×C4—91no—
123C22×C4—91no—
124C4⋊C4—184no—
125C4⋊C4—182no—
126C22⋊C4—64no—
127C22⋊C4—182no—
128C22×C3—24no—
129C22×C3—24no—
130C22×C3—24no—
131C22×C3—24no—
132C22×C3—22no—
133C22×C3—21no—
134C22×C3—21no—
135C22×C3—22no—
136C22×C3—21no—
137C22×C3—44no—
138C22×C3—44no—
139C22×C3—42no—
140C22×C3—42no—
141C22×C3—42no—
142C22×C3—42no—
143C22×C3—42no—
144C22×C3—42no—
145C22×C3C2×Dic612yes—
146C22×C3#23512yes—
147C22×C3D3×D412yes—
148C22×C3D3×D412yes—
149C22×C3#23712yes—
150C22×C3#23712yes—
151C22×C3C2×#6712yes—
152C3×C4—64no—
153C3×C4—122no—
154Dic3—24no—
155Dic3—42no—
156Dic3—64no—
157Dic3—122no—
158Dic3—122no—
159Dic3—122no—
160C32#39911yescharacteristic, complemented, Sylow
161C23—22no—
162C23—21no—
163C23—22no—
164C23—21no—
165C23#62712yes—
166C23C2×D3211yescharacteristic
167C2×C4—34no—
168C2×C4—62no—
169C2×C4—62no—
170C2×C4—62no—
171C2×C4—62no—
172C2×C4—62no—
173C2×C4—92no—
174C2×C4—182no—
175C2×C4—182no—
176C2×C4—181no—
177C2×C3—22no—
178C2×C3—22no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—44no—
183C2×C3—44no—
184C2×C3#87812yes—
185C2×C3#87812yes—
186C2×C3#88312yes—
187C2×C3#88312yes—
188C2×C3#92412yes—
189C2×C3#93512yes—
190C2×C3#94012yes—
191C22—24no—
192C22—22no—
193C22—42no—
194C22—41no—
195C22—41no—
196C22#380412yes—
197C22#380511yescharacteristic
198C22C2×#62711yescharacteristic
199C22D3×#6712yes—
200C22#381111yescharacteristic
201C4—64no—
202C4—122no—
203C4—182no—
204C4—361no—
205C3—21no—
206C3#494912yescomplemented
207C2—42no—
208C2#6396412yes—
209C2#6396912yes—
210C2#6397511yescharacteristic
211C2#6397911yescharacteristic
212C2#6398211yescharacteristic
subgroupG/H
center, FrattiniC23C2×D32
commutator, socle, cosocleC23×C32C23
Fitting, prime radicalC24×C32C22
hypercenterC24D32
hypocenterC32#399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
3. C2×#3724C2semidirect
4. C2×Dic3⋊Dic3C2semidirect
5. #63579C2semidirect
160. C32#399semidirect
206. C3#4949semidirect

Maximal subgroups

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

subgroupindex
C2×#37572
C2×C3×#2172
C2×#37242
C2×Dic3⋊Dic32
#635792
#49493