Finite Group Databasebeta

← #10594597

Subgroups — #10594597

Order 576.

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

normal subgroups only

This group has 435 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
1#64096C211yesmaximal, characteristic
2C3×#889C212yesmaximal
3#63919C211yesmaximal, characteristic
4C4×#627C211yesmaximal, characteristic
5#63870C211yesmaximal, characteristic
6#63870C211yesmaximal, characteristic
7#63846C212yesmaximal
8#63840C212yesmaximal
9#63838C211yesmaximal, characteristic
10#63838C211yesmaximal, characteristic
11#63837C212yesmaximal
12#5685—32nomaximal
13C2×#634C2211yescharacteristic
14C2×#627C2212yes—
15C2×#627C2211yescharacteristic
16C32×C4⋊C4C2211yescharacteristic
17#3750C2211yescharacteristic
18#3750C2211yescharacteristic
19C4×C3⋊Dic3C2211yescharacteristic
20C4×C3⋊Dic3C2211yescharacteristic
21C4×C3⋊Dic3C2211yescharacteristic
22C3×C4⋊Dic3C2212yes—
23C3×Dic3⋊C4C2212yes—
24C3×Dic3⋊C4C2212yes—
25C3×Dic3⋊C4C2212yes—
26C3×Dic3⋊C4C2212yes—
27C3×C4×Dic3C2212yes—
28#3724C2211yescharacteristic
29#3724C2211yescharacteristic
30#3724C2211yescharacteristic
31Dic3⋊Dic3C2212yes—
32Dic3⋊Dic3C2212yes—
33Dic3⋊Dic3C2212yes—
34Dic32C2212yes—
35Dic32C2212yes—
36C3×#125—32no—
37#890—32no—
38#889—32no—
39#889—32no—
40#889—32no—
41#889D312yes—
42#888—32no—
43#888—32no—
44#888—32no—
45#887—32no—
46#887—32no—
47#887—32no—
48#887—32no—
49#887—61no—
50C4×Dic6—32no—
51C4×Dic6—32no—
52C2×C32×C4C2311yescharacteristic
53C2×C32×C4C2311yescharacteristic
54C2×C32×C4C2311yescharacteristic
55C2×C3⋊Dic3C2311yescharacteristic
56C2×C3⋊Dic3C2311yescharacteristic
57C2×C3⋊Dic3C2311yescharacteristic
58C2×C3⋊Dic3C2311yescharacteristic
59#634—22no—
60C2×C3×Dic3C2312yes—
61C2×C3×Dic3C2312yes—
62C2×C3×Dic3C2312yes—
63C2×C3×Dic3C2312yes—
64#627—24no—
65#627Q814yescomplemented
66#557—91noSylow
67C2×Dic6—32no—
68C2×Dic6—32no—
69C2×Dic6—32no—
70C2×Dic6—32no—
71C2×Dic6—61no—
72C3×C4⋊C4—21no—
73C3×C4⋊C4—32no—
74C3×C4⋊C4—32no—
75C3×C4⋊C4—32no—
76C3×C4⋊C4—32no—
77C3×C4⋊C4—32no—
78C3×C4⋊C4C2×D312yes—
79C3×C42—32no—
80C4⋊Dic3—32no—
81C4⋊Dic3—32no—
82C4⋊Dic3—32no—
83C4⋊Dic3C2×D312yes—
84Dic3⋊C4—32no—
85Dic3⋊C4—32no—
86Dic3⋊C4—32no—
87Dic3⋊C4—32no—
88Dic3⋊C4—32no—
89Dic3⋊C4—32no—
90Dic3⋊C4—32no—
91Dic3⋊C4—32no—
92Dic3⋊C4—61no—
93Dic3⋊C4—61no—
94Dic3⋊C4C2×D312yes—
95Dic3⋊C4C2×D312yes—
96Dic3⋊C4C2×D312yes—
97Dic3⋊C4C2×D312yes—
98C4×Dic3—32no—
99C4×Dic3—32no—
100C4×Dic3—32no—
101C4×Dic3—32no—
102C4×Dic3—32no—
103C4×Dic3—32no—
104C4×Dic3—32no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3C2×D312yes—
109C22×C32C2411yescharacteristic
110C32×C4—21no—
111C32×C4—21no—
112C32×C4—21no—
113C3⋊Dic3—21no—
114C3⋊Dic3—21no—
115C3⋊Dic3C2×Q812yes—
116C3⋊Dic3#4112yes—
117C3×Dic3—22no—
118C3×Dic3—22no—
119C3×Dic3—22no—
120C3×Dic3C2×Q814yes—
121C4⋊Q8—92no—
122C4⋊Q8—91no—
123#125—32no—
124#125—91no—
125#125—91no—
126#125—92no—
127C4×Q8—91no—
128C4×Q8—92no—
129C4×Q8—91no—
130C4×Q8—91no—
131C4×Q8—91no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—32no—
136C2×C3×C4—32no—
137C2×C3×C4—32no—
138C2×C3×C4—32no—
139C2×C3×C4C22×D312yes—
140C2×C3×C4C22×D312yes—
141C2×C3×C4C22×D312yes—
142C2×Dic3—32no—
143C2×Dic3—32no—
144C2×Dic3—32no—
145C2×Dic3—32no—
146C2×Dic3—61no—
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C2×Dic3C22×D312yes—
151C2×Dic3C22×D312yes—
152C2×Dic3C22×D312yes—
153C2×Dic3C22×D312yes—
154Dic6—38no—
155Dic6—64no—
156Dic6—64no—
157Dic6—64no—
158Dic6—64no—
159C2×C32C22×Q811yescharacteristic
160C2×C32C2×#4111yescharacteristic
161C2×C322−1+411yescharacteristic
162C2×Q8—91no—
163C2×Q8—92no—
164C2×Q8—91no—
165C4⋊C4—32no—
166C4⋊C4—32no—
167C4⋊C4—32no—
168C4⋊C4—32no—
169C4⋊C4—32no—
170C4⋊C4—91no—
171C4⋊C4—92no—
172C4⋊C4—91no—
173C4⋊C4—91no—
174C4⋊C4—92no—
175C4⋊C4—92no—
176C4⋊C4—91no—
177C4⋊C4—91no—
178C4⋊C4D3211yescharacteristic
179C42—32no—
180C42—92no—
181C42—92no—
182C42—91no—
183C42—91no—
184C42—91no—
185C22×C3—21no—
186C22×C3C23×D312yes—
187C3×C4—22no—
188C3×C4—22no—
189C3×C4—22no—
190C3×C4—22no—
191C3×C4—34no—
192C3×C4—41no—
193C3×C4—41no—
194C3×C4—62no—
195C3×C4—62no—
196C3×C4—62no—
197Dic3—22no—
198Dic3—22no—
199Dic3—22no—
200Dic3—34no—
201Dic3—34no—
202Dic3—62no—
203Dic3—62no—
204Dic3—62no—
205Dic3—62no—
206Dic3—62no—
207Dic3—121no—
208Dic3D3×Q814yes—
209C32#55711yescharacteristic, complemented, Sylow
210Q8—94no—
211Q8—182no—
212Q8—184no—
213C2×C4—32no—
214C2×C4—32no—
215C2×C4—32no—
216C2×C4—32no—
217C2×C4—91no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—91no—
221C2×C4C2×D3211yescharacteristic
222C2×C4C2×D3211yescharacteristic
223C2×C4C2×D3211yescharacteristic
224C2×C3—21no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3C2×D3×Q812yes—
228C2×C3D3×#4112yes—
229C2×C3#101012yes—
230C22C22×D3211yescharacteristic
231C4—21no—
232C4—21no—
233C4—21no—
234C4—34no—
235C4—62no—
236C4—62no—
237C4—62no—
238C4—92no—
239C4—92no—
240C4—181no—
241C4—181no—
242C3—21no—
243C3#568512yescomplemented
244C2#6430611yescharacteristic
245C2#6430911yescharacteristic
246C2D32×Q811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, prime radical, cosocleC22×C32C24
FittingC32×C4⋊C4C22
hypercenterC4⋊C4D32
hypocenterC32#557
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
65. #627Q8semidirect
209. C32#557semidirect
243. C3#5685semidirect

Maximal subgroups

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

subgroupindex
#640962
C3×#8892
#639192
C4×#6272
#638702
#638462
#638402
#638382
#638372
#56853