Finite Group Databasebeta

← #10590562

Subgroups — #10590562

Order 576.

201 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 201 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C3×#890C211yesmaximal, characteristic
2#63866C211yesmaximal, characteristic
3#63637C211yesmaximal, characteristic
4C3×#810C211yesmaximal, characteristic
5#63567C211yesmaximal, characteristic
6#63565C211yesmaximal, characteristic
7#63554C211yesmaximal, characteristic
8#5069—31nomaximal
9#4797—31nomaximal
10C2×#634C2211yescharacteristic
11C2×C3×Dic6C2211yescharacteristic
12C32×C4⋊C4C2211yescharacteristic
13C2×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×C4⋊Dic3—21no—
15C3×C4⋊Dic3C2211yescharacteristic
16C3×Dic3⋊C4—21no—
17C3×C4×Dic3C2211yescharacteristic
18C2×C3×C3⋊C8C2211yescharacteristic
19Dic3⋊Dic3—21no—
20Dic3⋊Dic3—21no—
21C3×#125—31no—
22#944—31no—
23#890D311yescharacteristic
24#869—31no—
25C3×#103—31no—
26#835—31no—
27#816—31no—
28#815—31no—
29#810—31no—
30#810—31no—
31#810—31no—
32#810—31no—
33#810—61no—
34#810D311yescharacteristic
35#803—31no—
36C2×C32×C4—21no—
37C2×C32×C4C2311yescharacteristic
38C2×C3⋊Dic3—21no—
39#634—21no—
40#634—21no—
41C2×C3×Dic3—21no—
42C2×C3×Dic3—21no—
43C2×C3×Dic3D411yescharacteristic
44C2×C3×Dic3D411yescharacteristic
45C3×Dic6—21no—
46C3×Dic6—21no—
47C3⋊(C3⋊C8)—21no—
48C3×C3⋊C8—21no—
49#491—91noSylow
50C2×C3×Q8—31no—
51C2×Dic6—31no—
52C2×Dic6—31no—
53C2×Dic6—61no—
54C2×Dic6C2×D311yescharacteristic
55C2×C3×C8—31no—
56C3×C4⋊C4—21no—
57C3×C4⋊C4—31no—
58C3×C4⋊C4—61no—
59C3×C4⋊C4—61no—
60C3×C4⋊C4C2×D311yescharacteristic
61C3×C4⋊C4C2×D311yescharacteristic
62C3×C42—31no—
63C4⋊Dic3—21no—
64C4⋊Dic3—61no—
65C4⋊Dic3—61no—
66C4⋊Dic3C2×D311yescharacteristic
67Dic3⋊C4—21no—
68Dic3⋊C4—61no—
69Dic3⋊C4—61no—
70C4×Dic3C2×D311yescharacteristic
71C2×C3⋊C8—31no—
72C2×C3⋊C8—31no—
73C2×C3⋊C8—61no—
74C2×C3⋊C8C2×D311yescharacteristic
75C22×C32C2×D411yescharacteristic
76C32×C4—41no—
77C32×C4#4111yescharacteristic
78C32×C4#4111yescharacteristic
79C3⋊Dic3—41no—
80C3×Dic3—21no—
81C3×Dic3—21no—
82C3×Dic3—41no—
83C3×Dic3—41no—
84C4⋊Q8—91no—
85#125—31no—
86#103—31no—
87#103—91no—
88#103—91no—
89#103—91no—
90#97—91no—
91C3×Q8—61no—
92C3×Q8—61no—
93C2×C3×C4—21no—
94C2×C3×C4—21no—
95C2×C3×C4—21no—
96C2×C3×C4—31no—
97C2×C3×C4—31no—
98C2×C3×C4—41no—
99C2×C3×C4—61no—
100C2×C3×C4—61no—
101C2×C3×C4C22×D311yescharacteristic
102C2×C3×C4C22×D311yescharacteristic
103C2×Dic3—21no—
104C2×Dic3—21no—
105C2×Dic3—61no—
106C2×Dic3—61no—
107C2×Dic3—121no—
108C2×Dic3#6711yescharacteristic
109C2×Dic3#6711yescharacteristic
110Dic6—21no—
111Dic6—21no—
112Dic6—62no—
113Dic6—61no—
114Dic6—61no—
115Dic6—61no—
116Dic6—61no—
117Dic6—121no—
118C3×C8—61no—
119C3⋊C8—21no—
120C3⋊C8—61no—
121C3⋊C8—61no—
122C3⋊C8—121no—
123C2×C32#12411yescharacteristic
124C2×C32#13711yescharacteristic
125C2×C32#13711yescharacteristic
126C2×Q8—31no—
127C2×Q8—91no—
128C2×C8—31no—
129C2×C8—91no—
130C4⋊C4—31no—
131C4⋊C4—61no—
132C4⋊C4—61no—
133C4⋊C4—181no—
134C4⋊C4—181no—
135C4⋊C4D3211yescharacteristic
136C42—31no—
137C22×C3—21no—
138C22×C3D3×D411yescharacteristic
139C22×C3C2×#6711yescharacteristic
140C3×C4—21no—
141C3×C4—21no—
142C3×C4—41no—
143C3×C4—41no—
144C3×C4—61no—
145C3×C4—61no—
146C3×C4—81no—
147C3×C4—121no—
148C3×C4—121no—
149C3×C4#23511yescharacteristic
150C3×C4#23711yescharacteristic
151C3×C4#23911yescharacteristic
152C3×C4#23911yescharacteristic
153Dic3—21no—
154Dic3—21no—
155Dic3—41no—
156Dic3—41no—
157Dic3—122no—
158Dic3—121no—
159Dic3—121no—
160C32#49111yescharacteristic, complemented, Sylow
161Q8—61no—
162Q8—61no—
163Q8—181no—
164Q8—181no—
165C2×C4—21no—
166C2×C4—31no—
167C2×C4—31no—
168C2×C4—61no—
169C2×C4—61no—
170C2×C4—181no—
171C2×C4C2×D3211yescharacteristic
172C8—61no—
173C8—181no—
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3#88511yescharacteristic
178C2×C3#91511yescharacteristic
179C2×C3#91811yescharacteristic
180C2×C3#94711yescharacteristic
181C2×C3#95111yescharacteristic
182C2×C3#95111yescharacteristic
183C22D3×#6711yescharacteristic
184C4—41no—
185C4—61no—
186C4—61no—
187C4—121no—
188C4—121no—
189C4—361no—
190C4#379611yescharacteristic
191C4#379911yescharacteristic
192C3—21no—
193C3#479711yescharacteristic, complemented
194C3#506911yescharacteristic, complemented
195C2#6390711yescharacteristic
196C2#6392911yescharacteristic
197C2#6394311yescharacteristic
subgroupG/H
centerC22D3×#67
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC32×C4⋊C4C22
socle, prime radicalC22×C32C2×D4
hypercenterC4⋊C4D32
hypocenterC32#491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
160. C32#491semidirect
193. C3#4797semidirect
194. C3#5069semidirect

Maximal subgroups

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

subgroupindex
C3×#8902
#638662
#636372
C3×#8102
#635672
#635652
#635542
#50693
#47973