Finite Group Databasebeta

← #10590866

Subgroups — #10590866

Order 576.

220 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 58 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#63919C211yesmaximal, characteristic, complemented
2#63863C211yesmaximal, characteristic
3#63642C211yesmaximal, characteristic, complemented
4C3×#821C211yesmaximal, characteristic
5C3×#816C211yesmaximal, characteristic, complemented
6#63565C211yesmaximal, characteristic, complemented
7#63562C211yesmaximal, characteristic
8#4794—31nomaximal
9#4765—31nomaximal
10C2×C3×D12C2211yescharacteristic
11C2×C3×Dic6C2211yescharacteristic
12C2×#627—21no—
13C2×C32×C8C2211yescharacteristic
14C4×C3⋊Dic3C2211yescharacteristic
15C2×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×C4⋊Dic3C2211yescharacteristic
17C3×C4⋊Dic3C2211yescharacteristic
18#3724—21no—
19(C2×D3)⋊Dic3—21no—
20(C2×D3)⋊Dic3—21no—
21#947—31no—
22#936—31no—
23#888—31no—
24#888—31no—
25C3×#103—31no—
26C3×#102—31no—
27#835—31no—
28#832—31no—
29#821D311yescharacteristic
30#816D311yescharacteristic, complemented
31#815—31no—
32#815—31no—
33#815—61no—
34#810—31no—
35#809—31no—
36C22×C3×D3—21no—
37C2×C32×C4C2311yescharacteristic
38C2×C3⋊Dic3D411yescharacteristic
39C2×C3⋊Dic3D411yescharacteristic
40C2×C3×Dic3—21no—
41C2×C3×Dic3—21no—
42C2×C3×Dic3—21no—
43C3×D12—21no—
44C3×D12—21no—
45C3×Dic6—21no—
46C3×Dic6—21no—
47#627—42no—
48C32×C8—21no—
49C3⋊(C3⋊C8)—21no—
50#489—91noSylow
51C2×C3×Q8—31no—
52C2×C3×D4—31no—
53C2×D12C2×D311yescharacteristic
54C2×Dic6—61no—
55C2×Dic6—61no—
56C2×Dic6C2×D311yescharacteristic
57C2×C3×C8—21no—
58C2×C3×C8C2×D311yescharacteristic
59C2×C3×C8C2×D311yescharacteristic
60C3×C4⋊C4—31no—
61C3×C4⋊C4—31no—
62#217—61no—
63#217—61no—
64(C2×D3)⋊C4—61no—
65(C2×D3)⋊C4—61no—
66C4⋊Dic3C2×D311yescharacteristic
67C4⋊Dic3C2×D311yescharacteristic
68Dic3⋊C4—61no—
69Dic3⋊C4—61no—
70C4×Dic3—31no—
71C4×Dic3—31no—
72C4×Dic3—61no—
73C2×C3⋊C8—31no—
74C2×C3⋊C8—31no—
75C2×C3⋊C8—61no—
76C22×C32C2×D411yescharacteristic
77C2×C3×D3—41no—
78C2×C3×D3—41no—
79C2×C3×D3—41no—
80C32×C4#4111yescharacteristic
81C32×C4#4111yescharacteristic
82C3⋊Dic3—21no—
83C3⋊Dic3—21no—
84C3×Dic3—41no—
85C3×Dic3—41no—
86C3×Dic3—41no—
87C4⋊Q8—91no—
88#124—91no—
89#103—31no—
90#103—91no—
91#102—31no—
92#102—91no—
93#97—91no—
94C23×C3—61no—
95C22×D3—21no—
96C3×Q8—61no—
97C3×Q8—61no—
98C3×D4—61no—
99C3×D4—61no—
100C2×C3×C4—21no—
101C2×C3×C4—61no—
102C2×C3×C4—61no—
103C2×C3×C4—61no—
104C2×C3×C4C22×D311yescharacteristic
105C2×C3×C4C22×D311yescharacteristic
106C2×Dic3—21no—
107C2×Dic3—21no—
108C2×Dic3—21no—
109C2×Dic3—31no—
110C2×Dic3—31no—
111C2×Dic3—31no—
112C2×Dic3—31no—
113C2×Dic3—61no—
114C2×Dic3—61no—
115D12—21no—
116D12—21no—
117Dic6—21no—
118Dic6—21no—
119Dic6—122no—
120Dic6—122no—
121C3×C8—22no—
122C3×C8—21no—
123C3×C8—21no—
124C3⋊C8—62no—
125C3⋊C8—61no—
126C3⋊C8—61no—
127C2×C32#12411yescharacteristic
128C2×C32AGL(1,ℤ/8)11yescharacteristic
129C2×C32#13711yescharacteristic
130C3×D3—81no—
131C2×Q8—31no—
132C2×Q8—181no—
133C2×D4—31no—
134C2×C8—91no—
135C2×C8D3211yescharacteristic
136C4⋊C4—31no—
137C4⋊C4—31no—
138C4⋊C4—181no—
139C22⋊C4—181no—
140C22⋊C4—181no—
141C42—91no—
142C22×C3—21no—
143C22×C3—121no—
144C22×C3—121no—
145C22×C3—121no—
146C22×C3D3×D411yescharacteristic
147C22×C3D3×D411yescharacteristic
148C2×D3—41no—
149C2×D3—41no—
150C2×D3—41no—
151C3×C4—21no—
152C3×C4—21no—
153C3×C4—121no—
154C3×C4—121no—
155C3×C4—121no—
156C3×C4#23511yescharacteristic
157C3×C4#23511yescharacteristic
158C3×C4#23711yescharacteristic
159C3×C4#23711yescharacteristic
160Dic3—41no—
161Dic3—41no—
162Dic3—41no—
163Dic3—61no—
164Dic3—61no—
165Dic3—61no—
166Dic3—61no—
167Dic3—121no—
168Dic3—121no—
169C32#48911yescharacteristic, complemented, Sylow
170C23—61no—
171Q8—61no—
172Q8—61no—
173Q8—362no—
174D4—61no—
175D4—61no—
176C2×C4—61no—
177C2×C4—61no—
178C2×C4—61no—
179C2×C4—91no—
180C2×C4—91no—
181C2×C4C2×D3211yescharacteristic
182C8—21no—
183C8—181no—
184C2×C3—21no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—241no—
188C2×C3#88511yescharacteristic
189C2×C3#88511yescharacteristic
190C2×C3#91111yescharacteristic
191C2×C3#91411yescharacteristic
192C2×C3#91511yescharacteristic
193C2×C3#91811yescharacteristic
194D3—81no—
195C22—121no—
196C22—121no—
197C22—121no—
198C22#380211yescharacteristic
199C4—121no—
200C4—121no—
201C4—121no—
202C4—181no—
203C4—181no—
204C4#379811yescharacteristic
205C4#380511yescharacteristic
206C3—21no—
207C3#476511yescharacteristic, complemented
208C3#479411yescharacteristic, complemented
209C2—241no—
210C2#6379811yescharacteristic
211C2#6381111yescharacteristic
212C2#6391511yescharacteristic
subgroupG/H
centerC22#3802
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC2×C32×C8C22
socleC22×C32C2×D4
prime radicalC2×C3×D12C22
hypercenterC2×C8D32
hypocenterC32#489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. #63919C2semidirect
3. #63642C2semidirect
5. C3×#816C2semidirect
6. #63565C2semidirect
30. #816D3semidirect
169. C32#489semidirect
207. C3#4765semidirect
208. C3#4794semidirect

Maximal subgroups

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

subgroupindex
#639192
#638632
#636422
C3×#8212
C3×#8162
#635652
#635622
#47943
#47653