Finite Group Databasebeta

← #10590498

Subgroups — #10590498

Order 576.

246 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 64 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×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2#63908C211yesmaximal, characteristic
3#63634C211yesmaximal, characteristic, complemented
4C3×#809C211yesmaximal, characteristic, complemented
5#63575C211yesmaximal, characteristic, complemented
6#63562C211yesmaximal, characteristic, complemented
7(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#4967—31nomaximal
9#4774—31nomaximal
10C2×C3×D12C2211yescharacteristic
11C2×C3×C4×D3—21no—
12C2×C3×C4×D3C2211yescharacteristic
13C2×#625—21no—
14C32×C4⋊C4C2211yescharacteristic
15C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×C4⋊Dic3C2211yescharacteristic
18C3×Dic3⋊C4—21no—
19C2×C3×C3⋊C8C2211yescharacteristic
20(C2×D3)⋊Dic3—21no—
21C2×C3×C4⋊C4—31no—
22#938—31no—
23#930—31no—
24D3×C4⋊C4D311yescharacteristic, complemented
25C3×#102—31no—
26#832—31no—
27#830—31no—
28(C2×D3)⋊C8—31no—
29#818—31no—
30#809—31no—
31#809D311yescharacteristic, complemented
32#807—31no—
33#807—31no—
34#807—31no—
35#807—61no—
36C22×C3×D3—21no—
37C22×C3×D3D411yescharacteristic
38C2×C32×C4—21no—
39C2×C32×C4C2311yescharacteristic
40C2×C3⋊Dic3—21no—
41C2×C3×Dic3—21no—
42C2×C3×Dic3D411yescharacteristic
43C3×D12—21no—
44C3×D12—21no—
45C3×C4×D3—21no—
46C3×C4×D3—21no—
47C3×C4×D3—42no—
48#625—42no—
49C3⋊(C3⋊C8)—21no—
50C3×C3⋊C8—21no—
51#480—91noSylow
52C2×C3×D4—31no—
53C22×C3×C4—31no—
54C22×C3×C4—61no—
55C2×#67—61no—
56C2×#67—61no—
57C2×D12C2×D311yescharacteristic
58C2×C4×D3—21no—
59C2×C4×D3C2×D311yescharacteristic
60C2×C3×C8—31no—
61C3×C4⋊C4—21no—
62C3×C4⋊C4—31no—
63C3×C4⋊C4—61no—
64C3×C4⋊C4C2×D311yescharacteristic
65C3×C4⋊C4C2×D311yescharacteristic
66#217—61no—
67(C2×D3)⋊C4—61no—
68C4⋊Dic3—31no—
69C4⋊Dic3—31no—
70C4⋊Dic3—61no—
71C4⋊Dic3C2×D311yescharacteristic
72Dic3⋊C4—21no—
73C2×C3⋊C8—31no—
74C2×C3⋊C8—31no—
75C2×C3⋊C8—61no—
76C2×C3⋊C8C2×D311yescharacteristic
77C22×C32C2×D411yescharacteristic
78C2×C3×D3—21no—
79C2×C3×D3—21no—
80C2×C3×D3—41no—
81C2×C3×D3—41no—
82C2×C3×D3—41no—
83C2×C3×D3D812yes—
84C32×C4—41no—
85C32×C4#4111yescharacteristic
86C32×C4#4111yescharacteristic
87C3⋊Dic3—41no—
88C3×Dic3—21no—
89C3×Dic3—41no—
90#121—91no—
91C2×C4⋊C4—31no—
92#107—91no—
93#107—91no—
94#102—31no—
95#102—91no—
96C22⋊C8—91no—
97C23×C3—31no—
98C23×C3—61no—
99C22×D3—21no—
100C22×D3#6711yescharacteristic
101C3×D4—61no—
102C3×D4—61no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—31no—
107C2×C3×C4—41no—
108C2×C3×C4—61no—
109C2×C3×C4—61no—
110C2×C3×C4—61no—
111C2×C3×C4—122no—
112C2×C3×C4C22×D311yescharacteristic
113C2×C3×C4C22×D311yescharacteristic
114#67—122no—
115#67—122no—
116C2×Dic3—21no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—121no—
120C2×Dic3#6711yescharacteristic
121D12—21no—
122D12—21no—
123C4×D3—21no—
124C4×D3—21no—
125C4×D3—42no—
126C3×C8—61no—
127C3⋊C8—21no—
128C3⋊C8—62no—
129C3⋊C8—61no—
130C3⋊C8—61no—
131C2×C32#12311yescharacteristic
132C2×C32C2×D811yescharacteristic
133C2×C32#13711yescharacteristic
134C3×D3—22no—
135C3×D3—81no—
136C2×D4—31no—
137C2×D4—181no—
138C22×C4—31no—
139C22×C4—61no—
140C2×C8—31no—
141C2×C8—91no—
142C4⋊C4—31no—
143C4⋊C4—61no—
144C4⋊C4—91no—
145C4⋊C4D3211yescharacteristic
146C22⋊C4—181no—
147C22×C3—21no—
148C22×C3—32no—
149C22×C3—61no—
150C22×C3—61no—
151C22×C3—121no—
152C22×C3—121no—
153C22×C3—121no—
154C22×C3D3×D411yescharacteristic
155C22×C3C2×#6711yescharacteristic
156C2×D3—21no—
157C2×D3—21no—
158C2×D3—41no—
159C2×D3—41no—
160C2×D3—41no—
161C2×D3#21312yes—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—41no—
165C3×C4—41no—
166C3×C4—61no—
167C3×C4—81no—
168C3×C4—121no—
169C3×C4#23511yescharacteristic
170C3×C4#23511yescharacteristic
171C3×C4#23511yescharacteristic
172C3×C4#23711yescharacteristic
173Dic3—21no—
174Dic3—41no—
175Dic3—121no—
176Dic3—121no—
177Dic3—241no—
178C32#48011yescharacteristic, complemented, Sylow
179C23—31no—
180C23—61no—
181D4—61no—
182D4—61no—
183D4—362no—
184C2×C4—21no—
185C2×C4—31no—
186C2×C4—61no—
187C2×C4—61no—
188C2×C4—61no—
189C2×C4—122no—
190C2×C4—181no—
191C2×C4C2×D3211yescharacteristic
192C8—61no—
193C8—181no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3—62no—
198C2×C3—241no—
199C2×C3#88311yescharacteristic
200C2×C3D3×D811yescharacteristic
201C2×C3#91511yescharacteristic
202C2×C3#92911yescharacteristic
203C2×C3C2×#21311yescharacteristic
204C2×C3#94211yescharacteristic
205D3—22no—
206D3—81no—
207C22—32no—
208C22—61no—
209C22—61no—
210C22—121no—
211C22—121no—
212C22—121no—
213C22D3×#6711yescharacteristic
214C4—41no—
215C4—61no—
216C4—121no—
217C4—361no—
218C4#379511yescharacteristic
219C4#379811yescharacteristic
220C3—21no—
221C3#477411yescharacteristic, complemented
222C3#496711yescharacteristic, complemented
223C2—62no—
224C2—241no—
225C2#6390511yescharacteristic
226C2D3×#21311yescharacteristic
227C2#6394611yescharacteristic
subgroupG/H
centerC22D3×#67
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
FittingC32×C4⋊C4C22
socleC22×C32C2×D4
prime radical#63908C2
hypercenterC4⋊C4D32
hypocenterC32#480
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
1. C3×D3×C4⋊C4C2semidirect
3. #63634C2semidirect
4. C3×#809C2semidirect
5. #63575C2semidirect
6. #63562C2semidirect
7. (C2×D3)⋊(C3⋊C8)C2semidirect
24. D3×C4⋊C4D3semidirect
31. #809D3semidirect
178. C32#480semidirect
221. C3#4774semidirect
222. C3#4967semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊C42
#639082
#636342
C3×#8092
#635752
#635622
(C2×D3)⋊(C3⋊C8)2
#49673
#47743