Finite Group Databasebeta

← #10591411

Subgroups — #10591411

Order 576.

229 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 229 conjugacy classes of subgroups — too many to draw. Only its 68 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×D4×Dic3C211yesmaximal, characteristic
2#63869C211yesmaximal, characteristic, complemented
3#63659C211yesmaximal, characteristic
4C3×#832C211yesmaximal, characteristic
5#63575C211yesmaximal, characteristic, complemented
6#63574C211yesmaximal, characteristic, complemented
7Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#5009—31nomaximal
9#4766—31nomaximal
10C2×C32×D4C2211yescharacteristic
11C22×C3×Dic3—21no—
12C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#217—21no—
15C3×C4⋊Dic3C2211yescharacteristic
16C3×C4⋊Dic3C2211yescharacteristic
17C3×C4×Dic3C2211yescharacteristic
18C2×C3×C3⋊C8C2211yescharacteristic
19#3724—21no—
20Dic3⋊Dic3—21no—
21C3×C4×D4—31no—
22D4×Dic3D311yescharacteristic
23#890—31no—
24#870—31no—
25C3×#102—31no—
26#832—31no—
27#832—31no—
28#832—61no—
29#832D311yescharacteristic
30#818—31no—
31Dic3⋊C8—31no—
32#808—31no—
33#808—31no—
34#807—31no—
35C4⋊(C3⋊C8)—31no—
36C23×C32—21no—
37C32×D4—21no—
38C32×D4Q812yes—
39C2×C32×C4C2311yescharacteristic
40C2×C3⋊Dic3—21no—
41C2×C3×Dic3—21no—
42C2×C3×Dic3—21no—
43C2×C3×Dic3—42no—
44C2×C3×Dic3D411yescharacteristic
45C2×C3×Dic3D411yescharacteristic
46C3⋊(C3⋊C8)—21no—
47C3×C3⋊C8—21no—
48#478—91noSylow
49C2×C3×D4—21no—
50C2×C3×D4C2×D311yescharacteristic
51C2×C3×D4C2×D311yescharacteristic
52C22×C3×C4—61no—
53C22×Dic3—21no—
54C2×C3×C8—31no—
55C3×C4⋊C4—31no—
56C3×C4⋊C4—31no—
57C3×C22⋊C4—61no—
58C3×C42—31no—
59#217—21no—
60C4⋊Dic3—31no—
61C4⋊Dic3—31no—
62C4⋊Dic3—61no—
63C4⋊Dic3—61no—
64C4⋊Dic3C2×D311yescharacteristic
65C4⋊Dic3C2×D311yescharacteristic
66Dic3⋊C4—61no—
67Dic3⋊C4—61no—
68Dic3⋊C4—61no—
69C4×Dic3C2×D311yescharacteristic
70C2×C3⋊C8—31no—
71C2×C3⋊C8—31no—
72C2×C3⋊C8—61no—
73C2×C3⋊C8C2×D311yescharacteristic
74C22×C32—22no—
75C22×C32—41no—
76C22×C32—41no—
77C22×C32C2×D411yescharacteristic
78C32×C4C2×Q811yescharacteristic
79C32×C4#4111yescharacteristic
80C3⋊Dic3—41no—
81C3×Dic3—21no—
82C3×Dic3—21no—
83C3×Dic3—41no—
84C3×Dic3—41no—
85#125—91no—
86C4×D4—31no—
87#107—91no—
88#106—91no—
89C4⋊C8—91no—
90#102—31no—
91#102—91no—
92C23×C3—21no—
93C23×C3—21no—
94C23×C3—41no—
95C3×D4—21no—
96C3×D4—21no—
97C3×D4—22no—
98C3×D4—41no—
99C3×D4Dic612yes—
100C3×D4Dic612yes—
101C2×C3×C4—21no—
102C2×C3×C4—31no—
103C2×C3×C4—31no—
104C2×C3×C4—61no—
105C2×C3×C4—61no—
106C2×C3×C4—122no—
107C2×C3×C4C22×D311yescharacteristic
108C2×C3×C4C22×D311yescharacteristic
109C2×Dic3—21no—
110C2×Dic3—21no—
111C2×Dic3—42no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—121no—
115C2×Dic3#6711yescharacteristic
116C2×Dic3#6711yescharacteristic
117C3×C8—61no—
118C3⋊C8—21no—
119C3⋊C8—61no—
120C3⋊C8—61no—
121C3⋊C8—121no—
122C2×C32—42no—
123C2×C32C22⋊Q811yescharacteristic
124C2×C32#13511yescharacteristic
125C2×C32AGL(1,ℤ/8)11yescharacteristic
126C2×D4D3211yescharacteristic
127C22×C4—61no—
128C2×C8—31no—
129C2×C8—91no—
130C4⋊C4—31no—
131C4⋊C4—31no—
132C4⋊C4—91no—
133C4⋊C4—181no—
134C4⋊C4—181no—
135C22⋊C4—61no—
136C42—31no—
137C22×C3—22no—
138C22×C3—22no—
139C22×C3—21no—
140C22×C3—42no—
141C22×C3—41no—
142C22×C3—41no—
143C22×C3—41no—
144C22×C3—41no—
145C22×C3—81no—
146C22×C3—81no—
147C22×C3D3×D411yescharacteristic
148C22×C3C2×#6711yescharacteristic
149C3×C4—21no—
150C3×C4—21no—
151C3×C4—61no—
152C3×C4—61no—
153C3×C4—121no—
154C3×C4—121no—
155C3×C4C2×Dic611yescharacteristic
156C3×C4C2×Dic611yescharacteristic
157C3×C4#23511yescharacteristic
158C3×C4#23711yescharacteristic
159Dic3—21no—
160Dic3—21no—
161Dic3—41no—
162Dic3—41no—
163Dic3—121no—
164Dic3—121no—
165Dic3—241no—
166C32#47811yescharacteristic, complemented, Sylow
167C23—21no—
168D4—21no—
169D4#62712yes—
170C2×C4—31no—
171C2×C4—31no—
172C2×C4—61no—
173C2×C4—61no—
174C2×C4—122no—
175C2×C4—181no—
176C2×C4C2×D3211yescharacteristic
177C8—61no—
178C8—181no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—42no—
183C2×C3—42no—
184C2×C3—82no—
185C2×C3#87811yescharacteristic
186C2×C3#91211yescharacteristic
187C2×C3#91411yescharacteristic
188C2×C3#92411yescharacteristic
189C2×C3#93211yescharacteristic
190C2×C3#95011yescharacteristic
191C22—22no—
192C22—41no—
193C22—41no—
194C22D3×#6711yescharacteristic
195C4—61no—
196C4—61no—
197C4—121no—
198C4—121no—
199C4—361no—
200C4#380411yescharacteristic
201C4C2×#62711yescharacteristic
202C3—21no—
203C3#476611yescharacteristic, complemented
204C3#500911yescharacteristic, complemented
205C2—42no—
206C2#6393311yescharacteristic
207C2#6393411yescharacteristic
208C2#6396411yescharacteristic
subgroupG/H
centerC22D3×#67
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C2×D32
Fitting, prime radicalC2×C32×D4C22
socleC22×C32C2×D4
hypercenterC2×D4D32
hypocenterC32#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #63869C2semidirect
5. #63575C2semidirect
6. #63574C2semidirect
7. Dic3⋊(C3⋊C8)C2semidirect
166. C32#478semidirect
203. C3#4766semidirect
204. C3#5009semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic32
#638692
#636592
C3×#8322
#635752
#635742
Dic3⋊(C3⋊C8)2
#50093
#47663