Finite Group Databasebeta

← #11899753

Subgroups — #11899753

Order 1152.

1050 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 205 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#10596237C212yesmaximal, complemented
2C2×C32×Q32C211yesmaximal, characteristic, complemented
3#10592878C212yesmaximal, complemented
4#10592618C212yesmaximal, complemented
5#10592617C214yesmaximal, complemented
6C3⋊D3×Q32C212yesmaximal, complemented
7#10592603C211yesmaximal, characteristic, complemented
8#10592600C211yesmaximal, characteristic, complemented
9#82028—34nomaximal
10#64364—22no—
11C2×C32×Q16C2212yes—
12#64151—22no—
13#64128C2214yes—
14#64127—24no—
15Q16×C3⋊D3C2214yes—
16#64113C2212yes—
17#64110C2211yescharacteristic
18C32×Q32C2212yes—
19C32×Q32C2212yes—
20C2×C32×C16C2211yescharacteristic
21#63656C2214yes—
22#63655C2214yes—
23#63639C2211yescharacteristic
24#63628C2211yescharacteristic
25#63627C2212yes—
26#63626C2211yescharacteristic
27#63625C2212yes—
28C16×C3⋊D3C2212yes—
29#5766—38no—
30C2×C3×Q32D314yescomplemented
31#5179—38no—
32#4919—38no—
33#4918—316no—
34D3×Q32—38no—
35#4904—34no—
36#4901—34no—
37C2×C32×Q8—22no—
38#3832—24no—
39#3832—42no—
40Q8×C3⋊D3—24no—
41Q8×C3⋊D3—42no—
42#3828—22no—
43#3828—44no—
44#3828D411yescharacteristic
45C32×Q16—22no—
46C32×Q16C2314yes—
47C2×C32×C8C2311yescharacteristic
48#3756—24no—
49#3755—24no—
50#3748D411yescharacteristic
51#3746C2312yes—
52#3745C2312yes—
53#3744—22no—
54#3743D412yes—
55C8×C3⋊D3C2312yes—
56C32×C16C2311yescharacteristic
57C32×C16C2311yescharacteristic
58C3⋊(C3⋊C16)C2312yes—
59#3417—91noSylow
60#1007—68no—
61C2×C3×Q16C2×D318yes—
62#942—68no—
63#919—316no—
64#918—616no—
65D3×Q16—316no—
66#904—38no—
67#901—34no—
68C3×Q32C2×D318yes—
69C3×Q32C2×D318yes—
70C2×C3×C16C2×D314yes—
71#829—316no—
72#828—316no—
73#812—34no—
74Dic24—34no—
75#800—38no—
76D48—34no—
77#798—38no—
78D3×C16—38no—
79C32×Q8—24no—
80C32×Q8—42no—
81C2×C32×C4—42no—
82C2×C32×C4C2×D411yescharacteristic
83#638—42no—
84#638D812yes—
85C4⋊(C3⋊D3)—22no—
86C4⋊(C3⋊D3)—44no—
87C4⋊(C3⋊D3)D811yescharacteristic
88C4×C3⋊D3—44no—
89C4×C3⋊D3—42no—
90C4×C3⋊D3—44no—
91C4×C3⋊D3C2×D412yes—
92#634—22no—
93#634—44no—
94#634D811yescharacteristic
95C32×C8C2×D411yescharacteristic
96C32×C8C2411yescharacteristic
97C3⋊(C3⋊C8)C2×D412yes—
98#578—92no—
99#510—92no—
100#510—94no—
101#508—92no—
102#508—91no—
103C2×Q32—92no—
104C2×Q32C3⋊D311yescharacteristic, complemented
105#504—91no—
106C2×C3×Q8—28no—
107#239—616no—
108#239—128no—
109D3×Q8—616no—
110D3×Q8—128no—
111#235—34no—
112#235—68no—
113#235—1216no—
114C3×Q16—28no—
115C3×Q16C22×D3116yes—
116C2×C3×C8C22×D314yes—
117#216—616no—
118#215—616no—
119#208—34no—
120Dic12—38no—
121D24—38no—
122#204—68no—
123ΓL(1,𝔽25)—38no—
124D3×C8—38no—
125C3×C16C22×D314yes—
126C3×C16C22×D314yes—
127C3⋊C16—38no—
128C22×C32C2×D811yescharacteristic
129C2×C3⋊D3—42no—
130C2×C3⋊D3C2×D812yes—
131C32×C4—44no—
132C32×C4C2×D811yescharacteristic
133C32×C4C22×D411yescharacteristic
134C3⋊Dic3—42no—
135C3⋊Dic3C2×D812yes—
1362−1+4—182no—
137#137—184no—
138#137—182no—
139#135—94no—
140#135—92no—
141C2×Q16—94no—
142C2×Q16C2×C3⋊D312yes—
143#131—91no—
144Q32—94no—
145Q32—91no—
146Q32C2×C3⋊D312yes—
147Q32C2×C3⋊D312yes—
148SD32—94no—
149SD32—92no—
150D16—91no—
151M32—91no—
152M32—92no—
153C2×C16—92no—
154C2×C16C2×C3⋊D311yescharacteristic
155C3×Q8—216no—
156C3×Q8—48no—
157C2×C3×C4—48no—
158C2×C3×C4D3×D414yes—
159#67—38no—
160#67—128no—
161D12—34no—
162D12—68no—
163D12—1216no—
164C4×D3—38no—
165C4×D3—1216no—
166C4×D3—1216no—
167C4×D3—128no—
168Dic6—34no—
169Dic6—68no—
170Dic6—1216no—
171C3×C8D3×D414yes—
172C3×C8C23×D314yes—
173C3⋊C8—38no—
174C2×C32—21no—
175C2×C32C22×D811yescharacteristic
176C3⋊D3—22no—
177C3⋊D3—82no—
178#41—91no—
179#41—184no—
180#41—182no—
181#41—364no—
182#41—362no—
183C2×Q8—22no—
184C2×Q8—184no—
185C2×Q8—362no—
186Q16—22no—
187Q16—92no—
188Q16—184no—
189Q16C22×C3⋊D314yes—
190SD16—184no—
191SD16—182no—
192D8—92no—
193M16—91no—
194M16—92no—
195C2×C8—92no—
196C2×C8C22×C3⋊D311yescharacteristic
197C16—92no—
198C16C22×C3⋊D311yescharacteristic
199C16C22×C3⋊D311yescharacteristic
200C22×C3D3×D814yes—
201C2×D3—38no—
202C2×D3—128no—
203C3×C4—416no—
204C3×C4D3×D814yes—
205C3×C4C2×D3×D414yes—
206Dic3—38no—
207Dic3—128no—
208C32#341711yescharacteristic, complemented, Sylow
209Q8—24no—
210Q8—42no—
211Q8—91no—
212Q8—182no—
213Q8—364no—
214D4—92no—
215D4—91no—
216D4—182no—
217D4—364no—
218D4—362no—
219C2×C4—42no—
220C2×C4—92no—
221C2×C4—364no—
222C2×C4—364no—
223C2×C4—362no—
224C2×C4D4×C3⋊D311yescharacteristic
225C8—92no—
226C8D4×C3⋊D311yescharacteristic
227C8C23×C3⋊D311yescharacteristic
228C2×C3—24no—
229C2×C3C2×D3×D814yes—
230D3—68no—
231D3—248no—
232C22—92no—
233C22—362no—
234C22D8×C3⋊D311yescharacteristic
235C4—44no—
236C4—92no—
237C4—362no—
238C4D8×C3⋊D311yescharacteristic
239C4C2×D4×C3⋊D311yescharacteristic
240C3#8202814yescomplemented
241C2—21no—
242C2—182no—
243C2—722no—
244C2C2×D8×C3⋊D311yescharacteristic
subgroupG/H
centerC2C2×D8×C3⋊D3
commutator, cosocleC32×C8C24
FrattiniC8C23×C3⋊D3
FittingC2×C32×Q32C2
socleC2×C32C22×D8
hypercenterC2×Q32C3⋊D3
hypocenterC32#3417
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
1. #10596237C2semidirect
2. C2×C32×Q32C2semidirect
3. #10592878C2semidirect
4. #10592618C2semidirect
5. #10592617C2semidirect
6. C3⋊D3×Q32C2semidirect
7. #10592603C2semidirect
8. #10592600C2semidirect
30. C2×C3×Q32D3semidirect
104. C2×Q32C3⋊D3semidirect
208. C32#3417semidirect
240. C3#82028semidirect

Maximal subgroups

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

subgroupindex
#105962372
C2×C32×Q322
#105928782
#105926182
#105926172
C3⋊D3×Q322
#105926032
#105926002
#820283