Finite Group Databasebeta

← #11783517

Subgroups — #11783517

Order 1152.

561 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 561 conjugacy classes of subgroups — too many to draw. Only its 180 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
1C2×C8×C3⋊Dic3C211yesmaximal, characteristic
2#10591222C211yesmaximal, characteristic
3C2×#63555C211yesmaximal, characteristic
4C3×#4550C212yesmaximal
5#10589155C212yesmaximal
6#68598—32nomaximal
7C22×C32×C8C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4×Dic3C2212yes—
11C22×C3×C3⋊C8C2212yes—
12C8×C3⋊Dic3C414yescomplemented
13#63579C412yes—
14#63579C412yes—
15#63555C414yescomplemented
16C2×#815—32no—
17C2×C8×Dic3—32no—
18C2×C8×Dic3—61no—
19#4932—32no—
20C3×#336—32no—
21#4550—32no—
22#4550D312yes—
23#4524—32no—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3×Dic3C2×C414yes—
28C2×C32×C8—22no—
29C2×C32×C8C2×C412yes—
30C4×C3⋊Dic3C2×C412yes—
31C4×C3⋊Dic3C2×C412yes—
32C2×C3⋊(C3⋊C8)—22no—
33C2×C3⋊(C3⋊C8)C2×C412yes—
34C3×C4×Dic3—22no—
35C3×C4×Dic3—22no—
36C2×C3×C3⋊C8—22no—
37C2×C3×C3⋊C8—22no—
38C2×C3×C3⋊C8C2×C414yes—
39#1746—91noSylow
40C22×C3×C8—21no—
41C22×C3×C8—32no—
42C22×C3×C8C2×D312yes—
43C2×C3×C42—32no—
44C2×C4×Dic3—32no—
45C2×C4×Dic3—61no—
46C2×C4×Dic3C2×D312yes—
47C22×C3⋊C8—32no—
48C22×C3⋊C8—61no—
49C22×C3⋊C8C2×D312yes—
50C3⋊#95—34no—
51C3⋊#95—34no—
52#815—38no—
53C8×Dic3—38no—
54C8×Dic3—64no—
55C23×C32C22×C411yescharacteristic
56C2×C32×C4C22×C411yescharacteristic
57C2×C32×C4C22×C411yescharacteristic
58C2×C32×C4#4112yes—
59C2×C32×C4#4112yes—
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3C4212yes—
63C2×C3⋊Dic3C4212yes—
64C2×C3×Dic3—24no—
65C2×C3×Dic3—24no—
66C2×C3×Dic3—24no—
67C32×C8—22no—
68C3⋊(C3⋊C8)—22no—
69C3×C3⋊C8—24no—
70C2×#97—91no—
71C2×C4×C8—91no—
72#376—91no—
73#336—32no—
74#336—92no—
75C22×C3×C4—21no—
76C22×C3×C4—34no—
77C22×C3×C4C22×D312yes—
78C22×Dic3—32no—
79C22×Dic3—32no—
80C22×Dic3—61no—
81C22×Dic3—61no—
82C22×Dic3C4×D314yes—
83C2×C3×C8—24no—
84C2×C3×C8—22no—
85C2×C3×C8—22no—
86C2×C3×C8—22no—
87C2×C3×C8—34no—
88C2×C3×C8—62no—
89C2×C3×C8—62no—
90C2×C3×C8C4×D314yes—
91C3×C42—62no—
92C3×C42—62no—
93C4×Dic3—22no—
94C4×Dic3—22no—
95C4×Dic3—34no—
96C4×Dic3—34no—
97C4×Dic3—62no—
98C4×Dic3—62no—
99C2×C3⋊C8—22no—
100C2×C3⋊C8—22no—
101C2×C3⋊C8—34no—
102C2×C3⋊C8—62no—
103C2×C3⋊C8—64no—
104C2×C3⋊C8—62no—
105C2×C3⋊C8—62no—
106C2×C3⋊C8C4×D314yes—
107C22×C32C2×C4211yescharacteristic
108C22×C32#11712yes—
109C22×C32#13112yes—
110C22×C32#13112yes—
111C32×C4#11711yescharacteristic
112C32×C4#11712yes—
113C32×C4#11711yescharacteristic
114C3⋊Dic3—22no—
115C3⋊Dic3—22no—
116C3×Dic3—44no—
117C22×C8—32no—
118C22×C8—91no—
119C22×C8D3211yescharacteristic
120C2×C42—32no—
121C2×C42—91no—
122#97—94no—
123C4×C8—94no—
124#95—92no—
125#95—92no—
126C23×C3—21no—
127C23×C3C2×C4×D312yes—
128C2×C3×C4—22no—
129C2×C3×C4—21no—
130C2×C3×C4—22no—
131C2×C3×C4—21no—
132C2×C3×C4—64no—
133C2×C3×C4—64no—
134C2×C3×C4—64no—
135C2×C3×C4C2×C4×D312yes—
136C2×C3×C4C2×C4×D312yes—
137C2×C3×C4#23712yes—
138C2×C3×C4#23712yes—
139C2×C3×C4#23712yes—
140C2×C3×C4#23912yes—
141C2×Dic3—24no—
142C2×Dic3—24no—
143C2×Dic3—24no—
144C2×Dic3—34no—
145C2×Dic3—34no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C2×Dic3—64no—
149C2×Dic3—64no—
150C2×Dic3—64no—
151C2×Dic3—64no—
152C3×C8—24no—
153C3×C8—24no—
154C3×C8—64no—
155C3⋊C8—24no—
156C3⋊C8—64no—
157C3⋊C8—64no—
158C2×C32#37611yescharacteristic
159C2×C32#40511yescharacteristic
160C2×C32#40511yescharacteristic
161C2×C32#43314yes—
162C22×C4—34no—
163C22×C4—91no—
164C22×C4—91no—
165C22×C4C2×D3211yescharacteristic
166C2×C8—22no—
167C2×C8—34no—
168C2×C8—62no—
169C2×C8—62no—
170C2×C8—92no—
171C2×C8—182no—
172C2×C8#62412yes—
173C42—62no—
174C42—62no—
175C42—92no—
176C42—92no—
177C22×C3—22no—
178C22×C3—22no—
179C22×C3—22no—
180C22×C3—21no—
181C22×C3C42×D312yes—
182C22×C3#87712yes—
183C22×C3#89212yes—
184C22×C3#90114yes—
185C22×C3#90714yes—
186C3×C4—21no—
187C3×C4—22no—
188C3×C4—21no—
189C3×C4—124no—
190C3×C4#87712yes—
191C3×C4#87712yes—
192C3×C4#89212yes—
193C3×C4#89212yes—
194Dic3—44no—
195Dic3—64no—
196Dic3—64no—
197Dic3—64no—
198Dic3—64no—
199C32#174611yescharacteristic, complemented, Sylow
200C23C4×D3211yescharacteristic
201C2×C4—64no—
202C2×C4—64no—
203C2×C4—64no—
204C2×C4—92no—
205C2×C4—92no—
206C2×C4—182no—
207C2×C4—182no—
208C2×C4#379612yes—
209C2×C4C4×D3211yescharacteristic
210C2×C4#380512yes—
211C2×C4C2×#62411yescharacteristic
212C8—22no—
213C8—64no—
214C8—182no—
215C2×C3—21no—
216C2×C3—24no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3#464812yes—
220C2×C3#468912yes—
221C2×C3#470812yes—
222C2×C3#472014yes—
223C2×C3#484014yes—
224C22#6380312yes—
225C22#6380512yes—
226C22#6387812yes—
227C22C4×#62411yescharacteristic
228C4—124no—
229C4—182no—
230C4—182no—
231C4#6384911yescharacteristic
232C4#6387812yes—
233C4#6395711yescharacteristic
234C3—21no—
235C3#6859812yescomplemented
236C2#1059069814yes—
237C2#1059070011yescharacteristic
238C2#1059070311yescharacteristic
239C2#1059125211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC22×C32×C8C22
socle, prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1746
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
12. C8×C3⋊Dic3C4semidirect
15. #63555C4semidirect
199. C32#1746semidirect
235. C3#68598semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C3⋊Dic32
#105912222
C2×#635552
C3×#45502
#105891552
#685983