Finite Group Databasebeta

← #11783524

Subgroups — #11783524

Order 1152.

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

normal subgroups only

This group has 553 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×#63642C211yesmaximal, characteristic
2#10591222C211yesmaximal, characteristic
3C2×#63553C211yesmaximal, 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—
12#63642C414yescomplemented
13#63579C414yes—
14#63553C414yescomplemented
15C2×#815—32no—
16C2×#815—61no—
17C2×C8×Dic3—32no—
18#4932—32no—
19C3×#336—32no—
20#4550—32no—
21#4550D312yes—
22#4524—32no—
23C22×C32×C4C2311yescharacteristic
24C22×C3⋊Dic3C2×C412yes—
25C22×C3×Dic3C2×C414yes—
26C2×C32×C8—22no—
27C2×C32×C8C2×C412yes—
28C4×C3⋊Dic3C2×C412yes—
29C4×C3⋊Dic3C2×C412yes—
30C2×C3⋊(C3⋊C8)—22no—
31C2×C3⋊(C3⋊C8)C2×C412yes—
32C3×C4×Dic3—22no—
33C3×C4×Dic3—22no—
34C2×C3×C3⋊C8—22no—
35C2×C3×C3⋊C8—22no—
36C2×C3×C3⋊C8C2×C414yes—
37#1746—91noSylow
38C22×C3×C8—21no—
39C22×C3×C8—32no—
40C22×C3×C8C2×D312yes—
41C2×C3×C42—32no—
42C2×C4×Dic3—32no—
43C2×C4×Dic3—61no—
44C2×C4×Dic3C2×D312yes—
45C22×C3⋊C8—32no—
46C22×C3⋊C8—61no—
47C22×C3⋊C8C2×D312yes—
48C3⋊#95—34no—
49C3⋊#95—34no—
50#815—38no—
51#815—64no—
52C8×Dic3—38no—
53C23×C32C22×C411yescharacteristic
54C2×C32×C4C22×C411yescharacteristic
55C2×C32×C4C22×C411yescharacteristic
56C2×C32×C4#4112yes—
57C2×C32×C4#4112yes—
58C2×C3⋊Dic3—24no—
59C2×C3⋊Dic3C4214yes—
60C2×C3×Dic3—24no—
61C2×C3×Dic3—24no—
62C2×C3×Dic3—24no—
63C32×C8—22no—
64C3⋊(C3⋊C8)—22no—
65C3×C3⋊C8—24no—
66C2×#97—91no—
67C2×C4×C8—91no—
68#376—91no—
69#336—32no—
70#336—92no—
71C22×C3×C4—21no—
72C22×C3×C4—34no—
73C22×C3×C4C22×D312yes—
74C22×Dic3—32no—
75C22×Dic3—32no—
76C22×Dic3—62no—
77C22×Dic3C4×D314yes—
78C2×C3×C8—24no—
79C2×C3×C8—22no—
80C2×C3×C8—22no—
81C2×C3×C8—22no—
82C2×C3×C8—34no—
83C2×C3×C8—62no—
84C2×C3×C8—62no—
85C2×C3×C8C4×D314yes—
86C3×C42—62no—
87C3×C42—62no—
88C4×Dic3—22no—
89C4×Dic3—22no—
90C4×Dic3—34no—
91C4×Dic3—34no—
92C4×Dic3—62no—
93C4×Dic3—62no—
94C2×C3⋊C8—22no—
95C2×C3⋊C8—22no—
96C2×C3⋊C8—34no—
97C2×C3⋊C8—62no—
98C2×C3⋊C8—64no—
99C2×C3⋊C8—62no—
100C2×C3⋊C8—62no—
101C2×C3⋊C8C4×D314yes—
102C22×C32C2×C4211yescharacteristic
103C22×C32#11712yes—
104C22×C32#13114yes—
105C32×C4#11711yescharacteristic
106C32×C4#11712yes—
107C32×C4#11711yescharacteristic
108C3⋊Dic3—24no—
109C3×Dic3—44no—
110C22×C8—32no—
111C22×C8—91no—
112C22×C8D3211yescharacteristic
113C2×C42—32no—
114C2×C42—91no—
115#97—94no—
116C4×C8—94no—
117#95—94no—
118C23×C3—21no—
119C23×C3C2×C4×D312yes—
120C2×C3×C4—22no—
121C2×C3×C4—21no—
122C2×C3×C4—22no—
123C2×C3×C4—21no—
124C2×C3×C4—64no—
125C2×C3×C4—64no—
126C2×C3×C4—64no—
127C2×C3×C4C2×C4×D312yes—
128C2×C3×C4C2×C4×D312yes—
129C2×C3×C4#23712yes—
130C2×C3×C4#23712yes—
131C2×C3×C4#23712yes—
132C2×C3×C4#23912yes—
133C2×Dic3—24no—
134C2×Dic3—24no—
135C2×Dic3—24no—
136C2×Dic3—34no—
137C2×Dic3—34no—
138C2×Dic3—64no—
139C2×Dic3—64no—
140C2×Dic3—64no—
141C2×Dic3—124no—
142C3×C8—24no—
143C3×C8—24no—
144C3×C8—64no—
145C3⋊C8—24no—
146C3⋊C8—64no—
147C3⋊C8—64no—
148C2×C32#37611yescharacteristic
149C2×C32#40512yes—
150C2×C32#43314yes—
151C22×C4—34no—
152C22×C4—92no—
153C22×C4C2×D3211yescharacteristic
154C2×C8—22no—
155C2×C8—34no—
156C2×C8—62no—
157C2×C8—62no—
158C2×C8—92no—
159C2×C8—182no—
160C2×C8#62412yes—
161C42—62no—
162C42—62no—
163C42—92no—
164C42—92no—
165C22×C3—24no—
166C22×C3—22no—
167C22×C3—21no—
168C22×C3C42×D312yes—
169C22×C3#87712yes—
170C22×C3#89212yes—
171C22×C3#90114yes—
172C22×C3#90714yes—
173C3×C4—21no—
174C3×C4—22no—
175C3×C4—21no—
176C3×C4—124no—
177C3×C4#87712yes—
178C3×C4#87712yes—
179C3×C4#89212yes—
180C3×C4#89212yes—
181Dic3—44no—
182Dic3—64no—
183Dic3—64no—
184Dic3—124no—
185C32#174611yescharacteristic, complemented, Sylow
186C23C4×D3211yescharacteristic
187C2×C4—64no—
188C2×C4—64no—
189C2×C4—64no—
190C2×C4—94no—
191C2×C4—184no—
192C2×C4#379612yes—
193C2×C4C4×D3211yescharacteristic
194C2×C4#380512yes—
195C2×C4C2×#62411yescharacteristic
196C8—22no—
197C8—64no—
198C8—182no—
199C2×C3—21no—
200C2×C3—22no—
201C2×C3—24no—
202C2×C3#464812yes—
203C2×C3#468912yes—
204C2×C3#470812yes—
205C2×C3#472014yes—
206C2×C3#484014yes—
207C22#6380414yes—
208C22#6387812yes—
209C22C4×#62411yescharacteristic
210C4—124no—
211C4—184no—
212C4#6384911yescharacteristic
213C4#6387812yes—
214C4#6395711yescharacteristic
215C3—21no—
216C3#6859812yescomplemented
217C2#1059069914yes—
218C2#1059091012yes—
219C2#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. #63642C4semidirect
14. #63553C4semidirect
185. C32#1746semidirect
216. C3#68598semidirect

Maximal subgroups

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

subgroupindex
C2×#636422
#105912222
C2×#635532
C3×#45502
#105891552
#685983