Finite Group Databasebeta

← #11795359

Subgroups — #11795359

Order 1152.

666 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C32×#407C211yesmaximal, characteristic
2#10592906C212yesmaximal
3#10592824C211yesmaximal, characteristic, complemented
4#10592823C212yesmaximal, complemented
5#10589426C211yesmaximal, characteristic, complemented
6#69987—34nomaximal
7C23×C32×C4C2211yescharacteristic
8C2×C32×M16C2211yescharacteristic
9C2×C32×M16C2211yescharacteristic
10C2×#3748C2212yes—
11C2×#3748C2212yes—
12C32×C22⋊C8—22no—
13#63657—24no—
14#63649—24no—
15#63646—22no—
16C3×#407D314yes—
17#5207—38no—
18#5125—34no—
19#5124—38no—
20C3⋊#338—34no—
21C24×C32Q811yescharacteristic
22C22×C32×C4—22no—
23C22×C32×C4—21no—
24C22×C32×C4—21no—
25C22×C32×C4—22no—
26C22×C32×C4Q811yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C32×M16—22no—
29C32×M16—22no—
30C2×C32×C8—21no—
31C2×C32×C8D412yes—
32#3748—22no—
33#3748—22no—
34#3748—22no—
35#3748—22no—
36C2×C3⋊(C3⋊C8)—22no—
37C2×C3⋊(C3⋊C8)D414yes—
38#2091—91noSylow
39C23×C3×C4C2×D314yes—
40C2×C3×M16C2×D314yes—
41C2×C3×M16C2×D314yes—
42C2×#208—38no—
43C2×#208—38no—
44C3×C22⋊C8—28no—
45#830—616no—
46#822—616no—
47#819—68no—
48C23×C32—22no—
49C23×C32—21no—
50C23×C32—42no—
51C23×C32C2×Q811yescharacteristic
52C2×C32×C4—22no—
53C2×C32×C4—21no—
54C2×C32×C4—42no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4C2×D412yes—
58C2×C32×C4C2×D411yescharacteristic
59C2×C32×C4#4111yescharacteristic
60C2×C32×C4#4112yes—
61C32×C8—22no—
62C32×C8—41no—
63C3⋊(C3⋊C8)—24no—
64C3⋊(C3⋊C8)—42no—
65#430—92no—
66#430—91no—
67#407—92no—
68#407C3⋊D311yescharacteristic
69#338—91no—
70C24×C3Dic614yes—
71C22×C3×C4—24no—
72C22×C3×C4—28no—
73C22×C3×C4—28no—
74C22×C3×C4—24no—
75C22×C3×C4Dic614yes—
76C22×C3×C4C22×D314yes—
77C3×M16—28no—
78C3×M16—28no—
79C2×C3×C8—24no—
80C2×C3×C8#6718yes—
81#208—68no—
82#208—68no—
83#208—68no—
84#208—68no—
85C2×C3⋊C8—316no—
86C2×C3⋊C8—68no—
87C22×C32—24no—
88C22×C32—22no—
89C22×C32—41no—
90C22×C32—42no—
91C22×C32—41no—
92C22×C32—41no—
93C22×C32C22⋊Q812yes—
94C22×C32C22⋊Q811yescharacteristic
95C32×C4—41no—
96C32×C4#12312yes—
97C32×C4#12311yescharacteristic
98C32×C4#12711yescharacteristic
99C23×C4C2×C3⋊D311yescharacteristic
100C2×M16—92no—
101C2×M16—92no—
102C2×M16C2×C3⋊D311yescharacteristic
103C2×M16C2×C3⋊D311yescharacteristic
104#108—184no—
105#108—182no—
106C22⋊C8—22no—
107C22⋊C8—184no—
108C23×C3—28no—
109C23×C3—24no—
110C23×C3—48no—
111C23×C3C2×Dic614yes—
112C2×C3×C4—28no—
113C2×C3×C4—24no—
114C2×C3×C4—48no—
115C2×C3×C4—44no—
116C2×C3×C4—44no—
117C2×C3×C4#23514yes—
118C2×C3×C4D3×D418yes—
119C2×C3×C4#23718yes—
120C2×C3×C4C2×#6714yes—
121C3×C8—28no—
122C3×C8—44no—
123C3⋊C8—616no—
124C3⋊C8—128no—
125C2×C32—22no—
126C2×C32—21no—
127C2×C32—42no—
128C2×C32#39911yescharacteristic
129C24#63411yescharacteristic
130C22×C4—21no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—21no—
134C22×C4#63411yescharacteristic
135C22×C4C22×C3⋊D311yescharacteristic
136M16—22no—
137M16—22no—
138M16—182no—
139M16—182no—
140M16—182no—
141M16—182no—
142C2×C8—21no—
143C2×C8—94no—
144C2×C8—182no—
145C2×C8#63812yes—
146C22×C3—216no—
147C22×C3—28no—
148C22×C3—44no—
149C22×C3—48no—
150C22×C3—44no—
151C22×C3—44no—
152C22×C3#87818yes—
153C22×C3#92414yes—
154C3×C4—44no—
155C3×C4#88318yes—
156C3×C4#93514yes—
157C3×C4#94014yes—
158C32#209111yescharacteristic, complemented, Sylow
159C23—22no—
160C23—21no—
161C23—42no—
162C23C2×#63411yescharacteristic
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4#382811yescharacteristic
169C2×C4D4×C3⋊D312yes—
170C2×C4#383012yes—
171C2×C4C2×#63811yescharacteristic
172C8—22no—
173C8—41no—
174C8—184no—
175C8—362no—
176C2×C3—28no—
177C2×C3—24no—
178C2×C3—48no—
179C2×C3#494914yes—
180C22—24no—
181C22—22no—
182C22—41no—
183C22—42no—
184C22—41no—
185C22—41no—
186C22#6408712yes—
187C22#6413311yescharacteristic
188C4—41no—
189C4#6409212yes—
190C4#6414411yescharacteristic
191C4#6414911yescharacteristic
192C3#6998714yescomplemented
193C2—22no—
194C2—21no—
195C2—42no—
196C2#1059264811yescharacteristic
subgroupG/H
centerC4#64149
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#407C2
socleC2×C32#399
prime radicalC24×C32Q8
hypercenter#407C3⋊D3
hypocenterC32#2091
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #10592824C2semidirect
4. #10592823C2semidirect
5. #10589426C2semidirect
158. C32#2091semidirect
192. C3#69987semidirect

Maximal subgroups

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

subgroupindex
C32×#4072
#105929062
#105928242
#105928232
#105894262
#699873