Finite Group Databasebeta

← #11795356

Subgroups — #11795356

Order 1152.

666 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 155 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×#430C211yesmaximal, characteristic, complemented
2#10592825C211yesmaximal, characteristic
3#10592825C212yesmaximal
4#10592823C212yesmaximal, complemented
5#10589426C211yesmaximal, characteristic, complemented
6#70729—34nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C32×M16C2212yes—
9C2×C32×M16C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11C2×#3748C2212yes—
12C32×#108—22no—
13#63649—24no—
14#63647—22no—
15#63647—24no—
16C3×#430D314yescomplemented
17#5126—38no—
18#5126—34no—
19#5124—38no—
20C3⋊#338—34no—
21C23×C3⋊D3Q811yescharacteristic
22C22×C32×C4C2311yescharacteristic
23C22×C3⋊Dic3Q811yescharacteristic
24C2×C4×C3⋊D3—22no—
25C2×C4×C3⋊D3—21no—
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3—21no—
28C32×M16—22no—
29C32×M16—22no—
30C32×M16—22no—
31C2×C32×C8—22no—
32C2×C32×C8D412yes—
33#3748—22no—
34#3748—22no—
35#3748—22no—
36C2×C3⋊(C3⋊C8)—21no—
37C2×C3⋊(C3⋊C8)D414yes—
38#2091—91noSylow
39C22×C4×D3—34no—
40C2×C3×M16C2×D318yes—
41C2×C3×M16C2×D314yes—
42C2×#208—38no—
43C2×#208—34no—
44C3×#108—28no—
45#822—616no—
46(C2×D3)⋊C8—616no—
47(C2×D3)⋊C8—68no—
48C23×C32C2×Q811yescharacteristic
49C22×C3⋊D3—22no—
50C22×C3⋊D3—21no—
51C22×C3⋊D3—42no—
52C2×C32×C4C2×D412yes—
53C2×C32×C4C2×D411yescharacteristic
54C2×C32×C4#4112yes—
55C2×C32×C4#4111yescharacteristic
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—21no—
58C4×C3⋊D3—42no—
59C4×C3⋊D3—41no—
60C4×C3⋊D3—41no—
61C32×C8—22no—
62C32×C8—42no—
63C3⋊(C3⋊C8)—24no—
64C3⋊(C3⋊C8)—41no—
65#430—92no—
66#430C3⋊D311yescharacteristic, complemented
67#407—92no—
68#407—91no—
69#338—91no—
70C23×D3—34no—
71C22×C3×C4C22×D314yes—
72C22×Dic3—34no—
73C2×C4×D3—68no—
74C2×C4×D3—68no—
75C2×C4×D3—64no—
76C2×C4×D3—64no—
77C3×M16—28no—
78C3×M16—28no—
79C3×M16—28no—
80C2×C3×C8—28no—
81C2×C3×C8#6718yes—
82#208—68no—
83#208—68no—
84#208—68no—
85C2×C3⋊C8—316no—
86C2×C3⋊C8—64no—
87C22×C32—41no—
88C22×C32C22⋊Q812yes—
89C22×C32C22⋊Q811yescharacteristic
90C2×C3⋊D3—24no—
91C2×C3⋊D3—22no—
92C2×C3⋊D3—42no—
93C2×C3⋊D3—41no—
94C2×C3⋊D3—41no—
95C32×C4#12312yes—
96C32×C4#12311yescharacteristic
97C32×C4#12711yescharacteristic
98C3⋊Dic3—41no—
99C23×C4—91no—
100C2×M16—92no—
101C2×M16—91no—
102C2×M16C2×C3⋊D312yes—
103C2×M16C2×C3⋊D311yescharacteristic
104#108—22no—
105#108—184no—
106C22⋊C8—184no—
107C22⋊C8—182no—
108C23×C3D3×Q814yes—
109C22×D3—68no—
110C22×D3—64no—
111C22×D3—128no—
112C2×C3×C4#23518yes—
113C2×C3×C4D3×D418yes—
114C2×C3×C4#23914yes—
115C2×C3×C4C2×#6714yes—
116C2×Dic3—68no—
117C2×Dic3—64no—
118C4×D3—128no—
119C4×D3—124no—
120C4×D3—124no—
121C3×C8—28no—
122C3×C8—48no—
123C3⋊C8—616no—
124C3⋊C8—124no—
125C2×C32—22no—
126C2×C32—21no—
127C2×C32#39911yescharacteristic
128C3⋊D3—42no—
129C24—91no—
130C22×C4—91no—
131C22×C4—182no—
132C22×C4—182no—
133C22×C4—181no—
134C22×C4—181no—
135C22×C4C22×C3⋊D311yescharacteristic
136M16—22no—
137M16—22no—
138M16—22no—
139M16—182no—
140M16—182no—
141M16—182no—
142C2×C8—22no—
143C2×C8—94no—
144C2×C8—181no—
145C2×C8#63812yes—
146C22×C3—44no—
147C22×C3#89618yes—
148C22×C3#94614yes—
149C2×D3—616no—
150C2×D3—68no—
151C2×D3—128no—
152C2×D3—124no—
153C2×D3—124no—
154C3×C4#89418yes—
155C3×C4#92914yes—
156C3×C4#94014yes—
157Dic3—124no—
158C32#209111yescharacteristic, complemented, Sylow
159C23—182no—
160C23—181no—
161C23—362no—
162C23Q8×C3⋊D311yescharacteristic
163C2×C4—182no—
164C2×C4—181no—
165C2×C4—362no—
166C2×C4—361no—
167C2×C4—361no—
168C2×C4#382812yes—
169C2×C4D4×C3⋊D312yes—
170C2×C4#383211yescharacteristic
171C2×C4C2×#63811yescharacteristic
172C8—22no—
173C8—42no—
174C8—184no—
175C8—361no—
176C2×C3—28no—
177C2×C3—24no—
178C2×C3#499314yes—
179D3—128no—
180C22—41no—
181C22—184no—
182C22—182no—
183C22—362no—
184C22—361no—
185C22—361no—
186C22#6410512yes—
187C22#6415511yescharacteristic
188C4—361no—
189C4#6410312yes—
190C4#6413811yescharacteristic
191C4#6414911yescharacteristic
192C3#7072914yescomplemented
193C2—22no—
194C2—21no—
195C2—362no—
196C2#1059269211yescharacteristic
subgroupG/H
centerC4#64149
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#430C2
socleC2×C32#399
prime radicalC23×C3⋊D3Q8
hypercenter#430C3⋊D3
hypocenterC32#2091
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
1. C32×#430C2semidirect
4. #10592823C2semidirect
5. #10589426C2semidirect
16. C3×#430D3semidirect
66. #430C3⋊D3semidirect
158. C32#2091semidirect
192. C3#70729semidirect

Maximal subgroups

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

subgroupindex
C32×#4302
#105928252
#105928232
#105894262
#707293