Finite Group Databasebeta

← #11787103

Subgroups — #11787103

Order 1152.

780 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 249 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#10596290C211yesmaximal, characteristic
2C32×#410C211yesmaximal, characteristic
3#10592933C211yesmaximal, characteristic
4#10592698C212yesmaximal, complemented
5#10589399C212yesmaximal, complemented
6#70044—34nomaximal
7C2×C32×#41C2211yescharacteristic
8C32×#117C2212yes—
9#64157—24no—
10C2×#3748—22no—
11C2×#3748C2211yescharacteristic
12C2×#3748C2212yes—
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C32×#99C414yes—
15#63657—22no—
16C4⋊(C3⋊(C3⋊C8))—24no—
17#5819—34no—
18C3×#410D314yes—
19#5234—34no—
20#4999—38no—
21#4533—38no—
22C32×#41—22no—
23C32×#41—22no—
24C2×C32×Q8Q811yescharacteristic
25C2×C32×D4C2×C412yes—
26C2×C32×D4Q811yescharacteristic
27C22×C32×C4D412yes—
28C22×C32×C4C2311yescharacteristic
29C32×C4⋊C4—22no—
30C32×C22⋊C4C2×C414yes—
31C32×C42—22no—
32#3748—24no—
33#3748—22no—
34#3748—22no—
35#3748—22no—
36C2×C3⋊(C3⋊C8)—24no—
37C2×C3⋊(C3⋊C8)—22no—
38C2×C3⋊(C3⋊C8)—21no—
39C2×C3⋊(C3⋊C8)—21no—
40C2×C3⋊(C3⋊C8)D414yes—
41#1868—91noSylow
42C2×C3×#41C2×D314yes—
43C3×#117C2×D318yes—
44#948—616no—
45C2×#208—38no—
46C2×#208—34no—
47C2×#208—68no—
48C22×C3⋊C8—34no—
49C3×#99Dic3116yes—
50#830—68no—
51C4⋊(C3⋊C8)—616no—
52C23×C32C4⋊C412yes—
53C23×C32C22×C411yescharacteristic
54C32×Q8—22no—
55C32×D4—24no—
56C32×D4—22no—
57C2×C32×C4—22no—
58C2×C32×C4—22no—
59C2×C32×C4—24no—
60C2×C32×C4C4⋊C412yes—
61C2×C32×C4C2×D411yescharacteristic
62C2×C32×C4C2×D412yes—
63C2×C32×C4C2×Q811yescharacteristic
64C2×C32×C4#4112yes—
65C3⋊(C3⋊C8)—24no—
66C3⋊(C3⋊C8)—41no—
67C3⋊(C3⋊C8)—41no—
68#568—91no—
69#424—92no—
70#410C3⋊D311yescharacteristic
71#408—91no—
72#344—92no—
73C3×#41—28no—
74C3×#41—28no—
75C2×C3×Q8Dic614yes—
76C2×C3×D4Dic614yes—
77C2×C3×D4C2×Dic318yes—
78C22×C3×C4D1218yes—
79C22×C3×C4C22×D314yes—
80C3×C4⋊C4—28no—
81C3×C22⋊C4C2×Dic3116yes—
82C3×C42—28no—
83#208—616no—
84#208—68no—
85#208—68no—
86#208—68no—
87C2×C3⋊C8—316no—
88C2×C3⋊C8—616no—
89C2×C3⋊C8—64no—
90C2×C3⋊C8—64no—
91C2×C3⋊C8—68no—
92C22×C32—22no—
93C22×C32—41no—
94C22×C32—42no—
95C22×C32C2×C4⋊C411yescharacteristic
96C22×C32C4×D412yes—
97C32×C4—22no—
98C32×C4—44no—
99C32×C4#12011yescharacteristic
100C32×C4C22⋊Q812yes—
101C32×C4#12311yescharacteristic
102C2×#41C2×C3⋊D311yescharacteristic
103#131—184no—
104C2×M16—92no—
105C2×M16—91no—
106C2×M16—182no—
107C22×C8—91no—
108#117C2×C3⋊D312yes—
109C4⋊C8—184no—
110#99C3⋊Dic314yes—
111C22⋊C8—182no—
112C23×C3C4⋊Dic318yes—
113C23×C3C22×Dic314yes—
114C3×Q8—28no—
115C3×D4—216no—
116C3×D4—28no—
117C2×C3×C4—28no—
118C2×C3×C4—28no—
119C2×C3×C4—216no—
120C2×C3×C4C4⋊Dic318yes—
121C2×C3×C4C2×Dic614yes—
122C2×C3×C4C2×D1214yes—
123C2×C3×C4D3×D418yes—
124C2×C3×C4#23718yes—
125C3⋊C8—616no—
126C3⋊C8—124no—
127C3⋊C8—124no—
128C2×C32—22no—
129C2×C32—21no—
130C2×C32—42no—
131C2×C32#38511yescharacteristic
132#41—22no—
133#41—22no—
134C2×Q8#63411yescharacteristic
135C2×D4#63411yescharacteristic
136C2×D4C2×C3⋊Dic312yes—
137C22×C4C4⋊(C3⋊D3)12yes—
138C22×C4C22×C3⋊D311yescharacteristic
139M16—184no—
140M16—182no—
141M16—182no—
142M16—182no—
143C2×C8—94no—
144C2×C8—184no—
145C2×C8—181no—
146C2×C8—181no—
147C2×C8—182no—
148C4⋊C4—22no—
149C22⋊C4C2×C3⋊Dic314yes—
150C42—22no—
151C22×C3—28no—
152C22×C3—44no—
153C22×C3—48no—
154C22×C3C2×C4⋊Dic314yes—
155C22×C3D4×Dic318yes—
156C3×C4—28no—
157C3×C4—416no—
158C3×C4#87818yes—
159C3×C4#88214yes—
160C3×C4#88614yes—
161C32#186811yescharacteristic, complemented, Sylow
162C23C4⋊(C3⋊Dic3)12yes—
163C23C22×C3⋊Dic311yescharacteristic
164Q8—22no—
165D4—24no—
166D4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4C4⋊(C3⋊Dic3)12yes—
171C2×C4C2×#63411yescharacteristic
172C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
173C2×C4D4×C3⋊D312yes—
174C2×C4#383012yes—
175C8—184no—
176C8—361no—
177C8—361no—
178C2×C3—28no—
179C2×C3—24no—
180C2×C3—48no—
181C2×C3#495014yes—
182C22—22no—
183C22—41no—
184C22—42no—
185C22C2×C4⋊(C3⋊Dic3)11yescharacteristic
186C22D4×C3⋊Dic312yes—
187C4—22no—
188C4—44no—
189C4#6408712yes—
190C4#6409111yescharacteristic
191C4#6409511yescharacteristic
192C3#7004414yescomplemented
193C2—22no—
194C2—21no—
195C2—42no—
196C2#1059264911yescharacteristic
subgroupG/H
centerC4#64091
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#410C2
socleC2×C32#385
prime radicalC2×C32×#41C22
cosocleC22×C32×C4C23
hypercenter#410C3⋊D3
hypocenterC32#1868
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
4. #10592698C2semidirect
5. #10589399C2semidirect
161. C32#1868semidirect
192. C3#70044semidirect

Maximal subgroups

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

subgroupindex
#105962902
C32×#4102
#105929332
#105926982
#105893992
#700443