Finite Group Databasebeta

← #44400282

Subgroups — #44400282

Order 29056.

340 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 93 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#28409799C211yesmaximal, characteristic, complemented
2#28409016C211yesmaximal, characteristic, complemented
3C2×#20300205C212yesmaximal, complemented
4#28408802C212yesmaximal, complemented
5#535×C227C211yesmaximal, characteristic
6#20300295—24no—
7C2×#16813868—22no—
8C2×#16813868C2212yes—
9C2×#16813868C2212yes—
10#20300207—21no—
11#20300205—24no—
12#20300205—21no—
13C2×#41×C227C2211yescharacteristic
14C22×D4×C227C2211yescharacteristic
15#127×C227—21no—
16#124×C227—21no—
17#121×C227—22no—
18#120×C227C414yes—
19#117×C227C2211yescharacteristic
20#16813868—24no—
21#16813868—22no—
22#16813868—22no—
23#16813868—22no—
24#16813868D414yescomplemented
25C2×C227⋊C8—24no—
26C2×C227⋊C8—22no—
27C2×C227⋊C8—22no—
28C24×C227C2×C412yes—
29#41×C227—22no—
30#41×C227—22no—
31C2×Q8×C227D411yescharacteristic
32C2×D4×C227—24no—
33C2×D4×C227—21no—
34C2×D4×C227—21no—
35C2×D4×C227—22no—
36C2×D4×C227—22no—
37C2×D4×C227C2×C412yes—
38C2×D4×C227D411yescharacteristic
39C22×C4×C227D412yes—
40C22×C4×C227C2311yescharacteristic
41C4⋊C4×C227—21no—
42C22⋊C4×C227—24no—
43C22⋊C4×C227C2×C412yes—
44C42×C227—21no—
45C227⋊C8—24no—
46C227⋊C8—42no—
47C23×C227—22no—
48C23×C227—24no—
49C23×C227—82no—
50C23×C227C22⋊C412yes—
51C23×C227C22×C411yescharacteristic
52Q8×C227—22no—
53D4×C227—24no—
54D4×C227—22no—
55D4×C227—41no—
56D4×C227—42no—
57D4×C227—41no—
58D4×C227—84no—
59C2×C4×C227—22no—
60C2×C4×C227—22no—
61C2×C4×C227—22no—
62C2×C4×C227C22⋊C412yes—
63C2×C4×C227C2×D412yes—
64C2×C4×C227C2×D411yescharacteristic
65C2×C4×C227C2×D411yescharacteristic
66C2×C4×C227#4112yes—
67C22×C227—22no—
68C22×C227—41no—
69C22×C227—42no—
70C22×C227—44no—
71C22×C227—42no—
72C22×C227—84no—
73C22×C227C2×C22⋊C411yescharacteristic
74C22×C227C4×D412yes—
75C4×C227—22no—
76C4×C227—42no—
77C4×C227#12011yescharacteristic
78C4×C227#12112yes—
79C4×C227#12311yescharacteristic
80C2×C227—21no—
81C2×C227—22no—
82C2×C227—42no—
83C2×C227—82no—
84C2×C227#38611yescharacteristic
85C227#191411yescharacteristic, complemented, Sylow
86#1914—2271nomaximal, Sylow
87#568—2271no—
88#535D22711yescharacteristic
89#413—2271no—
90C2×#100—2272no—
91#344—2272no—
92C2×#41C2×D22711yescharacteristic
93C22×D4C2×D22711yescharacteristic
94#131—4544no—
95C2×M16—4542no—
96C2×M16—2272no—
97C2×M16—2272no—
98#127—21no—
99#124—21no—
100#121—22no—
101#120Dic22714yes—
102#117C2×D22711yescharacteristic
103#101—4541no—
104#100—4541no—
105#100—4544no—
106C24C2×Dic22712yes—
107#41—22no—
108#41—22no—
109C2×Q8C22⋊D22711yescharacteristic
110C2×D4—24no—
111C2×D4—22no—
112C2×D4—21no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4C2×Dic22712yes—
116C2×D4C22⋊D22711yescharacteristic
117C22×C4C22⋊D22712yes—
118C22×C4C22×D22711yescharacteristic
119M16—4542no—
120M16—4542no—
121M16—4544no—
122M16—4542no—
123M16—2274no—
124C2×C8—4542no—
125C2×C8—4544no—
126C2×C8—4542no—
127C4⋊C4—21no—
128C22⋊C4—24no—
129C22⋊C4C2×Dic22712yes—
130C42—21no—
131C23—22no—
132C23—24no—
133C23—82no—
134C23C22⋊Dic22712yes—
135C23C22×Dic22711yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—41no—
140D4—42no—
141D4—41no—
142D4—84no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4C22⋊Dic22712yes—
147C2×C4D4×D22712yes—
148C2×C4C2×C22⋊D22711yescharacteristic
149C2×C4C2×C22⋊D22711yescharacteristic
150C2×C4#1681388312yes—
151C8—9082no—
152C8—4544no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—44no—
157C22—42no—
158C22—84no—
159C22C2×C22⋊Dic22711yescharacteristic
160C22D4×Dic22712yes—
161C4—22no—
162C4—42no—
163C4#2030025611yescharacteristic
164C4#2030026012yes—
165C4#2030026911yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#2840891211yescharacteristic
subgroupG/H
centerC2#28408912
commutatorC23×C227C22×C4
FrattiniC22×C4C22×D227
Fitting, prime radical#535×C227C2
socleC2×C227#386
cosocleC22×C4×C227C23
hypercenter#535D227
hypocenterC227#1914
LCSG ▷ C23×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #28409799C2semidirect
2. #28409016C2semidirect
3. C2×#20300205C2semidirect
4. #28408802C2semidirect
24. #16813868D4semidirect
85. C227#1914semidirect

Maximal subgroups

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

subgroupindex
#284097992
#284090162
C2×#203002052
#284088022
#535×C2272
#1914227