Finite Group Databasebeta

← #44550893

Subgroups — #44550893

Order 32128.

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

normal subgroups only

This group has 344 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#30632454C211yesmaximal, characteristic, complemented
2#30631692C212yesmaximal, complemented
3#30631661C211yesmaximal, characteristic, complemented
4#30631443C212yesmaximal, complemented
5#535×C251C211yesmaximal, characteristic
6#22548722—24no—
7C2×#16860794—22no—
8C2×#16860794C2212yes—
9#22548674C2212yes—
10#22548636—24no—
11#22548630—22no—
12C2×#41×C251C2211yescharacteristic
13C22×D4×C251C2211yescharacteristic
14#127×C251C412yescomplemented
15#124×C251C412yescomplemented
16#121×C251—22no—
17#120×C251—22no—
18#117×C251C2211yescharacteristic
19#16860794—24no—
20#16860794—22no—
21#16860794—22no—
22C2×C251⋊C8—24no—
23C2×C251⋊C8D414yescomplemented
24C4⋊Dic251—22no—
25C22⋊Dic251—22no—
26C4×Dic251—22no—
27C24×C251—21no—
28#41×C251—22no—
29#41×C251—22no—
30C2×Q8×C251C2×C411yescharacteristic
31C2×D4×C251—24no—
32C2×D4×C251—22no—
33C2×D4×C251—21no—
34C2×D4×C251—22no—
35C2×D4×C251C2×C412yes—
36C2×D4×C251C2×C411yescharacteristic
37C2×D4×C251D412yes—
38C22×C4×C251D412yes—
39C22×C4×C251C2311yescharacteristic
40C4⋊C4×C251—21no—
41C22⋊C4×C251—21no—
42C22⋊C4×C251—24no—
43C42×C251C2×C412yes—
44C2×Dic251—42no—
45C251⋊C8—24no—
46C23×C251—22no—
47C23×C251—42no—
48C23×C251—82no—
49C23×C251C22⋊C412yes—
50C23×C251C2×D411yescharacteristic
51Q8×C251—22no—
52D4×C251—24no—
53D4×C251—22no—
54D4×C251—24no—
55D4×C251—41no—
56D4×C251—41no—
57D4×C251—84no—
58C2×C4×C251—22no—
59C2×C4×C251—22no—
60C2×C4×C251—22no—
61C2×C4×C251C22⋊C412yes—
62C2×C4×C251C22×C411yescharacteristic
63C2×C4×C251C2×D412yes—
64C2×C4×C251C2×D411yescharacteristic
65C2×C4×C251#4112yes—
66C22×C251—22no—
67C22×C251—41no—
68C22×C251—42no—
69C22×C251—44no—
70C22×C251—42no—
71C22×C251—84no—
72C22×C251C2×C22⋊C411yescharacteristic
73C22×C251#12112yes—
74C4×C251—22no—
75C4×C251—42no—
76C4×C251C4×D412yes—
77C4×C251#12011yescharacteristic
78C4×C251#12311yescharacteristic
79Dic251—82no—
80C2×C251—22no—
81C2×C251—21no—
82C2×C251—42no—
83C2×C251—82no—
84C2×C251#38611yescharacteristic
85C251#191011yescharacteristic, complemented, Sylow
86#1910—2511nomaximal, Sylow
87#568—2511no—
88#535D25111yescharacteristic
89#418—2512no—
90#410—2511no—
91H(3,ℤ/4)—2512no—
92C2×#41C2×D25111yescharacteristic
93C22×D4C2×D25111yescharacteristic
94#131—5024no—
95C2×M16—5022no—
96C2×M16—2512no—
97#127Dic25112yescomplemented
98#124Dic25112yescomplemented
99#121—22no—
100#120—22no—
101#117—2512no—
102#117C2×D25111yescharacteristic
103#102—5024no—
104#99—5022no—
105C24—21no—
106#41—22no—
107#41—22no—
108C2×Q8C2×Dic25111yescharacteristic
109C2×D4—24no—
110C2×D4—22no—
111C2×D4—21no—
112C2×D4—22no—
113C2×D4C2×Dic25112yes—
114C2×D4C2×Dic25111yescharacteristic
115C2×D4C22⋊D25112yes—
116C22×C4C22⋊D25112yes—
117C22×C4C22×D25111yescharacteristic
118M16—5024no—
119M16—5022no—
120M16—5022no—
121C2×C8—5024no—
122C2×C8—2514no—
123C4⋊C4—21no—
124C4⋊C4—5022no—
125C22⋊C4—21no—
126C22⋊C4—24no—
127C22⋊C4—5022no—
128C42—5022no—
129C42C2×Dic25112yes—
130C23—22no—
131C23—42no—
132C23—82no—
133C23C22⋊Dic25112yes—
134C23C2×C22⋊D25111yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—24no—
139D4—41no—
140D4—41no—
141D4—84no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—10042no—
146C2×C4C22⋊Dic25112yes—
147C2×C4C22×Dic25111yescharacteristic
148C2×C4D4×D25112yes—
149C2×C4C2×C22⋊D25111yescharacteristic
150C2×C4#1686080912yes—
151C8—5024no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22—84no—
158C22C2×C22⋊Dic25111yescharacteristic
159C22#2254868712yes—
160C4—22no—
161C4—42no—
162C4—20082no—
163C4D4×Dic25112yes—
164C4#2254868311yescharacteristic
165C4#2254869611yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#3063156711yescharacteristic
subgroupG/H
centerC2#30631567
commutatorC2×C4×C251C22×C4
FrattiniC22×C4C22×D251
Fitting, prime radical#535×C251C2
socleC2×C251#386
cosocleC22×C4×C251C23
hypercenter#535D251
hypocenterC251#1910
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #30632454C2semidirect
2. #30631692C2semidirect
3. #30631661C2semidirect
4. #30631443C2semidirect
14. #127×C251C4semidirect
15. #124×C251C4semidirect
23. C2×C251⋊C8D4semidirect
85. C251#1910semidirect
97. #127Dic251semidirect
98. #124Dic251semidirect

Maximal subgroups

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

subgroupindex
#306324542
#306316922
#306316612
#306314432
#535×C2512
#1910251