Finite Group Databasebeta

← #24994127

Subgroups — #24994127

Order 11008.

436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 95 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#19144971C211yesmaximal, characteristic
2#19143701C211yesmaximal, characteristic, complemented
3#19133308C212yesmaximal
4#19132468C212yesmaximal, complemented
5C43×#1537C211yesmaximal, characteristic, complemented
6C2×#13063322C2211yescharacteristic
7#14583265—22no—
8#14583247C414yes—
9#14583030—24no—
10#14582960—22no—
11#14582956C2212yes—
12#14582903—22no—
13C4×#10621877C2211yescharacteristic
14#14582642—24no—
15C43×#533C2211yescharacteristic
16C43×#432C2212yes—
17C43×#330—22no—
18C22×D172—21no—
19C22×D172—22no—
20C2×#10621877—21no—
21#13063322—22no—
22#13063322—21no—
23#13063322C2×C412yes—
24C4⋊(C43⋊C8)—24no—
25C4⋊(C43⋊C8)D414yes—
26#13063245—28no—
27C22⋊(C43⋊C8)—22no—
28#13063236—22no—
29#13063236—21no—
30#13063236—22no—
31C4×C43⋊C8—22no—
32C4×C43⋊C8C2×C412yes—
33C4⋊Q8×C43C2×C412yes—
34#125×C43D412yes—
35C22⋊Q8×C43—22no—
36C4×Q8×C43—22no—
37#117×C43D412yes—
38C2×C42×C43C2311yescharacteristic
39C4⋊C8×C43—22no—
40C22⋊C8×C43—22no—
41#97×C43—22no—
42C23×D43—41no—
43C2×Q8×C43—22no—
44C22×C4×C43C2×D411yescharacteristic
45C22×C4×C43#4112yes—
46C2×D172—22no—
47C2×D172—24no—
48C2×D172—41no—
49C2×D172—42no—
50C2×D172—44no—
51C2×D172—84no—
52C2×C8×C43—42no—
53C4⋊C4×C43—22no—
54C4⋊C4×C43—24no—
55C4⋊C4×C43C22⋊C414yes—
56C22⋊C4×C43—22no—
57C42×C43—22no—
58C42×C43C22×C411yescharacteristic
59C42×C43C2×D412yes—
60C42×C43C2×D411yescharacteristic
61#10621877—42no—
62C2×C43⋊C8—22no—
63C2×C43⋊C8—24no—
64C23×C43#12311yescharacteristic
65C22×D43—42no—
66C22×D43—82no—
67C22×D43—84no—
68Q8×C43—82no—
69C2×C4×C43—22no—
70C2×C4×C43—24no—
71C2×C4×C43—42no—
72C2×C4×C43C2×C22⋊C411yescharacteristic
73C2×C4×C43C4×D412yes—
74C2×C4×C43#12011yescharacteristic
75C2×C4×C43#12112yes—
76D172—44no—
77D172—84no—
78D172—84no—
79D172—82no—
80C8×C43—82no—
81C43⋊C8—42no—
82C43⋊C8—44no—
83#9424—431nomaximal, Sylow
84C22×C43—21no—
85C22×C43—22no—
86C22×C43#38611yescharacteristic
87C2×D43—82no—
88C2×D43—84no—
89C2×D43—164no—
90C4×C43—21no—
91C4×C43—22no—
92C4×C43—22no—
93C4×C43—44no—
94C4×C43#45412yes—
95#3138—431no—
96#2987—431no—
97#1555—432no—
98#1537D4311yescharacteristic, complemented
99#1291—432no—
100C2×C43—41no—
101C2×C43#188811yescharacteristic
102C2×C43#190312yes—
103D43—162no—
104#533C2×D4311yescharacteristic
105C2×#127—431no—
106#490—862no—
107#486—434no—
108#446—864no—
109#433—862no—
110#432—432no—
111#432C2×D4312yes—
112#418—862no—
113C4×M16—431no—
114#331—864no—
115#330—22no—
116C43#942411yescharacteristic, complemented, Sylow
117C22×D4—861no—
118C22×D4—862no—
119C2×M16—861no—
120C4⋊Q8C4×D4312yes—
121#127—432no—
122#127—862no—
123#127—861no—
124#125C22⋊D4312yes—
125C22⋊Q8—22no—
126C4×Q8—22no—
127#117D17212yes—
128C2×C42C22×D4311yescharacteristic
129C4⋊C8—22no—
130C4⋊C8—434no—
131C4⋊C8—864no—
132#102—868no—
133C22⋊C8—22no—
134C22⋊C8—862no—
135#97—22no—
136#97—862no—
137#97—862no—
138#97—861no—
139C4×C8—432no—
140C4×C8—862no—
141C24—1721no—
142C2×Q8—22no—
143C2×D4—862no—
144C2×D4—864no—
145C2×D4—3444no—
146C2×D4—1724no—
147C2×D4—1721no—
148C2×D4—1722no—
149C22×C4C2×D17211yescharacteristic
150C22×C4#1062190012yes—
151M16—1722no—
152C2×C8—42no—
153C2×C8—862no—
154C2×C8—864no—
155C4⋊C4—22no—
156C4⋊C4—24no—
157C4⋊C4(C2×D43)⋊C414yes—
158C22⋊C4—22no—
159C42—22no—
160C42C2×C4×D4311yescharacteristic
161C42D4×D4312yes—
162C42C2×C22⋊D4311yescharacteristic
163C23—3444no—
164C23—3442no—
165C23—1722no—
166C23#1306330911yescharacteristic
167Q8—82no—
168D4—3444no—
169D4—3444no—
170D4—3442no—
171D4—1724no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—42no—
175C2×C4C2×(C2×D43)⋊C411yescharacteristic
176C2×C4(C22⋊D43)⋊C412yes—
177C2×C4#1306329511yescharacteristic
178C2×C4#1306329712yes—
179C8—82no—
180C8—1722no—
181C8—1724no—
182C22—21no—
183C22—22no—
184C22—3442no—
185C22—3444no—
186C22—6884no—
187C22#1458277611yescharacteristic
188C4—21no—
189C4—22no—
190C4—22no—
191C4—44no—
192C4#1458307412yes—
193C2—41no—
194C2—6882no—
195C2#1913499611yescharacteristic
196C2#1913507312yes—
subgroupG/H
centerC22#14582776
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1537C2
socleC22×C43#386
prime radicalC2×#13063322C22
cosocleC2×C42×C43C23
hypercenter#1537D43
hypocenterC43#9424
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
2. #19143701C2semidirect
4. #19132468C2semidirect
5. C43×#1537C2semidirect
98. #1537D43semidirect
116. C43#9424semidirect

Maximal subgroups

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

subgroupindex
#191449712
#191437012
#191333082
#191324682
C43×#15372
#942443