Finite Group Databasebeta

← #25000737

Subgroups — #25000737

Order 11008.

370 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 77 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#19134735C211yesmaximal, characteristic, complemented
2#19133317C212yesmaximal, complemented
3#19133206C212yesmaximal, complemented
4#19132506C211yesmaximal, characteristic, complemented
5C43×#3253C211yesmaximal, characteristic
6#14582956C2212yes—
7#14582923C2211yescharacteristic
8C2×#13063236C2211yescharacteristic
9#14582663—22no—
10#14582645—22no—
11#14582643—22no—
12#14582639—24no—
13C43×#532C2212yes—
14C43×#476—22no—
15C43×#469—22no—
16C43×#459—22no—
17C43×#423C2211yescharacteristic
18C2×#10621877—21no—
19C22×C43⋊C8—21no—
20C4⋊(C43⋊C8)—22no—
21C4⋊(C43⋊C8)—22no—
22C22⋊(C43⋊C8)—22no—
23#13063236—21no—
24#13063236—22no—
25#13063236D412yes—
26C2×#41×C43—22no—
27C2×D8×C43—22no—
28C2×M16×C43D412yes—
29C4⋊Q8×C43D412yes—
30#127×C43D412yes—
31#124×C43—22no—
32#121×C43—22no—
33#121×C43—22no—
34C4×D4×C43—22no—
35C4×D4×C43—22no—
36C2×C42×C43C2311yescharacteristic
37#106×C43—22no—
38C4⋊C8×C43—22no—
39#102×C43—24no—
40#41×C43—84no—
41C2×Q8×C43—22no—
42C2×D4×C43—22no—
43C2×D4×C43—22no—
44C2×D4×C43—22no—
45C2×D4×C43—42no—
46C22×C4×C43—42no—
47C22×C4×C43C2×D411yescharacteristic
48C22×C4×C43#4112yes—
49D8×C43—82no—
50M16×C43—42no—
51C2×C8×C43—22no—
52C4⋊C4×C43—22no—
53C4⋊C4×C43—22no—
54C22⋊C4×C43—42no—
55C22⋊C4×C43—42no—
56C42×C43C2×D411yescharacteristic
57C42×C43C2×D412yes—
58C42×C43#4111yescharacteristic
59#10621877—42no—
60C2×C43⋊C8—22no—
61C2×C43⋊C8—41no—
62C2×C43⋊C8—41no—
63C2×C43⋊C8—41no—
64C2×C43⋊C8—42no—
65C23×C43—42no—
66C23×C43#12411yescharacteristic
67Q8×C43—82no—
68D4×C43—42no—
69D4×C43—42no—
70D4×C43—82no—
71D4×C43—82no—
72D4×C43—84no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—42no—
76C2×C4×C43—42no—
77C2×C4×C43—84no—
78C2×C4×C43#12011yescharacteristic
79C2×C4×C43#12111yescharacteristic
80C2×C4×C43#12112yes—
81C2×C4×C43#12312yes—
82C8×C43—42no—
83C43⋊C8—42no—
84C43⋊C8—82no—
85C43⋊C8—81no—
86#10525—431nomaximal, Sylow
87C22×C43—22no—
88C22×C43—21no—
89C22×C43—82no—
90C22×C43—82no—
91C22×C43—82no—
92C22×C43#39411yescharacteristic
93C4×C43—22no—
94C4×C43—22no—
95C4×C43—21no—
96C4×C43—82no—
97C4×C43#45411yescharacteristic
98C4×C43#45511yescharacteristic
99#3253D4311yescharacteristic
100#1838—431no—
101#1557—432no—
102#1530—432no—
103#1307—431no—
104C2×C43—41no—
105C2×C43—162no—
106C2×C43#204011yescharacteristic
107C2×C43#204812yes—
108#532C2×D4312yes—
109#476—22no—
110#469—22no—
111#459—22no—
112#432—432no—
113#423—431no—
114#423C2×D4311yescharacteristic
115C2×#97—431no—
116#341—862no—
117#332—862no—
118#331—862no—
119#329—864no—
120C43#1052511yescharacteristic, complemented, Sylow
121C2×#41—22no—
122C2×D8—22no—
123C2×M16—861no—
124C2×M16C22⋊D4312yes—
125C22×C8—861no—
126C4⋊Q8C22⋊D4312yes—
127#127C22⋊D4312yes—
128#124—22no—
129#121—22no—
130#121—22no—
131C4×D4—22no—
132C4×D4—22no—
133C2×C42C22×D4311yescharacteristic
134#106—22no—
135C4⋊C8—22no—
136C4⋊C8—862no—
137C4⋊C8—862no—
138#102—24no—
139C22⋊C8—862no—
140#97—432no—
141#97—862no—
142#97—861no—
143#41—84no—
144C2×Q8—22no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—22no—
148C2×D4—42no—
149C22×C4—42no—
150C22×C4#1062190012yes—
151C22×C4C2×C22⋊D4311yescharacteristic
152D8—82no—
153M16—42no—
154M16—1722no—
155C2×C8—22no—
156C2×C8—862no—
157C2×C8—1721no—
158C2×C8—1722no—
159C2×C8—1721no—
160C2×C8—1721no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C22⋊C4—42no—
164C22⋊C4—42no—
165C42D4×D4311yescharacteristic
166C42#1062190011yescharacteristic
167C42C2×C22⋊D4312yes—
168C23—42no—
169C23#1306331211yescharacteristic
170Q8—82no—
171D4—42no—
172D4—42no—
173D4—82no—
174D4—82no—
175D4—84no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—84no—
181C2×C4#1306329411yescharacteristic
182C2×C4#1306329611yescharacteristic
183C2×C4#1306329712yes—
184C2×C4#1306330612yes—
185C8—42no—
186C8—3442no—
187C8—3441no—
188C8—1722no—
189C22—21no—
190C22—22no—
191C22—82no—
192C22—82no—
193C22—82no—
194C22#1458281311yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—82no—
199C4#1458307211yescharacteristic
200C4#1458307711yescharacteristic
201C2—41no—
202C2—162no—
203C2#1913582111yescharacteristic
204C2#1913586512yes—
subgroupG/H
centerC22#14582813
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3253C2
socleC22×C43#394
hypercenter#3253D43
hypocenterC43#10525
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #19134735C2semidirect
2. #19133317C2semidirect
3. #19133206C2semidirect
4. #19132506C2semidirect
120. C43#10525semidirect

Maximal subgroups

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

subgroupindex
#191347352
#191333172
#191332062
#191325062
C43×#32532
#1052543