Finite Group Databasebeta

← #24996574

Subgroups — #24996574

Order 11008.

412 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 123 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#19144918C211yesmaximal, characteristic
2#19134733C211yesmaximal, characteristic, complemented
3#19133051C212yesmaximal, complemented
4#19133047C212yesmaximal
5C2×C43×#322C211yesmaximal, characteristic, complemented
6#14583456C2211yescharacteristic
7#14583449C2211yescharacteristic
8#14583254—22no—
9#14583250C412yes—
10#14583246C412yes—
11#14582923C2212yes—
12#14582896—22no—
13#14582664—22no—
14#14582631—24no—
15#14582628—24no—
16C2×C4×C8×C43C2212yes—
17C2×C4×C8×C43C2211yescharacteristic
18C43×#322—22no—
19C2×#10621898—21no—
20C2×#10621877—22no—
21#13063325C2×C411yescharacteristic
22#13063325C2×C412yes—
23#13063322C2×C411yescharacteristic
24#13063317—21no—
25#13063313—21no—
26#13063304—22no—
27#13063299—22no—
28C4×Dic86—22no—
29C4×D172—22no—
30#13063284—21no—
31C4⋊(C43⋊C8)—22no—
32C4⋊(C43⋊C8)—22no—
33#13063250—24no—
34#13063247—24no—
35C22×C8×C43—22no—
36C22×C8×C43D412yes—
37C2×C42×C43C2311yescharacteristic
38C4×C8×C43—22no—
39C4×C8×C43C2×C412yes—
40C4×C8×C43D414yes—
41C4×C8×C43D412yes—
42C22×C4×C43C2×D411yescharacteristic
43C22×C4×C43#4112yes—
44C2×C22⋊D43—41no—
45#10621898—44no—
46C2×D172—21no—
47C2×D172—22no—
48C2×C4×D43—41no—
49C2×Dic86—21no—
50C2×Dic86—22no—
51C2×C8×C43—24no—
52C2×C8×C43—24no—
53C2×C8×C43—44no—
54C2×C8×C43C22⋊C414yes—
55C42×C43C22×C411yescharacteristic
56C42×C43C2×D412yes—
57C42×C43C2×D411yescharacteristic
58C22⋊Dic43—41no—
59(C2×D43)⋊C4—42no—
60C4⋊Dic43—22no—
61C4⋊Dic43—22no—
62C4⋊Dic43—22no—
63Dic43⋊C4—42no—
64C4×Dic43—41no—
65#10621877—44no—
66C2×C43⋊C8—42no—
67C23×C43#12411yescharacteristic
68C22×D43—41no—
69C2×C4×C43—24no—
70C2×C4×C43C2×C22⋊C411yescharacteristic
71C2×C4×C43C4×D412yes—
72C2×C4×C43#12112yes—
73C2×C4×C43#12711yescharacteristic
74C2×C4×C43#13514yes—
75C22⋊D43—82no—
76C2×Dic43—42no—
77C2×Dic43—41no—
78D172—42no—
79D172—44no—
80C4×D43—82no—
81Dic86—42no—
82Dic86—44no—
83C8×C43—24no—
84C8×C43—44no—
85C43⋊C8—82no—
86#9863—431nomaximal, Sylow
87C22×C43—22no—
88C22×C43#39011yescharacteristic
89C22×C43#48812yes—
90C2×D43—81no—
91C2×D43—82no—
92C4×C43—22no—
93C4×C43#41612yes—
94C4×C43#44414yes—
95C4×C43#49512yes—
96Dic43—81no—
97Dic43—82no—
98#3131—431no—
99#1837—431no—
100#1493—432no—
101#1492—432no—
102C2×#322D4311yescharacteristic, complemented
103C2×C43—22no—
104C2×C43#195811yescharacteristic
105C2×C43#197512yes—
106D43—161no—
107#533—431no—
108#532—431no—
109#488—862no—
110#487—432no—
111#486—432no—
112#423—432no—
113#416—862no—
114C2×C4×C8C2×D4312yes—
115C2×C4×C8C2×D4311yescharacteristic
116#341—862no—
117Q8⋊C8—864no—
118D4⋊C8—864no—
119#322—22no—
120C43#986311yescharacteristic, complemented, Sylow
121C2×#41—861no—
122C2×M16—862no—
123C22×C8—22no—
124C22×C8D17212yes—
125C4⋊Q8—431no—
126C4⋊Q8—432no—
127#127—431no—
128#125—861no—
129#124—861no—
130C22⋊Q8—862no—
131#121—862no—
132C4×Q8—862no—
133C4×D4—862no—
134#117—861no—
135C2×C42C22×D4311yescharacteristic
136C4⋊C8—862no—
137C4⋊C8—862no—
138#103—864no—
139#102—864no—
140C4×C8—22no—
141C4×C8C4×D4312yes—
142C4×C8D17214yes—
143C4×C8C22⋊D4312yes—
144#41—1724no—
145C2×Q8—861no—
146C2×Q8—862no—
147C2×D4—861no—
148C2×D4—862no—
149C2×D4—1721no—
150C22×C4—1721no—
151C22×C4C2×D17211yescharacteristic
152C22×C4#1062189812yes—
153M16—1724no—
154C2×C8—24no—
155C2×C8—24no—
156C2×C8—44no—
157C2×C8—1722no—
158C2×C8(C2×D43)⋊C414yes—
159C4⋊C4—862no—
160C4⋊C4—862no—
161C4⋊C4—862no—
162C4⋊C4—1722no—
163C22⋊C4—1721no—
164C22⋊C4—1722no—
165C42—1721no—
166C42C2×C4×D4311yescharacteristic
167C42C2×D17212yes—
168C42C2×C22⋊D4311yescharacteristic
169C23—1721no—
170C23#1306331311yescharacteristic
171Q8—1722no—
172Q8—1724no—
173D4—3442no—
174D4—1722no—
175D4—1724no—
176C2×C4—24no—
177C2×C4—3442no—
178C2×C4—1722no—
179C2×C4—1721no—
180C2×C4C2×(C2×D43)⋊C411yescharacteristic
181C2×C4C4×D17212yes—
182C2×C4#1306329912yes—
183C2×C4#1306332211yescharacteristic
184C2×C4#1306334714yes—
185C8—24no—
186C8—44no—
187C8—3442no—
188C22—22no—
189C22—3442no—
190C22—3441no—
191C22#1458280111yescharacteristic
192C22#1458325412yes—
193C4—22no—
194C4—3442no—
195C4—3441no—
196C4#1458289612yes—
197C4#1458302214yes—
198C4#1458328312yes—
199C2—22no—
200C2—6881no—
201C2#1913540611yescharacteristic
202C2#1913548812yes—
subgroupG/H
centerC2×C4#13063322
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#322C2
socleC22×C43#390
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenterC2×#322D43
hypocenterC43#9863
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#322

Complements

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

NH ≅ G/Ntype
2. #19134733C2semidirect
3. #19133051C2semidirect
5. C2×C43×#322C2semidirect
102. C2×#322D43semidirect
120. C43#9863semidirect

Maximal subgroups

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

subgroupindex
#191449182
#191347332
#191330512
#191330472
C2×C43×#3222
#986343