Finite Group Databasebeta

← #24990981

Subgroups — #24990981

Order 11008.

396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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#19135565C211yesmaximal, characteristic
2#19134728C212yesmaximal
3C2×#14582641C211yesmaximal, characteristic
4#19132476C212yesmaximal
5C43×#2382C211yesmaximal, characteristic
6C2×#13063236C2211yescharacteristic
7C2×#13063236C2212yes—
8#14582769C2211yescharacteristic
9#14582661—22no—
10#14582661—22no—
11#14582661—22no—
12#14582641C414yescomplemented
13C2×#125×C43C2211yescharacteristic
14C43×#389—22no—
15C43×#387—22no—
16C43×#387—22no—
17C43×#382C2212yes—
18C22×C43⋊C8—21no—
19C22×C43⋊C8—22no—
20C2×C4⋊Dic43—21no—
21C2×C4⋊Dic43—22no—
22#13063236—22no—
23#13063236—22no—
24#13063236C2×C414yes—
25#125×C43—22no—
26#125×C43C2×C412yes—
27#125×C43Q812yes—
28C2×C4⋊C4×C43—22no—
29C2×C4⋊C4×C43—22no—
30C2×C4⋊C4×C43D412yes—
31C2×C4⋊C4×C43D412yes—
32C2×C4⋊C4×C43D412yes—
33C2×C42×C43—22no—
34C2×C42×C43C2311yescharacteristic
35#95×C43—22no—
36#95×C43—22no—
37#95×C43—22no—
38#95×C43—22no—
39C22×C4×C43—22no—
40C22×C4×C43—22no—
41C22×C4×C43—22no—
42C22×C4×C43C2×D411yescharacteristic
43C22×C4×C43C2×D412yes—
44C22×Dic43—41no—
45C4⋊C4×C43—24no—
46C4⋊C4×C43—24no—
47C4⋊C4×C43—22no—
48C4⋊C4×C43—42no—
49C4⋊C4×C43—42no—
50C4⋊C4×C43—82no—
51C4⋊C4×C43C4⋊C414yes—
52C42×C43—82no—
53C42×C43C22×C411yescharacteristic
54C42×C43C2×Q811yescharacteristic
55C42×C43#4112yes—
56C4⋊Dic43—42no—
57C4⋊Dic43—44no—
58C2×C43⋊C8—22no—
59C2×C43⋊C8—24no—
60C2×C43⋊C8—41no—
61C2×C43⋊C8—42no—
62C2×C43⋊C8—42no—
63C2×C43⋊C8—41no—
64C23×C43#12011yescharacteristic
65C2×C4×C43—21no—
66C2×C4×C43—22no—
67C2×C4×C43—22no—
68C2×C4×C43—21no—
69C2×C4×C43—24no—
70C2×C4×C43—42no—
71C2×C4×C43—42no—
72C2×C4×C43—42no—
73C2×C4×C43—42no—
74C2×C4×C43—42no—
75C2×C4×C43—42no—
76C2×C4×C43—42no—
77C2×C4×C43—42no—
78C2×C4×C43C2×C4⋊C411yescharacteristic
79C2×C4×C43C4×D412yes—
80C2×C4×C43C22⋊Q812yes—
81C2×C4×C43#12311yescharacteristic
82C2×Dic43—81no—
83C2×Dic43—82no—
84C43⋊C8—42no—
85C43⋊C8—44no—
86#8915—431nomaximal, Sylow
87C22×C43#38511yescharacteristic
88C22×C43#45411yescharacteristic
89C22×C43#45412yes—
90C22×C43#45512yes—
91C22×C43#45611yescharacteristic
92C4×C43—21no—
93C4×C43—21no—
94C4×C43—22no—
95C4×C43—22no—
96C4×C43—44no—
97C4×C43—82no—
98C4×C43—82no—
99Dic43—161no—
100#2382D4311yescharacteristic
101#1992—431no—
102#1836—432no—
103C2×#330—431no—
104#1295—432no—
105C2×C43#165811yescharacteristic
106C2×C43#166211yescharacteristic
107C2×C43#166412yes—
108C2×C43#185711yescharacteristic
109C2×C43#186012yes—
110C2×#125C2×D4311yescharacteristic
111C2×#97—432no—
112C2×#97—431no—
113#389—22no—
114#387—22no—
115#387—22no—
116#384—431no—
117#382C2×D4312yes—
118#340—862no—
119#340—862no—
120#340—862no—
121#330—434no—
122C43#891511yescharacteristic, complemented, Sylow
123C22×C8—861no—
124C22×C8—862no—
125#125—22no—
126#125Dic8612yes—
127#125C4×D4312yes—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—861no—
131C2×C4⋊C4—862no—
132C2×C4⋊C4C22⋊D4312yes—
133C2×C4⋊C4C22⋊D4312yes—
134C2×C4⋊C4C22⋊D4312yes—
135C2×C42—22no—
136C2×C42C22×D4311yescharacteristic
137#97—434no—
138#97—862no—
139#97—862no—
140#95—22no—
141#95—22no—
142#95—22no—
143#95—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—1721no—
148C22×C4C2×C22⋊D4311yescharacteristic
149C22×C4C2×C22⋊D4312yes—
150C2×C8—862no—
151C2×C8—864no—
152C2×C8—1721no—
153C2×C8—1722no—
154C2×C8—1722no—
155C2×C8—1721no—
156C4⋊C4—24no—
157C4⋊C4—24no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—82no—
162C4⋊C4—1722no—
163C4⋊C4—1724no—
164C4⋊C4Dic43⋊C414yes—
165C42—82no—
166C42C2×Dic8611yescharacteristic
167C42C2×C4×D4311yescharacteristic
168C42#1062189812yes—
169C23#1306329411yescharacteristic
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—3441no—
184C2×C4—3442no—
185C2×C4C2×Dic43⋊C411yescharacteristic
186C2×C4C4×C22⋊D4312yes—
187C2×C4#1306330412yes—
188C2×C4#1306330811yescharacteristic
189C8—1722no—
190C8—1724no—
191C22#1458277211yescharacteristic
192C22#1458307211yescharacteristic
193C22#1458307212yes—
194C22#1458307712yes—
195C22#1458308211yescharacteristic
196C4—21no—
197C4—21no—
198C4—22no—
199C4—22no—
200C4—44no—
201C4—82no—
202C4—82no—
203C4—6881no—
204C2#1913389711yescharacteristic
205C2#1913391811yescharacteristic
206C2#1913392912yes—
207C2#1913481011yescharacteristic
208C2#1913482812yes—
subgroupG/H
centerC23#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2382C2
socle, prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#2382D43
hypocenterC43#8915
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2382

Complements

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

NH ≅ G/Ntype
12. #14582641C4semidirect
122. C43#8915semidirect

Maximal subgroups

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

subgroupindex
#191355652
#191347282
C2×#145826412
#191324762
C43×#23822
#891543