Finite Group Databasebeta

← #24990980

Subgroups — #24990980

Order 11008.

396 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 111 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#19137781C211yesmaximal, characteristic
2#19134730C212yesmaximal
3C2×#14582641C211yesmaximal, characteristic
4#19132477C212yesmaximal
5C43×#1992C211yesmaximal, characteristic
6C2×#13063236C2212yes—
7#14582798—22no—
8#14582785—22no—
9#14582785—22no—
10#14582765C2212yes—
11#14582661—22no—
12#14582661—22no—
13#14582641C414yescomplemented
14C2×#125×C43C2211yescharacteristic
15C2×#97×C43C2211yescharacteristic
16C43×#384C2211yescharacteristic
17C43×#340—22no—
18C22×C43⋊C8—22no—
19C2×C4⋊Dic43—22no—
20C2×C4⋊Dic43D412yes—
21C2×C4⋊Dic43D412yes—
22C2×C4×Dic43—22no—
23#13063236—22no—
24#13063236C2×C414yes—
25C43⋊#95—22no—
26C43⋊#95—22no—
27C43⋊#95—22no—
28C43⋊#95—22no—
29C22×C8×C43—21no—
30#125×C43—22no—
31#125×C43C2×C412yes—
32#125×C43Q812yes—
33C2×C4⋊C4×C43—22no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43D412yes—
37C2×C42×C43C2311yescharacteristic
38#97×C43—22no—
39C22×C4×C43—22no—
40C22×C4×C43—41no—
41C22×C4×C43C2×D412yes—
42C22×C4×C43C2×D411yescharacteristic
43C22×Dic43—22no—
44C22×Dic43—22no—
45C2×C8×C43—22no—
46C2×C8×C43—41no—
47C2×C8×C43—41no—
48C4⋊C4×C43—24no—
49C4⋊C4×C43—24no—
50C4⋊C4×C43—22no—
51C4⋊C4×C43—44no—
52C4⋊C4×C43—42no—
53C4⋊C4×C43C4⋊C414yes—
54C42×C43C22×C411yescharacteristic
55C42×C43C2×Q811yescharacteristic
56C42×C43#4112yes—
57C4⋊Dic43—42no—
58C4⋊Dic43—42no—
59C4⋊Dic43—82no—
60C4×Dic43—82no—
61C2×C43⋊C8—24no—
62C2×C43⋊C8—42no—
63C2×C43⋊C8—42no—
64C23×C43#12011yescharacteristic
65C2×C4×C43—22no—
66C2×C4×C43—21no—
67C2×C4×C43—22no—
68C2×C4×C43—21no—
69C2×C4×C43—24no—
70C2×C4×C43—42no—
71C2×C4×C43—42no—
72C2×C4×C43—82no—
73C2×C4×C43—81no—
74C2×C4×C43C2×C4⋊C411yescharacteristic
75C2×C4×C43C4×D412yes—
76C2×C4×C43C22⋊Q812yes—
77C2×C4×C43#12311yescharacteristic
78C2×Dic43—42no—
79C2×Dic43—42no—
80C2×Dic43—42no—
81C2×Dic43—42no—
82C2×Dic43—42no—
83C2×Dic43—42no—
84C8×C43—42no—
85C43⋊C8—44no—
86#8915—431nomaximal, Sylow
87C22×C43#38511yescharacteristic
88C22×C43#45412yes—
89C22×C43#45411yescharacteristic
90C22×C43#45512yes—
91C22×C43#45611yescharacteristic
92C4×C43—21no—
93C4×C43—21no—
94C4×C43—22no—
95C4×C43—22no—
96C4×C43—44no—
97C4×C43—161no—
98Dic43—82no—
99Dic43—82no—
100#2382—431no—
101#1992D4311yescharacteristic
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×#97C2×D4311yescharacteristic
113#389—862no—
114#387—862no—
115#387—862no—
116#384C2×D4311yescharacteristic
117#382—432no—
118#340—22no—
119#340—862no—
120#340—862no—
121#330—434no—
122C43#891511yescharacteristic, complemented, Sylow
123C22×C8—21no—
124C22×C8—862no—
125#125—22no—
126#125Dic8612yes—
127#125C4×D4312yes—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—432no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—862no—
134C2×C4⋊C4C22⋊D4312yes—
135C2×C42—862no—
136C2×C42C22×D4311yescharacteristic
137#97—22no—
138#97—434no—
139#97—862no—
140#95—862no—
141#95—862no—
142#95—862no—
143#95—862no—
144C22×C4—22no—
145C22×C4—41no—
146C22×C4—862no—
147C22×C4—862no—
148C22×C4D4×D4312yes—
149C22×C4C2×C22⋊D4311yescharacteristic
150C2×C8—22no—
151C2×C8—41no—
152C2×C8—41no—
153C2×C8—864no—
154C2×C8—1722no—
155C2×C8—1722no—
156C4⋊C4—24no—
157C4⋊C4—24no—
158C4⋊C4—22no—
159C4⋊C4—44no—
160C4⋊C4—42no—
161C4⋊C4—3442no—
162C4⋊C4—1722no—
163C4⋊C4—1722no—
164C4⋊C4Dic43⋊C414yes—
165C42—3442no—
166C42C2×Dic8611yescharacteristic
167C42C2×C4×D4311yescharacteristic
168C42#1062190012yes—
169C23#1306329311yescharacteristic
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—82no—
178C2×C4—81no—
179C2×C4—1722no—
180C2×C4—1722no—
181C2×C4—1722no—
182C2×C4—1722no—
183C2×C4—1722no—
184C2×C4—1722no—
185C2×C4C2×Dic43⋊C411yescharacteristic
186C2×C4(C22⋊D43)⋊C412yes—
187C2×C4#1306330212yes—
188C2×C4#1306330611yescharacteristic
189C8—42no—
190C8—1724no—
191C22#1458277111yescharacteristic
192C22#1458307012yes—
193C22#1458307111yescharacteristic
194C22#1458307512yes—
195C22#1458308111yescharacteristic
196C4—21no—
197C4—21no—
198C4—22no—
199C4—22no—
200C4—44no—
201C4—161no—
202C4—3442no—
203C4—3442no—
204C2#1913389611yescharacteristic
205C2#1913391611yescharacteristic
206C2#1913392712yes—
207C2#1913480911yescharacteristic
208C2#1913482612yes—
subgroupG/H
centerC23#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1992C2
socle, prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#1992D43
hypocenterC43#8915
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
13. #14582641C4semidirect
122. C43#8915semidirect

Maximal subgroups

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

subgroupindex
#191377812
#191347302
C2×#145826412
#191324772
C43×#19922
#891543