Finite Group Databasebeta

← #25010765

Subgroups — #25010765

Order 11008.

218 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 63 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#19136734C211yesmaximal, characteristic
2#19136646C211yesmaximal, characteristic
3#19134193C211yesmaximal, characteristic
4#19133401C211yesmaximal, characteristic
5#19132658C211yesmaximal, characteristic
6#19132643C211yesmaximal, characteristic
7C43×#1364C211yesmaximal, characteristic
8C2×Dic344—21no—
9#14583295—21no—
10#14583279C2211yescharacteristic
11#14583249—21no—
12#14583023—21no—
13C4×Dic172C2211yescharacteristic
14#14582726—21no—
15C4⋊(C43⋊C16)C2211yescharacteristic
16#14582704—21no—
17#14582702—21no—
18#14582629—21no—
19C8×C43⋊C8C2211yescharacteristic
20C43×#500C2211yescharacteristic
21C43×C4⋊C16C2211yescharacteristic
22C43×#335C2211yescharacteristic
23C2×Dic172—21no—
24C2×Dic172—21no—
25C2×Dic172D411yescharacteristic
26#13063325—21no—
27C4×Dic86—21no—
28Dic344—42no—
29C2×C43⋊C16—21no—
30#13063259D411yescharacteristic
31#13063256—42no—
32Dic43⋊C8—41no—
33#13063250—21no—
34#13063249—41no—
35#13063249—41no—
36C4×C43⋊C8D411yescharacteristic
37C4×C43⋊C8D411yescharacteristic
38C8×Dic43—41no—
39C4⋊Q8×C43—21no—
40C2×C16×C43—21no—
41#107×C43—21no—
42#107×C43—21no—
43C4⋊C8×C43—21no—
44C4×C8×C43C2311yescharacteristic
45C2×Q8×C43—41no—
46C2×Dic86—21no—
47C2×Dic86—41no—
48C2×C8×C43—41no—
49C2×C8×C43C2×D411yescharacteristic
50C2×C8×C43#4111yescharacteristic
51C4⋊C4×C43—41no—
52C4⋊C4×C43—41no—
53C42×C43C2×D411yescharacteristic
54C4⋊Dic43—21no—
55C4⋊Dic43—41no—
56C4⋊Dic43—41no—
57Dic43⋊C4—41no—
58C4×Dic43—41no—
59C2×C43⋊C8—21no—
60C2×C43⋊C8D811yescharacteristic
61C2×C43⋊C8D811yescharacteristic
62Dic172—21no—
63Dic172—41no—
64Dic172—41no—
65Dic172—81no—
66Dic172SD1612yes—
67C16×C43—41no—
68C43⋊C16—41no—
69Q8×C43—81no—
70Q8×C43—81no—
71C2×C4×C43—81no—
72C2×C4×C43#12111yescharacteristic
73C2×C4×C43C2×D811yescharacteristic
74C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
75C2×Dic43—41no—
76C2×Dic43—41no—
77C2×Dic43—81no—
78Dic86—22no—
79Dic86—41no—
80Dic86—81no—
81Dic86—81no—
82C8×C43—21no—
83C8×C43—81no—
84C8×C43C2×SD1611yescharacteristic
85C8×C43#13511yescharacteristic
86C43⋊C8—22no—
87C43⋊C8—21no—
88C43⋊C8—21no—
89#12423—431nomaximal, Sylow
90C22×C43#45911yescharacteristic
91C4×C43—21no—
92C4×C43—161no—
93C4×C43#46511yescharacteristic
94C4×C43#47111yescharacteristic
95C4×C43#50811yescharacteristic
96C4×C43#51011yescharacteristic
97Dic43—42no—
98Dic43—81no—
99Dic43—161no—
100#2225—431no—
101#2209—431no—
102#1707—431no—
103C8×Q16—431no—
104#1367—431no—
105#1364D4311yescharacteristic
106#1362—431no—
107C2×C43#166511yescharacteristic
108C2×C43#221111yescharacteristic
109C2×C43#221411yescharacteristic
110C2×Q32—861no—
111#500C2×D4311yescharacteristic
112#498—861no—
113#494—431no—
114#487—861no—
115C8×Q8—861no—
116C4×Q16—431no—
117#367—861no—
118C4⋊C16—431no—
119C4⋊C16C2×D4311yescharacteristic
120#358—861no—
121#358—861no—
122#335C2×D4311yescharacteristic
123Q8⋊C8—861no—
124C82—431no—
125C43#1242311yescharacteristic, complemented, Sylow
126C2×Q16—431no—
127C2×Q16—861no—
128C2×Q16—861no—
129C4⋊Q8—21no—
130C4⋊Q8—861no—
131C4×Q8—861no—
132Q32—1722no—
133C2×C16—21no—
134C2×C16—861no—
135#107—21no—
136#107—21no—
137#107—431no—
138#106—1722no—
139C4⋊C8—21no—
140C4⋊C8—1721no—
141#103—861no—
142#103—1721no—
143#103—1721no—
144C4×C8—431no—
145C4×C8—431no—
146C4×C8—1721no—
147C4×C8C22×D4311yescharacteristic
148C2×Q8—41no—
149C2×Q8—861no—
150C2×Q8—1721no—
151Q16—432no—
152Q16—861no—
153Q16—3441no—
154Q16—1721no—
155Q16—1721no—
156C2×C8—41no—
157C2×C8—431no—
158C2×C8—431no—
159C2×C8—861no—
160C2×C8#1062189811yescharacteristic
161C2×C8D4×D4311yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—861no—
165C4⋊C4—1721no—
166C4⋊C4—1721no—
167C4⋊C4—1721no—
168C42—1721no—
169C42D4×D4311yescharacteristic
170C16—41no—
171C16—1721no—
172Q8—81no—
173Q8—81no—
174Q8—862no—
175Q8—3441no—
176Q8—3441no—
177Q8—1721no—
178C2×C4—81no—
179C2×C4—3441no—
180C2×C4—1721no—
181C2×C4—1721no—
182C2×C4#1306329811yescharacteristic
183C2×C4D8×D4311yescharacteristic
184C2×C4#1306335211yescharacteristic
185C8—21no—
186C8—81no—
187C8—862no—
188C8—861no—
189C8—861no—
190C8SD16×D4311yescharacteristic
191C8#1306334811yescharacteristic
192C22#1458309311yescharacteristic
193C4—21no—
194C4—161no—
195C4—3441no—
196C4—1722no—
197C4—6881no—
198C4#1458313111yescharacteristic
199C4#1458316511yescharacteristic
200C4#1458332811yescharacteristic
201C4#1458333811yescharacteristic
202C2#1913393911yescharacteristic
203C2#1913665611yescharacteristic
204C2#1913667511yescharacteristic
subgroupG/H
centerC22#14583093
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1364C2
socle, prime radicalC22×C43#459
hypercenter#1364D43
hypocenterC43#12423
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
125. C43#12423semidirect

Maximal subgroups

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

subgroupindex
#191367342
#191366462
#191341932
#191334012
#191326582
#191326432
C43×#13642
#1242343