Finite Group Databasebeta

← #24999679

Subgroups — #24999679

Order 11008.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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#19142870C211yesmaximal, characteristic
2#19135568C212yesmaximal
3#19135414C211yesmaximal, characteristic
4#19132477C212yesmaximal
5C43×#1295C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7C2×#13063248—22no—
8C2×#13063236C2211yescharacteristic
9#14582833—22no—
10#14582832—22no—
11#14582831—22no—
12#14582765C2212yes—
13#14582662—22no—
14#14582662—22no—
15C2×#97×C43C2212yes—
16C43×#382C2211yescharacteristic
17C22×Dic86—21no—
18C22×C43⋊C8—21no—
19#13063325—22no—
20#13063325—21no—
21#13063325Q812yes—
22C2×C4⋊Dic43—22no—
23C2×C4⋊Dic43—22no—
24C2×C4⋊Dic43D412yes—
25C2×C4⋊Dic43D412yes—
26C2×Dic43⋊C4—22no—
27C2×Dic43⋊C4—22no—
28#13063248—44no—
29#13063236—22no—
30C43⋊#95—22no—
31C43⋊#95—22no—
32C43⋊#95—22no—
33C22×C8×C43—22no—
34C2×C4⋊C4×C43D412yes—
35C2×C42×C43C2311yescharacteristic
36#97×C43—22no—
37#97×C43—22no—
38#95×C43—22no—
39C22×C4×C43—22no—
40C22×C4×C43C2×D411yescharacteristic
41C22×C4×C43C2×D412yes—
42C22×Dic43—22no—
43C22×Dic43—22no—
44C22×Dic43—41no—
45C2×Dic86—22no—
46C2×Dic86—42no—
47C2×Dic86—42no—
48C2×Dic86—41no—
49C2×C8×C43—24no—
50C2×C8×C43—42no—
51C2×C8×C43—42no—
52C4⋊C4×C43—42no—
53C42×C43C2×Q811yescharacteristic
54C42×C43#4112yes—
55C42×C43#4111yescharacteristic
56C4⋊Dic43—24no—
57C4⋊Dic43—42no—
58C4⋊Dic43—42no—
59C4⋊Dic43—42no—
60C4⋊Dic43—82no—
61Dic43⋊C4—82no—
62Dic43⋊C4—82no—
63C2×C43⋊C8—22no—
64C2×C43⋊C8—41no—
65C2×C43⋊C8—41no—
66C23×C43#12011yescharacteristic
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—42no—
72C2×C4×C43—42no—
73C2×C4×C43—42no—
74C2×C4×C43C22⋊Q812yes—
75C2×C4×C43C22⋊Q811yescharacteristic
76C2×C4×C43#12412yes—
77C2×C4×C43#12411yescharacteristic
78C2×Dic43—42no—
79C2×Dic43—42no—
80C2×Dic43—42no—
81C2×Dic43—42no—
82C2×Dic43—42no—
83C2×Dic43—42no—
84C2×Dic43—42no—
85C2×Dic43—81no—
86C2×Dic43—81no—
87Dic86—44no—
88Dic86—82no—
89C8×C43—44no—
90C43⋊C8—42no—
91#10361—431nomaximal, Sylow
92C22×C43#39311yescharacteristic
93C22×C43#45311yescharacteristic
94C22×C43#45411yescharacteristic
95C22×C43#45512yes—
96C22×C43#45612yes—
97C4×C43—21no—
98C4×C43—21no—
99C4×C43—22no—
100C4×C43—22no—
101C4×C43—82no—
102Dic43—82no—
103Dic43—82no—
104Dic43—82no—
105#2845—431no—
106#1993—432no—
107#1960—431no—
108#1295—432no—
109#1295D4311yescharacteristic
110C2×C43#166112yes—
111C2×C43#166211yescharacteristic
112C2×C43#166311yescharacteristic
113C2×C43#202711yescharacteristic
114C2×C43#202812yes—
115C2×C4⋊Q8—431no—
116C2×#103—862no—
117C2×#97—431no—
118C2×#97C2×D4312yes—
119#398—862no—
120#398—862no—
121#398—862no—
122#382—432no—
123#382C2×D4311yescharacteristic
124#340—862no—
125#340—862no—
126C43#1036111yescharacteristic, complemented, Sylow
127C22×Q8—861no—
128C22×C8—22no—
129C22×C8—861no—
130C4⋊Q8—432no—
131C4⋊Q8—862no—
132C4⋊Q8—861no—
133C2×C4⋊C4—432no—
134C2×C4⋊C4—432no—
135C2×C4⋊C4—862no—
136C2×C4⋊C4—862no—
137C2×C4⋊C4—862no—
138C2×C4⋊C4—862no—
139C2×C4⋊C4D17212yes—
140C2×C42C22×D4311yescharacteristic
141#103—1724no—
142#97—22no—
143#97—22no—
144#97—862no—
145#95—22no—
146#95—862no—
147#95—862no—
148#95—862no—
149C2×Q8—862no—
150C2×Q8—1722no—
151C2×Q8—1722no—
152C2×Q8—1721no—
153C22×C4—22no—
154C22×C4—862no—
155C22×C4—862no—
156C22×C4—1721no—
157C22×C4C2×D17211yescharacteristic
158C22×C4D4×D4312yes—
159C2×C8—24no—
160C2×C8—42no—
161C2×C8—42no—
162C2×C8—862no—
163C2×C8—1721no—
164C2×C8—1721no—
165C4⋊C4—42no—
166C4⋊C4—864no—
167C4⋊C4—3442no—
168C4⋊C4—3442no—
169C4⋊C4—3442no—
170C4⋊C4—1722no—
171C4⋊C4—1722no—
172C4⋊C4—1722no—
173C42#1062189812yes—
174C42#1062190011yescharacteristic
175C42Q8×D4311yescharacteristic
176C23#1306329511yescharacteristic
177Q8—3442no—
178Q8—1724no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—3441no—
187C2×C4—3441no—
188C2×C4—1722no—
189C2×C4—1722no—
190C2×C4—1722no—
191C2×C4—1722no—
192C2×C4—1722no—
193C2×C4—1722no—
194C2×C4—1722no—
195C2×C4#1306330312yes—
196C2×C4#1306330511yescharacteristic
197C2×C4#1306331112yes—
198C2×C4#1306331311yescharacteristic
199C8—44no—
200C8—1722no—
201C22#1458281211yescharacteristic
202C22#1458306911yescharacteristic
203C22#1458307411yescharacteristic
204C22#1458307812yes—
205C22#1458308312yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—3442no—
212C4—3442no—
213C4—3442no—
214C2#1913391312yes—
215C2#1913391911yescharacteristic
216C2#1913392411yescharacteristic
217C2#1913575211yescharacteristic
218C2#1913575512yes—
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socle, prime radicalC23×C43#120
hypercenter#1295D43
hypocenterC43#10361
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
126. C43#10361semidirect

Maximal subgroups

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

subgroupindex
#191428702
#191355682
#191354142
#191324772
C43×#12952
#1036143