Finite Group Databasebeta

← #25000672

Subgroups — #25000672

Order 11008.

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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#19145905C211yesmaximal, characteristic
2#19133288C212yesmaximal, complemented
3#19133102C212yesmaximal, complemented
4#19132465C211yesmaximal, characteristic, complemented
5C43×#1832C211yesmaximal, characteristic, complemented
6#14583449C2212yes—
7#14583180—22no—
8#14583135—22no—
9#14583095—22no—
10#14582956C2212yes—
11#14582647—22no—
12#14582642—22no—
13#14582632—24no—
14C2×C4⋊C8×C43C2211yescharacteristic
15C2×C4⋊C8×C43C2211yescharacteristic
16C43×#376C2211yescharacteristic
17C43×#336—22no—
18C2×#10621898—22no—
19C2×D344—22no—
20#13063325D412yes—
21#13063322D412yes—
22#13063313—22no—
23#13063299—22no—
24#13063299—22no—
25C4×D172—22no—
26C4×D172—22no—
27#13063259—22no—
28C4⋊(C43⋊C8)—22no—
29#13063247—24no—
30C22⋊(C43⋊C8)—22no—
31#13063236—22no—
32C22×C8×C43—21no—
33C22×C8×C43D412yes—
34C2×C42×C43—21no—
35C2×C42×C43C2311yescharacteristic
36C4⋊C8×C43—22no—
37C4⋊C8×C43—22no—
38#95×C43—21no—
39#95×C43D412yes—
40C22×C4×C43—22no—
41C22×C4×C43C2×D411yescharacteristic
42C22×C4×C43C2×D411yescharacteristic
43C22×C4×C43#4111yescharacteristic
44C2×C22⋊D43—42no—
45#10621898—84no—
46C2×D172—22no—
47C2×D172—22no—
48C2×D172—22no—
49C2×C4×D43—42no—
50C2×Dic86—22no—
51C2×C8×C43—22no—
52C2×C8×C43—42no—
53C2×C8×C43—42no—
54C2×C8×C43—41no—
55C42×C43—41no—
56C42×C43—41no—
57C42×C43C2×D412yes—
58C42×C43#4112yes—
59(C2×D43)⋊C4—42no—
60(C2×D43)⋊C4—42no—
61C4⋊Dic43—22no—
62C4⋊Dic43—22no—
63C2×C43⋊C8—42no—
64D344—82no—
65C23×C43#12111yescharacteristic
66C22×D43—42no—
67C2×C4×C43—22no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—41no—
71C2×C4×C43—42no—
72C2×C4×C43—42no—
73C2×C4×C43—42no—
74C2×C4×C43#12011yescharacteristic
75C2×C4×C43#12112yes—
76C2×C4×C43#12312yes—
77C2×C4×C43#12411yescharacteristic
78C22⋊D43—84no—
79C2×Dic43—42no—
80D172—42no—
81D172—42no—
82D172—82no—
83D172—82no—
84C4×D43—84no—
85Dic86—82no—
86C8×C43—42no—
87C8×C43—81no—
88C43⋊C8—82no—
89#10513—431nomaximal, Sylow
90C22×C43—21no—
91C22×C43—21no—
92C22×C43#39411yescharacteristic
93C22×C43#47212yes—
94C2×D43—82no—
95C2×D43—82no—
96C2×D43—82no—
97C4×C43—22no—
98C4×C43—21no—
99C4×C43—22no—
100C4×C43—82no—
101C4×C43#45411yescharacteristic
102C4×C43#45511yescharacteristic
103Dic43—82no—
104#3245—431no—
105#1832D4311yescharacteristic, complemented
106#1551—432no—
107#1505—432no—
108#1290—431no—
109C2×C43—22no—
110C2×C43#204011yescharacteristic
111C2×C43#204511yescharacteristic
112C2×C43#205311yescharacteristic
113D43—162no—
114#532—432no—
115#474—862no—
116#466—862no—
117#459—862no—
118#432—432no—
119C2×C4⋊C8C2×D4311yescharacteristic
120C2×C4⋊C8C2×D4311yescharacteristic
121#376C2×D4311yescharacteristic
122#336—22no—
123#333—862no—
124#331—862no—
125#327—864no—
126C43#1051311yescharacteristic, complemented, Sylow
127C2×#41—862no—
128C2×D8—862no—
129C22×C8—21no—
130C22×C8C22⋊D4312yes—
131C4⋊Q8—432no—
132#127—432no—
133#124—862no—
134#121—862no—
135#121—862no—
136C4×D4—862no—
137C4×D4—862no—
138C2×C42—21no—
139C2×C42C22×D4311yescharacteristic
140#107—862no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—862no—
144#102—864no—
145C22⋊C8—862no—
146#97—862no—
147#95—21no—
148#95D17212yes—
149#41—3444no—
150C2×Q8—862no—
151C2×D4—862no—
152C2×D4—862no—
153C2×D4—862no—
154C2×D4—1722no—
155C22×C4—22no—
156C22×C4—1722no—
157C22×C4C2×D17211yescharacteristic
158C22×C4#1062189811yescharacteristic
159C22×C4C2×C22⋊D4311yescharacteristic
160D8—3442no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—41no—
165C2×C8—1722no—
166C4⋊C4—862no—
167C4⋊C4—862no—
168C22⋊C4—1722no—
169C22⋊C4—1722no—
170C42—41no—
171C42—41no—
172C42D4×D4312yes—
173C42#1062190212yes—
174C23—1722no—
175C23#1306329911yescharacteristic
176Q8—3442no—
177D4—3442no—
178D4—3442no—
179D4—3444no—
180D4—1722no—
181D4—1722no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—3444no—
190C2×C4—1722no—
191C2×C4#1306329311yescharacteristic
192C2×C4#1306330012yes—
193C2×C4#1306331012yes—
194C2×C4#1306331411yescharacteristic
195C8—42no—
196C8—81no—
197C8—3442no—
198C22—21no—
199C22—21no—
200C22—3442no—
201C22—3442no—
202C22—3442no—
203C22#1458281611yescharacteristic
204C22#1458316912yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—82no—
209C4—3442no—
210C4#1458307111yescharacteristic
211C4#1458307611yescharacteristic
212C2—22no—
213C2—6882no—
214C2#1913582411yescharacteristic
215C2#1913585111yescharacteristic
216C2#1913590111yescharacteristic
subgroupG/H
centerC22#14582816
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1832C2
socleC22×C43#394
prime radical#19145905C2
hypercenter#1832D43
hypocenterC43#10513
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1832

Complements

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

NH ≅ G/Ntype
2. #19133288C2semidirect
3. #19133102C2semidirect
4. #19132465C2semidirect
5. C43×#1832C2semidirect
105. #1832D43semidirect
126. C43#10513semidirect

Maximal subgroups

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

subgroupindex
#191459052
#191332882
#191331022
#191324652
C43×#18322
#1051343