Finite Group Databasebeta

← #25000669

Subgroups — #25000669

Order 11008.

388 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 81 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#19134714C211yesmaximal, characteristic, complemented
2#19133290C212yesmaximal, complemented
3#19133103C212yesmaximal, complemented
4#19132465C211yesmaximal, characteristic, complemented
5C43×#3245C211yesmaximal, characteristic
6#14582956C2212yes—
7C2×C4⋊(C43⋊C8)C2211yescharacteristic
8#14582745C2211yescharacteristic
9#14582653—22no—
10#14582648—22no—
11#14582643—22no—
12#14582633—24no—
13C43×#532C2212yes—
14C43×#474—22no—
15C43×#466—22no—
16C43×#459—22no—
17C2×C4⋊C8×C43C2211yescharacteristic
18C22×C43⋊C8—21no—
19C2×C4×Dic43—21no—
20C4⋊(C43⋊C8)—22no—
21C4⋊(C43⋊C8)—22no—
22C22⋊(C43⋊C8)—22no—
23#13063236—22no—
24C43⋊#95—21no—
25C43⋊#95D412yes—
26C2×#41×C43—22no—
27C2×D8×C43—22no—
28C22×C8×C43D412yes—
29C4⋊Q8×C43D412yes—
30#127×C43D412yes—
31#124×C43—22no—
32#121×C43—22no—
33#121×C43—22no—
34C4×D4×C43—22no—
35C4×D4×C43—22no—
36C2×C42×C43C2311yescharacteristic
37#107×C43—22no—
38C4⋊C8×C43—22no—
39#102×C43—24no—
40#41×C43—84no—
41C2×Q8×C43—22no—
42C2×D4×C43—22no—
43C2×D4×C43—22no—
44C2×D4×C43—22no—
45C2×D4×C43—42no—
46C22×C4×C43—42no—
47C22×C4×C43C2×D411yescharacteristic
48C22×C4×C43C2×D411yescharacteristic
49C22×C4×C43#4111yescharacteristic
50C22×Dic43—22no—
51D8×C43—82no—
52C2×C8×C43—22no—
53C2×C8×C43—42no—
54C4⋊C4×C43—22no—
55C4⋊C4×C43—22no—
56C22⋊C4×C43—42no—
57C22⋊C4×C43—42no—
58C42×C43C2×D412yes—
59C42×C43#4112yes—
60C4×Dic43—41no—
61C4×Dic43—41no—
62C2×C43⋊C8—42no—
63C2×C43⋊C8—41no—
64C2×C43⋊C8—42no—
65C23×C43—42no—
66C23×C43#12111yescharacteristic
67Q8×C43—82no—
68D4×C43—42no—
69D4×C43—42no—
70D4×C43—82no—
71D4×C43—82no—
72D4×C43—84no—
73C2×C4×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—41no—
77C2×C4×C43—42no—
78C2×C4×C43—84no—
79C2×C4×C43#12011yescharacteristic
80C2×C4×C43#12112yes—
81C2×C4×C43#12312yes—
82C2×C4×C43#12411yescharacteristic
83C2×Dic43—42no—
84C2×Dic43—42no—
85C2×Dic43—42no—
86C8×C43—42no—
87C43⋊C8—82no—
88C43⋊C8—81no—
89#10513—431nomaximal, Sylow
90C22×C43—21no—
91C22×C43—21no—
92C22×C43—82no—
93C22×C43—82no—
94C22×C43—82no—
95C22×C43#39411yescharacteristic
96C22×C43#47212yes—
97C4×C43—22no—
98C4×C43—21no—
99C4×C43—22no—
100C4×C43—82no—
101C4×C43#45411yescharacteristic
102C4×C43#45511yescharacteristic
103Dic43—82no—
104#3245D4311yescharacteristic
105#1832—431no—
106#1551—432no—
107#1505—432no—
108#1290—431no—
109C2×C43—22no—
110C2×C43—162no—
111C2×C43#204011yescharacteristic
112C2×C43#204511yescharacteristic
113C2×C43#205311yescharacteristic
114#532C2×D4312yes—
115#474—22no—
116#466—22no—
117#459—22no—
118#432—432no—
119C2×C4⋊C8—431no—
120C2×C4⋊C8C2×D4311yescharacteristic
121#376—431no—
122#336—862no—
123#333—862no—
124#331—862no—
125#327—864no—
126C43#1051311yescharacteristic, complemented, Sylow
127C2×#41—22no—
128C2×D8—22no—
129C22×C8—861no—
130C22×C8C22⋊D4312yes—
131C4⋊Q8C22⋊D4312yes—
132#127C22⋊D4312yes—
133#124—22no—
134#121—22no—
135#121—22no—
136C4×D4—22no—
137C4×D4—22no—
138C2×C42—861no—
139C2×C42C22×D4311yescharacteristic
140#107—22no—
141C4⋊C8—22no—
142C4⋊C8—862no—
143C4⋊C8—862no—
144#102—24no—
145C22⋊C8—862no—
146#97—862no—
147#95—432no—
148#95—861no—
149#41—84no—
150C2×Q8—22no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—42no—
155C22×C4—42no—
156C22×C4—862no—
157C22×C4D4×D4311yescharacteristic
158C22×C4#1062190011yescharacteristic
159C22×C4C2×C22⋊D4311yescharacteristic
160D8—82no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—1722no—
164C2×C8—1721no—
165C2×C8—1722no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C22⋊C4—42no—
169C22⋊C4—42no—
170C42—1721no—
171C42—1721no—
172C42#1062190012yes—
173C42C2×C22⋊D4312yes—
174C23—42no—
175C23#1306329611yescharacteristic
176Q8—82no—
177D4—42no—
178D4—42no—
179D4—82no—
180D4—82no—
181D4—84no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—84no—
188C2×C4—1722no—
189C2×C4—1722no—
190C2×C4—1722no—
191C2×C4#1306329411yescharacteristic
192C2×C4#1306329712yes—
193C2×C4#1306330612yes—
194C2×C4#1306331211yescharacteristic
195C8—42no—
196C8—3442no—
197C8—3441no—
198C22—21no—
199C22—21no—
200C22—82no—
201C22—82no—
202C22—82no—
203C22#1458281311yescharacteristic
204C22#1458316612yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—82no—
209C4—3442no—
210C4#1458307211yescharacteristic
211C4#1458307711yescharacteristic
212C2—22no—
213C2—162no—
214C2#1913582111yescharacteristic
215C2#1913584811yescharacteristic
216C2#1913589811yescharacteristic
subgroupG/H
centerC22#14582813
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3245C2
socleC22×C43#394
hypercenter#3245D43
hypocenterC43#10513
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #19134714C2semidirect
2. #19133290C2semidirect
3. #19133103C2semidirect
4. #19132465C2semidirect
126. C43#10513semidirect

Maximal subgroups

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

subgroupindex
#191347142
#191332902
#191331032
#191324652
C43×#32452
#1051343