Finite Group Databasebeta

← #25001497

Subgroups — #25001497

Order 11008.

236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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#19133323C211yesmaximal, characteristic
2#19133293C211yesmaximal, characteristic
3#19133069C211yesmaximal, characteristic
4#19132506C211yesmaximal, characteristic
5#19132465C211yesmaximal, characteristic
6#19132457C211yesmaximal, characteristic
7C43×#1570C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14582956C2211yescharacteristic
10#14582956C2211yescharacteristic
11#14582956C2211yescharacteristic
12#14582647—21no—
13#14582646—21no—
14#14582646—21no—
15#14582644—21no—
16#14582631—22no—
17C43×#431C2211yescharacteristic
18C43×#423C2211yescharacteristic
19C2×C4⋊C8×C43C2211yescharacteristic
20C43×#334—22no—
21#13063325D411yescharacteristic
22#13063325D411yescharacteristic
23#13063317—21no—
24#13063304—21no—
25#13063304—21no—
26C4×Dic86—21no—
27C4×Dic86—21no—
28#13063284—21no—
29C4⋊(C43⋊C8)—21no—
30C4⋊(C43⋊C8)—21no—
31C4⋊(C43⋊C8)—21no—
32C22⋊(C43⋊C8)—21no—
33C22⋊(C43⋊C8)—21no—
34C22⋊(C43⋊C8)—21no—
35#13063236—21no—
36#13063236—21no—
37#13063236—21no—
38C2×M16×C43—21no—
39C22×C8×C43—21no—
40C2×C42×C43C2311yescharacteristic
41C4⋊C8×C43—21no—
42C4⋊C8×C43—21no—
43C4⋊C8×C43—21no—
44C4⋊C8×C43—21no—
45C4⋊C8×C43—21no—
46C22⋊C8×C43—21no—
47C4×C8×C43D412yes—
48C22×C4×C43#4111yescharacteristic
49C22×C4×C43#4111yescharacteristic
50C22×C4×C43#4111yescharacteristic
51C2×Dic86—21no—
52C2×Dic86—21no—
53M16×C43—81no—
54C2×C8×C43—22no—
55C2×C8×C43—41no—
56C2×C8×C43—41no—
57C2×C8×C43—81no—
58C42×C43C2×D411yescharacteristic
59C42×C43C2×D411yescharacteristic
60C42×C43#4111yescharacteristic
61C42×C43#4111yescharacteristic
62C22⋊Dic43—41no—
63C4⋊Dic43—21no—
64C4⋊Dic43—21no—
65C4⋊Dic43—21no—
66C4⋊Dic43—21no—
67Dic43⋊C4—41no—
68Dic43⋊C4—41no—
69C4×Dic43—41no—
70C2×C43⋊C8—41no—
71C2×C43⋊C8—41no—
72C2×C43⋊C8—41no—
73C23×C43#12611yescharacteristic
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43#12111yescharacteristic
79C2×C4×C43#12311yescharacteristic
80C2×C4×C43#12311yescharacteristic
81C2×C4×C43#12311yescharacteristic
82C2×C4×C43#12411yescharacteristic
83C2×C4×C43#12611yescharacteristic
84C2×Dic43—41no—
85C2×Dic43—41no—
86Dic86—41no—
87Dic86—41no—
88Dic86—81no—
89C8×C43—42no—
90C8×C43—81no—
91C8×C43—81no—
92C43⋊C8—81no—
93C43⋊C8—81no—
94C43⋊C8—81no—
95#10648—431nomaximal, Sylow
96C22×C43—21no—
97C22×C43—21no—
98C22×C43—21no—
99C22×C43#39711yescharacteristic
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—21no—
103C4×C43—21no—
104C4×C43—21no—
105C4×C43#47111yescharacteristic
106C4×C43#47111yescharacteristic
107Dic43—81no—
108Dic43—81no—
109#1570D4311yescharacteristic
110#1559—431no—
111#1552—431no—
112#1497—431no—
113#1307—431no—
114#1290—431no—
115#1287—431no—
116C2×C43—41no—
117C2×C43#207911yescharacteristic
118C2×C43#208011yescharacteristic
119C2×C43#208211yescharacteristic
120#533—431no—
121#432—431no—
122#432—431no—
123#432—431no—
124#431C2×D4311yescharacteristic
125#423C2×D4311yescharacteristic
126C2×C4⋊C8C2×D4311yescharacteristic
127#334—22no—
128#333—861no—
129#332—861no—
130#332—861no—
131#332—861no—
132Q8⋊C8—862no—
133C43#1064811yescharacteristic, complemented, Sylow
134C2×M16—21no—
135C22×C8—21no—
136C4⋊Q8—431no—
137C4⋊Q8—431no—
138#125—861no—
139C22⋊Q8—861no—
140C22⋊Q8—861no—
141C4×Q8—861no—
142C4×Q8—861no—
143#117—861no—
144C2×C42C22×D4311yescharacteristic
145C4⋊C8—21no—
146C4⋊C8—21no—
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—861no—
151C4⋊C8—861no—
152C4⋊C8—861no—
153C22⋊C8—21no—
154C22⋊C8—861no—
155C22⋊C8—861no—
156C22⋊C8—861no—
157#97—861no—
158#97—861no—
159#97—861no—
160C4×C8C22⋊D4312yes—
161C2×Q8—861no—
162C2×Q8—861no—
163C22×C4#1062189811yescharacteristic
164C22×C4#1062190011yescharacteristic
165C22×C4#1062190211yescharacteristic
166M16—81no—
167C2×C8—22no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—81no—
171C2×C8—1721no—
172C2×C8—1721no—
173C2×C8—1721no—
174C4⋊C4—861no—
175C4⋊C4—861no—
176C4⋊C4—861no—
177C4⋊C4—861no—
178C4⋊C4—1721no—
179C4⋊C4—1721no—
180C22⋊C4—1721no—
181C42—1721no—
182C42#1062189811yescharacteristic
183C42D4×D4311yescharacteristic
184C42#1062190211yescharacteristic
185C42C2×C22⋊D4311yescharacteristic
186C23#1306332011yescharacteristic
187Q8—3441no—
188Q8—1721no—
189Q8—1721no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—1721no—
195C2×C4—1721no—
196C2×C4#1306329611yescharacteristic
197C2×C4#1306330811yescharacteristic
198C2×C4#1306331011yescharacteristic
199C2×C4#1306331011yescharacteristic
200C2×C4#1306331411yescharacteristic
201C2×C4#1306332011yescharacteristic
202C8—42no—
203C8—81no—
204C8—81no—
205C8—3441no—
206C8—3441no—
207C8—3441no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1458282511yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—3441no—
218C4—3441no—
219C4#1458315911yescharacteristic
220C4#1458315911yescharacteristic
221C2—41no—
222C2#1913604111yescharacteristic
223C2#1913604611yescharacteristic
224C2#1913606011yescharacteristic
subgroupG/H
centerC22#14582825
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1570C2
socleC22×C43#397
prime radicalC23×C43#126
hypercenter#1570D43
hypocenterC43#10648
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
133. C43#10648semidirect

Maximal subgroups

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

subgroupindex
#191333232
#191332932
#191330692
#191325062
#191324652
#191324572
C43×#15702
#1064843