Finite Group Databasebeta

← #24988972

Subgroups — #24988972

Order 11008.

620 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 107 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#19149090C211yesmaximal, characteristic
2#19133323C212yesmaximal
3#19133233C211yesmaximal, characteristic
4#19133106C212yesmaximal
5C43×#1995C211yesmaximal, characteristic
6C43⋊#564—22no—
7#14583628—22no—
8#14583627—22no—
9#14583624C414yescomplemented
10#14583511—22no—
11#14583509—24no—
12#14583456C2212yes—
13#14582956C2212yes—
14#14582647—22no—
15#14582646—22no—
16#14582641—22no—
17#14582635—24no—
18C43×#533C2211yescharacteristic
19C43×#423C2211yescharacteristic
20C43×#376C2211yescharacteristic
21C43×#339—22no—
22#13063325—22no—
23#13063325D412yes—
24#13063325D412yes—
25#13063323—24no—
26#13063318—28no—
27#13063317—22no—
28#13063317—22no—
29#13063316—28no—
30#13063316—24no—
31#13063315—28no—
32#13063315—28no—
33#13063304—22no—
34#13063304D414yes—
35Q8×Dic43—24no—
36C4×Dic86—24no—
37C4×Dic86—22no—
38C4×Dic86C2×C414yes—
39#13063290—24no—
40#13063284—22no—
41C4⋊(C43⋊C8)—22no—
42C22⋊(C43⋊C8)—22no—
43#13063236—22no—
44C2×M16×C43—21no—
45C4⋊Q8×C43C2×C412yes—
46#125×C43D412yes—
47C22⋊Q8×C43—22no—
48C4×Q8×C43—22no—
49#117×C43D412yes—
50C2×C42×C43—21no—
51C2×C42×C43C2311yescharacteristic
52C4⋊C8×C43—22no—
53#95×C43—22no—
54C2×Q8×C43—22no—
55C22×C4×C43—41no—
56C22×C4×C43C2×D412yes—
57C22×C4×C43C2×D411yescharacteristic
58C2×Dic86—22no—
59C2×Dic86C22⋊C414yes—
60M16×C43—42no—
61C2×C8×C43—41no—
62C4⋊C4×C43—22no—
63C4⋊C4×C43—24no—
64C4⋊C4×C43C22⋊C414yes—
65C22⋊C4×C43—22no—
66C42×C43—22no—
67C42×C43—22no—
68C42×C43—41no—
69C42×C43C22×C411yescharacteristic
70C42×C43C2×D411yescharacteristic
71C42×C43C2×D412yes—
72C22⋊Dic43—24no—
73C4⋊Dic43—28no—
74C4⋊Dic43—22no—
75C4⋊Dic43—22no—
76C4⋊Dic43—22no—
77C4⋊Dic43C22⋊C414yes—
78Dic43⋊C4—28no—
79Dic43⋊C4—28no—
80Dic43⋊C4—24no—
81Dic43⋊C4—24no—
82C4×Dic43—28no—
83C4×Dic43—24no—
84C2×C43⋊C8—42no—
85C23×C43#12011yescharacteristic
86Q8×C43—44no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—24no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43—82no—
93C2×C4×C43C2×C22⋊C412yes—
94C2×C4×C43C2×C22⋊C411yescharacteristic
95C2×C4×C43#12011yescharacteristic
96C2×C4×C43#12012yes—
97C2×Dic43—24no—
98C2×Dic43—24no—
99Dic86—42no—
100Dic86—42no—
101Dic86—44no—
102C8×C43—81no—
103C43⋊C8—82no—
104#8495—431nomaximal, Sylow
105C22×C43—21no—
106C22×C43—22no—
107C22×C43#37911yescharacteristic
108C4×C43—21no—
109C4×C43—22no—
110C4×C43—22no—
111C4×C43—44no—
112C4×C43—82no—
113C4×C43#45411yescharacteristic
114C4×C43#45611yescharacteristic
115Dic43—44no—
116Dic43—44no—
117#3556—431no—
118#1995D4311yescharacteristic
119#1559—432no—
120#1537—431no—
121#1506—432no—
122C2×C43—41no—
123C2×C43#179311yescharacteristic
124C2×C43#179612yes—
125#564—862no—
126#557—434no—
127#557—862no—
128#557—862no—
129#541—864no—
130#541—862no—
131#533—432no—
132#533C2×D4311yescharacteristic
133#432—432no—
134#423C2×D4311yescharacteristic
135#376C2×D4311yescharacteristic
136#339—22no—
137#333—862no—
138#332—862no—
139#330—862no—
140#328—864no—
141C43#849511yescharacteristic, complemented, Sylow
142C2×M16—21no—
143C4⋊Q8—432no—
144C4⋊Q8—432no—
145C4⋊Q8—862no—
146C4⋊Q8—864no—
147C4⋊Q8C4×D4312yes—
148#126—868no—
149#125—862no—
150#125—864no—
151#125—868no—
152#125—868no—
153#125—868no—
154#125—862no—
155#125D17212yes—
156C22⋊Q8—22no—
157C22⋊Q8—434no—
158C22⋊Q8—862no—
159C4×Q8—22no—
160C4×Q8—434no—
161C4×Q8—864no—
162C4×Q8—864no—
163C4×Q8—864no—
164C4×Q8—862no—
165#117—862no—
166#117C22⋊D4312yes—
167C2×C42—21no—
168C2×C42C22×D4311yescharacteristic
169C4⋊C8—22no—
170C4⋊C8—862no—
171C22⋊C8—862no—
172#97—862no—
173#95—22no—
174C2×Q8—22no—
175C2×Q8—434no—
176C2×Q8—862no—
177C22×C4—41no—
178C22×C4D4×D4312yes—
179C22×C4C2×C22⋊D4311yescharacteristic
180M16—42no—
181C2×C8—41no—
182C2×C8—1722no—
183C4⋊C4—22no—
184C4⋊C4—24no—
185C4⋊C4—434no—
186C4⋊C4—868no—
187C4⋊C4—868no—
188C4⋊C4—868no—
189C4⋊C4—864no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—862no—
193C4⋊C4—864no—
194C4⋊C4(C2×D43)⋊C414yes—
195C22⋊C4—22no—
196C22⋊C4—864no—
197C42—22no—
198C42—22no—
199C42—41no—
200C42—868no—
201C42—864no—
202C42C2×C4×D4311yescharacteristic
203C42C2×D17211yescharacteristic
204C42D4×D4312yes—
205C23#1306329311yescharacteristic
206Q8—44no—
207Q8—1724no—
208Q8—1722no—
209Q8—1722no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—82no—
216C2×C4—864no—
217C2×C4—864no—
218C2×C4C22⋊C4×D4312yes—
219C2×C4C2×(C2×D43)⋊C411yescharacteristic
220C2×C4#1306329311yescharacteristic
221C2×C4#1306329512yes—
222C8—81no—
223C8—3442no—
224C22—21no—
225C22—22no—
226C22#1458275411yescharacteristic
227C4—21no—
228C4—22no—
229C4—22no—
230C4—44no—
231C4—82no—
232C4—1724no—
233C4—1724no—
234C4#1458307111yescharacteristic
235C4#1458308111yescharacteristic
236C2—41no—
237C2#1913455311yescharacteristic
238C2#1913456912yes—
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1995C2
socleC22×C43#379
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#1995D43
hypocenterC43#8495
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
9. #14583624C4semidirect
141. C43#8495semidirect

Maximal subgroups

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

subgroupindex
#191490902
#191333232
#191332332
#191331062
C43×#19952
#849543