Finite Group Databasebeta

← #24988967

Subgroups — #24988967

Order 11008.

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

normal subgroups only

This group has 732 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#19148995C211yesmaximal, characteristic
2#19133315C212yesmaximal, complemented
3#19133233C211yesmaximal, characteristic, complemented
4#19133102C212yesmaximal, complemented
5C43×#1995C211yesmaximal, characteristic, complemented
6#14583647—22no—
7#14583609—22no—
8#14583571—22no—
9#14583552C414yescomplemented
10#14583504—22no—
11#14583479—24no—
12#14583449C2212yes—
13#14582956C2212yes—
14#14582644—22no—
15#14582642—22no—
16#14582641—22no—
17#14582632—24no—
18C43×#533C2211yescharacteristic
19C43×#423C2211yescharacteristic
20C43×#376C2211yescharacteristic
21C43×#339—22no—
22C2×#10621902—24no—
23C2×#10621898—22no—
24#13063325D412yes—
25#13063322—22no—
26#13063322D412yes—
27#13063317—22no—
28#13063313—22no—
29#13063310—28no—
30#13063303—28no—
31#13063301—24no—
32#13063300—28no—
33#13063300—24no—
34#13063299—22no—
35#13063299D414yes—
36#13063298—28no—
37C4×D172—24no—
38C4×D172—22no—
39C4×D172C2×C414yes—
40C4⋊C4×D43—24no—
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×C22⋊D43—24no—
59#10621902—88no—
60#10621898—84no—
61C2×D172—22no—
62C2×D172—28no—
63C2×D172—22no—
64C2×D172C22⋊C414yes—
65C2×C4×D43—24no—
66C2×C4×D43—28no—
67C2×Dic86—22no—
68M16×C43—42no—
69C2×C8×C43—41no—
70C4⋊C4×C43—22no—
71C4⋊C4×C43—24no—
72C4⋊C4×C43C22⋊C414yes—
73C22⋊C4×C43—22no—
74C42×C43—22no—
75C42×C43—22no—
76C42×C43—41no—
77C42×C43C22×C411yescharacteristic
78C42×C43C2×D411yescharacteristic
79C42×C43C2×D412yes—
80(C2×D43)⋊C4—28no—
81(C2×D43)⋊C4—24no—
82(C2×D43)⋊C4—24no—
83C4⋊Dic43—22no—
84C4⋊Dic43C22⋊C414yes—
85Dic43⋊C4—28no—
86C2×C43⋊C8—42no—
87C23×C43#12011yescharacteristic
88C22×D43—24no—
89Q8×C43—44no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—24no—
93C2×C4×C43—42no—
94C2×C4×C43—42no—
95C2×C4×C43—82no—
96C2×C4×C43C2×C22⋊C412yes—
97C2×C4×C43C2×C22⋊C411yescharacteristic
98C2×C4×C43#12011yescharacteristic
99C2×C4×C43#12012yes—
100C22⋊D43—84no—
101C2×Dic43—24no—
102D172—44no—
103D172—42no—
104D172—42no—
105D172—82no—
106D172—88no—
107C4×D43—48no—
108C4×D43—88no—
109Dic86—82no—
110C8×C43—81no—
111C43⋊C8—82no—
112#8494—431nomaximal, Sylow
113C22×C43—21no—
114C22×C43—22no—
115C22×C43#37911yescharacteristic
116C2×D43—44no—
117C2×D43—44no—
118C2×D43—44no—
119C4×C43—21no—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—44no—
123C4×C43—82no—
124C4×C43#45411yescharacteristic
125C4×C43#45611yescharacteristic
126Dic43—44no—
127#3548—431no—
128#1995D4311yescharacteristic, complemented
129#1557—432no—
130#1537—431no—
131#1505—432no—
132C2×C43—41no—
133C2×C43#179311yescharacteristic
134C2×C43#179512yes—
135D43—84no—
136#562—862no—
137#554—862no—
138#550—862no—
139#547—434no—
140#540—862no—
141#537—864no—
142#533C2×D4311yescharacteristic
143#532—432no—
144#432—432no—
145#423C2×D4311yescharacteristic
146#376C2×D4311yescharacteristic
147#339—22no—
148#332—862no—
149#331—862no—
150#330—862no—
151#327—864no—
152C43#849411yescharacteristic, complemented, Sylow
153C2×#41—864no—
154C2×#41—862no—
155C2×M16—21no—
156C4⋊Q8—432no—
157C4⋊Q8C4×D4312yes—
158#127—432no—
159#127—862no—
160#125—862no—
161#125D17212yes—
162#124—862no—
163#123—868no—
164C22⋊Q8—22no—
165C22⋊Q8—868no—
166C22⋊Q8—864no—
167#121—434no—
168#121—868no—
169#121—864no—
170#121—868no—
171#121—862no—
172C4×Q8—22no—
173C4×D4—434no—
174C4×D4—864no—
175C4×D4—862no—
176#117C22⋊D4312yes—
177C2×C4⋊C4—864no—
178C2×C42—21no—
179C2×C42C22×D4311yescharacteristic
180C4⋊C8—22no—
181C4⋊C8—862no—
182C22⋊C8—862no—
183#97—862no—
184#95—22no—
185#41—3444no—
186#41—3448no—
187C2×Q8—22no—
188C2×Q8—862no—
189C2×D4—434no—
190C2×D4—868no—
191C2×D4—864no—
192C2×D4—862no—
193C2×D4—862no—
194C22×C4—41no—
195C22×C4—868no—
196C22×C4—864no—
197C22×C4D4×D4312yes—
198C22×C4C2×C22⋊D4311yescharacteristic
199M16—42no—
200C2×C8—41no—
201C2×C8—1722no—
202C4⋊C4—22no—
203C4⋊C4—24no—
204C4⋊C4—434no—
205C4⋊C4—868no—
206C4⋊C4—862no—
207C4⋊C4(C2×D43)⋊C414yes—
208C22⋊C4—22no—
209C22⋊C4—868no—
210C22⋊C4—864no—
211C22⋊C4—864no—
212C42—22no—
213C42—22no—
214C42—41no—
215C42C2×C4×D4311yescharacteristic
216C42C2×D17211yescharacteristic
217C42D4×D4312yes—
218C23—864no—
219C23#1306329311yescharacteristic
220Q8—44no—
221Q8—3442no—
222D4—3442no—
223D4—3448no—
224D4—3444no—
225D4—1724no—
226D4—1722no—
227D4—1722no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—24no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—82no—
234C2×C4—864no—
235C2×C4—3448no—
236C2×C4—1728no—
237C2×C4C22⋊C4×D4312yes—
238C2×C4C2×(C2×D43)⋊C411yescharacteristic
239C2×C4#1306329311yescharacteristic
240C2×C4#1306329512yes—
241C8—81no—
242C8—3442no—
243C22—21no—
244C22—22no—
245C22—1724no—
246C22—1724no—
247C22—1724no—
248C22#1458275411yescharacteristic
249C4—21no—
250C4—22no—
251C4—22no—
252C4—44no—
253C4—82no—
254C4—1724no—
255C4#1458307111yescharacteristic
256C4#1458308111yescharacteristic
257C2—41no—
258C2—3444no—
259C2#1913455311yescharacteristic
260C2#1913456412yes—
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1995C2
socleC22×C43#379
prime radical#19148995C2
cosocleC2×C42×C43C23
hypercenter#1995D43
hypocenterC43#8494
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
2. #19133315C2semidirect
3. #19133233C2semidirect
4. #19133102C2semidirect
5. C43×#1995C2semidirect
9. #14583552C4semidirect
128. #1995D43semidirect
152. C43#8494semidirect

Maximal subgroups

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

subgroupindex
#191489952
#191333152
#191332332
#191331022
C43×#19952
#849443