Finite Group Databasebeta

← #24988955

Subgroups — #24988955

Order 11008.

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

normal subgroups only

This group has 692 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#19149009C211yesmaximal, characteristic
2#19133323C212yesmaximal, complemented
3#19133230C211yesmaximal, characteristic
4#19133106C212yesmaximal, complemented
5C43×#1963C211yesmaximal, characteristic
6#14583649—22no—
7#14583635C412yescomplemented
8#14583629C412yescomplemented
9#14583619—22no—
10D4×Dic86—22no—
11#14583516—24no—
12#14583470—22no—
13#14583456C2212yes—
14#14582956C2212yes—
15#14582647—22no—
16#14582646—22no—
17#14582639—22no—
18#14582635—24no—
19C43×#532C2211yescharacteristic
20C43×#423C2211yescharacteristic
21C2×#104×C43—22no—
22C43×#376C2211yescharacteristic
23C22×Dic86—22no—
24#13063325D412yes—
25#13063325D412yes—
26#13063324—24no—
27#13063323—24no—
28#13063318—28no—
29#13063317—22no—
30#13063312—24no—
31#13063312—24no—
32#13063306—24no—
33#13063306—24no—
34#13063304—24no—
35#13063304—22no—
36#13063304D414yes—
37#13063302—28no—
38C4×Dic86—22no—
39C4×Dic86C2×C414yes—
40#13063290—24no—
41D4×Dic43—24no—
42#13063284—22no—
43#13063284—22no—
44C4⋊(C43⋊C8)—22no—
45C22⋊(C43⋊C8)—22no—
46#13063236—22no—
47C2×#41×C43D412yes—
48C2×M16×C43—21no—
49C4⋊Q8×C43C2×C411yescharacteristic
50#127×C43C2×C411yescharacteristic
51#124×C43D412yes—
52#121×C43—22no—
53C4×D4×C43—22no—
54C2×C42×C43—21no—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—22no—
57#104×C43—44no—
58#95×C43—22no—
59#41×C43—42no—
60#41×C43—42no—
61C2×Q8×C43C22⋊C412yes—
62C2×D4×C43—22no—
63C2×D4×C43—22no—
64C2×D4×C43C22⋊C412yes—
65C22×C4×C43—22no—
66C22×C4×C43—41no—
67C22×C4×C43C2×D412yes—
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—24no—
70C2×Dic86—22no—
71C2×Dic86—24no—
72C2×Dic86—82no—
73C2×Dic86—82no—
74C2×Dic86C22⋊C414yes—
75M16×C43—42no—
76C2×C8×C43—41no—
77C4⋊C4×C43—22no—
78C22⋊C4×C43—24no—
79C42×C43—22no—
80C42×C43—41no—
81C42×C43C22×C411yescharacteristic
82C42×C43C2×D411yescharacteristic
83C42×C43C2×D412yes—
84C22⋊Dic43—24no—
85C22⋊Dic43—28no—
86C22⋊Dic43—24no—
87C4⋊Dic43—22no—
88C4⋊Dic43—22no—
89C4⋊Dic43—22no—
90C4⋊Dic43C22⋊C414yes—
91Dic43⋊C4—28no—
92Dic43⋊C4—24no—
93Dic43⋊C4—24no—
94C4×Dic43—24no—
95C4×Dic43—24no—
96C2×C43⋊C8—42no—
97C23×C43—22no—
98C23×C43#12011yescharacteristic
99Q8×C43—42no—
100D4×C43—42no—
101D4×C43—44no—
102D4×C43—82no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—82no—
111C2×C4×C43C2×C22⋊C412yes—
112C2×C4×C43C2×C22⋊C411yescharacteristic
113C2×C4×C43#12011yescharacteristic
114C2×C4×C43#12012yes—
115C2×Dic43—24no—
116C2×Dic43—24no—
117C2×Dic43—84no—
118Dic86—42no—
119Dic86—42no—
120Dic86—44no—
121Dic86—84no—
122C8×C43—81no—
123C43⋊C8—82no—
124#8492—431nomaximal, Sylow
125C22×C43—21no—
126C22×C43—22no—
127C22×C43—42no—
128C22×C43—44no—
129C22×C43#37911yescharacteristic
130C4×C43—21no—
131C4×C43—22no—
132C4×C43—22no—
133C4×C43—42no—
134C4×C43—82no—
135C4×C43#45311yescharacteristic
136C4×C43#45511yescharacteristic
137Dic43—44no—
138Dic43—44no—
139#3550—431no—
140#1963D4311yescharacteristic
141#1559—432no—
142#1536—431no—
143#1506—432no—
144C2×C43—41no—
145C2×C43—82no—
146C2×C43#179211yescharacteristic
147C2×C43#179612yes—
148#563—862no—
149#559—432no—
150Q82—432no—
151#556—862no—
152D4×Q8—862no—
153#542—864no—
154#536—862no—
155#533—432no—
156#532C2×D4311yescharacteristic
157#432—432no—
158#423C2×D4311yescharacteristic
159C2×#104—22no—
160#376C2×D4311yescharacteristic
161#333—862no—
162#332—862no—
163#329—862no—
164#328—864no—
165C43#849211yescharacteristic, complemented, Sylow
166C2×#41C22⋊D4312yes—
167C22×Q8—862no—
168C2×M16—21no—
169C4⋊Q8—432no—
170C4⋊Q8—432no—
171C4⋊Q8—864no—
172C4⋊Q8—864no—
173C4⋊Q8C4×D4311yescharacteristic
174#127C4×D4311yescharacteristic
175#126—868no—
176#125—862no—
177#124—864no—
178#124—864no—
179#124D17212yes—
180#123—864no—
181#123—864no—
182C22⋊Q8—434no—
183C22⋊Q8—868no—
184C22⋊Q8—864no—
185C22⋊Q8—862no—
186#121—22no—
187C4×Q8—434no—
188C4×Q8—864no—
189C4×Q8—862no—
190C4×D4—22no—
191C4×D4—864no—
192#117—862no—
193#117—862no—
194C2×C42—21no—
195C2×C42C22×D4311yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—862no—
198#104—44no—
199C22⋊C8—862no—
200#97—862no—
201#95—22no—
202#41—42no—
203#41—42no—
204C2×Q8—434no—
205C2×Q8—864no—
206C2×Q8—862no—
207C2×Q8—3442no—
208C2×Q8—3442no—
209C2×Q8(C2×D43)⋊C412yes—
210C2×D4—22no—
211C2×D4—22no—
212C2×D4(C2×D43)⋊C412yes—
213C22×C4—22no—
214C22×C4—41no—
215C22×C4—864no—
216C22×C4D4×D4312yes—
217C22×C4C2×C22⋊D4311yescharacteristic
218M16—42no—
219C2×C8—41no—
220C2×C8—1722no—
221C4⋊C4—22no—
222C4⋊C4—434no—
223C4⋊C4—868no—
224C4⋊C4—864no—
225C4⋊C4—862no—
226C4⋊C4—862no—
227C4⋊C4—862no—
228C4⋊C4—864no—
229C22⋊C4—24no—
230C22⋊C4—864no—
231C22⋊C4—868no—
232C22⋊C4—864no—
233C42—22no—
234C42—41no—
235C42—864no—
236C42—864no—
237C42C2×C4×D4311yescharacteristic
238C42C2×D17211yescharacteristic
239C42D4×D4312yes—
240C23—22no—
241C23#1306329311yescharacteristic
242Q8—42no—
243Q8—3444no—
244Q8—1724no—
245Q8—1722no—
246Q8—1722no—
247D4—42no—
248D4—44no—
249D4—82no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—82no—
258C2×C4—864no—
259C2×C4—864no—
260C2×C4—3444no—
261C2×C4C22⋊C4×D4312yes—
262C2×C4C2×(C2×D43)⋊C411yescharacteristic
263C2×C4#1306329311yescharacteristic
264C2×C4#1306329512yes—
265C8—81no—
266C8—3442no—
267C22—21no—
268C22—22no—
269C22—42no—
270C22—44no—
271C22#1458275411yescharacteristic
272C4—21no—
273C4—22no—
274C4—22no—
275C4—42no—
276C4—82no—
277C4—1724no—
278C4—1724no—
279C4#1458306611yescharacteristic
280C4#1458307611yescharacteristic
281C2—41no—
282C2—82no—
283C2#1913454811yescharacteristic
284C2#1913456912yes—
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1963C2
socleC22×C43#379
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#1963D43
hypocenterC43#8492
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #19133323C2semidirect
4. #19133106C2semidirect
7. #14583635C4semidirect
8. #14583629C4semidirect
165. C43#8492semidirect

Maximal subgroups

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

subgroupindex
#191490092
#191333232
#191332302
#191331062
C43×#19632
#849243