Finite Group Databasebeta

← #25009418

Subgroups — #25009418

Order 11008.

460 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 59 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#19140967C211yesmaximal, characteristic
2#19135751C211yesmaximal, characteristic
3#19133571C212yesmaximal, complemented
4#19132626C212yesmaximal, complemented
5C43×#1318C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7C2×#13063302—22no—
8#14583057—22no—
9#14582904—21no—
10#14582822—22no—
11#14582819C2212yes—
12#14582797—21no—
13#14582779—21no—
14#14582668C2211yescharacteristic
15#14582659—21no—
16#14582637—22no—
17C43×#390C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86D412yes—
20C23×Dic43—21no—
21C2×Dic172—42no—
22C2×#10621877—21no—
23#13063324—41no—
24#13063316—41no—
25#13063304—22no—
26#13063302—48no—
27#13063284—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—22no—
32C2×C22⋊Dic43—22no—
33C2×C22⋊Dic43—21no—
34#13063250—42no—
35#13063246—41no—
36#13063246—41no—
37C43⋊#95—22no—
38C43⋊#95D412yes—
39C22×D4×C43D411yescharacteristic
40C2×C4⋊C4×C43C2311yescharacteristic
41C2×C22⋊C4×C43—22no—
42C2×C42×C43D411yescharacteristic
43C22⋊C8×C43—22no—
44C24×C43—21no—
45C2×D4×C43—21no—
46C2×D4×C43—41no—
47C2×D4×C43—41no—
48C2×D4×C43Q1612yescomplemented
49C22×C4×C43—21no—
50C22×C4×C43C2×D411yescharacteristic
51C22×C4×C43C2×D412yes—
52C22×Dic43—22no—
53C22×Dic43—22no—
54C22×Dic43—44no—
55C22×Dic43—81no—
56C2×Dic86—22no—
57C2×Dic86—42no—
58C2×Dic86—44no—
59C2×C8×C43—42no—
60C4⋊C4×C43—41no—
61C22⋊C4×C43—44no—
62C42×C43—41no—
63C22⋊Dic43—44no—
64C22⋊Dic43—41no—
65C22⋊Dic43—81no—
66C4⋊Dic43—24no—
67C4⋊Dic43—21no—
68C4⋊Dic43—21no—
69C4⋊Dic43—22no—
70C4⋊Dic43—81no—
71Dic43⋊C4—44no—
72Dic43⋊C4—44no—
73Dic43⋊C4—42no—
74C4×Dic43—41no—
75#10621877—41no—
76#10621877—41no—
77C2×C43⋊C8—41no—
78Dic172—84no—
79C23×C43—22no—
80C23×C43—42no—
81C23×C43—42no—
82C23×C43—41no—
83C23×C43—41no—
84C23×C43#12011yescharacteristic
85D4×C43—42no—
86D4×C43—81no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—42no—
94C2×C4×C43C2×Q1611yescharacteristic
95C2×C4×C43#13711yescharacteristic
96C2×Dic43—24no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—42no—
100C2×Dic43—42no—
101C2×Dic43—42no—
102C2×Dic43—41no—
103C2×Dic43—41no—
104C2×Dic43—84no—
105Dic86—44no—
106Dic86—82no—
107Dic86—82no—
108C8×C43—82no—
109C43⋊C8—81no—
110#12220—431nomaximal, Sylow
111C22×C43—21no—
112C22×C43—21no—
113C22×C43—44no—
114C22×C43—42no—
115C22×C43—82no—
116C22×C43—81no—
117C22×C43—81no—
118C22×C43#45111yescharacteristic
119C22×C43#45511yescharacteristic
120C22×C43B(4,𝔽2)11yescharacteristic
121C4×C43—21no—
122C4×C43—21no—
123C4×C43—42no—
124C4×C43—42no—
125Dic43—44no—
126Dic43—82no—
127Dic43—81no—
128Dic43—81no—
129#2683—431no—
130#2027—431no—
131#1605—432no—
132#1354—432no—
133#1318D4311yescharacteristic
134C2×C43—21no—
135C2×C43—21no—
136C2×C43—82no—
137C2×C43#160211yescharacteristic
138C2×C43#219611yescharacteristic
139C2×C43#220311yescharacteristic
140#544—431no—
141C2×C22⋊Q8—862no—
142#451—862no—
143#418—861no—
144#396—862no—
145#395—432no—
146#390C2×D4311yescharacteristic
147#389—861no—
148#386—861no—
149#343—431no—
150#339—861no—
151#328—862no—
152#324C2×D4312yes—
153C43#1222011yescharacteristic, complemented, Sylow
154C22×Q8—432no—
155C22×D4D17211yescharacteristic
156C23×C4—861no—
157C2×Q16—1722no—
158C2×M16—861no—
159C4⋊Q8—1721no—
160#125—1721no—
161C22⋊Q8—862no—
162C22⋊Q8—1728no—
163#117—861no—
164C2×C4⋊C4—861no—
165C2×C4⋊C4—861no—
166C2×C4⋊C4—862no—
167C2×C4⋊C4—862no—
168C2×C4⋊C4C22×D4311yescharacteristic
169C2×C22⋊C4—22no—
170C2×C22⋊C4—861no—
171C2×C22⋊C4—862no—
172C2×C42D17211yescharacteristic
173#103—1722no—
174#102—1721no—
175#102—1721no—
176C22⋊C8—22no—
177#95—432no—
178#95—862no—
179C24—21no—
180C2×Q8—862no—
181C2×Q8—1722no—
182C2×Q8—1724no—
183C2×D4—21no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4Dic17212yescomplemented
187C22×C4—21no—
188C22×C4—862no—
189C22×C4—862no—
190C22×C4—3441no—
191C22×C4—1724no—
192C22×C4C2×D17211yescharacteristic
193C22×C4D4×D4312yes—
194Q16—3444no—
195M16—1721no—
196M16—1721no—
197C2×C8—42no—
198C2×C8—1721no—
199C4⋊C4—41no—
200C4⋊C4—864no—
201C4⋊C4—861no—
202C4⋊C4—861no—
203C4⋊C4—862no—
204C4⋊C4—3441no—
205C4⋊C4—1724no—
206C4⋊C4—1722no—
207C4⋊C4—1724no—
208C22⋊C4—44no—
209C22⋊C4—3441no—
210C22⋊C4—1724no—
211C22⋊C4—1721no—
212C42—41no—
213C42—1721no—
214C23—22no—
215C23—42no—
216C23—42no—
217C23—41no—
218C23—41no—
219C23#1306329511yescharacteristic
220Q8—3442no—
221Q8—3442no—
222Q8—1724no—
223D4—42no—
224D4—81no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—864no—
233C2×C4—3444no—
234C2×C4—1722no—
235C2×C4—1722no—
236C2×C4—1722no—
237C2×C4—1721no—
238C2×C4—1721no—
239C2×C4—1722no—
240C2×C4—1722no—
241C2×C4C2×Dic17211yescharacteristic
242C2×C4#1306335811yescharacteristic
243C8—82no—
244C8—3441no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—81no—
252C22#1458305711yescharacteristic
253C22#1458307911yescharacteristic
254C22#1458308711yescharacteristic
255C4—21no—
256C4—21no—
257C4—42no—
258C4—42no—
259C4—3442no—
260C4—3441no—
261C4—3441no—
262C4—1724no—
263C2—21no—
264C2—21no—
265C2—82no—
266C2#1913355411yescharacteristic
267C2#1913658111yescharacteristic
268C2#1913661811yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1318C2
socleC22×C43B(4,𝔽2)
prime radicalC22×D4×C43D4
hypercenter#1318D43
hypocenterC43#12220
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
3. #19133571C2semidirect
4. #19132626C2semidirect
48. C2×D4×C43Q16semidirect
153. C43#12220semidirect
186. C2×D4Dic172semidirect

Maximal subgroups

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

subgroupindex
#191409672
#191357512
#191335712
#191326262
C43×#13182
#1222043