Finite Group Databasebeta

← #24994038

Subgroups — #24994038

Order 11008.

618 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 115 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#19136952C211yesmaximal, characteristic
2#19133115C212yesmaximal
3#19132925C211yesmaximal, characteristic
4#19132481C212yesmaximal
5C43×#2583C211yesmaximal, characteristic
6C2×#13063284—21no—
7#14582863C2212yes—
8C4⋊C4×Dic43—24no—
9C4×C22⋊Dic43—21no—
10C4×C22⋊Dic43C2212yes—
11#14582636—24no—
12#14582625—22no—
13C2×C22⋊Q8×C43C2211yescharacteristic
14C22×C4⋊C4×C43C2211yescharacteristic
15C43×#398C412yescomplemented
16C43×#395C412yescomplemented
17C43×#389—22no—
18C43×#385—21no—
19C43×#385—21no—
20C4×C22⋊C4×C43C2211yescharacteristic
21C2×#10621877—22no—
22#13063284—28no—
23C2×C4⋊Dic43—22no—
24C2×C22⋊Dic43—22no—
25C2×C4×Dic43—22no—
26C2×C4×Dic43—22no—
27C2×C4×Dic43—22no—
28C22⋊(C43⋊C8)—22no—
29C22⋊(C43⋊C8)—22no—
30C43⋊#95—22no—
31C43⋊#95D414yes—
32C22×Q8×C43C2×C411yescharacteristic
33C23×C4×C43D411yescharacteristic
34C23×C4×C43D411yescharacteristic
35C23×C4×C43C2311yescharacteristic
36C22⋊Q8×C43—22no—
37C22⋊Q8×C43—22no—
38C2×C4⋊C4×C43—22no—
39C2×C4⋊C4×C43—22no—
40C2×C4⋊C4×C43—22no—
41C2×C4⋊C4×C43—21no—
42C2×C4⋊C4×C43—22no—
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C4⋊C4×C43C2×C412yes—
45C2×C4⋊C4×C43D412yes—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43—21no—
48C2×C42×C43—21no—
49#95×C43—22no—
50#95×C43—22no—
51#95×C43C2×C412yes—
52C24×C43C2×D411yescharacteristic
53C2×Q8×C43—22no—
54C2×Q8×C43—81no—
55C22×C4×C43—24no—
56C22×C4×C43—22no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—81no—
64C22×C4×C43—81no—
65C22×C4×C43C22⋊C412yes—
66C22×C4×C43C22⋊C412yes—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D412yes—
70C22×C4×C43#4112yes—
71C22×Dic43—24no—
72C4⋊C4×C43—24no—
73C4⋊C4×C43—24no—
74C4⋊C4×C43—22no—
75C4⋊C4×C43—44no—
76C4⋊C4×C43—42no—
77C4⋊C4×C43—82no—
78C22⋊C4×C43—24no—
79C22⋊C4×C43—41no—
80C22⋊C4×C43—41no—
81C42×C43—81no—
82C22⋊Dic43—28no—
83C4⋊Dic43—28no—
84C4×Dic43—28no—
85C4×Dic43—82no—
86C4×Dic43—82no—
87#10621877—82no—
88C2×C43⋊C8—42no—
89C23×C43—22no—
90C23×C43—22no—
91C23×C43—41no—
92C23×C43C2×C22⋊C411yescharacteristic
93C23×C43#12011yescharacteristic
94C23×C43#12311yescharacteristic
95Q8×C43—82no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—24no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—24no—
102C2×C4×C43—22no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—42no—
115C2×C4×C43—81no—
116C2×C4×C43#10414yes—
117C2×C4×C43C4×D412yes—
118C2×C4×C43#12112yes—
119C2×Dic43—28no—
120C2×Dic43—44no—
121C2×Dic43—44no—
122C43⋊C8—82no—
123#9408—431nomaximal, Sylow
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—21no—
127C22×C43—21no—
128C22×C43—21no—
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—44no—
132C22×C43#38611yescharacteristic
133C22×C43C2×#10412yes—
134C22×C43#45612yes—
135C4×C43—24no—
136C4×C43—22no—
137C4×C43—22no—
138C4×C43—44no—
139C4×C43—42no—
140C4×C43—81no—
141C4×C43—81no—
142Dic43—48no—
143#2583D4311yescharacteristic
144#2274—431no—
145#1508—432no—
146#1463—431no—
147#1297—432no—
148C2×C43—22no—
149C2×C43—22no—
150C2×C43—41no—
151C2×C43#188611yescharacteristic
152C2×C43#189611yescharacteristic
153C2×C43#191311yescharacteristic
154C2×C22⋊Q8C2×D4311yescharacteristic
155C2×#117—861no—
156C22×C4⋊C4C2×D4311yescharacteristic
157#407—432no—
158#398Dic4312yescomplemented
159#395Dic4312yescomplemented
160#389—22no—
161#385—21no—
162#385—21no—
163C4×C4⋊C4—864no—
164C4×C22⋊C4—432no—
165C4×C22⋊C4—861no—
166C4×C22⋊C4C2×D4311yescharacteristic
167#328—864no—
168#324—862no—
169C43#940811yescharacteristic, complemented, Sylow
170C22×Q8C2×Dic4311yescharacteristic
171C23×C4C22⋊D4311yescharacteristic
172C23×C4C22⋊D4311yescharacteristic
173C23×C4C22×D4311yescharacteristic
174C2×M16—862no—
175C22⋊Q8—22no—
176C22⋊Q8—22no—
177#117—868no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—862no—
184C2×C4⋊C4C2×Dic4311yescharacteristic
185C2×C4⋊C4C2×Dic4312yes—
186C2×C4⋊C4C22⋊D4312yes—
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—862no—
190C2×C42—21no—
191C2×C42—862no—
192C2×C42—862no—
193C2×C42—862no—
194C22⋊C8—862no—
195C22⋊C8—862no—
196#95—22no—
197#95—22no—
198#95—434no—
199#95—862no—
200#95C2×Dic4312yes—
201C24C2×C22⋊D4311yescharacteristic
202C2×Q8—22no—
203C2×Q8—81no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—81no—
213C22×C4—81no—
214C22×C4—864no—
215C22×C4C22⋊Dic4312yes—
216C22×C4C22⋊Dic4312yes—
217C22×C4D4×D4312yes—
218C22×C4#1062190012yes—
219C22×C4C22×Dic4311yescharacteristic
220C22×C4C2×C22⋊D4311yescharacteristic
221M16—3442no—
222C2×C8—1722no—
223C4⋊C4—24no—
224C4⋊C4—24no—
225C4⋊C4—22no—
226C4⋊C4—44no—
227C4⋊C4—42no—
228C4⋊C4—82no—
229C4⋊C4—868no—
230C22⋊C4—24no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—868no—
234C42—81no—
235C42—868no—
236C42—3442no—
237C42—3442no—
238C23—22no—
239C23—22no—
240C23—41no—
241C23C2×C22⋊Dic4311yescharacteristic
242C23#1306329311yescharacteristic
243C23#1306330611yescharacteristic
244Q8—82no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—868no—
266C2×C4—1724no—
267C2×C4—1724no—
268C2×C4#1306325214yes—
269C2×C4D4×Dic4312yes—
270C2×C4#1306329712yes—
271C8—3442no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—44no—
280C22#1458277911yescharacteristic
281C22C2×#1306325212yes—
282C22#1458308112yes—
283C4—24no—
284C4—22no—
285C4—22no—
286C4—44no—
287C4—42no—
288C4—81no—
289C4—81no—
290C4—1728no—
291C2—22no—
292C2—22no—
293C2—41no—
294C2#1913498911yescharacteristic
295C2#1913503911yescharacteristic
296C2#1913513811yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2583C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#2583D43
hypocenterC43#9408
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
15. C43×#398C4semidirect
16. C43×#395C4semidirect
158. #398Dic43semidirect
159. #395Dic43semidirect
169. C43#9408semidirect

Maximal subgroups

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

subgroupindex
#191369522
#191331152
#191329252
#191324812
C43×#25832
#940843