Finite Group Databasebeta

← #24994045

Subgroups — #24994045

Order 11008.

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

normal subgroups only

This group has 644 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#19140075C211yesmaximal, characteristic
2#19136952C211yesmaximal, characteristic, complemented
3#19133112C212yesmaximal
4#19132480C212yesmaximal, complemented
5C43×#1463C211yesmaximal, characteristic, complemented
6C2×#13063299C2211yescharacteristic
7C2×#13063284—21no—
8#14582838C412yescomplemented
9#14582816C412yescomplemented
10#14582789—22no—
11#14582778—21no—
12#14582778—21no—
13C4⋊C4×Dic43—24no—
14C4×C22⋊Dic43—21no—
15C4×C22⋊Dic43C2211yescharacteristic
16C4×C22⋊Dic43C2212yes—
17#14582634—24no—
18C22×C4⋊C4×C43C2211yescharacteristic
19C43×#407C2212yes—
20C43×#324—22no—
21C22×D172C2×C411yescharacteristic
22C22×C22⋊D43—21no—
23#13063299—22no—
24#13063299—22no—
25#13063284—28no—
26C2×C4⋊Dic43—22no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—21no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—22no—
33C2×C4×Dic43—22no—
34C2×C4×Dic43—22no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95C2×C412yes—
41C43⋊#95D414yes—
42C23×C4×C43D411yescharacteristic
43C23×C4×C43D411yescharacteristic
44C23×C4×C43C2311yescharacteristic
45C2×M16×C43—22no—
46C2×C4⋊C4×C43—22no—
47C2×C4⋊C4×C43—22no—
48C2×C4⋊C4×C43C2×C412yes—
49C2×C4⋊C4×C43D412yes—
50C22⋊C8×C43—22no—
51C22⋊C8×C43—22no—
52C24×C43C2×D411yescharacteristic
53C23×D43—21no—
54C22×C4×C43—24no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—81no—
60C22×C4×C43—81no—
61C22×C4×C43C22⋊C412yes—
62C22×C4×C43C22⋊C412yes—
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D412yes—
66C22×C4×C43#4112yes—
67C2×C22⋊D43—44no—
68C2×C22⋊D43—41no—
69C2×C22⋊D43—41no—
70C22×Dic43—21no—
71C22×Dic43—22no—
72C22×Dic43—24no—
73C2×D172—22no—
74C2×D172—81no—
75M16×C43—82no—
76C2×C8×C43—42no—
77C4⋊C4×C43—24no—
78C4⋊C4×C43—24no—
79C22⋊Dic43—28no—
80C22⋊Dic43—42no—
81(C2×D43)⋊C4—44no—
82(C2×D43)⋊C4—42no—
83(C2×D43)⋊C4—82no—
84C4⋊Dic43—28no—
85C4⋊Dic43—22no—
86C4×Dic43—28no—
87C4×Dic43—82no—
88C4×Dic43—82no—
89C4×Dic43—81no—
90C23×C43—22no—
91C23×C43—22no—
92C23×C43—41no—
93C23×C43C2×C22⋊C411yescharacteristic
94C23×C43#12011yescharacteristic
95C23×C43#12311yescharacteristic
96C22×D43—42no—
97C22×D43—42no—
98C22×D43—41no—
99C22×D43—42no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—24no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—42no—
107C2×C4×C43—41no—
108C2×C4×C43—42no—
109C2×C4×C43—41no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—81no—
113C2×C4×C43#10414yes—
114C2×C4×C43C4×D412yes—
115C2×C4×C43#12112yes—
116C22⋊D43—82no—
117C22⋊D43—82no—
118C2×Dic43—28no—
119C2×Dic43—44no—
120C2×Dic43—44no—
121C2×Dic43—42no—
122C2×Dic43—42no—
123C2×Dic43—42no—
124C2×Dic43—41no—
125C2×Dic43—42no—
126D172—82no—
127C8×C43—82no—
128#9410—431nomaximal, Sylow
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—44no—
137C22×C43#38611yescharacteristic
138C22×C43C2×#10412yes—
139C22×C43#45412yes—
140C2×D43—84no—
141C2×D43—81no—
142C2×D43—81no—
143C2×D43—81no—
144C4×C43—24no—
145C4×C43—22no—
146C4×C43—22no—
147C4×C43—42no—
148Dic43—48no—
149Dic43—82no—
150Dic43—81no—
151#2591—431no—
152#2274—431no—
153#1507—432no—
154#1463D4311yescharacteristic, complemented
155#1297—432no—
156C2×C43—22no—
157C2×C43—22no—
158C2×C43—41no—
159C2×C43#188811yescharacteristic
160C2×C43#189611yescharacteristic
161C2×C43#191311yescharacteristic
162D43—161no—
163C2×#121—431no—
164C2×#117—861no—
165C22×C4⋊C4C2×D4311yescharacteristic
166#407C2×D4312yes—
167#400—432no—
168#394—432no—
169#388—862no—
170#386—861no—
171#386—861no—
172C4×C4⋊C4—864no—
173C4×C22⋊C4—431no—
174C4×C22⋊C4—432no—
175C4×C22⋊C4—861no—
176#327—864no—
177#324—22no—
178C43#941011yescharacteristic, complemented, Sylow
179C22×D4—431no—
180C22×D4—861no—
181C23×C4D17211yescharacteristic
182C23×C4D17211yescharacteristic
183C23×C4C22×D4311yescharacteristic
184C2×M16—22no—
185#121—862no—
186#121—862no—
187#117—868no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—431no—
191C2×C4⋊C4—862no—
192C2×C4⋊C4C4×D4312yes—
193C2×C4⋊C4C22⋊D4312yes—
194C2×C22⋊C4—862no—
195C2×C22⋊C4—862no—
196C2×C22⋊C4—861no—
197C2×C22⋊C4—862no—
198C2×C22⋊C4—861no—
199C2×C42—862no—
200C2×C42—862no—
201C2×C42—862no—
202C2×C42—861no—
203C22⋊C8—22no—
204C22⋊C8—22no—
205#95—432no—
206#95—434no—
207#95—862no—
208#95—862no—
209#95—862no—
210C24—861no—
211C24C2×D17211yescharacteristic
212C2×D4—862no—
213C2×D4—3441no—
214C2×D4—1724no—
215C2×D4—1721no—
216C2×D4—1721no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—24no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—81no—
223C22×C4—81no—
224C22×C4—864no—
225C22×C4—862no—
226C22×C4—861no—
227C22×C4(C2×D43)⋊C412yes—
228C22×C4(C2×D43)⋊C412yes—
229C22×C4C2×C4×D4311yescharacteristic
230C22×C4D4×D4312yes—
231C22×C4#1062190012yes—
232C22×C4C2×C22⋊D4311yescharacteristic
233M16—82no—
234C2×C8—42no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—868no—
238C4⋊C4—862no—
239C22⋊C4—868no—
240C22⋊C4—3442no—
241C22⋊C4—1722no—
242C22⋊C4—1724no—
243C22⋊C4—1722no—
244C42—868no—
245C42—3442no—
246C42—3441no—
247C42—3442no—
248C23—22no—
249C23—22no—
250C23—41no—
251C23—1722no—
252C23—1722no—
253C23—1722no—
254C23—1721no—
255C23C2×(C2×D43)⋊C411yescharacteristic
256C23#1306329511yescharacteristic
257C23#1306330911yescharacteristic
258D4—3442no—
259D4—3442no—
260D4—3442no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—868no—
275C2×C4—1722no—
276C2×C4—1722no—
277C2×C4—1722no—
278C2×C4—1722no—
279C2×C4—1721no—
280C2×C4—1724no—
281C2×C4—1724no—
282C2×C4#1306325114yes—
283C2×C4(C22⋊D43)⋊C412yes—
284C2×C4#1306329712yes—
285C8—82no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—44no—
294C22—3444no—
295C22—3441no—
296C22—3441no—
297C22—3441no—
298C22#1458277611yescharacteristic
299C22C2×#1306325112yes—
300C22#1458307412yes—
301C4—24no—
302C4—22no—
303C4—22no—
304C4—42no—
305C4—3442no—
306C4—3441no—
307C4—1728no—
308C2—22no—
309C2—22no—
310C2—41no—
311C2—6881no—
312C2#1913499611yescharacteristic
313C2#1913503611yescharacteristic
314C2#1913513511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1463C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1463D43
hypocenterC43#9410
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #19136952C2semidirect
4. #19132480C2semidirect
5. C43×#1463C2semidirect
8. #14582838C4semidirect
9. #14582816C4semidirect
154. #1463D43semidirect
178. C43#9410semidirect

Maximal subgroups

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

subgroupindex
#191400752
#191369522
#191331122
#191324802
C43×#14632
#941043