Finite Group Databasebeta

← #24994409

Subgroups — #24994409

Order 11008.

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

normal subgroups only

This group has 610 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#19138882C211yesmaximal, characteristic
2#19136952C211yesmaximal, characteristic
3#19134692C212yesmaximal
4#19132449C212yesmaximal
5C43×#1463C211yesmaximal, characteristic
6C2×#13063284—21no—
7C2×#13063284C2211yescharacteristic
8#14582838C412yescomplemented
9#14582829C412yescomplemented
10#14582780—22no—
11#14582772—21no—
12#14582762—21no—
13#14582762C2211yescharacteristic
14C4⋊C4×Dic43—24no—
15C4×C22⋊Dic43—21no—
16C4×C22⋊Dic43C2212yes—
17#14582660—24no—
18C22×C4⋊C4×C43C2211yescharacteristic
19C43×#407C2212yes—
20C43×#324—22no—
21#13063284—28no—
22#13063284—22no—
23#13063284—22no—
24C2×C4⋊Dic43—22no—
25C2×C4⋊Dic43C2×C411yescharacteristic
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—22no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—21no—
31C2×C4×Dic43—22no—
32C2×C4×Dic43—21no—
33C2×C4×Dic43—22no—
34C2×C4×Dic43D414yes—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95—21no—
41C43⋊#95C2×C412yes—
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
53C22×C4×C43—24no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—42no—
59C22×C4×C43—42no—
60C22×C4×C43C22⋊C412yes—
61C22×C4×C43C22⋊C412yes—
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D412yes—
65C22×C4×C43#4112yes—
66C22×Dic43—22no—
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—24no—
70M16×C43—44no—
71C2×C8×C43—42no—
72C4⋊C4×C43—24no—
73C4⋊C4×C43—24no—
74C22⋊Dic43—28no—
75C22⋊Dic43—42no—
76C22⋊Dic43—41no—
77C22⋊Dic43—41no—
78C4⋊Dic43—28no—
79C4⋊Dic43—22no—
80C4⋊Dic43—22no—
81Dic43⋊C4—44no—
82C4×Dic43—28no—
83C4×Dic43—42no—
84C4×Dic43—44no—
85C4×Dic43—82no—
86C23×C43—22no—
87C23×C43—22no—
88C23×C43—41no—
89C23×C43C2×C22⋊C411yescharacteristic
90C23×C43#12011yescharacteristic
91C23×C43#12311yescharacteristic
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—24no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—24no—
98C2×C4×C43—22no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—81no—
105C2×C4×C43#10414yes—
106C2×C4×C43C4×D412yes—
107C2×C4×C43#12112yes—
108C2×Dic43—28no—
109C2×Dic43—44no—
110C2×Dic43—44no—
111C2×Dic43—42no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—41no—
115C2×Dic43—41no—
116C2×Dic43—42no—
117C2×Dic43—42no—
118C8×C43—82no—
119#9478—431nomaximal, Sylow
120C22×C43—21no—
121C22×C43—21no—
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—21no—
127C22×C43—44no—
128C22×C43#38611yescharacteristic
129C22×C43C2×#10412yes—
130C22×C43#45812yes—
131C4×C43—22no—
132C4×C43—22no—
133C4×C43—24no—
134C4×C43—42no—
135Dic43—48no—
136Dic43—82no—
137Dic43—81no—
138Dic43—81no—
139#2484—431no—
140#2274—431no—
141#1826—432no—
142#1463D4311yescharacteristic
143#1284—432no—
144C2×C43—22no—
145C2×C43—22no—
146C2×C43—41no—
147C2×C43#189011yescharacteristic
148C2×C43#189611yescharacteristic
149C2×C43#191211yescharacteristic
150C2×#117—431no—
151C2×#117—861no—
152C22×C4⋊C4C2×D4311yescharacteristic
153#407C2×D4312yes—
154#400—432no—
155#398—432no—
156#387—862no—
157#385—861no—
158#381—431no—
159#381—861no—
160C4×C4⋊C4—864no—
161C4×C22⋊C4—432no—
162C4×C22⋊C4—861no—
163#339—864no—
164#324—22no—
165C43#947811yescharacteristic, complemented, Sylow
166C23×C4D17211yescharacteristic
167C23×C4D17211yescharacteristic
168C23×C4C22×D4311yescharacteristic
169C2×M16—22no—
170#117—868no—
171#117—862no—
172#117—862no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—431no—
176C2×C4⋊C4—431no—
177C2×C4⋊C4—862no—
178C2×C4⋊C4—862no—
179C2×C4⋊C4C4×D4312yes—
180C2×C4⋊C4C22⋊D4312yes—
181C2×C22⋊C4—862no—
182C2×C22⋊C4—861no—
183C2×C22⋊C4—861no—
184C2×C42—434no—
185C2×C42—862no—
186C2×C42—862no—
187C2×C42—861no—
188C22⋊C8—22no—
189C22⋊C8—22no—
190#95—432no—
191#95—862no—
192#95—862no—
193#95—862no—
194#95—862no—
195#95—862no—
196#95—861no—
197C24C2×D17211yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—24no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—864no—
206C22×C4—862no—
207C22×C4—861no—
208C22×C4—861no—
209C22×C4(C2×D43)⋊C412yes—
210C22×C4(C2×D43)⋊C412yes—
211C22×C4C2×C4×D4311yescharacteristic
212C22×C4D4×D4312yes—
213C22×C4#1062190012yes—
214C22×C4C2×C22⋊D4311yescharacteristic
215M16—44no—
216C2×C8—42no—
217C4⋊C4—24no—
218C4⋊C4—24no—
219C4⋊C4—868no—
220C4⋊C4—862no—
221C4⋊C4—862no—
222C4⋊C4—1724no—
223C22⋊C4—868no—
224C22⋊C4—1722no—
225C22⋊C4—1721no—
226C22⋊C4—1721no—
227C42—868no—
228C42—3442no—
229C42—1724no—
230C42—1722no—
231C23—22no—
232C23—22no—
233C23—41no—
234C23C2×(C2×D43)⋊C411yescharacteristic
235C23#1306329511yescharacteristic
236C23#1306330911yescharacteristic
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—24no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4—868no—
251C2×C4—1722no—
252C2×C4—1722no—
253C2×C4—1722no—
254C2×C4—1722no—
255C2×C4—1722no—
256C2×C4—1721no—
257C2×C4—1721no—
258C2×C4—1724no—
259C2×C4—1724no—
260C2×C4#1306325114yes—
261C2×C4(C22⋊D43)⋊C412yes—
262C2×C4#1306329712yes—
263C8—82no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22#1458277611yescharacteristic
273C22C2×#1306325112yes—
274C22#1458309012yes—
275C4—22no—
276C4—22no—
277C4—24no—
278C4—42no—
279C4—3442no—
280C4—3441no—
281C4—3441no—
282C4—1728no—
283C2—22no—
284C2—22no—
285C2—41no—
286C2#1913500611yescharacteristic
287C2#1913503611yescharacteristic
288C2#1913513011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1463C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1463D43
hypocenterC43#9478
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
8. #14582838C4semidirect
9. #14582829C4semidirect
165. C43#9478semidirect

Maximal subgroups

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

subgroupindex
#191388822
#191369522
#191346922
#191324492
C43×#14632
#947843