Finite Group Databasebeta

← #25005837

Subgroups — #25005837

Order 11008.

386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 87 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#19143288C211yesmaximal, characteristic
2#19136204C212yesmaximal, complemented
3#19132537C211yesmaximal, characteristic, complemented
4#19132520C212yesmaximal, complemented
5C43×#1323C211yesmaximal, characteristic, complemented
6C2×#13063333C411yescharacteristic
7C22×C8×D43C2211yescharacteristic
8#14583411C411yescharacteristic
9C2×#13063264—22no—
10#14582969—22no—
11#14582964—22no—
12#14582865C2211yescharacteristic
13#14582862C411yescharacteristic
14#14582855C411yescharacteristic
15C22⋊(C43⋊C16)C2212yes—
16(C2×D43)⋊C16—22no—
17C43×#424C2211yescharacteristic
18C43×C22⋊C16C2212yes—
19C2×#10621898C2×C411yescharacteristic
20C22×C4×D43C2×C411yescharacteristic
21#13063333—42no—
22C2×#10621877C2×C411yescharacteristic
23C2×#10621872—21no—
24C22×C43⋊C8C2×C411yescharacteristic
25C2×C8×D43—21no—
26C2×C8×D43—42no—
27C2×C8×D43D412yes—
28C2×C8×D43D412yes—
29#13063309—21no—
30#13063305C812yes—
31#13063300C812yes—
32#13063295—21no—
33C4×D172—22no—
34#13063264—44no—
35C2×C43⋊C16—22no—
36(C2×D43)⋊C8—22no—
37(C2×D43)⋊C8—22no—
38#13063236—21no—
39C4×C43⋊C8—21no—
40C2×M16×C43C2×C411yescharacteristic
41C22×C8×C43C2311yescharacteristic
42#117×C43C2×C411yescharacteristic
43C2×C16×C43—22no—
44C4⋊C8×C43—22no—
45C23×D43M1611yescharacteristic
46C22×C4×C43C22×C411yescharacteristic
47C2×C22⋊D43—21no—
48C22×Dic43M1611yescharacteristic
49#10621898—41no—
50#10621898—41no—
51C2×D172—22no—
52C2×D172C2×C811yescharacteristic
53C2×C4×D43—21no—
54C2×C4×D43—41no—
55C2×C4×D43—41no—
56C2×C4×D43C22⋊C412yes—
57C2×C4×D43C2×C812yes—
58C2×Dic86C2×C811yescharacteristic
59M16×C43—41no—
60C2×C8×C43—21no—
61C2×C8×C43—41no—
62C2×C8×C43C2×D412yes—
63C4⋊C4×C43C2×C812yes—
64C22⋊C4×C43—21no—
65C42×C43—21no—
66(C2×D43)⋊C4—22no—
67(C2×D43)⋊C4—22no—
68C4⋊Dic43—22no—
69#10621877—41no—
70C2×C43⋊C8—22no—
71C2×C43⋊C8—21no—
72C2×C43⋊C8C22⋊C411yescharacteristic
73C2×C43⋊C8C22⋊C411yescharacteristic
74#10621872—42no—
75C8×D43—24no—
76C8×D43—42no—
77C8×D43—42no—
78C16×C43—42no—
79C43⋊C16—42no—
80C23×C43C2×M1611yescharacteristic
81C22×D43—21no—
82C22×D43—41no—
83C22×D43—42no—
84C22×D43C22⋊C812yes—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43C2×C22⋊C411yescharacteristic
89C2×C4×C43C22×C811yescharacteristic
90C22⋊D43—42no—
91C2×Dic43—21no—
92C2×Dic43—41no—
93C2×Dic43C22⋊C812yes—
94D172—41no—
95D172—44no—
96C4×D43—22no—
97C4×D43—22no—
98C4×D43—42no—
99C4×D43—41no—
100C4×D43—41no—
101Dic86—41no—
102C8×C43—22no—
103C8×C43—41no—
104C43⋊C8—21no—
105C43⋊C8—41no—
106C43⋊C8#9912yes—
107#11469—431nomaximal, Sylow
108C22×C43—22no—
109C22×C43—21no—
110C22×C43C2×C22⋊C811yescharacteristic
111C2×D43—22no—
112C2×D43—22no—
113C2×D43—22no—
114C2×D43—44no—
115C2×D43—42no—
116C2×D43—41no—
117C4×C43—21no—
118C4×C43—42no—
119C4×C43C2×#9911yescharacteristic
120C4×C43#41311yescharacteristic
121Dic43—22no—
122Dic43—41no—
123#2929—431no—
124#2112—432no—
125#1323—431no—
126#1323D4311yescharacteristic, complemented
127#1315—432no—
128C2×C43—41no—
129C2×C43#145911yescharacteristic
130C2×C43#211712yes—
131D43—42no—
132D43—81no—
133C2×#131—431no—
134C23×C8—431no—
135#525—431no—
136C2×M32—862no—
137#435—862no—
138C8×D4—862no—
139#424C2×D4311yescharacteristic
140#408—431no—
141#407—431no—
142#405—431no—
143C22⋊C16—432no—
144C22⋊C16—862no—
145C22⋊C16C2×D4312yes—
146C43#1146911yescharacteristic, complemented, Sylow
147C2×#41—431no—
148C23×C4—431no—
149#131—1722no—
150C2×M16—431no—
151C2×M16—861no—
152C2×M16C4×D4311yescharacteristic
153C22×C8—431no—
154C22×C8—432no—
155C22×C8—432no—
156C22×C8—861no—
157C22×C8—1722no—
158C22×C8C22×D4311yescharacteristic
159#123—861no—
160C22⋊Q8—432no—
161#121—432no—
162#120—861no—
163C4×D4—862no—
164#117C4×D4311yescharacteristic
165M32—1724no—
166C2×C16—22no—
167C2×C16—862no—
168C4⋊C8—22no—
169C22⋊C8—862no—
170C22⋊C8—862no—
171#97—861no—
172C4×C8—861no—
173C24—431no—
174#41—1721no—
175#41—1721no—
176C2×Q8—431no—
177C2×D4—431no—
178C2×D4—862no—
179C2×D4—861no—
180C22×C4—431no—
181C22×C4—432no—
182C22×C4—432no—
183C22×C4—861no—
184C22×C4—1721no—
185C22×C4—1721no—
186C22×C4C2×C4×D4311yescharacteristic
187M16—41no—
188M16—1722no—
189M16—1721no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—431no—
193C2×C8—431no—
194C2×C8—864no—
195C2×C8—862no—
196C2×C8—861no—
197C2×C8—1722no—
198C2×C8—1722no—
199C2×C8D4×D4312yes—
200C4⋊C4—862no—
201C4⋊C4C8×D4312yes—
202C22⋊C4—21no—
203C22⋊C4—862no—
204C22⋊C4—862no—
205C42—21no—
206C16—42no—
207C16—1722no—
208C23—432no—
209C23—861no—
210C23—1721no—
211C23—1722no—
212C23M16×D4311yescharacteristic
213Q8—1721no—
214D4—1721no—
215D4—1724no—
216D4—1722no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—432no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4—861no—
224C2×C4—1722no—
225C2×C4—1721no—
226C2×C4—1721no—
227C2×C4—1721no—
228C2×C4C22⋊C4×D4311yescharacteristic
229C2×C4C2×C8×D4311yescharacteristic
230C8—22no—
231C8—41no—
232C8—432no—
233C8—861no—
234C8—1721no—
235C22—22no—
236C22—21no—
237C22—862no—
238C22—862no—
239C22—862no—
240C22—1724no—
241C22—1722no—
242C22—1721no—
243C22C22⋊C8×D4311yescharacteristic
244C4—21no—
245C4—42no—
246C4—862no—
247C4—1721no—
248C4#99×D4311yescharacteristic
249C4#1458288211yescharacteristic
250C2—41no—
251C2—3441no—
252C2—1722no—
253C2#1913291211yescharacteristic
254C2#1913622112yes—
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#1323C2
socleC22×C43C2×C22⋊C8
prime radical#14583411C4
cosocleC22×C8×C43C23
hypercenter#1323D43
hypocenterC43#11469
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #19136204C2semidirect
3. #19132537C2semidirect
4. #19132520C2semidirect
5. C43×#1323C2semidirect
126. #1323D43semidirect
146. C43#11469semidirect

Maximal subgroups

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

subgroupindex
#191432882
#191362042
#191325372
#191325202
C43×#13232
#1146943