Finite Group Databasebeta

← #24999831

Subgroups — #24999831

Order 11008.

414 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 77 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#19134695C212yesmaximal
2#19134670C211yesmaximal, characteristic
3#19132503C211yesmaximal, characteristic
4#19132448C212yesmaximal
5C43×#2607C211yesmaximal, characteristic
6C2×#13063284C2211yescharacteristic
7#14582863C2212yes—
8#14582762C2211yescharacteristic
9#14582665—21no—
10#14582665—21no—
11#14582659—22no—
12#14582659—22no—
13C43×#399—21no—
14C43×#393—21no—
15C43×#391—22no—
16C43×#387—22no—
17C43×#381C2211yescharacteristic
18C4×C22⋊C4×C43C2212yes—
19C2×#10621877—22no—
20#13063284—22no—
21#13063284—22no—
22C2×C4⋊Dic43Q812yescomplemented
23C2×C22⋊Dic43—21no—
24C2×C22⋊Dic43—21no—
25C2×C4×Dic43—21no—
26C22⋊(C43⋊C8)—22no—
27C22⋊(C43⋊C8)—22no—
28C43⋊#95—22no—
29C22×Q8×C43—21no—
30C23×C4×C43C2311yescharacteristic
31C2×C4⋊C4×C43—22no—
32C2×C4⋊C4×C43—21no—
33C2×C22⋊C4×C43—22no—
34C2×C22⋊C4×C43D411yescharacteristic
35C2×C22⋊C4×C43D411yescharacteristic
36C2×C42×C43D412yes—
37C2×C42×C43D412yes—
38#95×C43—21no—
39#95×C43—22no—
40#95×C43—21no—
41#95×C43—22no—
42#95×C43—22no—
43C24×C43C2×D411yescharacteristic
44C2×Q8×C43—44no—
45C2×Q8×C43—81no—
46C22×C4×C43—22no—
47C22×C4×C43—21no—
48C22×C4×C43—22no—
49C22×C4×C43—21no—
50C22×C4×C43—41no—
51C22×C4×C43—41no—
52C22×C4×C43C2×D412yes—
53C22×C4×C43C2×Q811yescharacteristic
54C22×C4×C43#4111yescharacteristic
55C22×C4×C43#4112yes—
56C22×Dic43—22no—
57C22×Dic43—41no—
58C4⋊C4×C43—44no—
59C4⋊C4×C43—81no—
60C22⋊C4×C43—41no—
61C22⋊C4×C43—41no—
62C22⋊C4×C43—44no—
63C42×C43—42no—
64C42×C43—42no—
65C22⋊Dic43—41no—
66C22⋊Dic43—41no—
67C22⋊Dic43—41no—
68C22⋊Dic43—41no—
69C4⋊Dic43—24no—
70C4×Dic43—42no—
71#10621877—42no—
72#10621877—42no—
73C2×C43⋊C8—42no—
74C23×C43—21no—
75C23×C43—21no—
76C23×C43—42no—
77C23×C43#12011yescharacteristic
78C23×C43C22⋊Q811yescharacteristic
79C23×C43#12411yescharacteristic
80Q8×C43—84no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—24no—
84C2×C4×C43—41no—
85C2×C4×C43—41no—
86C2×C4×C43—42no—
87C2×C4×C43—42no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43—42no—
93C2×C4×C43—42no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43C22⋊Q812yes—
97C2×C4×C43#12412yes—
98C2×Dic43—42no—
99C2×Dic43—82no—
100C2×Dic43—81no—
101C2×Dic43—82no—
102C43⋊C8—82no—
103#10387—431nomaximal, Sylow
104C22×C43—22no—
105C22×C43—21no—
106C22×C43—21no—
107C22×C43—22no—
108C22×C43—22no—
109C22×C43—81no—
110C22×C43—81no—
111C22×C43#39311yescharacteristic
112C22×C43#45811yescharacteristic
113C22×C43#45811yescharacteristic
114C4×C43—22no—
115C4×C43—22no—
116C4×C43—44no—
117C4×C43—82no—
118C4×C43—81no—
119C4×C43—81no—
120Dic43—82no—
121Dic43—161no—
122#2607D4311yescharacteristic
123#1826—432no—
124#1820—431no—
125#1306—431no—
126#1284—432no—
127C2×C43—21no—
128C2×C43—21no—
129C2×C43—41no—
130C2×C43—41no—
131C2×C43#203011yescharacteristic
132C2×C43#203112yes—
133C2×#117—431no—
134#407—432no—
135#399—21no—
136#393—21no—
137#391—22no—
138#387—22no—
139#381—431no—
140#381C2×D4311yescharacteristic
141C4×C22⋊C4C2×D4312yes—
142#342—861no—
143#342—861no—
144#339—862no—
145#339—862no—
146C43#1038711yescharacteristic, complemented, Sylow
147C22×Q8—21no—
148C23×C4C22×D4311yescharacteristic
149C2×M16—862no—
150#117—862no—
151#117—862no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—432no—
155C2×C22⋊C4—22no—
156C2×C22⋊C4—861no—
157C2×C22⋊C4—861no—
158C2×C22⋊C4C22⋊D4311yescharacteristic
159C2×C22⋊C4C22⋊D4311yescharacteristic
160C2×C42—861no—
161C2×C42C22⋊D4312yes—
162C2×C42C22⋊D4312yes—
163C22⋊C8—862no—
164C22⋊C8—862no—
165#95—21no—
166#95—22no—
167#95—21no—
168#95—22no—
169#95—22no—
170#95—862no—
171C24C2×C22⋊D4311yescharacteristic
172C2×Q8—44no—
173C2×Q8—81no—
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—22no—
177C22×C4—21no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—862no—
181C22×C4—1721no—
182C22×C4Q8×D4311yescharacteristic
183C22×C4#1062190212yes—
184C22×C4#1062190211yescharacteristic
185C22×C4C2×C22⋊D4312yes—
186M16—1722no—
187M16—1722no—
188C2×C8—1722no—
189C4⋊C4—44no—
190C4⋊C4—81no—
191C4⋊C4—864no—
192C22⋊C4—44no—
193C22⋊C4—41no—
194C22⋊C4—41no—
195C22⋊C4—1721no—
196C22⋊C4—1721no—
197C22⋊C4—1721no—
198C22⋊C4—1721no—
199C42—42no—
200C42—42no—
201C42—1722no—
202C23—21no—
203C23—21no—
204C23—42no—
205C23#1306329411yescharacteristic
206C23#1306330111yescharacteristic
207C23#1306331411yescharacteristic
208Q8—84no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—24no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—3442no—
225C2×C4—3441no—
226C2×C4—3442no—
227C2×C4—1722no—
228C2×C4#1306330112yes—
229C2×C4#1306331412yes—
230C8—3442no—
231C22—22no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—22no—
236C22—81no—
237C22—81no—
238C22#1458281011yescharacteristic
239C22#1458308911yescharacteristic
240C22#1458308911yescharacteristic
241C4—22no—
242C4—22no—
243C4—44no—
244C4—81no—
245C4—82no—
246C4—81no—
247C4—3442no—
248C4—6881no—
249C2—21no—
250C2—21no—
251C2—41no—
252C2—41no—
253C2#1913576111yescharacteristic
254C2#1913576412yes—
subgroupG/H
centerC22#14582810
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2607C2
socleC22×C43#393
prime radicalC24×C43C2×D4
hypercenter#2607D43
hypocenterC43#10387
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2607

Complements

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

NH ≅ G/Ntype
22. C2×C4⋊Dic43Q8semidirect
146. C43#10387semidirect

Maximal subgroups

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

subgroupindex
#191346952
#191346702
#191325032
#191324482
C43×#26072
#1038743