Finite Group Databasebeta

← #25016284

Subgroups — #25016284

Order 11008.

384 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 81 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#19134809C212yesmaximal
2#19134809C211yesmaximal, characteristic
3#19132722C211yesmaximal, characteristic
4#19132722C212yesmaximal
5C43×#2809C211yesmaximal, characteristic
6#14583377C2211yescharacteristic
7#14582939—22no—
8#14582939—21no—
9C2×#13063244C2212yes—
10C2×#13063244C2211yescharacteristic
11#14582659—22no—
12#14582659—21no—
13C43×#400—21no—
14C43×#398—22no—
15C43×#391C2211yescharacteristic
16C43×#391C2212yes—
17C43×#389—21no—
18C43×#387—22no—
19C2×#10621877—22no—
20C2×#10621877—21no—
21Q8×Dic43—41no—
22Q8×Dic43—41no—
23#13063284—22no—
24#13063284—21no—
25#13063258—42no—
26#13063258—41no—
27#13063256—42no—
28#13063256—41no—
29#13063244—22no—
30#13063244—21no—
31#13063244Q814yes—
32#13063244Q812yes—
33C22×Q8×C43C2311yescharacteristic
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43D412yes—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C42×C43D412yes—
41C2×C42×C43D411yescharacteristic
42#95×C43—21no—
43#95×C43—22no—
44#95×C43—22no—
45#95×C43—22no—
46#95×C43—22no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43C2×Q812yes—
50C2×Q8×C43C2×Q811yescharacteristic
51C2×Q8×C43#4111yescharacteristic
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43C2×D412yes—
57C22×C4×C43C2×D411yescharacteristic
58C4⋊C4×C43—42no—
59C4⋊C4×C43—41no—
60C4⋊C4×C43—44no—
61C4⋊C4×C43—42no—
62C4⋊C4×C43—81no—
63C4⋊C4×C43—81no—
64C42×C43—41no—
65C42×C43—42no—
66C22⋊Dic43—41no—
67C4⋊Dic43—22no—
68C4⋊Dic43—21no—
69C4⋊Dic43—21no—
70C4⋊Dic43—22no—
71C4×Dic43—42no—
72C4×Dic43—41no—
73#10621877—24no—
74#10621877—22no—
75#10621877—41no—
76#10621877—42no—
77C2×C43⋊C8—42no—
78C2×C43⋊C8—41no—
79C23×C43#12011yescharacteristic
80Q8×C43—42no—
81Q8×C43—41no—
82Q8×C43—41no—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43—42no—
93C2×C4×C43—42no—
94C2×C4×C43—42no—
95C2×C4×C43—41no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43C22⋊Q812yes—
99C2×C4×C43C22⋊Q811yescharacteristic
100C2×C4×C43C4⋊Q812yes—
101C2×C4×C43C4⋊Q811yescharacteristic
102C2×Dic43—41no—
103C2×Dic43—41no—
104C43⋊C8—44no—
105C43⋊C8—42no—
106#13465—431nomaximal, Sylow
107C22×C43—21no—
108C22×C43—21no—
109C22×C43#39511yescharacteristic
110C22×C43B(4,𝔽2)11yescharacteristic
111C22×C43#45811yescharacteristic
112C4×C43—22no—
113C4×C43—21no—
114C4×C43—22no—
115C4×C43—21no—
116C4×C43—42no—
117C4×C43—82no—
118C4×C43—81no—
119C4×C43—82no—
120Dic43—81no—
121Dic43—81no—
122#2809D4311yescharacteristic
123#1857—432no—
124#1857—431no—
125#1394—431no—
126#1394—432no—
127C2×C43—21no—
128C2×C43—21no—
129C2×C43#206211yescharacteristic
130C2×C43#220311yescharacteristic
131C2×C43#220411yescharacteristic
132#519—431no—
133#428—862no—
134#428—861no—
135C2×#101—432no—
136C2×#101—431no—
137#400—21no—
138#398—22no—
139#391C2×D4311yescharacteristic
140#391C2×D4312yes—
141#389—21no—
142#387—22no—
143#339—862no—
144#339—861no—
145C43#1346511yescharacteristic, complemented, Sylow
146C22×Q8C22×D4311yescharacteristic
147C2×M16—862no—
148C2×M16—861no—
149C4×Q8—1721no—
150C4×Q8—1721no—
151#117—862no—
152#117—861no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C22⋊D4312yes—
158C2×C4⋊C4C22⋊D4311yescharacteristic
159C2×C42C22⋊D4312yes—
160C2×C42C22⋊D4311yescharacteristic
161#107—1722no—
162#107—1721no—
163#106—1722no—
164#106—1721no—
165#101—434no—
166#101—432no—
167#101—862no—
168#101—861no—
169#95—21no—
170#95—22no—
171#95—22no—
172#95—22no—
173#95—22no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8Q8×D4312yes—
177C2×Q8Q8×D4311yescharacteristic
178C2×Q8#1062190211yescharacteristic
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4C2×C22⋊D4312yes—
184C22×C4C2×C22⋊D4311yescharacteristic
185M16—864no—
186M16—862no—
187M16—1721no—
188M16—1722no—
189C2×C8—1722no—
190C2×C8—1721no—
191C4⋊C4—42no—
192C4⋊C4—41no—
193C4⋊C4—44no—
194C4⋊C4—42no—
195C4⋊C4—81no—
196C4⋊C4—81no—
197C4⋊C4—862no—
198C4⋊C4—861no—
199C4⋊C4—861no—
200C4⋊C4—862no—
201C22⋊C4—1721no—
202C42—41no—
203C42—42no—
204C42—1722no—
205C42—1721no—
206C23#1306329411yescharacteristic
207Q8—42no—
208Q8—41no—
209Q8—41no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—1721no—
226C2×C4—1721no—
227C2×C4#1306330112yes—
228C2×C4#1306330111yescharacteristic
229C2×C4#1306332312yes—
230C2×C4#1306332311yescharacteristic
231C8—1724no—
232C8—1722no—
233C22—21no—
234C22—21no—
235C22#1458281811yescharacteristic
236C22#1458308611yescharacteristic
237C22#1458308911yescharacteristic
238C4—22no—
239C4—21no—
240C4—22no—
241C4—21no—
242C4—42no—
243C4—82no—
244C4—81no—
245C4—82no—
246C4—3441no—
247C4—3441no—
248C2—21no—
249C2—21no—
250C2#1913594711yescharacteristic
251C2#1913661611yescharacteristic
252C2#1913662111yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC22×Q8×C43C23
FrattiniC22×Q8C22×D43
FittingC43×#2809C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#2809D43
hypocenterC43#13465
LCSG ▷ C22×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #2809

Complements

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

NH ≅ G/Ntype
145. C43#13465semidirect

Maximal subgroups

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

subgroupindex
#191348092
#191327222
C43×#28092
#1346543