Finite Group Databasebeta

← #25016287

Subgroups — #25016287

Order 11008.

384 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 79 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#19142583C211yesmaximal, characteristic
2#19134810C212yesmaximal
3#19132722C211yesmaximal, characteristic
4#19132721C212yesmaximal
5C43×#1857C211yesmaximal, characteristic
6#14582942—22no—
7C2×#13063244C2212yes—
8#14582838—21no—
9#14582831—22no—
10#14582806C2212yes—
11#14582797—21no—
12#14582786—22no—
13#14582658—22no—
14C43×#519C2211yescharacteristic
15C43×#428—21no—
16C2×#101×C43C2211yescharacteristic
17C43×#391C2211yescharacteristic
18C43×#339—21no—
19C2×#10621877—22no—
20C2×C4⋊Dic43—21no—
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43D412yes—
24C2×Dic43⋊C4—22no—
25C2×C4×Dic43D412yes—
26#13063258—42no—
27#13063256—42no—
28#13063244—22no—
29#13063244Q814yes—
30C43⋊#95—21no—
31C43⋊#95—22no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C22×Q8×C43C2311yescharacteristic
35C2×M16×C43—21no—
36C4×Q8×C43—41no—
37C4×Q8×C43—41no—
38#117×C43—21no—
39#117×C43—22no—
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C42×C43D411yescharacteristic
42#107×C43—41no—
43#106×C43—41no—
44#101×C43—21no—
45#101×C43Q812yes—
46#95×C43—22no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43C2×Q811yescharacteristic
50C2×Q8×C43C2×Q812yes—
51C2×Q8×C43#4111yescharacteristic
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43C2×D412yes—
55C22×C4×C43C2×D411yescharacteristic
56C22×Dic43—22no—
57C22×Dic43—22no—
58M16×C43—22no—
59M16×C43—41no—
60C2×C8×C43—41no—
61C4⋊C4×C43—21no—
62C4⋊C4×C43—21no—
63C4⋊C4×C43—22no—
64C4⋊C4×C43—22no—
65C4⋊C4×C43—41no—
66C22⋊C4×C43—41no—
67C42×C43—41no—
68C42×C43—42no—
69C42×C43—41no—
70C4⋊Dic43—42no—
71C4⋊Dic43—42no—
72C4⋊Dic43—81no—
73C4⋊Dic43—81no—
74Dic43⋊C4—44no—
75C4×Dic43—42no—
76#10621877—24no—
77#10621877—42no—
78C2×C43⋊C8—42no—
79C23×C43#12011yescharacteristic
80Q8×C43—41no—
81Q8×C43—42no—
82Q8×C43—41no—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—42no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43C22⋊Q812yes—
95C2×C4×C43C22⋊Q811yescharacteristic
96C2×C4×C43C4⋊Q811yescharacteristic
97C2×C4×C43C4⋊Q812yes—
98C2×Dic43—42no—
99C2×Dic43—42no—
100C2×Dic43—42no—
101C2×Dic43—42no—
102C2×Dic43—42no—
103C2×Dic43—42no—
104C8×C43—42no—
105C43⋊C8—44no—
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—21no—
115C4×C43—22no—
116C4×C43—42no—
117C4×C43—81no—
118C4×C43—81no—
119C4×C43—81no—
120Dic43—82no—
121Dic43—82no—
122#2809—431no—
123#1857—432no—
124#1857D4311yescharacteristic
125#1394—432no—
126#1394—431no—
127C2×C43—21no—
128C2×C43—21no—
129C2×C43#206211yescharacteristic
130C2×C43#220311yescharacteristic
131C2×C43#220411yescharacteristic
132#519C2×D4311yescharacteristic
133#428—21no—
134#428—862no—
135C2×#101—432no—
136C2×#101C2×D4311yescharacteristic
137#400—861no—
138#398—862no—
139#391—432no—
140#391C2×D4311yescharacteristic
141#389—861no—
142#387—862no—
143#339—21no—
144#339—862no—
145C43#1346511yescharacteristic, complemented, Sylow
146C22×Q8C22×D4311yescharacteristic
147C2×M16—21no—
148C2×M16—862no—
149C4×Q8—41no—
150C4×Q8—41no—
151#117—22no—
152#117—21no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4—861no—
155C2×C4⋊C4—861no—
156C2×C4⋊C4—862no—
157C2×C4⋊C4—861no—
158C2×C4⋊C4C22⋊D4311yescharacteristic
159C2×C42—432no—
160C2×C42C22⋊D4311yescharacteristic
161#107—41no—
162#107—1722no—
163#106—41no—
164#106—1722no—
165#101—21no—
166#101—434no—
167#101—862no—
168#101Dic8612yes—
169#95—22no—
170#95—861no—
171#95—862no—
172#95—862no—
173#95—862no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8C2×Dic8611yescharacteristic
177C2×Q8#1062189811yescharacteristic
178C2×Q8Q8×D4312yes—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—862no—
182C22×C4—862no—
183C22×C4D4×D4312yes—
184C22×C4C2×C22⋊D4311yescharacteristic
185M16—22no—
186M16—41no—
187M16—864no—
188M16—1722no—
189C2×C8—41no—
190C2×C8—1722no—
191C4⋊C4—21no—
192C4⋊C4—22no—
193C4⋊C4—21no—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—3441no—
197C4⋊C4—3441no—
198C4⋊C4—1722no—
199C4⋊C4—1724no—
200C4⋊C4—1722no—
201C22⋊C4—41no—
202C42—41no—
203C42—41no—
204C42—42no—
205C42—1722no—
206C23#1306329311yescharacteristic
207Q8—41no—
208Q8—41no—
209Q8—42no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—1722no—
222C2×C4—1722no—
223C2×C4—1722no—
224C2×C4—1722no—
225C2×C4—1722no—
226C2×C4—1722no—
227C2×C4#1306330312yes—
228C2×C4#1306330411yescharacteristic
229C2×C4#1306332311yescharacteristic
230C2×C4#1306332412yes—
231C8—42no—
232C8—1724no—
233C22—21no—
234C22—21no—
235C22#1458281911yescharacteristic
236C22#1458308511yescharacteristic
237C22#1458308811yescharacteristic
238C4—21no—
239C4—22no—
240C4—21no—
241C4—22no—
242C4—42no—
243C4—81no—
244C4—81no—
245C4—81no—
246C4—3442no—
247C4—3442no—
248C2—21no—
249C2—21no—
250C2#1913594811yescharacteristic
251C2#1913661511yescharacteristic
252C2#1913662011yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC22×Q8×C43C23
FrattiniC22×Q8C22×D43
FittingC43×#1857C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1857D43
hypocenterC43#13465
LCSG ▷ C22×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

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
#191425832
#191348102
#191327222
#191327212
C43×#18572
#1346543