Finite Group Databasebeta

← #25016288

Subgroups — #25016288

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#19142583C211yesmaximal, characteristic
2#19134812C212yesmaximal
3#19134809C211yesmaximal, characteristic
4#19132721C212yesmaximal
5C43×#1394C211yesmaximal, characteristic
6#14583377C2211yescharacteristic
7#14582941—22no—
8#14582939—21no—
9C2×#13063244C2211yescharacteristic
10#14582838—21no—
11#14582831—22no—
12#14582806C2212yes—
13#14582797—21no—
14#14582786—22no—
15#14582660—22no—
16#14582659—21no—
17C2×#101×C43C2212yes—
18C43×#391C2211yescharacteristic
19C2×#10621877—21no—
20Q8×Dic43—41no—
21Q8×Dic43—41no—
22#13063284—21no—
23#13063284—22no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43D412yes—
28C2×Dic43⋊C4—22no—
29C2×C4×Dic43D412yes—
30#13063259—42no—
31#13063258—41no—
32#13063257—42no—
33#13063256—41no—
34#13063244—21no—
35#13063244Q812yes—
36C43⋊#95—21no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C22×Q8×C43C2311yescharacteristic
41C2×M16×C43—22no—
42C2×C4⋊C4×C43D411yescharacteristic
43C2×C42×C43D411yescharacteristic
44#101×C43—22no—
45#101×C43Q814yes—
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×C43C2×D411yescharacteristic
55C22×C4×C43C2×D412yes—
56C22×Dic43—22no—
57C22×Dic43—22no—
58M16×C43—24no—
59M16×C43—42no—
60C2×C8×C43—42no—
61C4⋊C4×C43—41no—
62C42×C43—41no—
63C22⋊Dic43—41no—
64C4⋊Dic43—21no—
65C4⋊Dic43—22no—
66C4⋊Dic43—21no—
67C4⋊Dic43—22no—
68C4⋊Dic43—42no—
69C4⋊Dic43—42no—
70C4⋊Dic43—81no—
71C4⋊Dic43—81no—
72Dic43⋊C4—44no—
73C4×Dic43—41no—
74C4×Dic43—42no—
75C4×Dic43—42no—
76#10621877—22no—
77#10621877—41no—
78C2×C43⋊C8—41no—
79C23×C43#12011yescharacteristic
80Q8×C43—42no—
81Q8×C43—41no—
82Q8×C43—41no—
83C2×C4×C43—21no—
84C2×C4×C43—22no—
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—41no—
92C2×C4×C43C22⋊Q812yes—
93C2×C4×C43C22⋊Q811yescharacteristic
94C2×C4×C43C4⋊Q812yes—
95C2×C4×C43C4⋊Q811yescharacteristic
96C2×Dic43—42no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—42no—
100C2×Dic43—41no—
101C2×Dic43—41no—
102C2×Dic43—42no—
103C2×Dic43—42no—
104C8×C43—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—21no—
113C4×C43—22no—
114C4×C43—22no—
115C4×C43—21no—
116C4×C43—42no—
117C4×C43—81no—
118Dic43—82no—
119Dic43—81no—
120Dic43—81no—
121Dic43—82no—
122#2809—431no—
123#1857—432no—
124#1857—431no—
125#1394—432no—
126#1394D4311yescharacteristic
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—431no—
136C2×#101C2×D4312yes—
137#400—861no—
138#398—862no—
139#391—432no—
140#391C2×D4311yescharacteristic
141#389—861no—
142#387—862no—
143#339—862no—
144#339—861no—
145C43#1346511yescharacteristic, complemented, Sylow
146C22×Q8C22×D4311yescharacteristic
147C2×M16—22no—
148C2×M16—861no—
149C4×Q8—1721no—
150C4×Q8—1721no—
151#117—861no—
152#117—862no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4—861no—
155C2×C4⋊C4—861no—
156C2×C4⋊C4—862no—
157C2×C4⋊C4—861no—
158C2×C4⋊C4D17211yescharacteristic
159C2×C42—432no—
160C2×C42D17211yescharacteristic
161#107—1721no—
162#107—1722no—
163#106—1721no—
164#106—1722no—
165#101—22no—
166#101—432no—
167#101—861no—
168#101Dic8614yes—
169#95—22no—
170#95—861no—
171#95—862no—
172#95—862no—
173#95—862no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8C2×Dic8612yes—
177C2×Q8#1062190011yescharacteristic
178C2×Q8Q8×D4311yescharacteristic
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—862no—
182C22×C4—862no—
183C22×C4C2×D17211yescharacteristic
184C22×C4D4×D4312yes—
185M16—24no—
186M16—42no—
187M16—862no—
188M16—1721no—
189C2×C8—42no—
190C2×C8—1721no—
191C4⋊C4—41no—
192C4⋊C4—861no—
193C4⋊C4—862no—
194C4⋊C4—861no—
195C4⋊C4—862no—
196C4⋊C4—3441no—
197C4⋊C4—3441no—
198C4⋊C4—1722no—
199C4⋊C4—1724no—
200C4⋊C4—1722no—
201C22⋊C4—1721no—
202C42—41no—
203C42—1722no—
204C42—1721no—
205C42—1722no—
206C23#1306329511yescharacteristic
207Q8—42no—
208Q8—41no—
209Q8—41no—
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—1722no—
220C2×C4—1722no—
221C2×C4—1722no—
222C2×C4—1722no—
223C2×C4—1721no—
224C2×C4—1721no—
225C2×C4—1722no—
226C2×C4—1722no—
227C2×C4#1306330212yes—
228C2×C4#1306330511yescharacteristic
229C2×C4#1306332412yes—
230C2×C4#1306332511yescharacteristic
231C8—44no—
232C8—1722no—
233C22—21no—
234C22—21no—
235C22#1458282011yescharacteristic
236C22#1458308711yescharacteristic
237C22#1458309011yescharacteristic
238C4—22no—
239C4—21no—
240C4—22no—
241C4—21no—
242C4—42no—
243C4—81no—
244C4—3442no—
245C4—3441no—
246C4—3442no—
247C4—3441no—
248C2—21no—
249C2—21no—
250C2#1913594911yescharacteristic
251C2#1913661811yescharacteristic
252C2#1913662311yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC22×Q8×C43C23
FrattiniC22×Q8C22×D43
FittingC43×#1394C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1394D43
hypocenterC43#13465
LCSG ▷ C22×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

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
#191348122
#191348092
#191327212
C43×#13942
#1346543