Finite Group Databasebeta

← #25009597

Subgroups — #25009597

Order 11008.

394 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 59 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#19139968C211yesmaximal, characteristic
2#19135940C211yesmaximal, characteristic
3#19133605C212yesmaximal
4#19132602C212yesmaximal
5C43×#1325C211yesmaximal, characteristic
6#14583530C2211yescharacteristic
7C2×C4×Dic86—21no—
8#14583230—22no—
9#14582939—21no—
10#14582829—21no—
11#14582829C2212yes—
12#14582804—22no—
13#14582798—22no—
14#14582668C2211yescharacteristic
15#14582659—21no—
16#14582637—22no—
17C43×#384C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86—21no—
20C2×#10621877—21no—
21#13063324—41no—
22#13063316—41no—
23#13063304—22no—
24C4×Dic86—42no—
25C4×Dic86—42no—
26#13063284—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43D412yes—
30C2×Dic43⋊C4—22no—
31C2×C4×Dic43—22no—
32#13063258—41no—
33#13063257—42no—
34#13063256—41no—
35#13063250—42no—
36C43⋊#95—22no—
37C43⋊#95—21no—
38C43⋊#95—22no—
39C43⋊#95D412yes—
40C2×C4⋊C4×C43—22no—
41C2×C4⋊C4×C43D411yescharacteristic
42C2×C4⋊C4×C43C2311yescharacteristic
43C2×C42×C43D411yescharacteristic
44C22⋊C8×C43—22no—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43C2×D411yescharacteristic
48C22×C4×C43C2×D412yes—
49C22×Dic43—22no—
50C22×Dic43—22no—
51C2×Dic86—24no—
52C2×Dic86—22no—
53C2×Dic86—42no—
54C2×Dic86—42no—
55C2×C8×C43—42no—
56C4⋊C4×C43—41no—
57C4⋊C4×C43—41no—
58C4⋊C4×C43—44no—
59C42×C43—21no—
60C42×C43SD1612yes—
61C22⋊Dic43—41no—
62C4⋊Dic43—21no—
63C4⋊Dic43—22no—
64C4⋊Dic43—21no—
65C4⋊Dic43—42no—
66C4⋊Dic43—42no—
67C4⋊Dic43—81no—
68Dic43⋊C4—42no—
69Dic43⋊C4—42no—
70Dic43⋊C4—42no—
71C4×Dic43—44no—
72C4×Dic43—41no—
73#10621877—22no—
74#10621877—41no—
75C2×C43⋊C8—41no—
76C23×C43#12011yescharacteristic
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43—41no—
86C2×C4×C43C2×SD1611yescharacteristic
87C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
88C2×Dic43—24no—
89C2×Dic43—42no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—42no—
93C2×Dic43—41no—
94C2×Dic43—41no—
95C2×Dic43—42no—
96Dic86—48no—
97Dic86—82no—
98C8×C43—82no—
99C43⋊C8—42no—
100#12247—431nomaximal, Sylow
101C22×C43—21no—
102C22×C43—21no—
103C22×C43#45011yescharacteristic
104C22×C43#45611yescharacteristic
105C22×C43B(4,𝔽2)11yescharacteristic
106C4×C43—24no—
107C4×C43—21no—
108C4×C43—21no—
109C4×C43—42no—
110C4×C43—81no—
111Dic43—44no—
112Dic43—82no—
113Dic43—81no—
114Dic43—81no—
115#2582—431no—
116#2060—431no—
117#1611—432no—
118#1346—432no—
119#1325D4311yescharacteristic
120C2×C43—21no—
121C2×C43—21no—
122C2×C43#160411yescharacteristic
123C2×C43#219811yescharacteristic
124C2×C43#220511yescharacteristic
125#544—431no—
126C2×C4×Q8—861no—
127#483—862no—
128#428—861no—
129#398—432no—
130#398—861no—
131#391—862no—
132#389—862no—
133#384C2×D4311yescharacteristic
134#343—431no—
135#339—861no—
136#328—862no—
137#324C2×D4312yes—
138C43#1224711yescharacteristic, complemented, Sylow
139C22×Q8—861no—
140C2×M16—861no—
141C4⋊Q8—1721no—
142#125—1721no—
143C22⋊Q8—862no—
144C4×Q8—1722no—
145C4×Q8—1722no—
146#117—861no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—432no—
149C2×C4⋊C4—861no—
150C2×C4⋊C4—861no—
151C2×C4⋊C4—862no—
152C2×C4⋊C4D17211yescharacteristic
153C2×C4⋊C4C22×D4311yescharacteristic
154C2×C42—862no—
155C2×C42D17211yescharacteristic
156#107—1721no—
157#106—1721no—
158#106—1722no—
159#103—1722no—
160C22⋊C8—22no—
161#95—432no—
162#95—862no—
163#95—861no—
164#95—862no—
165C2×Q8—864no—
166C2×Q8—862no—
167C2×Q8—1722no—
168C2×Q8—1722no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—862no—
172C22×C4—862no—
173C22×C4C2×D17211yescharacteristic
174C22×C4D4×D4312yes—
175M16—862no—
176M16—1721no—
177C2×C8—42no—
178C2×C8—1721no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—44no—
182C4⋊C4—861no—
183C4⋊C4—862no—
184C4⋊C4—861no—
185C4⋊C4—3441no—
186C4⋊C4—1722no—
187C4⋊C4—1722no—
188C4⋊C4—1722no—
189C4⋊C4—1722no—
190C4⋊C4—1722no—
191C22⋊C4—1721no—
192C42—21no—
193C42—1724no—
194C42—1721no—
195C42#1062187312yes—
196C23#1306329511yescharacteristic
197Q8—3442no—
198Q8—1728no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—864no—
209C2×C4—1722no—
210C2×C4—1722no—
211C2×C4—1721no—
212C2×C4—1721no—
213C2×C4—1722no—
214C2×C4—1722no—
215C2×C4—1722no—
216C2×C4C2×#1062187311yescharacteristic
217C2×C4#1306335311yescharacteristic
218C8—82no—
219C8—1722no—
220C22—21no—
221C22—21no—
222C22#1458305211yescharacteristic
223C22#1458308411yescharacteristic
224C22#1458308711yescharacteristic
225C4—24no—
226C4—21no—
227C4—21no—
228C4—42no—
229C4—81no—
230C4—3441no—
231C4—3441no—
232C4—3442no—
233C4—1724no—
234C2—21no—
235C2—21no—
236C2#1913356611yescharacteristic
237C2#1913659311yescharacteristic
238C2#1913662611yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1325C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1325D43
hypocenterC43#12247
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
138. C43#12247semidirect

Maximal subgroups

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

subgroupindex
#191399682
#191359402
#191336052
#191326022
C43×#13252
#1224743