Finite Group Databasebeta

← #25009929

Subgroups — #25009929

Order 11008.

324 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 55 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#19145419C211yesmaximal, characteristic
2#19136815C212yesmaximal, complemented
3#19136111C211yesmaximal, characteristic
4#19132590C212yesmaximal, complemented
5C43×#1320C211yesmaximal, characteristic
6C2×#13063304—21no—
7#14583230—22no—
8#14583157—21no—
9#14583157C2212yes—
10#14583057—22no—
11#14582948C2211yescharacteristic
12#14582947—21no—
13#14582863—21no—
14#14582722—22no—
15#14582716—22no—
16C43⋊#338C2211yescharacteristic
17C43×#407C2211yescharacteristic
18C43×#349C2212yes—
19C22×Dic86—21no—
20C2×Dic172—21no—
21C2×Dic172D412yes—
22C2×#10621877—21no—
23C2×#10621877—21no—
24#13063304—22no—
25#13063304—22no—
26#13063304—41no—
27#13063304—41no—
28C2×C4⋊Dic43—21no—
29C2×Dic43⋊C4—41no—
30C2×C22⋊Dic43—41no—
31#13063261—22no—
32#13063260—42no—
33#13063257—21no—
34#13063257D412yes—
35#13063250—22no—
36#13063250—22no—
37C22⋊(C43⋊C8)—42no—
38C23×C4×C43D411yescharacteristic
39C2×M16×C43D411yescharacteristic
40C2×M16×C43C2311yescharacteristic
41M32×C43—22no—
42C22⋊C8×C43—22no—
43C24×C43SD1611yescharacteristic
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43—41no—
47C22×C4×C43—41no—
48C22×C4×C43SD1611yescharacteristic
49C22×C4×C43C2×D411yescharacteristic
50C22×Dic43—41no—
51C22×Dic43—41no—
52C2×Dic86—22no—
53C2×Dic86—41no—
54C2×Dic86—81no—
55C2×Dic86—81no—
56M16×C43—41no—
57M16×C43—41no—
58C2×C8×C43—21no—
59C2×C8×C43C2×D412yes—
60C22⋊Dic43—42no—
61C22⋊Dic43—42no—
62C4⋊Dic43—22no—
63C4⋊Dic43—41no—
64Dic43⋊C4—42no—
65Dic43⋊C4—42no—
66#10621877—41no—
67#10621877—41no—
68#10621877—41no—
69#10621877—41no—
70C2×C43⋊C8—22no—
71C2×C43⋊C8—41no—
72Dic172—42no—
73Dic172—81no—
74C16×C43—42no—
75C23×C43—21no—
76C23×C43—41no—
77C23×C43—42no—
78C23×C43C2×SD1611yescharacteristic
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—41no—
83C2×C4×C43—41no—
84C2×C4×C43—41no—
85C2×C4×C43—81no—
86C2×C4×C43#12011yescharacteristic
87C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
88C2×Dic43—42no—
89C2×Dic43—42no—
90C2×Dic43—82no—
91C2×Dic43—82no—
92Dic86—42no—
93Dic86—42no—
94Dic86—82no—
95C8×C43—22no—
96C8×C43—41no—
97C43⋊C8—42no—
98C43⋊C8—81no—
99#12299—431nomaximal, Sylow
100C22×C43—22no—
101C22×C43—21no—
102C22×C43—41no—
103C22×C43—41no—
104C22×C43—42no—
105C22×C43—41no—
106C22×C43—81no—
107C22×C43#45011yescharacteristic
108C4×C43—21no—
109C4×C43—41no—
110C4×C43#45311yescharacteristic
111C4×C43#45811yescharacteristic
112Dic43—82no—
113Dic43—82no—
114#3195—431no—
115#2239—432no—
116#2091—431no—
117#1342—432no—
118#1320D4311yescharacteristic
119C2×C43—21no—
120C2×C43—42no—
121C2×C43—41no—
122C2×C43#161311yescharacteristic
123C2×C22⋊Q8—861no—
124#483—862no—
125#470—432no—
126#470—861no—
127#451—862no—
128#430—431no—
129#430—861no—
130#407—861no—
131#407C2×D4311yescharacteristic
132#365—862no—
133#362—862no—
134#349C2×D4312yes—
135#338—431no—
136C43#1229911yescharacteristic, complemented, Sylow
137C22×Q8—861no—
138C23×C4D17211yescharacteristic
139C2×Q16—432no—
140C2×Q16—861no—
141C2×M16—861no—
142C2×M16—861no—
143C2×M16D17211yescharacteristic
144C2×M16C22×D4311yescharacteristic
145C22⋊Q8—862no—
146C22⋊Q8—862no—
147C22⋊Q8—1721no—
148C22⋊Q8—1721no—
149C2×C4⋊C4—861no—
150C2×C4⋊C4—1721no—
151C2×C22⋊C4—1721no—
152M32—22no—
153#108—862no—
154#108—1722no—
155#106—432no—
156#106—861no—
157#103—862no—
158#103—862no—
159C22⋊C8—22no—
160C22⋊C8—1722no—
161C24#1062187311yescharacteristic
162C2×Q8—862no—
163C2×Q8—3441no—
164C2×Q8—3441no—
165C2×Q8—1721no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—1721no—
171C22×C4—1721no—
172C22×C4#1062187311yescharacteristic
173C22×C4C2×D17211yescharacteristic
174Q16—3441no—
175Q16—1722no—
176M16—41no—
177M16—41no—
178M16—1721no—
179M16—1721no—
180M16—1721no—
181M16—1721no—
182C2×C8—21no—
183C2×C8—862no—
184C2×C8—1721no—
185C2×C8D4×D4312yes—
186C4⋊C4—862no—
187C4⋊C4—1721no—
188C4⋊C4—1722no—
189C4⋊C4—1722no—
190C22⋊C4—1722no—
191C22⋊C4—1722no—
192C16—42no—
193C23—21no—
194C23—41no—
195C23—42no—
196C23C2×#1062187311yescharacteristic
197Q8—3442no—
198Q8—1722no—
199Q8—1722no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—81no—
207C2×C4—3442no—
208C2×C4—3442no—
209C2×C4—1722no—
210C2×C4—1722no—
211C2×C4#1306329511yescharacteristic
212C2×C4#1306335311yescharacteristic
213C8—22no—
214C8—41no—
215C8—3441no—
216C8—1722no—
217C22—22no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22#1458305211yescharacteristic
225C4—21no—
226C4—41no—
227C4—3442no—
228C4—3442no—
229C4#1458306911yescharacteristic
230C4#1458309011yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1913361711yescharacteristic
subgroupG/H
centerC2#19133617
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#1320C2
socleC2×C43#1613
prime radicalC24×C43SD16
hypercenter#1320D43
hypocenterC43#12299
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #19136815C2semidirect
4. #19132590C2semidirect
136. C43#12299semidirect

Maximal subgroups

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

subgroupindex
#191454192
#191368152
#191361112
#191325902
C43×#13202
#1229943