Finite Group Databasebeta

← #24998843

Subgroups — #24998843

Order 11008.

542 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 103 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#19145536C212yesmaximal
2#19145119C211yesmaximal, characteristic, complemented
3#19133158C212yesmaximal, complemented
4#19132440C211yesmaximal, characteristic, complemented
5C43×#1961C211yesmaximal, characteristic
6#14583456C2212yes—
7#14583308—22no—
8#14583308—22no—
9#14583271—22no—
10#14583245—22no—
11#14583096—24no—
12#14583050—24no—
13#14582952C2212yes—
14#14582937—22no—
15#14582635—24no—
16C2×#127×C43C2211yescharacteristic
17C2×#102×C43—22no—
18C2×#97×C43C2211yescharacteristic
19C43×#382C2211yescharacteristic
20C2×#10621883—28no—
21#13063325D412yes—
22#13063325D412yes—
23#13063317—22no—
24#13063304—22no—
25#13063304—22no—
26C4×Dic86—22no—
27C4×Dic86—22no—
28#13063284—22no—
29#13063259—24no—
30#13063257—22no—
31#13063257—22no—
32C4⋊(C43⋊C8)—22no—
33#13063246—28no—
34C22⋊(C43⋊C8)D414yes—
35C4×C43⋊C8—22no—
36C22×D4×C43—21no—
37C22×D4×C43—22no—
38C22×C8×C43D412yes—
39#127×C43—22no—
40#127×C43—21no—
41#127×C43D412yes—
42C2×C4⋊C4×C43—21no—
43C2×C42×C43C2311yescharacteristic
44#102×C43—44no—
45#97×C43—22no—
46#95×C43—22no—
47C24×C43—41no—
48C2×D4×C43—24no—
49C2×D4×C43—22no—
50C2×D4×C43—41no—
51C2×D4×C43—42no—
52C2×D4×C43—42no—
53C2×D4×C43—42no—
54C2×D4×C43—84no—
55C22×C4×C43—41no—
56C22×C4×C43C2×D412yes—
57C22×C4×C43C2×D411yescharacteristic
58C2×Dic86—22no—
59C2×Dic86—22no—
60C2×C8×C43—22no—
61C2×C8×C43—22no—
62C2×C8×C43SD1614yescomplemented
63C4⋊C4×C43—42no—
64C42×C43C2×D411yescharacteristic
65C42×C43C2×D412yes—
66C42×C43#4111yescharacteristic
67C22⋊Dic43—42no—
68#10621883—88no—
69C4⋊Dic43—22no—
70C4⋊Dic43—22no—
71C4⋊Dic43—22no—
72C4⋊Dic43—22no—
73Dic43⋊C4—42no—
74Dic43⋊C4—42no—
75C4×Dic43—42no—
76C2×C43⋊C8—24no—
77C23×C43—42no—
78C23×C43—84no—
79C23×C43—81no—
80C23×C43—81no—
81C23×C43#12711yescharacteristic
82D4×C43—48no—
83D4×C43—44no—
84D4×C43—84no—
85D4×C43—82no—
86C2×C4×C43—42no—
87C2×C4×C43—82no—
88C2×C4×C43—81no—
89C2×C4×C43#12011yescharacteristic
90C2×C4×C43#12012yes—
91C2×C4×C43#12112yes—
92C2×C4×C43#12111yescharacteristic
93C2×C4×C43C2×SD1612yes—
94C2×C4×C43#13712yes—
95C2×Dic43—42no—
96C2×Dic43—42no—
97Dic86—44no—
98Dic86—82no—
99C8×C43—24no—
100C43⋊C8—44no—
101#10220—431nomaximal, Sylow
102C22×C43—22no—
103C22×C43—84no—
104C22×C43—82no—
105C22×C43—162no—
106C22×C43—162no—
107C22×C43#39211yescharacteristic
108C22×C43#49211yescharacteristic
109C22×C43#49711yescharacteristic
110C4×C43—22no—
111C4×C43—22no—
112C4×C43—161no—
113C4×C43#44812yes—
114C4×C43#46112yes—
115Dic43—82no—
116Dic43—82no—
117#3208—432no—
118#3162—431no—
119#1961D4311yescharacteristic
120#1518—432no—
121#1281—431no—
122C2×C43—21no—
123C2×C43—21no—
124C2×C43—162no—
125C2×C43#200812yes—
126C2×C43#201311yescharacteristic
127#533—432no—
128C2×#127C2×D4311yescharacteristic
129#501—862no—
130#501—862no—
131#492—862no—
132#486—862no—
133#460—864no—
134#450—864no—
135#431—432no—
136#427—862no—
137C2×#102—22no—
138C2×#97C2×D4311yescharacteristic
139#382C2×D4311yescharacteristic
140#328—864no—
141C43#1022011yescharacteristic, complemented, Sylow
142C22×D4—22no—
143C22×D4—21no—
144C2×SD16—868no—
145C22×C8C22⋊D4312yes—
146C4⋊Q8—432no—
147C4⋊Q8—432no—
148#127—21no—
149#127—22no—
150#127D17212yes—
151#125—862no—
152C22⋊Q8—862no—
153C22⋊Q8—862no—
154C4×Q8—862no—
155C4×Q8—862no—
156#117—862no—
157C2×C4⋊C4—21no—
158C2×C42C22×D4311yescharacteristic
159#107—864no—
160#106—862no—
161#106—862no—
162C4⋊C8—862no—
163#102—44no—
164#102—868no—
165C22⋊C8—434no—
166#97—22no—
167C4×C8—862no—
168#95—22no—
169C24—41no—
170C2×Q8—862no—
171C2×Q8—862no—
172C2×D4—24no—
173C2×D4—22no—
174C2×D4—41no—
175C2×D4—42no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—84no—
179C22×C4—41no—
180C22×C4D4×D4312yes—
181C22×C4C2×C22⋊D4311yescharacteristic
182SD16—3448no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—864no—
186C2×C8#1062188314yescomplemented
187C4⋊C4—42no—
188C4⋊C4—862no—
189C4⋊C4—862no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—1722no—
193C4⋊C4—1722no—
194C22⋊C4—1722no—
195C42—1722no—
196C42C2×D17211yescharacteristic
197C42#1062189811yescharacteristic
198C42D4×D4312yes—
199C23—42no—
200C23—84no—
201C23—81no—
202C23—81no—
203C23#1306332111yescharacteristic
204Q8—3442no—
205Q8—1724no—
206D4—48no—
207D4—44no—
208D4—84no—
209D4—82no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—81no—
213C2×C4—1722no—
214C2×C4—1722no—
215C2×C4#1306329311yescharacteristic
216C2×C4#1306329512yes—
217C2×C4#1306329812yes—
218C2×C4#1306329911yescharacteristic
219C2×C4C2×#1062188312yes—
220C2×C4#1306335512yes—
221C8—24no—
222C8—1724no—
223C22—22no—
224C22—84no—
225C22—82no—
226C22—162no—
227C22—162no—
228C22#1458280811yescharacteristic
229C22#1458327111yescharacteristic
230C22#1458329411yescharacteristic
231C4—22no—
232C4—22no—
233C4—161no—
234C4—3442no—
235C4—3442no—
236C4#1458303712yes—
237C4#1458310412yes—
238C2—21no—
239C2—21no—
240C2—162no—
241C2#1913565012yes—
242C2#1913567711yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1961C2
socleC22×C43#392
prime radicalC2×#127×C43C22
hypercenter#1961D43
hypocenterC43#10220
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
2. #19145119C2semidirect
3. #19133158C2semidirect
4. #19132440C2semidirect
62. C2×C8×C43SD16semidirect
141. C43#10220semidirect
186. C2×C8#10621883semidirect

Maximal subgroups

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

subgroupindex
#191455362
#191451192
#191331582
#191324402
C43×#19612
#1022043