Finite Group Databasebeta

← #24997587

Subgroups — #24997587

Order 11008.

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

normal subgroups only

This group has 528 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#19145119C211yesmaximal, characteristic, complemented
2#19144603C212yesmaximal
3#19132997C212yesmaximal, complemented
4#19132426C211yesmaximal, characteristic, complemented
5C43×#1955C211yesmaximal, characteristic
6#14583456C2212yes—
7#14583308—22no—
8#14583308—22no—
9#14583229—22no—
10#14583189—22no—
11#14583104—22no—
12#14583050—22no—
13C4×#10621883—24no—
14#14582952C2212yes—
15#14582937—22no—
16#14582629—24no—
17C2×C4×D4×C43C2211yescharacteristic
18C2×C4⋊C8×C43C2211yescharacteristic
19C2×C22⋊C8×C43—22no—
20C2×#97×C43C2211yescharacteristic
21C2×#10621883—24no—
22#13063325D412yes—
23#13063325D412yes—
24#13063317—22no—
25#13063304—22no—
26#13063304—22no—
27C4×Dic86—22no—
28C4×Dic86—22no—
29#13063284—22no—
30#13063259—22no—
31#13063259—22no—
32#13063257—24no—
33#13063256—24no—
34C4⋊(C43⋊C8)—22no—
35#13063248—24no—
36#13063246—24no—
37C22⋊(C43⋊C8)—22no—
38C4×C43⋊C8D414yes—
39C22×D4×C43D411yescharacteristic
40C23×C4×C43—21no—
41C22×C8×C43—21no—
42C22×C8×C43D412yes—
43C4×D4×C43—22no—
44C4×D4×C43—22no—
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C22⋊C4×C43—21no—
47C2×C42×C43C2311yescharacteristic
48C4⋊C8×C43—22no—
49C22⋊C8×C43—44no—
50#97×C43—22no—
51C24×C43—21no—
52C2×D4×C43—22no—
53C2×D4×C43—42no—
54C22×C4×C43—21no—
55C22×C4×C43—41no—
56C22×C4×C43—41no—
57C22×C4×C43—42no—
58C22×C4×C43—42no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43#4111yescharacteristic
62C2×Dic86—22no—
63C2×Dic86—22no—
64C2×C8×C43—22no—
65C2×C8×C43—22no—
66C2×C8×C43—41no—
67C2×C8×C43—42no—
68C2×C8×C43SD1614yescomplemented
69C4⋊C4×C43—22no—
70C22⋊C4×C43—42no—
71C42×C43C2×D412yes—
72C42×C43C2×D412yes—
73C22⋊Dic43—42no—
74#10621883—48no—
75C4⋊Dic43—22no—
76C4⋊Dic43—22no—
77C4⋊Dic43—22no—
78C4⋊Dic43—22no—
79Dic43⋊C4—42no—
80Dic43⋊C4—42no—
81C4×Dic43—42no—
82C2×C43⋊C8—24no—
83C23×C43—22no—
84C23×C43—41no—
85C23×C43—42no—
86C23×C43—41no—
87C23×C43—42no—
88C23×C43#12111yescharacteristic
89D4×C43—24no—
90D4×C43—42no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—42no—
95C2×C4×C43—82no—
96C2×C4×C43—81no—
97C2×C4×C43—81no—
98C2×C4×C43#12011yescharacteristic
99C2×C4×C43#12012yes—
100C2×C4×C43#12112yes—
101C2×C4×C43#12711yescharacteristic
102C2×C4×C43C2×SD1612yes—
103C2×C4×C43#13712yes—
104C2×Dic43—42no—
105C2×Dic43—42no—
106Dic86—44no—
107Dic86—44no—
108C8×C43—24no—
109C8×C43—81no—
110C43⋊C8—44no—
111#10036—431nomaximal, Sylow
112C22×C43—21no—
113C22×C43—21no—
114C22×C43—44no—
115C22×C43—42no—
116C22×C43—82no—
117C22×C43—81no—
118C22×C43—81no—
119C22×C43#39211yescharacteristic
120C22×C43#46112yes—
121C4×C43—22no—
122C4×C43—22no—
123C4×C43—81no—
124C4×C43#44812yes—
125C4×C43#49211yescharacteristic
126C4×C43#49711yescharacteristic
127Dic43—82no—
128Dic43—82no—
129#3162—431no—
130#3101—432no—
131#1955D4311yescharacteristic
132#1481—432no—
133#1275—431no—
134C2×C43—22no—
135C2×C43—82no—
136C2×C43#201011yescharacteristic
137C2×C43#201311yescharacteristic
138C2×C43#201711yescharacteristic
139#533—432no—
140C2×C4×D4C2×D4311yescharacteristic
141#501—862no—
142#501—862no—
143#483—862no—
144#476—862no—
145#461—862no—
146#450—862no—
147C4×SD16—864no—
148#431—432no—
149#427—862no—
150C2×C4⋊C8C2×D4311yescharacteristic
151C2×C22⋊C8—22no—
152C2×#97C2×D4311yescharacteristic
153Q8⋊C8—864no—
154C43#1003611yescharacteristic, complemented, Sylow
155C22×D4D17211yescharacteristic
156C23×C4—21no—
157C2×SD16—864no—
158C22×C8—21no—
159C22×C8C22⋊D4312yes—
160C4⋊Q8—432no—
161C4⋊Q8—432no—
162#125—862no—
163C22⋊Q8—862no—
164C22⋊Q8—862no—
165C4×Q8—862no—
166C4×Q8—862no—
167C4×D4—22no—
168C4×D4—22no—
169#117—862no—
170C2×C4⋊C4D17211yescharacteristic
171C2×C22⋊C4—21no—
172C2×C42C22×D4311yescharacteristic
173#107—862no—
174#107—862no—
175#106—864no—
176#106—864no—
177C4⋊C8—22no—
178C4⋊C8—862no—
179#103—864no—
180#102—864no—
181C22⋊C8—44no—
182C22⋊C8—862no—
183#97—22no—
184C4×C8—434no—
185C24—21no—
186C2×Q8—862no—
187C2×Q8—862no—
188C2×D4—22no—
189C2×D4—42no—
190C22×C4—21no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4C2×D17211yescharacteristic
196C22×C4#1062189811yescharacteristic
197C22×C4C2×C22⋊D4311yescharacteristic
198SD16—1728no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—41no—
202C2×C8—42no—
203C2×C8—864no—
204C2×C8#1062188314yescomplemented
205C4⋊C4—22no—
206C4⋊C4—862no—
207C4⋊C4—862no—
208C4⋊C4—862no—
209C4⋊C4—862no—
210C4⋊C4—1722no—
211C4⋊C4—1722no—
212C22⋊C4—42no—
213C22⋊C4—1722no—
214C42—1722no—
215C42D4×D4312yes—
216C42D4×D4312yes—
217C23—22no—
218C23—41no—
219C23—42no—
220C23—41no—
221C23—42no—
222C23#1306329911yescharacteristic
223Q8—1724no—
224Q8—1724no—
225D4—24no—
226D4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4—81no—
234C2×C4—1722no—
235C2×C4—1722no—
236C2×C4#1306329311yescharacteristic
237C2×C4#1306329512yes—
238C2×C4#1306329812yes—
239C2×C4#1306332111yescharacteristic
240C2×C4C2×#1062188312yes—
241C2×C4#1306335512yes—
242C8—24no—
243C8—81no—
244C8—1724no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—81no—
252C22#1458280811yescharacteristic
253C22#1458310412yes—
254C4—22no—
255C4—22no—
256C4—81no—
257C4—3442no—
258C4—3442no—
259C4#1458303712yes—
260C4#1458327111yescharacteristic
261C4#1458329411yescharacteristic
262C2—22no—
263C2—82no—
264C2#1913566211yescharacteristic
265C2#1913567711yescharacteristic
266C2#1913569911yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1955C2
socleC22×C43#392
prime radicalC22×D4×C43D4
hypercenter#1955D43
hypocenterC43#10036
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #19145119C2semidirect
3. #19132997C2semidirect
4. #19132426C2semidirect
68. C2×C8×C43SD16semidirect
154. C43#10036semidirect
204. C2×C8#10621883semidirect

Maximal subgroups

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

subgroupindex
#191451192
#191446032
#191329972
#191324262
C43×#19552
#1003643