Finite Group Databasebeta

← #24997585

Subgroups — #24997585

Order 11008.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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#19144599C212yesmaximal
2#19135393C211yesmaximal, characteristic
3#19132998C212yesmaximal, complemented
4#19132426C211yesmaximal, characteristic, complemented
5C43×#3162C211yesmaximal, characteristic, complemented
6C2×C4×D172C2211yescharacteristic
7#14583227—22no—
8#14583186—22no—
9#14583101—22no—
10#14583049—22no—
11C4×#10621884—24no—
12#14582952C2212yes—
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×(C2×D43)⋊C8—22no—
15Q8⋊(C43⋊C8)—24no—
16C43×#533C2212yes—
17C43×#501—22no—
18C43×#501—22no—
19C43×#427—22no—
20C2×#97×C43C2211yescharacteristic
21C22×D172D411yescharacteristic
22C22×C4×D43—21no—
23C2×#10621884—24no—
24C22×C43⋊C8—21no—
25C4×D172—22no—
26C4×D172—22no—
27C2×C4⋊Dic43D411yescharacteristic
28C2×(C2×D43)⋊C4—21no—
29#13063256—24no—
30C4⋊(C43⋊C8)—22no—
31C4⋊(C43⋊C8)—22no—
32#13063249—24no—
33#13063245—24no—
34C22⋊(C43⋊C8)—22no—
35(C2×D43)⋊C8—44no—
36C4×C43⋊C8D414yes—
37C22×C8×C43D412yes—
38C4⋊Q8×C43D412yes—
39C4⋊Q8×C43D412yes—
40#125×C43—22no—
41C22⋊Q8×C43—22no—
42C22⋊Q8×C43—22no—
43C4×Q8×C43—22no—
44C4×Q8×C43—22no—
45#117×C43—22no—
46C2×C42×C43C2311yescharacteristic
47#107×C43—22no—
48#107×C43—22no—
49#106×C43—24no—
50#97×C43—22no—
51C23×D43—21no—
52C2×Q8×C43—22no—
53C2×Q8×C43—22no—
54C22×C4×C43C2×D411yescharacteristic
55C22×C4×C43C2×D411yescharacteristic
56C22×C4×C43#4111yescharacteristic
57C22×Dic43—21no—
58C2×D172—22no—
59C2×D172—42no—
60C2×C4×D43—41no—
61C2×C4×D43—41no—
62C2×C4×D43—42no—
63C2×C4×D43—42no—
64C2×C8×C43—22no—
65C2×C8×C43—22no—
66C2×C8×C43SD1614yescomplemented
67C4⋊C4×C43—22no—
68C4⋊C4×C43—22no—
69C4⋊C4×C43—22no—
70C4⋊C4×C43—22no—
71C4⋊C4×C43—42no—
72C4⋊C4×C43—42no—
73C22⋊C4×C43—42no—
74C42×C43—42no—
75C42×C43C2×D412yes—
76C42×C43C2×D412yes—
77#10621884—48no—
78(C2×D43)⋊C4—42no—
79C4⋊Dic43—22no—
80C2×C43⋊C8—24no—
81C2×C43⋊C8—41no—
82C2×C43⋊C8—42no—
83C23×C43#12111yescharacteristic
84C22×D43—22no—
85C22×D43—41no—
86C22×D43—42no—
87C22×D43—41no—
88C22×D43—42no—
89Q8×C43—44no—
90Q8×C43—44no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—42no—
94C2×C4×C43—42no—
95C2×C4×C43#12012yes—
96C2×C4×C43#12011yescharacteristic
97C2×C4×C43#12112yes—
98C2×C4×C43#12711yescharacteristic
99C2×C4×C43C2×SD1612yes—
100C2×C4×C43#13712yes—
101C2×Dic43—41no—
102C2×Dic43—42no—
103D172—24no—
104D172—42no—
105C4×D43—82no—
106C4×D43—81no—
107C4×D43—81no—
108C8×C43—24no—
109C43⋊C8—44no—
110C43⋊C8—81no—
111#10036—431nomaximal, Sylow
112C22×C43—21no—
113C22×C43—21no—
114C22×C43#39211yescharacteristic
115C22×C43#46112yes—
116C2×D43—44no—
117C2×D43—42no—
118C2×D43—82no—
119C2×D43—81no—
120C2×D43—81no—
121C4×C43—22no—
122C4×C43—22no—
123C4×C43—82no—
124C4×C43—82no—
125C4×C43#44812yes—
126C4×C43#49211yescharacteristic
127C4×C43#49711yescharacteristic
128Dic43—81no—
129#3162D4311yescharacteristic, complemented
130#3101—432no—
131#1955—431no—
132#1481—432no—
133#1275—431no—
134C2×C43—22no—
135C2×C43#201011yescharacteristic
136C2×C43#201311yescharacteristic
137C2×C43#201711yescharacteristic
138D43—82no—
139#533C2×D4312yes—
140C2×C4×D4—431no—
141#501—22no—
142#501—22no—
143#483—862no—
144#476—862no—
145#461—862no—
146#450—862no—
147C4×SD16—864no—
148#431—432no—
149#427—22no—
150C2×C4⋊C8—431no—
151C2×C22⋊C8—862no—
152C2×#97C2×D4311yescharacteristic
153Q8⋊C8—864no—
154C43#1003611yescharacteristic, complemented, Sylow
155C22×D4—431no—
156C23×C4—861no—
157C2×SD16—864no—
158C22×C8—861no—
159C22×C8C22⋊D4312yes—
160C4⋊Q8C22⋊D4312yes—
161C4⋊Q8C22⋊D4312yes—
162#125—22no—
163C22⋊Q8—22no—
164C22⋊Q8—22no—
165C4×Q8—22no—
166C4×Q8—22no—
167C4×D4—862no—
168C4×D4—862no—
169#117—22no—
170C2×C4⋊C4—431no—
171C2×C22⋊C4—861no—
172C2×C42C22×D4311yescharacteristic
173#107—22no—
174#107—22no—
175#106—24no—
176#106—864no—
177C4⋊C8—862no—
178C4⋊C8—862no—
179#103—864no—
180#102—864no—
181C22⋊C8—862no—
182C22⋊C8—1724no—
183#97—22no—
184C4×C8—434no—
185C24—861no—
186C2×Q8—22no—
187C2×Q8—22no—
188C2×D4—862no—
189C2×D4—1722no—
190C22×C4—861no—
191C22×C4—1721no—
192C22×C4—1721no—
193C22×C4—1722no—
194C22×C4—1722no—
195C22×C4D4×D4311yescharacteristic
196C22×C4#1062190011yescharacteristic
197C22×C4C2×C22⋊D4311yescharacteristic
198SD16—1728no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—864no—
202C2×C8—1721no—
203C2×C8—1722no—
204C2×C8#1062188414yescomplemented
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—862no—
212C22⋊C4—42no—
213C22⋊C4—1722no—
214C42—42no—
215C42D4×D4312yes—
216C42C2×C22⋊D4312yes—
217C23—862no—
218C23—1721no—
219C23—1722no—
220C23—1721no—
221C23—1722no—
222C23#1306329611yescharacteristic
223Q8—44no—
224Q8—44no—
225D4—864no—
226D4—1722no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—3441no—
232C2×C4—3441no—
233C2×C4—3442no—
234C2×C4—1721no—
235C2×C4—1722no—
236C2×C4#1306329312yes—
237C2×C4#1306329411yescharacteristic
238C2×C4#1306329712yes—
239C2×C4#1306332111yescharacteristic
240C2×C4C2×#1062188412yes—
241C2×C4#1306335612yes—
242C8—24no—
243C8—3441no—
244C8—1724no—
245C22—21no—
246C22—21no—
247C22—3442no—
248C22—3441no—
249C22—3441no—
250C22—1724no—
251C22—1722no—
252C22#1458280711yescharacteristic
253C22#1458310112yes—
254C4—22no—
255C4—22no—
256C4—82no—
257C4—82no—
258C4—3441no—
259C4#1458303812yes—
260C4#1458327311yescharacteristic
261C4#1458329111yescharacteristic
262C2—22no—
263C2—3442no—
264C2#1913565911yescharacteristic
265C2#1913567811yescharacteristic
266C2#1913569811yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3162C2
socleC22×C43#392
prime radicalC22×D172D4
hypercenter#3162D43
hypocenterC43#10036
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
3. #19132998C2semidirect
4. #19132426C2semidirect
5. C43×#3162C2semidirect
66. C2×C8×C43SD16semidirect
129. #3162D43semidirect
154. C43#10036semidirect
204. C2×C8#10621884semidirect

Maximal subgroups

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

subgroupindex
#191445992
#191353932
#191329982
#191324262
C43×#31622
#1003643