Finite Group Databasebeta

← #24999670

Subgroups — #24999670

Order 11008.

400 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 91 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#19142867C211yesmaximal, characteristic
2#19135569C212yesmaximal
3#19132477C212yesmaximal
4#19132476C211yesmaximal, characteristic
5C43×#1960C211yesmaximal, characteristic
6C2×#13063236C2212yes—
7#14582841—22no—
8#14582838—21no—
9#14582820—22no—
10#14582819—21no—
11#14582765C2212yes—
12#14582661—22no—
13#14582661—22no—
14C2×C4⋊Q8×C43C2211yescharacteristic
15C2×#103×C43—21no—
16C2×#103×C43—21no—
17C2×#97×C43C2211yescharacteristic
18C43×#382C2211yescharacteristic
19C22×Dic86—21no—
20C22×C43⋊C8—22no—
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43D412yes—
23C2×C4⋊Dic43D412yes—
24C2×Dic43⋊C4—22no—
25#13063236—22no—
26#13063236—22no—
27C43⋊#95—21no—
28C43⋊#95—22no—
29C43⋊#95—21no—
30C43⋊#95—22no—
31C43⋊#95—22no—
32C22×Q8×C43—21no—
33C22×C8×C43—21no—
34C4⋊Q8×C43—22no—
35C4⋊Q8×C43—21no—
36C4⋊Q8×C43Q812yescomplemented
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43D411yescharacteristic
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C42×C43C2311yescharacteristic
41#103×C43—42no—
42#103×C43—42no—
43#97×C43—22no—
44#95×C43—22no—
45C2×Q8×C43—22no—
46C2×Q8×C43—41no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43—41no—
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43—41no—
54C22×C4×C43C2×D412yes—
55C22×C4×C43C2×D411yescharacteristic
56C22×Dic43—22no—
57C22×Dic43—22no—
58C2×Dic86—81no—
59C2×Dic86—82no—
60C2×C8×C43—22no—
61C2×C8×C43—41no—
62C2×C8×C43—41no—
63C4⋊C4×C43—24no—
64C4⋊C4×C43—41no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—42no—
67C42×C43C2×Q811yescharacteristic
68C42×C43#4111yescharacteristic
69C42×C43#4112yes—
70C4⋊Dic43—42no—
71C4⋊Dic43—42no—
72C4⋊Dic43—81no—
73Dic43⋊C4—82no—
74C2×C43⋊C8—24no—
75C2×C43⋊C8—42no—
76C2×C43⋊C8—42no—
77C23×C43#12011yescharacteristic
78Q8×C43—42no—
79Q8×C43—42no—
80Q8×C43—81no—
81Q8×C43—81no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—42no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—81no—
92C2×C4×C43—81no—
93C2×C4×C43C22⋊Q812yes—
94C2×C4×C43C22⋊Q811yescharacteristic
95C2×C4×C43#12412yes—
96C2×C4×C43#12411yescharacteristic
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—42no—
100C2×Dic43—42no—
101C2×Dic43—42no—
102C2×Dic43—42no—
103Dic86—84no—
104C8×C43—42no—
105C43⋊C8—44no—
106#10359—431nomaximal, Sylow
107C22×C43#39311yescharacteristic
108C22×C43#45311yescharacteristic
109C22×C43#45411yescharacteristic
110C22×C43#45512yes—
111C22×C43#45612yes—
112C4×C43—21no—
113C4×C43—21no—
114C4×C43—22no—
115C4×C43—22no—
116C4×C43—81no—
117C4×C43—81no—
118C4×C43—82no—
119Dic43—82no—
120Dic43—82no—
121#2844—431no—
122#1993—432no—
123#1960D4311yescharacteristic
124#1295—432no—
125#1295—431no—
126C2×C43#165911yescharacteristic
127C2×C43#166011yescharacteristic
128C2×C43#166412yes—
129C2×C43#202711yescharacteristic
130C2×C43#202812yes—
131C2×C4⋊Q8C2×D4311yescharacteristic
132C2×#103—21no—
133C2×#103—21no—
134C2×#97—432no—
135C2×#97C2×D4311yescharacteristic
136#400—862no—
137#400—861no—
138#395—862no—
139#395—861no—
140#382—432no—
141#382C2×D4311yescharacteristic
142#340—862no—
143#340—862no—
144C43#1035911yescharacteristic, complemented, Sylow
145C22×Q8—21no—
146C22×Q8—861no—
147C22×C8—21no—
148C22×C8—862no—
149C4⋊Q8—21no—
150C4⋊Q8—22no—
151C4⋊Q8Dic8612yescomplemented
152C2×C4⋊C4—22no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4—432no—
155C2×C4⋊C4—862no—
156C2×C4⋊C4—861no—
157C2×C4⋊C4C22⋊D4311yescharacteristic
158C2×C4⋊C4C22⋊D4311yescharacteristic
159C2×C42C22×D4311yescharacteristic
160#103—42no—
161#103—42no—
162#97—22no—
163#97—862no—
164#97—862no—
165#95—22no—
166#95—862no—
167#95—861no—
168#95—861no—
169#95—862no—
170#95—862no—
171C2×Q8—22no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—3441no—
178C2×Q8—3442no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—862no—
183C22×C4—862no—
184C22×C4D4×D4312yes—
185C22×C4C2×C22⋊D4311yescharacteristic
186C2×C8—22no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—864no—
190C2×C8—1722no—
191C2×C8—1722no—
192C4⋊C4—24no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—3442no—
197C4⋊C4—3441no—
198C4⋊C4—1722no—
199C4⋊C4—1722no—
200C42C2×Dic8611yescharacteristic
201C42#1062189811yescharacteristic
202C42#1062190012yes—
203C23#1306329311yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—81no—
207Q8—81no—
208Q8—3444no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—1722no—
221C2×C4—1722no—
222C2×C4—1722no—
223C2×C4—1722no—
224C2×C4—1722no—
225C2×C4—1722no—
226C2×C4#1306330212yes—
227C2×C4#1306330411yescharacteristic
228C2×C4#1306331112yes—
229C2×C4#1306331211yescharacteristic
230C8—42no—
231C8—1724no—
232C22#1458281111yescharacteristic
233C22#1458306611yescharacteristic
234C22#1458307111yescharacteristic
235C22#1458307512yes—
236C22#1458308012yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—82no—
242C4—81no—
243C4—81no—
244C4—3442no—
245C4—3442no—
246C2#1913389911yescharacteristic
247C2#1913390411yescharacteristic
248C2#1913392612yes—
249C2#1913575111yescharacteristic
250C2#1913575412yes—
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1960C2
socle, prime radicalC23×C43#120
hypercenter#1960D43
hypocenterC43#10359
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
36. C4⋊Q8×C43Q8semidirect
144. C43#10359semidirect
151. C4⋊Q8Dic86semidirect

Maximal subgroups

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

subgroupindex
#191428672
#191355692
#191324772
#191324762
C43×#19602
#1035943