Finite Group Databasebeta

← #24999671

Subgroups — #24999671

Order 11008.

400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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#19135568C212yesmaximal
3#19135414C211yesmaximal, characteristic
4#19132477C212yesmaximal
5C43×#1295C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7C2×#13063248—21no—
8C2×#13063248—21no—
9C2×#13063236C2211yescharacteristic
10#14582841—22no—
11#14582838—21no—
12#14582820—22no—
13#14582819—21no—
14#14582765C2212yes—
15#14582662—22no—
16#14582662—22no—
17C2×#97×C43C2212yes—
18C43×#382C2211yescharacteristic
19C22×Dic86—21no—
20C22×Dic86—21no—
21C22×C43⋊C8—21no—
22#13063325—22no—
23#13063325—21no—
24#13063325Q812yescomplemented
25C2×C4⋊Dic43—22no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43D412yes—
28C2×C4⋊Dic43D412yes—
29C2×Dic43⋊C4—22no—
30#13063248—42no—
31#13063248—42no—
32#13063236—22no—
33C43⋊#95—21no—
34C43⋊#95—22no—
35C43⋊#95—21no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C22×C8×C43—22no—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C42×C43C2311yescharacteristic
42#97×C43—22no—
43#97×C43—22no—
44#95×C43—22no—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43C2×D411yescharacteristic
48C22×C4×C43C2×D412yes—
49C22×Dic43—22no—
50C22×Dic43—22no—
51C22×Dic43—41no—
52C2×Dic86—22no—
53C2×Dic86—41no—
54C2×Dic86—41no—
55C2×Dic86—41no—
56C2×Dic86—41no—
57C2×Dic86—41no—
58C2×Dic86—81no—
59C2×Dic86—82no—
60C2×C8×C43—24no—
61C2×C8×C43—42no—
62C2×C8×C43—42no—
63C4⋊C4×C43—41no—
64C4⋊C4×C43—41no—
65C42×C43C2×Q811yescharacteristic
66C42×C43#4112yes—
67C42×C43#4111yescharacteristic
68C4⋊Dic43—24no—
69C4⋊Dic43—42no—
70C4⋊Dic43—42no—
71C4⋊Dic43—42no—
72C4⋊Dic43—81no—
73Dic43⋊C4—82no—
74C2×C43⋊C8—22no—
75C2×C43⋊C8—41no—
76C2×C43⋊C8—41no—
77C23×C43#12011yescharacteristic
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—41no—
83C2×C4×C43—41no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43C22⋊Q812yes—
87C2×C4×C43C22⋊Q811yescharacteristic
88C2×C4×C43#12412yes—
89C2×C4×C43#12411yescharacteristic
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—42no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—42no—
97C2×Dic43—81no—
98C2×Dic43—81no—
99Dic86—42no—
100Dic86—42no—
101Dic86—81no—
102Dic86—81no—
103Dic86—84no—
104C8×C43—44no—
105C43⋊C8—42no—
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—
118Dic43—82no—
119Dic43—82no—
120Dic43—82no—
121#2844—431no—
122#1993—432no—
123#1960—431no—
124#1295—432no—
125#1295D4311yescharacteristic
126C2×C43#165911yescharacteristic
127C2×C43#166011yescharacteristic
128C2×C43#166412yes—
129C2×C43#202711yescharacteristic
130C2×C43#202812yes—
131C2×C4⋊Q8—431no—
132C2×#103—861no—
133C2×#103—861no—
134C2×#97—431no—
135C2×#97C2×D4312yes—
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—861no—
146C22×Q8—861no—
147C22×C8—22no—
148C22×C8—861no—
149C4⋊Q8—432no—
150C4⋊Q8—862no—
151C4⋊Q8—861no—
152C2×C4⋊C4—432no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4—862no—
155C2×C4⋊C4—862no—
156C2×C4⋊C4—861no—
157C2×C4⋊C4D17211yescharacteristic
158C2×C4⋊C4D17211yescharacteristic
159C2×C42C22×D4311yescharacteristic
160#103—1722no—
161#103—1722no—
162#97—22no—
163#97—22no—
164#97—862no—
165#95—22no—
166#95—862no—
167#95—861no—
168#95—861no—
169#95—862no—
170#95—862no—
171C2×Q8—862no—
172C2×Q8—3441no—
173C2×Q8—3442no—
174C2×Q8—1721no—
175C2×Q8—1721no—
176C2×Q8—1721no—
177C2×Q8—1721no—
178C2×Q8—1721no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—862no—
182C22×C4—862no—
183C22×C4—1721no—
184C22×C4C2×D17211yescharacteristic
185C22×C4D4×D4312yes—
186C2×C8—24no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—862no—
190C2×C8—1721no—
191C2×C8—1721no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—864no—
195C4⋊C4—3442no—
196C4⋊C4—3441no—
197C4⋊C4—1722no—
198C4⋊C4—1722no—
199C4⋊C4—1722no—
200C42#1062189812yes—
201C42#1062190011yescharacteristic
202C42Q8×D4311yescharacteristic
203C23#1306329511yescharacteristic
204Q8—3441no—
205Q8—3441no—
206Q8—3444no—
207Q8—1722no—
208Q8—1722no—
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—3441no—
218C2×C4—3441no—
219C2×C4—1722no—
220C2×C4—1722no—
221C2×C4—1722no—
222C2×C4—1722no—
223C2×C4—1722no—
224C2×C4—1722no—
225C2×C4—1722no—
226C2×C4#1306330312yes—
227C2×C4#1306330511yescharacteristic
228C2×C4#1306331112yes—
229C2×C4#1306331311yescharacteristic
230C8—44no—
231C8—1722no—
232C22#1458281211yescharacteristic
233C22#1458306911yescharacteristic
234C22#1458307411yescharacteristic
235C22#1458307812yes—
236C22#1458308312yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—81no—
243C4—3442no—
244C4—3442no—
245C4—3442no—
246C2#1913390211yescharacteristic
247C2#1913390711yescharacteristic
248C2#1913393012yes—
249C2#1913575211yescharacteristic
250C2#1913575512yes—
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socle, prime radicalC23×C43#120
hypercenter#1295D43
hypocenterC43#10359
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
24. #13063325Q8semidirect
144. C43#10359semidirect

Maximal subgroups

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

subgroupindex
#191428672
#191355682
#191354142
#191324772
C43×#12952
#1035943