Finite Group Databasebeta

← #24984177

Subgroups — #24984177

Order 11008.

332 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 37 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#19135759C211yesmaximal, characteristic
2C43⋊#1304C211yesmaximal, characteristic
3C43×#1316C211yesmaximal, characteristic
4#14583525C411yescharacteristic, complemented
5#14582755—21no—
6#14582755—21no—
7#14582666C411yescharacteristic, complemented
8#14582665—21no—
9C43×#379C2211yescharacteristic
10C43×#323—21no—
11#13063304—41no—
12#13063302—42no—
13C2×C22⋊Dic43—21no—
14C2×C22⋊Dic43—21no—
15C2×C22⋊Dic43—22no—
16C2×C22⋊Dic43—42no—
17C2×C22⋊Dic43—41no—
18C2×C22⋊Dic43—41no—
19C25×C43D411yescharacteristic
20C2×C22⋊C4×C43—41no—
21C2×C22⋊C4×C43C2×C411yescharacteristic
22C2×C22⋊C4×C43D411yescharacteristic
23C22⋊C8×C43—41no—
24C24×C43—21no—
25C24×C43—21no—
26C24×C43—41no—
27C24×C43—41no—
28C24×C43—82no—
29C24×C43C22⋊C411yescharacteristic
30C24×C43SD1611yescharacteristic
31C24×C43Q1611yescharacteristic
32C22×C4×C43—21no—
33C22×C4×C43—21no—
34C22×Dic43—22no—
35C22×Dic43—42no—
36C22×Dic43—41no—
37C2×Dic86—41no—
38C2×C8×C43—81no—
39C22⋊C4×C43—41no—
40C22⋊C4×C43—41no—
41C22⋊C4×C43—82no—
42C22⋊Dic43—41no—
43C22⋊Dic43—41no—
44C22⋊Dic43—41no—
45C22⋊Dic43—41no—
46C22⋊Dic43—82no—
47C22⋊Dic43—82no—
48C22⋊Dic43—84no—
49C22⋊Dic43—81no—
50C22⋊Dic43—81no—
51C4⋊Dic43—41no—
52Dic43⋊C4—42no—
53C23×C43—21no—
54C23×C43—21no—
55C23×C43—21no—
56C23×C43—21no—
57C23×C43—42no—
58C23×C43—41no—
59C23×C43—41no—
60C23×C43—42no—
61C23×C43—42no—
62C23×C43—44no—
63C23×C43—41no—
64C23×C43—41no—
65C23×C43—81no—
66C23×C43—81no—
67C23×C43—81no—
68C23×C43—81no—
69C23×C43—81no—
70C23×C43—82no—
71C23×C43—82no—
72C23×C43—82no—
73C23×C43#9911yescharacteristic
74C23×C43#10311yescharacteristic
75C23×C43#10411yescharacteristic
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43—81no—
79C2×C4×C43—81no—
80C2×Dic43—42no—
81C2×Dic43—82no—
82C2×Dic43—81no—
83C2×Dic43—82no—
84C2×Dic43—82no—
85C2×Dic43—82no—
86C2×Dic43—82no—
87Dic86—161no—
88C8×C43—161no—
89#7426—431nomaximal, Sylow
90C22×C43—22no—
91C22×C43—21no—
92C22×C43—21no—
93C22×C43—41no—
94C22×C43—41no—
95C22×C43—41no—
96C22×C43—42no—
97C22×C43—41no—
98C22×C43—41no—
99C22×C43—41no—
100C22×C43—42no—
101C22×C43—41no—
102C22×C43—42no—
103C22×C43—41no—
104C22×C43—81no—
105C22×C43—82no—
106C22×C43—82no—
107C22×C43—81no—
108C22×C43—84no—
109C22×C43—81no—
110C22×C43#32811yescharacteristic
111C22×C43AΣL(1,𝔽16)11yescharacteristic
112C22×C43#35411yescharacteristic
113C4×C43—81no—
114C4×C43—81no—
115Dic43—82no—
116Dic43—161no—
117Dic43—162no—
118#2029—431no—
119#1316D4311yescharacteristic
120#1304—431no—
121C2×C43—21no—
122C2×C43—21no—
123C2×C43—21no—
124C2×C43—42no—
125C2×C43—41no—
126C2×C43—41no—
127C2×C43—81no—
128C2×C43#135111yescharacteristic
129#543—431no—
130#379—861no—
131#379—861no—
132#379C2×D4311yescharacteristic
133#342—431no—
134#342—861no—
135#323—21no—
136C43#742611yescharacteristic, complemented, Sylow
137C25D17211yescharacteristic
138C22⋊Q8—1722no—
139C22⋊Q8—1721no—
140C2×C22⋊C4—41no—
141C2×C22⋊C4—862no—
142C2×C22⋊C4—861no—
143C2×C22⋊C4—861no—
144C2×C22⋊C4—1722no—
145C2×C22⋊C4—1721no—
146C2×C22⋊C4—1721no—
147C2×C22⋊C4C4×D4311yescharacteristic
148C2×C22⋊C4C22⋊D4311yescharacteristic
149C22⋊C8—41no—
150C24—21no—
151C24—21no—
152C24—41no—
153C24—41no—
154C24—82no—
155C24#1062187311yescharacteristic
156C24Dic17211yescharacteristic
157C24(C2×D43)⋊C411yescharacteristic
158C2×Q8—1721no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—862no—
162C22×C4—1722no—
163C22×C4—1721no—
164C2×C8—81no—
165C4⋊C4—1722no—
166C4⋊C4—1721no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—82no—
170C22⋊C4—3444no—
171C22⋊C4—3442no—
172C22⋊C4—3441no—
173C22⋊C4—3441no—
174C22⋊C4—3442no—
175C22⋊C4—1721no—
176C22⋊C4—1721no—
177C22⋊C4—1721no—
178C22⋊C4—1721no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—21no—
183C23—42no—
184C23—41no—
185C23—41no—
186C23—42no—
187C23—42no—
188C23—44no—
189C23—41no—
190C23—41no—
191C23—81no—
192C23—81no—
193C23—81no—
194C23—81no—
195C23—81no—
196C23—82no—
197C23—82no—
198C23—82no—
199C23#1306323911yescharacteristic
200C23#1306325011yescharacteristic
201C23#1306325111yescharacteristic
202Q8—6881no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—81no—
206C2×C4—81no—
207C2×C4—3442no—
208C2×C4—3442no—
209C2×C4—3441no—
210C2×C4—3442no—
211C2×C4—3442no—
212C2×C4—3442no—
213C2×C4—1722no—
214C8—161no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—41no—
227C22—42no—
228C22—41no—
229C22—81no—
230C22—82no—
231C22—82no—
232C22—81no—
233C22—84no—
234C22—81no—
235C22#1458263711yescharacteristic
236C22#1458268711yescharacteristic
237C22#1458269311yescharacteristic
238C4—81no—
239C4—81no—
240C4—3442no—
241C4—6882no—
242C4—6881no—
243C2—21no—
244C2—21no—
245C2—21no—
246C2—42no—
247C2—41no—
248C2—41no—
249C2—81no—
250C2#1913261711yescharacteristic
subgroupG/H
centerC2#19132617
commutatorC2×C22⋊C4×C43C2×C4
Frattini#379C2×D43
FittingC43×#1316C2
socleC2×C43#1351
prime radicalC25×C43D4
cosocleC43×#379C22
hypercenter#1316D43
hypocenterC43#7426
LCSG ▷ C2×C22⋊C4×C43 ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #379 ◁ #1316

Complements

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

NH ≅ G/Ntype
4. #14583525C4semidirect
7. #14582666C4semidirect
136. C43#7426semidirect

Maximal subgroups

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

subgroupindex
#191357592
C43⋊#13042
C43×#13162
#742643