Finite Group Databasebeta

← #24983295

Subgroups — #24983295

Order 11008.

316 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 45 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#19135593C211yesmaximal, characteristic
2#19132472C211yesmaximal, characteristic, complemented
3C43×#1314C211yesmaximal, characteristic, complemented
4C22×D344C411yescharacteristic
5C2×#13063299—21no—
6C2×#13063247—21no—
7#14582863—21no—
8#14582662C411yescharacteristic
9C2×C22⋊C8×C43C2211yescharacteristic
10C43×C22⋊C16—21no—
11C22×D172—21no—
12C22×C22⋊D43—41no—
13C2×D344—41no—
14C2×D344—42no—
15C2×#10621877—41no—
16#13063299—42no—
17#13063299—42no—
18C2×C4⋊Dic43—21no—
19C2×(C2×D43)⋊C4—41no—
20#13063247—42no—
21C22⋊(C43⋊C8)—22no—
22C22⋊(C43⋊C8)—41no—
23C23×C4×C43D411yescharacteristic
24C22×C8×C43C2×C411yescharacteristic
25C22×C8×C43D411yescharacteristic
26C2×C16×C43—41no—
27C22⋊C8×C43—41no—
28C24×C43SD1611yescharacteristic
29C23×D43—41no—
30C22×C4×C43—21no—
31C22×C4×C43—21no—
32C22×C4×C43—41no—
33C22×C4×C43—41no—
34C22×C4×C43C22⋊C411yescharacteristic
35C22×C4×C43D811yescharacteristic
36C2×C22⋊D43—44no—
37C2×C22⋊D43—82no—
38C2×C22⋊D43—82no—
39C22×Dic43—41no—
40C2×D172—22no—
41C2×D172—41no—
42C2×D172—41no—
43C2×D172—41no—
44C2×D172—41no—
45C2×D172—41no—
46C2×C8×C43—21no—
47C2×C8×C43—21no—
48C2×C8×C43—41no—
49C2×C8×C43—41no—
50(C2×D43)⋊C4—44no—
51C4⋊Dic43—22no—
52C4⋊Dic43—41no—
53#10621877—81no—
54#10621877—81no—
55C2×C43⋊C8—42no—
56D344—42no—
57D344—42no—
58C16×C43—81no—
59C23×C43—21no—
60C23×C43—21no—
61C23×C43—21no—
62C23×C43—41no—
63C23×C43—41no—
64C23×C43#10211yescharacteristic
65C22×D43—42no—
66C22×D43—81no—
67C22×D43—81no—
68C22×D43—81no—
69C22×D43—81no—
70C22×D43—81no—
71C22×D43—81no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43—81no—
79C2×C4×C43#9911yescharacteristic
80C2×C4×C43#10411yescharacteristic
81C22⋊D43—88no—
82C2×Dic43—42no—
83C2×Dic43—81no—
84C2×Dic43—81no—
85D172—42no—
86D172—42no—
87D172—81no—
88D172—81no—
89C8×C43—41no—
90C8×C43—41no—
91C43⋊C8—82no—
92#7084—431nomaximal, Sylow
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—42no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43—41no—
99C22×C43—81no—
100C22×C43#32711yescharacteristic
101C22×C43#35911yescharacteristic
102C22×C43#36111yescharacteristic
103C2×D43—82no—
104C2×D43—82no—
105C2×D43—82no—
106C2×D43—161no—
107C2×D43—161no—
108C2×D43—161no—
109C2×D43—161no—
110C4×C43—21no—
111C4×C43—41no—
112C4×C43AΣL(1,𝔽16)11yescharacteristic
113C4×C43#35311yescharacteristic
114Dic43—82no—
115#1999—431no—
116#1314D4311yescharacteristic, complemented
117#1293—431no—
118C2×C43—21no—
119C2×C43—21no—
120C2×C43—81no—
121C2×C43#134111yescharacteristic
122C2×C43#134311yescharacteristic
123C2×C43#134911yescharacteristic
124D43—162no—
125C22×D8—431no—
126C2×#121—861no—
127C2×#102—861no—
128#407—861no—
129C2×C22⋊C8C2×D4311yescharacteristic
130C22⋊C16—21no—
131#340—431no—
132C43#708411yescharacteristic, complemented, Sylow
133C22×D4—861no—
134C22×D4—1721no—
135C23×C4D17211yescharacteristic
136C2×D8—1721no—
137C2×D8—1722no—
138C2×M16—1721no—
139C22×C8C4×D4311yescharacteristic
140C22×C8C22⋊D4311yescharacteristic
141#121—1722no—
142#121—1722no—
143C2×C4⋊C4—861no—
144C2×C22⋊C4—1721no—
145C2×C16—41no—
146#102—1722no—
147C22⋊C8—41no—
148C22⋊C8—862no—
149C22⋊C8—1721no—
150C24—1721no—
151C24#1062187311yescharacteristic
152C2×D4—862no—
153C2×D4—3442no—
154C2×D4—3442no—
155C2×D4—1721no—
156C2×D4—1721no—
157C2×D4—1721no—
158C2×D4—1724no—
159C2×D4—1721no—
160C2×D4—1721no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—1721no—
166C22×C4D34411yescharacteristic
167C22×C4(C2×D43)⋊C411yescharacteristic
168D8—1722no—
169D8—1722no—
170M16—3441no—
171M16—3441no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—1722no—
177C4⋊C4—862no—
178C4⋊C4—1721no—
179C22⋊C4—1724no—
180C16—81no—
181C23—21no—
182C23—21no—
183C23—21no—
184C23—41no—
185C23—41no—
186C23—3441no—
187C23—3441no—
188C23—3441no—
189C23—3441no—
190C23—3441no—
191C23—3441no—
192C23—1722no—
193C23#1306324711yescharacteristic
194D4—3441no—
195D4—3448no—
196D4—3441no—
197D4—1722no—
198D4—1722no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—81no—
206C2×C4—3441no—
207C2×C4—3441no—
208C2×C4—1722no—
209C2×C4#1306323911yescharacteristic
210C2×C4#1306325111yescharacteristic
211C8—41no—
212C8—41no—
213C8—3442no—
214C22—21no—
215C22—21no—
216C22—42no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—3442no—
222C22—3442no—
223C22—3442no—
224C22—6881no—
225C22—6881no—
226C22—6881no—
227C22—6881no—
228C22#1458263411yescharacteristic
229C22#1458270711yescharacteristic
230C22#1458271311yescharacteristic
231C4—21no—
232C4—41no—
233C4—3442no—
234C4#1458268711yescharacteristic
235C4#1458269111yescharacteristic
236C2—21no—
237C2—21no—
238C2—81no—
239C2—6882no—
240C2#1913258711yescharacteristic
241C2#1913259311yescharacteristic
242C2#1913261111yescharacteristic
subgroupG/H
centerC22#14582634
commutatorC22×C8×C43C2×C4
FrattiniC2×C22⋊C8C2×D43
FittingC43×#1314C2
socleC22×C43#327
prime radical#19135593C2
cosocleC2×C22⋊C8×C43C22
hypercenter#1314D43
hypocenterC43#7084
LCSG ▷ C22×C8×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #19132472C2semidirect
3. C43×#1314C2semidirect
116. #1314D43semidirect
132. C43#7084semidirect

Maximal subgroups

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

subgroupindex
#191355932
#191324722
C43×#13142
#708443