Finite Group Databasebeta

← #24999861

Subgroups — #24999861

Order 11008.

526 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 73 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#19142859C211yesmaximal, characteristic
2#19134667C212yesmaximal
3#19134667C211yesmaximal, characteristic
4C43⋊#1304C212yesmaximal
5C43×#1304C211yesmaximal, characteristic
6C22×C22⋊Dic43C2211yescharacteristic
7#14582835—22no—
8#14582822—24no—
9#14582755C2211yescharacteristic
10#14582755C2212yes—
11#14582665—24no—
12#14582665—22no—
13C43×#379C2212yes—
14C43×#379C2211yescharacteristic
15C23×Dic43Q812yes—
16C2×C4⋊Dic43—22no—
17C2×Dic43⋊C4—24no—
18C2×C22⋊Dic43—21no—
19C2×C22⋊Dic43—22no—
20C2×C22⋊Dic43—22no—
21C2×C22⋊Dic43—21no—
22C2×C22⋊Dic43—21no—
23C2×C22⋊Dic43—22no—
24C2×C22⋊Dic43—22no—
25C2×C22⋊Dic43—22no—
26C2×C22⋊Dic43D414yes—
27C43⋊#95—22no—
28C25×C43C2311yescharacteristic
29C2×C22⋊C4×C43—22no—
30C2×C22⋊C4×C43—22no—
31C2×C22⋊C4×C43—22no—
32C2×C22⋊C4×C43—22no—
33C2×C22⋊C4×C43D412yes—
34C24×C43—42no—
35C24×C43—82no—
36C24×C43C2×D411yescharacteristic
37C24×C43C2×D412yes—
38C24×C43C2×Q811yescharacteristic
39C24×C43#4112yes—
40C24×C43#4111yescharacteristic
41C22×C4×C43—22no—
42C22×C4×C43—42no—
43C22×Dic43—24no—
44C22×Dic43—22no—
45C22×Dic43—22no—
46C22×Dic43—22no—
47C22×Dic43—41no—
48C22×Dic43—82no—
49C22⋊C4×C43—42no—
50C22⋊C4×C43—44no—
51C22⋊C4×C43—82no—
52C22⋊C4×C43—82no—
53C22⋊C4×C43—82no—
54C22⋊Dic43—44no—
55C22⋊Dic43—42no—
56C22⋊Dic43—41no—
57C22⋊Dic43—42no—
58C22⋊Dic43—41no—
59C22⋊Dic43—82no—
60C22⋊Dic43—82no—
61C22⋊Dic43—82no—
62C4⋊Dic43—82no—
63Dic43⋊C4—84no—
64C23×C43—22no—
65C23×C43—24no—
66C23×C43—42no—
67C23×C43—41no—
68C23×C43—42no—
69C23×C43—42no—
70C23×C43—42no—
71C23×C43—42no—
72C23×C43—42no—
73C23×C43—42no—
74C23×C43—42no—
75C23×C43—41no—
76C23×C43—88no—
77C23×C43#12011yescharacteristic
78C23×C43C22⋊Q812yes—
79C23×C43C22⋊Q811yescharacteristic
80C23×C43#12412yes—
81C23×C43#12411yescharacteristic
82C2×C4×C43—44no—
83C2×C4×C43—42no—
84C2×C4×C43—82no—
85C2×C4×C43—82no—
86C2×C4×C43—82no—
87C2×Dic43—44no—
88C2×Dic43—44no—
89C2×Dic43—42no—
90C2×Dic43—44no—
91C2×Dic43—82no—
92C2×Dic43—82no—
93C2×Dic43—82no—
94C2×Dic43—81no—
95C2×Dic43—82no—
96#10393—431nomaximal, Sylow
97C22×C43—22no—
98C22×C43—22no—
99C22×C43—21no—
100C22×C43—21no—
101C22×C43—22no—
102C22×C43—22no—
103C22×C43—22no—
104C22×C43—22no—
105C22×C43—22no—
106C22×C43—22no—
107C22×C43—22no—
108C22×C43—44no—
109C22×C43—82no—
110C22×C43—84no—
111C22×C43—84no—
112C22×C43—82no—
113C22×C43#39311yescharacteristic
114C22×C43#45812yes—
115C4×C43—82no—
116C4×C43—162no—
117Dic43—84no—
118Dic43—82no—
119Dic43—161no—
120#2842—431no—
121#1819—432no—
122#1819—431no—
123#1304—432no—
124#1304D4311yescharacteristic
125C2×C43—22no—
126C2×C43—41no—
127C2×C43—42no—
128C2×C43—42no—
129C2×C43—41no—
130C2×C43#203011yescharacteristic
131C2×C43#203212yes—
132C22×C22⋊C4—431no—
133#399—862no—
134#396—864no—
135#379—432no—
136#379—431no—
137#379C2×D4312yes—
138#379C2×D4311yescharacteristic
139#342—864no—
140#342—862no—
141C43#1039311yescharacteristic, complemented, Sylow
142C25C22×D4311yescharacteristic
143C23×C4—432no—
144C2×C4⋊C4—864no—
145C2×C4⋊C4—862no—
146C2×C22⋊C4—22no—
147C2×C22⋊C4—22no—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4—434no—
151C2×C22⋊C4—862no—
152C2×C22⋊C4—862no—
153C2×C22⋊C4—862no—
154C2×C22⋊C4—861no—
155C2×C22⋊C4—862no—
156C2×C22⋊C4—862no—
157C2×C22⋊C4—861no—
158C2×C22⋊C4—861no—
159C2×C22⋊C4D17212yes—
160#95—862no—
161C24—42no—
162C24—82no—
163C24C2×D17211yescharacteristic
164C24#1062189812yes—
165C24D4×D4312yes—
166C24#1062190011yescharacteristic
167C24Q8×D4311yescharacteristic
168C22×C4—22no—
169C22×C4—42no—
170C22×C4—862no—
171C22×C4—862no—
172C22×C4—862no—
173C22×C4—864no—
174C22×C4—3442no—
175C22×C4—1721no—
176C4⋊C4—3444no—
177C4⋊C4—3442no—
178C22⋊C4—42no—
179C22⋊C4—44no—
180C22⋊C4—82no—
181C22⋊C4—82no—
182C22⋊C4—82no—
183C22⋊C4—3442no—
184C22⋊C4—3442no—
185C22⋊C4—3442no—
186C22⋊C4—1722no—
187C22⋊C4—1721no—
188C22⋊C4—1722no—
189C22⋊C4—1721no—
190C22⋊C4—1724no—
191C23—22no—
192C23—24no—
193C23—42no—
194C23—41no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—42no—
201C23—42no—
202C23—41no—
203C23—88no—
204C23#1306329511yescharacteristic
205C23#1306330312yes—
206C23#1306330511yescharacteristic
207C23#1306331112yes—
208C23#1306331311yescharacteristic
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—82no—
213C2×C4—82no—
214C2×C4—3442no—
215C2×C4—3442no—
216C2×C4—3442no—
217C2×C4—3442no—
218C2×C4—3441no—
219C2×C4—1724no—
220C2×C4—1724no—
221C2×C4—1722no—
222C2×C4—1724no—
223C22—22no—
224C22—22no—
225C22—21no—
226C22—22no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—44no—
235C22—84no—
236C22—82no—
237C22—82no—
238C22—84no—
239C22#1458281211yescharacteristic
240C22#1458309012yes—
241C4—82no—
242C4—162no—
243C4—3444no—
244C4—3442no—
245C4—6881no—
246C2—22no—
247C2—42no—
248C2—41no—
249C2—42no—
250C2—41no—
251C2#1913576311yescharacteristic
252C2#1913577312yes—
subgroupG/H
centerC22#14582812
commutator, prime radical, cosocleC25×C43C23
FrattiniC25C22×D43
FittingC43×#1304C2
socleC22×C43#393
hypercenter#1304D43
hypocenterC43#10393
LCSG ▷ C25×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #1304

Complements

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

NH ≅ G/Ntype
141. C43#10393semidirect

Maximal subgroups

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

subgroupindex
#191428592
#191346672
C43⋊#13042
C43×#13042
#1039343