Finite Group Databasebeta

← #25009879

Subgroups — #25009879

Order 11008.

354 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 67 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#19145905C211yesmaximal, characteristic
2#19136781C212yesmaximal, complemented
3#19136088C211yesmaximal, characteristic, complemented
4#19132605C212yesmaximal, complemented
5C43×#1322C211yesmaximal, characteristic, complemented
6#14583449—21no—
7#14583180—22no—
8#14583135—21no—
9#14583135C2212yes—
10#14583095—22no—
11C2×#13063259C2211yescharacteristic
12#14582797—21no—
13#14582727—22no—
14#14582701—22no—
15#14582662—21no—
16#14582662C2211yescharacteristic
17C2×C4⋊C8×C43C2211yescharacteristic
18C43×C22⋊C16C2212yes—
19C2×#10621898—41no—
20C2×D344—21no—
21C2×D344D412yes—
22#13063325—21no—
23#13063322—21no—
24#13063313—41no—
25#13063299—22no—
26#13063299—41no—
27C4×D172—22no—
28C4×D172—41no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×Dic43⋊C4—41no—
32#13063259—21no—
33#13063259—22no—
34#13063259D412yes—
35#13063247—22no—
36#13063247—22no—
37C43⋊#95—41no—
38C22×C8×C43D411yescharacteristic
39C22×C8×C43C2311yescharacteristic
40C2×C42×C43D411yescharacteristic
41C2×C16×C43—22no—
42C4⋊C8×C43—22no—
43C22×C4×C43D811yescharacteristic
44C22×C4×C43D811yescharacteristic
45C22×C4×C43C2×D411yescharacteristic
46C2×C22⋊D43—42no—
47C22×Dic43—41no—
48C22×Dic43—41no—
49#10621898—82no—
50#10621898—82no—
51C2×D172—22no—
52C2×D172—41no—
53C2×D172—41no—
54C2×C4×D43—42no—
55C2×Dic86—41no—
56C2×C8×C43—21no—
57C2×C8×C43—41no—
58C2×C8×C43—41no—
59C2×C8×C43C2×D412yes—
60C42×C43—21no—
61C42×C43—21no—
62(C2×D43)⋊C4—42no—
63(C2×D43)⋊C4—42no—
64C4⋊Dic43—22no—
65C4⋊Dic43—22no—
66C4⋊Dic43—41no—
67C4⋊Dic43—41no—
68C4⋊Dic43—41no—
69C4⋊Dic43—41no—
70Dic43⋊C4—82no—
71D344—42no—
72D344—81no—
73C16×C43—42no—
74C23×C43C2×D811yescharacteristic
75C22×D43—42no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43—41no—
82C2×C4×C43SD3212yes—
83C2×C4×C43#12011yescharacteristic
84C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
85C22⋊D43—82no—
86C22⋊D43—82no—
87C2×Dic43—42no—
88C2×Dic43—42no—
89C2×Dic43—81no—
90C2×Dic43—81no—
91C2×Dic43—81no—
92C2×Dic43—81no—
93C2×Dic43—81no—
94D172—42no—
95D172—42no—
96D172—82no—
97D172—82no—
98C4×D43—84no—
99Dic86—82no—
100C8×C43—22no—
101C8×C43—41no—
102#12291—431nomaximal, Sylow
103C22×C43—21no—
104C22×C43—21no—
105C22×C43#44711yescharacteristic
106C22×C43C2×SD3211yescharacteristic
107C22×C43#50911yescharacteristic
108C2×D43—82no—
109C2×D43—82no—
110C2×D43—82no—
111C4×C43—21no—
112C4×C43—22no—
113C4×C43—41no—
114C4×C43#45611yescharacteristic
115C4×C43#45811yescharacteristic
116Dic43—82no—
117Dic43—82no—
118Dic43—161no—
119#3245—431no—
120#2233—432no—
121#2087—431no—
122#1347—432no—
123#1322D4311yescharacteristic, complemented
124C2×C43—21no—
125C2×C43—21no—
126C2×C43#161011yescharacteristic
127C2×C43#218711yescharacteristic
128C2×C43#219011yescharacteristic
129D43—162no—
130#532—861no—
131#474—862no—
132#466—432no—
133#466—861no—
134#459—862no—
135C2×#107—431no—
136C2×C4⋊C8C2×D4311yescharacteristic
137#389—861no—
138#367—862no—
139#357—862no—
140C22⋊C16C2×D4312yes—
141#340—431no—
142#340—861no—
143C43#1229111yescharacteristic, complemented, Sylow
144C2×#41—1721no—
145C2×D8—432no—
146C2×D8—861no—
147C22×C8D17211yescharacteristic
148C22×C8C22×D4311yescharacteristic
149C4⋊Q8—861no—
150#127—861no—
151#124—1721no—
152#121—862no—
153#121—1721no—
154C4×D4—862no—
155C4×D4—1721no—
156C2×C4⋊C4—861no—
157C2×C4⋊C4—861no—
158C2×C4⋊C4—1721no—
159C2×C42D17211yescharacteristic
160C2×C16—22no—
161#107—432no—
162#107—861no—
163#107—862no—
164C4⋊C8—22no—
165#102—862no—
166#102—862no—
167#95—1721no—
168#41—3442no—
169#41—3442no—
170C2×Q8—1721no—
171C2×D4—862no—
172C2×D4—1721no—
173C2×D4—1721no—
174C2×D4—1722no—
175C22×C4—1722no—
176C22×C4—1721no—
177C22×C4—1721no—
178C22×C4D34411yescharacteristic
179C22×C4D34411yescharacteristic
180C22×C4C2×D17211yescharacteristic
181D8—3441no—
182D8—1722no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8D4×D4312yes—
187C4⋊C4—862no—
188C4⋊C4—862no—
189C4⋊C4—3442no—
190C4⋊C4—1721no—
191C4⋊C4—1721no—
192C4⋊C4—1721no—
193C4⋊C4—1721no—
194C22⋊C4—1722no—
195C22⋊C4—1722no—
196C42—21no—
197C42—21no—
198C16—42no—
199C23—1722no—
200C23C2×D34411yescharacteristic
201Q8—3442no—
202D4—3442no—
203D4—3442no—
204D4—3442no—
205D4—3442no—
206D4—1722no—
207D4—1722no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—3444no—
215C2×C4—3441no—
216C2×C4—3441no—
217C2×C4—3441no—
218C2×C4—3441no—
219C2×C4—3441no—
220C2×C4—1722no—
221C2×C4—1722no—
222C2×C4#1306327012yes—
223C2×C4#1306329511yescharacteristic
224C2×C4#1306335311yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—3442no—
230C22—3442no—
231C22—3442no—
232C22#1458303511yescharacteristic
233C22C2×#1306327011yescharacteristic
234C22#1458333711yescharacteristic
235C4—22no—
236C4—21no—
237C4—41no—
238C4—3442no—
239C4—3442no—
240C4—6881no—
241C4#1458308411yescharacteristic
242C4#1458309011yescharacteristic
243C2—21no—
244C2—21no—
245C2—6882no—
246C2#1913360011yescharacteristic
247C2#1913652611yescharacteristic
248C2#1913654311yescharacteristic
subgroupG/H
centerC22#14583035
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1322C2
socleC22×C43#447
prime radical#19145905C2
hypercenter#1322D43
hypocenterC43#12291
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
2. #19136781C2semidirect
3. #19136088C2semidirect
4. #19132605C2semidirect
5. C43×#1322C2semidirect
123. #1322D43semidirect
143. C43#12291semidirect

Maximal subgroups

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

subgroupindex
#191459052
#191367812
#191360882
#191326052
C43×#13222
#1229143