Finite Group Databasebeta

← #25009859

Subgroups — #25009859

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#19136775C212yesmaximal, complemented
3#19132603C212yesmaximal, complemented
4#19132535C211yesmaximal, characteristic, complemented
5C43×#2086C211yesmaximal, characteristic, complemented
6#14583449—21no—
7#14583180—22no—
8#14583135—21no—
9#14583135C2212yes—
10#14583095—22no—
11#14582724—22no—
12#14582699—22no—
13C22⋊(C43⋊C16)C2212yes—
14C2×#107×C43C2211yescharacteristic
15C2×C4⋊C8×C43C2211yescharacteristic
16C43×#389—21no—
17C43×#340—21no—
18C43×#340C2211yescharacteristic
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×C43⋊C16—22no—
30#13063259—21no—
31#13063259D412yes—
32#13063247—22no—
33#13063247—22no—
34C22×C8×C43D411yescharacteristic
35C22×C8×C43C2311yescharacteristic
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—41no—
39C2×C42×C43D411yescharacteristic
40#107×C43—22no—
41C4⋊C8×C43—22no—
42#95×C43—41no—
43C22×C4×C43—41no—
44C22×C4×C43—41no—
45C22×C4×C43D811yescharacteristic
46C22×C4×C43D811yescharacteristic
47C22×C4×C43C2×D411yescharacteristic
48C2×C22⋊D43—42no—
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—
60C4⋊C4×C43—22no—
61C4⋊C4×C43—41no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—41no—
64C4⋊C4×C43—82no—
65C42×C43—21no—
66C42×C43—21no—
67(C2×D43)⋊C4—42no—
68(C2×D43)⋊C4—42no—
69C4⋊Dic43—22no—
70C4⋊Dic43—41no—
71D344—42no—
72D344—81no—
73C43⋊C16—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×C43—42no—
83C2×C4×C43—81no—
84C2×C4×C43—81no—
85C2×C4×C43—81no—
86C2×C4×C43—81no—
87C2×C4×C43—81no—
88C2×C4×C43D1612yes—
89C2×C4×C43#12011yescharacteristic
90C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
91C22⋊D43—82no—
92C22⋊D43—82no—
93C2×Dic43—42no—
94D172—42no—
95D172—42no—
96D172—82no—
97D172—82no—
98C4×D43—84no—
99Dic86—82no—
100C8×C43—22no—
101C8×C43—41no—
102#12288—431nomaximal, Sylow
103C22×C43—21no—
104C22×C43—21no—
105C22×C43#44711yescharacteristic
106C22×C43C2×D1611yescharacteristic
107C22×C43#50911yescharacteristic
108C2×D43—82no—
109C2×D43—82no—
110C2×D43—82no—
111C4×C43—21no—
112C4×C43—22no—
113C4×C43—41no—
114C4×C43—82no—
115C4×C43—161no—
116C4×C43#45611yescharacteristic
117C4×C43#45811yescharacteristic
118Dic43—82no—
119#3245—431no—
120#2232—432no—
121#2086D4311yescharacteristic, complemented
122#1347—432no—
123#1322—431no—
124C2×C43—21no—
125C2×C43—21no—
126C2×C43#161011yescharacteristic
127C2×C43#218411yescharacteristic
128C2×C43#219111yescharacteristic
129D43—162no—
130#532—861no—
131#474—862no—
132#466—432no—
133#466—861no—
134#459—862no—
135C2×#107C2×D4311yescharacteristic
136C2×C4⋊C8C2×D4311yescharacteristic
137#389—21no—
138#366—862no—
139#357—862no—
140C22⋊C16—432no—
141#340—21no—
142#340C2×D4311yescharacteristic
143C43#1228811yescharacteristic, complemented, Sylow
144C2×#41—1721no—
145C2×D8—432no—
146C2×D8—861no—
147C22×C8C22⋊D4311yescharacteristic
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—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—41no—
159C2×C42C22⋊D4311yescharacteristic
160C2×C16—862no—
161#107—22no—
162#107—432no—
163#107—861no—
164C4⋊C8—22no—
165#102—862no—
166#102—862no—
167#95—41no—
168#41—3442no—
169#41—3442no—
170C2×Q8—1721no—
171C2×D4—862no—
172C2×D4—1721no—
173C2×D4—1721no—
174C2×D4—1722no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—1722no—
178C22×C4#1062188211yescharacteristic
179C22×C4#1062188211yescharacteristic
180C22×C4C2×C22⋊D4311yescharacteristic
181D8—3441no—
182D8—1722no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8D4×D4312yes—
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—82no—
192C4⋊C4—862no—
193C4⋊C4—1721no—
194C22⋊C4—1722no—
195C22⋊C4—1722no—
196C42—21no—
197C42—21no—
198C16—1722no—
199C23—1722no—
200C23C2×#1062188211yescharacteristic
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—42no—
215C2×C4—81no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—3444no—
221C2×C4—1722no—
222C2×C4#1306326612yes—
223C2×C4#1306329311yescharacteristic
224C2×C4#1306335011yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—3442no—
230C22—3442no—
231C22—3442no—
232C22#1458303211yescharacteristic
233C22C2×#1306326611yescharacteristic
234C22#1458333411yescharacteristic
235C4—21no—
236C4—22no—
237C4—41no—
238C4—82no—
239C4—161no—
240C4—3442no—
241C4#1458308111yescharacteristic
242C4#1458308811yescharacteristic
243C2—21no—
244C2—21no—
245C2—6882no—
246C2#1913359711yescharacteristic
247C2#1913650611yescharacteristic
248C2#1913654511yescharacteristic
subgroupG/H
centerC22#14583032
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#2086C2
socleC22×C43#447
prime radical#19145905C2
hypercenter#2086D43
hypocenterC43#12288
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2086

Complements

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

NH ≅ G/Ntype
2. #19136775C2semidirect
3. #19132603C2semidirect
4. #19132535C2semidirect
5. C43×#2086C2semidirect
121. #2086D43semidirect
143. C43#12288semidirect

Maximal subgroups

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

subgroupindex
#191459052
#191367752
#191326032
#191325352
C43×#20862
#1228843