Finite Group Databasebeta

← #25017294

Subgroups — #25017294

Order 11008.

284 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 55 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#19147732C211yesmaximal, characteristic
2#19136913C211yesmaximal, characteristic, complemented
3#19136717C211yesmaximal, characteristic, complemented
4#19132785C211yesmaximal, characteristic, complemented
5#19132780C211yesmaximal, characteristic, complemented
6#19132736C211yesmaximal, characteristic, complemented
7C2×C43×SD64C211yesmaximal, characteristic, complemented
8#14583700—21no—
9#14583335—21no—
10#14583333—22no—
11#14583331C2211yescharacteristic
12#14583328—21no—
13D16×D43—21no—
14#14583315C2211yescharacteristic
15#14583171—21no—
16#14582739—21no—
17#14582736—21no—
18#14582733C2211yescharacteristic, complemented
19#14582729C2211yescharacteristic, complemented
20#14582715—21no—
21C2×Q32×C43C2211yescharacteristic, complemented
22C2×D16×C43C2211yescharacteristic
23C43×SD64—22no—
24C2×C32×C43C2211yescharacteristic, complemented
25#13063370—41no—
26#13063356—41no—
27#13063351—41no—
28#13063349—42no—
29#13063347—21no—
30#13063344—22no—
31D8×D43—22no—
32#13063331D411yescharacteristic
33Dic344D411yescharacteristic
34#13063270—21no—
35#13063269—22no—
36D688D411yescharacteristic
37#13063266—22no—
38#13063265D411yescharacteristic
39#13063264—21no—
40C16×D43—21no—
41#13063261—21no—
42#13063244—41no—
43C43⋊C32—21no—
44C2×Q16×C43—21no—
45C2×D8×C43—21no—
46Q32×C43—21no—
47Q32×C43—21no—
48D16×C43—21no—
49D16×C43D412yes—
50C2×C16×C43C2311yescharacteristic
51C32×C43—21no—
52C2×Q8×C43—41no—
53C2×D4×C43—41no—
54C2×C22⋊D43—82no—
55#10621900—42no—
56#10621900—81no—
57D4×D43—42no—
58D4×D43—81no—
59#10621898—41no—
60#10621898D811yescharacteristic
61Q16×C43—41no—
62Q16×C43—41no—
63D8×C43—22no—
64D8×C43—41no—
65C2×C8×C43C2×D411yescharacteristic
66#10621885—81no—
67#10621884—81no—
68#10621883—42no—
69#10621882—42no—
70#10621877—41no—
71#10621877D811yescharacteristic
72Dic172—21no—
73D344—21no—
74#10621873—41no—
75#10621872—21no—
76C8×D43—21no—
77C16×C43C2×D411yescharacteristic
78C16×C43C2×D411yescharacteristic
79C43⋊C16—21no—
80C23×C43—81no—
81C22×D43—82no—
82Q8×C43—81no—
83Q8×C43—81no—
84D4×C43—42no—
85D4×C43—81no—
86C2×C4×C43—81no—
87C2×C4×C43C2×D811yescharacteristic
88C22⋊D43—21no—
89C22⋊D43—82no—
90C22⋊D43—82no—
91C22⋊D43—81no—
92C2×Dic43—82no—
93D172—41no—
94D172D1611yescharacteristic
95C4×D43—21no—
96C4×D43—81no—
97Dic86—41no—
98Dic86D1611yescharacteristic
99C8×C43#12011yescharacteristic
100C8×C43AGL(1,ℤ/8)11yescharacteristic
101C43⋊C8—21no—
102C43⋊C8—81no—
103#13671—431nomaximal, Sylow
104C22×C43—82no—
105C22×C43—321no—
106C22×C43#50911yescharacteristic
107C2×D43—21no—
108C2×D43—81no—
109C2×D43—322no—
110C4×C43—161no—
111C4×C43#44711yescharacteristic
112C4×C43C2×D1611yescharacteristic
113Dic43—21no—
114Dic43—81no—
115#3415—431no—
116#2264—431no—
117C2×SD64D4311yescharacteristic, complemented
118#2222—431no—
119#1419—431no—
120#1417—431no—
121#1401—431no—
122C2×C43—21no—
123C2×C43—162no—
124C2×C43#218411yescharacteristic
125D43—41no—
126D43—161no—
127#576—861no—
128#509—861no—
129#509—862no—
130#508—431no—
131#508—861no—
132C2×Q32C2×D4311yescharacteristic, complemented
133C2×D16—861no—
134C2×D16C2×D4311yescharacteristic
135#504—431no—
136#473—861no—
137Q64—861no—
138SD64—22no—
139SD64—861no—
140M64—431no—
141C2×C32C2×D4311yescharacteristic, complemented
142#368—431no—
143#362—861no—
144C43#1367111yescharacteristic, complemented, Sylow
145H(5,𝔽2)—1721no—
146#137—1721no—
147AGL(1,ℤ/8)—1721no—
148AGL(1,ℤ/8)—1722no—
149#135—862no—
150#135—861no—
151C2×Q16—21no—
152C2×D8—21no—
153C2×D8—862no—
154#131—431no—
155Q32—21no—
156Q32—21no—
157Q32—431no—
158SD32—862no—
159SD32—861no—
160D16—21no—
161D16—431no—
162D16—862no—
163D16C22⋊D4312yes—
164M32—431no—
165M32—861no—
166C2×C16—861no—
167C2×C16C22×D4311yescharacteristic
168#108—861no—
169#101—1721no—
170C32—21no—
171C32—861no—
172#41—431no—
173#41—3441no—
174#41—1722no—
175#41—1721no—
176C2×Q8—41no—
177C2×D4—41no—
178C2×D4—3441no—
179C2×D4—3442no—
180C2×D4—1722no—
181Q16—41no—
182Q16—41no—
183Q16—861no—
184Q16—3441no—
185SD16—3441no—
186SD16—1722no—
187SD16—1721no—
188D8—22no—
189D8—41no—
190D8—861no—
191D8—1722no—
192M16—431no—
193M16—861no—
194M16—1721no—
195C2×C8—861no—
196C2×C8D4×D4311yescharacteristic
197C16—861no—
198C16D4×D4311yescharacteristic
199C16C2×C22⋊D4311yescharacteristic
200C23—81no—
201C23—3442no—
202Q8—81no—
203Q8—81no—
204Q8—431no—
205Q8—1721no—
206D4—42no—
207D4—81no—
208D4—431no—
209D4—861no—
210D4—3442no—
211D4—3442no—
212D4—3441no—
213D4—1721no—
214C2×C4—81no—
215C2×C4—861no—
216C2×C4—3442no—
217C2×C4—3441no—
218C2×C4D8×D4311yescharacteristic
219C8—861no—
220C8—3441no—
221C8#1306329311yescharacteristic
222C8#1306334911yescharacteristic
223C22—82no—
224C22—321no—
225C22—861no—
226C22—3441no—
227C22—13762no—
228C22#1458333311yescharacteristic
229C4—161no—
230C4—861no—
231C4—3441no—
232C4#1458303111yescharacteristic
233C4D16×D4311yescharacteristic
234C2—21no—
235C2—162no—
236C2—1721no—
237C2—6881no—
238C2#1913650511yescharacteristic
subgroupG/H
centerC2#19136505
commutator, cosocleC2×C16×C43C23
FrattiniC2×C16C22×D43
FittingC2×C43×SD64C2
socleC2×C43#2184
prime radical#19147732C2
hypercenterC2×SD64D43
hypocenterC43#13671
LCSG ▷ C2×C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
2. #19136913C2semidirect
3. #19136717C2semidirect
4. #19132785C2semidirect
5. #19132780C2semidirect
6. #19132736C2semidirect
7. C2×C43×SD64C2semidirect
18. #14582733C22semidirect
19. #14582729C22semidirect
21. C2×Q32×C43C22semidirect
24. C2×C32×C43C22semidirect
117. C2×SD64D43semidirect
132. C2×Q32C2×D43semidirect
141. C2×C32C2×D43semidirect
144. C43#13671semidirect

Maximal subgroups

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

subgroupindex
#191477322
#191369132
#191367172
#191327852
#191327802
#191327362
C2×C43×SD642
#1367143