Finite Group Databasebeta

← #25017287

Subgroups — #25017287

Order 11008.

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

normal subgroups only

This group has 278 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#19147744C211yesmaximal, characteristic, complemented
2#19136908C211yesmaximal, characteristic, complemented
3#19136712C211yesmaximal, characteristic, complemented
4#19132788C211yesmaximal, characteristic, complemented
5#19132780C211yesmaximal, characteristic, complemented
6#19132736C211yesmaximal, characteristic, complemented
7C2×C43×SD64C211yesmaximal, characteristic, complemented
8#14583712—21no—
9#14583341—22no—
10#14583340—21no—
11#14583332—21no—
12#14583331C2211yescharacteristic
13Q32×D43—21no—
14#14583315C2211yescharacteristic
15#14583166—21no—
16#14582737—21no—
17#14582734—21no—
18#14582733C2211yescharacteristic
19#14582729C2211yescharacteristic
20#14582712—21no—
21C2×Q32×C43C2211yescharacteristic
22C2×D16×C43C2211yescharacteristic
23C43×SD64—22no—
24C2×C32×C43C2211yescharacteristic
25#13063373—41no—
26#13063357—42no—
27#13063356—41no—
28#13063351—41no—
29#13063348—22no—
30#13063347—21no—
31Q16×D43—22no—
32#13063331D411yescharacteristic
33Dic344D411yescharacteristic
34#13063271—22no—
35#13063270—21no—
36#13063268—22no—
37D688D411yescharacteristic
38#13063265D411yescharacteristic
39#13063264—21no—
40C16×D43—21no—
41#13063261—21no—
42#13063242—41no—
43C43⋊C32—21no—
44C2×Q16×C43—21no—
45C2×D8×C43—21no—
46Q32×C43—21no—
47Q32×C43D412yes—
48D16×C43—21no—
49D16×C43—21no—
50C2×C16×C43C2311yescharacteristic
51C32×C43—21no—
52C2×Q8×C43—41no—
53C2×D4×C43—41no—
54#10621902—42no—
55#10621902—81no—
56Q8×D43—42no—
57Q8×D43—81no—
58#10621898—41no—
59#10621898—82no—
60#10621898D811yescharacteristic
61Q16×C43—22no—
62Q16×C43—41no—
63D8×C43—41no—
64D8×C43—41no—
65C2×C8×C43C2×D411yescharacteristic
66#10621885—42no—
67#10621884—42no—
68#10621883—81no—
69#10621882—81no—
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—
81Q8×C43—42no—
82Q8×C43—81no—
83D4×C43—81no—
84D4×C43—81no—
85C2×C4×C43—81no—
86C2×C4×C43C2×D811yescharacteristic
87C22⋊D43—21no—
88C22⋊D43—81no—
89D172—41no—
90D172—82no—
91D172D1611yescharacteristic
92C4×D43—21no—
93C4×D43—82no—
94C4×D43—82no—
95C4×D43—81no—
96Dic86—41no—
97Dic86—82no—
98Dic86D1611yescharacteristic
99C8×C43#12011yescharacteristic
100C8×C43AGL(1,ℤ/8)11yescharacteristic
101C43⋊C8—21no—
102C43⋊C8—81no—
103#13670—431nomaximal, Sylow
104C22×C43—161no—
105C22×C43—321no—
106C22×C43#50911yescharacteristic
107C2×D43—21no—
108C2×D43—81no—
109C4×C43—82no—
110C4×C43#44711yescharacteristic
111C4×C43C2×D1611yescharacteristic
112Dic43—21no—
113Dic43—81no—
114#3417—431no—
115#2263—431no—
116C2×SD64D4311yescharacteristic, complemented
117#2221—431no—
118#1420—431no—
119#1417—431no—
120#1401—431no—
121C2×C43—21no—
122C2×C43—321no—
123C2×C43#218411yescharacteristic
124D43—41no—
125D43—161no—
126#578—861no—
127#510—861no—
128#510—862no—
129#508—431no—
130#508—861no—
131C2×Q32—861no—
132C2×Q32C2×D4311yescharacteristic
133C2×D16C2×D4311yescharacteristic
134#504—431no—
135#472—861no—
136SD64—22no—
137SD64—861no—
138D32—861no—
139M64—431no—
140C2×C32C2×D4311yescharacteristic
141#368—431no—
142#361—861no—
143C43#1367011yescharacteristic, complemented, Sylow
1442−1+4—1721no—
145#137—1721no—
146#137—1722no—
147AGL(1,ℤ/8)—1721no—
148#135—862no—
149#135—861no—
150C2×Q16—21no—
151C2×Q16—862no—
152C2×D8—21no—
153#131—431no—
154Q32—21no—
155Q32—431no—
156Q32—862no—
157Q32C22⋊D4312yes—
158SD32—862no—
159SD32—861no—
160D16—21no—
161D16—21no—
162D16—431no—
163M32—431no—
164M32—861no—
165C2×C16—861no—
166C2×C16C22×D4311yescharacteristic
167#108—861no—
168#100—1721no—
169C32—21no—
170C32—861no—
171#41—431no—
172#41—3442no—
173#41—3441no—
174#41—1722no—
175#41—1721no—
176C2×Q8—41no—
177C2×Q8—3441no—
178C2×Q8—1722no—
179C2×D4—41no—
180Q16—22no—
181Q16—41no—
182Q16—861no—
183Q16—1722no—
184SD16—3441no—
185SD16—1722no—
186SD16—1721no—
187D8—41no—
188D8—41no—
189D8—861no—
190D8—3441no—
191M16—431no—
192M16—861no—
193M16—1721no—
194C2×C8—861no—
195C2×C8D4×D4311yescharacteristic
196C16—861no—
197C16D4×D4311yescharacteristic
198C16C2×C22⋊D4311yescharacteristic
199C23—81no—
200Q8—42no—
201Q8—81no—
202Q8—431no—
203Q8—3442no—
204Q8—1721no—
205D4—81no—
206D4—81no—
207D4—431no—
208D4—861no—
209D4—3442no—
210D4—3441no—
211D4—1721no—
212C2×C4—81no—
213C2×C4—861no—
214C2×C4—3442no—
215C2×C4—3442no—
216C2×C4—3441no—
217C2×C4D8×D4311yescharacteristic
218C8—861no—
219C8—3441no—
220C8#1306329311yescharacteristic
221C8#1306334911yescharacteristic
222C22—161no—
223C22—321no—
224C22—861no—
225C22—3441no—
226C22#1458333311yescharacteristic
227C4—82no—
228C4—861no—
229C4—3441no—
230C4#1458303111yescharacteristic
231C4D16×D4311yescharacteristic
232C2—21no—
233C2—321no—
234C2—1721no—
235C2—6881no—
236C2#1913650511yescharacteristic
subgroupG/H
centerC2#19136505
commutator, cosocleC2×C16×C43C23
FrattiniC2×C16C22×D43
FittingC2×C43×SD64C2
socleC2×C43#2184
hypercenterC2×SD64D43
hypocenterC43#13670
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
1. #19147744C2semidirect
2. #19136908C2semidirect
3. #19136712C2semidirect
4. #19132788C2semidirect
5. #19132780C2semidirect
6. #19132736C2semidirect
7. C2×C43×SD64C2semidirect
116. C2×SD64D43semidirect
143. C43#13670semidirect

Maximal subgroups

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

subgroupindex
#191477442
#191369082
#191367122
#191327882
#191327802
#191327362
C2×C43×SD642
#1367043