Finite Group Databasebeta

← #25017301

Subgroups — #25017301

Order 11008.

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

normal subgroups only

This group has 274 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
2#19136913C211yesmaximal, characteristic, complemented
3#19136717C211yesmaximal, characteristic, complemented
4#19132788C211yesmaximal, characteristic, complemented
5#19132780C211yesmaximal, characteristic, complemented
6#19132736C211yesmaximal, characteristic, complemented
7C2×C43×Q64C211yesmaximal, characteristic, complemented
8#14583712—21no—
9#14583341—22no—
10#14583340—21no—
11#14583332—21no—
12#14583331C2211yescharacteristic
13Q32×D43—21no—
14#14583315C2211yescharacteristic
15#14583171—21no—
16#14582739—21no—
17#14582736—21no—
18#14582733C2211yescharacteristic
19#14582729C2211yescharacteristic
20#14582715—21no—
21C2×Q32×C43C2211yescharacteristic
22C2×Q32×C43C2211yescharacteristic
23C43×Q64—22no—
24C2×C32×C43C2211yescharacteristic
25#13063373—41no—
26#13063357—42no—
27#13063356—41no—
28#13063356—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#13063244—41no—
43C43⋊C32—21no—
44C2×Q16×C43—21no—
45C2×Q16×C43—21no—
46Q32×C43—21no—
47Q32×C43—21no—
48Q32×C43—21no—
49Q32×C43D412yes—
50C2×C16×C43C2311yescharacteristic
51C32×C43—21no—
52C2×Q8×C43—41no—
53C2×Q8×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—
63Q16×C43—41no—
64Q16×C43—41no—
65C2×C8×C43C2×D411yescharacteristic
66#10621885—42no—
67#10621885—81no—
68#10621884—42no—
69#10621884—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—
80Q8×C43—42no—
81Q8×C43—81no—
82Q8×C43—81no—
83Q8×C43—81no—
84C2×C4×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#13672—431nomaximal, Sylow
104C22×C43#50911yescharacteristic
105C2×D43—21no—
106C2×D43—81no—
107C4×C43—82no—
108C4×C43—161no—
109C4×C43#44711yescharacteristic
110C4×C43C2×D1611yescharacteristic
111Dic43—21no—
112Dic43—81no—
113#3417—431no—
114#2264—431no—
115C2×Q64D4311yescharacteristic, complemented
116#2222—431no—
117#1420—431no—
118#1417—431no—
119#1401—431no—
120C2×C43—21no—
121C2×C43#218411yescharacteristic
122D43—41no—
123D43—161no—
124#578—861no—
125#510—861no—
126#510—862no—
127#508—431no—
128#508—861no—
129C2×Q32—861no—
130C2×Q32C2×D4311yescharacteristic
131C2×Q32C2×D4311yescharacteristic
132#504—431no—
133#473—861no—
134Q64—22no—
135Q64—861no—
136SD64—861no—
137M64—431no—
138C2×C32C2×D4311yescharacteristic
139#368—431no—
140#362—861no—
141C43#1367211yescharacteristic, complemented, Sylow
1422−1+4—1721no—
143#137—1721no—
144#137—1722no—
145#137—1721no—
146#135—862no—
147#135—861no—
148C2×Q16—21no—
149C2×Q16—21no—
150C2×Q16—862no—
151#131—431no—
152Q32—21no—
153Q32—21no—
154Q32—21no—
155Q32—431no—
156Q32—862no—
157Q32C22⋊D4312yes—
158SD32—862no—
159SD32—861no—
160D16—431no—
161M32—431no—
162M32—861no—
163C2×C16—861no—
164C2×C16C22×D4311yescharacteristic
165#108—861no—
166#101—1721no—
167C32—21no—
168C32—861no—
169#41—431no—
170#41—3442no—
171#41—3441no—
172#41—1722no—
173#41—1721no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—3441no—
177C2×Q8—1722no—
178Q16—22no—
179Q16—41no—
180Q16—41no—
181Q16—41no—
182Q16—861no—
183Q16—3441no—
184Q16—1722no—
185SD16—3441no—
186SD16—1722no—
187SD16—1721no—
188D8—861no—
189M16—431no—
190M16—861no—
191M16—1721no—
192C2×C8—861no—
193C2×C8D4×D4311yescharacteristic
194C16—861no—
195C16D4×D4311yescharacteristic
196C16C2×C22⋊D4311yescharacteristic
197Q8—42no—
198Q8—81no—
199Q8—81no—
200Q8—81no—
201Q8—431no—
202Q8—3442no—
203Q8—1721no—
204D4—431no—
205D4—861no—
206D4—3442no—
207D4—3441no—
208D4—1721no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—861no—
212C2×C4—3442no—
213C2×C4—3442no—
214C2×C4—3441no—
215C2×C4D8×D4311yescharacteristic
216C8—861no—
217C8—3441no—
218C8#1306329311yescharacteristic
219C8#1306334911yescharacteristic
220C22—861no—
221C22—3441no—
222C22#1458333311yescharacteristic
223C4—82no—
224C4—161no—
225C4—861no—
226C4—3441no—
227C4#1458303111yescharacteristic
228C4D16×D4311yescharacteristic
229C2—21no—
230C2—1721no—
231C2—6881no—
232C2#1913650511yescharacteristic
subgroupG/H
centerC2#19136505
commutator, cosocleC2×C16×C43C23
FrattiniC2×C16C22×D43
FittingC2×C43×Q64C2
socleC2×C43#2184
prime radical#19147744C2
hypercenterC2×Q64D43
hypocenterC43#13672
LCSG ▷ C2×C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q64

Complements

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

NH ≅ G/Ntype
2. #19136913C2semidirect
3. #19136717C2semidirect
4. #19132788C2semidirect
5. #19132780C2semidirect
6. #19132736C2semidirect
7. C2×C43×Q64C2semidirect
115. C2×Q64D43semidirect
141. C43#13672semidirect

Maximal subgroups

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

subgroupindex
#191477442
#191369132
#191367172
#191327882
#191327802
#191327362
C2×C43×Q642
#1367243