Finite Group Databasebeta

← #25010841

Subgroups — #25010841

Order 11008.

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

normal subgroups only

This group has 214 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#19136847C211yesmaximal, characteristic, complemented
2#19136677C211yesmaximal, characteristic
3#19136673C211yesmaximal, characteristic
4#19136431C211yesmaximal, characteristic
5#19132670C211yesmaximal, characteristic, complemented
6#19132633C211yesmaximal, characteristic, complemented
7C43×#1358C211yesmaximal, characteristic, complemented
8#14583342—21no—
9#14583340—21no—
10C2×#13063271—21no—
11C2×#13063271—21no—
12#14583317—21no—
13#14583279C2211yescharacteristic
14#14583017C2211yescharacteristic
15#14582720C2211yescharacteristic
16#14582716—21no—
17#14582715—21no—
18#14582684—21no—
19C4×C43⋊C16C2211yescharacteristic
20C43×#494C2211yescharacteristic
21C43×#364C2211yescharacteristic
22C43×#364C2211yescharacteristic
23#13063347D411yescharacteristic
24C2×Dic172—21no—
25C2×Dic172—21no—
26#13063331—21no—
27#13063325—21no—
28Dic344—41no—
29#13063271—42no—
30#13063271—41no—
31#13063271—41no—
32#13063271—41no—
33#13063270—41no—
34#13063268—41no—
35#13063265—21no—
36#13063264—41no—
37C2×C43⋊C16D411yescharacteristic
38C2×C43⋊C16D411yescharacteristic
39C16×D43—41no—
40#13063261D411yescharacteristic
41#13063253—21no—
42C2×Q16×C43—21no—
43C2×Q16×C43—21no—
44C4⋊Q8×C43—21no—
45M32×C43—21no—
46M32×C43—21no—
47C4×C8×C43C2311yescharacteristic
48C2×Q8×C43—41no—
49#10621898—21no—
50C2×Dic86—41no—
51Q16×C43—41no—
52Q16×C43—41no—
53Q16×C43—41no—
54Q16×C43—41no—
55C2×C8×C43C2×D411yescharacteristic
56C2×C8×C43C2×D411yescharacteristic
57C4⋊C4×C43—81no—
58C42×C43#4111yescharacteristic
59C4⋊Dic43—81no—
60#10621877—21no—
61Dic172—41no—
62Dic172—41no—
63Dic172—41no—
64Dic172—41no—
65Dic172D811yescharacteristic
66D344D811yescharacteristic
67#10621873—21no—
68#10621872—41no—
69C8×D43—41no—
70C16×C43—41no—
71C16×C43—41no—
72C43⋊C16—21no—
73C43⋊C16—41no—
74C43⋊C16D811yescharacteristic
75C43⋊C16D811yescharacteristic
76Q8×C43—81no—
77Q8×C43—81no—
78C2×C4×C43—21no—
79C2×C4×C43—81no—
80C2×C4×C43#12111yescharacteristic
81C22⋊D43—41no—
82C2×Dic43—81no—
83D172—21no—
84C4×D43—41no—
85Dic86—21no—
86Dic86—81no—
87Dic86—81no—
88C8×C43C2×D811yescharacteristic
89C8×C43C2×D811yescharacteristic
90C8×C43#13511yescharacteristic
91C8×C43AGL(1,ℤ/8)11yescharacteristic
92C43⋊C8—41no—
93#12437—431nomaximal, Sylow
94C22×C43#47211yescharacteristic
95C2×D43—41no—
96C4×C43—22no—
97C4×C43—161no—
98C4×C43#45911yescharacteristic
99C4×C43#46611yescharacteristic
100Dic43—41no—
101Dic43—161no—
102#2247—431no—
103#2214—431no—
104#2214—431no—
105#2170—431no—
106#1373—431no—
107#1358—431no—
108#1358D4311yescharacteristic, complemented
109C2×C43—21no—
110C2×C43#166711yescharacteristic
111D43—81no—
112#510—861no—
113#510—861no—
114C2×Q32—861no—
115C2×Q32—861no—
116#504—861no—
117#494—431no—
118#494C2×D4311yescharacteristic
119#443—431no—
120#364—431no—
121#364C2×D4311yescharacteristic
122#364C2×D4311yescharacteristic
123#362—861no—
124#362—861no—
125#350—861no—
126C4×C16—431no—
127C43#1243711yescharacteristic, complemented, Sylow
128#135—431no—
129C2×Q16—21no—
130C2×Q16—21no—
131C2×Q16—861no—
132C2×Q16—861no—
133#131—861no—
134C4⋊Q8—21no—
135C4⋊Q8—861no—
136Q32—1721no—
137Q32—1721no—
138Q32—1721no—
139Q32—1722no—
140Q32—1721no—
141SD32—1721no—
142SD32—1721no—
143M32—21no—
144M32—21no—
145M32—861no—
146M32—1721no—
147C2×C16—431no—
148C2×C16—431no—
149C2×C16—1721no—
150#108—431no—
151#104—861no—
152C4×C8C22×D4311yescharacteristic
153#41—861no—
154C2×Q8—41no—
155C2×Q8—1721no—
156Q16—41no—
157Q16—41no—
158Q16—41no—
159Q16—41no—
160Q16—431no—
161Q16—1721no—
162Q16—1721no—
163Q16—1721no—
164Q16—1721no—
165SD16—861no—
166D8—431no—
167M16—861no—
168M16—1721no—
169C2×C8—1721no—
170C2×C8D4×D4311yescharacteristic
171C2×C8D4×D4311yescharacteristic
172C4⋊C4—81no—
173C4⋊C4—3441no—
174C42#1062189811yescharacteristic
175C16—41no—
176C16—41no—
177C16—431no—
178C16—431no—
179C16—861no—
180C16—1721no—
181Q8—81no—
182Q8—81no—
183Q8—861no—
184Q8—3441no—
185Q8—3441no—
186D4—861no—
187D4—1721no—
188C2×C4—21no—
189C2×C4—81no—
190C2×C4—3441no—
191C2×C4—1721no—
192C2×C4#1306329811yescharacteristic
193C8—1721no—
194C8D8×D4311yescharacteristic
195C8D8×D4311yescharacteristic
196C8#1306334611yescharacteristic
197C8#1306335211yescharacteristic
198C22—1721no—
199C22#1458316811yescharacteristic
200C4—22no—
201C4—161no—
202C4—1721no—
203C4—6881no—
204C4#1458309311yescharacteristic
205C4#1458313411yescharacteristic
206C2—21no—
207C2—3441no—
208C2#1913394911yescharacteristic
subgroupG/H
centerC2#19133949
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1358C2
socleC2×C43#1667
prime radical#13063347D4
hypercenter#1358D43
hypocenterC43#12437
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1358

Complements

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

NH ≅ G/Ntype
1. #19136847C2semidirect
5. #19132670C2semidirect
6. #19132633C2semidirect
7. C43×#1358C2semidirect
108. #1358D43semidirect
127. C43#12437semidirect

Maximal subgroups

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

subgroupindex
#191368472
#191366772
#191366732
#191364312
#191326702
#191326332
C43×#13582
#1243743