Finite Group Databasebeta

← #25010850

Subgroups — #25010850

Order 11008.

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

normal subgroups only

This group has 224 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#19136852C211yesmaximal, characteristic, complemented
2#19136673C211yesmaximal, characteristic, complemented
3#19136672C211yesmaximal, characteristic
4#19136431C211yesmaximal, characteristic, complemented
5#19132670C211yesmaximal, characteristic, complemented
6#19132631C211yesmaximal, characteristic, complemented
7C43×#1358C211yesmaximal, characteristic, complemented
8#14583340—21no—
9#14583337—21no—
10C2×#13063268—21no—
11C2×#13063268—21no—
12#14583317—21no—
13#14583276C2211yescharacteristic
14#14583017C2211yescharacteristic
15#14582720C2211yescharacteristic
16#14582715—21no—
17#14582713—21no—
18#14582684—21no—
19C4×C43⋊C16C2211yescharacteristic
20C43×#494C2211yescharacteristic
21C43×#364C2211yescharacteristic
22C43×#364C2211yescharacteristic
23#13063347D411yescharacteristic
24C2×D344—21no—
25C2×D344—21no—
26#13063331—21no—
27#13063322—21no—
28#13063271—41no—
29#13063270—41no—
30#13063268—42no—
31#13063268—41no—
32#13063268—41no—
33#13063268—41no—
34D688—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×D172—41no—
51C2×D172—81no—
52Q16×C43—41no—
53Q16×C43—41no—
54Q16×C43—41no—
55Q16×C43—41no—
56C2×C8×C43C2×D411yescharacteristic
57C2×C8×C43C2×D411yescharacteristic
58C4⋊C4×C43—81no—
59C42×C43#4111yescharacteristic
60#10621877—21no—
61Dic172D811yescharacteristic
62D344—41no—
63D344—41no—
64D344—41no—
65D344—41no—
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
76C22×D43—81no—
77Q8×C43—81no—
78Q8×C43—81no—
79C2×C4×C43—21no—
80C2×C4×C43—81no—
81C2×C4×C43#12111yescharacteristic
82C22⋊D43—41no—
83D172—21no—
84D172—81no—
85D172—81no—
86D172—162no—
87C4×D43—41no—
88Dic86—21no—
89C8×C43C2×D811yescharacteristic
90C8×C43C2×D811yescharacteristic
91C8×C43#13511yescharacteristic
92C8×C43AGL(1,ℤ/8)11yescharacteristic
93C43⋊C8—41no—
94#12438—431nomaximal, Sylow
95C22×C43#47211yescharacteristic
96C2×D43—41no—
97C2×D43—162no—
98C2×D43—161no—
99C4×C43—22no—
100C4×C43—161no—
101C4×C43#45911yescharacteristic
102C4×C43#46611yescharacteristic
103Dic43—41no—
104#2248—431no—
105#2214—431no—
106#2213—431no—
107#2170—431no—
108#1373—431no—
109#1358D4311yescharacteristic, complemented
110#1357—431no—
111C2×C43—21no—
112C2×C43#166711yescharacteristic
113D43—81no—
114D43—321no—
115#510—861no—
116#509—861no—
117C2×SD32—861no—
118C2×SD32—861no—
119#504—861no—
120#494C2×D4311yescharacteristic
121#493—431no—
122#443—431no—
123#364—431no—
124#364C2×D4311yescharacteristic
125#364C2×D4311yescharacteristic
126#362—861no—
127#361—861no—
128#350—861no—
129C4×C16—431no—
130C43#1243811yescharacteristic, complemented, Sylow
131#135—431no—
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8—861no—
135C2×D8—861no—
136#131—861no—
137C4⋊Q8—21no—
138#127—861no—
139Q32—1721no—
140SD32—1721no—
141SD32—1721no—
142SD32—1721no—
143SD32—1722no—
144SD32—1721no—
145D16—1721no—
146M32—21no—
147M32—21no—
148M32—861no—
149M32—1721no—
150C2×C16—431no—
151C2×C16—431no—
152C2×C16—1721no—
153#108—431no—
154#104—861no—
155C4×C8C22×D4311yescharacteristic
156#41—861no—
157C2×Q8—41no—
158C2×D4—3441no—
159C2×D4—1721no—
160Q16—41no—
161Q16—41no—
162Q16—41no—
163Q16—41no—
164Q16—431no—
165SD16—861no—
166D8—431no—
167D8—1721no—
168D8—1721no—
169D8—1721no—
170D8—1721no—
171M16—861no—
172M16—1721no—
173C2×C8—1721no—
174C2×C8D4×D4311yescharacteristic
175C2×C8D4×D4311yescharacteristic
176C4⋊C4—81no—
177C42#1062189811yescharacteristic
178C16—41no—
179C16—41no—
180C16—431no—
181C16—431no—
182C16—861no—
183C16—1721no—
184C23—3441no—
185Q8—81no—
186Q8—81no—
187Q8—861no—
188D4—861no—
189D4—3441no—
190D4—3441no—
191D4—1721no—
192D4—6882no—
193C2×C4—21no—
194C2×C4—81no—
195C2×C4—1721no—
196C2×C4#1306329811yescharacteristic
197C8—1721no—
198C8D8×D4311yescharacteristic
199C8D8×D4311yescharacteristic
200C8#1306334611yescharacteristic
201C8#1306335211yescharacteristic
202C22—1721no—
203C22—6882no—
204C22—6881no—
205C22#1458316811yescharacteristic
206C4—22no—
207C4—161no—
208C4—1721no—
209C4#1458309311yescharacteristic
210C4#1458313411yescharacteristic
211C2—21no—
212C2—3441no—
213C2—13761no—
214C2#1913394911yescharacteristic
subgroupG/H
centerC2#19133949
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1358C2
socleC2×C43#1667
prime radical#19136672C2
hypercenter#1358D43
hypocenterC43#12438
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. #19136852C2semidirect
2. #19136673C2semidirect
4. #19136431C2semidirect
5. #19132670C2semidirect
6. #19132631C2semidirect
7. C43×#1358C2semidirect
109. #1358D43semidirect
130. C43#12438semidirect

Maximal subgroups

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

subgroupindex
#191368522
#191366732
#191366722
#191364312
#191326702
#191326312
C43×#13582
#1243843