Finite Group Databasebeta

← #25010835

Subgroups — #25010835

Order 11008.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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#19136844C211yesmaximal, characteristic, complemented
2#19136671C211yesmaximal, characteristic, complemented
3#19136432C211yesmaximal, characteristic, complemented
4#19132670C211yesmaximal, characteristic, complemented
5#19132632C211yesmaximal, characteristic, complemented
6#19132631C211yesmaximal, characteristic, complemented
7C43×#2213C211yesmaximal, characteristic, complemented
8#14583334—21no—
9C2×#13063266—21no—
10C2×#13063266—21no—
11#14583316—21no—
12#14583276C2211yescharacteristic
13#14582720C2211yescharacteristic
14#14582720C2211yescharacteristic
15#14582711—21no—
16#14582683—21no—
17C4×C43⋊C16C2211yescharacteristic
18C43×#509—21no—
19C43×#493C2211yescharacteristic
20C43×#443C2211yescharacteristic
21C43×#364C2211yescharacteristic
22C43×#361—21no—
23C2×D344—21no—
24C2×D344—21no—
25#13063322—21no—
26#13063268—41no—
27#13063266—42no—
28#13063266—41no—
29#13063266—41no—
30#13063266—41no—
31#13063265—21no—
32#13063265—21no—
33#13063265—41no—
34C2×C43⋊C16—41no—
35C2×C43⋊C16D411yescharacteristic
36C2×C43⋊C16D411yescharacteristic
37#135×C43D411yescharacteristic
38C2×D8×C43—21no—
39C2×D8×C43—21no—
40#131×C43—21no—
41#127×C43—21no—
42SD32×C43—41no—
43D16×C43—41no—
44M32×C43—21no—
45#108×C43D411yescharacteristic
46#104×C43—21no—
47C4×C8×C43C2311yescharacteristic
48#41×C43—21no—
49C2×D4×C43—41no—
50C2×D4×C43—81no—
51C2×D172—41no—
52C2×D172—81no—
53Q16×C43D811yescharacteristic
54SD16×C43—21no—
55D8×C43—41no—
56D8×C43—41no—
57D8×C43—41no—
58D8×C43—41no—
59D8×C43D811yescharacteristic
60M16×C43—21no—
61M16×C43—41no—
62C2×C8×C43—41no—
63C2×C8×C43C2×D411yescharacteristic
64C2×C8×C43C2×D411yescharacteristic
65C42×C43#4111yescharacteristic
66D344—41no—
67D344—41no—
68D344—41no—
69D344—41no—
70C16×C43—41no—
71C43⋊C16—21no—
72C43⋊C16—41no—
73C43⋊C16—41no—
74C43⋊C16D811yescharacteristic
75C43⋊C16D811yescharacteristic
76C23×C43—81no—
77C22×D43—81no—
78Q8×C43—21no—
79D4×C43—21no—
80D4×C43—41no—
81D4×C43—81no—
82D4×C43—81no—
83D4×C43—162no—
84C2×C4×C43—21no—
85C2×C4×C43—41no—
86C2×C4×C43#12111yescharacteristic
87D172—81no—
88D172—81no—
89D172—162no—
90C8×C43—41no—
91C8×C43C2×D811yescharacteristic
92C8×C43C2×D811yescharacteristic
93C8×C43#13511yescharacteristic
94C8×C43AGL(1,ℤ/8)11yescharacteristic
95#12436—431nomaximal, Sylow
96C22×C43—41no—
97C22×C43—162no—
98C22×C43—161no—
99C22×C43#47211yescharacteristic
100C2×D43—162no—
101C2×D43—161no—
102C4×C43—22no—
103C4×C43—41no—
104C4×C43#45911yescharacteristic
105C4×C43#46611yescharacteristic
106#2246—431no—
107#2213—431no—
108#2213D4311yescharacteristic, complemented
109#2170—431no—
110#1373—431no—
111#1357—431no—
112#1357—431no—
113C2×C43—21no—
114C2×C43—81no—
115C2×C43—321no—
116C2×C43#166711yescharacteristic
117D43—321no—
118#509—21no—
119#509—861no—
120C2×D16—861no—
121C2×D16—861no—
122#504—861no—
123#493—431no—
124#493C2×D4311yescharacteristic
125#443C2×D4311yescharacteristic
126#364—431no—
127#364—431no—
128#364C2×D4311yescharacteristic
129#361—21no—
130#361—861no—
131#350—861no—
132C4×C16—431no—
133C43#1243611yescharacteristic, complemented, Sylow
134#135C22⋊D4311yescharacteristic
135C2×D8—21no—
136C2×D8—21no—
137C2×D8—861no—
138C2×D8—861no—
139#131—21no—
140#127—21no—
141#127—861no—
142SD32—41no—
143SD32—1721no—
144D16—41no—
145D16—1721no—
146D16—1721no—
147D16—1722no—
148D16—1721no—
149M32—21no—
150M32—861no—
151M32—861no—
152M32—1721no—
153C2×C16—431no—
154C2×C16—431no—
155C2×C16—1721no—
156#108C22⋊D4311yescharacteristic
157#104—21no—
158C4×C8C22×D4311yescharacteristic
159#41—21no—
160C2×D4—41no—
161C2×D4—81no—
162C2×D4—3441no—
163C2×D4—1721no—
164Q16#1062188211yescharacteristic
165SD16—21no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8—1721no—
171D8—1721no—
172D8—1721no—
173D8—1721no—
174D8#1062188211yescharacteristic
175M16—21no—
176M16—41no—
177C2×C8—41no—
178C2×C8D4×D4311yescharacteristic
179C2×C8C2×C22⋊D4311yescharacteristic
180C42#1062190011yescharacteristic
181C16—41no—
182C16—431no—
183C16—431no—
184C16—861no—
185C16—1721no—
186C16—1721no—
187C23—81no—
188C23—3441no—
189Q8—21no—
190D4—21no—
191D4—41no—
192D4—81no—
193D4—81no—
194D4—162no—
195D4—3441no—
196D4—3441no—
197D4—6882no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4#1306329711yescharacteristic
201C8—41no—
202C8D8×D4311yescharacteristic
203C8C2×#1062188211yescharacteristic
204C8#1306334511yescharacteristic
205C8#1306334911yescharacteristic
206C22—41no—
207C22—162no—
208C22—161no—
209C22—6882no—
210C22—6881no—
211C22#1458316711yescharacteristic
212C4—22no—
213C4—41no—
214C4#1458309211yescharacteristic
215C4#1458313311yescharacteristic
216C2—21no—
217C2—81no—
218C2—321no—
219C2—13761no—
220C2#1913394811yescharacteristic
subgroupG/H
centerC2#19133948
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2213C2
socleC2×C43#1667
hypercenter#2213D43
hypocenterC43#12436
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. #19136844C2semidirect
2. #19136671C2semidirect
3. #19136432C2semidirect
4. #19132670C2semidirect
5. #19132632C2semidirect
6. #19132631C2semidirect
7. C43×#2213C2semidirect
108. #2213D43semidirect
133. C43#12436semidirect

Maximal subgroups

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

subgroupindex
#191368442
#191366712
#191364322
#191326702
#191326322
#191326312
C43×#22132
#1243643