Finite Group Databasebeta

← #25010836

Subgroups — #25010836

Order 11008.

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

normal subgroups only

This group has 234 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#19136844C211yesmaximal, characteristic, complemented
2#19136672C211yesmaximal, characteristic, complemented
3#19136668C211yesmaximal, characteristic, complemented
4#19136431C211yesmaximal, characteristic, complemented
5#19132670C211yesmaximal, characteristic, complemented
6#19132631C211yesmaximal, characteristic, complemented
7C43×#1357C211yesmaximal, characteristic, complemented
8#14583337—21no—
9#14583335—21no—
10C2×#13063266—21no—
11C2×#13063266—21no—
12#14583317—21no—
13#14583276C2211yescharacteristic
14#14583017C2211yescharacteristic
15#14582720C2211yescharacteristic
16#14582713—21no—
17#14582712—21no—
18#14582684—21no—
19C4×C43⋊C16C2211yescharacteristic
20C43×#493C2211yescharacteristic
21C43×#364C2211yescharacteristic
22C43×#364C2211yescharacteristic
23#13063347D411yescharacteristic
24C2×D344—21no—
25C2×D344—21no—
26#13063331—21no—
27#13063322—21no—
28#13063270—41no—
29#13063269—41no—
30D688—41no—
31#13063266—42no—
32#13063266—41no—
33#13063266—41no—
34#13063266—41no—
35#13063265—21no—
36#13063264—41no—
37C2×C43⋊C16D411yescharacteristic
38C2×C43⋊C16D411yescharacteristic
39C16×D43—41no—
40#13063261D411yescharacteristic
41#13063253—21no—
42C2×D8×C43—21no—
43C2×D8×C43—21no—
44#127×C43—21no—
45M32×C43—21no—
46M32×C43—21no—
47C4×C8×C43C2311yescharacteristic
48C2×D4×C43—41no—
49C2×D4×C43—81no—
50#10621898—21no—
51C2×D172—41no—
52C2×D172—81no—
53D8×C43—41no—
54D8×C43—41no—
55D8×C43—41no—
56D8×C43—41no—
57C2×C8×C43C2×D411yescharacteristic
58C2×C8×C43C2×D411yescharacteristic
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
76C23×C43—81no—
77C22×D43—81no—
78D4×C43—81no—
79D4×C43—81no—
80D4×C43—162no—
81C2×C4×C43—21no—
82C2×C4×C43#12111yescharacteristic
83C22⋊D43—41no—
84D172—21no—
85D172—81no—
86D172—81no—
87D172—162no—
88C4×D43—41no—
89Dic86—21no—
90C8×C43C2×D811yescharacteristic
91C8×C43C2×D811yescharacteristic
92C8×C43#13511yescharacteristic
93C8×C43AGL(1,ℤ/8)11yescharacteristic
94C43⋊C8—41no—
95#12436—431nomaximal, Sylow
96C22×C43—162no—
97C22×C43—161no—
98C22×C43#47211yescharacteristic
99C2×D43—41no—
100C2×D43—162no—
101C2×D43—161no—
102C4×C43—22no—
103C4×C43#45911yescharacteristic
104C4×C43#46611yescharacteristic
105Dic43—41no—
106#2246—431no—
107#2213—431no—
108#2213—431no—
109#2170—431no—
110#1373—431no—
111#1357—431no—
112#1357D4311yescharacteristic, complemented
113C2×C43—21no—
114C2×C43—321no—
115C2×C43#166711yescharacteristic
116D43—81no—
117D43—321no—
118#509—861no—
119#509—861no—
120C2×D16—861no—
121C2×D16—861no—
122#504—861no—
123#493—431no—
124#493C2×D4311yescharacteristic
125#443—431no—
126#364—431no—
127#364C2×D4311yescharacteristic
128#364C2×D4311yescharacteristic
129#361—861no—
130#361—861no—
131#350—861no—
132C4×C16—431no—
133C43#1243611yescharacteristic, complemented, Sylow
134#135—431no—
135C2×D8—21no—
136C2×D8—21no—
137C2×D8—861no—
138C2×D8—861no—
139#131—861no—
140#127—21no—
141#127—861no—
142SD32—1721no—
143SD32—1721no—
144D16—1721no—
145D16—1721no—
146D16—1721no—
147D16—1722no—
148D16—1721no—
149M32—21no—
150M32—21no—
151M32—861no—
152M32—1721no—
153C2×C16—431no—
154C2×C16—431no—
155C2×C16—1721no—
156#108—431no—
157#104—861no—
158C4×C8C22×D4311yescharacteristic
159#41—861no—
160C2×D4—41no—
161C2×D4—81no—
162C2×D4—3441no—
163C2×D4—1721no—
164Q16—431no—
165SD16—861no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8—431no—
171D8—1721no—
172D8—1721no—
173D8—1721no—
174D8—1721no—
175M16—861no—
176M16—1721no—
177C2×C8—1721no—
178C2×C8D4×D4311yescharacteristic
179C2×C8D4×D4311yescharacteristic
180C42#1062189811yescharacteristic
181C16—41no—
182C16—41no—
183C16—431no—
184C16—431no—
185C16—861no—
186C16—1721no—
187C23—81no—
188C23—3441no—
189Q8—861no—
190D4—81no—
191D4—81no—
192D4—162no—
193D4—861no—
194D4—3441no—
195D4—3441no—
196D4—1721no—
197D4—6882no—
198C2×C4—21no—
199C2×C4—1721no—
200C2×C4#1306329811yescharacteristic
201C8—1721no—
202C8D8×D4311yescharacteristic
203C8D8×D4311yescharacteristic
204C8#1306334611yescharacteristic
205C8#1306335211yescharacteristic
206C22—162no—
207C22—161no—
208C22—1721no—
209C22—6882no—
210C22—6881no—
211C22#1458316811yescharacteristic
212C4—22no—
213C4—1721no—
214C4#1458309311yescharacteristic
215C4#1458313411yescharacteristic
216C2—21no—
217C2—321no—
218C2—3441no—
219C2—13761no—
220C2#1913394911yescharacteristic
subgroupG/H
centerC2#19133949
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1357C2
socleC2×C43#1667
hypercenter#1357D43
hypocenterC43#12436
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1357

Complements

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

NH ≅ G/Ntype
1. #19136844C2semidirect
2. #19136672C2semidirect
3. #19136668C2semidirect
4. #19136431C2semidirect
5. #19132670C2semidirect
6. #19132631C2semidirect
7. C43×#1357C2semidirect
112. #1357D43semidirect
133. C43#12436semidirect

Maximal subgroups

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

subgroupindex
#191368442
#191366722
#191366682
#191364312
#191326702
#191326312
C43×#13572
#1243643