Finite Group Databasebeta

← #25017269

Subgroups — #25017269

Order 11008.

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

normal subgroups only

This group has 294 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#19147731C211yesmaximal, characteristic, complemented
2#19136908C212yesmaximal, complemented
3#19132781C212yesmaximal, complemented
4#19132735C211yesmaximal, characteristic, complemented
5C43×#2218C211yesmaximal, characteristic, complemented
6C2×#13063347—21no—
7#14583342—22no—
8#14583337—22no—
9#14583331—21no—
10#14583331C2212yes—
11#14582737—22no—
12#14582734—22no—
13#14582733C2212yescomplemented
14C2×D16×C43C2211yescharacteristic, complemented
15C2×M32×C43C2211yescharacteristic
16C43×#466—21no—
17C43×#367C2211yescharacteristic, complemented
18C43×#357—21no—
19C2×#10621898—41no—
20#13063347—22no—
21#13063347—22no—
22#13063347—41no—
23#13063347—41no—
24C2×Dic172—21no—
25C2×#10621873—41no—
26C2×D344—21no—
27Dic344—21no—
28Dic344D412yescomplemented
29#13063270—22no—
30#13063270—22no—
31D688—21no—
32D688D412yescomplemented
33C43⋊C32—22no—
34C2×D8×C43—21no—
35C22×C8×C43D411yescharacteristic
36#121×C43—41no—
37D16×C43—22no—
38M32×C43—22no—
39C2×C16×C43D411yescharacteristic
40C2×C16×C43C2311yescharacteristic
41#107×C43—21no—
42#102×C43—41no—
43C2×D4×C43—41no—
44C2×D4×C43—81no—
45C22×C4×C43D811yescharacteristic
46C2×C22⋊D43—81no—
47#10621898—42no—
48#10621898—42no—
49#10621898—81no—
50#10621898—81no—
51C2×D172—41no—
52C2×C4×D43—81no—
53C2×Dic86—41no—
54D8×C43—41no—
55D8×C43—41no—
56C2×C8×C43—21no—
57C2×C8×C43—21no—
58C2×C8×C43D811yescharacteristic
59C2×C8×C43C2×D411yescharacteristic
60C4⋊C4×C43—41no—
61C22⋊C4×C43—81no—
62Dic172—22no—
63Dic172—41no—
64D344—22no—
65D344—41no—
66#10621873—42no—
67#10621873—42no—
68C16×C43—21no—
69C16×C43C2×D412yes—
70C23×C43—81no—
71C23×C43D1611yescharacteristic
72C22×D43—81no—
73D4×C43—81no—
74D4×C43—81no—
75D4×C43—162no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—81no—
79C2×C4×C43D1611yescharacteristic
80C2×C4×C43C2×D811yescharacteristic
81C22⋊D43—82no—
82C22⋊D43—82no—
83C2×Dic43—81no—
84D172—42no—
85D172—81no—
86C4×D43—82no—
87C4×D43—82no—
88Dic86—42no—
89Dic86—81no—
90C8×C43—21no—
91C8×C43#12011yescharacteristic
92C8×C43AGL(1,ℤ/8)11yescharacteristic
93#13667—431nomaximal, Sylow
94C22×C43—21no—
95C22×C43—41no—
96C22×C43—161no—
97C22×C43—161no—
98C22×C43—161no—
99C22×C43C2×D1611yescharacteristic
100C2×D43—82no—
101C2×D43—162no—
102C4×C43—21no—
103C4×C43—161no—
104C4×C43#44711yescharacteristic
105C4×C43#50911yescharacteristic
106Dic43—82no—
107#3414—431no—
108#2263—432no—
109#2218D4311yescharacteristic, complemented
110#1418—432no—
111#1400—431no—
112C2×C43—21no—
113C2×C43—41no—
114C2×C43—321no—
115C2×C43#218411yescharacteristic
116D43—162no—
117C2×#135—861no—
118#510—862no—
119#509—862no—
120#508—432no—
121#508—861no—
122C2×D16C2×D4311yescharacteristic, complemented
123C2×M32C2×D4311yescharacteristic
124#466—21no—
125SD64—862no—
126D32—862no—
127M64—432no—
128#367C2×D4311yescharacteristic, complemented
129#357—21no—
130C43#1366711yescharacteristic, complemented, Sylow
131C2×#41—1721no—
132#135—862no—
133#135—862no—
134#135—1721no—
135#135—1721no—
136C2×Q16—861no—
137C2×SD16—1721no—
138C2×D8—21no—
139C2×D8—861no—
140C22×C8C22⋊D4311yescharacteristic
141#121—41no—
142Q32—432no—
143Q32—861no—
144SD32—862no—
145SD32—862no—
146D16—22no—
147D16—432no—
148D16—861no—
149M32—22no—
150C2×C16C22⋊D4311yescharacteristic
151C2×C16C22×D4311yescharacteristic
152#107—21no—
153#102—41no—
154C32—862no—
155#41—3441no—
156#41—3441no—
157#41—1722no—
158#41—1722no—
159C2×Q8—1721no—
160C2×D4—41no—
161C2×D4—81no—
162C2×D4—3441no—
163C2×D4—1721no—
164C22×C4—3441no—
165C22×C4#1062188211yescharacteristic
166Q16—862no—
167Q16—1721no—
168SD16—1722no—
169SD16—1722no—
170D8—41no—
171D8—41no—
172D8—862no—
173D8—1721no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8#1062188211yescharacteristic
177C2×C8C2×C22⋊D4311yescharacteristic
178C4⋊C4—41no—
179C22⋊C4—81no—
180C16—21no—
181C16D4×D4312yes—
182C23—81no—
183C23—3441no—
184C23#1306326611yescharacteristic
185Q8—3441no—
186Q8—1722no—
187D4—81no—
188D4—81no—
189D4—162no—
190D4—3441no—
191D4—3442no—
192D4—3442no—
193D4—1722no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—81no—
197C2×C4—3442no—
198C2×C4—3441no—
199C2×C4—3442no—
200C2×C4#1306326611yescharacteristic
201C2×C4C2×#1062188211yescharacteristic
202C8—21no—
203C8#1306329311yescharacteristic
204C8#1306335011yescharacteristic
205C22—21no—
206C22—41no—
207C22—161no—
208C22—161no—
209C22—161no—
210C22—3442no—
211C22—6882no—
212C22C2×#1306326611yescharacteristic
213C4—21no—
214C4—161no—
215C4—3442no—
216C4#1458303211yescharacteristic
217C4#1458333411yescharacteristic
218C2—21no—
219C2—41no—
220C2—321no—
221C2—6882no—
222C2#1913650611yescharacteristic
subgroupG/H
centerC2#19136506
commutator, cosocleC2×C16×C43C23
FrattiniC2×C16C22×D43
FittingC43×#2218C2
socleC2×C43#2184
hypercenter#2218D43
hypocenterC43#13667
LCSG ▷ C2×C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32 ◁ #2218

Complements

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

NH ≅ G/Ntype
1. #19147731C2semidirect
2. #19136908C2semidirect
3. #19132781C2semidirect
4. #19132735C2semidirect
5. C43×#2218C2semidirect
13. #14582733C22semidirect
14. C2×D16×C43C22semidirect
17. C43×#367C22semidirect
28. Dic344D4semidirect
32. D688D4semidirect
109. #2218D43semidirect
122. C2×D16C2×D43semidirect
128. #367C2×D43semidirect
130. C43#13667semidirect

Maximal subgroups

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

subgroupindex
#191477312
#191369082
#191327812
#191327352
C43×#22182
#1366743