Finite Group Databasebeta

← #25009076

Subgroups — #25009076

Order 11008.

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

normal subgroups only

This group has 350 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#19146049C211yesmaximal, characteristic, complemented
2#19136524C212yesmaximal
3#19132612C212yesmaximal, complemented
4#19132537C211yesmaximal, characteristic, complemented
5C43×#2045C211yesmaximal, characteristic
6#14583511—21no—
7C2×#13063269—22no—
8#14583207—22no—
9#14583157—21no—
10#14583140C2212yes—
11#14583110—22no—
12#14582700—22no—
13C22⋊(C43⋊C16)C2212yes—
14C22×D8×C43C2211yescharacteristic
15C43×#424C2211yescharacteristic
16C43×#418—21no—
17C2×#100×C43—21no—
18C43×#341C2211yescharacteristic
19C2×Dic172—21no—
20C2×Dic172D412yes—
21#13063325—21no—
22#13063318—42no—
23#13063317—21no—
24#13063315—42no—
25#13063304—22no—
26C4×Dic86—22no—
27#13063269—44no—
28C2×C43⋊C16—22no—
29#13063259D412yes—
30#13063257—21no—
31#13063250—22no—
32#13063250—22no—
33C22×D4×C43—21no—
34C2×D8×C43—22no—
35C2×D8×C43—42no—
36C2×M16×C43—21no—
37C2×M16×C43D411yescharacteristic
38C22×C8×C43C2311yescharacteristic
39#117×C43D411yescharacteristic
40C4⋊C8×C43—22no—
41#102×C43—42no—
42#100×C43—42no—
43C24×C43—41no—
44C2×D4×C43—22no—
45C2×D4×C43—41no—
46C2×D4×C43—41no—
47C2×D4×C43—41no—
48C2×D4×C43—41no—
49C2×D4×C43—41no—
50C22×C4×C43C2×D411yescharacteristic
51C2×Dic86—22no—
52D8×C43—24no—
53D8×C43—42no—
54M16×C43—41no—
55M16×C43—41no—
56M16×C43—41no—
57C2×C8×C43—21no—
58C2×C8×C43—41no—
59C2×C8×C43—41no—
60C2×C8×C43C2×D412yes—
61C4⋊C4×C43D812yes—
62C22⋊C4×C43—21no—
63C42×C43—21no—
64C22⋊Dic43—42no—
65C4⋊Dic43—22no—
66C4⋊Dic43—42no—
67Dic43⋊C4—42no—
68Dic43⋊C4—42no—
69Dic43⋊C4—42no—
70C4×Dic43—42no—
71Dic172—42no—
72Dic172—81no—
73C43⋊C16—42no—
74C23×C43—42no—
75C23×C43—81no—
76C23×C43—81no—
77C23×C43—162no—
78C23×C43AGL(1,ℤ/8)11yescharacteristic
79D4×C43—42no—
80D4×C43—42no—
81D4×C43—81no—
82D4×C43—81no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43#12011yescharacteristic
87C2×C4×C43C2×D811yescharacteristic
88C2×Dic43—42no—
89C2×Dic43—42no—
90Dic86—42no—
91Dic86—42no—
92C8×C43—22no—
93C8×C43—41no—
94C8×C43—81no—
95#12165—431nomaximal, Sylow
96C22×C43—21no—
97C22×C43—22no—
98C22×C43—82no—
99C22×C43—162no—
100C22×C43—162no—
101C22×C43—162no—
102C22×C43#44711yescharacteristic
103C4×C43—21no—
104C4×C43—42no—
105C4×C43#45411yescharacteristic
106C4×C43B(4,𝔽2)11yescharacteristic
107Dic43—82no—
108Dic43—82no—
109#3261—431no—
110#2187—432no—
111#2045D4311yescharacteristic
112#1350—432no—
113#1323—431no—
114C2×C43—41no—
115C2×C43—162no—
116C2×C43#159811yescharacteristic
117C2×C43#219312yes—
118C22×D8C2×D4311yescharacteristic
119#541—861no—
120C2×SD32—862no—
121#479—862no—
122#470—861no—
123#467—432no—
124#462—862no—
125#424C2×D4311yescharacteristic
126#418—21no—
127C2×#100—21no—
128#357—862no—
129C22⋊C16—432no—
130#341C2×D4311yescharacteristic
131C43#1216511yescharacteristic, complemented, Sylow
132C22×D4—21no—
133C2×Q16—432no—
134C2×Q16—861no—
135C2×D8—22no—
136C2×D8—42no—
137C2×M16—21no—
138C2×M16C22⋊D4311yescharacteristic
139C22×C8C22×D4311yescharacteristic
140C4⋊Q8—861no—
141#126—1722no—
142#125—861no—
143#125—1722no—
144C22⋊Q8—862no—
145C4×Q8—862no—
146#117C22⋊D4311yescharacteristic
147SD32—1724no—
148C2×C16—862no—
149#107—432no—
150#106—861no—
151C4⋊C8—22no—
152#103—862no—
153#103—862no—
154#102—42no—
155#100—42no—
156C24—41no—
157C2×Q8—862no—
158C2×D4—22no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164C22×C4C2×C22⋊D4311yescharacteristic
165Q16—3441no—
166Q16—1722no—
167D8—24no—
168D8—42no—
169M16—41no—
170M16—41no—
171M16—41no—
172C2×C8—21no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8D4×D4312yes—
176C4⋊C4—862no—
177C4⋊C4—1722no—
178C4⋊C4—1722no—
179C4⋊C4—1722no—
180C4⋊C4—1722no—
181C4⋊C4#1062188212yes—
182C22⋊C4—21no—
183C22⋊C4—1722no—
184C42—21no—
185C42—1722no—
186C16—1722no—
187C23—42no—
188C23—81no—
189C23—81no—
190C23—162no—
191C23#1306335011yescharacteristic
192Q8—1722no—
193Q8—1722no—
194D4—42no—
195D4—42no—
196D4—81no—
197D4—81no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—1722no—
202C2×C4—1722no—
203C2×C4#1306329311yescharacteristic
204C2×C4C2×#1062188211yescharacteristic
205C8—22no—
206C8—41no—
207C8—81no—
208C22—22no—
209C22—21no—
210C22—82no—
211C22—162no—
212C22—162no—
213C22—162no—
214C22#1458303211yescharacteristic
215C4—21no—
216C4—42no—
217C4—3442no—
218C4—3442no—
219C4#1458307111yescharacteristic
220C4#1458308511yescharacteristic
221C2—41no—
222C2—162no—
223C2#1913352911yescharacteristic
224C2#1913655712yes—
subgroupG/H
centerC22#14583032
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#2045C2
socleC22×C43#447
prime radicalC22×D8×C43C22
hypercenter#2045D43
hypocenterC43#12165
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424 ◁ #2045

Complements

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

NH ≅ G/Ntype
1. #19146049C2semidirect
3. #19132612C2semidirect
4. #19132537C2semidirect
131. C43#12165semidirect

Maximal subgroups

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

subgroupindex
#191460492
#191365242
#191326122
#191325372
C43×#20452
#1216543