Finite Group Databasebeta

← #25007790

Subgroups — #25007790

Order 11008.

326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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#19144970C211yesmaximal, characteristic
2#19136407C211yesmaximal, characteristic, complemented
3#19132627C214yesmaximal, complemented
4C43×#2165C211yesmaximal, characteristic, complemented
5#14583456C411yescharacteristic
6C2×#13063322C411yescharacteristic
7#14583264C412yes—
8#14583264C2212yes—
9#14583246—21no—
10#14583246—21no—
11#14582905—21no—
12#14582905—21no—
13#14582720—21no—
14#14582681—21no—
15#14582677C2212yescomplemented
16C4×M16×C43C2211yescharacteristic
17C43×#364—21no—
18C43×#349—21no—
19C43×#347C2212yescomplemented
20C22×D172—21no—
21C22×D172—41no—
22#13063325—21no—
23#13063322—21no—
24#13063322—41no—
25#13063322C2×C412yes—
26#13063317C2×C412yes—
27#13063304—41no—
28C4×Dic86—41no—
29#13063284—21no—
30#13063265—22no—
31#13063247—22no—
32#13063247—22no—
33#13063247—22no—
34#13063247—22no—
35C2×M16×C43D411yescharacteristic
36C2×M16×C43D411yescharacteristic
37C2×C42×C43C2×C411yescharacteristic
38M32×C43—22no—
39#97×C43C2×C411yescharacteristic
40#97×C43C2311yescharacteristic
41C4×C8×C43D411yescharacteristic
42C4×C8×C43D411yescharacteristic
43C23×D43—41no—
44C22×C4×C43—21no—
45C22×C4×C43C22⋊C411yescharacteristic
46C2×D172—22no—
47C2×D172—42no—
48C2×D172—41no—
49C2×D172—42no—
50C2×D172—42no—
51C2×D172—42no—
52C2×D172—84no—
53C2×Dic86—41no—
54M16×C43—41no—
55M16×C43—41no—
56C2×C8×C43C22⋊C411yescharacteristic
57C2×C8×C43C22⋊C411yescharacteristic
58C2×C8×C43C2×D411yescharacteristic
59C2×C8×C43C2×D411yescharacteristic
60C42×C43—21no—
61C42×C43C22⋊C411yescharacteristic
62C42×C43C22×C411yescharacteristic
63C22⋊Dic43—41no—
64C4⋊Dic43—22no—
65C4⋊Dic43—41no—
66Dic43⋊C4—42no—
67C4×Dic43—41no—
68C16×C43—42no—
69C43⋊C16—42no—
70C23×C43#10011yescharacteristic
71C22×D43—42no—
72C22×D43—82no—
73C22×D43—84no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—42no—
79C2×C4×C43#10011yescharacteristic
80C2×C4×C43C2×C22⋊C411yescharacteristic
81C2×Dic43—42no—
82D172—42no—
83D172—42no—
84D172—82no—
85D172—84no—
86D172—84no—
87Dic86—82no—
88C8×C43—21no—
89C8×C43—21no—
90C8×C43—21no—
91C8×C43—21no—
92#11915—431nomaximal, Sylow
93C22×C43—21no—
94C22×C43—41no—
95C22×C43C2×#10011yescharacteristic
96C2×D43—84no—
97C2×D43—82no—
98C2×D43—164no—
99C4×C43—22no—
100C4×C43—21no—
101C4×C43—41no—
102C4×C43#42111yescharacteristic
103C4×C43#42111yescharacteristic
104Dic43—82no—
105#3138—431no—
106#2165—431no—
107#2165D4311yescharacteristic, complemented
108#1355—434no—
109C2×C43—21no—
110C2×C43—41no—
111C2×C43#153311yescharacteristic
112D43—162no—
113#533—431no—
114C2×#127—431no—
115#490—432no—
116#490—432no—
117#486—861no—
118#486—861no—
119#418—861no—
120#418—861no—
121C4×M16C2×D4311yescharacteristic
122#364—21no—
123#364—861no—
124#349—21no—
125#349—861no—
126#347—432no—
127#347C2×D4312yescomplemented
128C43#1191511yescharacteristic, complemented, Sylow
129C22×D4—861no—
130C22×D4—1721no—
131C2×M16D17211yescharacteristic
132C2×M16C22⋊D4311yescharacteristic
133C4⋊Q8—861no—
134#127—432no—
135#127—861no—
136#127—1721no—
137#125—432no—
138C22⋊Q8—1721no—
139C4×Q8—1721no—
140#117—861no—
141C2×C42C4×D4311yescharacteristic
142M32—22no—
143M32—862no—
144#102—862no—
145#102—862no—
146#102—862no—
147#102—862no—
148#97C4×D4311yescharacteristic
149#97C22×D4311yescharacteristic
150C4×C8D17211yescharacteristic
151C4×C8C22⋊D4311yescharacteristic
152C24—1721no—
153C2×Q8—1721no—
154C2×D4—862no—
155C2×D4—3444no—
156C2×D4—1722no—
157C2×D4—1722no—
158C2×D4—1722no—
159C2×D4—1722no—
160C2×D4—1721no—
161C22×C4—21no—
162C22×C4(C2×D43)⋊C411yescharacteristic
163M16—41no—
164M16—41no—
165C2×C8(C2×D43)⋊C411yescharacteristic
166C2×C8(C2×D43)⋊C411yescharacteristic
167C2×C8C2×D17211yescharacteristic
168C2×C8C2×C22⋊D4311yescharacteristic
169C4⋊C4—862no—
170C4⋊C4—1722no—
171C4⋊C4—1721no—
172C22⋊C4—1721no—
173C42—21no—
174C42—1721no—
175C42(C2×D43)⋊C411yescharacteristic
176C42C2×C4×D4311yescharacteristic
177C16—42no—
178C16—1722no—
179C23—3442no—
180C23—3444no—
181C23—1722no—
182C23#1306324111yescharacteristic
183Q8—3442no—
184D4—3444no—
185D4—3442no—
186D4—3444no—
187D4—1722no—
188D4—1722no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—42no—
194C2×C4—1722no—
195C2×C4#1306324111yescharacteristic
196C2×C4C2×(C2×D43)⋊C411yescharacteristic
197C8—21no—
198C8—21no—
199C8—21no—
200C8—21no—
201C22—21no—
202C22—41no—
203C22—3444no—
204C22—3442no—
205C22—6884no—
206C22C2×#1306324111yescharacteristic
207C4—22no—
208C4—21no—
209C4—41no—
210C4—3442no—
211C4#1458291511yescharacteristic
212C4#1458291711yescharacteristic
213C2—21no—
214C2—41no—
215C2—6882no—
216C2#1913321811yescharacteristic
subgroupG/H
centerC2#19133218
commutatorC42×C43C22×C4
Frattini#97C22×D43
FittingC43×#2165C2
socleC2×C43#1533
prime radicalC2×#13063322C4
cosocle#97×C43C23
hypercenter#2165D43
hypocenterC43#11915
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #19136407C2semidirect
3. #19132627C2semidirect
4. C43×#2165C2semidirect
15. #14582677C22semidirect
19. C43×#347C22semidirect
107. #2165D43semidirect
127. #347C2×D43semidirect
128. C43#11915semidirect

Maximal subgroups

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

subgroupindex
#191449702
#191364072
#191326272
C43×#21652
#1191543