Finite Group Databasebeta

← #25007793

Subgroups — #25007793

Order 11008.

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

normal subgroups only

This group has 274 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#19144976C211yesmaximal, characteristic
2#19136407C211yesmaximal, characteristic
3#19132629C214yesmaximal, complemented
4C43×#2165C211yesmaximal, characteristic
5#14583456C411yescharacteristic
6C2×#13063325C411yescharacteristic
7#14583268C412yes—
8#14583268C2212yes—
9#14583250—21no—
10#14583250—21no—
11#14582909—21no—
12#14582909—21no—
13#14582720—21no—
14#14582681—21no—
15#14582677C2212yes—
16C4×M16×C43C2211yescharacteristic
17C43×#364—21no—
18C43×#349—21no—
19C43×#347C2212yes—
20C22×Dic86—21no—
21#13063325—21no—
22#13063325—21no—
23#13063325—41no—
24#13063325C2×C412yes—
25#13063317C2×C412yes—
26#13063304—41no—
27C4×Dic86—41no—
28#13063284—21no—
29C2×C4⋊Dic43—41no—
30#13063265—22no—
31#13063250—22no—
32#13063250—22no—
33#13063250—22no—
34#13063250—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
43C22×C4×C43—21no—
44C22×C4×C43C22⋊C411yescharacteristic
45C22×Dic43—41no—
46C2×Dic86—22no—
47C2×Dic86—42no—
48C2×Dic86—42no—
49C2×Dic86—41no—
50C2×Dic86—41no—
51M16×C43—41no—
52M16×C43—41no—
53C2×C8×C43C22⋊C411yescharacteristic
54C2×C8×C43C22⋊C411yescharacteristic
55C2×C8×C43C2×D411yescharacteristic
56C2×C8×C43C2×D411yescharacteristic
57C42×C43—21no—
58C42×C43C22⋊C411yescharacteristic
59C42×C43C22×C411yescharacteristic
60C22⋊Dic43—41no—
61C4⋊Dic43—22no—
62C4⋊Dic43—42no—
63C4⋊Dic43—41no—
64C4⋊Dic43—42no—
65Dic43⋊C4—42no—
66C4×Dic43—41no—
67C16×C43—42no—
68C43⋊C16—42no—
69C23×C43#10011yescharacteristic
70C2×C4×C43—21no—
71C2×C4×C43—21no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43—42no—
75C2×C4×C43#10011yescharacteristic
76C2×C4×C43C2×C22⋊C411yescharacteristic
77C2×Dic43—42no—
78C2×Dic43—42no—
79C2×Dic43—82no—
80Dic86—42no—
81Dic86—42no—
82Dic86—82no—
83Dic86—82no—
84C8×C43—21no—
85C8×C43—21no—
86C8×C43—21no—
87C8×C43—21no—
88#11916—431nomaximal, Sylow
89C22×C43—21no—
90C22×C43—41no—
91C22×C43C2×#10011yescharacteristic
92C4×C43—22no—
93C4×C43—21no—
94C4×C43—41no—
95C4×C43#42111yescharacteristic
96C4×C43#42111yescharacteristic
97Dic43—82no—
98Dic43—82no—
99#3139—431no—
100#2165—431no—
101#2165D4311yescharacteristic
102#1356—434no—
103C2×C43—21no—
104C2×C43—41no—
105C2×C43#153311yescharacteristic
106#533—431no—
107C2×C4⋊Q8—431no—
108#491—432no—
109#491—432no—
110#487—861no—
111#487—861no—
112#419—861no—
113#419—861no—
114C4×M16C2×D4311yescharacteristic
115#364—21no—
116#364—861no—
117#349—21no—
118#349—861no—
119#347—432no—
120#347C2×D4312yes—
121C43#1191611yescharacteristic, complemented, Sylow
122C22×Q8—861no—
123C2×M16D17211yescharacteristic
124C2×M16C22⋊D4311yescharacteristic
125C4⋊Q8—432no—
126C4⋊Q8—861no—
127C4⋊Q8—861no—
128C4⋊Q8—1721no—
129#125—432no—
130C22⋊Q8—1721no—
131C4×Q8—1721no—
132#117—861no—
133C2×C4⋊C4—1721no—
134C2×C42C4×D4311yescharacteristic
135M32—22no—
136M32—862no—
137#103—862no—
138#103—862no—
139#103—862no—
140#103—862no—
141#97C4×D4311yescharacteristic
142#97C22×D4311yescharacteristic
143C4×C8D17211yescharacteristic
144C4×C8C22⋊D4311yescharacteristic
145C2×Q8—862no—
146C2×Q8—1722no—
147C2×Q8—1722no—
148C2×Q8—1721no—
149C2×Q8—1721no—
150C22×C4—21no—
151C22×C4—1721no—
152C22×C4(C2×D43)⋊C411yescharacteristic
153M16—41no—
154M16—41no—
155C2×C8(C2×D43)⋊C411yescharacteristic
156C2×C8(C2×D43)⋊C411yescharacteristic
157C2×C8C2×D17211yescharacteristic
158C2×C8C2×C22⋊D4311yescharacteristic
159C4⋊C4—862no—
160C4⋊C4—1722no—
161C4⋊C4—1722no—
162C4⋊C4—1722no—
163C4⋊C4—1721no—
164C22⋊C4—1721no—
165C42—21no—
166C42—1721no—
167C42(C2×D43)⋊C411yescharacteristic
168C42C2×C4×D4311yescharacteristic
169C16—42no—
170C16—1722no—
171C23#1306324111yescharacteristic
172Q8—3442no—
173Q8—3442no—
174Q8—1722no—
175Q8—1722no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—3442no—
182C2×C4—1722no—
183C2×C4—1722no—
184C2×C4#1306324111yescharacteristic
185C2×C4C2×(C2×D43)⋊C411yescharacteristic
186C8—21no—
187C8—21no—
188C8—21no—
189C8—21no—
190C22—21no—
191C22—41no—
192C22C2×#1306324111yescharacteristic
193C4—22no—
194C4—21no—
195C4—41no—
196C4—3442no—
197C4—3442no—
198C4#1458291511yescharacteristic
199C4#1458291711yescharacteristic
200C2—21no—
201C2—41no—
202C2#1913321811yescharacteristic
subgroupG/H
centerC2#19133218
commutatorC42×C43C22×C4
Frattini#97C22×D43
FittingC43×#2165C2
socleC2×C43#1533
prime radicalC23×C43#100
cosocle#97×C43C23
hypercenter#2165D43
hypocenterC43#11916
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
3. #19132629C2semidirect
121. C43#11916semidirect

Maximal subgroups

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

subgroupindex
#191449762
#191364072
#191326292
C43×#21652
#1191643