Finite Group Databasebeta

← #25006030

Subgroups — #25006030

Order 11008.

284 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 69 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#19143230C211yesmaximal, characteristic
2#19136404C212yesmaximal, complemented
3#19132545C212yesmaximal, complemented
4#19132531C211yesmaximal, characteristic
5C43×#1320C211yesmaximal, characteristic
6C2×#13063284C411yescharacteristic
7#14582957—22no—
8#14582957—22no—
9#14582922C411yescharacteristic
10#14582922C2211yescharacteristic
11#14582863C411yescharacteristic
12M16×Dic43C411yescharacteristic
13M16×Dic43C2211yescharacteristic
14#14582719—22no—
15#14582681C2212yes—
16#14582676—22no—
17C43×#407C2211yescharacteristic
18C43×#349C2212yes—
19C2×#10621877C2×C411yescharacteristic
20C2×#10621877C2×C411yescharacteristic
21#13063284—21no—
22#13063284—21no—
23#13063284—22no—
24C2×C4⋊Dic43—21no—
25C2×C22⋊Dic43—21no—
26C2×C4×Dic43C2×C411yescharacteristic
27C2×C4×Dic43C2×C411yescharacteristic
28#13063265—22no—
29Dic43⋊C8—22no—
30Dic43⋊C8—22no—
31C22⋊(C43⋊C8)—22no—
32#13063235—21no—
33#13063235D412yes—
34C8×Dic43—21no—
35C8×Dic43D412yes—
36C23×C4×C43C2×C411yescharacteristic
37C2×M16×C43C2×C411yescharacteristic
38C2×M16×C43C2311yescharacteristic
39M32×C43—22no—
40C22⋊C8×C43—22no—
41C24×C43M1611yescharacteristic
42C22×C4×C43—21no—
43C22×C4×C43—21no—
44C22×C4×C43—41no—
45C22×C4×C43—41no—
46C22×C4×C43M1611yescharacteristic
47C22×C4×C43C22×C411yescharacteristic
48C22×Dic43—21no—
49C22×Dic43—21no—
50M16×C43—41no—
51M16×C43—41no—
52C2×C8×C43—21no—
53C2×C8×C43C2×D412yes—
54C22⋊Dic43—22no—
55C22⋊Dic43—22no—
56C4⋊Dic43—22no—
57C4⋊Dic43—22no—
58C4×Dic43—21no—
59C4×Dic43—21no—
60C4×Dic43C22⋊C411yescharacteristic
61C4×Dic43C22⋊C411yescharacteristic
62C4×Dic43M1612yes—
63#10621877—41no—
64#10621877—41no—
65C2×C43⋊C8—21no—
66C2×C43⋊C8C22⋊C412yes—
67C16×C43—42no—
68C43⋊C16—42no—
69C23×C43—21no—
70C23×C43—41no—
71C23×C43—81no—
72C23×C43C2×M1611yescharacteristic
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—42no—
77C2×C4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43C2×C22⋊C411yescharacteristic
81C2×C4×C43C2×M1611yescharacteristic
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—22no—
85C2×Dic43—81no—
86C2×Dic43—81no—
87C8×C43—22no—
88C8×C43—41no—
89C43⋊C8—22no—
90C43⋊C8—41no—
91#11522—431nomaximal, Sylow
92C22×C43—21no—
93C22×C43—41no—
94C22×C43—42no—
95C22×C43—41no—
96C22×C43—82no—
97C22×C43#40711yescharacteristic
98C4×C43—21no—
99C4×C43—41no—
100C4×C43#41011yescharacteristic
101C4×C43#41311yescharacteristic
102Dic43—41no—
103Dic43—41no—
104Dic43—42no—
105#2921—431no—
106#2165—432no—
107#1327—432no—
108#1320—431no—
109#1320D4311yescharacteristic
110C2×C43—21no—
111C2×C43—41no—
112C2×C43—81no—
113C2×C43#146411yescharacteristic
114C2×#117—431no—
115#433—862no—
116#433—862no—
117#423—431no—
118#423—431no—
119#407—431no—
120#407C2×D4311yescharacteristic
121C4×M16—431no—
122C4×M16—431no—
123#364—862no—
124#349—432no—
125#349C2×D4312yes—
126#347—862no—
127C43#1152211yescharacteristic, complemented, Sylow
128C23×C4C4×D4311yescharacteristic
129C2×M16—431no—
130C2×M16—431no—
131C2×M16C4×D4311yescharacteristic
132C2×M16C22×D4311yescharacteristic
133#117—862no—
134#117—861no—
135#117—861no—
136C2×C4⋊C4—861no—
137C2×C22⋊C4—861no—
138C2×C42—431no—
139C2×C42—431no—
140M32—22no—
141M32—862no—
142C4⋊C8—862no—
143C4⋊C8—862no—
144C22⋊C8—22no—
145C22⋊C8—862no—
146#97—432no—
147#97—861no—
148C4×C8—432no—
149C4×C8—861no—
150C24#1062187211yescharacteristic
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—861no—
156C22×C4—861no—
157C22×C4#1062187211yescharacteristic
158C22×C4C2×C4×D4311yescharacteristic
159M16—41no—
160M16—41no—
161M16—1721no—
162M16—1721no—
163C2×C8—21no—
164C2×C8—432no—
165C2×C8—861no—
166C2×C8D4×D4312yes—
167C4⋊C4—862no—
168C4⋊C4—862no—
169C22⋊C4—862no—
170C22⋊C4—862no—
171C42—431no—
172C42—431no—
173C42—432no—
174C42—861no—
175C42—861no—
176C16—42no—
177C16—1722no—
178C23—21no—
179C23—41no—
180C23—81no—
181C23C2×#1062187211yescharacteristic
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—42no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—861no—
190C2×C4—861no—
191C2×C4—862no—
192C2×C4—3441no—
193C2×C4—3441no—
194C2×C4C22⋊C4×D4311yescharacteristic
195C2×C4M16×D4311yescharacteristic
196C8—22no—
197C8—41no—
198C8—862no—
199C8—1721no—
200C22—21no—
201C22—41no—
202C22—42no—
203C22—41no—
204C22—82no—
205C22#1458286111yescharacteristic
206C4—21no—
207C4—41no—
208C4—1721no—
209C4—1721no—
210C4—1722no—
211C4#1458287111yescharacteristic
212C4#1458288011yescharacteristic
213C2—21no—
214C2—41no—
215C2—81no—
216C2#1913292611yescharacteristic
subgroupG/H
centerC4#14582871
commutatorC22×C4×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#1320C2
socleC2×C43#1464
prime radicalC24×C43M16
cosocleC2×M16×C43C23
hypercenter#1320D43
hypocenterC43#11522
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #19136404C2semidirect
3. #19132545C2semidirect
127. C43#11522semidirect

Maximal subgroups

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

subgroupindex
#191432302
#191364042
#191325452
#191325312
C43×#13202
#1152243