Finite Group Databasebeta

← #25006106

Subgroups — #25006106

Order 11008.

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

normal subgroups only

This group has 262 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#19143532C211yesmaximal, characteristic
2#19136408C212yesmaximal
3#19132547C212yesmaximal
4#19132546C211yesmaximal, characteristic
5C43×#1327C211yesmaximal, characteristic
6#14583456C411yescharacteristic
7#14583028—22no—
8#14583028—22no—
9#14582927C411yescharacteristic
10#14582927C2211yescharacteristic
11#14582857C411yescharacteristic
12#14582857C2211yescharacteristic
13C2×#13063236C411yescharacteristic
14#14582719—22no—
15#14582681C2212yes—
16#14582676—22no—
17C43×#423C2211yescharacteristic
18C43×#349C2212yes—
19C22×C43⋊C8C2×C411yescharacteristic
20C22×C43⋊C8C2×C411yescharacteristic
21#13063325—21no—
22#13063317—21no—
23#13063304—22no—
24C4×Dic86—22no—
25#13063284C2×C411yescharacteristic
26#13063284C2×C411yescharacteristic
27#13063265—22no—
28Dic43⋊C8—22no—
29Dic43⋊C8—22no—
30#13063236—21no—
31#13063236—21no—
32#13063235—21no—
33#13063235D412yes—
34C8×Dic43—21no—
35C8×Dic43D412yes—
36C2×M16×C43C2×C411yescharacteristic
37C2×M16×C43C2311yescharacteristic
38C2×C42×C43C2×C411yescharacteristic
39M32×C43—22no—
40C4⋊C8×C43—22no—
41C22×C4×C43—21no—
42C22×C4×C43C22×C411yescharacteristic
43C2×Dic86—22no—
44M16×C43—41no—
45M16×C43—41no—
46C2×C8×C43—21no—
47C2×C8×C43C2×D412yes—
48C42×C43—21no—
49C42×C43M1611yescharacteristic
50C42×C43M1611yescharacteristic
51C22⋊Dic43—21no—
52C22⋊Dic43M1612yes—
53C4⋊Dic43—22no—
54C4⋊Dic43—21no—
55C4⋊Dic43—21no—
56Dic43⋊C4—24no—
57C4×Dic43—21no—
58C4×Dic43C22⋊C412yes—
59C2×C43⋊C8—22no—
60C2×C43⋊C8—21no—
61C2×C43⋊C8—41no—
62C2×C43⋊C8C22⋊C411yescharacteristic
63C2×C43⋊C8C22⋊C411yescharacteristic
64C16×C43—42no—
65C43⋊C16—42no—
66C23×C43C2×M1611yescharacteristic
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—21no—
71C2×C4×C43—81no—
72C2×C4×C43C2×C22⋊C411yescharacteristic
73C2×C4×C43C2×M1611yescharacteristic
74C2×Dic43—22no—
75C2×Dic43—22no—
76Dic86—82no—
77C8×C43—22no—
78C8×C43—41no—
79C43⋊C8—21no—
80C43⋊C8—41no—
81C43⋊C8#10112yes—
82#11540—431nomaximal, Sylow
83C22×C43—21no—
84C22×C43—41no—
85C22×C43#40711yescharacteristic
86C4×C43—21no—
87C4×C43—41no—
88C4×C43—41no—
89C4×C43#41011yescharacteristic
90C4×C43C2×#10111yescharacteristic
91Dic43—42no—
92Dic43—42no—
93#2961—431no—
94#2166—432no—
95#1328—432no—
96#1327—431no—
97#1327D4311yescharacteristic
98C2×C43—21no—
99C2×C43—41no—
100C2×C43#146711yescharacteristic
101#533—431no—
102#446—862no—
103#446—862no—
104#424—431no—
105#424—431no—
106#423C2×D4311yescharacteristic
107#405—431no—
108#405—431no—
109C2×#97—431no—
110#364—862no—
111#349—432no—
112#349C2×D4312yes—
113#347—862no—
114C43#1154011yescharacteristic, complemented, Sylow
115C2×M16C4×D4311yescharacteristic
116C2×M16C22×D4311yescharacteristic
117C22×C8—431no—
118C22×C8—431no—
119C4⋊Q8—861no—
120#125—861no—
121C22⋊Q8—862no—
122C4×Q8—862no—
123#117—431no—
124#117—431no—
125C2×C42C4×D4311yescharacteristic
126M32—22no—
127M32—862no—
128C4⋊C8—22no—
129C4⋊C8—862no—
130C4⋊C8—862no—
131#97—432no—
132#97—861no—
133#97—861no—
134#97—861no—
135C4×C8—432no—
136C4×C8—861no—
137C2×Q8—862no—
138C22×C4—21no—
139C22×C4C2×C4×D4311yescharacteristic
140M16—41no—
141M16—41no—
142C2×C8—21no—
143C2×C8—431no—
144C2×C8—431no—
145C2×C8—862no—
146C2×C8—861no—
147C2×C8—1721no—
148C2×C8D4×D4312yes—
149C4⋊C4—864no—
150C4⋊C4—862no—
151C4⋊C4—861no—
152C4⋊C4—861no—
153C22⋊C4—432no—
154C22⋊C4—861no—
155C42—21no—
156C42—432no—
157C42—861no—
158C42#1062187211yescharacteristic
159C42#1062187211yescharacteristic
160C16—42no—
161C16—1722no—
162C23M16×D4311yescharacteristic
163Q8—3442no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—81no—
169C2×C4—862no—
170C2×C4—862no—
171C2×C4C22⋊C4×D4311yescharacteristic
172C2×C4C2×#1062187211yescharacteristic
173C8—22no—
174C8—41no—
175C8—432no—
176C8—861no—
177C8—1721no—
178C22—21no—
179C22—41no—
180C22#1458286111yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—1722no—
185C4—1722no—
186C4#1458287111yescharacteristic
187C4#101×D4311yescharacteristic
188C2—21no—
189C2—41no—
190C2#1913293711yescharacteristic
subgroupG/H
centerC4#14582871
commutatorC22×C4×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#1327C2
socleC2×C43#1467
prime radicalC23×C43C2×M16
cosocleC2×M16×C43C23
hypercenter#1327D43
hypocenterC43#11540
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
114. C43#11540semidirect

Maximal subgroups

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

subgroupindex
#191435322
#191364082
#191325472
#191325462
C43×#13272
#1154043