Finite Group Databasebeta

← #25006032

Subgroups — #25006032

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#19143232C211yesmaximal, characteristic
2#19136404C212yesmaximal, complemented
3#19132546C211yesmaximal, characteristic, complemented
4#19132530C212yesmaximal
5C43×#1327C211yesmaximal, characteristic, complemented
6C2×#13063282C411yescharacteristic
7#14582959—22no—
8#14582959—22no—
9#14582923C411yescharacteristic
10#14582862C411yescharacteristic
11#14582862C2211yescharacteristic
12M16×Dic43C411yescharacteristic
13M16×Dic43C2211yescharacteristic
14#14582719—22no—
15#14582681C2212yes—
16#14582676—22no—
17C43×#423C2211yescharacteristic
18C43×#349C2212yes—
19C22×C4×D43C2×C411yescharacteristic
20C2×#10621877C2×C411yescharacteristic
21C2×#10621877C2×C411yescharacteristic
22#13063282—22no—
23#13063282—21no—
24#13063282—21no—
25C2×Dic43⋊C4—21no—
26C2×(C2×D43)⋊C4—21no—
27C2×C4×Dic43C2×C411yescharacteristic
28#13063265—22no—
29C4⋊(C43⋊C8)—22no—
30(C2×D43)⋊C8—22no—
31(C2×D43)⋊C8—22no—
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—
41C23×D43M1611yescharacteristic
42C22×C4×C43—21no—
43C22×C4×C43C22×C411yescharacteristic
44C22×Dic43—21no—
45C22×Dic43M1611yescharacteristic
46C2×C4×D43—21no—
47C2×C4×D43—21no—
48C2×C4×D43—41no—
49C2×C4×D43—41no—
50M16×C43—41no—
51M16×C43—41no—
52C2×C8×C43—21no—
53C2×C8×C43C2×D412yes—
54C42×C43—21no—
55C42×C43M1612yes—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58Dic43⋊C4—22no—
59Dic43⋊C4—22no—
60C4×Dic43—21no—
61C4×Dic43C22⋊C411yescharacteristic
62C4×Dic43C22⋊C411yescharacteristic
63#10621877—41no—
64#10621877—41no—
65C2×C43⋊C8—21no—
66C2×C43⋊C8C22⋊C412yes—
67C16×C43—42no—
68C43⋊C16—42no—
69C23×C43C2×M1611yescharacteristic
70C22×D43—21no—
71C22×D43—41no—
72C22×D43—81no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—81no—
77C2×C4×C43C2×C22⋊C411yescharacteristic
78C2×C4×C43C2×M1611yescharacteristic
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—41no—
83C2×Dic43—81no—
84C4×D43—42no—
85C4×D43—41no—
86C4×D43—41no—
87C8×C43—22no—
88C8×C43—41no—
89C43⋊C8—22no—
90C43⋊C8—41no—
91#11522—431nomaximal, Sylow
92C22×C43—21no—
93C22×C43—41no—
94C22×C43#40711yescharacteristic
95C2×D43—42no—
96C2×D43—41no—
97C2×D43—82no—
98C4×C43—21no—
99C4×C43—42no—
100C4×C43#41011yescharacteristic
101C4×C43#41311yescharacteristic
102Dic43—41no—
103Dic43—41no—
104Dic43—41no—
105#2921—431no—
106#2165—432no—
107#1327—431no—
108#1327D4311yescharacteristic, complemented
109#1320—432no—
110C2×C43—21no—
111C2×C43—41no—
112C2×C43#146411yescharacteristic
113D43—81no—
114C2×#117—431no—
115#433—862no—
116#433—862no—
117#423—431no—
118#423C2×D4311yescharacteristic
119#407—431no—
120#407—431no—
121C4×M16—431no—
122C4×M16—431no—
123#364—862no—
124#349—432no—
125#349C2×D4312yes—
126#347—862no—
127C43#1152211yescharacteristic, complemented, Sylow
128C23×C4—431no—
129C2×M16—431no—
130C2×M16—431no—
131C2×M16C4×D4311yescharacteristic
132C2×M16C22×D4311yescharacteristic
133#117—861no—
134#117—861no—
135#117—862no—
136C2×C4⋊C4—861no—
137C2×C22⋊C4—861no—
138C2×C42—431no—
139C2×C42C4×D4311yescharacteristic
140M32—22no—
141M32—862no—
142C4⋊C8—22no—
143C4⋊C8—862no—
144C22⋊C8—862no—
145C22⋊C8—862no—
146#97—432no—
147#97—861no—
148C4×C8—432no—
149C4×C8—861no—
150C24—431no—
151C22×C4—21no—
152C22×C4—431no—
153C22×C4—861no—
154C22×C4—861no—
155C22×C4—861no—
156C22×C4—1721no—
157C22×C4—1721no—
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—21no—
172C42—431no—
173C42—431no—
174C42—861no—
175C42#1062187212yes—
176C16—42no—
177C16—1722no—
178C23—861no—
179C23—3441no—
180C23—1721no—
181C23M16×D4311yescharacteristic
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—81no—
186C2×C4—861no—
187C2×C4—861no—
188C2×C4—861no—
189C2×C4—3441no—
190C2×C4—1722no—
191C2×C4—1721no—
192C2×C4—1721no—
193C2×C4—1721no—
194C2×C4C22⋊C4×D4311yescharacteristic
195C2×C4C2×#1062187211yescharacteristic
196C8—22no—
197C8—41no—
198C8—862no—
199C8—1721no—
200C22—21no—
201C22—41no—
202C22—3442no—
203C22—1722no—
204C22—1721no—
205C22#1458286111yescharacteristic
206C4—21no—
207C4—42no—
208C4—1721no—
209C4—1721no—
210C4—1721no—
211C4#1458287111yescharacteristic
212C4#1458288211yescharacteristic
213C2—21no—
214C2—41no—
215C2—3441no—
216C2#1913292811yescharacteristic
subgroupG/H
centerC4#14582871
commutatorC22×C4×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#1327C2
socleC2×C43#1464
prime radicalC23×D43M16
cosocleC2×M16×C43C23
hypercenter#1327D43
hypocenterC43#11522
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
2. #19136404C2semidirect
3. #19132546C2semidirect
5. C43×#1327C2semidirect
108. #1327D43semidirect
127. C43#11522semidirect

Maximal subgroups

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

subgroupindex
#191432322
#191364042
#191325462
#191325302
C43×#13272
#1152243