Finite Group Databasebeta

← #24983219

Subgroups — #24983219

Order 11008.

248 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 53 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#19135388C211yesmaximal, characteristic
2#19132535C211yesmaximal, characteristic, complemented
3C43×#1322C211yesmaximal, characteristic, complemented
4C2×C4×D172C411yescharacteristic
5C2×(C2×D43)⋊C8—21no—
6C2×(C2×D43)⋊C8—21no—
7C2×C4×C43⋊C8C411yescharacteristic
8C22⋊(C43⋊C16)—21no—
9C2×C4⋊C8×C43C2211yescharacteristic
10C43×C22⋊C16—21no—
11C22×D172C811yescharacteristic
12C22×C4×D43—21no—
13C22×C43⋊C8—21no—
14C4×D172—41no—
15C4×D172—41no—
16C2×C4⋊Dic43C811yescharacteristic
17C2×(C2×D43)⋊C4—21no—
18C2×C43⋊C16—41no—
19(C2×D43)⋊C8—42no—
20(C2×D43)⋊C8—42no—
21C4×C43⋊C8—41no—
22C22×C8×C43D411yescharacteristic
23C22×C8×C43D411yescharacteristic
24C2×C42×C43C2×C411yescharacteristic
25C2×C16×C43—41no—
26C4⋊C8×C43—41no—
27C23×D43—21no—
28C22×C4×C43C22⋊C411yescharacteristic
29C22×C4×C43C2×C811yescharacteristic
30C22×C4×C43M1611yescharacteristic
31C22×Dic43—21no—
32C2×D172—21no—
33C2×D172—41no—
34C2×D172—41no—
35C2×D172C1612yescomplemented
36C2×C4×D43—41no—
37C2×C4×D43—41no—
38C2×C4×D43—41no—
39C2×C4×D43—41no—
40C2×C4×D43—41no—
41C2×C4×D43—41no—
42C2×C8×C43—21no—
43C2×C8×C43—21no—
44C2×C8×C43—41no—
45C2×C8×C43—41no—
46C42×C43—21no—
47C42×C43—21no—
48(C2×D43)⋊C4—42no—
49C4⋊Dic43—41no—
50C2×C43⋊C8—22no—
51C2×C43⋊C8—41no—
52C2×C43⋊C8—41no—
53C16×C43—81no—
54C43⋊C16—81no—
55C23×C43C22⋊C811yescharacteristic
56C22×D43—22no—
57C22×D43—41no—
58C22×D43—41no—
59C22×D43—41no—
60C22×D43—41no—
61C22×D43—41no—
62C22×D43—41no—
63C2×C4×C43—21no—
64C2×C4×C43—21no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—41no—
69C2×C4×C43#9911yescharacteristic
70C2×C4×C43#10011yescharacteristic
71C2×C4×C43C2×C1611yescharacteristic
72C2×C4×C43M3211yescharacteristic
73C2×Dic43—41no—
74C2×Dic43—41no—
75C2×Dic43—41no—
76D172—42no—
77D172—42no—
78C4×D43—81no—
79C4×D43—81no—
80C4×D43—81no—
81C4×D43—81no—
82C8×C43—41no—
83C8×C43—41no—
84C43⋊C8—42no—
85#7056—431nomaximal, Sylow
86C22×C43—21no—
87C22×C43—21no—
88C22×C43#32311yescharacteristic
89C22×C43C22⋊C1611yescharacteristic
90C22×C43#34911yescharacteristic
91C2×D43—42no—
92C2×D43—42no—
93C2×D43—42no—
94C2×D43—81no—
95C2×D43—81no—
96C2×D43—81no—
97C2×D43—81no—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—21no—
101C4×C43—41no—
102C4×C43#35311yescharacteristic
103C4×C43#35511yescharacteristic
104Dic43—81no—
105#1954—431no—
106#1322—431no—
107#1322D4311yescharacteristic, complemented
108C2×C43—21no—
109C2×C43—21no—
110C2×C43#131411yescharacteristic
111C2×C43#131811yescharacteristic
112C2×C43#132111yescharacteristic
113D43—82no—
114C2×C4×D4—431no—
115C2×C4⋊C8C2×D4311yescharacteristic
116C2×C22⋊C8—861no—
117C2×C22⋊C8—861no—
118C2×C4×C8—431no—
119C22⋊C16—21no—
120C22⋊C16—861no—
121C43#705611yescharacteristic, complemented, Sylow
122C22×D4—431no—
123C23×C4—861no—
124C22×C8—861no—
125C22×C8D17211yescharacteristic
126C22×C8C22⋊D4311yescharacteristic
127C4×D4—1721no—
128C4×D4—1721no—
129C2×C4⋊C4—431no—
130C2×C22⋊C4—861no—
131C2×C42C4×D4311yescharacteristic
132C2×C16—41no—
133C2×C16—1721no—
134C4⋊C8—41no—
135C22⋊C8—1722no—
136C22⋊C8—1722no—
137C4×C8—1721no—
138C24—861no—
139C2×D4—432no—
140C2×D4—861no—
141C2×D4—1721no—
142C2×D4—1721no—
143C22×C4—861no—
144C22×C4—1721no—
145C22×C4—1721no—
146C22×C4—1721no—
147C22×C4—1721no—
148C22×C4—1721no—
149C22×C4—1721no—
150C22×C4C8×D4311yescharacteristic
151C22×C4#1062187211yescharacteristic
152C22×C4(C2×D43)⋊C411yescharacteristic
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—862no—
158C2×C8—1721no—
159C2×C8—1721no—
160C4⋊C4—1721no—
161C22⋊C4—1722no—
162C42—21no—
163C42—21no—
164C16—81no—
165C16—3441no—
166C23—862no—
167C23—1721no—
168C23—1721no—
169C23—1721no—
170C23—1721no—
171C23—1721no—
172C23—1721no—
173C23(C2×D43)⋊C811yescharacteristic
174D4—1722no—
175D4—1722no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—3441no—
183C2×C4—3441no—
184C2×C4—3441no—
185C2×C4—3441no—
186C2×C4—1721no—
187C2×C4—1721no—
188C2×C4—1721no—
189C2×C4#1306323911yescharacteristic
190C2×C4#1306324111yescharacteristic
191C2×C4C16×D4311yescharacteristic
192C2×C4#1306326411yescharacteristic
193C8—41no—
194C8—41no—
195C8—1722no—
196C22—21no—
197C22—21no—
198C22—3441no—
199C22—3441no—
200C22—3441no—
201C22—3441no—
202C22—1722no—
203C22—1722no—
204C22—1722no—
205C22#1458262211yescharacteristic
206C22(C2×D43)⋊C1611yescharacteristic
207C22#1458268011yescharacteristic
208C4—21no—
209C4—21no—
210C4—21no—
211C4—41no—
212C4—3441no—
213C4#1458269111yescharacteristic
214C4#1458269511yescharacteristic
215C2—21no—
216C2—21no—
217C2—3442no—
218C2#1913251811yescharacteristic
219C2#1913252611yescharacteristic
220C2#1913253211yescharacteristic
subgroupG/H
centerC2×C4#13063239
commutatorC2×C4×C43C2×C16
FrattiniC2×C4⋊C8C2×D43
FittingC43×#1322C2
socleC22×C43#323
prime radicalC22×D172C8
cosocleC2×C4⋊C8×C43C22
hypercenter#1322D43
hypocenterC43#7056
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
2. #19132535C2semidirect
3. C43×#1322C2semidirect
35. C2×D172C16semidirect
107. #1322D43semidirect
121. C43#7056semidirect

Maximal subgroups

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

subgroupindex
#191353882
#191325352
C43×#13222
#705643