Finite Group Databasebeta

← #24983979

Subgroups — #24983979

Order 11008.

268 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 43 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#19135400C211yesmaximal, characteristic
2#19132541C211yesmaximal, characteristic, complemented
3C43×#1325C211yesmaximal, characteristic, complemented
4C2×#13063322C411yescharacteristic
5C2×#13063245—21no—
6C2×#13063245—21no—
7C2×C4×C43⋊C8C411yescharacteristic
8#14582625—21no—
9C43×#384C2211yescharacteristic
10C43×#324—21no—
11C22×D172—21no—
12C22×D172—41no—
13C22×C43⋊C8—21no—
14#13063322—21no—
15#13063322—41no—
16#13063322C812yescomplemented
17#13063245—42no—
18#13063245—42no—
19C22⋊(C43⋊C8)—41no—
20C4×C43⋊C8—41no—
21C2×C4⋊C4×C43—41no—
22C2×C4⋊C4×C43D411yescharacteristic
23C2×C4⋊C4×C43D411yescharacteristic
24C2×C42×C43C2×C411yescharacteristic
25C22⋊C8×C43—41no—
26C23×D43—41no—
27C22×C4×C43—21no—
28C22×C4×C43—21no—
29C22×C4×C43—21no—
30C22×C4×C43C22⋊C411yescharacteristic
31C2×D172—22no—
32C2×D172—42no—
33C2×D172—41no—
34C2×D172—42no—
35C2×D172—41no—
36C2×D172—41no—
37C2×D172—41no—
38C2×D172—41no—
39C2×D172—82no—
40C2×D172—82no—
41C2×C8×C43—81no—
42C4⋊C4×C43—41no—
43C4⋊C4×C43—41no—
44C4⋊C4×C43—82no—
45C42×C43—21no—
46C42×C43C2×C811yescharacteristic
47C42×C43M1611yescharacteristic
48C2×C43⋊C8—22no—
49C2×C43⋊C8—41no—
50C2×C43⋊C8—41no—
51C2×C43⋊C8—81no—
52C23×C43#9911yescharacteristic
53C22×D43—42no—
54C22×D43—82no—
55C22×D43—82no—
56C22×D43—81no—
57C22×D43—81no—
58C2×C4×C43—22no—
59C2×C4×C43—22no—
60C2×C4×C43—21no—
61C2×C4×C43—21no—
62C2×C4×C43—21no—
63C2×C4×C43—21no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43—81no—
67C2×C4×C43—81no—
68C2×C4×C43C22⋊C811yescharacteristic
69C2×C4×C43#10011yescharacteristic
70D172—42no—
71D172—42no—
72D172—81no—
73D172—81no—
74D172—84no—
75D172—84no—
76C8×C43—161no—
77C43⋊C8—42no—
78C43⋊C8—161no—
79#7354—431nomaximal, Sylow
80C22×C43—21no—
81C22×C43—21no—
82C22×C43#32311yescharacteristic
83C22×C43#35311yescharacteristic
84C22×C43#35511yescharacteristic
85C2×D43—84no—
86C2×D43—82no—
87C2×D43—162no—
88C2×D43—161no—
89C2×D43—161no—
90C4×C43—22no—
91C4×C43—22no—
92C4×C43—21no—
93C4×C43—21no—
94C4×C43—81no—
95C4×C43—81no—
96#1957—431no—
97#1325—431no—
98#1325D4311yescharacteristic, complemented
99C2×C43—21no—
100C2×C43—21no—
101C2×C43#131811yescharacteristic
102C2×C43#140811yescharacteristic
103C2×C43#141011yescharacteristic
104D43—162no—
105C2×#127—431no—
106C2×#102—861no—
107C2×#102—861no—
108C2×C4×C8—431no—
109#384C2×D4311yescharacteristic
110#324—21no—
111#324—861no—
112C43#735411yescharacteristic, complemented, Sylow
113C22×D4—861no—
114C22×D4—1721no—
115C22×C8—861no—
116#127—432no—
117#127—861no—
118#127—1721no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4D17211yescharacteristic
121C2×C4⋊C4C22⋊D4311yescharacteristic
122C2×C42C4×D4311yescharacteristic
123#102—1722no—
124#102—1722no—
125C22⋊C8—41no—
126C22⋊C8—1721no—
127C4×C8—1721no—
128C24—1721no—
129C2×D4—862no—
130C2×D4—3442no—
131C2×D4—3442no—
132C2×D4—1722no—
133C2×D4—1722no—
134C2×D4—1721no—
135C2×D4—1721no—
136C2×D4—1721no—
137C2×D4—1721no—
138C2×D4—1721no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4(C2×D43)⋊C411yescharacteristic
143C2×C8—81no—
144C2×C8—862no—
145C2×C8—3441no—
146C2×C8—1721no—
147C2×C8—1721no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—82no—
151C42—21no—
152C42C8×D4311yescharacteristic
153C42#1062187211yescharacteristic
154C23—3442no—
155C23—3442no—
156C23—3441no—
157C23—3441no—
158C23—1722no—
159C23#1306323911yescharacteristic
160D4—3444no—
161D4—3444no—
162D4—3441no—
163D4—3441no—
164D4—1722no—
165D4—1722no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4(C2×D43)⋊C811yescharacteristic
177C2×C4#1306324111yescharacteristic
178C8—161no—
179C8—1722no—
180C8—6881no—
181C22—21no—
182C22—21no—
183C22—3444no—
184C22—3442no—
185C22—6882no—
186C22—6881no—
187C22—6881no—
188C22#1458262211yescharacteristic
189C22#1458269111yescharacteristic
190C22#1458269511yescharacteristic
191C4—22no—
192C4—22no—
193C4—21no—
194C4—21no—
195C4—81no—
196C4—81no—
197C2—21no—
198C2—21no—
199C2—6882no—
200C2#1913252611yescharacteristic
201C2#1913275711yescharacteristic
202C2#1913276111yescharacteristic
subgroupG/H
centerC22#14582691
commutatorC42×C43C2×C8
Frattini#384C2×D43
FittingC43×#1325C2
socleC22×C43#353
prime radicalC2×#13063322C4
cosocleC43×#384C22
hypercenter#1325D43
hypocenterC43#7354
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1325

Complements

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

NH ≅ G/Ntype
2. #19132541C2semidirect
3. C43×#1325C2semidirect
16. #13063322C8semidirect
98. #1325D43semidirect
112. C43#7354semidirect

Maximal subgroups

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

subgroupindex
#191354002
#191325412
C43×#13252
#735443