Finite Group Databasebeta

← #24990189

Subgroups — #24990189

Order 11008.

378 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 107 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#19137560C211yesmaximal, characteristic
2#19134591C211yesmaximal, characteristic
3#19132497C212yesmaximal
4#19132454C212yesmaximal
5C43×#1461C211yesmaximal, characteristic
6#14582923C2212yes—
7C2×#13063244—21no—
8#14582806—21no—
9#14582785—22no—
10#14582767C412yes—
11#14582765C2211yescharacteristic
12C4⋊C4×Dic43—21no—
13C4×C4⋊Dic43C2211yescharacteristic
14#14582745C412yes—
15#14582668—21no—
16C2×C4×Q8×C43C2211yescharacteristic
17C43×#431C2212yes—
18C43×#324—22no—
19C2×#10621877—22no—
20C2×C4⋊Dic43—21no—
21C2×C4⋊Dic43—21no—
22C2×C4×Dic43—22no—
23C2×C4×Dic43—21no—
24C4⋊(C43⋊C8)—22no—
25C4⋊(C43⋊C8)—22no—
26#13063244—42no—
27C43⋊#95—22no—
28C43⋊#95—22no—
29C43⋊#95—22no—
30C43⋊#95—21no—
31C43⋊#95C2×C411yescharacteristic
32C43⋊#95C2×C412yes—
33C43⋊#95C2×C411yescharacteristic
34C22×Q8×C43D411yescharacteristic
35C4×Q8×C43—22no—
36C4×Q8×C43—22no—
37C2×C4⋊C4×C43D411yescharacteristic
38C2×C4⋊C4×C43D412yes—
39C2×C42×C43C2×C412yes—
40C2×C42×C43C2311yescharacteristic
41C4⋊C8×C43—22no—
42C22⋊C8×C43—22no—
43C4×C8×C43—22no—
44C2×Q8×C43—22no—
45C2×Q8×C43—22no—
46C2×Q8×C43—21no—
47C2×Q8×C43—21no—
48C22×C4×C43C22⋊C412yes—
49C22×C4×C43C22⋊C412yes—
50C22×C4×C43C22×C411yescharacteristic
51C22×C4×C43C2×D411yescharacteristic
52C22×C4×C43C2×D411yescharacteristic
53C22×Dic43—21no—
54C22×Dic43—22no—
55C22×Dic43—21no—
56C2×C8×C43—42no—
57C4⋊C4×C43—24no—
58C4⋊C4×C43—22no—
59C42×C43—22no—
60C42×C43—22no—
61C42×C43#4112yes—
62C42×C43#4112yes—
63C4⋊Dic43—42no—
64C4⋊Dic43—41no—
65C4⋊Dic43—41no—
66C4×Dic43—44no—
67C4×Dic43—42no—
68#10621877—42no—
69#10621877—42no—
70C2×C43⋊C8—42no—
71C23×C43C2×C22⋊C411yescharacteristic
72Q8×C43—42no—
73Q8×C43—42no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43—42no—
81C2×C4×C43#11711yescharacteristic
82C2×C4×C43#11711yescharacteristic
83C2×C4×C43#12312yes—
84C2×C4×C43#12312yes—
85C2×C4×C43#13512yes—
86C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
87C2×C4×C43#13711yescharacteristic
88C2×Dic43—22no—
89C2×Dic43—41no—
90C2×Dic43—41no—
91C2×Dic43—42no—
92C2×Dic43—41no—
93C2×Dic43—41no—
94C2×Dic43—42no—
95C2×Dic43—41no—
96C2×Dic43—42no—
97C8×C43—82no—
98C43⋊C8—82no—
99#8769—431nomaximal, Sylow
100C22×C43—21no—
101C22×C43—21no—
102C22×C43#38111yescharacteristic
103C22×C43#41611yescharacteristic
104C22×C43#41711yescharacteristic
105C4×C43—22no—
106C4×C43—21no—
107C4×C43—21no—
108C4×C43—42no—
109C4×C43—42no—
110C4×C43#48212yes—
111C4×C43#48512yes—
112Dic43—42no—
113Dic43—81no—
114Dic43—82no—
115#2356—431no—
116#1801—431no—
117#1461D4311yescharacteristic
118#1303—432no—
119#1286—432no—
120C2×C43—21no—
121C2×C43—21no—
122C2×C43#182511yescharacteristic
123C2×C43#182711yescharacteristic
124C2×C43#183011yescharacteristic
125C2×C4×Q8C2×D4311yescharacteristic
126#431C2×D4312yes—
127#423—432no—
128C2×#101—861no—
129#391—861no—
130#387—862no—
131#383—432no—
132#382—431no—
133C4×C4⋊C4—431no—
134C4×C4⋊C4—861no—
135#376—432no—
136#343—861no—
137#324—22no—
138C43#876911yescharacteristic, complemented, Sylow
139C22×Q8D17211yescharacteristic
140C2×M16—862no—
141C4×Q8—22no—
142C4×Q8—22no—
143C2×C4⋊C4—861no—
144C2×C4⋊C4—861no—
145C2×C4⋊C4D17211yescharacteristic
146C2×C4⋊C4C22⋊D4312yes—
147C2×C42—862no—
148C2×C42—861no—
149C2×C42C4×D4312yes—
150C2×C42C22×D4311yescharacteristic
151C4⋊C8—22no—
152C4⋊C8—862no—
153C4⋊C8—862no—
154#101—1722no—
155C22⋊C8—22no—
156C4×C8—22no—
157#95—431no—
158#95—432no—
159#95—431no—
160#95—862no—
161#95—862no—
162#95—862no—
163#95—861no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—21no—
167C2×Q8—21no—
168C22×C4—861no—
169C22×C4—862no—
170C22×C4—861no—
171C22×C4(C2×D43)⋊C412yes—
172C22×C4(C2×D43)⋊C412yes—
173C22×C4C2×C4×D4311yescharacteristic
174C22×C4C2×D17211yescharacteristic
175C22×C4C2×C22⋊D4311yescharacteristic
176M16—1722no—
177M16—1722no—
178C2×C8—42no—
179C2×C8—1722no—
180C4⋊C4—24no—
181C4⋊C4—22no—
182C4⋊C4—1722no—
183C4⋊C4—1721no—
184C4⋊C4—1721no—
185C42—22no—
186C42—22no—
187C42—1724no—
188C42—1722no—
189C42#1062190012yes—
190C42#1062190012yes—
191C23C2×(C2×D43)⋊C411yescharacteristic
192Q8—42no—
193Q8—42no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—862no—
202C2×C4—1722no—
203C2×C4—1721no—
204C2×C4—1722no—
205C2×C4—1721no—
206C2×C4—1721no—
207C2×C4—1722no—
208C2×C4—1721no—
209C2×C4—1721no—
210C2×C4#1306328111yescharacteristic
211C2×C4#1306328111yescharacteristic
212C2×C4#1306330612yes—
213C2×C4#1306330912yes—
214C2×C4#1306334712yes—
215C2×C4#1306335311yescharacteristic
216C2×C4#1306335811yescharacteristic
217C8—82no—
218C8—3442no—
219C22—21no—
220C22—21no—
221C22#1458276011yescharacteristic
222C22#1458289611yescharacteristic
223C22#1458290111yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—42no—
228C4—42no—
229C4—3442no—
230C4—3441no—
231C4—1722no—
232C4#1458322412yes—
233C4#1458324112yes—
234C2—21no—
235C2—21no—
236C2#1913469111yescharacteristic
237C2#1913469611yescharacteristic
238C2#1913470711yescharacteristic
subgroupG/H
centerC22#14582760
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1461C2
socleC22×C43#381
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1461D43
hypocenterC43#8769
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
138. C43#8769semidirect

Maximal subgroups

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

subgroupindex
#191375602
#191345912
#191324972
#191324542
C43×#14612
#876943