Finite Group Databasebeta

← #25064351

Subgroups — #25064351

Order 11008.

938 conjugacy classes of subgroups; only the 355 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 355 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#19148405C211yesmaximal, characteristic
2#19137516C211yesmaximal, characteristic
3#19133160C216yesmaximal
4#19133095C216yesmaximal
5C43×#2982C211yesmaximal, characteristic
6Q8×Dic86C414yescomplemented
7#14583628C414yescomplemented
8#14583625—24no—
9#14583530—23no—
10#14583456C2216yes—
11#14583377—21no—
12C2×Q8×Dic43—21no—
13#14582798—23no—
14#14582765C2213yes—
15C4×C4⋊Dic43C2213yes—
16#14582637C2214yes—
17#14582637C22112yes—
18C2×C4×Q8×C43C2211yescharacteristic
19C8×Q8×C43—24no—
20C43×#431C2216yes—
21#13063325C2×C416yes—
22#13063325C2×C416yes—
23#13063324—212no—
24#13063317—26no—
25#13063316—212no—
26#13063304—26no—
27#13063304C2314yes—
28Q8×Dic43—24no—
29Q8×Dic43—24no—
30Q8×Dic43—44no—
31C4×Dic86—26no—
32C4×Dic86C2×C4112yes—
33#13063284—26no—
34C2×C4⋊Dic43—23no—
35C2×C4⋊Dic43—23no—
36C2×C4×Dic43—23no—
37C43⋊#95—23no—
38C43⋊#95C2311yescharacteristic
39C43⋊#95C2313yes—
40C22×Q8×C43D411yescharacteristic
41C4×Q8×C43C2×C414yes—
42C4×Q8×C43D414yes—
43C2×C4⋊C4×C43D413yes—
44C2×C42×C43C2313yes—
45C4⋊C8×C43—26no—
46C22⋊C8×C43C2314yes—
47C4×C8×C43—26no—
48C2×Q8×C43C22⋊C414yes—
49C2×Q8×C43SD1614yes—
50C2×Q8×C43Q1614yes—
51C22×C4×C43C2×D413yes—
52C22×C4×C43C2×D413yes—
53C22×C4×C43C2411yescharacteristic
54C22×Dic43—21no—
55C22×Dic43—23no—
56C2×Dic86—26no—
57C2×Dic86C22×C414yes—
58C2×C8×C43—24no—
59C4⋊C4×C43C22⋊C4112yes—
60C42×C43C22×C416yes—
61C42×C43C2×D416yes—
62C22⋊Dic43—24no—
63C4⋊Dic43—26no—
64C4⋊Dic43—26no—
65C4⋊Dic43—26no—
66C4⋊Dic43—46no—
67C4⋊Dic43—46no—
68C4⋊Dic43C22×C414yes—
69Dic43⋊C4—212no—
70Dic43⋊C4—24no—
71C4×Dic43—212no—
72C4×Dic43—46no—
73C23×C43C22×D411yescharacteristic
74Q8×C43#103116yes—
75C2×C4×C43—43no—
76C2×C4×C43—41no—
77C2×C4×C43C2×C22⋊C416yes—
78C2×C4×C43C2×C22⋊C416yes—
79C2×C4×C43C2×SD1616yes—
80C2×C4×C43C2×Q1616yes—
81C2×C4×C43C23×C411yescharacteristic
82C2×C4×C43C22×D411yescharacteristic
83C2×Dic43—22no—
84C2×Dic43—24no—
85C2×Dic43—24no—
86C2×Dic43—41no—
87C2×Dic43—41no—
88C2×Dic43—43no—
89C2×Dic43—43no—
90C2×Dic43—43no—
91Dic86—44no—
92Dic86—86no—
93C8×C43—44no—
94#17619—431nomaximal, Sylow
95C22×C43—21no—
96C22×C43—21no—
97C22×C43C22×C22⋊C411yescharacteristic
98C22×C43C22×SD1611yescharacteristic
99C22×C43C22×Q1611yescharacteristic
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—26no—
103C4×C43C2×#103112yes—
104Dic43—42no—
105Dic43—44no—
106Dic43—44no—
107Dic43—83no—
108#3502—431no—
109#2982D4311yescharacteristic
110#2351—431no—
111#1518—436no—
112#1503—436no—
113C2×C43—21no—
114C2×C43—21no—
115C2×C43#288411yescharacteristic
116C2×C43C22×#10311yescharacteristic
117C2×C43#290111yescharacteristic
118Q82—434no—
119#557—434no—
120#557—864no—
121#544—863no—
122#533—436no—
123#519—861no—
124C2×C4×Q8—861no—
125C2×C4×Q8C2×D4311yescharacteristic
126C8×Q8—24no—
127#431C2×D4316yes—
128#389—863no—
129#382—433no—
130C4×C4⋊C4—433no—
131#328—434no—
132#328—4312no—
133C43#1761911yescharacteristic, complemented, Sylow
134C22×Q8D17211yescharacteristic
135C4⋊Q8—436no—
136C4⋊Q8—436no—
137C4⋊Q8—8612no—
138#125—8612no—
139#125—866no—
140C22⋊Q8—434no—
141C22⋊Q8—866no—
142C4×Q8—4312no—
143C4×Q8—864no—
144C4×Q8—864no—
145C4×Q8—866no—
146C4×Q8—1724no—
147C4×Q8C4×D4314yes—
148C4×Q8C22⋊D4314yes—
149#117—866no—
150C2×C4⋊C4—863no—
151C2×C4⋊C4—863no—
152C2×C4⋊C4D17213yes—
153C2×C42—863no—
154C2×C42C22×D4313yes—
155C4⋊C8—26no—
156C22⋊C8C22×D4314yes—
157C4×C8—26no—
158#95—431no—
159#95—433no—
160#95—863no—
161C2×Q8—434no—
162C2×Q8—866no—
163C2×Q8#1062187314yes—
164C2×Q8Dic17214yes—
165C2×Q8(C2×D43)⋊C414yes—
166C22×C4—861no—
167C22×C4—863no—
168C22×C4C2×D17213yes—
169C22×C4C2×D17213yes—
170C22×C4C23×D4311yescharacteristic
171C2×C8—24no—
172C4⋊C4—434no—
173C4⋊C4—866no—
174C4⋊C4—866no—
175C4⋊C4—8612no—
176C4⋊C4—866no—
177C4⋊C4—864no—
178C4⋊C4—1726no—
179C4⋊C4—1726no—
180C4⋊C4(C2×D43)⋊C4112yes—
181C22⋊C4—864no—
182C42—8612no—
183C42—1726no—
184C42C2×C4×D4316yes—
185C42C2×C22⋊D4316yes—
186C23C22×D17211yescharacteristic
187Q8—3446no—
188Q8—1724no—
189Q8#13063250116yes—
190C2×C4—43no—
191C2×C4—41no—
192C2×C4—862no—
193C2×C4—864no—
194C2×C4—864no—
195C2×C4—1723no—
196C2×C4—1723no—
197C2×C4—1723no—
198C2×C4—1721no—
199C2×C4—1721no—
200C2×C4C2×(C2×D43)⋊C416yes—
201C2×C4C2×(C2×D43)⋊C416yes—
202C2×C4C2×#1062187316yes—
203C2×C4C2×Dic17216yes—
204C2×C4C22×C4×D4311yescharacteristic
205C2×C4C22×C22⋊D4311yescharacteristic
206C8—44no—
207C22—21no—
208C22—21no—
209C22C22×(C2×D43)⋊C411yescharacteristic
210C22C22×#1062187311yescharacteristic
211C22C22×Dic17211yescharacteristic
212C4—21no—
213C4—21no—
214C4—26no—
215C4—3443no—
216C4—1722no—
217C4—1724no—
218C4—1724no—
219C4C2×#13063250112yes—
220C2—21no—
221C2—21no—
222C2#1914305811yescharacteristic
223C2C22×#1306325011yescharacteristic
224C2#1914314011yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2982C2
socleC22×C43C22×C22⋊C4
prime radicalC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenter#2982D43
hypocenterC43#17619
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2982

Complements

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

NH ≅ G/Ntype
6. Q8×Dic86C4semidirect
7. #14583628C4semidirect
133. C43#17619semidirect

Maximal subgroups

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

subgroupindex
#191484052
#191375162
#191331602
#191330952
C43×#29822
#1761943