Finite Group Databasebeta

← #24984869

Subgroups — #24984869

Order 11008.

468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 103 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#19137164C211yesmaximal, characteristic
2#19134342C212yesmaximal
3#19132421C211yesmaximal, characteristic
4#19132420C212yesmaximal
5C43×#1272C211yesmaximal, characteristic
6C2×#13063323C411yescharacteristic
7C2×Q8×Dic43C411yescharacteristic
8C2×#13063290C411yescharacteristic
9C2×#13063235—22no—
10#14582805C2211yescharacteristic
11#14582796—22no—
12#14582768C411yescharacteristic
13#14582750—22no—
14C42×Dic43C2211yescharacteristic
15#14582654C2212yes—
16#14582653—22no—
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86C2×C411yescharacteristic
20C22×C43⋊C8—22no—
21#13063323—22no—
22#13063323—22no—
23Q8×Dic43—42no—
24#13063290—42no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—22no—
30C2×C4×Dic43—21no—
31C2×C4×Dic43—21no—
32C2×C4×Dic43C2×C411yescharacteristic
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43D412yes—
35C2×C4×Dic43D412yes—
36#13063235—28no—
37C43⋊#95—22no—
38C22×Q8×C43C2×C411yescharacteristic
39C22×C8×C43—22no—
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C42×C43C2311yescharacteristic
42#95×C43—22no—
43C2×Q8×C43—21no—
44C2×Q8×C43—41no—
45C2×Q8×C43—41no—
46C2×Q8×C43M1612yes—
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43C22×C411yescharacteristic
50C22×C4×C43C2×D412yes—
51C22×Dic43—21no—
52C22×Dic43—21no—
53C22×Dic43C22⋊C411yescharacteristic
54C22×Dic43C22⋊C411yescharacteristic
55C22×Dic43C22⋊C412yes—
56C2×Dic86—21no—
57C2×Dic86—41no—
58C2×Dic86—41no—
59C2×Dic86M1612yes—
60C2×C8×C43—24no—
61C2×C8×C43—42no—
62C2×C8×C43—42no—
63C4⋊C4×C43—41no—
64C42×C43—41no—
65C4⋊Dic43—42no—
66C4⋊Dic43—41no—
67Dic43⋊C4—28no—
68Dic43⋊C4—42no—
69Dic43⋊C4—44no—
70C4×Dic43—21no—
71C4×Dic43—21no—
72C4×Dic43—22no—
73C4×Dic43—22no—
74C4×Dic43—22no—
75C4×Dic43—24no—
76C4×Dic43—42no—
77C4×Dic43—42no—
78C2×C43⋊C8—24no—
79C2×C43⋊C8—42no—
80C2×C43⋊C8—42no—
81C23×C43C2×C22⋊C411yescharacteristic
82Q8×C43—42no—
83Q8×C43—42no—
84C2×C4×C43—22no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—41no—
90C2×C4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43—42no—
93C2×C4×C43C2×M1611yescharacteristic
94C2×C4×C43C2×M1611yescharacteristic
95C2×C4×C43#13712yes—
96C2×C4×C43#13712yes—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—22no—
101C2×Dic43—21no—
102C2×Dic43—22no—
103C2×Dic43—41no—
104C2×Dic43—41no—
105C2×Dic43—41no—
106C2×Dic43—42no—
107C2×Dic43#10012yes—
108C2×Dic43#10414yes—
109Dic86—42no—
110Dic86—42no—
111C8×C43—44no—
112C43⋊C8—44no—
113#7639—431nomaximal, Sylow
114C22×C43#40711yescharacteristic
115C22×C43#41011yescharacteristic
116C22×C43C2×#10011yescharacteristic
117C22×C43#41912yes—
118C22×C43C2×#10412yes—
119C4×C43—21no—
120C4×C43—21no—
121C4×C43—22no—
122C4×C43—22no—
123C4×C43—42no—
124C4×C43—81no—
125Dic43—22no—
126Dic43—24no—
127Dic43—42no—
128Dic43—41no—
129Dic43—81no—
130C4×C4⋊Q8—431no—
131#1745—432no—
132#1272—431no—
133#1272—432no—
134#1272D4311yescharacteristic
135C2×C43#146611yescharacteristic
136C2×C43#149112yes—
137C2×C43#150612yes—
138C2×C43#152511yescharacteristic
139C2×C43#155811yescharacteristic
140C2×C4⋊Q8—431no—
141C2×C4×Q8—431no—
142C2×C4×Q8—431no—
143C2×#97—862no—
144#391—431no—
145#391C2×D4311yescharacteristic
146#389—862no—
147#384—431no—
148C4×C4⋊C4—862no—
149C43—431no—
150#336—432no—
151#336—862no—
152#336C2×D4312yes—
153C43#763911yescharacteristic, complemented, Sylow
154C22×Q8—431no—
155C22×Q8C4×D4311yescharacteristic
156C22×C8—22no—
157C22×C8—862no—
158C4⋊Q8—862no—
159C4⋊Q8—862no—
160C4×Q8—1722no—
161C4×Q8—1722no—
162C2×C4⋊C4—431no—
163C2×C4⋊C4—862no—
164C2×C4⋊C4—861no—
165C2×C4⋊C4—861no—
166C2×C4⋊C4—862no—
167C2×C4⋊C4C4×D4311yescharacteristic
168C2×C42—431no—
169C2×C42—431no—
170C2×C42—432no—
171C2×C42—432no—
172C2×C42—861no—
173C2×C42—861no—
174C2×C42C22×D4311yescharacteristic
175#97—868no—
176#95—22no—
177#95—862no—
178C2×Q8—21no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—432no—
182C2×Q8—861no—
183C2×Q8—1721no—
184C2×Q8—1721no—
185C2×Q8#1062187212yes—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—431no—
189C22×C4—432no—
190C22×C4—431no—
191C22×C4—861no—
192C22×C4—861no—
193C22×C4C2×C4×D4311yescharacteristic
194C22×C4D4×D4312yes—
195C2×C8—24no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—864no—
199C2×C8—1722no—
200C2×C8—1722no—
201C4⋊C4—41no—
202C4⋊C4—868no—
203C4⋊C4—1721no—
204C4⋊C4—1724no—
205C4⋊C4—1722no—
206C4⋊C4—1722no—
207C42—41no—
208C42—864no—
209C42—862no—
210C42—861no—
211C42—861no—
212C42—862no—
213C42—862no—
214C42—1722no—
215C42—1722no—
216C23C22⋊C4×D4311yescharacteristic
217Q8—42no—
218Q8—42no—
219Q8—1722no—
220Q8—1722no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—432no—
231C2×C4—434no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—862no—
235C2×C4—862no—
236C2×C4—861no—
237C2×C4—862no—
238C2×C4—1721no—
239C2×C4—1722no—
240C2×C4—1721no—
241C2×C4—1721no—
242C2×C4M16×D4311yescharacteristic
243C2×C4C2×#1062187211yescharacteristic
244C2×C4#1306335412yes—
245C2×C4#1306335712yes—
246C8—44no—
247C8—1724no—
248C22#1458286111yescharacteristic
249C22#1458287111yescharacteristic
250C22#100×D4311yescharacteristic
251C22#1458290612yes—
252C22#104×D4312yes—
253C4—21no—
254C4—21no—
255C4—22no—
256C4—22no—
257C4—42no—
258C4—81no—
259C4—864no—
260C4—862no—
261C4—3441no—
262C4—1721no—
263C4—1722no—
264C2#1913293411yescharacteristic
265C2#1913304012yes—
266C2#1913310512yes—
267C2#1913318511yescharacteristic
268C2#1913331911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socle, prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7639
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
153. C43#7639semidirect

Maximal subgroups

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

subgroupindex
#191371642
#191343422
#191324212
#191324202
C43×#12722
#763943