Finite Group Databasebeta

← #25006080

Subgroups — #25006080

Order 11008.

504 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 75 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#19137318C211yesmaximal, characteristic
2#19132932C212yesmaximal, complemented
3#19132539C211yesmaximal, characteristic, complemented
4#19132526C212yesmaximal, complemented
5C43×#1324C211yesmaximal, characteristic, complemented
6C2×#13063322C411yescharacteristic
7C2×#13063287C411yescharacteristic
8C2×#13063287C2211yescharacteristic
9#14582861—22no—
10#14582800C411yescharacteristic
11#14582800C2211yescharacteristic
12#14582777—22no—
13#14582777—22no—
14#14582745C411yescharacteristic
15#14582625C2212yes—
16#14582622—22no—
17C43×#382C2211yescharacteristic
18C43×#324C2212yes—
19C22×D172—22no—
20C22×D172C2×C411yescharacteristic
21C22×D172C2×C411yescharacteristic
22C22×C4×D43—21no—
23C22×C4×D43D412yes—
24C2×#10621872—42no—
25#13063322—22no—
26#13063322—22no—
27#13063287—42no—
28#13063287—42no—
29C2×(C2×D43)⋊C4—21no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—22no—
32C2×(C2×D43)⋊C4D412yes—
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43C2×C411yescharacteristic
35C22⋊(C43⋊C8)—22no—
36(C2×D43)⋊C8—42no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43C2311yescharacteristic
41C2×C42×C43C2×C411yescharacteristic
42C22⋊C8×C43—22no—
43#95×C43—22no—
44C23×D43—21no—
45C23×D43C22⋊C412yes—
46C22×C4×C43—21no—
47C22×C4×C43—21no—
48C22×C4×C43C22×C411yescharacteristic
49C22×C4×C43C2×D412yes—
50C22×Dic43—21no—
51C22×Dic43C22⋊C411yescharacteristic
52C22×Dic43C22⋊C411yescharacteristic
53C2×D172—21no—
54C2×D172—21no—
55C2×D172—21no—
56C2×D172—28no—
57C2×D172—41no—
58C2×D172—41no—
59C2×D172—41no—
60C2×D172—41no—
61C2×D172—82no—
62C2×D172—82no—
63C2×D172M1612yescomplemented
64C2×C4×D43—22no—
65C2×C4×D43—22no—
66C2×C4×D43—42no—
67C2×C4×D43—82no—
68C2×C4×D43—82no—
69C2×C8×C43—42no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—41no—
72C42×C43—21no—
73C42×C43M1612yescomplemented
74(C2×D43)⋊C4—42no—
75(C2×D43)⋊C4—42no—
76(C2×D43)⋊C4—82no—
77(C2×D43)⋊C4—82no—
78C4×Dic43—22no—
79C4×Dic43—41no—
80C2×C43⋊C8—42no—
81#10621872—84no—
82C23×C43C2×C22⋊C411yescharacteristic
83C22×D43—22no—
84C22×D43—22no—
85C22×D43—22no—
86C22×D43—22no—
87C22×D43—42no—
88C22×D43—42no—
89C22×D43—42no—
90C22×D43—42no—
91C22×D43—41no—
92C22×D43—41no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—41no—
102C2×C4×C43C2×M1611yescharacteristic
103C2×C4×C43C2×M1611yescharacteristic
104C2×Dic43—21no—
105C2×Dic43—41no—
106C2×Dic43—41no—
107C2×Dic43—41no—
108C2×Dic43—41no—
109C2×Dic43—41no—
110C2×Dic43#9912yes—
111D172—42no—
112D172—42no—
113D172—42no—
114D172—42no—
115D172—88no—
116C4×D43—44no—
117C4×D43—82no—
118C4×D43—84no—
119C8×C43—82no—
120C43⋊C8—82no—
121#11533—431nomaximal, Sylow
122C22×C43—21no—
123C22×C43—21no—
124C22×C43#40711yescharacteristic
125C22×C43C2×#9911yescharacteristic
126C22×C43#41311yescharacteristic
127C2×D43—44no—
128C2×D43—44no—
129C2×D43—42no—
130C2×D43—42no—
131C2×D43—42no—
132C2×D43—42no—
133C2×D43—82no—
134C2×D43—81no—
135C2×D43—81no—
136C2×D43—82no—
137C4×C43—21no—
138C4×C43—21no—
139C4×C43—42no—
140C4×C43—42no—
141C4×C43—81no—
142Dic43—22no—
143Dic43—41no—
144Dic43—81no—
145#2328—431no—
146#1465—432no—
147#1324—431no—
148#1324D4311yescharacteristic, complemented
149#1318—432no—
150C2×C43—21no—
151C2×C43—21no—
152C2×C43#146511yescharacteristic
153C2×C43#212711yescharacteristic
154C2×C43#213411yescharacteristic
155D43—82no—
156D43—82no—
157C2×#127—431no—
158C2×C4×D4—431no—
159C2×C4×D4—431no—
160#407—862no—
161#390—431no—
162#390—431no—
163#386—862no—
164#386—862no—
165#382C2×D4311yescharacteristic
166#376—431no—
167#324—432no—
168#324C2×D4312yes—
169#323—862no—
170C43#1153311yescharacteristic, complemented, Sylow
171C22×D4—431no—
172C22×D4—431no—
173C22×D4—862no—
174C23×C4—432no—
175C23×C4—861no—
176C2×M16—1722no—
177#127—862no—
178#127—862no—
179C4×D4—1722no—
180C4×D4—1722no—
181C2×C4⋊C4C4×D4311yescharacteristic
182C2×C4⋊C4C22×D4311yescharacteristic
183C2×C22⋊C4—432no—
184C2×C22⋊C4—862no—
185C2×C22⋊C4—862no—
186C2×C22⋊C4—861no—
187C2×C42—431no—
188C2×C42—431no—
189C2×C42C4×D4311yescharacteristic
190C22⋊C8—22no—
191C22⋊C8—862no—
192C22⋊C8—1722no—
193#95—22no—
194#95—861no—
195#95—861no—
196C24—432no—
197C24—861no—
198C2×D4—432no—
199C2×D4—868no—
200C2×D4—861no—
201C2×D4—861no—
202C2×D4—861no—
203C2×D4—3442no—
204C2×D4—3442no—
205C2×D4—1721no—
206C2×D4—1721no—
207C2×D4—1721no—
208C2×D4—1721no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—431no—
212C22×C4—431no—
213C22×C4—862no—
214C22×C4—862no—
215C22×C4—861no—
216C22×C4—3442no—
217C22×C4—3442no—
218C22×C4—1722no—
219C22×C4C2×C4×D4311yescharacteristic
220C22×C4D4×D4312yes—
221M16—3444no—
222C2×C8—42no—
223C2×C8—1722no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C22⋊C4—3442no—
227C22⋊C4—3442no—
228C22⋊C4—1722no—
229C22⋊C4—1722no—
230C42—21no—
231C42—862no—
232C42—1721no—
233C42#1062187212yescomplemented
234C23—862no—
235C23—862no—
236C23—862no—
237C23—862no—
238C23—1722no—
239C23—1722no—
240C23—1722no—
241C23—1722no—
242C23—1721no—
243C23—1721no—
244C23C22⋊C4×D4311yescharacteristic
245D4—3448no—
246D4—1722no—
247D4—1722no—
248D4—1722no—
249D4—1722no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—432no—
260C2×C4—861no—
261C2×C4—3442no—
262C2×C4—3444no—
263C2×C4—1724no—
264C2×C4—1721no—
265C2×C4—1721no—
266C2×C4—1721no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4M16×D4311yescharacteristic
270C2×C4C2×#1062187211yescharacteristic
271C8—82no—
272C8—3442no—
273C22—21no—
274C22—21no—
275C22—3442no—
276C22—3442no—
277C22—3441no—
278C22—3441no—
279C22—1724no—
280C22—1724no—
281C22—1722no—
282C22—1722no—
283C22—1722no—
284C22—1722no—
285C22#1458286111yescharacteristic
286C22#99×D4311yescharacteristic
287C22#1458288211yescharacteristic
288C4—21no—
289C4—21no—
290C4—42no—
291C4—42no—
292C4—81no—
293C4—862no—
294C4—3441no—
295C4—1721no—
296C2—21no—
297C2—21no—
298C2—3442no—
299C2—3442no—
300C2#1913293211yescharacteristic
301C2#1913626311yescharacteristic
302C2#1913628511yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1324C2
socleC22×C43C2×#99
prime radicalC2×#13063322C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1324D43
hypocenterC43#11533
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
2. #19132932C2semidirect
3. #19132539C2semidirect
4. #19132526C2semidirect
5. C43×#1324C2semidirect
63. C2×D172M16semidirect
73. C42×C43M16semidirect
148. #1324D43semidirect
170. C43#11533semidirect
233. C42#10621872semidirect

Maximal subgroups

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

subgroupindex
#191373182
#191329322
#191325392
#191325262
C43×#13242
#1153343