Finite Group Databasebeta

← #25006078

Subgroups — #25006078

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#19137319C211yesmaximal, characteristic
2#19132932C212yesmaximal, complemented
3#19132538C212yesmaximal, complemented
4#19132527C211yesmaximal, characteristic, complemented
5C43×#1318C211yesmaximal, characteristic, complemented
6C2×#13063321C411yescharacteristic
7C2×D4×Dic43C411yescharacteristic
8C2×#13063287C2211yescharacteristic
9#14582861—22no—
10#14582801C411yescharacteristic
11#14582776—22no—
12#14582775—22no—
13#14582764C2211yescharacteristic
14#14582745C411yescharacteristic
15#14582625C2212yes—
16#14582622—22no—
17C43×#390C2211yescharacteristic
18C43×#324C2212yes—
19C22×D172C2×C411yescharacteristic
20C22×C22⋊D43—22no—
21C23×Dic43—21no—
22C22×C4×D43D412yes—
23C2×#10621872—42no—
24#13063321—22no—
25#13063321—22no—
26D4×Dic43—42no—
27#13063287—42no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C22⋊Dic43—21no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4D412yes—
32C2×C4×Dic43C2×C411yescharacteristic
33C2×C4×Dic43C2×C411yescharacteristic
34C22⋊(C43⋊C8)—22no—
35(C2×D43)⋊C8—42no—
36C43⋊#95—22no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C22×D4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43C2311yescharacteristic
41C2×C22⋊C4×C43—22no—
42C2×C42×C43C2×C411yescharacteristic
43C22⋊C8×C43—22no—
44C24×C43—21no—
45C23×D43C22⋊C412yes—
46C2×D4×C43—21no—
47C2×D4×C43—41no—
48C2×D4×C43—41no—
49C2×D4×C43M1612yescomplemented
50C22×C4×C43—21no—
51C22×C4×C43C22×C411yescharacteristic
52C22×C4×C43C2×D412yes—
53C2×C22⋊D43—28no—
54C2×C22⋊D43—82no—
55C2×C22⋊D43—82no—
56C22×Dic43—21no—
57C22×Dic43—21no—
58C22×Dic43—42no—
59C22×Dic43—82no—
60C22×Dic43C22⋊C411yescharacteristic
61C22×Dic43C22⋊C411yescharacteristic
62C2×D172—21no—
63C2×D172—21no—
64C2×D172—41no—
65C2×D172—41no—
66C2×C4×D43—22no—
67C2×C4×D43—22no—
68C2×C4×D43—82no—
69C2×C8×C43—42no—
70C4⋊C4×C43—41no—
71C22⋊C4×C43—82no—
72C42×C43—41no—
73C22⋊Dic43—42no—
74(C2×D43)⋊C4—42no—
75(C2×D43)⋊C4—82no—
76C4⋊Dic43—41no—
77C4×Dic43—21no—
78C4×Dic43—22no—
79C4×Dic43M1612yescomplemented
80C2×C43⋊C8—42no—
81#10621872—84no—
82C23×C43—22no—
83C23×C43—42no—
84C23×C43—42no—
85C23×C43—41no—
86C23×C43—41no—
87C23×C43C2×C22⋊C411yescharacteristic
88C22×D43—22no—
89C22×D43—22no—
90C22×D43—22no—
91C22×D43—42no—
92C22×D43—42no—
93D4×C43—42no—
94D4×C43—42no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—42no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43C2×M1611yescharacteristic
103C2×C4×C43C2×M1611yescharacteristic
104C22⋊D43—88no—
105C2×Dic43—22no—
106C2×Dic43—21no—
107C2×Dic43—41no—
108C2×Dic43—41no—
109C2×Dic43—41no—
110C2×Dic43—41no—
111C2×Dic43—42no—
112C2×Dic43—41no—
113C2×Dic43—84no—
114C2×Dic43#9912yes—
115D172—42no—
116D172—42no—
117C4×D43—44no—
118C4×D43—82no—
119C8×C43—82no—
120C43⋊C8—82no—
121#11533—431nomaximal, Sylow
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—44no—
125C22×C43—42no—
126C22×C43—82no—
127C22×C43—81no—
128C22×C43—81no—
129C22×C43#40711yescharacteristic
130C22×C43C2×#9911yescharacteristic
131C22×C43#41311yescharacteristic
132C2×D43—44no—
133C2×D43—42no—
134C2×D43—42no—
135C2×D43—42no—
136C2×D43—82no—
137C4×C43—21no—
138C4×C43—21no—
139C4×C43—42no—
140C4×C43—81no—
141Dic43—22no—
142Dic43—42no—
143Dic43—41no—
144Dic43—81no—
145#2328—431no—
146#1465—432no—
147#1324—432no—
148#1318—431no—
149#1318D4311yescharacteristic, complemented
150C2×C43—21no—
151C2×C43—21no—
152C2×C43—82no—
153C2×C43#146511yescharacteristic
154C2×C43#212711yescharacteristic
155C2×C43#213411yescharacteristic
156D43—82no—
157C2×#127—431no—
158C2×C4×D4—431no—
159C2×C4×D4—431no—
160#407—862no—
161#390—431no—
162#390C2×D4311yescharacteristic
163#386—862no—
164#386—862no—
165#382—431no—
166#376—431no—
167#324—432no—
168#324C2×D4312yes—
169#323—862no—
170C43#1153311yescharacteristic, complemented, Sylow
171C22×D4—431no—
172C22×D4—862no—
173C22×D4C4×D4311yescharacteristic
174C23×C4—432no—
175C23×C4—861no—
176C2×M16—1722no—
177#127—862no—
178#127—862no—
179C4×D4—1722no—
180C4×D4—1722no—
181C2×C4⋊C4—431no—
182C2×C4⋊C4C22×D4311yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—432no—
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—861no—
194#95—861no—
195#95—862no—
196C24—21no—
197C24—432no—
198C2×D4—21no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4—868no—
202C2×D4—861no—
203C2×D4—861no—
204C2×D4—3442no—
205C2×D4—3442no—
206C2×D4—1721no—
207C2×D4—1721no—
208C2×D4#1062187212yescomplemented
209C22×C4—21no—
210C22×C4—431no—
211C22×C4—431no—
212C22×C4—862no—
213C22×C4—862no—
214C22×C4—861no—
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—1721no—
226C22⋊C4—82no—
227C22⋊C4—3442no—
228C22⋊C4—1722no—
229C22⋊C4—1722no—
230C42—41no—
231C42—432no—
232C42—862no—
233C42—861no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23—41no—
238C23—41no—
239C23—862no—
240C23—862no—
241C23—862no—
242C23—1722no—
243C23—1722no—
244C23C22⋊C4×D4311yescharacteristic
245D4—42no—
246D4—42no—
247D4—3448no—
248D4—1722no—
249D4—1722no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—432no—
258C2×C4—862no—
259C2×C4—861no—
260C2×C4—3442no—
261C2×C4—3444no—
262C2×C4—1724no—
263C2×C4—1721no—
264C2×C4—1722no—
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—44no—
276C22—42no—
277C22—82no—
278C22—81no—
279C22—81no—
280C22—3442no—
281C22—1724no—
282C22—1722no—
283C22—1722no—
284C22—1722no—
285C22#1458286111yescharacteristic
286C22#99×D4311yescharacteristic
287C22#1458288011yescharacteristic
288C4—21no—
289C4—21no—
290C4—42no—
291C4—81no—
292C4—862no—
293C4—3441no—
294C4—1722no—
295C4—1721no—
296C2—21no—
297C2—21no—
298C2—82no—
299C2—3442no—
300C2#1913293011yescharacteristic
301C2#1913626111yescharacteristic
302C2#1913628511yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1318C2
socleC22×C43C2×#99
prime radicalC2×#13063321C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1318D43
hypocenterC43#11533
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #19132932C2semidirect
3. #19132538C2semidirect
4. #19132527C2semidirect
5. C43×#1318C2semidirect
49. C2×D4×C43M16semidirect
79. C4×Dic43M16semidirect
149. #1318D43semidirect
170. C43#11533semidirect
208. C2×D4#10621872semidirect

Maximal subgroups

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

subgroupindex
#191373192
#191329322
#191325382
#191325272
C43×#13182
#1153343