Finite Group Databasebeta

← #25009004

Subgroups — #25009004

Order 11008.

588 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135819C211yesmaximal, characteristic, complemented
2#19133529C212yesmaximal, complemented
3#19132598C212yesmaximal, complemented
4#19132541C211yesmaximal, characteristic, complemented
5C43×#2537C211yesmaximal, characteristic, complemented
6#14583480C2211yescharacteristic
7#14583033—22no—
8C2×#13063253—21no—
9#14582898—21no—
10#14582668C2211yescharacteristic
11#14582632—22no—
12#14582625C2212yes—
13C2×#121×C43—22no—
14C2×C4×D4×C43—21no—
15C43×#394—21no—
16C43×#394C2212yes—
17C43×#384C2211yescharacteristic
18C43×#380—22no—
19C2×#10621898—21no—
20C2×#10621882—42no—
21C2×#10621877—21no—
22#13063305—41no—
23#13063300—41no—
24#13063299—22no—
25#13063253—42no—
26#13063248—41no—
27#13063246—42no—
28#13063245—41no—
29C22⋊(C43⋊C8)—22no—
30C22×D4×C43—21no—
31C22×D4×C43—21no—
32C22×D4×C43D412yes—
33C23×C4×C43—22no—
34#121×C43—48no—
35C4×D4×C43—42no—
36C4×D4×C43—42no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—22no—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C4⋊C4×C43C2311yescharacteristic
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—22no—
43C2×C22⋊C4×C43—22no—
44C2×C42×C43D411yescharacteristic
45#95×C43—21no—
46#95×C43D412yes—
47C24×C43—22no—
48C2×D4×C43—24no—
49C2×D4×C43—44no—
50C2×D4×C43—44no—
51C2×D4×C43—42no—
52C2×D4×C43—42no—
53C2×D4×C43—42no—
54C2×D4×C43—81no—
55C22×C4×C43—21no—
56C22×C4×C43—22no—
57C22×C4×C43—21no—
58C22×C4×C43—44no—
59C22×C4×C43—44no—
60C22×C4×C43—44no—
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D412yes—
63C2×C22⋊D43—41no—
64#10621898—41no—
65#10621898—41no—
66#10621898—41no—
67#10621898—41no—
68C2×D172—21no—
69C2×D172—22no—
70C2×C4×D43—41no—
71C2×Dic86—21no—
72C4⋊C4×C43—41no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—42no—
75C4⋊C4×C43—44no—
76C22⋊C4×C43—44no—
77C22⋊C4×C43—44no—
78C22⋊C4×C43—42no—
79C22⋊C4×C43—42no—
80C42×C43—21no—
81C42×C43D812yescomplemented
82#10621882—84no—
83(C2×D43)⋊C4—42no—
84C4⋊Dic43—22no—
85#10621877—41no—
86#10621877—41no—
87C2×C43⋊C8—42no—
88C2×C43⋊C8—41no—
89C23×C43—24no—
90C23×C43—42no—
91C23×C43—42no—
92C23×C43—42no—
93C23×C43—42no—
94C23×C43—42no—
95C23×C43—42no—
96C23×C43#12011yescharacteristic
97C22×D43—41no—
98D4×C43—48no—
99D4×C43—44no—
100D4×C43—82no—
101D4×C43—84no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—41no—
114C2×C4×C43—88no—
115C2×C4×C43C2×D811yescharacteristic
116C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
117C22⋊D43—81no—
118C22⋊D43—81no—
119C2×Dic43—41no—
120D172—41no—
121D172—41no—
122D172—82no—
123C4×D43—81no—
124C4×D43—81no—
125Dic86—41no—
126Dic86—41no—
127C43⋊C8—81no—
128C43⋊C8—82no—
129#12152—431nomaximal, Sylow
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—44no—
133C22×C43—44no—
134C22×C43—44no—
135C22×C43—82no—
136C22×C43—82no—
137C22×C43—82no—
138C22×C43—82no—
139C22×C43#44711yescharacteristic
140C22×C43#45411yescharacteristic
141C22×C43B(4,𝔽2)11yescharacteristic
142C2×D43—81no—
143C2×D43—81no—
144C2×D43—81no—
145C4×C43—24no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—42no—
149C4×C43—82no—
150C4×C43—81no—
151Dic43—81no—
152#2537D4311yescharacteristic, complemented
153#2039—431no—
154#1598—432no—
155#1345—432no—
156#1325—431no—
157C2×C43—21no—
158C2×C43—21no—
159C2×C43—84no—
160C2×C43#159811yescharacteristic
161C2×C43#219611yescharacteristic
162C2×C43#220411yescharacteristic
163D43—161no—
164#537—431no—
165C2×#121—22no—
166C2×C4×D4—21no—
167#447—862no—
168C2×#104—861no—
169#417—861no—
170#394—21no—
171#394C2×D4312yes—
172#384C2×D4311yescharacteristic
173#380—22no—
174#343—431no—
175#327—862no—
176#324—432no—
177C43#1215211yescharacteristic, complemented, Sylow
178C2×#41—861no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4C22⋊D4312yes—
182C23×C4—22no—
183C2×D8—1722no—
184C2×M16—861no—
185C22⋊Q8—1721no—
186#121—48no—
187#121—862no—
188#121—1721no—
189C4×D4—42no—
190C4×D4—42no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4C22⋊D4311yescharacteristic
194C2×C4⋊C4C22×D4311yescharacteristic
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C42C22⋊D4311yescharacteristic
199#104—1722no—
200#103—1721no—
201#102—1721no—
202#102—1722no—
203C22⋊C8—862no—
204#95—21no—
205#95C22⋊D4312yes—
206C24—22no—
207#41—1721no—
208#41—1721no—
209#41—1721no—
210#41—1721no—
211C2×Q8—861no—
212C2×D4—24no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—44no—
217C2×D4—44no—
218C2×D4—81no—
219C2×D4—862no—
220C2×D4—861no—
221C2×D4—1721no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—44no—
226C22×C4—44no—
227C22×C4—44no—
228C22×C4—1721no—
229C22×C4C2×C22⋊D4311yescharacteristic
230C22×C4C2×C22⋊D4312yes—
231D8—3444no—
232M16—1721no—
233M16—1721no—
234C2×C8—1722no—
235C2×C8—1721no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—44no—
240C4⋊C4—862no—
241C22⋊C4—44no—
242C22⋊C4—44no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—1722no—
246C42—21no—
247C42#1062188212yescomplemented
248C23—24no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—1721no—
256C23#1306329411yescharacteristic
257Q8—1721no—
258Q8—1721no—
259D4—48no—
260D4—44no—
261D4—82no—
262D4—84no—
263D4—3442no—
264D4—3441no—
265D4—3441no—
266D4—1721no—
267D4—1721no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—88no—
281C2×C4—3441no—
282C2×C4—3441no—
283C2×C4—1721no—
284C2×C4C2×#1062188211yescharacteristic
285C2×C4#1306335111yescharacteristic
286C8—3441no—
287C8—3442no—
288C22—21no—
289C22—21no—
290C22—44no—
291C22—44no—
292C22—44no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—3441no—
298C22—3441no—
299C22—3441no—
300C22#1458303311yescharacteristic
301C22#1458307211yescharacteristic
302C22#1458308611yescharacteristic
303C4—24no—
304C4—21no—
305C4—21no—
306C4—42no—
307C4—82no—
308C4—81no—
309C4—3441no—
310C2—21no—
311C2—21no—
312C2—84no—
313C2—6881no—
314C2#1913353011yescharacteristic
315C2#1913657911yescharacteristic
316C2#1913662111yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2537C2
socleC22×C43B(4,𝔽2)
hypercenter#2537D43
hypocenterC43#12152
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. #19135819C2semidirect
2. #19133529C2semidirect
3. #19132598C2semidirect
4. #19132541C2semidirect
5. C43×#2537C2semidirect
81. C42×C43D8semidirect
152. #2537D43semidirect
177. C43#12152semidirect
247. C42#10621882semidirect

Maximal subgroups

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

subgroupindex
#191358192
#191335292
#191325982
#191325412
C43×#25372
#1215243