Finite Group Databasebeta

← #25010385

Subgroups — #25010385

Order 11008.

366 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 67 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#19146353C211yesmaximal, characteristic
2#19136818C211yesmaximal, characteristic, complemented
3#19136738C211yesmaximal, characteristic, complemented
4#19133985C211yesmaximal, characteristic, complemented
5#19132558C211yesmaximal, characteristic, complemented
6#19132549C211yesmaximal, characteristic, complemented
7C43×#1361C211yesmaximal, characteristic, complemented
8C2×#13063344—21no—
9#14583569—21no—
10#14583304C2211yescharacteristic
11#14583132—21no—
12#14583105—21no—
13#14583096—21no—
14#14583041—22no—
15C4×Dic172C2211yescharacteristic
16C8×D172C2211yescharacteristic
17#14582727—21no—
18#14582704—21no—
19#14582700—22no—
20C4×C43⋊C16C2211yescharacteristic
21#14582646—21no—
22C43×#493C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×#10621900—22no—
26#13063344—42no—
27#13063344—42no—
28C2×Dic172D411yescharacteristic
29C2×#10621873—41no—
30C2×#10621883—22no—
31C2×C8×D43—21no—
32#13063325—21no—
33#13063321—41no—
34#13063297—42no—
35#13063296—22no—
36C4×Dic86—21no—
37C4×D172D411yescharacteristic
38D4×Dic43—41no—
39C2×C43⋊C16—21no—
40#13063259—21no—
41#13063259—21no—
42#13063259D411yescharacteristic
43C4⋊(C43⋊C8)D411yescharacteristic
44#13063250—21no—
45#13063250—41no—
46#13063246—22no—
47(C2×D43)⋊C8—21no—
48C2×D8×C43—21no—
49C2×D8×C43D412yes—
50#127×C43—21no—
51C2×C16×C43—21no—
52C4⋊C8×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×D4×C43—22no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×C22⋊D43—42no—
58C2×C22⋊D43—42no—
59C22×Dic43—42no—
60#10621900—44no—
61#10621900—82no—
62C2×D172D811yescharacteristic
63C2×C4×D43—21no—
64C2×Dic86—21no—
65C2×Dic86—41no—
66D8×C43—42no—
67D8×C43—41no—
68D8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43C2×D411yescharacteristic
71C2×C8×C43C2×D411yescharacteristic
72C42×C43C2×D411yescharacteristic
73C22⋊Dic43—42no—
74#10621883—44no—
75(C2×D43)⋊C4—21no—
76C4⋊Dic43—21no—
77C4⋊Dic43—41no—
78C4⋊Dic43—41no—
79C4⋊Dic43D811yescharacteristic
80Dic43⋊C4—41no—
81C4×Dic43—41no—
82C2×C43⋊C8—21no—
83Dic172—21no—
84Dic172SD1612yescomplemented
85#10621873—82no—
86C8×D43—41no—
87C8×D43—41no—
88C16×C43—41no—
89C43⋊C16—41no—
90C23×C43—42no—
91C22×D43—21no—
92D4×C43—42no—
93D4×C43—42no—
94D4×C43—81no—
95D4×C43—81no—
96D4×C43—161no—
97C2×C4×C43#12011yescharacteristic
98C2×C4×C43C2×D811yescharacteristic
99C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
100C22⋊D43—84no—
101C22⋊D43—162no—
102C2×Dic43—21no—
103C2×Dic43—41no—
104C2×Dic43—41no—
105C2×Dic43—84no—
106C2×Dic43—81no—
107D172—21no—
108D172—21no—
109C4×D43—41no—
110C4×D43—41no—
111Dic86—22no—
112Dic86—41no—
113Dic86—81no—
114Dic86—81no—
115C8×C43—21no—
116C8×C43—81no—
117C8×C43C2×SD1611yescharacteristic
118C8×C43AGL(1,ℤ/8)11yescharacteristic
119C43⋊C8—41no—
120#12369—431nomaximal, Sylow
121C22×C43—82no—
122C22×C43—82no—
123C22×C43—82no—
124C22×C43#44711yescharacteristic
125C2×D43—41no—
126C2×D43—41no—
127C2×D43—41no—
128C4×C43—21no—
129C4×C43#45011yescharacteristic
130C4×C43#45511yescharacteristic
131C4×C43#50811yescharacteristic
132C4×C43#50911yescharacteristic
133Dic43—42no—
134Dic43—41no—
135Dic43—81no—
136Dic43—161no—
137#3287—431no—
138#2240—431no—
139#2225—431no—
140#1673—431no—
141#1361D4311yescharacteristic, complemented
142#1332—431no—
143D4⋊C16—431no—
144C2×C43—162no—
145C2×C43#163911yescharacteristic
146C2×C43#218611yescharacteristic
147C2×C43#219411yescharacteristic
148D43—81no—
149C2×#135—861no—
150#550—861no—
151#500—431no—
152#493C2×D4311yescharacteristic
153#466—861no—
154#461—861no—
155#460—861no—
156#449—862no—
157C4×Q16—431no—
158C8×D4—431no—
159#367—861no—
160C4⋊C16C2×D4311yescharacteristic
161#358—861no—
162#357—862no—
163C4×C16—431no—
164#335C2×D4311yescharacteristic
165#332—861no—
166C43#1236911yescharacteristic, complemented, Sylow
167C2×#41—862no—
168#135—1722no—
169#135—1722no—
170C2×Q16—431no—
171C2×SD16—862no—
172C2×SD16—1721no—
173C2×D8—21no—
174C2×D8D17212yes—
175C22×C8—861no—
176C4⋊Q8—861no—
177#127—21no—
178#127—1721no—
179#121—862no—
180#121—1722no—
181C4×Q8—861no—
182C4×D4—431no—
183C4×D4—1721no—
184C2×C16—21no—
185C2×C16—861no—
186#107—431no—
187#107—861no—
188#107—861no—
189C4⋊C8—21no—
190C4⋊C8—431no—
191#103—861no—
192#103—1721no—
193#102—862no—
194C22⋊C8—861no—
195C4×C8C22×D4311yescharacteristic
196#41—3442no—
197#41—1724no—
198C2×Q8—861no—
199C2×Q8—1721no—
200C2×D4—22no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—431no—
204C2×D4—1722no—
205C2×D4—1722no—
206C22×C4—861no—
207C22×C4—1722no—
208Q16—432no—
209Q16—861no—
210SD16—3442no—
211SD16—1724no—
212D8—42no—
213D8—41no—
214D8—41no—
215C2×C8—41no—
216C2×C8—861no—
217C2×C8—1721no—
218C2×C8—1721no—
219C2×C8C2×D17211yescharacteristic
220C2×C8D4×D4311yescharacteristic
221C4⋊C4—431no—
222C4⋊C4—861no—
223C4⋊C4—1721no—
224C4⋊C4—1721no—
225C4⋊C4—1721no—
226C22⋊C4—861no—
227C22⋊C4—1722no—
228C42—1721no—
229C42D4×D4311yescharacteristic
230C16—41no—
231C16—1721no—
232C23—42no—
233C23—861no—
234Q8—862no—
235Q8—3441no—
236Q8—3441no—
237Q8—1721no—
238D4—42no—
239D4—42no—
240D4—81no—
241D4—81no—
242D4—161no—
243D4—861no—
244D4—861no—
245D4—3444no—
246D4—6882no—
247C2×C4—861no—
248C2×C4—3444no—
249C2×C4—3441no—
250C2×C4—1721no—
251C2×C4—1721no—
252C2×C4—1721no—
253C2×C4—1721no—
254C2×C4#1306329511yescharacteristic
255C2×C4D8×D4311yescharacteristic
256C2×C4#1306335211yescharacteristic
257C8—21no—
258C8—81no—
259C8—1721no—
260C8SD16×D4311yescharacteristic
261C8#1306334911yescharacteristic
262C22—82no—
263C22—82no—
264C22—82no—
265C22—1721no—
266C22—1721no—
267C22—1721no—
268C22#1458303411yescharacteristic
269C4—21no—
270C4—3441no—
271C4—1721no—
272C4—1722no—
273C4—6881no—
274C4#1458305111yescharacteristic
275C4#1458307911yescharacteristic
276C4#1458333011yescharacteristic
277C4#1458333311yescharacteristic
278C2—162no—
279C2—3441no—
280C2#1913377511yescharacteristic
281C2#1913651911yescharacteristic
282C2#1913656911yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1361C2
socleC22×C43#447
prime radical#19146353C2
hypercenter#1361D43
hypocenterC43#12369
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #19136818C2semidirect
3. #19136738C2semidirect
4. #19133985C2semidirect
5. #19132558C2semidirect
6. #19132549C2semidirect
7. C43×#1361C2semidirect
84. Dic172SD16semidirect
141. #1361D43semidirect
166. C43#12369semidirect

Maximal subgroups

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

subgroupindex
#191463532
#191368182
#191367382
#191339852
#191325582
#191325492
C43×#13612
#1236943