Finite Group Databasebeta

← #25010395

Subgroups — #25010395

Order 11008.

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

normal subgroups only

This group has 356 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#19146315C211yesmaximal, characteristic
2#19136729C211yesmaximal, characteristic, complemented
3#19133981C211yesmaximal, characteristic, complemented
4#19132644C211yesmaximal, characteristic, complemented
5#19132557C211yesmaximal, characteristic, complemented
6#19132551C211yesmaximal, characteristic, complemented
7C43×#2241C211yesmaximal, characteristic, complemented
8C2×#13063348—21no—
9#14583552—21no—
10#14583137—21no—
11#14583101—21no—
12#14583101—21no—
13#14583060—22no—
14C4×D344C2211yescharacteristic
15C8×D172C2211yescharacteristic
16#14582724—21no—
17C4⋊(C43⋊C16)C2211yescharacteristic
18#14582699—21no—
19#14582652C2211yescharacteristic
20#14582645—21no—
21C43×#500C2211yescharacteristic
22C43×#494C2211yescharacteristic
23C43×#358—22no—
24C4×C16×C43C2211yescharacteristic
25C2×#10621902—22no—
26#13063348—42no—
27#13063348—42no—
28C2×#10621884—22no—
29C2×#10621884—41no—
30C2×D344D411yescharacteristic
31C2×C8×D43—21no—
32#13063310—42no—
33#13063301—22no—
34#13063300—41no—
35C4×D172—21no—
36C4×D172D411yescharacteristic
37C4⋊C4×D43—41no—
38C2×C43⋊C16—21no—
39#13063259D411yescharacteristic
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)D411yescharacteristic
42#13063249—22no—
43#13063249—41no—
44#13063247—21no—
45(C2×D43)⋊C8—21no—
46C2×Q16×C43—21no—
47C2×Q16×C43D412yes—
48C4⋊Q8×C43—21no—
49C4⋊Q8×C43—21no—
50C2×C16×C43—21no—
51#107×C43—21no—
52#107×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—22no—
55C2×Q8×C43—41no—
56#10621902—44no—
57#10621902—82no—
58C2×D172—21no—
59C2×D172—42no—
60C2×D172D811yescharacteristic
61C2×C4×D43—21no—
62C2×C4×D43—42no—
63C2×C4×D43—41no—
64Q16×C43—42no—
65Q16×C43—41no—
66Q16×C43—41no—
67C2×C8×C43C2×D411yescharacteristic
68C2×C8×C43C2×D411yescharacteristic
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—41no—
72C4⋊C4×C43—41no—
73C42×C43C2×D411yescharacteristic
74#10621884—44no—
75#10621884—82no—
76(C2×D43)⋊C4—21no—
77(C2×D43)⋊C4—42no—
78(C2×D43)⋊C4—41no—
79C4⋊Dic43—21no—
80C4⋊Dic43D811yescharacteristic
81Dic43⋊C4—42no—
82C2×C43⋊C8—21no—
83C2×C43⋊C8—41no—
84D344—21no—
85D344SD1612yescomplemented
86C8×D43—41no—
87C8×D43—41no—
88C16×C43—41no—
89C43⋊C16—41no—
90C22×D43—21no—
91C22×D43—41no—
92Q8×C43—42no—
93Q8×C43—42no—
94Q8×C43—81no—
95Q8×C43—81no—
96C2×C4×C43—42no—
97C2×C4×C43—81no—
98C2×C4×C43#12011yescharacteristic
99C2×C4×C43C2×D811yescharacteristic
100C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
101C2×Dic43—21no—
102C2×Dic43—41no—
103D172—22no—
104D172—21no—
105D172—21no—
106D172—41no—
107D172—84no—
108C4×D43—41no—
109C4×D43—41no—
110C4×D43—84no—
111C4×D43—81no—
112C4×D43—81no—
113C8×C43—21no—
114C8×C43C2×SD1611yescharacteristic
115C8×C43AGL(1,ℤ/8)11yescharacteristic
116C43⋊C8—41no—
117C43⋊C8—81no—
118#12371—431nomaximal, Sylow
119C22×C43#44711yescharacteristic
120C2×D43—41no—
121C2×D43—42no—
122C2×D43—41no—
123C2×D43—41no—
124C2×D43—81no—
125C2×D43—81no—
126C4×C43—21no—
127C4×C43—82no—
128C4×C43—161no—
129C4×C43#45011yescharacteristic
130C4×C43#45511yescharacteristic
131C4×C43#50811yescharacteristic
132C4×C43#50911yescharacteristic
133Dic43—41no—
134Dic43—81no—
135#3283—431no—
136#2241D4311yescharacteristic, complemented
137#2224—431no—
138#1673—431no—
139#1362—431no—
140#1331—431no—
141D4⋊C16—431no—
142C2×C43#163911yescharacteristic
143C2×C43#218611yescharacteristic
144C2×C43#219511yescharacteristic
145D43—81no—
146D43—82no—
147C2×#135—861no—
148#547—861no—
149#500C2×D4311yescharacteristic
150#494C2×D4311yescharacteristic
151#467—861no—
152#461—861no—
153#461—861no—
154#452—862no—
155C4×D8—431no—
156C8×D4—431no—
157#366—861no—
158C4⋊C16—431no—
159#358—22no—
160#357—861no—
161C4×C16C2×D4311yescharacteristic
162#335—431no—
163#332—861no—
164C43#1237111yescharacteristic, complemented, Sylow
165C2×#41—862no—
166#135—1722no—
167#135—1722no—
168C2×Q16—21no—
169C2×Q16C22⋊D4312yes—
170C2×SD16—862no—
171C2×SD16—1721no—
172C2×D8—431no—
173C22×C8—861no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176#123—1722no—
177C22⋊Q8—862no—
178#121—1721no—
179C4×D4—431no—
180C4×D4—861no—
181C2×C4⋊C4—1721no—
182C2×C16—21no—
183C2×C16—861no—
184#107—21no—
185#107—21no—
186#107—431no—
187C4⋊C8—431no—
188C4⋊C8—861no—
189#103—862no—
190#103—1721no—
191#102—861no—
192C22⋊C8—861no—
193C4×C8C22×D4311yescharacteristic
194#41—3442no—
195#41—1724no—
196C2×Q8—22no—
197C2×Q8—41no—
198C2×D4—431no—
199C2×D4—861no—
200C2×D4—1722no—
201C22×C4—861no—
202C22×C4—1722no—
203C22×C4—1721no—
204Q16—42no—
205Q16—41no—
206Q16—41no—
207SD16—3442no—
208SD16—1724no—
209D8—432no—
210D8—861no—
211C2×C8—861no—
212C2×C8—1721no—
213C2×C8—1721no—
214C2×C8—1721no—
215C2×C8D4×D4311yescharacteristic
216C2×C8C2×C22⋊D4311yescharacteristic
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—431no—
222C4⋊C4—861no—
223C4⋊C4—1722no—
224C22⋊C4—861no—
225C22⋊C4—1722no—
226C22⋊C4—1721no—
227C42D4×D4311yescharacteristic
228C16—41no—
229C16—1721no—
230C23—861no—
231C23—1721no—
232Q8—42no—
233Q8—42no—
234Q8—81no—
235Q8—81no—
236D4—862no—
237D4—861no—
238D4—861no—
239D4—3444no—
240D4—1721no—
241C2×C4—42no—
242C2×C4—81no—
243C2×C4—861no—
244C2×C4—3444no—
245C2×C4—3441no—
246C2×C4—3441no—
247C2×C4—1721no—
248C2×C4—1721no—
249C2×C4—1721no—
250C2×C4#1306329311yescharacteristic
251C2×C4D8×D4311yescharacteristic
252C2×C4#1306334911yescharacteristic
253C8—21no—
254C8—3441no—
255C8—1721no—
256C8SD16×D4311yescharacteristic
257C8#1306335211yescharacteristic
258C22—3441no—
259C22—3441no—
260C22—1721no—
261C22—1721no—
262C22—1722no—
263C22—1721no—
264C22#1458303111yescharacteristic
265C4—21no—
266C4—82no—
267C4—161no—
268C4—3441no—
269C4—1721no—
270C4#1458304811yescharacteristic
271C4#1458307611yescharacteristic
272C4#1458333011yescharacteristic
273C4#1458333611yescharacteristic
274C2—3442no—
275C2—3441no—
276C2#1913377111yescharacteristic
277C2#1913651711yescharacteristic
278C2#1913657211yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2241C2
socleC22×C43#447
prime radical#19146315C2
hypercenter#2241D43
hypocenterC43#12371
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
2. #19136729C2semidirect
3. #19133981C2semidirect
4. #19132644C2semidirect
5. #19132557C2semidirect
6. #19132551C2semidirect
7. C43×#2241C2semidirect
85. D344SD16semidirect
136. #2241D43semidirect
164. C43#12371semidirect

Maximal subgroups

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

subgroupindex
#191463152
#191367292
#191339812
#191326442
#191325572
#191325512
C43×#22412
#1237143