Finite Group Databasebeta

← #25010420

Subgroups — #25010420

Order 11008.

344 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 69 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#19146345C211yesmaximal, characteristic
2#19136822C211yesmaximal, characteristic, complemented
3#19136748C211yesmaximal, characteristic, complemented
4#19133995C211yesmaximal, characteristic
5#19132558C211yesmaximal, characteristic, complemented
6#19132549C211yesmaximal, characteristic
7C43×#1362C211yesmaximal, characteristic, complemented
8C2×Q16×D43—21no—
9#14583564—21no—
10#14583304C2211yescharacteristic
11#14583190—21no—
12#14583137—21no—
13#14583106—21no—
14#14583053—22no—
15C4×Dic172C2211yescharacteristic
16C8×D172C2211yescharacteristic
17#14582725—21no—
18#14582704—21no—
19#14582703—22no—
20C4×C43⋊C16C2211yescharacteristic
21#14582647—21no—
22C43×#494C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Q8×D43—22no—
26C2×Dic172D411yescharacteristic
27C2×#10621885—22no—
28Q16×D43—42no—
29Q16×D43—42no—
30C2×C8×D43—21no—
31#13063325—21no—
32#13063324—41no—
33#13063303—42no—
34#13063301—22no—
35C4×Dic86—21no—
36C4×D172D411yescharacteristic
37#13063287—41no—
38C2×C43⋊C16—21no—
39#13063259—21no—
40#13063259—21no—
41#13063259D411yescharacteristic
42#13063257—41no—
43C4⋊(C43⋊C8)D411yescharacteristic
44#13063250—21no—
45#13063249—22no—
46#13063247—41no—
47(C2×D43)⋊C8—21no—
48C2×Q16×C43—21no—
49C2×Q16×C43D412yes—
50C4⋊Q8×C43—21no—
51C2×C16×C43—21no—
52C4⋊C8×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—22no—
55Q8×D43—44no—
56Q8×D43—82no—
57C2×D172D811yescharacteristic
58C2×C4×D43—21no—
59C2×C4×D43—42no—
60C2×Dic86—21no—
61C2×Dic86—42no—
62C2×Dic86—41no—
63Q16×C43—42no—
64Q16×C43—41no—
65Q16×C43—41no—
66C2×C8×C43—41no—
67C2×C8×C43C2×D411yescharacteristic
68C2×C8×C43C2×D411yescharacteristic
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C42×C43C2×D411yescharacteristic
72#10621885—44no—
73(C2×D43)⋊C4—21no—
74(C2×D43)⋊C4—42no—
75C4⋊Dic43—21no—
76C4⋊Dic43—41no—
77C4⋊Dic43—41no—
78C4⋊Dic43D811yescharacteristic
79Dic43⋊C4—42no—
80Dic43⋊C4—41no—
81C4×Dic43—41no—
82C2×C43⋊C8—21no—
83Dic172—21no—
84Dic172SD1612yes—
85C8×D43—41no—
86C8×D43—41no—
87C16×C43—41no—
88C43⋊C16—41no—
89C22×D43—21no—
90Q8×C43—42no—
91Q8×C43—42no—
92C2×C4×C43—42no—
93C2×C4×C43#12011yescharacteristic
94C2×C4×C43C2×D811yescharacteristic
95C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
96C2×Dic43—21no—
97C2×Dic43—41no—
98C2×Dic43—41no—
99C2×Dic43—81no—
100D172—21no—
101D172Q3212yes—
102C4×D43—41no—
103C4×D43—41no—
104C4×D43—84no—
105Dic86—22no—
106Dic86—41no—
107Dic86—84no—
108Dic86—161no—
109C8×C43—21no—
110C8×C43—81no—
111C8×C43C2×SD1611yescharacteristic
112C8×C43AGL(1,ℤ/8)11yescharacteristic
113C43⋊C8—41no—
114#12374—431nomaximal, Sylow
115C22×C43#44711yescharacteristic
116C2×D43—22no—
117C2×D43—41no—
118C2×D43—41no—
119C4×C43—21no—
120C4×C43—82no—
121C4×C43#45011yescharacteristic
122C4×C43#45511yescharacteristic
123C4×C43C2×Q3211yescharacteristic
124C4×C43#51011yescharacteristic
125Dic43—42no—
126Dic43—41no—
127Dic43—81no—
128Dic43—161no—
129D4×Q16—431no—
130#2241—431no—
131#2227—431no—
132#1675—431no—
133#1362D4311yescharacteristic, complemented
134#1332—431no—
135D4⋊C16—431no—
136C2×C43#163911yescharacteristic
137C2×C43#218811yescharacteristic
138C2×C43#219311yescharacteristic
139D43—42no—
140C22×Q16—861no—
141D4×Q8—861no—
142#500—431no—
143#494C2×D4311yescharacteristic
144#476—861no—
145#467—861no—
146#462—861no—
147#451—862no—
148C4×Q16—431no—
149C8×D4—431no—
150#366—861no—
151C4⋊C16C2×D4311yescharacteristic
152#358—861no—
153#358—862no—
154C4×C16—431no—
155#335C2×D4311yescharacteristic
156#333—861no—
157C43#1237411yescharacteristic, complemented, Sylow
158C22×Q8—862no—
159C2×Q16—21no—
160C2×Q16—431no—
161C2×Q16—862no—
162C2×Q16—1722no—
163C2×Q16—1722no—
164C2×Q16D17212yes—
165C22×C8—861no—
166C4⋊Q8—21no—
167C4⋊Q8—861no—
168C4⋊Q8—1721no—
169C22⋊Q8—862no—
170C22⋊Q8—1722no—
171C4×Q8—861no—
172C4×D4—431no—
173C4×D4—1721no—
174C2×C16—21no—
175C2×C16—861no—
176#107—431no—
177#107—861no—
178#107—861no—
179#106—1721no—
180C4⋊C8—21no—
181C4⋊C8—431no—
182#103—862no—
183#103—861no—
184#102—1721no—
185C22⋊C8—861no—
186C4×C8C22×D4311yescharacteristic
187C2×Q8—22no—
188C2×Q8—861no—
189C2×Q8—3442no—
190C2×Q8—1722no—
191C2×Q8—1724no—
192C2×Q8—1721no—
193C2×D4—431no—
194C22×C4—861no—
195C22×C4—1722no—
196Q16—42no—
197Q16—41no—
198Q16—41no—
199Q16—432no—
200Q16—861no—
201Q16—1724no—
202C2×C8—41no—
203C2×C8—861no—
204C2×C8—1721no—
205C2×C8—1721no—
206C2×C8C2×D17211yescharacteristic
207C2×C8D4×D4311yescharacteristic
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—431no—
211C4⋊C4—861no—
212C4⋊C4—1722no—
213C4⋊C4—1721no—
214C4⋊C4—1721no—
215C4⋊C4—1721no—
216C22⋊C4—861no—
217C22⋊C4—1722no—
218C42—1721no—
219C42D4×D4311yescharacteristic
220C16—41no—
221C16—1721no—
222C23—861no—
223Q8—42no—
224Q8—42no—
225Q8—862no—
226Q8—3444no—
227Q8—1721no—
228Q8—6881no—
229D4—432no—
230D4—861no—
231C2×C4—42no—
232C2×C4—861no—
233C2×C4—3444no—
234C2×C4—3441no—
235C2×C4—1721no—
236C2×C4—1721no—
237C2×C4—1721no—
238C2×C4—1721no—
239C2×C4#1306329511yescharacteristic
240C2×C4D8×D4311yescharacteristic
241C2×C4#1306335211yescharacteristic
242C8—21no—
243C8—81no—
244C8—1721no—
245C8SD16×D4311yescharacteristic
246C8#1306334911yescharacteristic
247C22—862no—
248C22—1721no—
249C22—1721no—
250C22#1458303411yescharacteristic
251C4—21no—
252C4—82no—
253C4—3441no—
254C4—1721no—
255C4—1722no—
256C4—6881no—
257C4#1458305111yescharacteristic
258C4#1458307911yescharacteristic
259C4Q32×D4311yescharacteristic
260C4#1458333811yescharacteristic
261C2—1722no—
262C2#1913377511yescharacteristic
263C2#1913653011yescharacteristic
264C2#1913656211yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1362C2
socleC22×C43#447
prime radicalC2×D172D8
hypercenter#1362D43
hypocenterC43#12374
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
2. #19136822C2semidirect
3. #19136748C2semidirect
5. #19132558C2semidirect
7. C43×#1362C2semidirect
133. #1362D43semidirect
157. C43#12374semidirect

Maximal subgroups

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

subgroupindex
#191463452
#191368222
#191367482
#191339952
#191325582
#191325492
C43×#13622
#1237443