Finite Group Databasebeta

← #25010213

Subgroups — #25010213

Order 11008.

318 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 65 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#19147019C211yesmaximal, characteristic, complemented
2#19136819C211yesmaximal, characteristic, complemented
3#19136630C211yesmaximal, characteristic, complemented
4#19133951C211yesmaximal, characteristic, complemented
5#19132654C211yesmaximal, characteristic, complemented
6#19132551C211yesmaximal, characteristic, complemented
7C43×#1331C211yesmaximal, characteristic, complemented
8#14583614—21no—
9C2×#13063266—21no—
10#14583304C2211yescharacteristic
11#14583276C2211yescharacteristic
12#14583221—22no—
13#14583189—21no—
14#14583132—21no—
15#14583095—21no—
16C8×D172C2211yescharacteristic
17#14582936—21no—
18C4⋊(C43⋊C16)C2211yescharacteristic
19#14582701—22no—
20#14582699—21no—
21#14582642—21no—
22C4×D8×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×D344—21no—
26C2×D344—21no—
27C2×D344—41no—
28C2×C8×D43—21no—
29#13063325—21no—
30#13063322—21no—
31#13063311—42no—
32#13063299—41no—
33#13063296—22no—
34C4×D172D411yescharacteristic
35#13063284—41no—
36#13063283—22no—
37#13063266—42no—
38C2×C43⋊C16—21no—
39#13063259—21no—
40#13063259D412yes—
41#13063256—22no—
42C4⋊(C43⋊C8)D411yescharacteristic
43#13063247—41no—
44#13063246—22no—
45(C2×D43)⋊C8—21no—
46C2×D8×C43D411yescharacteristic
47C4×D4×C43—21no—
48C2×C16×C43—21no—
49#107×C43D411yescharacteristic
50C4⋊C8×C43—21no—
51#102×C43—21no—
52C4×C8×C43C2311yescharacteristic
53C2×D4×C43—21no—
54C22×C4×C43—41no—
55C2×C22⋊D43—42no—
56C2×D172—41no—
57C2×D172—41no—
58C2×D172—41no—
59C2×D172D811yescharacteristic
60C2×C4×D43—21no—
61C2×Dic86—41no—
62D8×C43—21no—
63D8×C43—21no—
64C2×C8×C43—41no—
65C2×C8×C43C2×D411yescharacteristic
66C2×C8×C43C2×D411yescharacteristic
67C4⋊C4×C43—21no—
68C22⋊C4×C43—41no—
69C42×C43C2×D411yescharacteristic
70C22⋊Dic43—42no—
71(C2×D43)⋊C4—21no—
72(C2×D43)⋊C4—42no—
73C4⋊Dic43—22no—
74C4⋊Dic43—41no—
75C4⋊Dic43D811yescharacteristic
76C4×Dic43—42no—
77C2×C43⋊C8—21no—
78D344—42no—
79D344—41no—
80D344—41no—
81D344—82no—
82C8×D43—41no—
83C8×D43—41no—
84C16×C43—41no—
85C43⋊C16—41no—
86C23×C43—41no—
87C22×D43—21no—
88C22×D43—81no—
89D4×C43—41no—
90D4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43—81no—
93C2×C4×C43—81no—
94C2×C4×C43#12011yescharacteristic
95C2×C4×C43C2×D811yescharacteristic
96C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
97C22⋊D43—162no—
98C2×Dic43—21no—
99C2×Dic43—42no—
100D172—21no—
101D172—21no—
102D172—81no—
103D172—81no—
104D172—81no—
105D172—81no—
106D172—161no—
107C4×D43—41no—
108C4×D43—41no—
109Dic86—161no—
110C8×C43—21no—
111C8×C43—81no—
112C8×C43#13511yescharacteristic
113C8×C43AGL(1,ℤ/8)11yescharacteristic
114C43⋊C8—41no—
115#12343—431nomaximal, Sylow
116C22×C43—81no—
117C22×C43—81no—
118C22×C43—81no—
119C22×C43#44711yescharacteristic
120C2×D43—41no—
121C2×D43—41no—
122C2×D43—41no—
123C2×D43—161no—
124C2×D43—161no—
125C2×D43—161no—
126C4×C43—21no—
127C4×C43—81no—
128C4×C43#44911yescharacteristic
129C4×C43#45411yescharacteristic
130C4×C43#50811yescharacteristic
131C4×C43#50911yescharacteristic
132Dic43—41no—
133Dic43—82no—
134#3341—431no—
135#2240—431no—
136#2206—431no—
137#1667—431no—
138#1365—431no—
139#1331D4311yescharacteristic, complemented
140D4⋊C16—431no—
141C2×C43—161no—
142C2×C43#162511yescharacteristic
143C2×C43#218611yescharacteristic
144C2×C43#219211yescharacteristic
145D43—81no—
146D43—321no—
147#555—861no—
148C2×D16—861no—
149#500—431no—
150#493—431no—
151#482—862no—
152#476—861no—
153#466—861no—
154#459—861no—
155C4×D8C2×D4311yescharacteristic
156C8×D4—431no—
157#427—861no—
158C4⋊C16—431no—
159#357—862no—
160#357—861no—
161C4×C16C2×D4311yescharacteristic
162#335C2×D4311yescharacteristic
163#331—861no—
164C43#1234311yescharacteristic, complemented, Sylow
165C2×D8—861no—
166C2×D8—861no—
167C2×D8—1721no—
168C2×D8D17211yescharacteristic
169C22×C8—861no—
170C4⋊Q8—861no—
171#127—861no—
172#124—1722no—
173#121—862no—
174#121—1721no—
175C4×D4—21no—
176C4×D4—431no—
177#117—862no—
178#117—1721no—
179D16—1722no—
180C2×C16—21no—
181C2×C16—861no—
182#107—432no—
183#107—861no—
184#107D17211yescharacteristic
185#106—862no—
186C4⋊C8—21no—
187C4⋊C8—431no—
188#102—21no—
189#102—862no—
190#102—1721no—
191C22⋊C8—861no—
192C4×C8C22×D4311yescharacteristic
193C2×Q8—1721no—
194C2×D4—21no—
195C2×D4—431no—
196C2×D4—1722no—
197C2×D4—1721no—
198C2×D4—1721no—
199C2×D4—1721no—
200C22×C4—41no—
201C22×C4—861no—
202D8—21no—
203D8—21no—
204D8—3442no—
205D8—1722no—
206D8—1721no—
207D8—1721no—
208C2×C8—41no—
209C2×C8—861no—
210C2×C8—1721no—
211C2×C8—1721no—
212C2×C8C2×D17211yescharacteristic
213C2×C8D4×D4311yescharacteristic
214C4⋊C4—21no—
215C4⋊C4—431no—
216C4⋊C4—862no—
217C4⋊C4—1721no—
218C22⋊C4—41no—
219C22⋊C4—861no—
220C22⋊C4—1722no—
221C22⋊C4—1722no—
222C42—1722no—
223C42D4×D4311yescharacteristic
224C16—41no—
225C16—1721no—
226C23—41no—
227C23—861no—
228C23—3441no—
229Q8—6881no—
230D4—41no—
231D4—41no—
232D4—861no—
233D4—861no—
234D4—3441no—
235D4—3441no—
236D4—3441no—
237D4—3441no—
238D4—6881no—
239D4—6882no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—861no—
244C2×C4—1722no—
245C2×C4—1721no—
246C2×C4—1721no—
247C2×C4#1306329511yescharacteristic
248C2×C4D8×D4311yescharacteristic
249C2×C4#1306335211yescharacteristic
250C8—21no—
251C8—81no—
252C8—1721no—
253C8#1306334711yescharacteristic
254C8#1306335311yescharacteristic
255C22—81no—
256C22—81no—
257C22—81no—
258C22—1721no—
259C22—1721no—
260C22—1721no—
261C22—6881no—
262C22—6881no—
263C22—6881no—
264C22#1458303411yescharacteristic
265C4—21no—
266C4—81no—
267C4—3442no—
268C4—1721no—
269C4#1458304611yescharacteristic
270C4#1458307311yescharacteristic
271C4#1458333011yescharacteristic
272C4#1458333311yescharacteristic
273C2—161no—
274C2—3441no—
275C2—13761no—
276C2#1913368711yescharacteristic
277C2#1913651911yescharacteristic
278C2#1913655311yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1331C2
socleC22×C43#447
hypercenter#1331D43
hypocenterC43#12343
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
1. #19147019C2semidirect
2. #19136819C2semidirect
3. #19136630C2semidirect
4. #19133951C2semidirect
5. #19132654C2semidirect
6. #19132551C2semidirect
7. C43×#1331C2semidirect
139. #1331D43semidirect
164. C43#12343semidirect

Maximal subgroups

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

subgroupindex
#191470192
#191368192
#191366302
#191339512
#191326542
#191325512
C43×#13312
#1234343