Finite Group Databasebeta

← #25010462

Subgroups — #25010462

Order 11008.

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

normal subgroups only

This group has 344 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#19147568C211yesmaximal, characteristic
2#19136818C211yesmaximal, characteristic, complemented
3#19136733C211yesmaximal, characteristic, complemented
4#19133990C211yesmaximal, characteristic, complemented
5#19132573C211yesmaximal, characteristic, complemented
6#19132555C211yesmaximal, characteristic, complemented
7C43×#1361C211yesmaximal, characteristic, complemented
8#14583569—21no—
9#14583304C2211yescharacteristic
10#14583274—21no—
11#14583110—21no—
12#14583092—22no—
13#14583091—21no—
14C8×Dic86C2211yescharacteristic
15C4×D344C2211yescharacteristic
16D8×Dic43—21no—
17#14582725—21no—
18#14582701—21no—
19#14582700—22no—
20C4×C43⋊C16C2211yescharacteristic
21#14582646—21no—
22C43×#493C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×#10621900—41no—
26C2×Dic172—41no—
27C2×D344D411yescharacteristic
28C2×#10621882—22no—
29#13063325—21no—
30#13063321—22no—
31#13063297—42no—
32#13063296—41no—
33C4×Dic86D411yescharacteristic
34C4×D172—21no—
35D4×Dic43—22no—
36C2×C43⋊C16—21no—
37#13063259—21no—
38#13063259—21no—
39#13063259D411yescharacteristic
40C4⋊(C43⋊C8)D411yescharacteristic
41Dic43⋊C8—21no—
42#13063250—41no—
43#13063247—21no—
44#13063246—22no—
45C8×Dic43—21no—
46C2×D8×C43—21no—
47C2×D8×C43D412yes—
48#127×C43—21no—
49C2×C16×C43—21no—
50C4⋊C8×C43—21no—
51C4×C8×C43C2311yescharacteristic
52C2×D4×C43—22no—
53C2×D4×C43—41no—
54C2×D4×C43—41no—
55C2×C22⋊D43—42no—
56C2×C22⋊D43—42no—
57C22×Dic43—42no—
58#10621900—82no—
59#10621900—82no—
60C2×D172—21no—
61C2×C4×D43—41no—
62C2×Dic86—41no—
63C2×Dic86D811yescharacteristic
64D8×C43—42no—
65D8×C43—41no—
66D8×C43—41no—
67C2×C8×C43—41no—
68C2×C8×C43C2×D411yescharacteristic
69C2×C8×C43C2×D411yescharacteristic
70C42×C43C2×D411yescharacteristic
71C22⋊Dic43—42no—
72#10621882—82no—
73(C2×D43)⋊C4—41no—
74C4⋊Dic43—21no—
75C4⋊Dic43—41no—
76C4⋊Dic43—41no—
77C4⋊Dic43D811yescharacteristic
78Dic43⋊C4—21no—
79C4×Dic43—21no—
80C2×C43⋊C8—21no—
81Dic172—82no—
82D344—21no—
83D344—21no—
84C16×C43—41no—
85C43⋊C16—41no—
86C23×C43—42no—
87C22×D43—41no—
88D4×C43—42no—
89D4×C43—42no—
90D4×C43—81no—
91D4×C43—81no—
92D4×C43—161no—
93C2×C4×C43#12011yescharacteristic
94C2×C4×C43C2×D811yescharacteristic
95C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
96C22⋊D43—84no—
97C22⋊D43—162no—
98C2×Dic43—21no—
99C2×Dic43—21no—
100C2×Dic43—41no—
101C2×Dic43—84no—
102C2×Dic43—81no—
103D172—41no—
104D172—41no—
105C4×D43—81no—
106C4×D43—81no—
107Dic86—21no—
108Dic86—81no—
109Dic86—81no—
110Dic86D1612yes—
111C8×C43—21no—
112C8×C43—81no—
113C8×C43#13511yescharacteristic
114C8×C43#13711yescharacteristic
115C43⋊C8—41no—
116#12380—431nomaximal, Sylow
117C22×C43—82no—
118C22×C43—82no—
119C22×C43—82no—
120C22×C43#44711yescharacteristic
121C2×D43—81no—
122C2×D43—81no—
123C2×D43—81no—
124C4×C43—21no—
125C4×C43#45211yescharacteristic
126C4×C43#45511yescharacteristic
127C4×C43C2×D1611yescharacteristic
128C4×C43#50911yescharacteristic
129Dic43—22no—
130Dic43—41no—
131Dic43—81no—
132Dic43—161no—
133#3391—431no—
134#2240—431no—
135#2224—431no—
136#1674—431no—
137#1361D4311yescharacteristic, complemented
138Q8⋊C16—431no—
139#1331—431no—
140C2×C43—162no—
141C2×C43#164111yescharacteristic
142C2×C43#218411yescharacteristic
143C2×C43#219411yescharacteristic
144D43—161no—
145#550—861no—
146#500—431no—
147#493—861no—
148#493C2×D4311yescharacteristic
149#462—861no—
150#459—861no—
151#459—862no—
152C8×Q8—431no—
153C4×D8—431no—
154C4×D8—861no—
155#366—861no—
156C4⋊C16C2×D4311yescharacteristic
157#357—861no—
158#357—862no—
159C4×C16—431no—
160#335C2×D4311yescharacteristic
161#332—861no—
162C43#1238011yescharacteristic, complemented, Sylow
163C2×#41—1721no—
164C2×Q16—1721no—
165C2×D8—21no—
166C2×D8—431no—
167C2×D8—862no—
168C2×D8D17212yes—
169C4⋊Q8—861no—
170#127—21no—
171#127—862no—
172#121—1721no—
173#121—1722no—
174C4×Q8—431no—
175C4×D4—862no—
176C4×D4—861no—
177C2×C16—21no—
178C2×C16—861no—
179#107—431no—
180#107—861no—
181#107—861no—
182C4⋊C8—21no—
183C4⋊C8—431no—
184C4⋊C8—861no—
185#103—1721no—
186#102—862no—
187#102—861no—
188C4×C8—861no—
189C4×C8C22×D4311yescharacteristic
190#41—3442no—
191#41—3442no—
192C2×Q8—431no—
193C2×Q8—1721no—
194C2×D4—22no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—861no—
198C2×D4—1722no—
199C2×D4—1722no—
200C22×C4—1722no—
201C22×C4—1721no—
202Q16—3442no—
203D8—42no—
204D8—41no—
205D8—41no—
206D8—861no—
207D8—861no—
208D8—3442no—
209C2×C8—41no—
210C2×C8—861no—
211C2×C8C2×D17211yescharacteristic
212C2×C8D4×D4311yescharacteristic
213C4⋊C4—431no—
214C4⋊C4—861no—
215C4⋊C4—861no—
216C4⋊C4—1721no—
217C4⋊C4—1721no—
218C22⋊C4—1722no—
219C22⋊C4—1721no—
220C42—861no—
221C42D4×D4311yescharacteristic
222C16—41no—
223C16—1721no—
224C23—42no—
225C23—1721no—
226Q8—432no—
227Q8—861no—
228Q8—3441no—
229Q8—3441no—
230D4—42no—
231D4—42no—
232D4—81no—
233D4—81no—
234D4—161no—
235D4—3444no—
236D4—1721no—
237D4—1721no—
238D4—6882no—
239C2×C4—861no—
240C2×C4—861no—
241C2×C4—3444no—
242C2×C4—3441no—
243C2×C4—3441no—
244C2×C4—3441no—
245C2×C4—1721no—
246C2×C4#1306329511yescharacteristic
247C2×C4D8×D4311yescharacteristic
248C2×C4#1306335211yescharacteristic
249C8—21no—
250C8—81no—
251C8—1721no—
252C8#1306334411yescharacteristic
253C8#1306335411yescharacteristic
254C22—82no—
255C22—82no—
256C22—82no—
257C22—3441no—
258C22—3441no—
259C22—3441no—
260C22#1458303411yescharacteristic
261C4—21no—
262C4—862no—
263C4—3441no—
264C4—1721no—
265C4—6881no—
266C4#1458306211yescharacteristic
267C4#1458307911yescharacteristic
268C4D16×D4311yescharacteristic
269C4#1458333611yescharacteristic
270C2—162no—
271C2—6881no—
272C2#1913378911yescharacteristic
273C2#1913650811yescharacteristic
274C2#1913656911yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1361C2
socleC22×C43#447
prime radical#19147568C2
hypercenter#1361D43
hypocenterC43#12380
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. #19136733C2semidirect
4. #19133990C2semidirect
5. #19132573C2semidirect
6. #19132555C2semidirect
7. C43×#1361C2semidirect
137. #1361D43semidirect
162. C43#12380semidirect

Maximal subgroups

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

subgroupindex
#191475682
#191368182
#191367332
#191339902
#191325732
#191325552
C43×#13612
#1238043