Finite Group Databasebeta

← #25010485

Subgroups — #25010485

Order 11008.

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

normal subgroups only

This group has 294 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#19147581C211yesmaximal, characteristic
2#19136823C211yesmaximal, characteristic, complemented
3#19136732C211yesmaximal, characteristic
4#19133990C211yesmaximal, characteristic, complemented
5#19132643C211yesmaximal, characteristic, complemented
6#19132575C211yesmaximal, characteristic, complemented
7C43×#1331C211yesmaximal, characteristic
8#14583619—21no—
9#14583304C2211yescharacteristic
10#14583282—21no—
11#14583279C2211yescharacteristic
12#14583120—22no—
13#14583110—21no—
14#14583104—21no—
15C8×Dic86C2211yescharacteristic
16#14582993—21no—
17#14582724—21no—
18C4⋊(C43⋊C16)C2211yescharacteristic
19#14582704—22no—
20#14582700—21no—
21#14582646—21no—
22C4×D8×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Dic172—21no—
26C2×Dic172—41no—
27C2×Dic172D412yes—
28C2×#10621883—22no—
29#13063325—21no—
30#13063325—21no—
31#13063318—42no—
32#13063312—22no—
33#13063304—41no—
34C4×Dic86D411yescharacteristic
35#13063290—22no—
36#13063284—41no—
37C2×C43⋊C16—21no—
38#13063259—21no—
39#13063259—21no—
40C4⋊(C43⋊C8)D411yescharacteristic
41Dic43⋊C8—21no—
42#13063250—41no—
43#13063248—22no—
44C8×Dic43—21no—
45C2×D8×C43D411yescharacteristic
46C4×D4×C43—21no—
47C2×C16×C43—21no—
48#107×C43D411yescharacteristic
49C4⋊C8×C43—21no—
50#102×C43—21no—
51C4×C8×C43C2311yescharacteristic
52C2×D4×C43—21no—
53C22×C4×C43—41no—
54C2×Dic86—22no—
55C2×Dic86—41no—
56C2×Dic86D811yescharacteristic
57D8×C43—21no—
58D8×C43—21no—
59C2×C8×C43—41no—
60C2×C8×C43C2×D411yescharacteristic
61C2×C8×C43C2×D411yescharacteristic
62C4⋊C4×C43—21no—
63C22⋊C4×C43—41no—
64C42×C43C2×D411yescharacteristic
65C22⋊Dic43—42no—
66C22⋊Dic43—42no—
67#10621883—82no—
68C4⋊Dic43—41no—
69C4⋊Dic43—41no—
70C4⋊Dic43—41no—
71C4⋊Dic43—41no—
72C4⋊Dic43D811yescharacteristic
73Dic43⋊C4—21no—
74Dic43⋊C4—42no—
75C4×Dic43—21no—
76C4×Dic43—42no—
77C2×C43⋊C8—21no—
78Dic172—42no—
79Dic172—41no—
80Dic172—41no—
81Dic172—82no—
82C16×C43—41no—
83C43⋊C16—41no—
84C23×C43—41no—
85D4×C43—41no—
86D4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—81no—
89C2×C4×C43—81no—
90C2×C4×C43#12011yescharacteristic
91C2×C4×C43C2×D811yescharacteristic
92C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
93C2×Dic43—21no—
94C2×Dic43—21no—
95C2×Dic43—42no—
96C2×Dic43—81no—
97Dic86—21no—
98Dic86—21no—
99Dic86—42no—
100Dic86—42no—
101Dic86—81no—
102Dic86—81no—
103C8×C43—21no—
104C8×C43—81no—
105C8×C43#13511yescharacteristic
106C8×C43#13711yescharacteristic
107C43⋊C8—41no—
108#12383—431nomaximal, Sylow
109C22×C43—81no—
110C22×C43—81no—
111C22×C43—81no—
112C22×C43#44711yescharacteristic
113C4×C43—21no—
114C4×C43—81no—
115C4×C43#45211yescharacteristic
116C4×C43#45511yescharacteristic
117C4×C43#50811yescharacteristic
118C4×C43#50911yescharacteristic
119Dic43—41no—
120Dic43—41no—
121Dic43—82no—
122Dic43—161no—
123#3393—431no—
124#2241—431no—
125#2224—431no—
126#1674—431no—
127#1362—431no—
128Q8⋊C16—431no—
129#1331D4311yescharacteristic
130C2×C43—161no—
131C2×C43#164111yescharacteristic
132C2×C43#218611yescharacteristic
133C2×C43#219511yescharacteristic
134#556—861no—
135#500—431no—
136#495—861no—
137#494—431no—
138#464—862no—
139#462—861no—
140#461—861no—
141C8×Q8—431no—
142C4×Q16—861no—
143C4×D8C2×D4311yescharacteristic
144#366—861no—
145C4⋊C16—431no—
146#358—862no—
147#357—861no—
148C4×C16C2×D4311yescharacteristic
149#335C2×D4311yescharacteristic
150#332—861no—
151C43#1238311yescharacteristic, complemented, Sylow
152C2×Q16—432no—
153C2×Q16—861no—
154C2×Q16—1721no—
155C2×SD16—862no—
156C2×D8D17211yescharacteristic
157C4⋊Q8—861no—
158C4⋊Q8—861no—
159#126—1722no—
160#124—862no—
161C22⋊Q8—1721no—
162C4×Q8—431no—
163C4×Q8—862no—
164C4×D4—21no—
165#117—1721no—
166C2×C16—21no—
167C2×C16—861no—
168#107—861no—
169#107—861no—
170#107D17211yescharacteristic
171C4⋊C8—21no—
172C4⋊C8—431no—
173C4⋊C8—861no—
174#103—862no—
175#103—1721no—
176#102—21no—
177C4×C8—861no—
178C4×C8C22×D4311yescharacteristic
179C2×Q8—431no—
180C2×Q8—862no—
181C2×Q8—1721no—
182C2×D4—21no—
183C22×C4—41no—
184Q16—3442no—
185Q16—1722no—
186Q16—1721no—
187Q16—1721no—
188SD16—3442no—
189D8—21no—
190D8—21no—
191C2×C8—41no—
192C2×C8—861no—
193C2×C8C2×D17211yescharacteristic
194C2×C8D4×D4311yescharacteristic
195C4⋊C4—21no—
196C4⋊C4—431no—
197C4⋊C4—861no—
198C4⋊C4—1722no—
199C4⋊C4—1721no—
200C4⋊C4—1721no—
201C4⋊C4—1721no—
202C4⋊C4—1721no—
203C22⋊C4—41no—
204C22⋊C4—1722no—
205C22⋊C4—1722no—
206C42—861no—
207C42—1722no—
208C42D4×D4311yescharacteristic
209C16—41no—
210C16—1721no—
211C23—41no—
212Q8—861no—
213Q8—861no—
214Q8—3441no—
215Q8—3441no—
216Q8—1722no—
217Q8—1722no—
218D4—41no—
219D4—41no—
220C2×C4—41no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—861no—
224C2×C4—861no—
225C2×C4—3441no—
226C2×C4—1722no—
227C2×C4#1306329511yescharacteristic
228C2×C4D8×D4311yescharacteristic
229C2×C4#1306335211yescharacteristic
230C8—21no—
231C8—81no—
232C8—1721no—
233C8#1306334711yescharacteristic
234C8#1306335811yescharacteristic
235C22—81no—
236C22—81no—
237C22—81no—
238C22#1458303411yescharacteristic
239C4—21no—
240C4—81no—
241C4—3442no—
242C4—1721no—
243C4—1721no—
244C4—6881no—
245C4#1458306311yescharacteristic
246C4#1458307811yescharacteristic
247C4#1458333011yescharacteristic
248C4#1458333311yescharacteristic
249C2—161no—
250C2#1913379111yescharacteristic
251C2#1913651911yescharacteristic
252C2#1913657411yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1331C2
socleC22×C43#447
prime radicalC2×D8×C43D4
hypercenter#1331D43
hypocenterC43#12383
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
2. #19136823C2semidirect
4. #19133990C2semidirect
5. #19132643C2semidirect
6. #19132575C2semidirect
151. C43#12383semidirect

Maximal subgroups

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

subgroupindex
#191475812
#191368232
#191367322
#191339902
#191326432
#191325752
C43×#13312
#1238343