Finite Group Databasebeta

← #25010471

Subgroups — #25010471

Order 11008.

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

normal subgroups only

This group has 306 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#19147605C211yesmaximal, characteristic
2#19136819C211yesmaximal, characteristic
3#19136737C211yesmaximal, characteristic, complemented
4#19133990C211yesmaximal, characteristic, complemented
5#19132640C211yesmaximal, characteristic
6#19132575C211yesmaximal, characteristic, complemented
7C43×#1332C211yesmaximal, characteristic, complemented
8#14583634—21no—
9#14583304C2211yescharacteristic
10#14583284—21no—
11#14583276C2211yescharacteristic
12#14583117—22no—
13#14583110—21no—
14#14583099—21no—
15C8×Dic86C2211yescharacteristic
16#14582981—21no—
17#14582726—21no—
18C4⋊(C43⋊C16)C2211yescharacteristic
19#14582703—21no—
20#14582701—22no—
21#14582646—21no—
22C4×Q16×C43C2211yescharacteristic
23C4×C16×C43C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Dic172—41no—
26C2×#10621884—22no—
27C2×D344—21no—
28C2×D344D412yes—
29#13063325—21no—
30#13063322—21no—
31#13063314—22no—
32#13063313—41no—
33#13063310—42no—
34C4×Dic86D411yescharacteristic
35C4×D172—41no—
36#13063287—22no—
37C2×C43⋊C16—21no—
38#13063259—21no—
39#13063259—21no—
40C4⋊(C43⋊C8)D411yescharacteristic
41Dic43⋊C8—21no—
42#13063250—41no—
43#13063245—22no—
44C8×Dic43—21no—
45C2×Q16×C43D411yescharacteristic
46C4×Q8×C43—21no—
47C2×C16×C43—21no—
48#107×C43D411yescharacteristic
49C4⋊C8×C43—21no—
50#103×C43—21no—
51C4×C8×C43C2311yescharacteristic
52C2×Q8×C43—21no—
53C2×D172—22no—
54C2×D172—41no—
55C2×D172—41no—
56C2×C4×D43—42no—
57C2×Dic86—41no—
58C2×Dic86D811yescharacteristic
59Q16×C43—21no—
60Q16×C43—21no—
61C2×C8×C43—41no—
62C2×C8×C43C2×D411yescharacteristic
63C2×C8×C43C2×D411yescharacteristic
64C4⋊C4×C43—21no—
65C4⋊C4×C43—41no—
66C42×C43—41no—
67C42×C43C2×D411yescharacteristic
68#10621884—82no—
69(C2×D43)⋊C4—42no—
70(C2×D43)⋊C4—42no—
71(C2×D43)⋊C4—42no—
72C4⋊Dic43—41no—
73C4⋊Dic43—41no—
74C4⋊Dic43D811yescharacteristic
75Dic43⋊C4—21no—
76C4×Dic43—21no—
77C2×C43⋊C8—21no—
78Dic172—82no—
79D344—42no—
80D344—41no—
81D344—41no—
82C16×C43—41no—
83C43⋊C16—41no—
84C22×D43—42no—
85Q8×C43—41no—
86Q8×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
89C2×C4×C43#12011yescharacteristic
90C2×C4×C43C2×D811yescharacteristic
91C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
92C2×Dic43—21no—
93C2×Dic43—21no—
94C2×Dic43—81no—
95D172—42no—
96D172—42no—
97D172—81no—
98D172—81no—
99D172—161no—
100C4×D43—162no—
101Dic86—21no—
102Dic86—21no—
103Dic86—81no—
104Dic86—81no—
105C8×C43—21no—
106C8×C43—81no—
107C8×C43#13511yescharacteristic
108C8×C43#13711yescharacteristic
109C43⋊C8—41no—
110#12381—431nomaximal, Sylow
111C22×C43#44711yescharacteristic
112C2×D43—82no—
113C2×D43—82no—
114C2×D43—82no—
115C4×C43—21no—
116C4×C43—81no—
117C4×C43—81no—
118C4×C43#45211yescharacteristic
119C4×C43#45511yescharacteristic
120C4×C43#50811yescharacteristic
121C4×C43#50911yescharacteristic
122Dic43—41no—
123Dic43—41no—
124Dic43—161no—
125#3396—431no—
126#2240—431no—
127#2225—431no—
128#1674—431no—
129#1361—431no—
130Q8⋊C16—431no—
131#1332D4311yescharacteristic, complemented
132C2×C43#164111yescharacteristic
133C2×C43#218611yescharacteristic
134C2×C43#219411yescharacteristic
135D43—162no—
136#559—861no—
137#500—431no—
138#495—861no—
139#493—431no—
140#463—862no—
141#462—861no—
142#460—861no—
143C8×Q8—431no—
144C4×Q16C2×D4311yescharacteristic
145C4×D8—861no—
146#367—861no—
147C4⋊C16—431no—
148#358—861no—
149#357—862no—
150C4×C16C2×D4311yescharacteristic
151#335C2×D4311yescharacteristic
152#332—861no—
153C43#1238111yescharacteristic, complemented, Sylow
154C2×Q16—1721no—
155C2×Q16D17211yescharacteristic
156C2×SD16—862no—
157C2×D8—432no—
158C2×D8—861no—
159C4⋊Q8—861no—
160#127—861no—
161#124—862no—
162#124—1721no—
163#123—1722no—
164C4×Q8—21no—
165C4×Q8—431no—
166C4×D4—862no—
167C4×D4—1721no—
168C2×C16—21no—
169C2×C16—861no—
170#107—861no—
171#107—861no—
172#107D17211yescharacteristic
173C4⋊C8—21no—
174C4⋊C8—431no—
175C4⋊C8—861no—
176#103—21no—
177#103—1721no—
178#102—862no—
179C4×C8—861no—
180C4×C8C22×D4311yescharacteristic
181C2×Q8—21no—
182C2×Q8—431no—
183C2×Q8—1721no—
184C2×D4—862no—
185C2×D4—1721no—
186C2×D4—1721no—
187C22×C4—1722no—
188Q16—21no—
189Q16—21no—
190Q16—3442no—
191SD16—3442no—
192D8—1722no—
193D8—1721no—
194D8—1721no—
195C2×C8—41no—
196C2×C8—861no—
197C2×C8C2×D17211yescharacteristic
198C2×C8D4×D4311yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—41no—
201C4⋊C4—431no—
202C4⋊C4—861no—
203C4⋊C4—1721no—
204C4⋊C4—1721no—
205C22⋊C4—1722no—
206C22⋊C4—1722no—
207C22⋊C4—1722no—
208C42—41no—
209C42—861no—
210C42D4×D4311yescharacteristic
211C16—41no—
212C16—1721no—
213C23—1722no—
214Q8—41no—
215Q8—41no—
216Q8—861no—
217Q8—861no—
218Q8—3441no—
219Q8—3441no—
220D4—3441no—
221D4—3441no—
222D4—1722no—
223D4—1722no—
224D4—6881no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—861no—
228C2×C4—861no—
229C2×C4—3441no—
230C2×C4—6882no—
231C2×C4#1306329511yescharacteristic
232C2×C4D8×D4311yescharacteristic
233C2×C4#1306335211yescharacteristic
234C8—21no—
235C8—81no—
236C8—1721no—
237C8#1306334711yescharacteristic
238C8#1306335811yescharacteristic
239C22—3442no—
240C22—3442no—
241C22—3442no—
242C22#1458303411yescharacteristic
243C4—21no—
244C4—81no—
245C4—81no—
246C4—1721no—
247C4—1721no—
248C4—6881no—
249C4#1458306311yescharacteristic
250C4#1458307811yescharacteristic
251C4#1458333211yescharacteristic
252C4#1458333611yescharacteristic
253C2—6882no—
254C2#1913379111yescharacteristic
255C2#1913652111yescharacteristic
256C2#1913656711yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1332C2
socleC22×C43#447
prime radical#14583276C22
hypercenter#1332D43
hypocenterC43#12381
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
3. #19136737C2semidirect
4. #19133990C2semidirect
6. #19132575C2semidirect
7. C43×#1332C2semidirect
131. #1332D43semidirect
153. C43#12381semidirect

Maximal subgroups

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

subgroupindex
#191476052
#191368192
#191367372
#191339902
#191326402
#191325752
C43×#13322
#1238143