Finite Group Databasebeta

← #25010281

Subgroups — #25010281

Order 11008.

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

normal subgroups only

This group has 298 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#19147488C211yesmaximal, characteristic, complemented
2#19136820C211yesmaximal, characteristic
3#19136636C211yesmaximal, characteristic
4#19133956C211yesmaximal, characteristic
5#19132573C211yesmaximal, characteristic, complemented
6#19132558C211yesmaximal, characteristic, complemented
7C43×#1364C211yesmaximal, characteristic, complemented
8#14583624—21no—
9C2×#13063270—21no—
10#14583300—21no—
11#14583276C2211yescharacteristic
12#14583205—22no—
13#14583181—21no—
14#14583100—21no—
15C8×Dic86C2211yescharacteristic
16C4×Dic172C2211yescharacteristic
17#14582993—21no—
18#14582701—21no—
19#14582699—22no—
20C4×C43⋊C16C2211yescharacteristic
21#14582642—21no—
22C43×#500C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Dic172D411yescharacteristic
26C2×#10621873—41no—
27C2×D344—21no—
28C2×D344—21no—
29#13063323—41no—
30#13063322—21no—
31#13063316—22no—
32#13063315—42no—
33Q8×Dic43—41no—
34C4×Dic86—21no—
35C4×Dic86D411yescharacteristic
36#13063290—22no—
37#13063270—42no—
38C2×C43⋊C16—21no—
39#13063259D411yescharacteristic
40#13063256—22no—
41C4⋊(C43⋊C8)D411yescharacteristic
42Dic43⋊C8—21no—
43#13063250—21no—
44#13063248—22no—
45#13063247—41no—
46C8×Dic43—21no—
47C4⋊Q8×C43—21no—
48C2×C16×C43—21no—
49#107×C43—21no—
50#107×C43D412yes—
51C4⋊C8×C43—21no—
52C4×C8×C43C2311yescharacteristic
53C2×Q8×C43—41no—
54C2×D172—41no—
55C2×D172—41no—
56C2×D172—41no—
57C2×Dic86—21no—
58C2×Dic86D811yescharacteristic
59C2×C8×C43—41no—
60C2×C8×C43C2×D411yescharacteristic
61C2×C8×C43C2×D411yescharacteristic
62C4⋊C4×C43—22no—
63C4⋊C4×C43—41no—
64C42×C43C2×D411yescharacteristic
65C4⋊Dic43—21no—
66C4⋊Dic43—42no—
67C4⋊Dic43D811yescharacteristic
68Dic43⋊C4—21no—
69Dic43⋊C4—42no—
70Dic43⋊C4—42no—
71Dic43⋊C4—41no—
72C4×Dic43—21no—
73C4×Dic43—42no—
74C4×Dic43—41no—
75C2×C43⋊C8—21no—
76Dic172—21no—
77Dic172SD1612yescomplemented
78D344—42no—
79D344—41no—
80D344—41no—
81#10621873—82no—
82C16×C43—41no—
83C43⋊C16—41no—
84C22×D43—81no—
85Q8×C43—81no—
86Q8×C43—81no—
87C2×C4×C43—42no—
88C2×C4×C43#12011yescharacteristic
89C2×C4×C43C2×D811yescharacteristic
90C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
91C2×Dic43—21no—
92C2×Dic43—21no—
93C2×Dic43—41no—
94C2×Dic43—41no—
95D172—81no—
96D172—81no—
97D172—81no—
98D172—81no—
99D172—161no—
100Dic86—22no—
101Dic86—21no—
102Dic86—21no—
103Dic86—41no—
104C8×C43—21no—
105C8×C43—81no—
106C8×C43C2×SD1611yescharacteristic
107C8×C43#13711yescharacteristic
108C43⋊C8—41no—
109#12353—431nomaximal, Sylow
110C22×C43#44711yescharacteristic
111C2×D43—161no—
112C2×D43—161no—
113C2×D43—161no—
114C4×C43—21no—
115C4×C43—82no—
116C4×C43#44811yescharacteristic
117C4×C43#45411yescharacteristic
118C4×C43#50811yescharacteristic
119C4×C43#50911yescharacteristic
120Dic43—42no—
121Dic43—41no—
122Dic43—41no—
123Dic43—81no—
124#3383—431no—
125#2240—431no—
126#2207—431no—
127#1668—431no—
128#1364D4311yescharacteristic, complemented
129Q8⋊C16—431no—
130#1332—431no—
131C2×C43#162711yescharacteristic
132C2×C43#218611yescharacteristic
133C2×C43#219311yescharacteristic
134D43—321no—
135#557—861no—
136C2×SD32—861no—
137#500C2×D4311yescharacteristic
138#499—861no—
139#493—431no—
140#479—862no—
141#475—861no—
142#460—861no—
143C8×Q8—431no—
144C4×Q16—431no—
145C4×Q16—861no—
146C4⋊C16C2×D4311yescharacteristic
147#357—861no—
148#357—862no—
149C4×C16—431no—
150#335C2×D4311yescharacteristic
151#331—861no—
152C43#1235311yescharacteristic, complemented, Sylow
153C2×Q16—431no—
154C2×SD16—1721no—
155C2×D8—861no—
156C2×D8—861no—
157C4⋊Q8—21no—
158C4⋊Q8—1721no—
159#127—861no—
160#125—862no—
161#125—1722no—
162C4×Q8—431no—
163C4×Q8—862no—
164C4×Q8—861no—
165C4×Q8—1721no—
166SD32—1722no—
167C2×C16—21no—
168C2×C16—861no—
169#107—21no—
170#107—431no—
171#107D17212yes—
172#106—862no—
173C4⋊C8—21no—
174C4⋊C8—431no—
175C4⋊C8—861no—
176#103—862no—
177#103—861no—
178#102—1721no—
179C4×C8—861no—
180C4×C8C22×D4311yescharacteristic
181C2×Q8—41no—
182C2×Q8—431no—
183C2×Q8—861no—
184C2×D4—1721no—
185C2×D4—1721no—
186C2×D4—1721no—
187Q16—432no—
188Q16—861no—
189SD16—3442no—
190D8—1722no—
191D8—1721no—
192D8—1721no—
193C2×C8—41no—
194C2×C8—861no—
195C2×C8C2×D17211yescharacteristic
196C2×C8D4×D4311yescharacteristic
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—431no—
200C4⋊C4—861no—
201C4⋊C4—861no—
202C4⋊C4—1722no—
203C4⋊C4—1722no—
204C4⋊C4—1722no—
205C4⋊C4—1721no—
206C42—861no—
207C42—1722no—
208C42—1721no—
209C42D4×D4311yescharacteristic
210C16—41no—
211C16—1721no—
212C23—3441no—
213Q8—81no—
214Q8—81no—
215Q8—861no—
216Q8—861no—
217Q8—862no—
218Q8—1721no—
219D4—3441no—
220D4—3441no—
221D4—3441no—
222D4—3441no—
223D4—6881no—
224C2×C4—42no—
225C2×C4—861no—
226C2×C4—861no—
227C2×C4—1721no—
228C2×C4—1721no—
229C2×C4#1306329511yescharacteristic
230C2×C4D8×D4311yescharacteristic
231C2×C4#1306335211yescharacteristic
232C8—21no—
233C8—81no—
234C8—1721no—
235C8SD16×D4311yescharacteristic
236C8#1306335711yescharacteristic
237C22—6881no—
238C22—6881no—
239C22—6881no—
240C22#1458303411yescharacteristic
241C4—21no—
242C4—82no—
243C4—3441no—
244C4—1722no—
245C4—1721no—
246C4—1721no—
247C4#1458303911yescharacteristic
248C4#1458307411yescharacteristic
249C4#1458333011yescharacteristic
250C4#1458333311yescharacteristic
251C2—13761no—
252C2#1913369911yescharacteristic
253C2#1913651911yescharacteristic
254C2#1913656211yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1364C2
socleC22×C43#447
prime radical#14583276C22
hypercenter#1364D43
hypocenterC43#12353
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
1. #19147488C2semidirect
5. #19132573C2semidirect
6. #19132558C2semidirect
7. C43×#1364C2semidirect
77. Dic172SD16semidirect
128. #1364D43semidirect
152. C43#12353semidirect

Maximal subgroups

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

subgroupindex
#191474882
#191368202
#191366362
#191339562
#191325732
#191325582
C43×#13642
#1235343