Finite Group Databasebeta

← #25010309

Subgroups — #25010309

Order 11008.

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

normal subgroups only

This group has 282 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
2#19136824C211yesmaximal, characteristic
3#19136646C211yesmaximal, characteristic
4#19133966C211yesmaximal, characteristic
5#19132573C211yesmaximal, characteristic
6#19132558C211yesmaximal, characteristic
7C43×#1364C211yesmaximal, characteristic
8#14583624—21no—
9C2×Dic344—21no—
10#14583300—21no—
11#14583279C2211yescharacteristic
12#14583205—22no—
13#14583185—21no—
14#14583181—21no—
15C8×Dic86C2211yescharacteristic
16C4×Dic172C2211yescharacteristic
17#14582993—21no—
18#14582704—21no—
19#14582702—22no—
20C4×C43⋊C16C2211yescharacteristic
21#14582644—21no—
22C43×#500C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Dic172—21no—
26C2×Dic172—21no—
27C2×Dic172D411yescharacteristic
28#13063325—21no—
29#13063323—41no—
30#13063316—22no—
31#13063315—42no—
32Q8×Dic43—41no—
33C4×Dic86—21no—
34C4×Dic86D411yescharacteristic
35#13063290—22no—
36Dic344—42no—
37C2×C43⋊C16—21no—
38#13063259D411yescharacteristic
39#13063257—41no—
40#13063256—22no—
41C4⋊(C43⋊C8)D411yescharacteristic
42Dic43⋊C8—21no—
43#13063250—21no—
44#13063250—41no—
45#13063248—22no—
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×Dic86—21no—
55C2×Dic86—41no—
56C2×Dic86D811yescharacteristic
57C2×C8×C43—41no—
58C2×C8×C43C2×D411yescharacteristic
59C2×C8×C43C2×D411yescharacteristic
60C4⋊C4×C43—22no—
61C4⋊C4×C43—41no—
62C42×C43C2×D411yescharacteristic
63C4⋊Dic43—21no—
64C4⋊Dic43—42no—
65C4⋊Dic43—41no—
66C4⋊Dic43—41no—
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—
77Dic172—42no—
78Dic172—41no—
79Dic172—41no—
80Dic172SD1612yes—
81C16×C43—41no—
82C43⋊C16—41no—
83Q8×C43—81no—
84Q8×C43—81no—
85C2×C4×C43—42no—
86C2×C4×C43#12011yescharacteristic
87C2×C4×C43C2×D811yescharacteristic
88C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
89C2×Dic43—21no—
90C2×Dic43—21no—
91C2×Dic43—41no—
92C2×Dic43—41no—
93C2×Dic43—81no—
94Dic86—22no—
95Dic86—21no—
96Dic86—21no—
97Dic86—41no—
98Dic86—81no—
99Dic86—81no—
100C8×C43—21no—
101C8×C43—81no—
102C8×C43C2×SD1611yescharacteristic
103C8×C43#13711yescharacteristic
104C43⋊C8—41no—
105#12357—431nomaximal, Sylow
106C22×C43#44711yescharacteristic
107C4×C43—21no—
108C4×C43—82no—
109C4×C43#44811yescharacteristic
110C4×C43#45411yescharacteristic
111C4×C43#50811yescharacteristic
112C4×C43#51011yescharacteristic
113Dic43—42no—
114Dic43—41no—
115Dic43—41no—
116Dic43—81no—
117Dic43—161no—
118#3383—431no—
119#2241—431no—
120#2209—431no—
121#1670—431no—
122#1364D4311yescharacteristic
123Q8⋊C16—431no—
124#1332—431no—
125C2×C43#162711yescharacteristic
126C2×C43#218911yescharacteristic
127C2×C43#219511yescharacteristic
128#557—861no—
129C2×Q32—861no—
130#500C2×D4311yescharacteristic
131#499—861no—
132#494—431no—
133#479—862no—
134#475—861no—
135#475—861no—
136C8×Q8—431no—
137C4×Q16—431no—
138C4×Q16—861no—
139C4⋊C16C2×D4311yescharacteristic
140#358—861no—
141#358—862no—
142C4×C16—431no—
143#335C2×D4311yescharacteristic
144#332—861no—
145C43#1235711yescharacteristic, complemented, Sylow
146C2×Q16—431no—
147C2×Q16—861no—
148C2×Q16—861no—
149C4⋊Q8—21no—
150C4⋊Q8—861no—
151C4⋊Q8—1721no—
152#125—862no—
153#125—1722no—
154C4×Q8—431no—
155C4×Q8—862no—
156C4×Q8—861no—
157C4×Q8—1721no—
158Q32—1722no—
159C2×C16—21no—
160C2×C16—861no—
161#107—21no—
162#107—431no—
163#107D17212yes—
164#106—862no—
165#106—1721no—
166C4⋊C8—21no—
167C4⋊C8—431no—
168C4⋊C8—861no—
169#103—862no—
170#103—861no—
171#103—1721no—
172C4×C8—861no—
173C4×C8C22×D4311yescharacteristic
174C2×Q8—41no—
175C2×Q8—431no—
176C2×Q8—861no—
177C2×Q8—1721no—
178Q16—432no—
179Q16—861no—
180Q16—1722no—
181Q16—1721no—
182Q16—1721no—
183C2×C8—41no—
184C2×C8—861no—
185C2×C8C2×D17211yescharacteristic
186C2×C8D4×D4311yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—431no—
190C4⋊C4—861no—
191C4⋊C4—861no—
192C4⋊C4—1722no—
193C4⋊C4—1722no—
194C4⋊C4—1722no—
195C4⋊C4—1721no—
196C4⋊C4—1721no—
197C4⋊C4—1721no—
198C42—861no—
199C42—1722no—
200C42—1721no—
201C42D4×D4311yescharacteristic
202C16—41no—
203C16—1721no—
204Q8—81no—
205Q8—81no—
206Q8—861no—
207Q8—861no—
208Q8—862no—
209Q8—3441no—
210Q8—3441no—
211Q8—1721no—
212C2×C4—42no—
213C2×C4—861no—
214C2×C4—861no—
215C2×C4—3441no—
216C2×C4—1721no—
217C2×C4—1721no—
218C2×C4#1306329511yescharacteristic
219C2×C4D8×D4311yescharacteristic
220C2×C4#1306335211yescharacteristic
221C8—21no—
222C8—81no—
223C8—1721no—
224C8SD16×D4311yescharacteristic
225C8#1306335711yescharacteristic
226C22#1458303411yescharacteristic
227C4—21no—
228C4—82no—
229C4—3441no—
230C4—1722no—
231C4—1721no—
232C4—1721no—
233C4—6881no—
234C4#1458303911yescharacteristic
235C4#1458307411yescharacteristic
236C4#1458332811yescharacteristic
237C4#1458333811yescharacteristic
238C2#1913369911yescharacteristic
239C2#1913653611yescharacteristic
240C2#1913657611yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1364C2
socle, prime radicalC22×C43#447
hypercenter#1364D43
hypocenterC43#12357
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
145. C43#12357semidirect

Maximal subgroups

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

subgroupindex
#191474882
#191368242
#191366462
#191339662
#191325732
#191325582
C43×#13642
#1235743