Finite Group Databasebeta

← #25010881

Subgroups — #25010881

Order 11008.

228 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 71 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#19136851C211yesmaximal, characteristic
2#19133965C211yesmaximal, characteristic, complemented
3#19133955C211yesmaximal, characteristic
4#19132667C211yesmaximal, characteristic, complemented
5#19132645C211yesmaximal, characteristic, complemented
6#19132642C211yesmaximal, characteristic
7C43×#2183C211yesmaximal, characteristic, complemented
8C2×#13063270—21no—
9C2×#13063270—21no—
10#14583279C2211yescharacteristic
11#14583276C2211yescharacteristic
12#14583184—21no—
13#14583099—21no—
14#14582652C2211yescharacteristic
15#14582652C2211yescharacteristic
16#14582646—21no—
17#14582642—21no—
18C8×Q8×C43C2211yescharacteristic
19C43×C4⋊C16—21no—
20C43×C4⋊C16C2211yescharacteristic
21C43×#346—21no—
22C4×C16×C43C2211yescharacteristic
23C2×Dic172—21no—
24C2×Dic172—21no—
25C2×#10621884—41no—
26C2×D344—21no—
27C2×D344—21no—
28#13063325—21no—
29#13063322—21no—
30#13063270—42no—
31#13063270—42no—
32#13063256—41no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35#13063249—41no—
36#13063245—41no—
37C4×Q8×C43D411yescharacteristic
38C2×C16×C43—21no—
39C2×C16×C43D411yescharacteristic
40C2×C16×C43D411yescharacteristic
41C4⋊C8×C43—21no—
42C4⋊C8×C43D411yescharacteristic
43C4×C8×C43—21no—
44C4×C8×C43C2311yescharacteristic
45C2×Q8×C43D811yescharacteristic
46C2×D172—41no—
47C2×D172—41no—
48C2×D172—41no—
49C2×Dic86—41no—
50C2×C8×C43—21no—
51C2×C8×C43C2×D411yescharacteristic
52C2×C8×C43#4111yescharacteristic
53C4⋊C4×C43—21no—
54C4⋊C4×C43D811yescharacteristic
55C42×C43—21no—
56C42×C43C2×D411yescharacteristic
57#10621884—82no—
58C4⋊Dic43—41no—
59C4⋊Dic43—41no—
60C2×C43⋊C8—41no—
61C2×C43⋊C8—41no—
62Dic172—41no—
63Dic172—41no—
64Dic172—81no—
65D344—41no—
66D344—41no—
67D344—81no—
68C16×C43—21no—
69C16×C43—41no—
70C16×C43SD1612yescomplemented
71C22×D43—81no—
72Q8×C43—21no—
73Q8×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43#12111yescharacteristic
77C2×C4×C43C2×D811yescharacteristic
78C2×C4×C43#13511yescharacteristic
79C2×Dic43—81no—
80D172—81no—
81D172—81no—
82D172—81no—
83D172—81no—
84D172—161no—
85Dic86—81no—
86Dic86—81no—
87C8×C43—21no—
88C8×C43—41no—
89C8×C43C2×SD1611yescharacteristic
90C8×C43AGL(1,ℤ/8)11yescharacteristic
91C43⋊C8—81no—
92C43⋊C8—81no—
93#12444—431nomaximal, Sylow
94C22×C43#46611yescharacteristic
95C2×D43—161no—
96C2×D43—161no—
97C2×D43—161no—
98C4×C43—21no—
99C4×C43—41no—
100C4×C43—41no—
101C4×C43#46011yescharacteristic
102C4×C43#47211yescharacteristic
103C4×C43#50911yescharacteristic
104C4×C43#51011yescharacteristic
105Dic43—161no—
106#2248—431no—
107#2183D4311yescharacteristic, complemented
108#1670—431no—
109#1668—431no—
110#1371—431no—
111#1362—431no—
112#1361—431no—
113C2×C43#166811yescharacteristic
114C2×C43#222011yescharacteristic
115C2×C43#222311yescharacteristic
116D43—321no—
117C2×SD32—861no—
118C2×SD32—861no—
119#494—431no—
120#493—431no—
121#475—861no—
122#460—861no—
123C8×Q8C2×D4311yescharacteristic
124C4⋊C16—21no—
125C4⋊C16C2×D4311yescharacteristic
126#346—21no—
127C4×C16C2×D4311yescharacteristic
128#335—431no—
129#335—431no—
130#332—861no—
131#331—861no—
132C43#1244411yescharacteristic, complemented, Sylow
133C2×Q16—861no—
134C2×Q16—861no—
135C2×SD16—1721no—
136C2×D8—861no—
137C2×D8—861no—
138C4⋊Q8—861no—
139#127—861no—
140C4×Q8D17211yescharacteristic
141SD32—1722no—
142SD32—1722no—
143C2×C16—21no—
144C2×C16C22⋊D4311yescharacteristic
145C2×C16C22⋊D4311yescharacteristic
146#106—1721no—
147C4⋊C8—21no—
148C4⋊C8—861no—
149C4⋊C8—861no—
150C4⋊C8D17211yescharacteristic
151#103—1721no—
152#102—1721no—
153C4×C8—21no—
154C4×C8C22×D4311yescharacteristic
155C2×Q8—1721no—
156C2×Q8D34411yescharacteristic
157C2×D4—1721no—
158C2×D4—1721no—
159C2×D4—1721no—
160Q16—3441no—
161Q16—1721no—
162Q16—1721no—
163SD16—3442no—
164D8—3441no—
165D8—1721no—
166D8—1721no—
167C2×C8—21no—
168C2×C8—1721no—
169C2×C8—1721no—
170C2×C8#1062189811yescharacteristic
171C2×C8C2×C22⋊D4311yescharacteristic
172C4⋊C4—21no—
173C4⋊C4—1721no—
174C4⋊C4—1721no—
175C4⋊C4D34411yescharacteristic
176C42—21no—
177C42C2×D17211yescharacteristic
178C16—21no—
179C16—41no—
180C16#1062188412yescomplemented
181C23—3441no—
182Q8—21no—
183Q8—21no—
184Q8—3441no—
185Q8—3441no—
186D4—3441no—
187D4—3441no—
188D4—3441no—
189D4—3441no—
190D4—6881no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—3441no—
194C2×C4#1306329911yescharacteristic
195C2×C4C2×D34411yescharacteristic
196C2×C4#1306334711yescharacteristic
197C8—21no—
198C8—41no—
199C8—3441no—
200C8—3441no—
201C8C2×#1062188411yescharacteristic
202C8#1306335011yescharacteristic
203C22—6881no—
204C22—6881no—
205C22—6881no—
206C22#1458313511yescharacteristic
207C4—21no—
208C4—41no—
209C4—41no—
210C4—6881no—
211C4#1458309911yescharacteristic
212C4#1458316911yescharacteristic
213C4#1458333711yescharacteristic
214C4#1458334211yescharacteristic
215C2—13761no—
216C2#1913395511yescharacteristic
217C2#1913670811yescharacteristic
218C2#1913672511yescharacteristic
subgroupG/H
centerC22#14583135
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2183C2
socleC22×C43#466
prime radical#14583276C22
hypercenter#2183D43
hypocenterC43#12444
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #2183

Complements

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

NH ≅ G/Ntype
2. #19133965C2semidirect
4. #19132667C2semidirect
5. #19132645C2semidirect
7. C43×#2183C2semidirect
70. C16×C43SD16semidirect
107. #2183D43semidirect
132. C43#12444semidirect
180. C16#10621884semidirect

Maximal subgroups

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

subgroupindex
#191368512
#191339652
#191339552
#191326672
#191326452
#191326422
C43×#21832
#1244443