Finite Group Databasebeta

← #25010863

Subgroups — #25010863

Order 11008.

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

normal subgroups only

This group has 232 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#19136850C211yesmaximal, characteristic
2#19136497C211yesmaximal, characteristic, complemented
3#19133966C211yesmaximal, characteristic, complemented
4#19133952C211yesmaximal, characteristic
5#19132668C211yesmaximal, characteristic, complemented
6#19132645C211yesmaximal, characteristic, complemented
7C43×#1361C211yesmaximal, characteristic
8C2×#13063269—21no—
9C2×#13063269—21no—
10#14583279C2211yescharacteristic
11#14583185—21no—
12#14583096—21no—
13C8×Dic86C2211yescharacteristic
14Dic43⋊C16—21no—
15C4×C43⋊C16C2211yescharacteristic
16C16×Dic43—21no—
17#14582652C2211yescharacteristic
18#14582644—21no—
19#14582643—21no—
20C43×#493C2211yescharacteristic
21C43×C4⋊C16C2211yescharacteristic
22C43×#335C2211yescharacteristic
23C2×Dic172—21no—
24C2×Dic172—21no—
25C2×#10621883—41no—
26#13063325—21no—
27C4×Dic86D411yescharacteristic
28#13063269—42no—
29#13063269—42no—
30C2×C43⋊C16D411yescharacteristic
31C2×C43⋊C16D411yescharacteristic
32#13063257—41no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)D411yescharacteristic
35Dic43⋊C8—21no—
36#13063250—41no—
37#13063246—41no—
38C8×Dic43—21no—
39C2×D8×C43—21no—
40C2×D8×C43—21no—
41#127×C43—21no—
42C2×C16×C43—21no—
43C4⋊C8×C43—21no—
44C4×C8×C43C2311yescharacteristic
45C2×D4×C43—41no—
46C2×D4×C43—41no—
47C2×D4×C43—41no—
48C2×Dic86—41no—
49C2×Dic86D811yescharacteristic
50D8×C43—41no—
51D8×C43—41no—
52D8×C43—81no—
53C2×C8×C43—41no—
54C2×C8×C43C2×D411yescharacteristic
55C2×C8×C43#4111yescharacteristic
56C42×C43C2×D411yescharacteristic
57#10621883—82no—
58C4⋊Dic43—41no—
59C4⋊Dic43—41no—
60C4⋊Dic43D811yescharacteristic
61Dic43⋊C4—21no—
62C4×Dic43—21no—
63C2×C43⋊C8—21no—
64C2×C43⋊C8—41no—
65Dic172—41no—
66Dic172—41no—
67Dic172—81no—
68C16×C43—41no—
69C43⋊C16—21no—
70C43⋊C16SD1612yescomplemented
71C23×C43—81no—
72D4×C43—81no—
73D4×C43—81no—
74D4×C43—81no—
75D4×C43—81no—
76D4×C43—161no—
77C2×C4×C43#12111yescharacteristic
78C2×C4×C43C2×D811yescharacteristic
79C2×C4×C43#13511yescharacteristic
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—81no—
83Dic86—21no—
84Dic86—81no—
85Dic86—81no—
86Dic86SD3212yescomplemented
87C8×C43—21no—
88C8×C43—81no—
89C8×C43C2×SD1611yescharacteristic
90C8×C43AGL(1,ℤ/8)11yescharacteristic
91C43⋊C8—41no—
92C43⋊C8—81no—
93#12441—431nomaximal, Sylow
94C22×C43—161no—
95C22×C43—161no—
96C22×C43—161no—
97C22×C43#46611yescharacteristic
98C4×C43—21no—
99C4×C43#46011yescharacteristic
100C4×C43#47211yescharacteristic
101C4×C43C2×SD3211yescharacteristic
102C4×C43#50811yescharacteristic
103Dic43—22no—
104Dic43—41no—
105Dic43—161no—
106#2248—431no—
107Q8×C16—431no—
108#1670—431no—
109#1668—431no—
110#1372—431no—
111#1362—431no—
112#1361D4311yescharacteristic
113C2×C43—321no—
114C2×C43#166811yescharacteristic
115C2×C43#221711yescharacteristic
116C2×C43#222311yescharacteristic
117C2×SD32—861no—
118C2×SD32—861no—
119#494—431no—
120#493C2×D4311yescharacteristic
121#475—861no—
122#460—861no—
123C8×Q8—431no—
124C4⋊C16—861no—
125C4⋊C16C2×D4311yescharacteristic
126C4×C16—431no—
127C4×C16—861no—
128#335—431no—
129#335C2×D4311yescharacteristic
130#332—861no—
131#331—861no—
132C43#1244111yescharacteristic, complemented, Sylow
133C2×Q16—861no—
134C2×Q16—861no—
135C2×SD16—1721no—
136C2×D8—21no—
137C2×D8—21no—
138C4⋊Q8—861no—
139#127—21no—
140C4×Q8—431no—
141SD32—1722no—
142SD32—1722no—
143C2×C16—21no—
144C2×C16—431no—
145C2×C16—431no—
146#106—1721no—
147C4⋊C8—21no—
148C4⋊C8—431no—
149C4⋊C8—861no—
150C4⋊C8—861no—
151#103—1721no—
152#102—1721no—
153C4×C8—861no—
154C4×C8C22×D4311yescharacteristic
155C2×Q8—431no—
156C2×Q8—1721no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160Q16—3441no—
161Q16—1721no—
162Q16—1721no—
163SD16—3442no—
164D8—41no—
165D8—41no—
166D8—81no—
167C2×C8—41no—
168C2×C8—861no—
169C2×C8—1721no—
170C2×C8#1062189811yescharacteristic
171C2×C8D4×D4311yescharacteristic
172C4⋊C4—431no—
173C4⋊C4—861no—
174C4⋊C4—1721no—
175C4⋊C4—1721no—
176C42—861no—
177C42D4×D4311yescharacteristic
178C16—41no—
179C16—432no—
180C16—861no—
181C23—81no—
182Q8—432no—
183Q8—861no—
184Q8—3441no—
185Q8—3441no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—861no—
192C2×C4—861no—
193C2×C4—3441no—
194C2×C4#1306329811yescharacteristic
195C2×C4D8×D4311yescharacteristic
196C2×C4#1306334611yescharacteristic
197C8—21no—
198C8—81no—
199C8—3441no—
200C8—1721no—
201C8SD16×D4311yescharacteristic
202C8#1306334911yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1458313411yescharacteristic
207C4—21no—
208C4—862no—
209C4—1721no—
210C4—6881no—
211C4#1458309811yescharacteristic
212C4#1458316811yescharacteristic
213C4SD32×D4311yescharacteristic
214C4#1458332811yescharacteristic
215C2—321no—
216C2#1913395411yescharacteristic
217C2#1913669011yescharacteristic
218C2#1913672411yescharacteristic
subgroupG/H
centerC22#14583134
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1361C2
socleC22×C43#466
prime radicalC43×#493C22
hypercenter#1361D43
hypocenterC43#12441
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #19136497C2semidirect
3. #19133966C2semidirect
5. #19132668C2semidirect
6. #19132645C2semidirect
70. C43⋊C16SD16semidirect
86. Dic86SD32semidirect
132. C43#12441semidirect

Maximal subgroups

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

subgroupindex
#191368502
#191364972
#191339662
#191339522
#191326682
#191326452
C43×#13612
#1244143