Finite Group Databasebeta

← #24984372

Subgroups — #24984372

Order 11008.

290 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 59 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#19136280C211yesmaximal, characteristic
2#19136260C211yesmaximal, characteristic
3C43×#1962C211yesmaximal, characteristic
4#14582883—21no—
5#14582873—21no—
6#14582698C412yescomplemented
7#14582696—21no—
8#14582694—21no—
9#14582692C412yescomplemented
10C43×#532C2211yescharacteristic
11C43×#423C411yescharacteristic, complemented
12C2×#104×C43—21no—
13C2×#104×C43—21no—
14C43×C43C411yescharacteristic, complemented
15C2×#10621877—41no—
16#13063284—41no—
17#13063244—22no—
18#13063242—41no—
19#13063240—22no—
20#13063240—41no—
21C2×#41×C43D411yescharacteristic
22C2×#41×C43D411yescharacteristic
23C2×M16×C43—21no—
24C4⋊Q8×C43C2×C411yescharacteristic
25#127×C43C2×C411yescharacteristic
26#124×C43D411yescharacteristic
27#124×C43Q811yescharacteristic
28#121×C43—41no—
29C4×D4×C43—41no—
30C2×C42×C43—21no—
31C2×C42×C43—41no—
32C2×C42×C43C2×C411yescharacteristic
33C4⋊C8×C43—41no—
34#104×C43—42no—
35#104×C43—42no—
36#41×C43—41no—
37#41×C43—41no—
38#41×C43—41no—
39#41×C43—41no—
40C2×Q8×C43C22⋊C411yescharacteristic
41C2×Q8×C43C4⋊C411yescharacteristic
42C2×D4×C43—21no—
43C2×D4×C43—21no—
44C2×D4×C43—41no—
45C2×D4×C43C22⋊C411yescharacteristic
46C2×D4×C43C4⋊C411yescharacteristic
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43—41no—
51C22×C4×C43C22⋊C411yescharacteristic
52M16×C43—41no—
53M16×C43—41no—
54C2×C8×C43—41no—
55C4⋊C4×C43—41no—
56C22⋊C4×C43—41no—
57C22⋊C4×C43—41no—
58C42×C43—21no—
59C42×C43—22no—
60C42×C43—41no—
61C42×C43—44no—
62C42×C43C4211yescharacteristic
63C42×C43C4⋊C411yescharacteristic
64C22⋊Dic43—42no—
65C4⋊Dic43—81no—
66C4×Dic43—81no—
67#10621877—42no—
68#10621877—81no—
69C2×C43⋊C8—81no—
70C23×C43—21no—
71C23×C43—21no—
72C23×C43#9911yescharacteristic
73Q8×C43—41no—
74Q8×C43—41no—
75D4×C43—41no—
76D4×C43—41no—
77D4×C43—82no—
78D4×C43—81no—
79D4×C43—81no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—42no—
87C2×C4×C43—42no—
88C2×C4×C43—44no—
89C2×C4×C43—41no—
90C2×C4×C43—41no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43#9511yescharacteristic
94C2×C4×C43#9911yescharacteristic
95C2×Dic43—82no—
96C8×C43—81no—
97C43⋊C8—82no—
98#7497—431nomaximal, Sylow
99C22×C43—21no—
100C22×C43—41no—
101C22×C43—41no—
102C22×C43—41no—
103C22×C43—81no—
104C22×C43—81no—
105C22×C43#34211yescharacteristic
106C4×C43—22no—
107C4×C43—21no—
108C4×C43—41no—
109C4×C43—44no—
110C4×C43—41no—
111C4×C43—41no—
112C4×C43#35311yescharacteristic
113C4×C43#35411yescharacteristic
114Dic43—162no—
115#2132—431no—
116#2126—431no—
117#1962D4311yescharacteristic
118C2×C43—21no—
119C2×C43—41no—
120C2×C43—81no—
121C2×C43—81no—
122C2×C43#139311yescharacteristic
123#532C2×D4311yescharacteristic
124#423Dic4311yescharacteristic, complemented
125C2×#104—21no—
126C2×#104—21no—
127#413—861no—
128#410—861no—
129C43Dic4311yescharacteristic, complemented
130#356—432no—
131#355—861no—
132#354—861no—
133#353—432no—
134C43#749711yescharacteristic, complemented, Sylow
135C2×#41C22⋊D4311yescharacteristic
136C2×#41C22⋊D4311yescharacteristic
137C2×M16—21no—
138C2×M16—1721no—
139C4⋊Q8C4×D4311yescharacteristic
140#127C4×D4311yescharacteristic
141#124Dic8611yescharacteristic
142#124D17211yescharacteristic
143#121—41no—
144C4×D4—41no—
145#117—1721no—
146C2×C42—21no—
147C2×C42—41no—
148C2×C42C2×Dic4311yescharacteristic
149C4⋊C8—41no—
150#104—42no—
151#104—42no—
152#101—862no—
153#100—1721no—
154#99—862no—
155#99—1721no—
156#41—41no—
157#41—41no—
158#41—41no—
159#41—41no—
160C2×Q8Dic43⋊C411yescharacteristic
161C2×Q8(C2×D43)⋊C411yescharacteristic
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—41no—
165C2×D4Dic43⋊C411yescharacteristic
166C2×D4(C2×D43)⋊C411yescharacteristic
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—41no—
171C22×C4C22⋊Dic4311yescharacteristic
172M16—41no—
173M16—41no—
174M16—3441no—
175M16—1722no—
176C2×C8—41no—
177C2×C8—3441no—
178C4⋊C4—41no—
179C4⋊C4—3441no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—1722no—
183C42—21no—
184C42—22no—
185C42—41no—
186C42—44no—
187C42—3441no—
188C42C4×Dic4311yescharacteristic
189C42C4⋊Dic4311yescharacteristic
190C23—21no—
191C23—21no—
192C23#1306324011yescharacteristic
193Q8—41no—
194Q8—41no—
195D4—41no—
196D4—41no—
197D4—82no—
198D4—81no—
199D4—81no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—3442no—
214C2×C4C43⋊#9511yescharacteristic
215C2×C4#1306324011yescharacteristic
216C8—81no—
217C8—3442no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—81no—
223C22—81no—
224C22#1458266611yescharacteristic
225C4—22no—
226C4—21no—
227C4—41no—
228C4—44no—
229C4—41no—
230C4—41no—
231C4—6882no—
232C4#1458269211yescharacteristic
233C4#1458269411yescharacteristic
234C2—21no—
235C2—41no—
236C2—81no—
237C2—81no—
238C2#1913272011yescharacteristic
subgroupG/H
centerC4#14582692
commutatorC42×C43C42
Frattini#532C2×D43
FittingC43×#1962C2
socleC2×C43#1393
prime radical, cosocleC43×#532C22
hypercenter#1962D43
hypocenterC43#7497
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #1962

Complements

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

NH ≅ G/Ntype
6. #14582698C4semidirect
9. #14582692C4semidirect
11. C43×#423C4semidirect
14. C43×C43C4semidirect
124. #423Dic43semidirect
129. C43Dic43semidirect
134. C43#7497semidirect

Maximal subgroups

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

subgroupindex
#191362802
#191362602
C43×#19622
#749743