Finite Group Databasebeta

← #24984370

Subgroups — #24984370

Order 11008.

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

normal subgroups only

This group has 274 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#19134979C211yesmaximal, characteristic
3C43×#1560C211yesmaximal, characteristic
4#14583666C411yescharacteristic
5#14582916—21no—
6#14582883—21no—
7#14582873C411yescharacteristic
8#14582698—21no—
9#14582696C412yescomplemented
10#14582659—21no—
11C43×#532C2211yescharacteristic
12C43×#423—21no—
13C43×#333—21no—
14C43×#331C412yescomplemented
15#13063332—42no—
16C2×#10621877—21no—
17C2×#10621877—41no—
18C2×#10621877—41no—
19#13063284—21no—
20#13063252—42no—
21#13063244—22no—
22#13063242—41no—
23#13063240—41no—
24C2×#41×C43C2×C411yescharacteristic
25C2×#41×C43D411yescharacteristic
26C2×M16×C43—41no—
27C4⋊Q8×C43D411yescharacteristic
28#127×C43C2×C411yescharacteristic
29#124×C43C2×C411yescharacteristic
30#124×C43Q811yescharacteristic
31#121×C43—41no—
32C4×D4×C43—41no—
33C2×C42×C43D411yescharacteristic
34C4⋊C8×C43—22no—
35C4⋊C8×C43—41no—
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×C43C4211yescharacteristic
46C2×D4×C43C4⋊C411yescharacteristic
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43C22⋊C411yescharacteristic
51M16×C43—82no—
52C2×C8×C43—42no—
53C4⋊C4×C43—41no—
54C22⋊C4×C43—41no—
55C22⋊C4×C43—41no—
56C42×C43—21no—
57C42×C43C22⋊C411yescharacteristic
58C42×C43C4⋊C411yescharacteristic
59C22⋊Dic43—41no—
60C4⋊Dic43—41no—
61C4×Dic43—41no—
62#10621877—22no—
63#10621877—41no—
64#10621877—42no—
65#10621877—42no—
66#10621877—81no—
67C2×C43⋊C8—41no—
68C2×C43⋊C8—42no—
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—42no—
78D4×C43—81no—
79D4×C43—81no—
80D4×C43—81no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—41no—
88C2×C4×C43—41no—
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—81no—
96C8×C43—82no—
97C43⋊C8—42no—
98C43⋊C8—82no—
99#7496—431nomaximal, Sylow
100C22×C43—21no—
101C22×C43—41no—
102C22×C43—41no—
103C22×C43—41no—
104C22×C43—81no—
105C22×C43—81no—
106C22×C43#34211yescharacteristic
107C4×C43—21no—
108C4×C43—21no—
109C4×C43—21no—
110C4×C43—41no—
111C4×C43—41no—
112C4×C43—41no—
113C4×C43AΣL(1,𝔽16)11yescharacteristic
114C4×C43#35211yescharacteristic
115Dic43—161no—
116#2132—431no—
117#1884—431no—
118#1560D4311yescharacteristic
119C2×C43—21no—
120C2×C43—41no—
121C2×C43—81no—
122C2×C43—81no—
123C2×C43#139011yescharacteristic
124#568—431no—
125#532C2×D4311yescharacteristic
126#423—21no—
127#421—861no—
128#413—861no—
129#410—431no—
130#356—861no—
131#355—432no—
132#339—861no—
133#333—21no—
134#331Dic4312yescomplemented
135C43#749611yescharacteristic, complemented, Sylow
136C2×#41C4×D4311yescharacteristic
137C2×#41D17211yescharacteristic
138#131—1722no—
139C2×M16—41no—
140C2×M16—861no—
141C2×M16—1721no—
142C2×M16—1721no—
143C4⋊Q8C22⋊D4311yescharacteristic
144#127C2×Dic4311yescharacteristic
145#124Dic8611yescharacteristic
146#124C4×D4311yescharacteristic
147#121—41no—
148C4×D4—41no—
149#117—861no—
150C2×C42C22⋊D4311yescharacteristic
151C4⋊C8—22no—
152C4⋊C8—41no—
153#104—1722no—
154#101—862no—
155#100—1721no—
156#99—1721no—
157#41—41no—
158#41—41no—
159#41—41no—
160#41—41no—
161C2×Q8Dic43⋊C411yescharacteristic
162C2×Q8(C2×D43)⋊C411yescharacteristic
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—41no—
166C2×D4C4×Dic4311yescharacteristic
167C2×D4C4⋊Dic4311yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4(C2×D43)⋊C411yescharacteristic
172M16—82no—
173M16—862no—
174M16—3441no—
175M16—1722no—
176M16—1721no—
177M16—1722no—
178C2×C8—42no—
179C2×C8—3441no—
180C2×C8—1721no—
181C2×C8—1722no—
182C4⋊C4—41no—
183C4⋊C4—1721no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—1721no—
187C42—21no—
188C42—1721no—
189C42Dic43⋊C411yescharacteristic
190C42C22⋊Dic4311yescharacteristic
191C23—21no—
192C23—21no—
193C23#1306323911yescharacteristic
194Q8—41no—
195Q8—41no—
196D4—41no—
197D4—41no—
198D4—42no—
199D4—81no—
200D4—81no—
201D4—81no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—3441no—
215C2×C4C43⋊#9511yescharacteristic
216C2×C4#1306323911yescharacteristic
217C8—82no—
218C8—3442no—
219C8—1722no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—81no—
225C22—81no—
226C22#1458266511yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—6881no—
234C4#1458268711yescharacteristic
235C4#1458269011yescharacteristic
236C2—21no—
237C2—41no—
238C2—81no—
239C2—81no—
240C2#1913271411yescharacteristic
subgroupG/H
centerC2#19132714
commutatorC2×D4×C43C42
Frattini#532C2×D43
FittingC43×#1560C2
socleC2×C43#1390
prime radical, cosocleC43×#532C22
hypercenter#1560D43
hypocenterC43#7496
LCSG ▷ C2×D4×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #1560

Complements

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

NH ≅ G/Ntype
9. #14582696C4semidirect
14. C43×#331C4semidirect
134. #331Dic43semidirect
135. C43#7496semidirect

Maximal subgroups

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

subgroupindex
#191362802
#191349792
C43×#15602
#749643