Finite Group Databasebeta

← #24984327

Subgroups — #24984327

Order 11008.

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

normal subgroups only

This group has 278 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#19136260C211yesmaximal, characteristic
2#19133330C211yesmaximal, characteristic
3C43×#1884C211yesmaximal, characteristic
4#14582923—21no—
5#14582873—21no—
6#14582694C412yescomplemented
7#14582692—21no—
8#14582648C412yescomplemented
9#14582643—21no—
10C43×#568C411yescharacteristic, complemented
11C43×#532C2211yescharacteristic
12C43×#421—21no—
13C43×#410C411yescharacteristic, complemented
14C43×#339—21no—
15C2×#10621877—41no—
16#13063284—41no—
17C4⋊(C43⋊C8)—22no—
18C4⋊(C43⋊C8)—41no—
19#13063240—22no—
20#13063240—41no—
21C2×#41×C43C2×C411yescharacteristic
22C2×#41×C43D411yescharacteristic
23#131×C43—42no—
24C2×M16×C43—21no—
25C2×M16×C43—41no—
26C4⋊Q8×C43C2×C411yescharacteristic
27#127×C43D411yescharacteristic
28#124×C43C2×C411yescharacteristic
29#124×C43Q811yescharacteristic
30#121×C43—41no—
31C4×D4×C43—41no—
32#117×C43—21no—
33C2×C42×C43D411yescharacteristic
34#104×C43—42no—
35#99×C43—41no—
36#41×C43—41no—
37#41×C43—41no—
38#41×C43—41no—
39#41×C43—41no—
40C2×Q8×C43C4211yescharacteristic
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×C43C22⋊C411yescharacteristic
51M16×C43—22no—
52M16×C43—42no—
53M16×C43—41no—
54C2×C8×C43—41no—
55C2×C8×C43—42no—
56C4⋊C4×C43—41no—
57C4⋊C4×C43—41no—
58C22⋊C4×C43—41no—
59C22⋊C4×C43—41no—
60C22⋊C4×C43—41no—
61C42×C43—21no—
62C42×C43—41no—
63C42×C43C22⋊C411yescharacteristic
64C42×C43C4⋊C411yescharacteristic
65C22⋊Dic43—42no—
66C4⋊Dic43—81no—
67C4×Dic43—81no—
68#10621877—82no—
69C2×C43⋊C8—42no—
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—81no—
94C2×C4×C43#9511yescharacteristic
95C2×C4×C43#9911yescharacteristic
96C2×Dic43—82no—
97C8×C43—42no—
98C43⋊C8—82no—
99#7482—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×C43—161no—
114C4×C43AΣL(1,𝔽16)11yescharacteristic
115C4×C43#35211yescharacteristic
116Dic43—162no—
117#2126—431no—
118#1884D4311yescharacteristic
119#1560—431no—
120C2×C43—21no—
121C2×C43—41no—
122C2×C43—81no—
123C2×C43—81no—
124C2×C43#139011yescharacteristic
125#568Dic4311yescharacteristic, complemented
126#532C2×D4311yescharacteristic
127#423—861no—
128#421—21no—
129#410—861no—
130#410Dic4311yescharacteristic, complemented
131#354—432no—
132#353—861no—
133#339—21no—
134#333—432no—
135#331—861no—
136C43#748211yescharacteristic, complemented, Sylow
137C2×#41C2×Dic4311yescharacteristic
138C2×#41C22⋊D4311yescharacteristic
139#131—42no—
140C2×M16—21no—
141C2×M16—41no—
142C2×M16—1721no—
143C4⋊Q8C4×D4311yescharacteristic
144#127D17211yescharacteristic
145#124Dic8611yescharacteristic
146#124C4×D4311yescharacteristic
147#121—41no—
148C4×D4—41no—
149#117—21no—
150#117—1721no—
151C2×C42C22⋊D4311yescharacteristic
152C4⋊C8—862no—
153C4⋊C8—1721no—
154#104—42no—
155#99—41no—
156#99—862no—
157#99—1721no—
158#41—41no—
159#41—41no—
160#41—41no—
161#41—41no—
162C2×Q8C4×Dic4311yescharacteristic
163C2×Q8Dic43⋊C411yescharacteristic
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—41no—
167C2×D4C4⋊Dic4311yescharacteristic
168C2×D4(C2×D43)⋊C411yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4C22⋊Dic4311yescharacteristic
173M16—22no—
174M16—42no—
175M16—41no—
176M16—3442no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—1722no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C4⋊C4—3441no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—1722no—
187C42—21no—
188C42—41no—
189C42—3441no—
190C42Dic43⋊C411yescharacteristic
191C42(C2×D43)⋊C411yescharacteristic
192C23—21no—
193C23—21no—
194C23#1306324011yescharacteristic
195Q8—41no—
196Q8—41no—
197D4—41no—
198D4—41no—
199D4—42no—
200D4—81no—
201D4—81no—
202D4—81no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—81no—
216C2×C4—3442no—
217C2×C4C43⋊#9511yescharacteristic
218C2×C4#1306324011yescharacteristic
219C8—42no—
220C8—3442no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—81no—
227C22#1458266611yescharacteristic
228C4—21no—
229C4—21no—
230C4—21no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—161no—
235C4—6882no—
236C4#1458268611yescharacteristic
237C4#1458268911yescharacteristic
238C2—21no—
239C2—41no—
240C2—81no—
241C2—81no—
242C2#1913271311yescharacteristic
subgroupG/H
centerC2#19132713
commutatorC2×Q8×C43C42
Frattini#532C2×D43
FittingC43×#1884C2
socleC2×C43#1390
prime radical, cosocleC43×#532C22
hypercenter#1884D43
hypocenterC43#7482
LCSG ▷ C2×Q8×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #1884

Complements

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

NH ≅ G/Ntype
6. #14582694C4semidirect
8. #14582648C4semidirect
10. C43×#568C4semidirect
13. C43×#410C4semidirect
125. #568Dic43semidirect
130. #410Dic43semidirect
136. C43#7482semidirect

Maximal subgroups

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

subgroupindex
#191362602
#191333302
C43×#18842
#748243