Finite Group Databasebeta

← #24984378

Subgroups — #24984378

Order 11008.

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

normal subgroups only

This group has 294 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#19135424C211yesmaximal, characteristic
3C43×#2126C211yesmaximal, characteristic
4#14582923C411yescharacteristic, complemented
5C2×#13063252—21no—
6C2×#13063252—21no—
7#14582873—21no—
8C42×Dic43C411yescharacteristic, complemented
9#14582694C412yescomplemented
10#14582692—21no—
11C43×#532C2211yescharacteristic
12C43×#410—21no—
13C43×#354C412yescomplemented
14C43×#353—21no—
15C2×#10621877—21no—
16#13063284—41no—
17C2×C4×Dic43—21no—
18C2×C4×Dic43—41no—
19C4⋊(C43⋊C8)—41no—
20#13063252—42no—
21#13063252—42no—
22#13063240—22no—
23#13063240—41no—
24C2×#41×C43D411yescharacteristic
25C2×#41×C43D411yescharacteristic
26C4⋊Q8×C43Q811yescharacteristic
27#127×C43D411yescharacteristic
28#124×C43C2×C411yescharacteristic
29#124×C43C2×C411yescharacteristic
30#121×C43—41no—
31C4×D4×C43—41no—
32#117×C43—41no—
33C2×C42×C43C2×C411yescharacteristic
34#99×C43—22no—
35#99×C43—41no—
36#41×C43—41no—
37#41×C43—41no—
38#41×C43—41no—
39#41×C43—41no—
40C2×Q8×C43C4⋊C411yescharacteristic
41C2×Q8×C43C4⋊C411yescharacteristic
42C2×D4×C43—21no—
43C2×D4×C43—21no—
44C2×D4×C43—41no—
45C2×D4×C43C22⋊C411yescharacteristic
46C2×D4×C43C22⋊C411yescharacteristic
47C22×C4×C43—21no—
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43C22⋊C411yescharacteristic
51C22×Dic43—41no—
52C4⋊C4×C43—41no—
53C4⋊C4×C43—81no—
54C22⋊C4×C43—41no—
55C22⋊C4×C43—41no—
56C22⋊C4×C43—42no—
57C42×C43—21no—
58C42×C43—81no—
59C42×C43C4211yescharacteristic
60C42×C43C4⋊C411yescharacteristic
61C22⋊Dic43—42no—
62C4⋊Dic43—81no—
63C4×Dic43—22no—
64C4×Dic43—41no—
65C4×Dic43—44no—
66C4×Dic43—81no—
67#10621877—41no—
68#10621877—41no—
69C2×C43⋊C8—41no—
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—41no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—41no—
91C2×C4×C43—82no—
92C2×C4×C43#9511yescharacteristic
93C2×C4×C43#9911yescharacteristic
94C2×Dic43—42no—
95C2×Dic43—44no—
96C2×Dic43—82no—
97C43⋊C8—81no—
98#7500—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—41no—
110C4×C43—41no—
111C4×C43—162no—
112C4×C43#35311yescharacteristic
113C4×C43#35411yescharacteristic
114Dic43—44no—
115Dic43—162no—
116#2126—431no—
117#2126D4311yescharacteristic
118#1962—431no—
119C2×C43—21no—
120C2×C43—41no—
121C2×C43—81no—
122C2×C43—81no—
123C2×C43#139311yescharacteristic
124#532C2×D4311yescharacteristic
125#423—431no—
126C2×#104—861no—
127C2×#104—861no—
128#410—21no—
129#410—861no—
130C43—431no—
131#354—432no—
132#354Dic4312yescomplemented
133#353—21no—
134#353—861no—
135C43#750011yescharacteristic, complemented, Sylow
136C2×#41D17211yescharacteristic
137C2×#41C22⋊D4311yescharacteristic
138C2×M16—861no—
139C4⋊Q8Dic8611yescharacteristic
140#127C22⋊D4311yescharacteristic
141#124C4×D4311yescharacteristic
142#124C2×Dic4311yescharacteristic
143#121—41no—
144C4×D4—41no—
145#117—41no—
146#117—1721no—
147C2×C42—861no—
148C2×C42—1721no—
149C2×C42C4×D4311yescharacteristic
150C4⋊C8—1721no—
151#104—1722no—
152#104—1722no—
153#99—22no—
154#99—41no—
155#99—862no—
156#99—1721no—
157#41—41no—
158#41—41no—
159#41—41no—
160#41—41no—
161C2×Q8Dic43⋊C411yescharacteristic
162C2×Q8C4⋊Dic4311yescharacteristic
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—41no—
166C2×D4(C2×D43)⋊C411yescharacteristic
167C2×D4C22⋊Dic4311yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—1721no—
172C22×C4(C2×D43)⋊C411yescharacteristic
173M16—1721no—
174M16—1721no—
175C2×C8—1721no—
176C4⋊C4—41no—
177C4⋊C4—81no—
178C4⋊C4—3441no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—42no—
182C22⋊C4—1722no—
183C42—21no—
184C42—81no—
185C42—862no—
186C42—3441no—
187C42—1721no—
188C42—1724no—
189C42C4×Dic4311yescharacteristic
190C42Dic43⋊C411yescharacteristic
191C23—21no—
192C23—21no—
193C23#1306323911yescharacteristic
194Q8—41no—
195Q8—41no—
196D4—41no—
197D4—41no—
198D4—82no—
199D4—81no—
200D4—81no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—82no—
213C2×C4—3442no—
214C2×C4—1722no—
215C2×C4—1724no—
216C2×C4C43⋊#9511yescharacteristic
217C2×C4#1306323911yescharacteristic
218C8—3441no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—81no—
224C22—81no—
225C22#1458266511yescharacteristic
226C4—22no—
227C4—21no—
228C4—41no—
229C4—41no—
230C4—41no—
231C4—162no—
232C4—1724no—
233C4—6882no—
234C4#1458269111yescharacteristic
235C4#1458269311yescharacteristic
236C2—21no—
237C2—41no—
238C2—81no—
239C2—81no—
240C2#1913271911yescharacteristic
subgroupG/H
centerC4#14582693
commutatorC42×C43C42
Frattini#532C2×D43
FittingC43×#2126C2
socleC2×C43#1393
prime radical, cosocleC43×#532C22
hypercenter#2126D43
hypocenterC43#7500
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2126

Complements

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

NH ≅ G/Ntype
4. #14582923C4semidirect
8. C42×Dic43C4semidirect
9. #14582694C4semidirect
13. C43×#354C4semidirect
132. #354Dic43semidirect
135. C43#7500semidirect

Maximal subgroups

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

subgroupindex
#191362602
#191354242
C43×#21262
#750043