Finite Group Databasebeta

← #24984565

Subgroups — #24984565

Order 11008.

528 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 119 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#19137138C211yesmaximal, characteristic
2#19134339C212yesmaximal, complemented
3#19132421C211yesmaximal, characteristic, complemented
4#19132415C212yesmaximal
5C43×#1272C211yesmaximal, characteristic, complemented
6C2×#13063314C411yescharacteristic
7C2×Q8×Dic43C411yescharacteristic
8C2×#13063287C411yescharacteristic
9C2×C8×Dic43—22no—
10#14582801C2211yescharacteristic
11#14582791—22no—
12#14582764C411yescharacteristic
13#14582746—22no—
14C42×Dic43C2211yescharacteristic
15#14582654C2212yes—
16#14582653—22no—
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×D172C2×C411yescharacteristic
20C22×C4×D43—21no—
21C22×C43⋊C8—22no—
22#13063314—22no—
23#13063314C814yescomplemented
24Q8×Dic43—42no—
25#13063287—42no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×(C2×D43)⋊C4—22no—
29C2×(C2×D43)⋊C4—22no—
30C2×(C2×D43)⋊C4—21no—
31C2×C4×Dic43—21no—
32C2×C4×Dic43C2×C411yescharacteristic
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43D412yes—
35C2×C4×Dic43D412yes—
36C8×Dic43—28no—
37C43⋊#95—22no—
38C22×Q8×C43C2×C411yescharacteristic
39C22×C8×C43—22no—
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C42×C43C2311yescharacteristic
42#95×C43—22no—
43C23×D43—21no—
44C2×Q8×C43—21no—
45C2×Q8×C43—41no—
46C2×Q8×C43—41no—
47C2×Q8×C43C2×C812yes—
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43C22×C411yescharacteristic
51C22×C4×C43C2×D412yes—
52C22×Dic43—21no—
53C22×Dic43C22⋊C411yescharacteristic
54C22×Dic43C22⋊C412yes—
55C22×Dic43C22⋊C411yescharacteristic
56C2×D172—21no—
57C2×D172—41no—
58C2×D172—41no—
59C2×D172C2×C812yes—
60C2×C4×D43—42no—
61C2×C4×D43—44no—
62C2×C8×C43—24no—
63C2×C8×C43—42no—
64C2×C8×C43—42no—
65C4⋊C4×C43—41no—
66C42×C43—41no—
67(C2×D43)⋊C4—28no—
68(C2×D43)⋊C4—42no—
69(C2×D43)⋊C4—42no—
70(C2×D43)⋊C4—42no—
71C4⋊Dic43—42no—
72C4⋊Dic43—41no—
73C4×Dic43—22no—
74C4×Dic43—22no—
75C4×Dic43—22no—
76C4×Dic43—24no—
77C4×Dic43—42no—
78C4×Dic43C2×C812yes—
79C4×Dic43M1612yes—
80C2×C43⋊C8—24no—
81C2×C43⋊C8—42no—
82C2×C43⋊C8—42no—
83C23×C43C2×C22⋊C411yescharacteristic
84C22×D43—22no—
85C22×D43—41no—
86C22×D43—41no—
87C22×D43—42no—
88C22×D43—42no—
89Q8×C43—42no—
90Q8×C43—42no—
91C2×C4×C43—22no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—41no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43—42no—
100C2×C4×C43C22×C811yescharacteristic
101C2×C4×C43C2×M1611yescharacteristic
102C2×C4×C43#13512yes—
103C2×C4×C43#13512yes—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43—21no—
107C2×Dic43—22no—
108C2×Dic43—41no—
109C2×Dic43—42no—
110C2×Dic43C22⋊C814yes—
111C2×Dic43#10012yes—
112C2×Dic43#10414yes—
113D172—42no—
114D172—42no—
115C4×D43—84no—
116C8×C43—44no—
117C43⋊C8—44no—
118#7567—431nomaximal, Sylow
119C22×C43C2×C22⋊C811yescharacteristic
120C22×C43#41011yescharacteristic
121C22×C43C2×#10011yescharacteristic
122C22×C43#41612yes—
123C22×C43C2×#10412yes—
124C2×D43—42no—
125C2×D43—44no—
126C2×D43—81no—
127C2×D43—82no—
128C2×D43—81no—
129C4×C43—21no—
130C4×C43—21no—
131C4×C43—22no—
132C4×C43—22no—
133C4×C43—42no—
134C4×C43—81no—
135Dic43—24no—
136Dic43—41no—
137Dic43—81no—
138Dic43#32914yes—
139C4×#124—431no—
140#1744—432no—
141#1272—431no—
142#1272D4311yescharacteristic, complemented
143#1270—432no—
144C2×C43#146011yescharacteristic
145C2×C43#147612yes—
146C2×C43#150012yes—
147C2×C43C2×#32911yescharacteristic
148C2×C43#154311yescharacteristic
149D43—82no—
150C2×#124—431no—
151C2×C4×Q8—431no—
152C2×C4×D4—431no—
153C2×C4×C8—862no—
154#391C2×D4311yescharacteristic
155#390—431no—
156#388—862no—
157#382—431no—
158C4×C22⋊C4—862no—
159C43—431no—
160#336—432no—
161#336—862no—
162#336C2×D4312yes—
163C43#756711yescharacteristic, complemented, Sylow
164C22×Q8C4×D4311yescharacteristic
165C22×D4—431no—
166C23×C4—861no—
167C22×C8—22no—
168C22×C8—862no—
169#124—434no—
170#124—862no—
171C4×Q8—1722no—
172C4×D4—1722no—
173C2×C4⋊C4—431no—
174C2×C4⋊C4—861no—
175C2×C4⋊C4C4×D4311yescharacteristic
176C2×C22⋊C4—862no—
177C2×C22⋊C4—861no—
178C2×C22⋊C4—862no—
179C2×C42—431no—
180C2×C42—431no—
181C2×C42—432no—
182C2×C42—432no—
183C2×C42—861no—
184C2×C42C22×D4311yescharacteristic
185C4×C8—868no—
186#95—22no—
187#95—862no—
188C24—861no—
189C2×Q8—21no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8C8×D4312yes—
193C2×D4—432no—
194C2×D4—861no—
195C2×D4—1721no—
196C2×D4—1721no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—431no—
200C22×C4—432no—
201C22×C4—431no—
202C22×C4—861no—
203C22×C4—1722no—
204C22×C4—1724no—
205C22×C4C2×C4×D4311yescharacteristic
206C22×C4D4×D4312yes—
207C2×C8—24no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—864no—
211C2×C8—1722no—
212C2×C8—1722no—
213C4⋊C4—41no—
214C4⋊C4—1721no—
215C4⋊C4—1722no—
216C22⋊C4—868no—
217C22⋊C4—1722no—
218C22⋊C4—1722no—
219C22⋊C4—1722no—
220C42—41no—
221C42—432no—
222C42—432no—
223C42—864no—
224C42—862no—
225C42—862no—
226C42—862no—
227C42—1722no—
228C23—862no—
229C23—1721no—
230C23—1721no—
231C23—1722no—
232C23—1722no—
233C23C22⋊C4×D4311yescharacteristic
234Q8—42no—
235Q8—42no—
236D4—1722no—
237D4—1722no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—432no—
248C2×C4—434no—
249C2×C4—434no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—861no—
253C2×C4—862no—
254C2×C4—3444no—
255C2×C4—1721no—
256C2×C4—1722no—
257C2×C4C2×C8×D4311yescharacteristic
258C2×C4M16×D4311yescharacteristic
259C2×C4#1306334612yes—
260C2×C4#1306334812yes—
261C8—44no—
262C8—1724no—
263C22—3441no—
264C22—3442no—
265C22—3441no—
266C22—1724no—
267C22—1722no—
268C22C22⋊C8×D4311yescharacteristic
269C22#1458287111yescharacteristic
270C22#100×D4311yescharacteristic
271C22#1458289412yes—
272C22#104×D4312yes—
273C4—22no—
274C4—22no—
275C4—21no—
276C4—21no—
277C4—42no—
278C4—81no—
279C4—434no—
280C4—864no—
281C4—3441no—
282C4—1721no—
283C2—3442no—
284C2#1913291411yescharacteristic
285C2#1913297612yes—
286C2#1913308012yes—
287C2#329×D4311yescharacteristic
288C2#1913325611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7567
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #19134339C2semidirect
3. #19132421C2semidirect
5. C43×#1272C2semidirect
23. #13063314C8semidirect
142. #1272D43semidirect
163. C43#7567semidirect

Maximal subgroups

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

subgroupindex
#191371382
#191343392
#191324212
#191324152
C43×#12722
#756743