Finite Group Databasebeta

← #24989359

Subgroups — #24989359

Order 11008.

540 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 117 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#19137134C211yesmaximal, characteristic
2#19134449C212yesmaximal, complemented
3C2×#14582638C212yesmaximal
4#19132476C211yesmaximal, characteristic, complemented
5C43×#1295C211yesmaximal, characteristic, complemented
6C2×#13063313C2211yescharacteristic
7C2×#13063290C411yescharacteristic
8C2×#13063287C411yescharacteristic
9C2×Dic43⋊C8—22no—
10C2×#13063236C2212yes—
11#14582804C411yescharacteristic
12#14582800C411yescharacteristic
13#14582788—22no—
14#14582746—22no—
15C42×Dic43C2211yescharacteristic
16#14582653—22no—
17#14582638—24no—
18C2×#97×C43C2212yes—
19C43×#382C2211yescharacteristic
20C22×Dic86C2×C411yescharacteristic
21C22×D172C2×C411yescharacteristic
22C22×C4×D43—21no—
23C22×C43⋊C8—22no—
24#13063313—22no—
25#13063313D412yes—
26#13063313Q812yes—
27#13063290—42no—
28#13063287—42no—
29C2×Dic43⋊C4—21no—
30C2×(C2×D43)⋊C4—22no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—22no—
33C2×C4×Dic43—21no—
34C2×C4×Dic43C2×C411yescharacteristic
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43D412yes—
37C2×C4×Dic43D412yes—
38Dic43⋊C8—28no—
39#13063236—22no—
40#13063236—22no—
41C43⋊#95—22no—
42C22×C8×C43—22no—
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C42×C43C2311yescharacteristic
46#97×C43—22no—
47#97×C43—22no—
48#95×C43—22no—
49C23×D43—21no—
50C22×C4×C43—21no—
51C22×C4×C43—21no—
52C22×C4×C43C22×C411yescharacteristic
53C22×C4×C43C2×D412yes—
54C22×Dic43—21no—
55C22×Dic43C22⋊C412yes—
56C22×Dic43C22⋊C411yescharacteristic
57C22×Dic43C22⋊C411yescharacteristic
58C2×D172—21no—
59C2×D172—41no—
60C2×D172—41no—
61C2×D172C4⋊C412yes—
62C2×C4×D43—42no—
63C2×C4×D43—44no—
64C2×Dic86—21no—
65C2×Dic86—41no—
66C2×Dic86—41no—
67C2×Dic86C4⋊C412yes—
68C2×C8×C43—24no—
69C2×C8×C43—42no—
70C2×C8×C43—42no—
71C4⋊C4×C43—41no—
72C4⋊C4×C43—41no—
73C42×C43C2×D411yescharacteristic
74C42×C43C2×Q811yescharacteristic
75C42×C43#4112yes—
76(C2×D43)⋊C4—24no—
77(C2×D43)⋊C4—24no—
78(C2×D43)⋊C4—44no—
79(C2×D43)⋊C4—42no—
80Dic43⋊C4—42no—
81C4×Dic43—22no—
82C4×Dic43—24no—
83C4×Dic43—41no—
84C4×Dic43—42no—
85C4×Dic43—42no—
86C2×C43⋊C8—24no—
87C2×C43⋊C8—42no—
88C2×C43⋊C8—42no—
89C23×C43C2×C22⋊C411yescharacteristic
90C22×D43—22no—
91C22×D43—41no—
92C22×D43—41no—
93C22×D43—42no—
94C22×D43—42no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43C2×C4⋊C411yescharacteristic
104C2×C4×C43#11711yescharacteristic
105C2×C4×C43#12112yes—
106C2×C4×C43C22⋊Q812yes—
107C2×Dic43—22no—
108C2×Dic43—21no—
109C2×Dic43—22no—
110C2×Dic43—22no—
111C2×Dic43—22no—
112C2×Dic43—22no—
113C2×Dic43—41no—
114C2×Dic43—41no—
115C2×Dic43#10012yes—
116C2×Dic43#10414yes—
117D172—42no—
118D172—42no—
119C4×D43—84no—
120Dic86—42no—
121Dic86—42no—
122C8×C43—44no—
123C43⋊C8—44no—
124#8579—431nomaximal, Sylow
125C22×C43#38011yescharacteristic
126C22×C43C2×#10011yescharacteristic
127C22×C43#41311yescharacteristic
128C22×C43C2×#10412yes—
129C22×C43#42112yes—
130C2×D43—42no—
131C2×D43—44no—
132C2×D43—81no—
133C2×D43—81no—
134C2×D43—82no—
135C4×C43—21no—
136C4×C43—21no—
137C4×C43—22no—
138C4×C43—22no—
139C4×C43—81no—
140C4×C43—81no—
141Dic43—41no—
142Dic43—42no—
143Dic43—42no—
144Dic43#32914yescomplemented
145C4×#124—431no—
146#1767—432no—
147C2×#329—432no—
148#1295—431no—
149#1295D4311yescharacteristic, complemented
150C2×C43C2×#32911yescharacteristic
151C2×C43#152912yes—
152C2×C43#153611yescharacteristic
153C2×C43#180011yescharacteristic
154C2×C43#180612yes—
155D43—82no—
156C2×#124—431no—
157C2×C4×Q8—431no—
158C2×C4×D4—431no—
159C2×C4⋊C8—862no—
160C2×#97—432no—
161C2×#97C2×D4312yes—
162#391—431no—
163#390—431no—
164#388—862no—
165#382C2×D4311yescharacteristic
166C4×C22⋊C4—862no—
167C43—431no—
168#336—862no—
169#329—864no—
170C43#857911yescharacteristic, complemented, Sylow
171C22×Q8—431no—
172C22×D4—431no—
173C23×C4—861no—
174C22×C8—22no—
175C22×C8—862no—
176#124—432no—
177#124—432no—
178#124—862no—
179C4×Q8—1722no—
180C4×D4—1722no—
181C2×C4⋊C4—861no—
182C2×C4⋊C4C4×D4311yescharacteristic
183C2×C4⋊C4C4×D4311yescharacteristic
184C2×C22⋊C4—862no—
185C2×C22⋊C4—861no—
186C2×C22⋊C4—862no—
187C2×C42—431no—
188C2×C42—432no—
189C2×C42—431no—
190C2×C42—432no—
191C2×C42—861no—
192C2×C42C22×D4311yescharacteristic
193C4⋊C8—868no—
194#97—22no—
195#97—22no—
196#97—862no—
197#97—862no—
198#95—22no—
199#95—862no—
200C24—861no—
201C2×Q8—432no—
202C2×Q8—861no—
203C2×Q8—1721no—
204C2×Q8—1721no—
205C2×D4—432no—
206C2×D4—861no—
207C2×D4—1721no—
208C2×D4—1721no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—431no—
212C22×C4—432no—
213C22×C4—431no—
214C22×C4—861no—
215C22×C4—1722no—
216C22×C4—1724no—
217C22×C4C2×C4×D4311yescharacteristic
218C22×C4D4×D4312yes—
219C2×C8—24no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—864no—
223C2×C8—1722no—
224C2×C8—1722no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—1722no—
228C22⋊C4—864no—
229C22⋊C4—864no—
230C22⋊C4—1722no—
231C22⋊C4—1724no—
232C42—864no—
233C42—862no—
234C42—1721no—
235C42—1722no—
236C42—1722no—
237C42#1062189812yes—
238C42D4×D4311yescharacteristic
239C42Q8×D4311yescharacteristic
240C23—862no—
241C23—1721no—
242C23—1721no—
243C23—1722no—
244C23—1722no—
245C23C22⋊C4×D4311yescharacteristic
246Q8—1722no—
247Q8—1722no—
248D4—1722no—
249D4—1722no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—432no—
259C2×C4—434no—
260C2×C4—861no—
261C2×C4—862no—
262C2×C4—862no—
263C2×C4—862no—
264C2×C4—862no—
265C2×C4—862no—
266C2×C4—3444no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4C4⋊C4×D4311yescharacteristic
270C2×C4#1306328211yescharacteristic
271C2×C4#1306329812yes—
272C2×C4#1306330312yes—
273C8—44no—
274C8—1724no—
275C22—3442no—
276C22—3441no—
277C22—3441no—
278C22—1722no—
279C22—1724no—
280C22#1458275811yescharacteristic
281C22#100×D4311yescharacteristic
282C22#1458288211yescharacteristic
283C22#104×D4312yes—
284C22#1458291412yes—
285C4—21no—
286C4—21no—
287C4—22no—
288C4—22no—
289C4—81no—
290C4—81no—
291C4—434no—
292C4—1722no—
293C4—1721no—
294C4—1722no—
295C2—3442no—
296C2#329×D4311yescharacteristic
297C2#1913320112yes—
298C2#1913322811yescharacteristic
299C2#1913458611yescharacteristic
300C2#1913461412yes—
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1295D43
hypocenterC43#8579
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #19134449C2semidirect
4. #19132476C2semidirect
5. C43×#1295C2semidirect
144. Dic43#329semidirect
149. #1295D43semidirect
170. C43#8579semidirect

Maximal subgroups

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

subgroupindex
#191371342
#191344492
C2×#145826382
#191324762
C43×#12952
#857943