Finite Group Databasebeta

← #24992360

Subgroups — #24992360

Order 11008.

586 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 127 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#19142934C211yesmaximal, characteristic
2C2×#14582767C211yesmaximal, characteristic
3C2×#14582637C212yesmaximal
4#19132475C212yesmaximal
5C43×#1817C211yesmaximal, characteristic
6C2×#13063304C2211yescharacteristic
7#14582805C412yescomplemented
8#14582797C412yescomplemented
9#14582783—22no—
10#14582772—21no—
11#14582767—24no—
12#14582762—21no—
13#14582759C2211yescharacteristic
14C2×C43⋊#95—21no—
15C2×C43⋊#95—21no—
16C2×C43⋊#95C2212yes—
17#14582637—24no—
18C22×C42×C43C2211yescharacteristic
19C2×C22⋊C8×C43C2212yes—
20C43×#336—22no—
21C22×Dic86C2×C411yescharacteristic
22C23×Dic43—22no—
23#13063304—22no—
24#13063304—22no—
25C2×C4⋊Dic43C2×C411yescharacteristic
26C2×C4⋊Dic43C2×C412yes—
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—21no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—21no—
31C43⋊#95—24no—
32C43⋊#95—24no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95—21no—
38C43⋊#95D414yes—
39C23×C4×C43D411yescharacteristic
40C23×C4×C43D411yescharacteristic
41C23×C4×C43C2311yescharacteristic
42C22×C8×C43—22no—
43C2×C42×C43—22no—
44C2×C42×C43—22no—
45C2×C42×C43C2×C412yes—
46C2×C42×C43D412yes—
47C22⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49C24×C43C2×D411yescharacteristic
50C22×C4×C43—21no—
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—42no—
57C22×C4×C43—42no—
58C22×C4×C43C22⋊C412yes—
59C22×C4×C43C22⋊C412yes—
60C22×C4×C43C22×C411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D412yes—
63C22×C4×C43#4112yes—
64C22×Dic43—22no—
65C22×Dic43—21no—
66C22×Dic43—21no—
67C22×Dic43—24no—
68C22×Dic43—44no—
69C22×Dic43—44no—
70C22×Dic43—42no—
71C22×Dic43—42no—
72C2×Dic86—22no—
73C2×Dic86—42no—
74C2×C8×C43—44no—
75C2×C8×C43—42no—
76C42×C43—24no—
77C42×C43—24no—
78C22⋊Dic43—41no—
79C22⋊Dic43—41no—
80C22⋊Dic43—42no—
81C4⋊Dic43—22no—
82C4⋊Dic43—42no—
83Dic43⋊C4—44no—
84Dic43⋊C4—42no—
85C23×C43—22no—
86C23×C43—22no—
87C23×C43C2×C22⋊C411yescharacteristic
88C23×C43#12011yescharacteristic
89C23×C43#12311yescharacteristic
90C23×C43#13512yes—
91C23×C43#13712yes—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—42no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43C4×D412yes—
107C2×C4×C43#12112yes—
108C2×Dic43—44no—
109C2×Dic43—44no—
110C2×Dic43—41no—
111C2×Dic43—41no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—42no—
115C2×Dic43—42no—
116C2×Dic43—42no—
117C2×Dic43—44no—
118C2×Dic43—84no—
119C2×Dic43—84no—
120Dic86—82no—
121C8×C43—82no—
122#9153—431nomaximal, Sylow
123C22×C43—21no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—21no—
127C22×C43—24no—
128C22×C43—24no—
129C22×C43#38611yescharacteristic
130C22×C43#41012yes—
131C22×C43#41611yescharacteristic
132C22×C43#41911yescharacteristic
133C22×C43#42112yes—
134C22×C43#45212yes—
135C22×C43#48512yes—
136C4×C43—22no—
137C4×C43—22no—
138C4×C43—42no—
139C4×C43—42no—
140Dic43—84no—
141Dic43—81no—
142Dic43—81no—
143Dic43—82no—
144#2855—431no—
145C2×#383—431no—
146#1817D4311yescharacteristic
147C2×#328—432no—
148#1294—432no—
149C2×C43—22no—
150C2×C43—22no—
151C2×C43#151512yes—
152C2×C43#152112yes—
153C2×C43#187311yescharacteristic
154C2×C43#189711yescharacteristic
155C2×C43#189911yescharacteristic
156C2×C22⋊Q8—431no—
157C22×C42C2×D4311yescharacteristic
158C2×C22⋊C8C2×D4312yes—
159#391—432no—
160#389—432no—
161#387—862no—
162#385—861no—
163#383—864no—
164#381—861no—
165#380—431no—
166C2×#95—432no—
167C2×#95—861no—
168C2×#95—861no—
169#336—22no—
170#328—864no—
171C43#915311yescharacteristic, complemented, Sylow
172C22×Q8—431no—
173C23×C4—862no—
174C23×C4D17211yescharacteristic
175C23×C4D17211yescharacteristic
176C23×C4C22×D4311yescharacteristic
177C22×C8—22no—
178C22⋊Q8—862no—
179C22⋊Q8—862no—
180C2×C4⋊C4—431no—
181C2×C4⋊C4—432no—
182C2×C4⋊C4—862no—
183C2×C4⋊C4—861no—
184C2×C22⋊C4—861no—
185C2×C22⋊C4—861no—
186C2×C42—22no—
187C2×C42—22no—
188C2×C42C4×D4312yes—
189C2×C42C22⋊D4312yes—
190C22⋊C8—22no—
191C22⋊C8—22no—
192#95—434no—
193#95—864no—
194#95—864no—
195#95—862no—
196#95—862no—
197#95—862no—
198#95—862no—
199#95—861no—
200C24C2×D17211yescharacteristic
201C2×Q8—862no—
202C2×Q8—1722no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—862no—
212C22×C4—861no—
213C22×C4—861no—
214C22×C4—864no—
215C22×C4—1724no—
216C22×C4—1724no—
217C22×C4—1722no—
218C22×C4—1722no—
219C22×C4(C2×D43)⋊C412yes—
220C22×C4(C2×D43)⋊C412yes—
221C22×C4C2×C4×D4311yescharacteristic
222C22×C4D4×D4312yes—
223C22×C4#1062190012yes—
224C22×C4C2×C22⋊D4311yescharacteristic
225C2×C8—44no—
226C2×C8—42no—
227C4⋊C4—862no—
228C4⋊C4—1722no—
229C4⋊C4—1724no—
230C4⋊C4—1722no—
231C22⋊C4—1721no—
232C22⋊C4—1721no—
233C22⋊C4—1722no—
234C42—24no—
235C42—24no—
236C23—22no—
237C23—22no—
238C23C2×(C2×D43)⋊C411yescharacteristic
239C23#1306329511yescharacteristic
240C23#1306330911yescharacteristic
241C23#1306334712yes—
242C23#1306335812yes—
243Q8—3442no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—3444no—
259C2×C4—3444no—
260C2×C4—1724no—
261C2×C4—1724no—
262C2×C4—1724no—
263C2×C4—1722no—
264C2×C4—1722no—
265C2×C4—1722no—
266C2×C4—1722no—
267C2×C4—1722no—
268C2×C4—1721no—
269C2×C4—1721no—
270C2×C4(C22⋊D43)⋊C412yes—
271C2×C4#1306329712yes—
272C8—82no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—24no—
278C22—24no—
279C22#1458277611yescharacteristic
280C22#1458287212yes—
281C22#1458289611yescharacteristic
282C22#1458290911yescharacteristic
283C22#1458291512yes—
284C22#1458306312yes—
285C22#1458324112yes—
286C4—22no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—3444no—
291C4—3441no—
292C4—3441no—
293C4—3442no—
294C2—22no—
295C2—22no—
296C2#1913314712yes—
297C2#1913317312yes—
298C2#1913490511yescharacteristic
299C2#1913504111yescharacteristic
300C2#1913505111yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1817C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1817D43
hypocenterC43#9153
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
7. #14582805C4semidirect
8. #14582797C4semidirect
171. C43#9153semidirect

Maximal subgroups

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

subgroupindex
#191429342
C2×#145827672
C2×#145826372
#191324752
C43×#18172
#915343