Finite Group Databasebeta

← #24994284

Subgroups — #24994284

Order 11008.

498 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 103 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#19143624C211yesmaximal, characteristic
2#19139768C211yesmaximal, characteristic
3#19133313C212yesmaximal, complemented
4#19132450C212yesmaximal, complemented
5C43×#1466C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7#14582971—24no—
8#14582956C2212yes—
9#14582863—21no—
10C2×C22⋊(C43⋊C8)—21no—
11#14582811—21no—
12#14582811—21no—
13#14582802C412yes—
14#14582764C412yes—
15#14582759—21no—
16#14582759—21no—
17C4×C4⋊Dic43C2211yescharacteristic
18#14582646—24no—
19C2×C4×D4×C43C2211yescharacteristic
20C43×#432C2212yes—
21C43×#323—21no—
22C43×#323—21no—
23C22×Dic86—21no—
24C2×#10621877—22no—
25C22×C43⋊C8—22no—
26#13063325—22no—
27#13063325—22no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43C2×C412yes—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43—22no—
33C2×C4×Dic43C2×C412yes—
34C4⋊(C43⋊C8)D414yes—
35C22⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)—22no—
37C22⋊(C43⋊C8)—22no—
38#13063236—22no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C43⋊#95—21no—
42C22×D4×C43C2×C411yescharacteristic
43C23×C4×C43D411yescharacteristic
44C23×C4×C43D411yescharacteristic
45C4×D4×C43—22no—
46C4×D4×C43—22no—
47C2×C4⋊C4×C43C2×C411yescharacteristic
48C2×C22⋊C4×C43D411yescharacteristic
49C2×C22⋊C4×C43D411yescharacteristic
50C2×C42×C43C2311yescharacteristic
51C4⋊C8×C43—22no—
52C22⋊C8×C43—22no—
53#97×C43—22no—
54C24×C43C22⋊C411yescharacteristic
55C24×C43C22⋊C411yescharacteristic
56C2×D4×C43—22no—
57C2×D4×C43—22no—
58C2×D4×C43—41no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—42no—
64C22×C4×C43—42no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—22no—
71C22×Dic43—22no—
72C2×Dic86—42no—
73C2×Dic86—82no—
74C2×C8×C43—42no—
75C4⋊C4×C43—22no—
76C22⋊C4×C43—22no—
77C22⋊C4×C43—22no—
78C42×C43C2×D412yes—
79C42×C43#4112yes—
80C22⋊Dic43—82no—
81C22⋊Dic43—82no—
82C4⋊Dic43—24no—
83C4⋊Dic43—42no—
84C4⋊Dic43—41no—
85C4⋊Dic43—41no—
86C4×Dic43—42no—
87#10621877—82no—
88C2×C43⋊C8—24no—
89C2×C43⋊C8—82no—
90C23×C43—21no—
91C23×C43—21no—
92C23×C43—21no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—41no—
96C23×C43—41no—
97C23×C43—41no—
98C23×C43—41no—
99C23×C43#10112yes—
100C23×C43C2×C22⋊C411yescharacteristic
101D4×C43—44no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—41no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43C4×D412yes—
115C2×C4×C43#12011yescharacteristic
116C2×C4×C43#12112yes—
117C2×C4×C43#12311yescharacteristic
118C2×Dic43—42no—
119C2×Dic43—42no—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—42no—
123C2×Dic43—42no—
124Dic86—84no—
125C8×C43—82no—
126C43⋊C8—44no—
127#9453—431nomaximal, Sylow
128C22×C43—21no—
129C22×C43—21no—
130C22×C43—22no—
131C22×C43—42no—
132C22×C43—42no—
133C22×C43—41no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43—41no—
137C22×C43—41no—
138C22×C43—81no—
139C22×C43—81no—
140C22×C43#38611yescharacteristic
141C22×C43C2×#10111yescharacteristic
142C22×C43#41311yescharacteristic
143C4×C43—21no—
144C4×C43—22no—
145C4×C43—22no—
146C4×C43—41no—
147C4×C43—41no—
148C4×C43#45512yes—
149Dic43—82no—
150Dic43—82no—
151#2973—431no—
152#2563—431no—
153#1556—432no—
154#1466D4311yescharacteristic
155#1285—432no—
156C2×C43—21no—
157C2×C43—21no—
158C2×C43—42no—
159C2×C43—81no—
160C2×C43#188511yescharacteristic
161C2×C43#190111yescharacteristic
162C2×C43#191011yescharacteristic
163C2×C4⋊Q8—431no—
164C2×C4×D4C2×D4311yescharacteristic
165#435—864no—
166#432—432no—
167#432C2×D4312yes—
168#407—861no—
169C2×C22⋊C8—861no—
170#393—861no—
171#393—861no—
172#390—432no—
173#382—432no—
174#380—861no—
175#380—861no—
176C4×C4⋊C4—431no—
177#332—864no—
178#323—21no—
179#323—21no—
180C43#945311yescharacteristic, complemented, Sylow
181C22×Q8—861no—
182C22×D4C4×D4311yescharacteristic
183C23×C4D17211yescharacteristic
184C23×C4D17211yescharacteristic
185C2×M16—862no—
186C22×C8—862no—
187C4⋊Q8—862no—
188C4⋊Q8—862no—
189C4×D4—22no—
190C4×D4—22no—
191C2×C4⋊C4—432no—
192C2×C4⋊C4—861no—
193C2×C4⋊C4—861no—
194C2×C4⋊C4C4×D4311yescharacteristic
195C2×C22⋊C4—862no—
196C2×C22⋊C4—862no—
197C2×C22⋊C4C22⋊D4311yescharacteristic
198C2×C22⋊C4C22⋊D4311yescharacteristic
199C2×C42—432no—
200C2×C42C22×D4311yescharacteristic
201C4⋊C8—22no—
202C4⋊C8—434no—
203C22⋊C8—22no—
204C22⋊C8—862no—
205C22⋊C8—862no—
206C22⋊C8—862no—
207#97—22no—
208#97—862no—
209#95—862no—
210#95—862no—
211#95—861no—
212C24(C2×D43)⋊C411yescharacteristic
213C24(C2×D43)⋊C411yescharacteristic
214C2×Q8—3442no—
215C2×Q8—1722no—
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—862no—
226C22×C4—862no—
227C22×C4(C2×D43)⋊C411yescharacteristic
228C22×C4(C2×D43)⋊C411yescharacteristic
229C22×C4C2×C4×D4311yescharacteristic
230C22×C4C2×D17211yescharacteristic
231C22×C4C2×C22⋊D4311yescharacteristic
232M16—3442no—
233C2×C8—42no—
234C2×C8—864no—
235C2×C8—3442no—
236C4⋊C4—22no—
237C4⋊C4—864no—
238C4⋊C4—1722no—
239C4⋊C4—1721no—
240C4⋊C4—1721no—
241C22⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—3442no—
244C22⋊C4—3442no—
245C42—1722no—
246C42D4×D4312yes—
247C42#1062190012yes—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23#1306324312yes—
258C23C2×(C2×D43)⋊C411yescharacteristic
259Q8—3444no—
260D4—44no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—1722no—
274C2×C4—1722no—
275C2×C4—1722no—
276C2×C4—1722no—
277C2×C4—1722no—
278C2×C4—1722no—
279C2×C4(C22⋊D43)⋊C412yes—
280C2×C4#1306329511yescharacteristic
281C2×C4#1306329712yes—
282C2×C4#1306330911yescharacteristic
283C8—82no—
284C8—1724no—
285C22—21no—
286C22—21no—
287C22—22no—
288C22—42no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22#1458277611yescharacteristic
298C22C2×#1306324311yescharacteristic
299C22#1458288111yescharacteristic
300C4—21no—
301C4—22no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—3442no—
306C4—3442no—
307C4#1458307912yes—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—81no—
312C2#1913498111yescharacteristic
313C2#1913506111yescharacteristic
314C2#1913512011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1466C2
socleC22×C43#386
prime radicalC22×D4×C43C2×C4
cosocleC2×C42×C43C23
hypercenter#1466D43
hypocenterC43#9453
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #19133313C2semidirect
4. #19132450C2semidirect
180. C43#9453semidirect

Maximal subgroups

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

subgroupindex
#191436242
#191397682
#191333132
#191324502
C43×#14662
#945343