Finite Group Databasebeta

← #24986452

Subgroups — #24986452

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143228C211yesmaximal, characteristic
2#19143228C211yesmaximal, characteristic
3#19132459C214yesmaximal, complemented
4C2×C43×#383C211yesmaximal, characteristic
5#14582956—21no—
6#14582956—21no—
7#14582956C412yescomplemented
8#14582956C2212yes—
9#14582952—21no—
10#14582952—21no—
11#14582952C412yescomplemented
12#14582952C412yescomplemented
13#14582923—21no—
14#14582923—21no—
15#14582863—21no—
16#14582863—21no—
17C4×#10621877C412yescomplemented
18C4×#10621877C2212yes—
19C22×C42×C43C2211yescharacteristic
20C43×#383—21no—
21C43×#383—21no—
22C43×#383C412yes—
23C43×#383C2212yes—
24C2×#95×C43—21no—
25C2×#95×C43—21no—
26C2×#95×C43C412yes—
27C2×#10621877—22no—
28C2×#10621877—22no—
29C4⋊(C43⋊C8)—22no—
30C4⋊(C43⋊C8)—22no—
31C4⋊(C43⋊C8)—22no—
32C4⋊(C43⋊C8)—22no—
33C22⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)—22no—
35C22⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)—22no—
37#13063236—22no—
38#13063236C2×C414yescomplemented
39C4×C43⋊C8—22no—
40C4×C43⋊C8C2×C414yescomplemented
41C23×C4×C43—22no—
42C23×C4×C43C2×C411yescharacteristic
43C23×C4×C43D411yescharacteristic
44C23×C4×C43D411yescharacteristic
45C2×C42×C43C2×C411yescharacteristic
46C2×C42×C43C2×C411yescharacteristic
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43C2×C411yescharacteristic
49C2×C42×C43C2×C411yescharacteristic
50C2×C42×C43D411yescharacteristic
51C2×C42×C43D411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43Q811yescharacteristic
55C2×C42×C43Q811yescharacteristic
56C2×C42×C43C2311yescharacteristic
57#95×C43—22no—
58#95×C43—22no—
59#95×C43—22no—
60#95×C43—22no—
61#95×C43—22no—
62#95×C43C2×C414yes—
63C24×C43C22⋊C411yescharacteristic
64C22×C4×C43—24no—
65C22×C4×C43—42no—
66C22×C4×C43—42no—
67C22×C4×C43—42no—
68C22×C4×C43—44no—
69C22×C4×C43—44no—
70C22×C4×C43—44no—
71C22×C4×C43C4211yescharacteristic
72C22×C4×C43C4211yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C22⋊C411yescharacteristic
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C4⋊C411yescharacteristic
81C22×C4×C43C4⋊C411yescharacteristic
82C22×C4×C43C4⋊C411yescharacteristic
83C22×C4×C43C4⋊C411yescharacteristic
84C22×C4×C43C4⋊C411yescharacteristic
85C22×C4×C43C4⋊C411yescharacteristic
86C22×C4×C43C22×C411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C42×C43C4211yescharacteristic
90C42×C43C4211yescharacteristic
91C42×C43C22⋊C411yescharacteristic
92C42×C43C22⋊C411yescharacteristic
93C42×C43C22⋊C411yescharacteristic
94C42×C43C22⋊C411yescharacteristic
95C42×C43C4⋊C411yescharacteristic
96C42×C43C4⋊C411yescharacteristic
97C42×C43C4⋊C411yescharacteristic
98C42×C43C4⋊C411yescharacteristic
99C42×C43C4⋊C411yescharacteristic
100C42×C43C4⋊C411yescharacteristic
101C42×C43C22×C411yescharacteristic
102C42×C43C22×C411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43C2×Q811yescharacteristic
105#10621877—44no—
106#10621877—44no—
107C2×C43⋊C8—24no—
108C2×C43⋊C8—24no—
109C23×C43—22no—
110C23×C43—22no—
111C23×C43—22no—
112C23×C43#9511yescharacteristic
113C23×C43#9511yescharacteristic
114C23×C43C2×C22⋊C411yescharacteristic
115C2×C4×C43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—44no—
134C2×C4×C43—44no—
135C2×C4×C43—44no—
136C2×C4×C43—88no—
137C2×C4×C43#9511yescharacteristic
138C2×C4×C43#9511yescharacteristic
139C2×C4×C43#9511yescharacteristic
140C2×C4×C43#9511yescharacteristic
141C2×C4×C43#9511yescharacteristic
142C2×C4×C43#9511yescharacteristic
143C2×C4×C43C2×C4211yescharacteristic
144C2×C4×C43C2×C22⋊C411yescharacteristic
145C2×C4×C43C2×C22⋊C411yescharacteristic
146C2×C4×C43C2×C4⋊C411yescharacteristic
147C2×C4×C43C2×C4⋊C411yescharacteristic
148C2×C4×C43C2×C4⋊C411yescharacteristic
149C43⋊C8—44no—
150C43⋊C8—44no—
151#7975—431nomaximal, Sylow
152C22×C43—28no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43H(3,ℤ/4)12yes—
160C22×C43#34412yes—
161C22×C43C2×#9511yescharacteristic
162C22×C43#42112yes—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—84no—
176#2920—431no—
177#2920—431no—
178C2×#383D4311yescharacteristic
179#1288—434no—
180C2×C43—22no—
181C2×C43—22no—
182C2×C43—22no—
183C2×C43C2×H(3,ℤ/4)11yescharacteristic
184C2×C43#173311yescharacteristic
185C2×C43C2×#34411yescharacteristic
186C22×C42C2×D4311yescharacteristic
187#432—432no—
188#432—432no—
189#432—861no—
190#432—861no—
191#431—432no—
192#431—432no—
193#431—861no—
194#431—861no—
195#423—861no—
196#423—861no—
197#407—861no—
198#407—861no—
199C4×M16—432no—
200C4×M16—432no—
201#383—21no—
202#383—21no—
203#383Dic4312yes—
204#383C2×D4312yes—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95Dic4312yes—
208C43#797511yescharacteristic, complemented, Sylow
209C23×C4—22no—
210C23×C4C2×Dic4311yescharacteristic
211C23×C4C22⋊D4311yescharacteristic
212C23×C4C22⋊D4311yescharacteristic
213C2×M16—862no—
214C2×M16—862no—
215C2×C42Dic8611yescharacteristic
216C2×C42Dic8611yescharacteristic
217C2×C42C4×D4311yescharacteristic
218C2×C42C4×D4311yescharacteristic
219C2×C42C4×D4311yescharacteristic
220C2×C42C4×D4311yescharacteristic
221C2×C42D17211yescharacteristic
222C2×C42D17211yescharacteristic
223C2×C42C2×Dic4311yescharacteristic
224C2×C42C22⋊D4311yescharacteristic
225C2×C42C22⋊D4311yescharacteristic
226C2×C42C22×D4311yescharacteristic
227C4⋊C8—862no—
228C4⋊C8—862no—
229C4⋊C8—862no—
230C4⋊C8—862no—
231C22⋊C8—862no—
232C22⋊C8—862no—
233C22⋊C8—862no—
234C22⋊C8—862no—
235#97—434no—
236#97—862no—
237C4×C8—434no—
238C4×C8—862no—
239#95—22no—
240#95—22no—
241#95—22no—
242#95—22no—
243#95—22no—
244#95C2×Dic4314yes—
245C24C22⋊Dic4311yescharacteristic
246C22×C4—24no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—44no—
251C22×C4—44no—
252C22×C4—44no—
253C22×C4C4×Dic4311yescharacteristic
254C22×C4C4×Dic4311yescharacteristic
255C22×C4Dic43⋊C411yescharacteristic
256C22×C4Dic43⋊C411yescharacteristic
257C22×C4Dic43⋊C411yescharacteristic
258C22×C4Dic43⋊C411yescharacteristic
259C22×C4C4⋊Dic4311yescharacteristic
260C22×C4C4⋊Dic4311yescharacteristic
261C22×C4(C2×D43)⋊C411yescharacteristic
262C22×C4(C2×D43)⋊C411yescharacteristic
263C22×C4(C2×D43)⋊C411yescharacteristic
264C22×C4(C2×D43)⋊C411yescharacteristic
265C22×C4C22⋊Dic4311yescharacteristic
266C22×C4C22⋊Dic4311yescharacteristic
267C22×C4C22⋊Dic4311yescharacteristic
268C22×C4C22×Dic4311yescharacteristic
269C22×C4C2×C22⋊D4311yescharacteristic
270C22×C4C2×C22⋊D4311yescharacteristic
271M16—1724no—
272M16—1724no—
273C2×C8—864no—
274C2×C8—864no—
275C42C4×Dic4311yescharacteristic
276C42C4×Dic4311yescharacteristic
277C42Dic43⋊C411yescharacteristic
278C42Dic43⋊C411yescharacteristic
279C42Dic43⋊C411yescharacteristic
280C42Dic43⋊C411yescharacteristic
281C42C4⋊Dic4311yescharacteristic
282C42C4⋊Dic4311yescharacteristic
283C42(C2×D43)⋊C411yescharacteristic
284C42(C2×D43)⋊C411yescharacteristic
285C42(C2×D43)⋊C411yescharacteristic
286C42(C2×D43)⋊C411yescharacteristic
287C42C2×Dic8611yescharacteristic
288C42C2×C4×D4311yescharacteristic
289C42C2×C4×D4311yescharacteristic
290C42C2×D17211yescharacteristic
291C23—22no—
292C23—22no—
293C23—22no—
294C23C43⋊#9511yescharacteristic
295C23C43⋊#9511yescharacteristic
296C23C2×C22⋊Dic4311yescharacteristic
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—88no—
319C2×C4C43⋊#9511yescharacteristic
320C2×C4C43⋊#9511yescharacteristic
321C2×C4C43⋊#9511yescharacteristic
322C2×C4C43⋊#9511yescharacteristic
323C2×C4C43⋊#9511yescharacteristic
324C2×C4C43⋊#9511yescharacteristic
325C2×C4C2×C4×Dic4311yescharacteristic
326C2×C4C2×(C2×D43)⋊C411yescharacteristic
327C2×C4C2×(C2×D43)⋊C411yescharacteristic
328C2×C4C2×Dic43⋊C411yescharacteristic
329C2×C4C2×Dic43⋊C411yescharacteristic
330C2×C4C2×C4⋊Dic4311yescharacteristic
331C8—1724no—
332C8—1724no—
333C22—28no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22#1458265512yes—
341C22#1458266912yes—
342C22C2×C43⋊#9511yescharacteristic
343C22#1458291612yes—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—84no—
357C2—22no—
358C2—22no—
359C2—22no—
360C2C2×#1458265511yescharacteristic
361C2#1913430411yescharacteristic
362C2C2×#1458266911yescharacteristic
subgroupG/H
centerC22C2×C43⋊#95
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC2×C43×#383C2
socleC22×C43C2×#95
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×#383D43
hypocenterC43#7975
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
3. #19132459C2semidirect
7. #14582956C4semidirect
11. #14582952C4semidirect
12. #14582952C4semidirect
17. C4×#10621877C4semidirect
38. #13063236C2×C4semidirect
40. C4×C43⋊C8C2×C4semidirect
208. C43#7975semidirect

Maximal subgroups

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

subgroupindex
#191432282
#191324592
C2×C43×#3832
#797543