Finite Group Databasebeta

← #24986454

Subgroups — #24986454

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
2C2×#14582767C211yesmaximal, characteristic
3#19132461C214yesmaximal, complemented
4C43×#2920C211yesmaximal, characteristic
5#14582956—21no—
6#14582956—21no—
7#14582952C412yescomplemented
8#14582952C412yescomplemented
9#14582923—21no—
10#14582863—21no—
11C4×#10621877C2212yes—
12#14582767—21no—
13#14582767—21no—
14#14582767C412yes—
15#14582767C2212yes—
16C2×C43⋊#95—21no—
17C2×C43⋊#95—21no—
18C2×C43⋊#95C412yes—
19C22×C42×C43C2211yescharacteristic
20C43×#432C412yescomplemented
21C43×#432C2212yes—
22C43×#431—21no—
23C43×#431—21no—
24C43×#423—21no—
25C43×#407—21no—
26C4×M16×C43C412yescomplemented
27C23×Dic43—22no—
28C2×#10621877—22no—
29C4⋊(C43⋊C8)—22no—
30C4⋊(C43⋊C8)—22no—
31C22⋊(C43⋊C8)—22no—
32C22⋊(C43⋊C8)—22no—
33#13063236—22no—
34C4×C43⋊C8C2×C414yescomplemented
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95C2×C414yes—
41C23×C4×C43C2×C411yescharacteristic
42C23×C4×C43D411yescharacteristic
43C23×C4×C43D411yescharacteristic
44C2×M16×C43—22no—
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
57C4⋊C8×C43—22no—
58C4⋊C8×C43—22no—
59C22⋊C8×C43—22no—
60C22⋊C8×C43—22no—
61#97×C43C2×C414yescomplemented
62C4×C8×C43—22no—
63C24×C43C22⋊C411yescharacteristic
64C22×C4×C43—42no—
65C22×C4×C43—42no—
66C22×C4×C43—42no—
67C22×C4×C43C4211yescharacteristic
68C22×C4×C43C4211yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C4⋊C411yescharacteristic
77C22×C4×C43C4⋊C411yescharacteristic
78C22×C4×C43C4⋊C411yescharacteristic
79C22×C4×C43C4⋊C411yescharacteristic
80C22×C4×C43C4⋊C411yescharacteristic
81C22×C4×C43C4⋊C411yescharacteristic
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×Dic43—24no—
86C22×Dic43—44no—
87C22×Dic43—44no—
88C22×Dic43—44no—
89M16×C43—44no—
90C2×C8×C43—24no—
91C42×C43C4211yescharacteristic
92C42×C43C4211yescharacteristic
93C42×C43C22⋊C411yescharacteristic
94C42×C43C22⋊C411yescharacteristic
95C42×C43C22⋊C411yescharacteristic
96C42×C43C22⋊C411yescharacteristic
97C42×C43C4⋊C411yescharacteristic
98C42×C43C4⋊C411yescharacteristic
99C42×C43C4⋊C411yescharacteristic
100C42×C43C4⋊C411yescharacteristic
101C42×C43C4⋊C411yescharacteristic
102C42×C43C4⋊C411yescharacteristic
103C42×C43C22×C411yescharacteristic
104C42×C43C22×C411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×Q811yescharacteristic
107#10621877—44no—
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#9511yescharacteristic
134C2×C4×C43#9511yescharacteristic
135C2×C4×C43#9511yescharacteristic
136C2×C4×C43#9511yescharacteristic
137C2×C4×C43#9511yescharacteristic
138C2×C4×C43#9511yescharacteristic
139C2×C4×C43C2×C4211yescharacteristic
140C2×C4×C43C2×C22⋊C411yescharacteristic
141C2×C4×C43C2×C22⋊C411yescharacteristic
142C2×C4×C43C2×C4⋊C411yescharacteristic
143C2×C4×C43C2×C4⋊C411yescharacteristic
144C2×C4×C43C2×C4⋊C411yescharacteristic
145C2×Dic43—44no—
146C2×Dic43—44no—
147C2×Dic43—44no—
148C2×Dic43—88no—
149C8×C43—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—
175Dic43—84no—
176#2920—431no—
177#2920D4311yescharacteristic
178C2×#383—431no—
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—861no—
188#432—861no—
189#432Dic4312yescomplemented
190#432C2×D4312yes—
191#431—21no—
192#431—21no—
193#431—432no—
194#431—432no—
195#423—21no—
196#423—861no—
197#407—21no—
198#407—861no—
199C4×M16—432no—
200C4×M16Dic4312yescomplemented
201#383—432no—
202#383—432no—
203#383—861no—
204#383—861no—
205C2×#95—432no—
206C2×#95—861no—
207C2×#95—861no—
208C43#797511yescharacteristic, complemented, Sylow
209C23×C4—862no—
210C23×C4C4×D4311yescharacteristic
211C23×C4D17211yescharacteristic
212C23×C4C22⋊D4311yescharacteristic
213C2×M16—22no—
214C2×M16—862no—
215C2×C42Dic8611yescharacteristic
216C2×C42Dic8611yescharacteristic
217C2×C42C4×D4311yescharacteristic
218C2×C42C4×D4311yescharacteristic
219C2×C42C4×D4311yescharacteristic
220C2×C42D17211yescharacteristic
221C2×C42C2×Dic4311yescharacteristic
222C2×C42C2×Dic4311yescharacteristic
223C2×C42C22⋊D4311yescharacteristic
224C2×C42C22⋊D4311yescharacteristic
225C2×C42C22⋊D4311yescharacteristic
226C2×C42C22×D4311yescharacteristic
227C4⋊C8—22no—
228C4⋊C8—22no—
229C4⋊C8—862no—
230C4⋊C8—862no—
231C22⋊C8—22no—
232C22⋊C8—22no—
233C22⋊C8—862no—
234C22⋊C8—862no—
235#97—862no—
236#97C2×Dic4314yescomplemented
237C4×C8—22no—
238C4×C8—434no—
239#95—434no—
240#95—862no—
241#95—862no—
242#95—862no—
243#95—862no—
244#95—862no—
245C24(C2×D43)⋊C411yescharacteristic
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—864no—
250C22×C4—1724no—
251C22×C4—1724no—
252C22×C4—1724no—
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×C4(C2×D43)⋊C411yescharacteristic
266C22×C4C22⋊Dic4311yescharacteristic
267C22×C4C22⋊Dic4311yescharacteristic
268C22×C4C2×C4×D4311yescharacteristic
269C22×C4C2×D17211yescharacteristic
270C22×C4C2×C22⋊D4311yescharacteristic
271M16—44no—
272M16—1724no—
273C2×C8—24no—
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
285C42C22⋊Dic4311yescharacteristic
286C42C22⋊Dic4311yescharacteristic
287C42C2×Dic8611yescharacteristic
288C42C2×C4×D4311yescharacteristic
289C42C22×Dic4311yescharacteristic
290C42C2×C22⋊D4311yescharacteristic
291C23—22no—
292C23—22no—
293C23—22no—
294C23C43⋊#9511yescharacteristic
295C23C43⋊#9511yescharacteristic
296C23C2×(C2×D43)⋊C411yescharacteristic
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—3448no—
316C2×C4—1724no—
317C2×C4—1724no—
318C2×C4—1724no—
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×C22⋊Dic4311yescharacteristic
328C2×C4C2×Dic43⋊C411yescharacteristic
329C2×C4C2×Dic43⋊C411yescharacteristic
330C2×C4C2×C4⋊Dic4311yescharacteristic
331C8—44no—
332C8—1724no—
333C22—28no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22#1458265512yes—
341C22#1458267112yes—
342C22C2×C43⋊#9511yescharacteristic
343C22#1458291512yes—
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—3444no—
357C2—22no—
358C2—22no—
359C2—22no—
360C2C2×#1458265511yescharacteristic
361C2#1913430611yescharacteristic
362C2C2×#1458267111yescharacteristic
subgroupG/H
centerC22C2×C43⋊#95
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC43×#2920C2
socleC22×C43C2×#95
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#2920D43
hypocenterC43#7975
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
3. #19132461C2semidirect
7. #14582952C4semidirect
8. #14582952C4semidirect
20. C43×#432C4semidirect
26. C4×M16×C43C4semidirect
34. C4×C43⋊C8C2×C4semidirect
61. #97×C43C2×C4semidirect
189. #432Dic43semidirect
200. C4×M16Dic43semidirect
208. C43#7975semidirect
236. #97C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191432282
C2×#145827672
#191324612
C43×#29202
#797543