Finite Group Databasebeta

← #24986018

Subgroups — #24986018

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143228C211yesmaximal, characteristic
2C22×#13063236C211yesmaximal, characteristic
3#19132425C214yesmaximal, complemented
4C43×#2920C211yesmaximal, characteristic
5C23×C43⋊C8C412yes—
6#14582956—21no—
7#14582956—21no—
8#14582952C412yes—
9#14582952C2212yes—
10#14582923—21no—
11#14582863—21no—
12C4×#10621877C412yes—
13C2×#13063236—21no—
14C2×#13063236—21no—
15C2×#13063236—21no—
16C2×#13063236—21no—
17C2×#13063236C412yes—
18C2×#13063236C2212yes—
19C22×C42×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#432—21no—
22C43×#431C412yes—
23C43×#431C2212yes—
24C43×#423—21no—
25C43×#407—21no—
26C4×M16×C43C412yes—
27C2×#10621877—22no—
28C22×C43⋊C8—22no—
29C22×C43⋊C8—22no—
30C22×C43⋊C8—28no—
31C22×C43⋊C8C2×C414yes—
32C4⋊(C43⋊C8)—22no—
33C4⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)—22no—
35C22⋊(C43⋊C8)—22no—
36#13063236—22no—
37#13063236—22no—
38#13063236—22no—
39#13063236—22no—
40#13063236—22no—
41C4×C43⋊C8C2×C414yes—
42C23×C4×C43C2×C411yescharacteristic
43C23×C4×C43D411yescharacteristic
44C23×C4×C43Q811yescharacteristic
45C2×M16×C43—22no—
46C2×C42×C43C2×C411yescharacteristic
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43C2×C411yescharacteristic
49C2×C42×C43C2×C411yescharacteristic
50C2×C42×C43C2×C411yescharacteristic
51C2×C42×C43D411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C2×C42×C43D411yescharacteristic
56C2×C42×C43Q811yescharacteristic
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—22no—
59C4⋊C8×C43—22no—
60C22⋊C8×C43—22no—
61C22⋊C8×C43—22no—
62#97×C43—22no—
63C4×C8×C43C2×C414yes—
64C24×C43C4⋊C411yescharacteristic
65C22×C4×C43—24no—
66C22×C4×C43—42no—
67C22×C4×C43—42no—
68C22×C4×C43C4211yescharacteristic
69C22×C4×C43C4211yescharacteristic
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×C43C4⋊C411yescharacteristic
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×Q811yescharacteristic
86M16×C43—44no—
87C2×C8×C43—24no—
88C42×C43C4211yescharacteristic
89C42×C43C4211yescharacteristic
90C42×C43C22⋊C411yescharacteristic
91C42×C43C22⋊C411yescharacteristic
92C42×C43C22⋊C411yescharacteristic
93C42×C43C22⋊C411yescharacteristic
94C42×C43C22⋊C411yescharacteristic
95C42×C43C22⋊C411yescharacteristic
96C42×C43C4⋊C411yescharacteristic
97C42×C43C4⋊C411yescharacteristic
98C42×C43C4⋊C411yescharacteristic
99C42×C43C4⋊C411yescharacteristic
100C42×C43C22×C411yescharacteristic
101C42×C43C22×C411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104#10621877—44no—
105C2×C43⋊C8—28no—
106C2×C43⋊C8—28no—
107C2×C43⋊C8—24no—
108C2×C43⋊C8—24no—
109C2×C43⋊C8—24no—
110C2×C43⋊C8M1618yescomplemented
111C23×C43—22no—
112C23×C43—22no—
113C23×C43—22no—
114C23×C43#9511yescharacteristic
115C23×C43#9511yescharacteristic
116C23×C43C2×C4⋊C411yescharacteristic
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
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—41no—
134C2×C4×C43#9511yescharacteristic
135C2×C4×C43#9511yescharacteristic
136C2×C4×C43#9511yescharacteristic
137C2×C4×C43#9511yescharacteristic
138C2×C4×C43#9511yescharacteristic
139C2×C4×C43#9511yescharacteristic
140C2×C4×C43C2×C4211yescharacteristic
141C2×C4×C43C2×C22⋊C411yescharacteristic
142C2×C4×C43C2×C22⋊C411yescharacteristic
143C2×C4×C43C2×C22⋊C411yescharacteristic
144C2×C4×C43C2×C4⋊C411yescharacteristic
145C2×C4×C43C2×C4⋊C411yescharacteristic
146C2×C4×C43C2×M1614yes—
147C8×C43—44no—
148C43⋊C8—28no—
149C43⋊C8—44no—
150#7861—431nomaximal, Sylow
151C22×C43—28no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43H(3,ℤ/4)12yes—
159C22×C43#33812yes—
160C22×C43C2×#9511yescharacteristic
161C22×C43#42312yes—
162C4×C43—21no—
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×C43C4×M1612yes—
173C4×C43#40712yes—
174#2920—431no—
175#2920D4311yescharacteristic
176C22×#97—431no—
177#1275—434no—
178C2×C43—22no—
179C2×C43—22no—
180C2×C43—22no—
181C2×C43#172811yescharacteristic
182C2×C43C2×H(3,ℤ/4)11yescharacteristic
183C2×C43C2×#33811yescharacteristic
184C23×C8—432no—
185C22×C42C2×D4311yescharacteristic
186#432—21no—
187#432—21no—
188#432—861no—
189#432—861no—
190#431—432no—
191#431—432no—
192#431Dic4312yes—
193#431C2×D4312yes—
194#423—21no—
195#423—861no—
196#407—21no—
197#407—861no—
198C4×M16—432no—
199C4×M16Dic4312yes—
200C2×#97—432no—
201C2×#97—432no—
202C2×#97—861no—
203C2×#97—861no—
204C2×#97—861no—
205C2×#97—861no—
206C43#786111yescharacteristic, complemented, Sylow
207C23×C4Dic8611yescharacteristic
208C23×C4C4×D4311yescharacteristic
209C23×C4C22⋊D4311yescharacteristic
210C2×M16—22no—
211C2×M16—862no—
212C22×C8—434no—
213C22×C8—868no—
214C22×C8—862no—
215C22×C8—862no—
216C2×C42Dic8611yescharacteristic
217C2×C42C4×D4311yescharacteristic
218C2×C42C4×D4311yescharacteristic
219C2×C42C4×D4311yescharacteristic
220C2×C42D17211yescharacteristic
221C2×C42D17211yescharacteristic
222C2×C42C2×Dic4311yescharacteristic
223C2×C42C2×Dic4311yescharacteristic
224C2×C42C22⋊D4311yescharacteristic
225C2×C42C22⋊D4311yescharacteristic
226C2×C42C22⋊D4311yescharacteristic
227C2×C42C22×D4311yescharacteristic
228C4⋊C8—22no—
229C4⋊C8—22no—
230C4⋊C8—862no—
231C4⋊C8—862no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234C22⋊C8—862no—
235C22⋊C8—862no—
236#97—22no—
237#97—862no—
238#97—862no—
239#97—862no—
240#97—862no—
241#97—862no—
242C4×C8—434no—
243C4×C8C2×Dic4314yes—
244C24Dic43⋊C411yescharacteristic
245C22×C4—24no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4C4×Dic4311yescharacteristic
249C22×C4C4×Dic4311yescharacteristic
250C22×C4Dic43⋊C411yescharacteristic
251C22×C4Dic43⋊C411yescharacteristic
252C22×C4Dic43⋊C411yescharacteristic
253C22×C4Dic43⋊C411yescharacteristic
254C22×C4Dic43⋊C411yescharacteristic
255C22×C4C4⋊Dic4311yescharacteristic
256C22×C4C4⋊Dic4311yescharacteristic
257C22×C4(C2×D43)⋊C411yescharacteristic
258C22×C4(C2×D43)⋊C411yescharacteristic
259C22×C4(C2×D43)⋊C411yescharacteristic
260C22×C4(C2×D43)⋊C411yescharacteristic
261C22×C4C22⋊Dic4311yescharacteristic
262C22×C4C22⋊Dic4311yescharacteristic
263C22×C4C2×Dic8611yescharacteristic
264C22×C4C2×C4×D4311yescharacteristic
265C22×C4C2×C22⋊D4311yescharacteristic
266M16—44no—
267M16—1724no—
268C2×C8—24no—
269C2×C8—438no—
270C2×C8—868no—
271C2×C8—868no—
272C2×C8—864no—
273C2×C8—864no—
274C2×C8—864no—
275C42C4×Dic4311yescharacteristic
276C42C4×Dic4311yescharacteristic
277C42Dic43⋊C411yescharacteristic
278C42Dic43⋊C411yescharacteristic
279C42C4⋊Dic4311yescharacteristic
280C42C4⋊Dic4311yescharacteristic
281C42(C2×D43)⋊C411yescharacteristic
282C42(C2×D43)⋊C411yescharacteristic
283C42(C2×D43)⋊C411yescharacteristic
284C42(C2×D43)⋊C411yescharacteristic
285C42C22⋊Dic4311yescharacteristic
286C42C22⋊Dic4311yescharacteristic
287C42C2×C4×D4311yescharacteristic
288C42C2×D17211yescharacteristic
289C42C22×Dic4311yescharacteristic
290C42C2×C22⋊D4311yescharacteristic
291C23—22no—
292C23—22no—
293C23—22no—
294C23C43⋊#9511yescharacteristic
295C23C43⋊#9511yescharacteristic
296C23C2×Dic43⋊C411yescharacteristic
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
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×C4C43⋊#9511yescharacteristic
315C2×C4C43⋊#9511yescharacteristic
316C2×C4C43⋊#9511yescharacteristic
317C2×C4C43⋊#9511yescharacteristic
318C2×C4C43⋊#9511yescharacteristic
319C2×C4C43⋊#9511yescharacteristic
320C2×C4C2×C4×Dic4311yescharacteristic
321C2×C4C2×(C2×D43)⋊C411yescharacteristic
322C2×C4C2×(C2×D43)⋊C411yescharacteristic
323C2×C4C2×C22⋊Dic4311yescharacteristic
324C2×C4C2×Dic43⋊C411yescharacteristic
325C2×C4C2×C4⋊Dic4311yescharacteristic
326C2×C4M16×D4314yes—
327C8—44no—
328C8—868no—
329C8—1724no—
330C22—28no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22#1458265512yes—
338C22C43⋊#33812yes—
339C22C2×C43⋊#9511yescharacteristic
340C22#1458292212yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4M16×Dic4312yes—
352C4#1458286212yes—
353C2—22no—
354C2—22no—
355C2—22no—
356C2#1913428811yescharacteristic
357C2C2×#1458265511yescharacteristic
358C2C2×C43⋊#33811yescharacteristic
subgroupG/H
centerC2×C4C2×C4×Dic43
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC43×#2920C2
socleC22×C43C2×#95
prime radicalC24×C43C4⋊C4
cosocleC2×C42×C43C23
hypercenter#2920D43
hypocenterC43#7861
LCSG ▷ C2×C4×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #2920

Complements

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

NH ≅ G/Ntype
3. #19132425C2semidirect
110. C2×C43⋊C8M16semidirect
206. C43#7861semidirect

Maximal subgroups

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

subgroupindex
#191432282
C22×#130632362
#191324252
C43×#29202
#786143