Finite Group Databasebeta

← #24989650

Subgroups — #24989650

Order 11008.

542 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582964C211yesmaximal, characteristic
2#19134754C211yesmaximal, characteristic, complemented
3#19134596C211yesmaximal, characteristic
4#19134592C211yesmaximal, characteristic
5C2×#14582651C211yesmaximal, characteristic, complemented
6#19132479C211yesmaximal, characteristic, complemented
7C43×#1296C211yesmaximal, characteristic, complemented
8C22×C8×D43—21no—
9C2×C4×D172C2211yescharacteristic
10#14582964—22no—
11#14582964C414yescomplemented
12C2×#13063258—21no—
13C2×#13063258—21no—
14C2×C4⋊(C43⋊C8)C2211yescharacteristic
15C2×#13063247—21no—
16C2×#13063245—21no—
17C2×(C2×D43)⋊C8—21no—
18C2×C4×C43⋊C8C2211yescharacteristic
19#14582769C2211yescharacteristic
20#14582662—21no—
21#14582661—21no—
22#14582651—22no—
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C43×#384C2211yescharacteristic
26C22×D172D411yescharacteristic
27C22×C4×D43—21no—
28C22×C43⋊C8—21no—
29C22×C43⋊C8D411yescharacteristic
30C22×C43⋊C8D411yescharacteristic
31C2×C8×D43—24no—
32C2×C8×D43—42no—
33C2×C8×D43—42no—
34C4×D172—21no—
35C4×D172—21no—
36C4×D172C2×C412yes—
37C4×D172Q812yes—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×(C2×D43)⋊C4—21no—
43#13063258—42no—
44#13063258—42no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47#13063247—42no—
48#13063245—42no—
49(C2×D43)⋊C8—24no—
50C4×C43⋊C8C2×C412yes—
51C4×C43⋊C8D412yes—
52C22×C8×C43—21no—
53C22×C8×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—21no—
59C4⋊C8×C43—21no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43C2×C412yes—
62C23×D43—21no—
63C22×C4×C43—41no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43#4111yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—41no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172C4⋊C412yes—
73C2×D172D812yes—
74C2×D172Q1612yes—
75C2×C4×D43—22no—
76C2×C4×D43—22no—
77C2×C4×D43—41no—
78C2×C4×D43—41no—
79C2×C4×D43—41no—
80C2×C4×D43—41no—
81C2×C8×C43—22no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—81no—
92C42×C43C22×C411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43C2×Q811yescharacteristic
95C42×C43#4111yescharacteristic
96(C2×D43)⋊C4—22no—
97(C2×D43)⋊C4—22no—
98C4⋊Dic43—21no—
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101C4⋊Dic43—41no—
102C4⋊Dic43—41no—
103C4⋊Dic43—81no—
104C4⋊Dic43C4⋊C412yes—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—21no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8C22⋊C412yes—
111C2×C43⋊C8C22⋊C412yes—
112C2×C43⋊C8D812yes—
113C2×C43⋊C8SD1612yes—
114C8×D43—48no—
115C23×C43#12111yescharacteristic
116C22×D43—22no—
117C22×D43—22no—
118C22×D43—22no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43C2×C22⋊C411yescharacteristic
129C2×C4×C43C2×C4⋊C411yescharacteristic
130C2×C4×C43#11711yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43C22⋊Q811yescharacteristic
133C2×C4×C43C22⋊Q811yescharacteristic
134C2×C4×C43C2×D811yescharacteristic
135C2×C4×C43C2×D811yescharacteristic
136C2×C4×C43C2×SD1611yescharacteristic
137C2×C4×C43C2×Q1611yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C2×Dic43—22no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—81no—
146C2×Dic43—81no—
147C2×Dic43—81no—
148D172—22no—
149D172—22no—
150D172—22no—
151D172#10714yescomplemented
152C4×D43—42no—
153C4×D43—42no—
154C4×D43—42no—
155C4×D43—42no—
156C8×C43—42no—
157C8×C43—81no—
158C43⋊C8—22no—
159C43⋊C8—81no—
160C43⋊C8#10214yescomplemented
161#8644—431nomaximal, Sylow
162C22×C43#38011yescharacteristic
163C22×C43#45911yescharacteristic
164C22×C43#46111yescharacteristic
165C22×C43#46611yescharacteristic
166C22×C43#46711yescharacteristic
167C22×C43#47211yescharacteristic
168C22×C43#47311yescharacteristic
169C2×D43—24no—
170C2×D43—42no—
171C2×D43—42no—
172C2×D43—42no—
173C2×D43—42no—
174C2×D43—42no—
175C2×D43—42no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—161no—
179C4×C43C2×#10211yescharacteristic
180C4×C43#41711yescharacteristic
181C4×C43C2×#10711yescharacteristic
182C4×C43#42711yescharacteristic
183C4×C43#46611yescharacteristic
184C4×C43#46711yescharacteristic
185C4×C43#47411yescharacteristic
186C4×C43#47611yescharacteristic
187Dic43—42no—
188Dic43—161no—
189C2×C8×D4—431no—
190#1845—431no—
191#1802—431no—
192#1802—431no—
193C2×#335—431no—
194#1296—431no—
195#1296D4311yescharacteristic, complemented
196C2×C43#166711yescharacteristic
197C2×C43#166911yescharacteristic
198C2×C43#167311yescharacteristic
199C2×C43#167511yescharacteristic
200C2×C43#180211yescharacteristic
201C2×C43#180811yescharacteristic
202C2×C43#181611yescharacteristic
203D43—44no—
204C23×C8—861no—
205C2×C4×D4—431no—
206C8×D4—434no—
207C8×D4—862no—
208C2×#107—861no—
209C2×#107—861no—
210C2×C4⋊C8—431no—
211C2×C4⋊C8C2×D4311yescharacteristic
212C2×C4⋊C8C2×D4311yescharacteristic
213C2×#102—861no—
214C2×#102—861no—
215C2×C22⋊C8—861no—
216C2×C4×C8—431no—
217#384—431no—
218#384C2×D4311yescharacteristic
219#340—861no—
220#340—861no—
221#335—862no—
222C43#864411yescharacteristic, complemented, Sylow
223C22×D4—431no—
224C23×C4—861no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—431no—
228C22×C8—431no—
229C22×C8—864no—
230C22×C8—861no—
231C22×C8—1722no—
232C22×C8—1722no—
233C4×D4—432no—
234C4×D4—432no—
235C4×D4—861no—
236C4×D4—861no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—431no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C42C22×D4311yescharacteristic
246#107—1722no—
247#107—1722no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—861no—
252C4⋊C8—861no—
253C4⋊C8C4×D4312yes—
254#102—1722no—
255#102—1722no—
256C22⋊C8—864no—
257C4×C8—432no—
258C4×C8—432no—
259C24—861no—
260C2×D4—432no—
261C2×D4—432no—
262C2×D4—432no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—861no—
266C22×C4—41no—
267C22×C4—861no—
268C22×C4—862no—
269C22×C4—862no—
270C22×C4—1721no—
271C22×C4—1721no—
272C22×C4—1721no—
273C22×C4—1721no—
274C22×C4—1721no—
275C22×C4#1062189811yescharacteristic
276C22×C4D4×D4311yescharacteristic
277C22×C4D4×D4311yescharacteristic
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—432no—
285C2×C8—432no—
286C2×C8—432no—
287C2×C8—432no—
288C2×C8—861no—
289C2×C8—861no—
290C2×C8—1728no—
291C2×C8—1721no—
292C2×C8—1721no—
293C2×C8—1721no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—81no—
299C4⋊C4—432no—
300C4⋊C4—861no—
301C4⋊C4—3441no—
302C4⋊C4—1721no—
303C4⋊C4—1721no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C22⋊C4—862no—
307C22⋊C4—862no—
308C42C2×C4×D4311yescharacteristic
309C42#1062189811yescharacteristic
310C42D4×D4311yescharacteristic
311C42Q8×D4311yescharacteristic
312C23—862no—
313C23—862no—
314C23—862no—
315C23—1721no—
316C23—1721no—
317C23—1721no—
318C23—1721no—
319C23#1306329811yescharacteristic
320D4—434no—
321D4—862no—
322D4—862no—
323D4—862no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—862no—
330C2×C4—3441no—
331C2×C4—3441no—
332C2×C4—3441no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4—1722no—
338C2×C4—1722no—
339C2×C4C22⋊C4×D4311yescharacteristic
340C2×C4C4⋊C4×D4311yescharacteristic
341C2×C4#1306328211yescharacteristic
342C2×C4#1306329811yescharacteristic
343C2×C4#1306330311yescharacteristic
344C2×C4#1306330311yescharacteristic
345C2×C4D8×D4311yescharacteristic
346C2×C4D8×D4311yescharacteristic
347C2×C4SD16×D4311yescharacteristic
348C2×C4Q16×D4311yescharacteristic
349C2×C4#1306334611yescharacteristic
350C2×C4#1306334611yescharacteristic
351C2×C4#1306335211yescharacteristic
352C2×C4#1306335711yescharacteristic
353C8—42no—
354C8—81no—
355C8—434no—
356C8—862no—
357C8—3441no—
358C22—864no—
359C22—1722no—
360C22—1722no—
361C22—1722no—
362C22—1722no—
363C22—1722no—
364C22—1722no—
365C22#1458275811yescharacteristic
366C22#1458309311yescharacteristic
367C22#1458310311yescharacteristic
368C22#1458313411yescharacteristic
369C22#1458313911yescharacteristic
370C22#1458316811yescharacteristic
371C22#1458317311yescharacteristic
372C4—21no—
373C4—21no—
374C4—161no—
375C4—1722no—
376C4—6881no—
377C4#102×D4311yescharacteristic
378C4#1458289911yescharacteristic
379C4#107×D4311yescharacteristic
380C4#1458293411yescharacteristic
381C4#1458313411yescharacteristic
382C4#1458313911yescharacteristic
383C4#1458317811yescharacteristic
384C4#1458318811yescharacteristic
385C2—1724no—
386C2#1913394911yescharacteristic
387C2#1913395911yescharacteristic
388C2#1913398311yescharacteristic
389C2#1913399311yescharacteristic
390C2#1913459411yescharacteristic
391C2#1913462311yescharacteristic
392C2#1913465811yescharacteristic
subgroupG/H
centerC23#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1296C2
socleC23×C43#121
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1296D43
hypocenterC43#8644
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #19134754C2semidirect
5. C2×#14582651C2semidirect
6. #19132479C2semidirect
7. C43×#1296C2semidirect
11. #14582964C4semidirect
151. D172#107semidirect
160. C43⋊C8#102semidirect
195. #1296D43semidirect
222. C43#8644semidirect

Maximal subgroups

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

subgroupindex
C2×#145829642
#191347542
#191345962
#191345922
C2×#145826512
#191324792
C43×#12962
#864443