Finite Group Databasebeta

← #24995946

Subgroups — #24995946

Order 11008.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144918C211yesmaximal, characteristic
2C8×C4⋊Dic43C211yesmaximal, characteristic, complemented
3#19133095C211yesmaximal, characteristic, complemented
4#19133091C211yesmaximal, characteristic
5#19132999C211yesmaximal, characteristic, complemented
6#19132995C211yesmaximal, characteristic
7C43×#1564C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9#14583449C2211yescharacteristic
10#14583254—21no—
11#14583254—21no—
12#14583250C411yescharacteristic, complemented
13#14583250C411yescharacteristic, complemented
14#14583246C411yescharacteristic, complemented
15#14583246C411yescharacteristic, complemented
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17#14582896—21no—
18#14582896—21no—
19C2×C8×Dic43—21no—
20C4×C4⋊Dic43C2211yescharacteristic
21#14582653—21no—
22#14582637—22no—
23#14582634—22no—
24#14582631—22no—
25#14582628—22no—
26C43×#431C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C2×C4×C8×C43C2211yescharacteristic
29C43×#335—21no—
30C43×#334—21no—
31C2×#10621898—21no—
32C22×C43⋊C8—21no—
33#13063325C2×C411yescharacteristic
34#13063325C2×C411yescharacteristic
35#13063325C2×C411yescharacteristic
36#13063322C2×C411yescharacteristic
37#13063317—21no—
38#13063313—21no—
39#13063304—21no—
40#13063304—21no—
41#13063299—21no—
42#13063299—21no—
43C4×Dic86—21no—
44C4×Dic86—21no—
45C4×D172—21no—
46C4×D172—21no—
47#13063284—21no—
48C2×C4⋊Dic43—21no—
49C2×C4×Dic43—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)D412yes—
52#13063250—21no—
53#13063250—21no—
54#13063250—21no—
55#13063250—21no—
56#13063247—21no—
57#13063247—21no—
58#13063247—21no—
59#13063247—21no—
60C8×Dic43—42no—
61C43⋊#95D412yes—
62C22×C8×C43D411yescharacteristic
63C22×C8×C43D411yescharacteristic
64C2×C42×C43C2311yescharacteristic
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69C4×C8×C43—21no—
70C4×C8×C43—21no—
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43D411yescharacteristic
74C4×C8×C43D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C2×C22⋊D43—41no—
79C22×Dic43—22no—
80#10621898—41no—
81#10621898—41no—
82#10621898—41no—
83#10621898—41no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172—21no—
87C2×C4×D43—41no—
88C2×Dic86—21no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91C2×C8×C43—21no—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—21no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43C22⋊C411yescharacteristic
98C2×C8×C43C22⋊C411yescharacteristic
99C2×C8×C43C22⋊C411yescharacteristic
100C2×C8×C43C22⋊C411yescharacteristic
101C42×C43C22×C411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43#4111yescharacteristic
105C22⋊Dic43—41no—
106(C2×D43)⋊C4—41no—
107(C2×D43)⋊C4—41no—
108C4⋊Dic43—24no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115Dic43⋊C4—41no—
116Dic43⋊C4—41no—
117C4×Dic43—41no—
118C4×Dic43—41no—
119C4×Dic43—41no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C23×C43#12111yescharacteristic
124C22×D43—41no—
125C2×C4×C43—22no—
126C2×C4×C43—41no—
127C2×C4×C43C2×C22⋊C411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12411yescharacteristic
132C2×C4×C43#12711yescharacteristic
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43#13511yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C43#13711yescharacteristic
137C22⋊D43—81no—
138C22⋊D43—81no—
139C2×Dic43—24no—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145D172—41no—
146D172—41no—
147D172—42no—
148D172—81no—
149C4×D43—81no—
150C4×D43—81no—
151Dic86—41no—
152Dic86—41no—
153Dic86—42no—
154Dic86—81no—
155C8×C43—21no—
156C8×C43—21no—
157C8×C43—21no—
158C8×C43—21no—
159C8×C43—81no—
160C8×C43—81no—
161C43⋊C8—42no—
162#9751—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43#39011yescharacteristic
166C22×C43#46311yescharacteristic
167C22×C43#46411yescharacteristic
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43#41611yescharacteristic
175C4×C43#41711yescharacteristic
176C4×C43#44312yes—
177C4×C43#46311yescharacteristic
178C4×C43#46411yescharacteristic
179Dic43—44no—
180Dic43—81no—
181Dic43—81no—
182Dic43—81no—
183#3131—431no—
184C8×C4⋊C4—431no—
185#1564D4311yescharacteristic, complemented
186#1503—431no—
187#1502—431no—
188#1481—431no—
189#1480—431no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43#197411yescharacteristic
193C2×C43#197611yescharacteristic
194C2×C43#198311yescharacteristic
195D43—161no—
196#533—431no—
197#532—431no—
198#488—861no—
199#488—861no—
200#487—431no—
201#487—431no—
202#486—431no—
203#486—431no—
204#431C2×D4311yescharacteristic
205#431C2×D4311yescharacteristic
206C2×C4⋊C8—431no—
207#416—861no—
208#416—861no—
209C2×C4×C8—861no—
210C2×C4×C8C2×D4311yescharacteristic
211C4×C4⋊C4—431no—
212#336—861no—
213#335—21no—
214#334—21no—
215#328—862no—
216#327—862no—
217Q8⋊C8—862no—
218D4⋊C8—862no—
219C43#975111yescharacteristic, complemented, Sylow
220C2×#41—861no—
221C22×C8—861no—
222C22×C8D17211yescharacteristic
223C22×C8D17211yescharacteristic
224C4⋊Q8—431no—
225C4⋊Q8—431no—
226C4⋊Q8—431no—
227#127—431no—
228#125—861no—
229#124—861no—
230C22⋊Q8—861no—
231C22⋊Q8—861no—
232#121—861no—
233#121—861no—
234C4×Q8—861no—
235C4×Q8—861no—
236C4×D4—861no—
237C4×D4—861no—
238#117—861no—
239C2×C4⋊C4—861no—
240C2×C42—861no—
241C2×C42C22×D4311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—432no—
245C4⋊C8—861no—
246#103—861no—
247#103—861no—
248#103—861no—
249#103—861no—
250#102—861no—
251#102—861no—
252#102—861no—
253#102—861no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C4×C8—21no—
257C4×C8—21no—
258C4×C8—1722no—
259C4×C8C4×D4311yescharacteristic
260C4×C8C4×D4311yescharacteristic
261C4×C8C22⋊D4311yescharacteristic
262C4×C8C22⋊D4311yescharacteristic
263#95—432no—
264#41—1721no—
265#41—1721no—
266#41—1721no—
267#41—1721no—
268C2×Q8—861no—
269C2×Q8—861no—
270C2×Q8—861no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—1721no—
275C22×C4—862no—
276C22×C4—1721no—
277C22×C4C2×D17211yescharacteristic
278C22×C4D4×D4311yescharacteristic
279C22×C4#1062190211yescharacteristic
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—862no—
287C2×C8—1721no—
288C2×C8—1721no—
289C2×C8(C2×D43)⋊C411yescharacteristic
290C2×C8(C2×D43)⋊C411yescharacteristic
291C2×C8(C2×D43)⋊C411yescharacteristic
292C2×C8(C2×D43)⋊C411yescharacteristic
293C4⋊C4—864no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—1721no—
301C4⋊C4—1721no—
302C22⋊C4—1721no—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C42—1721no—
306C42—1721no—
307C42—1721no—
308C42C2×C4×D4311yescharacteristic
309C42D4×D4311yescharacteristic
310C42#1062190211yescharacteristic
311C42C2×C22⋊D4311yescharacteristic
312C23—1721no—
313C23#1306330011yescharacteristic
314Q8—3441no—
315Q8—1721no—
316Q8—1721no—
317Q8—1722no—
318D4—3441no—
319D4—3441no—
320D4—3441no—
321D4—1721no—
322D4—1721no—
323D4—1722no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—864no—
327C2×C4—3441no—
328C2×C4—3441no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1722no—
333C2×C4—1722no—
334C2×C4C2×(C2×D43)⋊C411yescharacteristic
335C2×C4#1306328711yescharacteristic
336C2×C4#1306328711yescharacteristic
337C2×C4#1306330011yescharacteristic
338C2×C4#1306331411yescharacteristic
339C2×C4#1306332111yescharacteristic
340C2×C4#1306334711yescharacteristic
341C2×C4#1306334711yescharacteristic
342C2×C4#1306335311yescharacteristic
343C2×C4#1306335811yescharacteristic
344C8—21no—
345C8—21no—
346C8—21no—
347C8—21no—
348C8—81no—
349C8—81no—
350C8—1722no—
351C22—21no—
352C22—21no—
353C22—3441no—
354C22—3441no—
355C22—3441no—
356C22#1458280011yescharacteristic
357C22#1458311511yescharacteristic
358C22#1458312211yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—3441no—
363C4—3441no—
364C4—3441no—
365C4—1724no—
366C4#1458289611yescharacteristic
367C4#1458290111yescharacteristic
368C4#1458301512yes—
369C4#1458311511yescharacteristic
370C4#1458312211yescharacteristic
371C2—21no—
372C2—21no—
373C2—6881no—
374C2#1913548111yescharacteristic
375C2#1913549111yescharacteristic
376C2#1913552511yescharacteristic
subgroupG/H
centerC2×C4#13063300
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1564C2
socleC22×C43#390
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1564D43
hypocenterC43#9751
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
2. C8×C4⋊Dic43C2semidirect
3. #19133095C2semidirect
5. #19132999C2semidirect
7. C43×#1564C2semidirect
12. #14583250C4semidirect
13. #14583250C4semidirect
14. #14583246C4semidirect
15. #14583246C4semidirect
185. #1564D43semidirect
219. C43#9751semidirect

Maximal subgroups

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

subgroupindex
#191449182
C8×C4⋊Dic432
#191330952
#191330912
#191329992
#191329952
C43×#15642
#975143