Finite Group Databasebeta

← #24996107

Subgroups — #24996107

Order 11008.

564 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583126C211yesmaximal, characteristic
2#19135579C211yesmaximal, characteristic, complemented
3#19135432C211yesmaximal, characteristic
4#19134618C211yesmaximal, characteristic, complemented
5#19134369C211yesmaximal, characteristic, complemented
6#19133168C211yesmaximal, characteristic, complemented
7C43×#1519C211yesmaximal, characteristic
8C22×#10621883C411yescharacteristic, complemented
9C23×C43⋊C8C2211yescharacteristic
10C2×#13063304C2211yescharacteristic
11#14583126—21no—
12#14583126—21no—
13#14583126—21no—
14#14583126—21no—
15C2×#13063256—21no—
16C2×#13063256C411yescharacteristic, complemented
17C2×#13063248C411yescharacteristic, complemented
18C2×#13063246C411yescharacteristic, complemented
19C2×#13063240—22no—
20C2×C8×Dic43—21no—
21#14582759C2211yescharacteristic
22C4×C22⋊Dic43C2211yescharacteristic
23#14582665—22no—
24#14582661—21no—
25#14582653—21no—
26#14582637—22no—
27C2×#121×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C43×#327—22no—
31C22×Dic86C2×C411yescharacteristic
32C2×#10621883—21no—
33C2×#10621883—21no—
34C2×#10621883—42no—
35C22×C43⋊C8—42no—
36C22×C43⋊C8C2×C411yescharacteristic
37C22×C43⋊C8C2×C411yescharacteristic
38C22×C43⋊C8D411yescharacteristic
39C22×C43⋊C8D411yescharacteristic
40C22×C43⋊C8D411yescharacteristic
41C22×C43⋊C8D411yescharacteristic
42#13063304—21no—
43#13063304—21no—
44#13063304—21no—
45#13063304—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43C2×C411yescharacteristic
48C2×Dic43⋊C4—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43D412yes—
52C2×C4×Dic43—21no—
53#13063256—21no—
54#13063256—21no—
55#13063256—42no—
56#13063248—21no—
57#13063248—21no—
58#13063246—21no—
59#13063246—21no—
60#13063240—44no—
61C8×Dic43—42no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C22×D4×C43—21no—
65C22×D4×C43C2×C411yescharacteristic
66C23×C4×C43C2311yescharacteristic
67C22×C8×C43—21no—
68#121×C43—21no—
69#121×C43—21no—
70#121×C43—21no—
71#121×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43C2×C411yescharacteristic
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43D412yes—
78#95×C43—21no—
79C24×C43—21no—
80C24×C43C2×D411yescharacteristic
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—41no—
84C2×D4×C43—41no—
85C2×D4×C43—42no—
86C2×D4×C43—42no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C22×C4×C43—21no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43C22×C411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—22no—
102C22×Dic43—41no—
103C2×Dic86—21no—
104C2×Dic86—21no—
105C2×Dic86—41no—
106C2×Dic86—41no—
107C2×C8×C43—22no—
108C2×C8×C43—41no—
109C2×C8×C43—41no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C22⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—42no—
117C22⋊Dic43—22no—
118C22⋊Dic43—41no—
119C22⋊Dic43—41no—
120C22⋊Dic43—42no—
121C22⋊Dic43SD1614yescomplemented
122#10621883—42no—
123#10621883—42no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—41no—
127C4⋊Dic43—41no—
128Dic43⋊C4—41no—
129Dic43⋊C4—41no—
130C4×Dic43—41no—
131C4×Dic43—41no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—41no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138C2×C43⋊C8C22⋊C411yescharacteristic
139C2×C43⋊C8C22⋊C411yescharacteristic
140C2×C43⋊C8C22⋊C411yescharacteristic
141C2×C43⋊C8C22⋊C411yescharacteristic
142C23×C43—41no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—42no—
146C23×C43—81no—
147C23×C43—81no—
148C23×C43C4×D411yescharacteristic
149C23×C43#12111yescharacteristic
150C23×C43#12711yescharacteristic
151C23×C43C2×SD1612yes—
152C23×C43#13512yes—
153D4×C43—41no—
154D4×C43—41no—
155D4×C43—81no—
156D4×C43—82no—
157D4×C43—81no—
158D4×C43—81no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—42no—
170C2×C4×C43—81no—
171C2×C4×C43—81no—
172C2×C4×C43—81no—
173C2×C4×C43C2×C22⋊C411yescharacteristic
174C2×C4×C43C4×D411yescharacteristic
175C2×C4×C43#12111yescharacteristic
176C2×C4×C43#12411yescharacteristic
177C2×Dic43—24no—
178C2×Dic43—42no—
179C2×Dic43—42no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43—81no—
183C2×Dic43—81no—
184C2×Dic43—81no—
185C2×Dic43—81no—
186C2×Dic43—81no—
187Dic86—41no—
188Dic86—41no—
189Dic86—81no—
190C8×C43—42no—
191C43⋊C8—21no—
192C43⋊C8—21no—
193C43⋊C8—21no—
194C43⋊C8#9912yescomplemented
195#9781—431nomaximal, Sylow
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—42no—
203C22×C43—42no—
204C22×C43—81no—
205C22×C43—81no—
206C22×C43—81no—
207C22×C43—162no—
208C22×C43#39011yescharacteristic
209C22×C43C4×SD1612yes—
210C22×C43#46512yes—
211C22×C43#49211yescharacteristic
212C22×C43#49511yescharacteristic
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—81no—
217C4×C43—161no—
218C4×C43C2×#9911yescharacteristic
219C4×C43#41011yescharacteristic
220Dic43—44no—
221Dic43—81no—
222Dic43—81no—
223Dic43—161no—
224C2×#465—431no—
225#1996—431no—
226#1964—431no—
227#1807—431no—
228C8×C22⋊C4—431no—
229#1520—431no—
230#1519D4311yescharacteristic
231C2×C43—22no—
232C2×C43—21no—
233C2×C43—21no—
234C2×C43—22no—
235C2×C43—161no—
236C2×C43#196411yescharacteristic
237C2×C43#196811yescharacteristic
238C2×C43#197611yescharacteristic
239C22×SD16—431no—
240C23×C8—431no—
241C2×C22⋊Q8—431no—
242C2×#121C2×D4311yescharacteristic
243#465—861no—
244#465—861no—
245#465—861no—
246#465—861no—
247C2×#106—431no—
248C2×#106—861no—
249C2×#103—431no—
250C2×#102—431no—
251C2×#99—862no—
252C2×C22⋊C8C2×D4311yescharacteristic
253C2×C4×C8—861no—
254#380—431no—
255#380C2×D4311yescharacteristic
256C4×C22⋊C4—431no—
257#342—862no—
258#340—861no—
259#336—861no—
260#328—862no—
261#327—22no—
262C43#978111yescharacteristic, complemented, Sylow
263C22×Q8—431no—
264C22×D4—21no—
265C22×D4C4×D4311yescharacteristic
266C23×C4C22×D4311yescharacteristic
267C2×SD16—861no—
268C2×SD16—861no—
269C2×SD16—1722no—
270C22×C8—21no—
271C22×C8—431no—
272C22×C8—431no—
273C22×C8—431no—
274C22×C8—431no—
275C22×C8—431no—
276C22×C8—431no—
277C22×C8—1722no—
278C22⋊Q8—861no—
279C22⋊Q8—861no—
280C22⋊Q8—861no—
281C22⋊Q8—861no—
282#121—21no—
283#121—21no—
284#121—21no—
285#121—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—431no—
288C2×C4⋊C4—861no—
289C2×C4⋊C4—861no—
290C2×C4⋊C4C4×D4311yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—432no—
294C2×C22⋊C4—861no—
295C2×C22⋊C4—861no—
296C2×C42—861no—
297#106—861no—
298#106—861no—
299#106—1722no—
300#103—861no—
301#103—861no—
302#102—861no—
303#102—861no—
304#99—1724no—
305C22⋊C8—21no—
306C22⋊C8C22⋊D4312yes—
307C4×C8—1722no—
308#95—21no—
309#95—861no—
310#95—861no—
311C24—21no—
312C24D4×D4311yescharacteristic
313C2×Q8—861no—
314C2×Q8—861no—
315C2×Q8—1721no—
316C2×Q8—1721no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—42no—
324C2×D4—42no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—862no—
330C22×C4—861no—
331C22×C4—861no—
332C22×C4—1721no—
333C22×C4C2×C4×D4311yescharacteristic
334C22×C4#1062189811yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4D4×D4311yescharacteristic
337C22×C4#1062190011yescharacteristic
338C22×C4C2×C22⋊D4311yescharacteristic
339SD16—1722no—
340SD16—1722no—
341C2×C8—22no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—431no—
345C2×C8—431no—
346C2×C8—431no—
347C2×C8—431no—
348C2×C8—862no—
349C2×C8—862no—
350C2×C8—862no—
351C2×C8—1721no—
352C2×C8—1721no—
353C2×C8—1721no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—861no—
359C4⋊C4—861no—
360C4⋊C4—1721no—
361C4⋊C4—1721no—
362C4⋊C4—1721no—
363C4⋊C4—1721no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—42no—
367C22⋊C4—434no—
368C22⋊C4—862no—
369C22⋊C4—1722no—
370C22⋊C4—1721no—
371C22⋊C4—1721no—
372C42—1721no—
373C42—1721no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23—81no—
379C23—81no—
380C23(C22⋊D43)⋊C411yescharacteristic
381C23#1306329811yescharacteristic
382C23#1306332111yescharacteristic
383C23SD16×D4312yes—
384C23#1306334412yes—
385Q8—3441no—
386Q8—1721no—
387Q8—1721no—
388D4—41no—
389D4—41no—
390D4—81no—
391D4—82no—
392D4—81no—
393D4—81no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—864no—
409C2×C4—3441no—
410C2×C4—3441no—
411C2×C4—3441no—
412C2×C4—3441no—
413C2×C4—3441no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4—1722no—
417C2×C4—1722no—
418C2×C4C22⋊C4×D4311yescharacteristic
419C2×C4C4×C22⋊D4311yescharacteristic
420C2×C4#1306329711yescharacteristic
421C2×C4#1306331111yescharacteristic
422C8—42no—
423C8—432no—
424C8—861no—
425C8—861no—
426C8—861no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—42no—
434C22—42no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—162no—
439C22#1458279911yescharacteristic
440C22#1458299012yes—
441C22#1458312712yes—
442C22#1458327011yescharacteristic
443C22#1458328211yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—81no—
448C4—161no—
449C4—3441no—
450C4—3441no—
451C4—1724no—
452C4—6881no—
453C4#99×D4311yescharacteristic
454C4#1458287111yescharacteristic
455C2—21no—
456C2—22no—
457C2—21no—
458C2—22no—
459C2—161no—
460C2#1913542911yescharacteristic
461C2#1913545011yescharacteristic
462C2#1913549211yescharacteristic
subgroupG/H
centerC22#14582799
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1519C2
socleC22×C43#390
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenter#1519D43
hypocenterC43#9781
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #19135579C2semidirect
4. #19134618C2semidirect
5. #19134369C2semidirect
6. #19133168C2semidirect
8. C22×#10621883C4semidirect
16. C2×#13063256C4semidirect
17. C2×#13063248C4semidirect
18. C2×#13063246C4semidirect
121. C22⋊Dic43SD16semidirect
194. C43⋊C8#99semidirect
262. C43#9781semidirect

Maximal subgroups

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

subgroupindex
C2×#145831262
#191355792
#191354322
#191346182
#191343692
#191331682
C43×#15192
#978143