Finite Group Databasebeta

← #25000989

Subgroups — #25000989

Order 11008.

532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145352C211yesmaximal, characteristic
2#19135580C211yesmaximal, characteristic, complemented
3#19135024C211yesmaximal, characteristic
4#19135016C211yesmaximal, characteristic, complemented
5#19134775C211yesmaximal, characteristic, complemented
6#19132462C211yesmaximal, characteristic, complemented
7C43×#1964C211yesmaximal, characteristic
8C23×C43⋊C8C2211yescharacteristic
9C2×#13063304C2211yescharacteristic
10#14583229—21no—
11#14583215—21no—
12#14583126—21no—
13#14583126—21no—
14#14583050—21no—
15#14583037—21no—
16C2×C4⋊(C43⋊C8)—21no—
17C2×#13063248—21no—
18C2×#13063246—21no—
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20#14582759C2211yescharacteristic
21#14582665—21no—
22#14582665—21no—
23#14582661—21no—
24#14582661—21no—
25#14582654—21no—
26C2×#121×C43C2211yescharacteristic
27C2×#99×C43—21no—
28C2×#99×C43—21no—
29C43×#380C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C2×#10621883—21no—
33C2×#10621883—21no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—42no—
38C22×C43⋊C8D411yescharacteristic
39C22×C43⋊C8D411yescharacteristic
40#13063304—21no—
41#13063304—21no—
42#13063304—21no—
43#13063304—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43D411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49#13063256—21no—
50#13063256—21no—
51C4⋊(C43⋊C8)—42no—
52#13063248—21no—
53#13063248—21no—
54#13063248—42no—
55#13063246—21no—
56#13063246—21no—
57#13063246—42no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—21no—
60C43⋊#95—21no—
61C22×D4×C43—21no—
62C22×D4×C43D411yescharacteristic
63C23×C4×C43C2311yescharacteristic
64#121×C43—21no—
65#121×C43—21no—
66#121×C43—21no—
67#121×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43D411yescharacteristic
73C2×C22⋊C4×C43D411yescharacteristic
74C2×C42×C43—21no—
75#99×C43—42no—
76#99×C43—42no—
77#95×C43—21no—
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—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43#4111yescharacteristic
101C22×C4×C43#4111yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—41no—
106C2×Dic86—21no—
107C2×Dic86—21no—
108C2×Dic86—41no—
109C2×Dic86—41no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C22⋊C4×C43—21no—
115C22⋊C4×C43—21no—
116C22⋊C4×C43—21no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43SD1612yescomplemented
122C42×C43—41no—
123C42×C43—41no—
124C22⋊Dic43—41no—
125C22⋊Dic43—41no—
126C22⋊Dic43—41no—
127C22⋊Dic43—41no—
128#10621883—81no—
129#10621883—81no—
130C4⋊Dic43—21no—
131C4⋊Dic43—21no—
132C4⋊Dic43—41no—
133C4⋊Dic43—41no—
134Dic43⋊C4—41no—
135Dic43⋊C4—41no—
136C2×C43⋊C8—22no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—22no—
139C2×C43⋊C8—21no—
140C2×C43⋊C8—21no—
141C2×C43⋊C8—41no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145C2×C43⋊C8—41no—
146C2×C43⋊C8—41no—
147C23×C43—41no—
148C23×C43—41no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43—81no—
153C23×C43—81no—
154C23×C43#12111yescharacteristic
155C23×C43#12111yescharacteristic
156C23×C43#12111yescharacteristic
157C23×C43C2×SD1611yescharacteristic
158C23×C43#13511yescharacteristic
159C23×C43AGL(1,ℤ/8)11yescharacteristic
160C23×C43#13711yescharacteristic
161D4×C43—42no—
162D4×C43—41no—
163D4×C43—41no—
164D4×C43—81no—
165D4×C43—81no—
166D4×C43—81no—
167D4×C43—81no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—22no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—81no—
187C2×C4×C43—81no—
188C2×C4×C43—81no—
189C2×C4×C43#12011yescharacteristic
190C2×C4×C43#12311yescharacteristic
191C2×C4×C43#12311yescharacteristic
192C2×C4×C43#12411yescharacteristic
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—81no—
196C2×Dic43—81no—
197C2×Dic43—81no—
198C2×Dic43—81no—
199C2×Dic43—81no—
200Dic86—42no—
201Dic86—41no—
202Dic86—41no—
203C43⋊C8—42no—
204C43⋊C8—41no—
205C43⋊C8—41no—
206#10565—431nomaximal, Sylow
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43—41no—
216C22×C43—41no—
217C22×C43—81no—
218C22×C43—81no—
219C22×C43—81no—
220C22×C43—161no—
221C22×C43—161no—
222C22×C43#39411yescharacteristic
223C22×C43#46011yescharacteristic
224C22×C43#46111yescharacteristic
225C22×C43#46311yescharacteristic
226C22×C43#46411yescharacteristic
227C22×C43#46511yescharacteristic
228C22×C43#46811yescharacteristic
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—42no—
233C4×C43—81no—
234C4×C43—81no—
235C4×C43—161no—
236C4×C43B(4,𝔽2)11yescharacteristic
237C4×C43#45811yescharacteristic
238Dic43—81no—
239Dic43—81no—
240Dic43—161no—
241#3187—431no—
242#1996—431no—
243#1964D4311yescharacteristic
244#1893—431no—
245#1892—431no—
246#1850—431no—
247#1289—431no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—21no—
251C2×C43—21no—
252C2×C43—21no—
253C2×C43—21no—
254C2×C43—161no—
255C2×C43#204411yescharacteristic
256C2×C43#205311yescharacteristic
257C2×C43#205511yescharacteristic
258C23×C8—431no—
259C2×C22⋊Q8—431no—
260C2×#121C2×D4311yescharacteristic
261#483—861no—
262#481—861no—
263#465—861no—
264#465—861no—
265#450—861no—
266#448—861no—
267C2×C4⋊C8—861no—
268C2×#103—861no—
269C2×#102—861no—
270C2×#99—21no—
271C2×#99—21no—
272C2×C22⋊C8—431no—
273#380—431no—
274#380C2×D4311yescharacteristic
275C4×C22⋊C4C2×D4311yescharacteristic
276#342—861no—
277#342—861no—
278#340—861no—
279#340—861no—
280#336—861no—
281C43#1056511yescharacteristic, complemented, Sylow
282C22×Q8—431no—
283C22×D4—21no—
284C22×D4D17211yescharacteristic
285C23×C4C22×D4311yescharacteristic
286C2×SD16—861no—
287C2×SD16—861no—
288C22×C8—431no—
289C22×C8—431no—
290C22×C8—861no—
291C22×C8—861no—
292C22×C8—861no—
293C22×C8—1722no—
294C22⋊Q8—861no—
295C22⋊Q8—861no—
296C22⋊Q8—861no—
297C22⋊Q8—861no—
298#121—21no—
299#121—21no—
300#121—21no—
301#121—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—431no—
304C2×C4⋊C4—861no—
305C2×C4⋊C4—861no—
306C2×C4⋊C4D17211yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—861no—
310C2×C22⋊C4—861no—
311C2×C22⋊C4C22⋊D4311yescharacteristic
312C2×C22⋊C4C22⋊D4311yescharacteristic
313C2×C42—21no—
314#106—861no—
315#106—861no—
316C4⋊C8—1722no—
317#103—861no—
318#103—861no—
319#103—1722no—
320#102—861no—
321#102—861no—
322#102—1722no—
323#99—42no—
324#99—42no—
325C22⋊C8—861no—
326C22⋊C8—861no—
327#95—21no—
328#95—21no—
329#95—861no—
330C24—21no—
331C24C2×C22⋊D4311yescharacteristic
332C2×Q8—861no—
333C2×Q8—861no—
334C2×Q8—1721no—
335C2×Q8—1721no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—861no—
353C22×C4—861no—
354C22×C4—1721no—
355C22×C4C2×D17211yescharacteristic
356C22×C4#1062189811yescharacteristic
357C22×C4D4×D4311yescharacteristic
358C22×C4D4×D4311yescharacteristic
359C22×C4#1062190011yescharacteristic
360C22×C4#1062190011yescharacteristic
361SD16—3441no—
362SD16—3441no—
363C2×C8—862no—
364C2×C8—862no—
365C2×C8—862no—
366C2×C8—861no—
367C2×C8—861no—
368C2×C8—1721no—
369C2×C8—1721no—
370C2×C8—1721no—
371C2×C8—1721no—
372C2×C8—1721no—
373C2×C8—1721no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—861no—
379C4⋊C4—861no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C4⋊C4—1721no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—1721no—
392C22⋊C4—1721no—
393C22⋊C4—1721no—
394C22⋊C4—1721no—
395C22⋊C4#1062188312yescomplemented
396C42—41no—
397C42—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—81no—
404C23—81no—
405C23#1306329611yescharacteristic
406C23#1306329711yescharacteristic
407C23#1306329911yescharacteristic
408C23C2×#1062188311yescharacteristic
409C23#1306334511yescharacteristic
410C23#1306335111yescharacteristic
411C23#1306335511yescharacteristic
412Q8—1722no—
413Q8—1721no—
414Q8—1721no—
415D4—42no—
416D4—41no—
417D4—41no—
418D4—81no—
419D4—81no—
420D4—81no—
421D4—81no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—3441no—
444C2×C4—3441no—
445C2×C4—3441no—
446C2×C4—3441no—
447C2×C4—3441no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4#1306329511yescharacteristic
451C2×C4#1306330711yescharacteristic
452C2×C4#1306330911yescharacteristic
453C2×C4#1306331111yescharacteristic
454C8—1722no—
455C8—1721no—
456C8—1721no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—161no—
471C22—161no—
472C22#1458281511yescharacteristic
473C22#1458309611yescharacteristic
474C22#1458310411yescharacteristic
475C22#1458311411yescharacteristic
476C22#1458311811yescharacteristic
477C22#1458312611yescharacteristic
478C22#1458314311yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—81no—
485C4—161no—
486C4—3441no—
487C4—3441no—
488C4—6881no—
489C4#1458308711yescharacteristic
490C4#1458309011yescharacteristic
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—161no—
498C2#1913584511yescharacteristic
499C2#1913590011yescharacteristic
500C2#1913591211yescharacteristic
subgroupG/H
centerC22#14582815
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1964C2
socleC22×C43#394
prime radicalC2×#121×C43C22
hypercenter#1964D43
hypocenterC43#10565
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #19135580C2semidirect
4. #19135016C2semidirect
5. #19134775C2semidirect
6. #19132462C2semidirect
121. C22⋊C4×C43SD16semidirect
281. C43#10565semidirect
395. C22⋊C4#10621883semidirect

Maximal subgroups

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

subgroupindex
#191453522
#191355802
#191350242
#191350162
#191347752
#191324622
C43×#19642
#1056543