Finite Group Databasebeta

← #25079783

Subgroups — #25079783

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145912C211yesmaximal, characteristic, complemented
2#19145902C211yesmaximal, characteristic
3#19144917C211yesmaximal, characteristic, complemented
4#19143306C211yesmaximal, characteristic, complemented
5#19134141C212yesmaximal, complemented
6#19134127C212yesmaximal, complemented
7#19134045C212yesmaximal, complemented
8#19134031C212yesmaximal, complemented
9C2×#14582651C211yesmaximal, characteristic, complemented
10#19133286C211yesmaximal, characteristic, complemented
11C43×#1547C211yesmaximal, characteristic, complemented
12C2×#13063333—21no—
13#14583456C2211yescharacteristic
14#14583449C2211yescharacteristic
15#14583253—21no—
16#14583253—21no—
17#14583249C2211yescharacteristic
18#14583249C2211yescharacteristic
19#14583245C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583190C2212yes—
22#14583185—21no—
23#14583179—21no—
24#14583176C2212yes—
25#14583133—22no—
26#14583128—22no—
27#14583105C2212yes—
28#14583100—21no—
29#14583094—21no—
30#14583091C2212yes—
31#14582976—21no—
32#14582976C2212yes—
33#14582964—21no—
34#14582964C2212yes—
35C2×C4⋊(C43⋊C8)C2211yescharacteristic
36#14582895—21no—
37#14582895—21no—
38#14582867—21no—
39C2×C4×C43⋊C8C2211yescharacteristic
40#14582651C2212yes—
41#14582651C2212yes—
42#14582647C2212yes—
43#14582644C2212yes—
44C43×#532C2211yescharacteristic
45C43×#423C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C43×#332C2212yes—
48C43×#331C2212yes—
49C2×#10621898—21no—
50C2×#10621873—22no—
51C2×#10621882—22no—
52#13063333—44no—
53C2×#10621872—22no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8D411yescharacteristic
56C22×C43⋊C8D411yescharacteristic
57C2×C8×D43—22no—
58#13063325D411yescharacteristic
59#13063325C2311yescharacteristic
60#13063325C2311yescharacteristic
61#13063322D411yescharacteristic
62#13063317—21no—
63#13063313—21no—
64#13063304—21no—
65#13063304—21no—
66#13063299—21no—
67#13063299D412yes—
68C4×Dic86—21no—
69C4×Dic86—21no—
70C4×D172—21no—
71C4×D172C2312yes—
72#13063284—21no—
73#13063258—22no—
74#13063257—22no—
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)C2312yes—
77#13063250—22no—
78#13063249—21no—
79#13063249—21no—
80#13063249—21no—
81#13063249—21no—
82#13063247—22no—
83#13063246—22no—
84#13063246—21no—
85#13063246—21no—
86#13063246—21no—
87#13063246—21no—
88#13063245—22no—
89(C2×D43)⋊C8—22no—
90(C2×D43)⋊C8—22no—
91C4×C43⋊C8D411yescharacteristic
92C4×C43⋊C8D411yescharacteristic
93C4×C43⋊C8C2311yescharacteristic
94C4×C43⋊C8C2311yescharacteristic
95C2×#41×C43—21no—
96C2×M16×C43—21no—
97C22×C8×C43—21no—
98C4⋊Q8×C43C2311yescharacteristic
99#127×C43C2311yescharacteristic
100#124×C43—21no—
101#121×C43—21no—
102#121×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C2×C42×C43C2311yescharacteristic
106C4⋊C8×C43—21no—
107C4⋊C8×C43—21no—
108C4⋊C8×C43C2312yes—
109C4⋊C8×C43C2312yes—
110#41×C43—42no—
111#41×C43—42no—
112C2×Q8×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C2×C22⋊D43—22no—
122#10621898—42no—
123#10621898—42no—
124C2×D172—21no—
125C2×D172—21no—
126C2×D172C2×D412yes—
127C2×C4×D43—22no—
128C2×Dic86—21no—
129C2×Dic86—21no—
130C2×Dic86—21no—
131M16×C43—42no—
132C2×C8×C43—22no—
133C2×C8×C43—22no—
134C2×C8×C43—81no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C22⋊C4×C43—41no—
138C22⋊C4×C43—41no—
139C42×C43C2×D411yescharacteristic
140C42×C43C2×D411yescharacteristic
141C42×C43#4111yescharacteristic
142C42×C43C2411yescharacteristic
143C22⋊Dic43—41no—
144#10621882—82no—
145(C2×D43)⋊C4—22no—
146(C2×D43)⋊C4—22no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—21no—
150C4⋊Dic43—21no—
151C4⋊Dic43—21no—
152C4⋊Dic43C2×D412yes—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155C4×Dic43—41no—
156C2×C43⋊C8—22no—
157C2×C43⋊C8—22no—
158C2×C43⋊C8—22no—
159C2×C43⋊C8—81no—
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162C2×C43⋊C8C2×D411yescharacteristic
163C2×C43⋊C8C2×D411yescharacteristic
164#10621873—82no—
165#10621872—44no—
166C8×D43—44no—
167C23×C43—41no—
168C23×C43#12111yescharacteristic
169C22×D43—22no—
170Q8×C43—41no—
171Q8×C43—41no—
172D4×C43—41no—
173D4×C43—41no—
174D4×C43—41no—
175D4×C43—41no—
176D4×C43—81no—
177D4×C43—82no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—82no—
183C2×C4×C43#12111yescharacteristic
184C2×C4×C43#12111yescharacteristic
185C2×C4×C43#12111yescharacteristic
186C2×C4×C43#13512yes—
187C2×C4×C43AGL(1,ℤ/8)12yes—
188C2×C4×C43C22×D411yescharacteristic
189C2×C4×C43C22×D411yescharacteristic
190C2×C4×C43C2×#4111yescharacteristic
191C22⋊D43—44no—
192C2×Dic43—22no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195D172—22no—
196D172—22no—
197D172—42no—
198D172—42no—
199C4×D43—42no—
200C4×D43—42no—
201Dic86—42no—
202Dic86—41no—
203Dic86—41no—
204Dic86—81no—
205C8×C43—42no—
206C8×C43—42no—
207C43⋊C8—21no—
208C43⋊C8—21no—
209C43⋊C8—21no—
210C43⋊C8—21no—
211C43⋊C8—42no—
212#19201—431nomaximal, Sylow
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—81no—
216C22×C43—81no—
217C22×C43—81no—
218C22×C43#46312yes—
219C22×C43C2×#12111yescharacteristic
220C2×D43—42no—
221C2×D43—42no—
222C2×D43—42no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—81no—
227C4×C43#46312yes—
228C4×C43C2×#13511yescharacteristic
229C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
230C4×C43#57611yescharacteristic
231C4×C43#57811yescharacteristic
232Dic43—42no—
233Dic43—81no—
234Dic43—81no—
235#3246—431no—
236#3245—431no—
237#3131—431no—
238#2931—431no—
239#1699—432no—
240#1697—432no—
241#1683—432no—
242#1681—432no—
243C2×#335—431no—
244#1550—431no—
245#1547D4311yescharacteristic, complemented
246C2×C43—22no—
247C2×C43—161no—
248C2×C43C2×#46311yescharacteristic
249C2×C43#306111yescharacteristic
250C2×C43#306711yescharacteristic
251D43—82no—
252C2×#131—861no—
253#533—431no—
254#532—431no—
255#532C2×D4311yescharacteristic
256#488—861no—
257#488—861no—
258#487—431no—
259#487—431no—
260#486—431no—
261#486—431no—
262#476—432no—
263#475—861no—
264#474—432no—
265#474—861no—
266#466—862no—
267#465—862no—
268#461—432no—
269#460—861no—
270#459—432no—
271#459—861no—
272#436—432no—
273#436—861no—
274C8×D4—432no—
275C8×D4—861no—
276#423C2×D4311yescharacteristic
277C2×C4⋊C8—431no—
278C2×C4⋊C8C2×D4311yescharacteristic
279#416—861no—
280#416—861no—
281#408—861no—
282C2×C4×C8—431no—
283#335—432no—
284#335—432no—
285#333—432no—
286#332—432no—
287#332C2×D4312yes—
288#331C2×D4312yes—
289C43#1920111yescharacteristic, complemented, Sylow
290C2×#41—21no—
291C2×#41—861no—
292C2×SD16—862no—
293C2×D8—862no—
294#131—1724no—
295C2×M16—21no—
296C2×M16—862no—
297C22×C8—21no—
298C22×C8—431no—
299C22×C8—431no—
300C22×C8—862no—
301C22×C8—861no—
302C4⋊Q8—431no—
303C4⋊Q8—431no—
304C4⋊Q8—431no—
305C4⋊Q8C22×D4311yescharacteristic
306#127—431no—
307#127C22×D4311yescharacteristic
308#125—861no—
309#124—21no—
310#124—861no—
311C22⋊Q8—861no—
312C22⋊Q8—861no—
313#121—21no—
314#121—21no—
315#121—432no—
316#121—861no—
317C4×Q8—861no—
318C4×Q8—861no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—432no—
322C4×D4—861no—
323#117—861no—
324C2×C42C22×D4311yescharacteristic
325#107—862no—
326#106—862no—
327C4⋊C8—21no—
328C4⋊C8—21no—
329C4⋊C8—432no—
330C4⋊C8—861no—
331C4⋊C8C22×D4312yes—
332C4⋊C8C22×D4312yes—
333#103—862no—
334#103—861no—
335#103—861no—
336#103—861no—
337#103—861no—
338#102—862no—
339#102—862no—
340#102—862no—
341#102—861no—
342#102—861no—
343#102—861no—
344#102—861no—
345C22⋊C8—862no—
346C22⋊C8—862no—
347C4×C8—431no—
348C4×C8—431no—
349C4×C8—431no—
350C4×C8—431no—
351#41—42no—
352#41—42no—
353#41—1722no—
354#41—1722no—
355C2×Q8—21no—
356C2×Q8—861no—
357C2×Q8—861no—
358C2×Q8—861no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—41no—
363C2×D4—432no—
364C2×D4—862no—
365C2×D4—861no—
366C2×D4—861no—
367C22×C4—41no—
368C22×C4—862no—
369C22×C4#1062189811yescharacteristic
370C22×C4D4×D4311yescharacteristic
371C22×C4D4×D4311yescharacteristic
372SD16—3442no—
373D8—3442no—
374M16—42no—
375M16—1724no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—81no—
379C2×C8—431no—
380C2×C8—431no—
381C2×C8—431no—
382C2×C8—431no—
383C2×C8—862no—
384C2×C8—862no—
385C2×C8—862no—
386C2×C8—3441no—
387C2×C8—1724no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—432no—
391C4⋊C4—861no—
392C4⋊C4—861no—
393C4⋊C4—861no—
394C4⋊C4—861no—
395C4⋊C4—861no—
396C4⋊C4—1721no—
397C4⋊C4—1721no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—862no—
401C22⋊C4—862no—
402C22⋊C4—1721no—
403C42—1721no—
404C42#1062189811yescharacteristic
405C42D4×D4311yescharacteristic
406C42D4×D4311yescharacteristic
407C42C23×D4311yescharacteristic
408C23—41no—
409C23—862no—
410C23#1306329811yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—3441no—
414Q8—1721no—
415Q8—1721no—
416Q8—1722no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—41no—
421D4—81no—
422D4—82no—
423D4—862no—
424D4—862no—
425D4—1722no—
426D4—1724no—
427D4—1722no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—82no—
433C2×C4—862no—
434C2×C4—1721no—
435C2×C4—1721no—
436C2×C4—1722no—
437C2×C4—1722no—
438C2×C4#1306329811yescharacteristic
439C2×C4#1306329811yescharacteristic
440C2×C4#1306329811yescharacteristic
441C2×C4#1306334612yes—
442C2×C4#1306334912yes—
443C2×C4C2×D4×D4311yescharacteristic
444C2×C4C2×D4×D4311yescharacteristic
445C2×C4C2×#1062189811yescharacteristic
446C8—42no—
447C8—42no—
448C8—861no—
449C8—861no—
450C8—861no—
451C8—861no—
452C8—1722no—
453C22—21no—
454C22—21no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—1722no—
459C22—1722no—
460C22—1722no—
461C22#1458311312yes—
462C22C2×#1306329811yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—81no—
467C4—3441no—
468C4—3441no—
469C4—1722no—
470C4#1458311312yes—
471C4C2×#1306334611yescharacteristic
472C4C2×#1306334911yescharacteristic
473C4#1458370311yescharacteristic
474C4#1458371511yescharacteristic
475C2—22no—
476C2—161no—
477C2—3442no—
478C2C2×#1458311311yescharacteristic
479C2#1914426411yescharacteristic
480C2#1914431411yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1547C2
socleC22×C43C2×#121
prime radical#19145902C2
hypercenter#1547D43
hypocenterC43#19201
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
1. #19145912C2semidirect
3. #19144917C2semidirect
4. #19143306C2semidirect
5. #19134141C2semidirect
6. #19134127C2semidirect
7. #19134045C2semidirect
8. #19134031C2semidirect
9. C2×#14582651C2semidirect
10. #19133286C2semidirect
11. C43×#1547C2semidirect
245. #1547D43semidirect
289. C43#19201semidirect

Maximal subgroups

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

subgroupindex
#191459122
#191459022
#191449172
#191433062
#191341412
#191341272
#191340452
#191340312
C2×#145826512
#191332862
C43×#15472
#1920143