Finite Group Databasebeta

← #25254207

Subgroups — #25254207

Order 11008.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146998C211yesmaximal, characteristic, complemented
2#19136871C211yesmaximal, characteristic, complemented
3#19136786C211yesmaximal, characteristic, complemented
4#19136783C211yesmaximal, characteristic, complemented
5#19136775C211yesmaximal, characteristic, complemented
6#19136773C211yesmaximal, characteristic, complemented
7#19136752C211yesmaximal, characteristic, complemented
8#19136749C211yesmaximal, characteristic, complemented
9#19136696C211yesmaximal, characteristic, complemented
10#19136696C211yesmaximal, characteristic, complemented
11C4×#13063266C211yesmaximal, characteristic, complemented
12#19136427C211yesmaximal, characteristic, complemented
13#19136384C211yesmaximal, characteristic, complemented
14#19136381C211yesmaximal, characteristic, complemented
15C43×#3339C211yesmaximal, characteristic, complemented
16#14583595—21no—
17C2×#13063266C2211yescharacteristic
18C2×#13063265C2211yescharacteristic
19C2×#13063265C2211yescharacteristic
20#14583301C2211yescharacteristic
21#14583224—21no—
22#14583218—21no—
23#14583200—21no—
24#14583135C2211yescharacteristic
25#14583135C2211yescharacteristic
26C4×D344C2211yescharacteristic
27#14582937C2211yescharacteristic
28C2×#13063259C2211yescharacteristic
29#14582726C2211yescharacteristic
30#14582726C2211yescharacteristic
31#14582726C2211yescharacteristic
32#14582726C2211yescharacteristic
33#14582724C2211yescharacteristic
34#14582724C2211yescharacteristic
35#14582724C2211yescharacteristic
36#14582724C2211yescharacteristic
37#14582724C2211yescharacteristic
38C4⋊(C43⋊C16)C2211yescharacteristic
39#14582700C2211yescharacteristic
40#14582700C2211yescharacteristic
41#14582700C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44#14582699C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46C22⋊(C43⋊C16)C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C43×#553—21no—
49C43×#499C2211yescharacteristic
50C43×#482—21no—
51C43×#481—21no—
52C43×#478—21no—
53C43×#466C2211yescharacteristic
54C43×#466C2211yescharacteristic
55C4×D8×C43C2211yescharacteristic
56C8×D4×C43C2211yescharacteristic
57C43×#427C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic
59C2×D344C2311yescharacteristic
60#13063320—41no—
61#13063317—21no—
62#13063307—41no—
63#13063299—21no—
64#13063299—21no—
65#13063297—41no—
66C4×D172—21no—
67(C22⋊D43)⋊C4—41no—
68#13063284—21no—
69C2×C4⋊Dic43—21no—
70#13063266—22no—
71#13063265—22no—
72#13063265—22no—
73C2×C43⋊C16C2311yescharacteristic
74C2×C43⋊C16C2311yescharacteristic
75C2×C43⋊C16C2311yescharacteristic
76C2×C43⋊C16C2311yescharacteristic
77#13063259—21no—
78#13063259C2311yescharacteristic
79#13063259C2311yescharacteristic
80#13063259C2311yescharacteristic
81#13063257—21no—
82#13063257—21no—
83#13063247—21no—
84#13063247—21no—
85#13063247—21no—
86C2×D8×C43C2311yescharacteristic
87C22×C8×C43C2311yescharacteristic
88C22×C8×C43C2311yescharacteristic
89#126×C43—41no—
90#125×C43—21no—
91#123×C43—41no—
92#121×C43—21no—
93#121×C43—21no—
94#121×C43—41no—
95C4×D4×C43—21no—
96C4×D4×C43—41no—
97C4×D4×C43D411yescharacteristic
98#117×C43—21no—
99C2×C4⋊C4×C43—21no—
100#107×C43—21no—
101#107×C43C2311yescharacteristic
102#107×C43C2311yescharacteristic
103#107×C43C2311yescharacteristic
104#106×C43—21no—
105#106×C43—21no—
106C4⋊C8×C43D411yescharacteristic
107#102×C43—21no—
108#102×C43—21no—
109#102×C43—21no—
110C22⋊C8×C43D411yescharacteristic
111C22⋊C8×C43D411yescharacteristic
112C4×C8×C43C2311yescharacteristic
113C2×D4×C43—21no—
114C2×D4×C43—41no—
115C2×D4×C43—41no—
116C2×D4×C43D811yescharacteristic
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C2×C22⋊D43—41no—
122C2×C22⋊D43—41no—
123C22×Dic43—41no—
124C2×D172—21no—
125C2×C4×D43—41no—
126D8×C43—21no—
127D8×C43—21no—
128C2×C8×C43—21no—
129C2×C8×C43—21no—
130C2×C8×C43—21no—
131C2×C8×C43—21no—
132C2×C8×C43C2×D411yescharacteristic
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2×D411yescharacteristic
135C2×C8×C43C2411yescharacteristic
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—41no—
140C4⋊C4×C43—41no—
141C4⋊C4×C43—41no—
142C4⋊C4×C43D811yescharacteristic
143C22⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C22⋊C4×C43D811yescharacteristic
148C22⋊C4×C43D811yescharacteristic
149C42×C43—41no—
150C42×C43C2×D411yescharacteristic
151C22⋊Dic43—41no—
152(C2×D43)⋊C4—41no—
153(C2×D43)⋊C4—41no—
154(C2×D43)⋊C4—41no—
155C4⋊Dic43—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43—21no—
158C4⋊Dic43—41no—
159Dic43⋊C4—41no—
160Dic43⋊C4—41no—
161C4×Dic43—41no—
162D344—21no—
163D344—21no—
164C43⋊C16—21no—
165C43⋊C16—21no—
166C43⋊C16—21no—
167C43⋊C16#4112yes—
168C23×C43—41no—
169C23×C43C2×D811yescharacteristic
170C23×C43C2×D811yescharacteristic
171C22×D43—41no—
172D4×C43—41no—
173D4×C43—41no—
174D4×C43—41no—
175D4×C43—82no—
176D4×C43—161no—
177C2×C4×C43—21no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—161no—
185C2×C4×C43—161no—
186C2×C4×C43C2×D811yescharacteristic
187C2×C4×C43C2×D811yescharacteristic
188C2×C4×C43C2×D811yescharacteristic
189C2×C4×C43C2×D811yescharacteristic
190C2×C4×C43C22×D411yescharacteristic
191C22⋊D43—82no—
192C22⋊D43—161no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—161no—
197D172—41no—
198D172—41no—
199C4×D43—161no—
200C8×C43—21no—
201C8×C43—21no—
202C8×C43—21no—
203C8×C43C2×#4111yescharacteristic
204C8×C432−1+411yescharacteristic
205#33922—431nomaximal, Sylow
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—81no—
213C22×C43—81no—
214C22×C43—81no—
215C22×C43C22×D811yescharacteristic
216C2×D43—81no—
217C2×D43—81no—
218C2×D43—81no—
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—81no—
224C4×C43—81no—
225C4×C43—81no—
226C4×C43#54711yescharacteristic
227C4×C43#57811yescharacteristic
228Dic43—81no—
229Dic43—81no—
230Dic43—81no—
231#3339—431no—
232#3339D4311yescharacteristic, complemented
233#2253—431no—
234#2234—431no—
235#2234—431no—
236#2232—431no—
237#2232—431no—
238#2228—431no—
239#2228—431no—
240#2218—431no—
241#2218—431no—
242C4×D16—431no—
243#2169—431no—
244#2159—431no—
245#2159—431no—
246C2×C43—41no—
247C2×C43—41no—
248C2×C43—161no—
249C2×C43#333411yescharacteristic
250C2×C43#341411yescharacteristic
251C2×C43#341511yescharacteristic
252D43—161no—
253#553—21no—
254#553—861no—
255C2×D16—431no—
256C2×M32—431no—
257C2×M32—431no—
258#499—431no—
259#499C2×D4311yescharacteristic
260#482—21no—
261#482—861no—
262#481—21no—
263#481—861no—
264#478—21no—
265#478—861no—
266#466—431no—
267#466—431no—
268#466C2×D4311yescharacteristic
269#466C2×D4311yescharacteristic
270C4×D8—431no—
271C4×D8C2×D4311yescharacteristic
272C8×D4C2×D4311yescharacteristic
273#427—431no—
274#427C2×D4311yescharacteristic
275C2×#107—431no—
276C2×#107C2×D4311yescharacteristic
277#367—431no—
278#367—431no—
279#367—431no—
280#367—431no—
281#366—431no—
282#366—431no—
283#366—431no—
284#366—431no—
285#366—431no—
286C4⋊C16—431no—
287#357—431no—
288#357—431no—
289#357—431no—
290#357—431no—
291#357—431no—
292#357—431no—
293C22⋊C16—431no—
294C22⋊C16—431no—
295C4×C16—431no—
296C43#3392211yescharacteristic, complemented, Sylow
297C2×D8—431no—
298C2×D8C22×D4311yescharacteristic
299C22×C8C22×D4311yescharacteristic
300C22×C8C22×D4311yescharacteristic
301#126—41no—
302#126—1721no—
303#125—21no—
304#125—861no—
305#123—41no—
306#123—1721no—
307#121—21no—
308#121—21no—
309#121—41no—
310#121—861no—
311#121—861no—
312#121—1721no—
313C4×D4—21no—
314C4×D4—41no—
315C4×D4—861no—
316C4×D4—1721no—
317C4×D4C22⋊D4311yescharacteristic
318#117—21no—
319#117—861no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—861no—
322D16—862no—
323M32—862no—
324M32—862no—
325C2×C16—431no—
326C2×C16—431no—
327C2×C16—431no—
328C2×C16—431no—
329#107—21no—
330#107—431no—
331#107—431no—
332#107—431no—
333#107—861no—
334#107C22×D4311yescharacteristic
335#107C22×D4311yescharacteristic
336#107C22×D4311yescharacteristic
337#106—21no—
338#106—21no—
339#106—861no—
340#106—861no—
341C4⋊C8C22⋊D4311yescharacteristic
342#102—21no—
343#102—21no—
344#102—21no—
345#102—861no—
346#102—861no—
347#102—861no—
348C22⋊C8C22⋊D4311yescharacteristic
349C22⋊C8C22⋊D4311yescharacteristic
350C4×C8C22×D4311yescharacteristic
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—861no—
355C2×D4—1721no—
356C2×D4—1721no—
357C2×D4#1062188211yescharacteristic
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—1721no—
361C22×C4—1721no—
362C22×C4C2×C22⋊D4311yescharacteristic
363C22×C4C2×C22⋊D4311yescharacteristic
364D8—21no—
365D8—21no—
366D8—861no—
367D8—861no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8C2×C22⋊D4311yescharacteristic
373C2×C8C2×C22⋊D4311yescharacteristic
374C2×C8C2×C22⋊D4311yescharacteristic
375C2×C8C23×D4311yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—861no—
383C4⋊C4—861no—
384C4⋊C4—861no—
385C4⋊C4—1721no—
386C4⋊C4—1721no—
387C4⋊C4—1721no—
388C4⋊C4#1062188211yescharacteristic
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—1721no—
394C22⋊C4—1721no—
395C22⋊C4—1721no—
396C22⋊C4—1721no—
397C22⋊C4#1062188211yescharacteristic
398C22⋊C4#1062188211yescharacteristic
399C42—41no—
400C42—1721no—
401C42C2×C22⋊D4311yescharacteristic
402C16—432no—
403C16—861no—
404C16—861no—
405C16—861no—
406C23—41no—
407C23—1721no—
408C23C2×#1062188211yescharacteristic
409C23C2×#1062188211yescharacteristic
410D4—41no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—161no—
415D4—3442no—
416D4—1721no—
417D4—1721no—
418D4—6881no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4—1721no—
429C2×C4—1721no—
430C2×C4—1721no—
431C2×C4—6881no—
432C2×C4—6881no—
433C2×C4C2×#1062188211yescharacteristic
434C2×C4C2×#1062188211yescharacteristic
435C2×C4C2×#1062188211yescharacteristic
436C2×C4C2×#1062188211yescharacteristic
437C2×C4C22×C22⋊D4311yescharacteristic
438C8—21no—
439C8—21no—
440C8—21no—
441C8#41×D4311yescharacteristic
442C8#1306337211yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—3441no—
453C22—3441no—
454C22—3441no—
455C22C22×#1062188211yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—3441no—
464C4—3441no—
465C4—3441no—
466C4#1458354811yescharacteristic
467C4#1458371411yescharacteristic
468C2—41no—
469C2—41no—
470C2—161no—
471C2—6881no—
472C2#1914693811yescharacteristic
473C2#1914772911yescharacteristic
474C2#1914773411yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3339C2
socleC22×C43C22×D8
hypercenter#3339D43
hypocenterC43#33922
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #19146998C2semidirect
2. #19136871C2semidirect
3. #19136786C2semidirect
4. #19136783C2semidirect
5. #19136775C2semidirect
6. #19136773C2semidirect
7. #19136752C2semidirect
8. #19136749C2semidirect
9. #19136696C2semidirect
10. #19136696C2semidirect
11. C4×#13063266C2semidirect
12. #19136427C2semidirect
13. #19136384C2semidirect
14. #19136381C2semidirect
15. C43×#3339C2semidirect
232. #3339D43semidirect
296. C43#33922semidirect

Maximal subgroups

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

subgroupindex
#191469982
#191368712
#191367862
#191367832
#191367752
#191367732
#191367522
#191367492
#191366962
C4×#130632662
#191364272
#191363842
#191363812
C43×#33392
#3392243