Finite Group Databasebeta

← #25251676

Subgroups — #25251676

Order 11008.

548 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145176C211yesmaximal, characteristic, complemented
2#135×Dic43C211yesmaximal, characteristic
3#19136804C211yesmaximal, characteristic, complemented
4#19136800C211yesmaximal, characteristic, complemented
5#19136745C211yesmaximal, characteristic, complemented
6#19136740C211yesmaximal, characteristic, complemented
7#19136643C211yesmaximal, characteristic, complemented
8#19136638C211yesmaximal, characteristic, complemented
9#19136535C211yesmaximal, characteristic
10#19136466C211yesmaximal, characteristic, complemented
11#19136463C211yesmaximal, characteristic, complemented
12#19136460C211yesmaximal, characteristic, complemented
13#19136456C211yesmaximal, characteristic, complemented
14#19136395C211yesmaximal, characteristic, complemented
15C43×#2189C211yesmaximal, characteristic
16#14583451—21no—
17#41×Dic43—21no—
18C2×#13063271C2211yescharacteristic
19C2×#13063269C2211yescharacteristic
20#14583303C2211yescharacteristic
21#14583277C2211yescharacteristic
22#14583248—21no—
23#14583140C2211yescharacteristic
24#14583138—21no—
25Q16×Dic43C2211yescharacteristic
26Q16×Dic43C2211yescharacteristic
27Q16×Dic43C2211yescharacteristic
28#14582993C2211yescharacteristic
29#14582991—21no—
30SD16×Dic43—21no—
31SD16×Dic43—21no—
32D8×Dic43C2211yescharacteristic
33D8×Dic43C2211yescharacteristic
34#14582937C2211yescharacteristic
35#14582895—21no—
36C2×C8×Dic43C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582726C2211yescharacteristic
39#14582725C2211yescharacteristic
40#14582724C2211yescharacteristic
41Dic43⋊C16C2211yescharacteristic
42Dic43⋊C16C2211yescharacteristic
43#14582704C2211yescharacteristic
44#14582704C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582703C2211yescharacteristic
47#14582703C2211yescharacteristic
48#14582700C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50#14582674C2211yescharacteristic
51#14582674C2211yescharacteristic
52C2×#135×C43C2211yescharacteristic
53C2×Q32×C43C2211yescharacteristic
54C2×SD32×C43C2211yescharacteristic
55C43×#467C2211yescharacteristic
56C43×#358C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×C22⋊C16C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621885—21no—
61C22×C43⋊C8D411yescharacteristic
62#13063324—21no—
63#13063323—21no—
64#13063315—41no—
65#13063304—21no—
66#13063302—41no—
67Q8×Dic43—21no—
68Q8×Dic43—21no—
69Q8×Dic43—21no—
70#13063290—21no—
71#13063290—41no—
72D4×Dic43—21no—
73D4×Dic43—21no—
74D4×Dic43—41no—
75D4×Dic43—41no—
76#13063284—21no—
77#13063284—41no—
78#13063281—41no—
79C2×C4×Dic43—41no—
80C2×C4×Dic43D411yescharacteristic
81#13063271—22no—
82#13063269—22no—
83C2×C43⋊C16C2311yescharacteristic
84C2×C43⋊C16C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063258—21no—
89#13063257—21no—
90#13063250—21no—
91#13063249—21no—
92#13063249—21no—
93#13063249—21no—
94#13063248—21no—
95#13063246—21no—
96#13063246—21no—
97C8×Dic43D411yescharacteristic
98C8×Dic43D411yescharacteristic
99C8×Dic43C2311yescharacteristic
100C8×Dic43C2311yescharacteristic
101C2×#41×C43—21no—
102#135×C43—22no—
103#135×C43—22no—
104C2×Q16×C43C2311yescharacteristic
105C2×Q16×C43C2311yescharacteristic
106C2×SD16×C43—21no—
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22⋊Q8×C43—21no—
110Q32×C43—22no—
111SD32×C43—22no—
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114#107×C43C2311yescharacteristic
115#103×C43—21no—
116#41×C43—24no—
117#41×C43—42no—
118C2×Q8×C43—21no—
119C2×Q8×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43C2×D411yescharacteristic
124C22×Dic43—41no—
125C22×Dic43—41no—
126C22×Dic43D811yescharacteristic
127C22×Dic43D811yescharacteristic
128C2×Dic86—21no—
129C2×Dic86—41no—
130Q16×C43—21no—
131Q16×C43—21no—
132Q16×C43—21no—
133Q16×C43#4112yes—
134SD16×C43—24no—
135D8×C43—21no—
136D8×C43#4112yes—
137C2×C8×C43—21no—
138C2×C8×C43—21no—
139C2×C8×C43C2×D411yescharacteristic
140C2×C8×C43C2411yescharacteristic
141C4⋊C4×C43—21no—
142C4⋊C4×C43—41no—
143C22⋊C4×C43—41no—
144C22⋊Dic43—41no—
145C22⋊Dic43—41no—
146C22⋊Dic43—41no—
147C22⋊Dic43—41no—
148#10621885—42no—
149C4⋊Dic43—21no—
150C4⋊Dic43—21no—
151C4⋊Dic43—21no—
152C4⋊Dic43—41no—
153C4⋊Dic43—41no—
154C4⋊Dic43—41no—
155Dic43⋊C4—41no—
156Dic43⋊C4—41no—
157Dic43⋊C4—41no—
158Dic43⋊C4—41no—
159Dic43⋊C4—41no—
160C4×Dic43—41no—
161C4×Dic43—41no—
162C4×Dic43—41no—
163C4×Dic43—41no—
164C4×Dic43—41no—
165C4×Dic43D811yescharacteristic
166C4×Dic43D811yescharacteristic
167C4×Dic43C2×D411yescharacteristic
168C4×Dic43C2×D411yescharacteristic
169C2×C43⋊C8—41no—
170C2×C43⋊C8C2×D411yescharacteristic
171C2×C43⋊C8C2×D411yescharacteristic
172Dic172—21no—
173Dic172—21no—
174C16×C43—21no—
175C16×C43—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—41no—
179C23×C43C2×D811yescharacteristic
180Q8×C43—22no—
181Q8×C43—41no—
182Q8×C43—41no—
183Q8×C43—41no—
184D4×C43—22no—
185D4×C43—44no—
186D4×C43—41no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—44no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43C2×D811yescharacteristic
194C2×C4×C43C22×D411yescharacteristic
195C2×Dic43—22no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—82no—
202C2×Dic43—82no—
203C2×Dic43C2×D811yescharacteristic
204C2×Dic43C2×D811yescharacteristic
205C2×Dic43C2×D811yescharacteristic
206C2×Dic43C2×D811yescharacteristic
207Dic86—41no—
208Dic86—41no—
209Dic86—82no—
210C8×C43—21no—
211C8×C43C2×#4111yescharacteristic
212C8×C43C2×#4111yescharacteristic
213C43⋊C8—21no—
214C43⋊C8—21no—
215#33676—431nomaximal, Sylow
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—21no—
219C22×C43—42no—
220C22×C43—81no—
221C22×C43—81no—
222C22×C43C22×D811yescharacteristic
223C4×C43—21no—
224C4×C43—42no—
225C4×C43—81no—
226C4×C43—81no—
227C4×C43#52511yescharacteristic
228C4×C43#57511yescharacteristic
229Dic43—21no—
230Dic43—21no—
231Dic43—21no—
232Dic43—81no—
233Dic43—81no—
234Dic43—81no—
235Dic43—81no—
236Dic43#51012yes—
237#3170—431no—
238C4×#135—431no—
239#2237—431no—
240#2237—431no—
241#2227—431no—
242#2226—431no—
243#2209—431no—
244#2208—431no—
245#2189—431no—
246#2189D4311yescharacteristic
247#2176—431no—
248#2176—431no—
249#2175—431no—
250#2175—431no—
251#2163—431no—
252C2×C43—41no—
253C2×C43—82no—
254C2×C43#310011yescharacteristic
255C2×C43C2×#51011yescharacteristic
256C2×C43#341411yescharacteristic
257C2×#135C2×D4311yescharacteristic
258#533—861no—
259C4×#41—861no—
260C2×Q32—431no—
261C2×Q32C2×D4311yescharacteristic
262C2×SD32—431no—
263C2×SD32C2×D4311yescharacteristic
264#500—431no—
265#494—431no—
266#487—861no—
267#467—431no—
268#467—861no—
269#467C2×D4311yescharacteristic
270C4×Q16—431no—
271C4×Q16—431no—
272C4×Q16—431no—
273C4×Q16—431no—
274C4×Q16—861no—
275C4×SD16—861no—
276C4×SD16—861no—
277C4×D8—431no—
278C4×D8—431no—
279#427—431no—
280#416—861no—
281C2×C4×C8—431no—
282#367—431no—
283#367—431no—
284#366—431no—
285#366—431no—
286C4⋊C16—431no—
287C4⋊C16—431no—
288#358—431no—
289#358—431no—
290#358—431no—
291#358—431no—
292#358—431no—
293#358C2×D4311yescharacteristic
294#357—431no—
295#357C2×D4311yescharacteristic
296C22⋊C16—431no—
297C22⋊C16C2×D4311yescharacteristic
298#346—431no—
299#346—431no—
300C43#3367611yescharacteristic, complemented, Sylow
301C2×#41—21no—
302#135—22no—
303#135—22no—
304C2×Q16—431no—
305C2×Q16—861no—
306C2×Q16C22×D4311yescharacteristic
307C2×Q16C22×D4311yescharacteristic
308C2×SD16—21no—
309C2×D8C22×D4311yescharacteristic
310C22×C8—431no—
311C22×C8C22×D4311yescharacteristic
312C4⋊Q8—861no—
313C4⋊Q8—861no—
314#125—1721no—
315C22⋊Q8—21no—
316C22⋊Q8—861no—
317C22⋊Q8—1721no—
318C4×Q8—861no—
319C4×Q8—861no—
320C4×Q8—861no—
321C4×Q8—861no—
322C4×Q8—1721no—
323C4×D4—861no—
324C4×D4—861no—
325C4×D4—1721no—
326C4×D4—1721no—
327#117—861no—
328#117—1721no—
329#117—1721no—
330C2×C42—431no—
331C2×C42—1721no—
332Q32—22no—
333Q32—862no—
334SD32—22no—
335SD32—862no—
336C2×C16—431no—
337C2×C16—431no—
338C2×C16C22×D4311yescharacteristic
339C2×C16C22×D4311yescharacteristic
340#107—431no—
341#107—431no—
342#107—431no—
343#107—861no—
344#107C22×D4311yescharacteristic
345#106—861no—
346#103—21no—
347#103—861no—
348#103—861no—
349#103—861no—
350#103—861no—
351#103—861no—
352#102—861no—
353#102—861no—
354C4×C8—431no—
355C4×C8—431no—
356C4×C8—431no—
357C4×C8—431no—
358#41—24no—
359#41—42no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—861no—
363C2×Q8—1721no—
364C2×D4—21no—
365C2×D4—41no—
366C22×C4—41no—
367C22×C4—431no—
368C22×C4—431no—
369C22×C4—1721no—
370C22×C4—1721no—
371C22×C4D4×D4311yescharacteristic
372Q16—21no—
373Q16—21no—
374Q16—21no—
375Q16—861no—
376Q16—861no—
377Q16—1722no—
378Q16#1062190012yes—
379SD16—24no—
380D8—21no—
381D8#1062190012yes—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—431no—
385C2×C8—431no—
386C2×C8—1721no—
387C2×C8D4×D4311yescharacteristic
388C2×C8C23×D4311yescharacteristic
389C4⋊C4—21no—
390C4⋊C4—41no—
391C4⋊C4—861no—
392C4⋊C4—861no—
393C4⋊C4—861no—
394C4⋊C4—1721no—
395C4⋊C4—1721no—
396C4⋊C4—1721no—
397C4⋊C4—1721no—
398C4⋊C4—1721no—
399C4⋊C4—1721no—
400C4⋊C4—1721no—
401C4⋊C4—1721no—
402C22⋊C4—41no—
403C22⋊C4—1721no—
404C22⋊C4—1721no—
405C22⋊C4—1721no—
406C22⋊C4—1721no—
407C42—431no—
408C42—431no—
409C42—431no—
410C42—431no—
411C42—1721no—
412C42—1721no—
413C42—1721no—
414C42—1721no—
415C42—1721no—
416C16—21no—
417C16—21no—
418C16—861no—
419C16—861no—
420C23—41no—
421C23D8×D4311yescharacteristic
422Q8—22no—
423Q8—41no—
424Q8—41no—
425Q8—41no—
426Q8—3442no—
427Q8—1721no—
428Q8—1721no—
429D4—22no—
430D4—44no—
431D4—41no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—44no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—431no—
439C2×C4—431no—
440C2×C4—431no—
441C2×C4—431no—
442C2×C4—862no—
443C2×C4—3442no—
444C2×C4—3442no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4—1721no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4D8×D4311yescharacteristic
451C2×C4C2×D4×D4311yescharacteristic
452C8—21no—
453C8—861no—
454C8—861no—
455C8C2×#1062190011yescharacteristic
456C8C2×#1062190011yescharacteristic
457C22—21no—
458C22—21no—
459C22—21no—
460C22—42no—
461C22—81no—
462C22—81no—
463C22C2×D8×D4311yescharacteristic
464C4—21no—
465C4—42no—
466C4—81no—
467C4—81no—
468C4—432no—
469C4—861no—
470C4—861no—
471C4—861no—
472C4—3441no—
473C4—3441no—
474C4—3441no—
475C4—3441no—
476C4#1458340511yescharacteristic
477C4#1458369511yescharacteristic
478C2—41no—
479C2—82no—
480C2#1914459011yescharacteristic
481C2#510×D4311yescharacteristic
482C2#1914772811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2189C2
socleC22×C43C22×D8
prime radicalC2×#135×C43C22
hypercenter#2189D43
hypocenterC43#33676
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2189

Complements

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

NH ≅ G/Ntype
1. #19145176C2semidirect
3. #19136804C2semidirect
4. #19136800C2semidirect
5. #19136745C2semidirect
6. #19136740C2semidirect
7. #19136643C2semidirect
8. #19136638C2semidirect
10. #19136466C2semidirect
11. #19136463C2semidirect
12. #19136460C2semidirect
13. #19136456C2semidirect
14. #19136395C2semidirect
300. C43#33676semidirect

Maximal subgroups

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

subgroupindex
#191451762
#135×Dic432
#191368042
#191368002
#191367452
#191367402
#191366432
#191366382
#191365352
#191364662
#191364632
#191364602
#191364562
#191363952
C43×#21892
#3367643