Finite Group Databasebeta

← #11863568

Subgroups — #11863568

Order 1152.

2153 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3802C211yesmaximal, characteristic
2C3⋊D3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×#63940C212yesmaximal, complemented
4C3×#5046C212yesmaximal, complemented
5#10591652C212yesmaximal, complemented
6#10591172C212yesmaximal, complemented
7#10591152C211yesmaximal, characteristic, complemented
8#10590597C212yesmaximal, complemented
9#10590593C212yesmaximal, complemented
10D3×#450—32nomaximal
11C23×D32—21no—
12C2×Q8×C3⋊D3C2211yescharacteristic, complemented
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×D12C2212yes—
15C22×#625—21no—
16C2×#3802—21no—
17C2×#3802—21no—
18C2×#3802—28no—
19C2×#3802C2212yes—
20C2×#3802C2212yes—
21C32×C22⋊Q8C2211yescharacteristic, complemented
22#64155C2211yescharacteristic, complemented
23#64133C2211yescharacteristic, complemented
24#64106C2211yescharacteristic, complemented
25#64105—21no—
26C4⋊C4×C3⋊D3—21no—
27C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
28C22⋊C4×C3⋊D3—21no—
29#64087—21no—
30C2×C3×#215C2214yescomplemented
31#63940—28no—
32C2×#3716C2214yescomplemented
33C2×#3710C2212yescomplemented
34C3×#830C2212yescomplemented
35C3×#809C2214yescomplemented
36#63563C2214yescomplemented
37#63557C2212yescomplemented
38C22×D3×D4—32no—
39C2×D3×SD16—34no—
40D3×C22⋊Q8—32no—
41D3×C22⋊Q8—61no—
42C3×#450—32no—
43#5218—32no—
44#5169—34no—
45#5046D312yescomplemented
46#4776—34no—
47D3×#102—34no—
48#4731—32no—
49D3×C22⋊C8—32no—
50C23×C3⋊D3D411yescharacteristic
51C23×C3×D3—22no—
52C22×D32—28no—
53C22×D32—22no—
54C22×D32—22no—
55C22×D32—44no—
56C22×D32—44no—
57C2×C32×Q8C2311yescharacteristic, complemented
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3D411yescharacteristic
60Q8×C3⋊D3—24no—
61C2×C4×C3⋊D3—24no—
62C2×C4×C3⋊D3—21no—
63C2×C4×C3⋊D3—21no—
64C2×C4×C3⋊D3D411yescharacteristic
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634—21no—
69C2×#634C2311yescharacteristic, complemented
70C2×C3×D12—22no—
71C2×C3×D12—28no—
72C2×C3×D12C2314yes—
73C2×#625—28no—
74C2×#625—22no—
75C2×#625—22no—
76#3802—28no—
77#3802—28no—
78#3802—24no—
79#3802—28no—
80#3802D418yes—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2311yescharacteristic, complemented
83C32×C22⋊C4—21no—
84#3757—21no—
85#3752—21no—
86#3752—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic, complemented
89#3750—21no—
90#3750—21no—
91#3750—21no—
92C3×#215—28no—
93C2×C3×C3⋊C8C2314yescomplemented
94#3716—28no—
95#3710—24no—
96C2×#450—91noSylow
97C24×D3—62no—
98C22×C3×D4—32no—
99C22×#67—62no—
100C2×D3×Q8—32no—
101C2×D3×Q8—61no—
102C2×D3×D4—34no—
103C2×D3×D4—34no—
104C2×D3×D4—62no—
105C2×D3×D4—62no—
106C2×D3×D4—616no—
107C22×D12C2×D312yes—
108C22×C4×D3—32no—
109C22×C4×D3—61no—
110C2×C3×SD16—34no—
111C3×C22⋊Q8—21no—
112C3×C22⋊Q8C2×D312yescomplemented
113#946—32no—
114#946—61no—
115C2×#215C2×D314yescomplemented
116C2×#214—34no—
117#924—32no—
118#924—61no—
119D3×SD16—616no—
120C2×#204—34no—
121C2×D3×C8—34no—
122#897—32no—
123#897—61no—
124#896—62no—
125#896—62no—
126D3×C4⋊C4—32no—
127D3×C4⋊C4—61no—
128D3×C4⋊C4—62no—
129D3×C4⋊C4—62no—
130D3×C22⋊C4—62no—
131D3×C22⋊C4—62no—
132#878—62no—
133#878—62no—
134C3×#102—34no—
135C3×C22⋊C8—32no—
136#832—34no—
137#830C2×D312yescomplemented
138#821—34no—
139(C2×D3)⋊C8—34no—
140#809C2×D314yescomplemented
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3SD1614yescomplemented
145C22×C3⋊D3C2×D411yescharacteristic
146C22×C3⋊D3C2×D411yescharacteristic
147C22×C3×D3—28no—
148C22×C3×D3—24no—
149C22×C3×D3—44no—
150C22×C3×D3—44no—
151C2×D32—28no—
152C2×D32—28no—
153C2×D32—44no—
154C2×D32—432no—
155C2×D32—44no—
156C2×D32—44no—
157C2×D32—44no—
158C32×Q8—22no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—22no—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2411yescharacteristic
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3C2×D411yescharacteristic
168C2×C3⋊Dic3C2×D411yescharacteristic
169C4×C3⋊D3—22no—
170C4×C3⋊D3—22no—
171C4×C3⋊D3—22no—
172C4×C3⋊D3—42no—
173C4×C3⋊D3—42no—
174C4×C3⋊D3C2×D414yes—
175#634—22no—
176#634—42no—
177C3×D12—28no—
178C3×D12—24no—
179C3×D12C2×D418yes—
180#625—28no—
181#625—28no—
182C3×C3⋊C8—24no—
183C23×D4—91no—
184C22×SD16—92no—
185C2×C22⋊Q8—91no—
186#450—32no—
187#450—92no—
188#450—92no—
189#450—92no—
190C2×#102—92no—
191C2×C22⋊C8—91no—
192C24×C3—62no—
193C23×D3—22no—
194C23×D3—32no—
195C23×D3—61no—
196C23×D3—64no—
197C23×D3—64no—
198C23×D3—616no—
199C23×D3—128no—
200C23×D3—128no—
201C2×C3×Q8—21no—
202C2×C3×Q8C22×D312yescomplemented
203C2×C3×D4—34no—
204C2×C3×D4—68no—
205C2×C3×D4—62no—
206C22×C3×C4—21no—
207C22×C3×C4C22×D312yes—
208C2×#67—64no—
209C2×#67—64no—
210C2×#67—616no—
211C22×Dic3—32no—
212C22×Dic3—61no—
213D3×Q8—68no—
214D3×Q8—124no—
215D3×D4—316no—
216D3×D4—68no—
217D3×D4—68no—
218D3×D4—616no—
219D3×D4—616no—
220D3×D4—68no—
221C2×D12—22no—
222C2×D12—28no—
223C2×D12C22×D314yes—
224C2×C4×D3—32no—
225C2×C4×D3—32no—
226C2×C4×D3—32no—
227C2×C4×D3—32no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—68no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—124no—
238C2×Dic6—32no—
239C2×Dic6—61no—
240C2×Dic6—62no—
241C2×Dic6—62no—
242C3×SD16—68no—
243C2×C3×C8—34no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—22no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4C22×D312yescomplemented
248C3×C22⋊C4—22no—
249C3×C22⋊C4—22no—
250#217—62no—
251#217—62no—
252#215—28no—
253#214—68no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258C4⋊Dic3—32no—
259C4⋊Dic3—61no—
260C4⋊Dic3—62no—
261C4⋊Dic3—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268C2×C3⋊C8C22×D314yescomplemented
269#204—68no—
270D3×C8—68no—
271C22×C32—21no—
272C22×C32—21no—
273C22×C32C2×SD1612yescomplemented
274C22×C32C22×D411yescharacteristic
275C2×C3⋊D3—21no—
276C2×C3⋊D3—21no—
277C2×C3⋊D3—28no—
278C2×C3⋊D3#12012yes—
279C2×C3⋊D3C2×SD1612yes—
280C2×C3⋊D3C2×SD1612yescomplemented
281C2×C3⋊D3AGL(1,ℤ/8)12yes—
282C2×C3×D3—28no—
283C2×C3×D3—416no—
284C2×C3×D3—44no—
285C2×C3×D3—44no—
286D32—416no—
287D32—416no—
288C32×C4—21no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4C22×D412yes—
292C3⋊Dic3—21no—
293C3⋊Dic3—41no—
294C3⋊Dic3—41no—
295C3⋊Dic3#12012yes—
296C25—181no—
297C22×Q8—91no—
298C22×D4—32no—
299C22×D4—92no—
300C22×D4—92no—
301C22×D4—181no—
302C22×D4—181no—
303C22×D4—181no—
304C22×D4—188no—
305C23×C4—91no—
306C2×SD16—34no—
307C2×SD16—94no—
308C2×SD16—188no—
309C22×C8—92no—
310C22⋊Q8—91no—
311C22⋊Q8—91no—
312C22⋊Q8—91no—
313C22⋊Q8—181no—
314C22⋊Q8—181no—
315C22⋊Q8D3211yescharacteristic, complemented
316C2×C4⋊C4—91no—
317C2×C4⋊C4—181no—
318C2×C22⋊C4—181no—
319#102—34no—
320#102—94no—
321C22⋊C8—32no—
322C22⋊C8—92no—
323C23×C3—21no—
324C23×C3—68no—
325C23×C3—64no—
326C23×C3—124no—
327C23×C3—124no—
328C23×C3D3×D412yes—
329C22×D3—28no—
330C22×D3—24no—
331C22×D3—32no—
332C22×D3—38no—
333C22×D3—32no—
334C22×D3—44no—
335C22×D3—44no—
336C22×D3—61no—
337C22×D3—64no—
338C22×D3—61no—
339C22×D3—616no—
340C22×D3—616no—
341C22×D3—64no—
342C22×D3—64no—
343C22×D3—122no—
344C22×D3—122no—
345C22×D3—128no—
346C22×D3—128no—
347C22×D3—128no—
348C22×D3—1264no—
349C22×D3—128no—
350C3×Q8—24no—
351C3×Q8—42no—
352C3×D4—38no—
353C3×D4—68no—
354C3×D4—64no—
355C2×C3×C4—24no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—42no—
363C2×C3×C4D3×D412yes—
364C2×C3×C4C23×D312yes—
365#67—616no—
366#67—616no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—122no—
377D12—28no—
378D12—24no—
379D12D3×D418yes—
380C4×D3—38no—
381C4×D3—64no—
382C4×D3—64no—
383C4×D3—64no—
384C4×D3—64no—
385C4×D3—122no—
386C4×D3—122no—
387C4×D3—122no—
388C4×D3—124no—
389C4×D3—124no—
390C4×D3—124no—
391C4×D3—124no—
392Dic6—64no—
393Dic6—122no—
394Dic6—124no—
395Dic6—124no—
396C3×C8—64no—
397C3⋊C8—24no—
398C2×C32—22no—
399C2×C32C2×#12011yescharacteristic
400C2×C32C22×SD1611yescharacteristic
401C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
402C3⋊D3—22no—
403C3⋊D3#45014yescomplemented
404C3×D3—48no—
405C24—62no—
406C24—91no—
407C24—182no—
408C24—182no—
409C24—188no—
410C24—364no—
411C24—364no—
412C2×Q8—91no—
413C2×Q8—181no—
414C2×Q8—184no—
415C2×Q8C2×D3211yescharacteristic, complemented
416C2×D4—34no—
417C2×D4—68no—
418C2×D4—62no—
419C2×D4—98no—
420C2×D4—184no—
421C2×D4—182no—
422C2×D4—182no—
423C2×D4—188no—
424C2×D4—188no—
425C2×D4—188no—
426C2×D4—188no—
427C22×C4—91no—
428C22×C4—91no—
429C22×C4—91no—
430C22×C4—91no—
431C22×C4—91no—
432C22×C4—184no—
433C22×C4—181no—
434C22×C4—181no—
435C22×C4C2×D3211yescharacteristic
436SD16—68no—
437SD16—188no—
438C2×C8—34no—
439C2×C8—184no—
440C4⋊C4—21no—
441C4⋊C4—91no—
442C4⋊C4—181no—
443C4⋊C4—181no—
444C4⋊C4—181no—
445C4⋊C4—181no—
446C4⋊C4C2×D3211yescharacteristic, complemented
447C22⋊C4—21no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C22⋊C4—181no—
451C22×C3—22no—
452C22×C3—22no—
453C22×C3—21no—
454C22×C3—22no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—68no—
458C22×C3—1216no—
459C22×C3—124no—
460C22×C3—124no—
461C22×C3D3×SD1614yescomplemented
462C22×C3C2×D3×D412yes—
463C2×D3—28no—
464C2×D3—34no—
465C2×D3—34no—
466C2×D3—34no—
467C2×D3—34no—
468C2×D3—416no—
469C2×D3—44no—
470C2×D3—44no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—62no—
474C2×D3—62no—
475C2×D3—616no—
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—128no—
479C2×D3—121no—
480C2×D3—121no—
481C2×D3—1232no—
482C2×D3—1232no—
483C3×C4—22no—
484C3×C4—22no—
485C3×C4—41no—
486C3×C4—42no—
487C3×C4—42no—
488C3×C4—42no—
489C3×C4—42no—
490C3×C4C2×D3×D414yes—
491Dic3—34no—
492Dic3—62no—
493Dic3—62no—
494Dic3—121no—
495Dic3—122no—
496Dic3—122no—
497Dic3—122no—
498Dic3—122no—
499C32C2×#45011yescharacteristic, complemented, Sylow
500C23—68no—
501C23—64no—
502C23—91no—
503C23—91no—
504C23—94no—
505C23—124no—
506C23—124no—
507C23—182no—
508C23—182no—
509C23—188no—
510C23—188no—
511C23—364no—
512C23—364no—
513C23—364no—
514C23—3632no—
515C23—364no—
516C23#381111yescharacteristic
517Q8—22no—
518Q8—182no—
519Q8—362no—
520D4—38no—
521D4—68no—
522D4—64no—
523D4—188no—
524D4—188no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—91no—
529C2×C4—94no—
530C2×C4—91no—
531C2×C4—182no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—182no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—362no—
538C2×C4—362no—
539C2×C4#381111yescharacteristic
540C2×C4C22×D3211yescharacteristic
541C8—64no—
542C2×C3—24no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—42no—
547C2×C3—128no—
548C2×C3D3×#12012yes—
549C2×C3C2×D3×SD1612yes—
550C2×C3D3×AGL(1,ℤ/8)12yes—
551D3—38no—
552D3—48no—
553D3—64no—
554D3—64no—
555D3—122no—
556C22—21no—
557C22—21no—
558C22—68no—
559C22—92no—
560C22—92no—
561C22—92no—
562C22—92no—
563C22—1216no—
564C22—124no—
565C22—124no—
566C22—188no—
567C22—181no—
568C22—181no—
569C22—3616no—
570C22—3616no—
571C22#6394012yescomplemented
572C22C2×#381111yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—92no—
577C4—181no—
578C4—361no—
579C4—361no—
580C4D32×D412yes—
581C3—21no—
582C3D3×#45012yescomplemented
583C2—22no—
584C2—94no—
585C2—128no—
586C2—182no—
587C2#1059527811yescharacteristic
588C2C2×#6394011yescharacteristic
589C2#1059545811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×#3802C2
hypercenterC22⋊Q8D32
hypocenterC32C2×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×C22⋊Q8C2semidirect
3. C2×#63940C2semidirect
4. C3×#5046C2semidirect
5. #10591652C2semidirect
6. #10591172C2semidirect
7. #10591152C2semidirect
8. #10590597C2semidirect
9. #10590593C2semidirect
12. C2×Q8×C3⋊D3C22semidirect
21. C32×C22⋊Q8C22semidirect
22. #64155C22semidirect
23. #64133C22semidirect
24. #64106C22semidirect
27. C4⋊C4×C3⋊D3C22semidirect
30. C2×C3×#215C22semidirect
32. C2×#3716C22semidirect
33. C2×#3710C22semidirect
34. C3×#830C22semidirect
35. C3×#809C22semidirect
36. #63563C22semidirect
37. #63557C22semidirect
45. #5046D3semidirect
57. C2×C32×Q8C23semidirect
69. C2×#634C23semidirect
82. C32×C4⋊C4C23semidirect
88. C4⋊(C3⋊Dic3)C23semidirect
93. C2×C3×C3⋊C8C23semidirect
112. C3×C22⋊Q8C2×D3semidirect
115. C2×#215C2×D3semidirect
137. #830C2×D3semidirect
140. #809C2×D3semidirect
144. C22×C3⋊D3SD16semidirect
202. C2×C3×Q8C22×D3semidirect
247. C3×C4⋊C4C22×D3semidirect
268. C2×C3⋊C8C22×D3semidirect
273. C22×C32C2×SD16semidirect
280. C2×C3⋊D3C2×SD16semidirect
315. C22⋊Q8D32semidirect
403. C3⋊D3#450semidirect
415. C2×Q8C2×D32semidirect
446. C4⋊C4C2×D32semidirect
461. C22×C3D3×SD16semidirect
499. C32C2×#450semidirect
571. C22#63940semidirect
582. C3D3×#450semidirect

Maximal subgroups

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

subgroupindex
C22×#38022
C3⋊D3×C22⋊Q82
C2×#639402
C3×#50462
#105916522
#105911722
#105911522
#105905972
#105905932
D3×#4503