Finite Group Databasebeta

← C3×#83826 #11866162

Subgroups — C3×#83826 #11866162

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×D8C211yesmaximal, characteristic, complemented
2C3×#5805C211yesmaximal, characteristic, complemented
3C3×#5798C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5C3×#5215C211yesmaximal, characteristic, complemented
6C3×#5153C214yesmaximal, complemented
7C3×#5150C214yesmaximal, complemented
8C3×#5113C211yesmaximal, characteristic, complemented
9C3×#5102C211yesmaximal, characteristic, complemented
10C3×#3041—31nomaximal
11#83826C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C22×C32×D4C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×C32×D8—24no—
16C2×C32×D8C2214yes—
17C22×C32×C8C2211yescharacteristic
18C3×#953—22no—
19C2×C3×#217—22no—
20C3×#940C2212yescomplemented
21C3×#938—22no—
22C3×#936C2212yescomplemented
23C3×D4×Dic3—22no—
24C3×D4×Dic3C2214yescomplemented
25C2×C3×#214C2212yescomplemented
26C3×#932—24no—
27C2×C3×#213C2212yescomplemented
28C3×#926C2211yescharacteristic
29C3×#926C2211yescharacteristic
30C2×C3×#208C2211yescharacteristic
31C3×#832C2214yescomplemented
32C3×#821C2212yescomplemented
33C3×#816C2212yescomplemented
34C3×Dic3⋊C8C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C22×C3×D8—21no—
37C22×C3×D8D311yescharacteristic, complemented
38C22×C3×D8C2×C311yescharacteristic, complemented
39C3×#535—31no—
40C3×#518—31no—
41#5805C2×C311yescharacteristic, complemented
42#5798C2×C311yescharacteristic, complemented
43C2×#932C2×C311yescharacteristic, complemented
44C3×#463—34no—
45C3×#459—34no—
46C3×#424—31no—
47C3×#418—31no—
48C3×#416—31no—
49#5215C2×C311yescharacteristic, complemented
50#5153C2×C314yescomplemented
51#5150C2×C314yescomplemented
52#5113C2×C311yescharacteristic, complemented
53#5102C2×C311yescharacteristic, complemented
54C24×C32—21no—
55C24×C32—21no—
56C2×C32×D4—21no—
57C2×C32×D4—22no—
58C2×C32×D4—21no—
59C2×C32×D4—22no—
60C2×C32×D4—22no—
61C2×C32×D4D414yescomplemented
62C2×C32×D4C2312yes—
63C2×C32×D4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—21no—
66C2×C3×#67—24no—
67C22×C3×Dic3—24no—
68C3×#235—22no—
69C3×#235—22no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6C2311yescharacteristic
73C32×D8—28no—
74C2×C32×C8—22no—
75C2×C32×C8C2312yes—
76C3×#217—21no—
77C3×#217—24no—
78C3×#217—24no—
79C3×#217D412yes—
80C3×#214—24no—
81C3×#213—24no—
82C3×C4⋊Dic3D412yes—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3—21no—
85C3×C4×Dic3C2312yes—
86C3×#208—22no—
87C2×C3×C3⋊C8C2312yes—
88#3041—31noSylow
89C2×C3×#41—31no—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4C2×D311yescharacteristic
93C22×C3×D4C2×D311yescharacteristic
94C22×C3×D4C22×C311yescharacteristic
95C22×C3×D4C22×C311yescharacteristic
96C2×#235C22×C311yescharacteristic
97C3×AGL(1,ℤ/8)—64no—
98C2×C3×SD16—32no—
99C2×C3×D8—28no—
100C2×C3×D8—24no—
101C2×C3×D8—24no—
102C2×C3×D8—24no—
103C2×C3×D8—32no—
104C2×C3×D8C2×D314yes—
105C2×C3×D8C22×C314yes—
106C2×C3×M16—31no—
107C22×C3×C8—21no—
108C22×C3×C8C2×D311yescharacteristic
109C22×C3×C8C22×C311yescharacteristic
110C3×#127—32no—
111C3×#124—32no—
112C3×#121—62no—
113C3×#120—62no—
114C3×C4×D4—34no—
115C3×C4×D4—62no—
116C3×#117—31no—
117C3×#117—31no—
118C2×C3×C22⋊C4—62no—
119#953—22no—
120C2×#217—22no—
121#940C22×C312yescomplemented
122#938—22no—
123#936C22×C312yescomplemented
124D4×Dic3—22no—
125D4×Dic3C22×C314yescomplemented
126C2×#214C22×C312yescomplemented
127#932—24no—
128C2×#213C22×C312yescomplemented
129#926C22×C311yescharacteristic
130#926C22×C311yescharacteristic
131C2×#208C22×C311yescharacteristic
132C3×C4⋊C8—34no—
133C3×#103—32no—
134C3×#102—34no—
135C3×#102—32no—
136#832C22×C314yescomplemented
137#821C22×C312yescomplemented
138#816C22×C312yescomplemented
139Dic3⋊C8C22×C314yescomplemented
140C23×C32—22no—
141C23×C32—24no—
142C23×C32—22no—
143C23×C32—42no—
144C23×C32—82no—
145C23×C32—82no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—21no—
148C32×D4—22no—
149C32×D4—24no—
150C32×D4—22no—
151C32×D4—22no—
152C32×D4—42no—
153C32×D4C2×D414yes—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D412yes—
156C2×C32×C4#4112yes—
157C2×C32×C4C2411yescharacteristic
158C3×#67—42no—
159C3×#67—84no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—84no—
163C2×C3×Dic3C2×D414yes—
164C3×D12—21no—
165C3×D12—21no—
166C3×C4×D3—42no—
167C3×Dic6—21no—
168C3×Dic6—21no—
169C32×C8—22no—
170C3×C3⋊C8—22no—
171C2×AGL(1,ℤ/8)—31no—
172C22×D8C3×D311yescharacteristic, complemented
173#535—31no—
174#518—31no—
175#463—34no—
176#459—34no—
177#424—31no—
178#418—31no—
179#416—31no—
180C24×C3—21no—
181C24×C3—21no—
182C24×C3—21no—
183C24×C3—21no—
184C24×C3—41no—
185C24×C3—41no—
186C3×#41—62no—
187C3×#41—62no—
188C2×C3×Q8—31no—
189C2×C3×D4—24no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—21no—
196C2×C3×D4—22no—
197C2×C3×D4—21no—
198C2×C3×D4—22no—
199C2×C3×D4—22no—
200C2×C3×D4—24no—
201C2×C3×D4—22no—
202C2×C3×D4—22no—
203C2×C3×D4—31no—
204C2×C3×D4—41no—
205C2×C3×D4—41no—
206C2×C3×D4—42no—
207C2×C3×D4—42no—
208C2×C3×D4—64no—
209C2×C3×D4—61no—
210C2×C3×D4#6714yescomplemented
211C2×C3×D4C3×D414yescomplemented
212C2×C3×D4C22×D312yes—
213C2×C3×D4C22×D312yes—
214C2×C3×D4C23×C312yes—
215C2×C3×D4C23×C312yes—
216C22×C3×C4—21no—
217C22×C3×C4—64no—
218C22×C3×C4—61no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C23×C311yescharacteristic
221C2×#67—21no—
222C2×#67—24no—
223C22×Dic3—24no—
224#235—22no—
225#235—22no—
226C2×D12C23×C311yescharacteristic
227C2×C4×D3—21no—
228C2×Dic6C23×C311yescharacteristic
229C3×SD16—64no—
230C3×D8—216no—
231C3×D8—28no—
232C3×D8—28no—
233C3×D8—64no—
234C3×M16—62no—
235C2×C3×C8—24no—
236C2×C3×C8—22no—
237C2×C3×C8—22no—
238C2×C3×C8—22no—
239C2×C3×C8—32no—
240C2×C3×C8C22×D312yes—
241C2×C3×C8C23×C312yes—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—32no—
244C3×C22⋊C4—32no—
245C3×C22⋊C4—64no—
246C3×C22⋊C4—64no—
247C3×C22⋊C4—61no—
248C3×C42—32no—
249C3×C42—61no—
250#217—21no—
251#217—24no—
252#217—24no—
253#217C3×D412yes—
254#214—24no—
255#213—24no—
256C4⋊Dic3C3×D412yes—
257C4⋊Dic3C23×C312yes—
258C4×Dic3—21no—
259C4×Dic3C23×C312yes—
260#208—22no—
261C2×C3⋊C8C23×C312yes—
262C22×C32—22no—
263C22×C32—24no—
264C22×C32—42no—
265C22×C32—44no—
266C22×C32—44no—
267C22×C32—84no—
268C22×C32—84no—
269C22×C32#12112yes—
270C22×C32C22×D411yescharacteristic
271C2×C3×D3—41no—
272C2×C3×D3—42no—
273C32×C4#12112yes—
274C32×C4C22×D411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3×Dic3—24no—
277C3×Dic3—41no—
278C3×Dic3—42no—
279C2×#41—31no—
280C22×D4C2×C3×D311yescharacteristic
281C22×D4C2×C3×D311yescharacteristic
282AGL(1,ℤ/8)—64no—
283C2×SD16—32no—
284C2×D8—24no—
285C2×D8—32no—
286C2×D8C2×C3×D314yes—
287C2×M16—31no—
288C22×C8C2×C3×D311yescharacteristic
289#127—32no—
290#124—32no—
291#121—62no—
292#120—62no—
293C4×D4—34no—
294C4×D4—62no—
295#117—31no—
296#117—31no—
297C2×C22⋊C4—62no—
298C4⋊C8—34no—
299#103—32no—
300#102—34no—
301#102—32no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—24no—
305C23×C3—24no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—42no—
310C23×C3—44no—
311C23×C3—42no—
312C23×C3—44no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—61no—
316C23×C3—82no—
317C23×C3—82no—
318C23×C3—82no—
319C23×C3—82no—
320C23×C3—84no—
321C23×C3—84no—
322C23×C3D3×D411yescharacteristic
323C23×C3C2×C3×D411yescharacteristic
324C22×D3—21no—
325C3×Q8—61no—
326C3×Q8—61no—
327C3×D4—24no—
328C3×D4—24no—
329C3×D4—24no—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—22no—
335C3×D4—22no—
336C3×D4—24no—
337C3×D4—44no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—44no—
341C3×D4—42no—
342C3×D4—42no—
343C3×D4—61no—
344C3×D4—61no—
345C3×D4—122no—
346C3×D4—244no—
347C3×D4C2×#6714yes—
348C3×D4C2×C3×D414yes—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—34no—
354C2×C3×C4—62no—
355C2×C3×C4—61no—
356C2×C3×C4—122no—
357C2×C3×C4—244no—
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4#23712yes—
360C2×C3×C4C2×#6712yes—
361C2×C3×C4C2×C3×D411yescharacteristic
362C2×C3×C4C2×C3×D412yes—
363C2×C3×C4C3×#4112yes—
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C24×C311yescharacteristic
366#67—42no—
367#67—84no—
368C2×Dic3—22no—
369C2×Dic3—21no—
370C2×Dic3—84no—
371C2×Dic3C2×C3×D414yes—
372D12—21no—
373D12—21no—
374C4×D3—42no—
375Dic6—21no—
376Dic6—21no—
377C3×C8—24no—
378C3×C8—22no—
379C3×C8—22no—
380C3×C8—62no—
381C3⋊C8—22no—
382C2×C32—22no—
383C2×C32—44no—
384C2×C32—82no—
385C2×C32C2×#12111yescharacteristic
386C2×C32#57612yes—
387C3×D3—81no—
388C24—21no—
389C24—21no—
390#41—62no—
391#41—62no—
392C2×Q8—31no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—31no—
399C2×D4—64no—
400C2×D4—61no—
401C2×D4C3×#6714yescomplemented
402C2×D4C22×C3×D312yes—
403C2×D4C22×C3×D312yes—
404C22×C4—64no—
405C22×C4—61no—
406C22×C4C22×C3×D311yescharacteristic
407SD16—64no—
408D8—28no—
409D8—64no—
410M16—62no—
411C2×C8—22no—
412C2×C8—32no—
413C2×C8C22×C3×D312yes—
414C4⋊C4—32no—
415C4⋊C4—32no—
416C22⋊C4—32no—
417C22⋊C4—64no—
418C22⋊C4—64no—
419C22⋊C4—61no—
420C42—32no—
421C42—61no—
422C22×C3—24no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—24no—
426C22×C3—24no—
427C22×C3—22no—
428C22×C3—21no—
429C22×C3—44no—
430C22×C3—44no—
431C22×C3—44no—
432C22×C3—44no—
433C22×C3—44no—
434C22×C3—44no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—84no—
438C22×C3—84no—
439C22×C3—84no—
440C22×C3—84no—
441C22×C3—88no—
442C22×C3—88no—
443C22×C3—84no—
444C22×C3—84no—
445C22×C3—122no—
446C22×C3—121no—
447C22×C3#93912yes—
448C22×C3C3×#12112yes—
449C22×C3C2×D3×D411yescharacteristic
450C22×C3C22×C3×D411yescharacteristic
451C2×D3—42no—
452C2×D3—41no—
453C3×C4—22no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—64no—
457C3×C4—122no—
458C3×C4—121no—
459C3×C4#93912yes—
460C3×C4C3×#12112yes—
461C3×C4C2×#23711yescharacteristic
462C3×C4C22×#6711yescharacteristic
463C3×C4C22×C3×D411yescharacteristic
464C3×C4C2×C3×#4111yescharacteristic
465Dic3—24no—
466Dic3—42no—
467Dic3—41no—
468C32#304111yescharacteristic, complemented, Sylow
469C23—22no—
470C23—24no—
471C23—22no—
472C23—42no—
473C23—61no—
474C23—82no—
475C23—82no—
476C23C3×D3×D411yescharacteristic
477Q8—61no—
478Q8—61no—
479D4—24no—
480D4—22no—
481D4—22no—
482D4—22no—
483D4—42no—
484D4—61no—
485D4—61no—
486D4—122no—
487D4—244no—
488D4C2×C3×#6714yes—
489C2×C4—34no—
490C2×C4—62no—
491C2×C4—61no—
492C2×C4—122no—
493C2×C4—244no—
494C2×C4C3×D3×D411yescharacteristic
495C2×C4C3×#23712yes—
496C2×C4C2×C3×#6712yes—
497C2×C4C23×C3×D311yescharacteristic
498C8—22no—
499C8—62no—
500C2×C3—24no—
501C2×C3—22no—
502C2×C3—22no—
503C2×C3—22no—
504C2×C3—21no—
505C2×C3—44no—
506C2×C3—44no—
507C2×C3—84no—
508C2×C3—84no—
509C2×C3—82no—
510C2×C3—82no—
511C2×C3—241no—
512C2×C3#575712yes—
513C2×C3C2×#93911yescharacteristic
514C2×C3C2×C3×#12111yescharacteristic
515C2×C3C3×#57612yes—
516D3—81no—
517C22—22no—
518C22—24no—
519C22—44no—
520C22—44no—
521C22—42no—
522C22—84no—
523C22—84no—
524C22—122no—
525C22—121no—
526C22C3×#93912yes—
527C22C2×C3×D3×D411yescharacteristic
528C4—64no—
529C4—122no—
530C4—121no—
531C4C3×#93912yes—
532C4C2×C3×#23711yescharacteristic
533C4C22×C3×#6711yescharacteristic
534C3—21no—
535C3#8382611yescharacteristic, direct product factor
536C3C3×#304111yescharacteristic, complemented
537C2—22no—
538C2—44no—
539C2—82no—
540C2—241no—
541C2C3×#575712yes—
542C2C2×C3×#93911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC22×C32×D8C2
socleC22×C32C22×D4
hypercenterC22×C3×D8D3
hypocenterC3C3×#3041
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×D8

Complements

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

NH ≅ G/Ntype
1. C22×C32×D8C2semidirect
2. C3×#5805C2semidirect
3. C3×#5798C2semidirect
4. C2×C3×#932C2semidirect
5. C3×#5215C2semidirect
6. C3×#5153C2semidirect
7. C3×#5150C2semidirect
8. C3×#5113C2semidirect
9. C3×#5102C2semidirect
11. #83826C3direct (N × H)
20. C3×#940C22semidirect
22. C3×#936C22semidirect
24. C3×D4×Dic3C22semidirect
25. C2×C3×#214C22semidirect
27. C2×C3×#213C22semidirect
31. C3×#832C22semidirect
32. C3×#821C22semidirect
33. C3×#816C22semidirect
34. C3×Dic3⋊C8C22semidirect
37. C22×C3×D8D3semidirect
38. C22×C3×D8C2×C3semidirect
41. #5805C2×C3semidirect
42. #5798C2×C3semidirect
43. C2×#932C2×C3semidirect
49. #5215C2×C3semidirect
50. #5153C2×C3semidirect
51. #5150C2×C3semidirect
52. #5113C2×C3semidirect
53. #5102C2×C3semidirect
61. C2×C32×D4D4semidirect
121. #940C22×C3semidirect
123. #936C22×C3semidirect
125. D4×Dic3C22×C3semidirect
126. C2×#214C22×C3semidirect
128. C2×#213C22×C3semidirect
136. #832C22×C3semidirect
137. #821C22×C3semidirect
138. #816C22×C3semidirect
139. Dic3⋊C8C22×C3semidirect
172. C22×D8C3×D3semidirect
210. C2×C3×D4#67semidirect
211. C2×C3×D4C3×D4semidirect
401. C2×D4C3×#67semidirect
468. C32#3041semidirect
535. C3#83826direct (N × H)
536. C3C3×#3041semidirect

Maximal subgroups

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

subgroupindex
C22×C32×D82
C3×#58052
C3×#57982
C2×C3×#9322
C3×#52152
C3×#51532
C3×#51502
C3×#51132
C3×#51022
C3×#30413
#838263