Finite Group Databasebeta

← C3×#84038 #11863924

Subgroups — C3×#84038 #11863924

Order 1152.

2669 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×D4C211yesmaximal, characteristic, complemented
2C2×C3×#932C212yesmaximal, complemented
3C3×#5791C211yesmaximal, characteristic, complemented
4C3×#5218C214yesmaximal, complemented
5C3×#5217C214yesmaximal, complemented
6C3×#5215C212yesmaximal, complemented
7C3×#5207C211yesmaximal, characteristic, complemented
8C3×#3003—31nomaximal
9#84038C311yesmaximal, characteristic, direct product factor
10C25×C32—21no—
11C22×C32×D4—28no—
12C22×C32×D4—22no—
13C22×C32×D4—21no—
14C22×C32×D4C2214yes—
15C22×C32×D4C2212yes—
16C23×C32×C4C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic, complemented
18C3×#953—21no—
19C2×C3×#214C2214yescomplemented
20C3×#932—28no—
21C2×C3×#213C2214yescomplemented
22C3×#930C2212yescomplemented
23C3×#929—21no—
24C3×C4×#67—22no—
25C3×#926C2211yescharacteristic, complemented
26C3×#924C2212yescomplemented
27C2×C3×#208C2212yescomplemented
28C3×#832C2218yescomplemented
29C3×#830C2214yescomplemented
30C23×C3×D4—21no—
31C23×C3×D4D311yescharacteristic, complemented
32C23×C3×D4C2×C311yescharacteristic, complemented
33C2×C3×AGL(1,ℤ/8)—32no—
34C3×#525—31no—
35C2×#932C2×C312yescomplemented
36#5791C2×C311yescharacteristic, complemented
37C3×#450—34no—
38C3×#447—34no—
39C3×#418—32no—
40C3×#407—31no—
41#5218C2×C314yescomplemented
42#5217C2×C314yescomplemented
43#5215C2×C312yescomplemented
44#5207C2×C311yescharacteristic, complemented
45C24×C32—28no—
46C24×C32—24no—
47C24×C32—22no—
48C24×C32—48no—
49C24×C32D411yescharacteristic
50C2×C32×D4—28no—
51C2×C32×D4—216no—
52C2×C32×D4—216no—
53C2×C32×D4—24no—
54C2×C32×D4—22no—
55C2×C32×D4—24no—
56C2×C32×D4D418yescomplemented
57C2×C32×D4C2314yes—
58C22×C32×C4—24no—
59C22×C32×C4D412yes—
60C22×C32×C4D411yescharacteristic
61C22×C32×C4C2312yes—
62C22×C32×C4C2311yescharacteristic
63C2×C3×#67—22no—
64C2×C3×#67—21no—
65C3×#235—24no—
66C2×C3×D12C2311yescharacteristic, complemented
67C2×C3×C4×D3—21no—
68C2×C3×Dic6C2311yescharacteristic, complemented
69C3×#217—22no—
70C3×#217—21no—
71C3×#214—28no—
72C3×#213—28no—
73C3×(C2×D3)⋊C4—22no—
74C3×C4⋊Dic3C2312yescomplemented
75C3×Dic3⋊C4—22no—
76C3×C4×Dic3—21no—
77C3×#208—24no—
78C2×C3×C3⋊C8C2314yescomplemented
79#3003—31noSylow
80C25×C3—22no—
81C25×C3—21no—
82C25×C3—21no—
83C2×C3×#41—31no—
84C22×C3×D4—216no—
85C22×C3×D4—24no—
86C22×C3×D4—22no—
87C22×C3×D4—28no—
88C22×C3×D4—28no—
89C22×C3×D4—22no—
90C22×C3×D4—21no—
91C22×C3×D4—22no—
92C22×C3×D4—21no—
93C22×C3×D4—24no—
94C22×C3×D4—22no—
95C22×C3×D4C2×D314yes—
96C22×C3×D4C2×D312yes—
97C22×C3×D4C22×C314yes—
98C22×C3×D4C22×C312yes—
99C23×C3×C4—21no—
100C23×C3×C4C2×D311yescharacteristic
101C23×C3×C4C22×C311yescharacteristic
102C2×#235C22×C311yescharacteristic, complemented
103C3×AGL(1,ℤ/8)—68no—
104C2×C3×SD16—34no—
105C2×C3×D8—34no—
106C2×C3×M16—32no—
107C3×#123—61no—
108C3×C22⋊Q8—32no—
109C3×#121—32no—
110C3×#120—61no—
111C3×C4×D4—62no—
112C3×#117—31no—
113#953—21no—
114C2×#214C22×C314yescomplemented
115#932—28no—
116C2×#213C22×C314yescomplemented
117#930C22×C312yescomplemented
118#929—21no—
119C4×#67—22no—
120#926C22×C311yescharacteristic, complemented
121#924C22×C312yescomplemented
122C2×#208C22×C312yescomplemented
123C3×#102—38no—
124C3×C22⋊C8—34no—
125#832C22×C318yescomplemented
126#830C22×C314yescomplemented
127C23×C32—22no—
128C23×C32—24no—
129C23×C32—216no—
130C23×C32—28no—
131C23×C32—24no—
132C23×C32—432no—
133C23×C32—48no—
134C23×C32—48no—
135C23×C32—48no—
136C23×C32C2×D411yescharacteristic
137C23×C32C2×D412yes—
138C22×C3×D3—21no—
139C32×D4—216no—
140C32×D4—28no—
141C32×D4—24no—
142C32×D4C2×D418yes—
143C2×C32×C4—22no—
144C2×C32×C4—24no—
145C2×C32×C4—24no—
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D414yes—
149C2×C32×C4C2411yescharacteristic
150C3×#67—42no—
151C3×#67—44no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—21no—
154C3×D12—22no—
155C3×C4×D3—42no—
156C3×Dic6—22no—
157C3×C3⋊C8—24no—
158C23×D4C3×D311yescharacteristic, complemented
159C2×AGL(1,ℤ/8)—32no—
160#525—31no—
161#450—34no—
162#447—34no—
163#418—32no—
164#407—31no—
165C24×C3—216no—
166C24×C3—28no—
167C24×C3—28no—
168C24×C3—28no—
169C24×C3—24no—
170C24×C3—24no—
171C24×C3—22no—
172C24×C3—24no—
173C24×C3—22no—
174C24×C3—21no—
175C24×C3—416no—
176C24×C3—48no—
177C24×C3—48no—
178C24×C3#6711yescharacteristic
179C24×C3C3×D411yescharacteristic
180C3×#41—64no—
181C2×C3×Q8—31no—
182C2×C3×D4—216no—
183C2×C3×D4—232no—
184C2×C3×D4—28no—
185C2×C3×D4—28no—
186C2×C3×D4—216no—
187C2×C3×D4—216no—
188C2×C3×D4—232no—
189C2×C3×D4—28no—
190C2×C3×D4—24no—
191C2×C3×D4—28no—
192C2×C3×D4—216no—
193C2×C3×D4—216no—
194C2×C3×D4—24no—
195C2×C3×D4—22no—
196C2×C3×D4—24no—
197C2×C3×D4—24no—
198C2×C3×D4—22no—
199C2×C3×D4—24no—
200C2×C3×D4—28no—
201C2×C3×D4—24no—
202C2×C3×D4—31no—
203C2×C3×D4—62no—
204C2×C3×D4—61no—
205C2×C3×D4#6718yescomplemented
206C2×C3×D4C3×D418yescomplemented
207C2×C3×D4C22×D314yes—
208C2×C3×D4C23×C314yes—
209C22×C3×C4—28no—
210C22×C3×C4—24no—
211C22×C3×C4—24no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—61no—
217C22×C3×C4#6712yes—
218C22×C3×C4#6711yescharacteristic
219C22×C3×C4C3×D412yes—
220C22×C3×C4C3×D411yescharacteristic
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C23×C312yes—
224C22×C3×C4C23×C311yescharacteristic
225C2×#67—22no—
226C2×#67—21no—
227#235—24no—
228C2×D12C23×C311yescharacteristic, complemented
229C2×C4×D3—21no—
230C2×Dic6C23×C311yescharacteristic, complemented
231C3×SD16—68no—
232C3×D8—68no—
233C3×M16—64no—
234C2×C3×C8—34no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—62no—
237C3×C22⋊C4—61no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—62no—
240C3×C42—61no—
241#217—22no—
242#217—21no—
243#214—28no—
244#213—28no—
245(C2×D3)⋊C4—22no—
246C4⋊Dic3C23×C312yescomplemented
247Dic3⋊C4—22no—
248C4×Dic3—21no—
249#208—24no—
250C2×C3⋊C8C23×C314yescomplemented
251C22×C32—28no—
252C22×C32—22no—
253C22×C32—22no—
254C22×C32—22no—
255C22×C32—28no—
256C22×C32—416no—
257C22×C32—432no—
258C22×C32—48no—
259C22×C32#12012yes—
260C22×C32AGL(1,ℤ/8)14yescomplemented
261C22×C32C22×D411yescharacteristic
262C2×C3×D3—41no—
263C2×C3×D3—42no—
264C32×C4—22no—
265C32×C4#12012yes—
266C32×C4C22×D412yes—
267C3×Dic3—41no—
268C3×Dic3—42no—
269C25—21no—
270C2×#41—31no—
271C22×D4—28no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4C2×C3×D314yes—
275C22×D4C2×C3×D312yes—
276C23×C4C2×C3×D311yescharacteristic
277AGL(1,ℤ/8)—68no—
278C2×SD16—34no—
279C2×D8—34no—
280C2×M16—32no—
281#123—61no—
282C22⋊Q8—32no—
283#121—32no—
284#120—61no—
285C4×D4—62no—
286#117—31no—
287#102—38no—
288C22⋊C8—34no—
289C23×C3—24no—
290C23×C3—28no—
291C23×C3—24no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—24no—
295C23×C3—232no—
296C23×C3—216no—
297C23×C3—216no—
298C23×C3—216no—
299C23×C3—28no—
300C23×C3—28no—
301C23×C3—28no—
302C23×C3—24no—
303C23×C3—24no—
304C23×C3—22no—
305C23×C3—21no—
306C23×C3—464no—
307C23×C3—432no—
308C23×C3—432no—
309C23×C3—416no—
310C23×C3—416no—
311C23×C3—48no—
312C23×C3—48no—
313C23×C3—48no—
314C23×C3—48no—
315C23×C3—416no—
316C23×C3—48no—
317C23×C3—48no—
318C23×C3—61no—
319C23×C3C2×#6712yes—
320C23×C3C2×#6711yescharacteristic
321C23×C3C2×C3×D411yescharacteristic
322C23×C3C2×C3×D412yes—
323C22×D3—21no—
324C3×Q8—62no—
325C3×D4—232no—
326C3×D4—216no—
327C3×D4—216no—
328C3×D4—216no—
329C3×D4—28no—
330C3×D4—28no—
331C3×D4—28no—
332C3×D4—24no—
333C3×D4—24no—
334C3×D4—28no—
335C3×D4—62no—
336C3×D4—124no—
337C3×D4—122no—
338C3×D4C2×#6718yes—
339C3×D4C2×C3×D418yes—
340C2×C3×C4—24no—
341C2×C3×C4—28no—
342C2×C3×C4—28no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—24no—
353C2×C3×C4—62no—
354C2×C3×C4—61no—
355C2×C3×C4—122no—
356C2×C3×C4C2×#6712yes—
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6714yes—
359C2×C3×C4C2×C3×D412yes—
360C2×C3×C4C2×C3×D411yescharacteristic
361C2×C3×C4C2×C3×D414yes—
362C2×C3×C4C23×D311yescharacteristic
363C2×C3×C4C24×C311yescharacteristic
364#67—42no—
365#67—44no—
366C2×Dic3—22no—
367C2×Dic3—21no—
368D12—22no—
369C4×D3—42no—
370Dic6—22no—
371C3×C8—64no—
372C3⋊C8—24no—
373C2×C32—22no—
374C2×C32—24no—
375C2×C32—48no—
376C2×C32C2×#12011yescharacteristic
377C2×C32C2×AGL(1,ℤ/8)12yes—
378C3×D3—81no—
379C24—28no—
380C24—24no—
381C24—22no—
382C24—48no—
383C24C3×#6711yescharacteristic
384#41—64no—
385C2×Q8—31no—
386C2×D4—28no—
387C2×D4—216no—
388C2×D4—216no—
389C2×D4—24no—
390C2×D4—22no—
391C2×D4—24no—
392C2×D4—31no—
393C2×D4—62no—
394C2×D4—61no—
395C2×D4C3×#6718yescomplemented
396C2×D4C22×C3×D314yes—
397C22×C4—24no—
398C22×C4—61no—
399C22×C4C3×#6712yes—
400C22×C4C3×#6711yescharacteristic
401C22×C4C22×C3×D312yes—
402C22×C4C22×C3×D311yescharacteristic
403SD16—68no—
404D8—68no—
405M16—64no—
406C2×C8—34no—
407C4⋊C4—32no—
408C4⋊C4—62no—
409C22⋊C4—61no—
410C22⋊C4—62no—
411C22⋊C4—62no—
412C42—61no—
413C22×C3—24no—
414C22×C3—216no—
415C22×C3—28no—
416C22×C3—28no—
417C22×C3—24no—
418C22×C3—24no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—216no—
426C22×C3—28no—
427C22×C3—28no—
428C22×C3—24no—
429C22×C3—22no—
430C22×C3—21no—
431C22×C3—464no—
432C22×C3—432no—
433C22×C3—432no—
434C22×C3—416no—
435C22×C3—416no—
436C22×C3—432no—
437C22×C3—416no—
438C22×C3—48no—
439C22×C3—48no—
440C22×C3—122no—
441C22×C3—121no—
442C22×C3#93214yescomplemented
443C22×C3#95312yes—
444C22×C3C3×#12012yes—
445C22×C3C3×AGL(1,ℤ/8)14yescomplemented
446C22×C3C22×#6711yescharacteristic
447C22×C3C22×C3×D411yescharacteristic
448C2×D3—42no—
449C2×D3—41no—
450C3×C4—24no—
451C3×C4—22no—
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—122no—
456C3×C4—121no—
457C3×C4#95312yes—
458C3×C4C3×#12012yes—
459C3×C4C22×#6712yes—
460C3×C4C22×C3×D412yes—
461Dic3—42no—
462Dic3—41no—
463C32#300311yescharacteristic, complemented, Sylow
464C23—24no—
465C23—22no—
466C23—216no—
467C23—28no—
468C23—24no—
469C23—432no—
470C23—48no—
471C23—48no—
472C23—48no—
473C23—61no—
474C23C2×C3×#6712yes—
475C23C2×C3×#6711yescharacteristic
476Q8—62no—
477D4—216no—
478D4—28no—
479D4—24no—
480D4—62no—
481D4—124no—
482D4—122no—
483D4C2×C3×#6718yes—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—62no—
488C2×C4—61no—
489C2×C4—122no—
490C2×C4C2×C3×#6712yes—
491C2×C4C2×C3×#6711yescharacteristic
492C2×C4C2×C3×#6714yes—
493C2×C4C23×C3×D311yescharacteristic
494C8—64no—
495C2×C3—28no—
496C2×C3—24no—
497C2×C3—24no—
498C2×C3—22no—
499C2×C3—22no—
500C2×C3—24no—
501C2×C3—22no—
502C2×C3—21no—
503C2×C3—416no—
504C2×C3—48no—
505C2×C3—48no—
506C2×C3—241no—
507C2×C3C2×#93212yes—
508C2×C3C2×#95311yescharacteristic
509C2×C3C2×C3×#12011yescharacteristic
510C2×C3C2×C3×AGL(1,ℤ/8)12yes—
511D3—81no—
512C22—28no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—28no—
517C22—432no—
518C22—416no—
519C22—48no—
520C22—122no—
521C22—121no—
522C22C3×#93214yescomplemented
523C22C3×#95312yes—
524C22C22×C3×#6711yescharacteristic
525C4—22no—
526C4—122no—
527C4—121no—
528C4C3×#95312yes—
529C4C22×C3×#6712yes—
530C3—21no—
531C3#8403811yescharacteristic, direct product factor
532C3C3×#300311yescharacteristic, complemented
533C2—24no—
534C2—22no—
535C2—48no—
536C2—241no—
537C2C2×C3×#93212yes—
538C2C2×C3×#95311yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC23×C32×D4C2
socleC22×C32C22×D4
hypercenterC23×C3×D4D3
hypocenterC3C3×#3003
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C23×C3×D4

Complements

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

NH ≅ G/Ntype
1. C23×C32×D4C2semidirect
2. C2×C3×#932C2semidirect
3. C3×#5791C2semidirect
4. C3×#5218C2semidirect
5. C3×#5217C2semidirect
6. C3×#5215C2semidirect
7. C3×#5207C2semidirect
9. #84038C3direct (N × H)
17. C2×C3×#235C22semidirect
19. C2×C3×#214C22semidirect
21. C2×C3×#213C22semidirect
22. C3×#930C22semidirect
25. C3×#926C22semidirect
26. C3×#924C22semidirect
27. C2×C3×#208C22semidirect
28. C3×#832C22semidirect
29. C3×#830C22semidirect
31. C23×C3×D4D3semidirect
32. C23×C3×D4C2×C3semidirect
35. C2×#932C2×C3semidirect
36. #5791C2×C3semidirect
41. #5218C2×C3semidirect
42. #5217C2×C3semidirect
43. #5215C2×C3semidirect
44. #5207C2×C3semidirect
56. C2×C32×D4D4semidirect
66. C2×C3×D12C23semidirect
68. C2×C3×Dic6C23semidirect
74. C3×C4⋊Dic3C23semidirect
78. C2×C3×C3⋊C8C23semidirect
102. C2×#235C22×C3semidirect
114. C2×#214C22×C3semidirect
116. C2×#213C22×C3semidirect
117. #930C22×C3semidirect
120. #926C22×C3semidirect
121. #924C22×C3semidirect
122. C2×#208C22×C3semidirect
125. #832C22×C3semidirect
126. #830C22×C3semidirect
158. C23×D4C3×D3semidirect
205. C2×C3×D4#67semidirect
206. C2×C3×D4C3×D4semidirect
228. C2×D12C23×C3semidirect
230. C2×Dic6C23×C3semidirect
246. C4⋊Dic3C23×C3semidirect
250. C2×C3⋊C8C23×C3semidirect
260. C22×C32AGL(1,ℤ/8)semidirect
395. C2×D4C3×#67semidirect
442. C22×C3#932semidirect
445. C22×C3C3×AGL(1,ℤ/8)semidirect
463. C32#3003semidirect
522. C22C3×#932semidirect
531. C3#84038direct (N × H)
532. C3C3×#3003semidirect

Maximal subgroups

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

subgroupindex
C23×C32×D42
C2×C3×#9322
C3×#57912
C3×#52182
C3×#52172
C3×#52152
C3×#52072
C3×#30033
#840383