Finite Group Databasebeta

← C3×#83415 #11865079

Subgroups — C3×#83415 #11865079

Order 1152.

1531 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C32×#536C211yesmaximal, characteristic, complemented
3C3×#5822C212yesmaximal, complemented
4C2×C3×#836C211yesmaximal, characteristic, complemented
5C3×#5095C214yesmaximal, complemented
6C3×#5062C214yesmaximal, complemented
7C3×#5005C212yesmaximal, complemented
8C3×#3020—31nomaximal
9#83415C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C32×Q8C2211yescharacteristic
12C3×#1007—22no—
13C3×#1007—24no—
14C3×#1007C2214yes—
15C2×C3×#239—22no—
16C2×C3×D3×Q8—22no—
17C2×C3×#235—22no—
18C2×C3×#235C2212yes—
19C32×C4⋊Q8C2212yescomplemented
20C32×#124C2212yescomplemented
21C32×#123—22no—
22C32×C22⋊Q8—22no—
23C32×#117C2211yescharacteristic
24C3×#951—22no—
25C3×#950—24no—
26C3×#949—22no—
27C3×#942C2214yescomplemented
28C3×#932C2214yescomplemented
29C2×C3×#208C2212yes—
30C3×#836C2214yescomplemented
31C3×#805C2218yescomplemented
32C2×C3×2−1+4—31no—
33C2×#1007C2×C311yescharacteristic, complemented
34C3×#575—32no—
35C3×#536—21no—
36C3×#536D311yescharacteristic, complemented
37C3×#536C2×C311yescharacteristic, complemented
38#5822C2×C312yescomplemented
39C3×#456—34no—
40C3×#454—34no—
41C3×#421—32no—
42C2×C3×#101—31no—
43C2×#836C2×C311yescharacteristic, complemented
44#5095C2×C314yescomplemented
45#5062C2×C314yescomplemented
46#5005C2×C312yescomplemented
47C32×#41—22no—
48C32×#41—22no—
49C2×C32×Q8—22no—
50C2×C32×Q8—22no—
51C2×C32×Q8D412yes—
52C2×C32×Q8C2311yescharacteristic
53C2×C32×Q8C2312yes—
54C2×C32×D4—21no—
55C2×C32×D4C2311yescharacteristic
56C22×C32×C4—21no—
57C22×C32×C4D412yes—
58C22×C32×C4C2311yescharacteristic
59C2×C3×#67—22no—
60C3×#239—28no—
61C3×#239—28no—
62C3×D3×Q8—28no—
63C3×D3×Q8—28no—
64C3×#235—28no—
65C3×#235—28no—
66C3×#235—22no—
67C3×#235—22no—
68C3×#235D414yes—
69C3×#235C2314yes—
70C2×C3×D12—22no—
71C2×C3×D12D412yes—
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6D412yes—
76C32×C4⋊C4—21no—
77C32×C4⋊C4—24no—
78C32×C22⋊C4—21no—
79C32×C22⋊C4—24no—
80C32×C42C2312yes—
81C3×#216—24no—
82C3×#215—24no—
83C3×#214—24no—
84C3×#213—24no—
85C3×#208—22no—
86C3×#208C2314yes—
87C2×C3×C3⋊C8—22no—
88#3020—31noSylow
89C3×2−1+4—34no—
90C3×2−1+4—64no—
91C3×2−1+4—62no—
92C2×C3×#41—21no—
93C2×C3×#41—32no—
94C2×C3×#41—62no—
95C2×C3×#41—62no—
96C2×C3×#41C2×D311yescharacteristic
97C2×C3×#41C22×C311yescharacteristic
98C22×C3×Q8—21no—
99C22×C3×Q8—62no—
100C22×C3×Q8C2×D311yescharacteristic
101C22×C3×Q8C22×C311yescharacteristic
102#1007—22no—
103#1007—24no—
104#1007C22×C314yes—
105C2×#239—22no—
106C2×D3×Q8—22no—
107C2×#235—22no—
108C2×#235C22×C312yes—
109C3×#137—34no—
110C3×#137—62no—
111C3×AGL(1,ℤ/8)—34no—
112C3×AGL(1,ℤ/8)—62no—
113C3×#135—64no—
114C2×C3×M16—32no—
115C3×C4⋊Q8—22no—
116C3×C4⋊Q8C2×D312yescomplemented
117C3×C4⋊Q8C22×C312yescomplemented
118C3×#124—22no—
119C3×#124C2×D312yescomplemented
120C3×#124C22×C312yescomplemented
121C3×#123—24no—
122C3×#123—22no—
123C3×#123—22no—
124C3×C22⋊Q8—24no—
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8—22no—
127C3×#117—21no—
128C3×#117C2×D311yescharacteristic
129C3×#117C22×C311yescharacteristic
130#951—22no—
131#950—24no—
132#949—22no—
133#942C22×C314yescomplemented
134#932C22×C314yescomplemented
135C2×#208C22×C312yes—
136C3×#104—38no—
137C3×#101—34no—
138#836C22×C314yescomplemented
139#805C22×C318yescomplemented
140C23×C32—21no—
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—22no—
143C32×Q8—24no—
144C32×Q8—24no—
145C32×Q8—22no—
146C32×D4—22no—
147C32×D4—41no—
148C32×D4—41no—
149C2×C32×C4—22no—
150C2×C32×C4—21no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—42no—
154C2×C32×C4C2×D412yes—
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2×D414yes—
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2411yescharacteristic
159C3×#67—24no—
160C3×#67—24no—
161C2×C3×Dic3—22no—
162C3×D12—28no—
163C3×D12—22no—
164C3×D12C2×D414yes—
165C3×C4×D3—216no—
166C3×C4×D3—24no—
167C3×C4×D3—24no—
168C3×Dic6—28no—
169C3×Dic6—22no—
170C3×Dic6C2×D414yes—
171C3×C3⋊C8—24no—
172C2×2−1+4—31no—
173#575—32no—
174#536C3×D311yescharacteristic, complemented
175#456—34no—
176#454—34no—
177#421—32no—
178C2×#101—31no—
179C3×#41—22no—
180C3×#41—22no—
181C3×#41—22no—
182C3×#41—22no—
183C3×#41—34no—
184C3×#41—34no—
185C3×#41—42no—
186C3×#41—42no—
187C3×#41—68no—
188C3×#41—68no—
189C3×#41—68no—
190C3×#41—62no—
191C3×#41—62no—
192C3×#41—68no—
193C2×C3×Q8—22no—
194C2×C3×Q8—22no—
195C2×C3×Q8—22no—
196C2×C3×Q8—22no—
197C2×C3×Q8—22no—
198C2×C3×Q8—22no—
199C2×C3×Q8—21no—
200C2×C3×Q8—32no—
201C2×C3×Q8—42no—
202C2×C3×Q8—42no—
203C2×C3×Q8—62no—
204C2×C3×Q8—68no—
205C2×C3×Q8—68no—
206C2×C3×Q8#6712yes—
207C2×C3×Q8C3×D412yes—
208C2×C3×Q8C22×D311yescharacteristic
209C2×C3×Q8C22×D312yes—
210C2×C3×Q8C23×C311yescharacteristic
211C2×C3×Q8C23×C312yes—
212C2×C3×D4—22no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—32no—
217C2×C3×D4—62no—
218C2×C3×D4—62no—
219C2×C3×D4C22×D311yescharacteristic
220C2×C3×D4C23×C311yescharacteristic
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—64no—
227C22×C3×C4—62no—
228C22×C3×C4#6712yes—
229C22×C3×C4C3×D412yes—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C23×C311yescharacteristic
232C2×#67—22no—
233#239—28no—
234#239—28no—
235D3×Q8—28no—
236D3×Q8—28no—
237#235—28no—
238#235—28no—
239#235—22no—
240#235—22no—
241#235C3×D414yes—
242#235C23×C314yes—
243C2×D12—22no—
244C2×D12C3×D412yes—
245C2×C4×D3—24no—
246C2×C4×D3—22no—
247C2×Dic6—22no—
248C2×Dic6C3×D412yes—
249C3×Q16—64no—
250C3×SD16—64no—
251C3×SD16—64no—
252C3×D8—64no—
253C3×M16—34no—
254C3×M16—62no—
255C2×C3×C8—62no—
256C3×C4⋊C4—22no—
257C3×C4⋊C4—28no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—24no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—28no—
264C3×C22⋊C4—21no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—24no—
267C3×C22⋊C4—24no—
268C3×C42—22no—
269C3×C42C22×D312yes—
270C3×C42C23×C312yes—
271#216—24no—
272#215—24no—
273#214—24no—
274#213—24no—
275#208—22no—
276#208C23×C314yes—
277C2×C3⋊C8—22no—
278C22×C32—41no—
279C22×C32—42no—
280C22×C32—41no—
281C22×C32#12011yescharacteristic
282C22×C32#12011yescharacteristic
283C22×C32C22×D411yescharacteristic
284C2×C3×D3—24no—
285C2×C3×D3—44no—
286C32×C4—24no—
287C32×C4—42no—
288C32×C4—41no—
289C32×C4#12012yes—
290C32×C4C22×D412yes—
291C3×Dic3—24no—
2922−1+4—34no—
2932−1+4—64no—
2942−1+4—62no—
295C2×#41—32no—
296C2×#41—62no—
297C2×#41—62no—
298C2×#41C2×C3×D311yescharacteristic
299C22×Q8—62no—
300C22×Q8C2×C3×D311yescharacteristic
301#137—34no—
302#137—62no—
303AGL(1,ℤ/8)—34no—
304AGL(1,ℤ/8)—62no—
305#135—64no—
306C2×M16—32no—
307C4⋊Q8C2×C3×D312yescomplemented
308#124C2×C3×D312yescomplemented
309#123—22no—
310C22⋊Q8—22no—
311#117C2×C3×D311yescharacteristic
312#104—38no—
313#101—34no—
314C23×C3—22no—
315C23×C3—21no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—62no—
319C23×C3C2×#6711yescharacteristic
320C23×C3C2×C3×D411yescharacteristic
321C22×D3—22no—
322C3×Q8—24no—
323C3×Q8—24no—
324C3×Q8—24no—
325C3×Q8—24no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—34no—
329C3×Q8—44no—
330C3×Q8—44no—
331C3×Q8—42no—
332C3×Q8—68no—
333C3×Q8—62no—
334C3×D4—22no—
335C3×D4—22no—
336C3×D4—34no—
337C3×D4—42no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—41no—
343C3×D4—41no—
344C3×D4—68no—
345C3×D4—64no—
346C3×D4—64no—
347C3×D4—62no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—24no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—24no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—44no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—616no—
369C2×C3×C4—62no—
370C2×C3×C4—64no—
371C2×C3×C4—64no—
372C2×C3×C4D3×D412yes—
373C2×C3×C4D3×D412yes—
374C2×C3×C4C2×#6714yes—
375C2×C3×C4C2×#6711yescharacteristic
376C2×C3×C4C2×C3×D412yes—
377C2×C3×C4C2×C3×D412yes—
378C2×C3×C4C2×C3×D414yes—
379C2×C3×C4C2×C3×D411yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381C2×C3×C4C24×C311yescharacteristic
382#67—24no—
383#67—24no—
384C2×Dic3—22no—
385D12—28no—
386D12—22no—
387D12C2×C3×D414yes—
388C4×D3—216no—
389C4×D3—24no—
390C4×D3—24no—
391Dic6—28no—
392Dic6—22no—
393Dic6C2×C3×D414yes—
394C3×C8—64no—
395C3⋊C8—24no—
396C2×C32—21no—
397C2×C32—21no—
398C2×C32—21no—
399C2×C32—81no—
400C2×C32C2×#12011yescharacteristic
401C3×D3—44no—
402#41—22no—
403#41—22no—
404#41—34no—
405#41—34no—
406#41—68no—
407#41—68no—
408#41—68no—
409#41—62no—
410#41—62no—
411#41—68no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—32no—
415C2×Q8—62no—
416C2×Q8—68no—
417C2×Q8—68no—
418C2×Q8C3×#6712yes—
419C2×Q8C22×C3×D311yescharacteristic
420C2×Q8C22×C3×D312yes—
421C2×D4—21no—
422C2×D4—32no—
423C2×D4—62no—
424C2×D4—62no—
425C2×D4C22×C3×D311yescharacteristic
426C22×C4—21no—
427C22×C4—64no—
428C22×C4—62no—
429C22×C4C3×#6712yes—
430C22×C4C22×C3×D311yescharacteristic
431Q16—64no—
432SD16—64no—
433SD16—64no—
434D8—64no—
435M16—34no—
436M16—62no—
437C2×C8—62no—
438C4⋊C4—21no—
439C4⋊C4—24no—
440C22⋊C4—21no—
441C22⋊C4—24no—
442C42C22×C3×D312yes—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—44no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—64no—
456C22×C3—124no—
457C22×C3#93711yescharacteristic
458C22×C3#93711yescharacteristic
459C22×C3C3×#12011yescharacteristic
460C22×C3C3×#12011yescharacteristic
461C22×C3C22×#6711yescharacteristic
462C22×C3C22×C3×D411yescharacteristic
463C2×D3—24no—
464C2×D3—44no—
465C3×C4—24no—
466C3×C4—24no—
467C3×C4—22no—
468C3×C4—22no—
469C3×C4—44no—
470C3×C4—42no—
471C3×C4—44no—
472C3×C4—42no—
473C3×C4—42no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—64no—
477C3×C4#93712yes—
478C3×C4C3×#12012yes—
479C3×C4C2×D3×D412yes—
480C3×C4C22×C3×D412yes—
481Dic3—24no—
482C32#302011yescharacteristic, complemented, Sylow
483C23—21no—
484C23—62no—
485C23C2×C3×#6711yescharacteristic
486Q8—24no—
487Q8—24no—
488Q8—22no—
489Q8—34no—
490Q8—68no—
491Q8—62no—
492D4—22no—
493D4—34no—
494D4—41no—
495D4—41no—
496D4—68no—
497D4—64no—
498D4—64no—
499D4—62no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—42no—
505C2×C4—616no—
506C2×C4—62no—
507C2×C4—64no—
508C2×C4—64no—
509C2×C4C3×D3×D412yes—
510C2×C4C3×D3×D412yes—
511C2×C4C2×C3×#6714yes—
512C2×C4C2×C3×#6711yescharacteristic
513C2×C4C23×C3×D311yescharacteristic
514C8—64no—
515C2×C3—22no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3—82no—
526C2×C3—81no—
527C2×C3—81no—
528C2×C3—124no—
529C2×C3C2×#93711yescharacteristic
530C2×C3C2×C3×#12011yescharacteristic
531D3—44no—
532C22—41no—
533C22—42no—
534C22—41no—
535C22—64no—
536C22—124no—
537C22C3×#93711yescharacteristic
538C22C3×#93711yescharacteristic
539C22C22×C3×#6711yescharacteristic
540C4—24no—
541C4—42no—
542C4—41no—
543C4—64no—
544C4C3×#93712yes—
545C4C2×C3×D3×D412yes—
546C3—21no—
547C3#8341511yescharacteristic, direct product factor
548C3C3×#302011yescharacteristic, complemented
549C2—21no—
550C2—21no—
551C2—21no—
552C2—81no—
553C2—124no—
554C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC2×C3C2×#937
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#536C2
socleC2×C32C2×#120
hypercenterC3×#536D3
hypocenterC3C3×#3020
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#536

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C32×#536C2semidirect
3. C3×#5822C2semidirect
4. C2×C3×#836C2semidirect
5. C3×#5095C2semidirect
6. C3×#5062C2semidirect
7. C3×#5005C2semidirect
9. #83415C3direct (N × H)
19. C32×C4⋊Q8C22semidirect
20. C32×#124C22semidirect
27. C3×#942C22semidirect
28. C3×#932C22semidirect
30. C3×#836C22semidirect
31. C3×#805C22semidirect
33. C2×#1007C2×C3semidirect
36. C3×#536D3semidirect
37. C3×#536C2×C3semidirect
38. #5822C2×C3semidirect
43. C2×#836C2×C3semidirect
44. #5095C2×C3semidirect
45. #5062C2×C3semidirect
46. #5005C2×C3semidirect
116. C3×C4⋊Q8C2×D3semidirect
117. C3×C4⋊Q8C22×C3semidirect
119. C3×#124C2×D3semidirect
120. C3×#124C22×C3semidirect
133. #942C22×C3semidirect
134. #932C22×C3semidirect
138. #836C22×C3semidirect
139. #805C22×C3semidirect
174. #536C3×D3semidirect
307. C4⋊Q8C2×C3×D3semidirect
308. #124C2×C3×D3semidirect
482. C32#3020semidirect
547. C3#83415direct (N × H)
548. C3C3×#3020semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C32×#5362
C3×#58222
C2×C3×#8362
C3×#50952
C3×#50622
C3×#50052
C3×#30203
#834153