Finite Group Databasebeta

← C3×#83394 #11865023

Subgroups — C3×#83394 #11865023

Order 1152.

1691 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C32×#535C211yesmaximal, characteristic, complemented
3C3×#5822C212yesmaximal, complemented
4C2×C3×#833C211yesmaximal, characteristic, complemented
5C3×#5077C214yesmaximal, complemented
6C3×#5061C214yesmaximal, complemented
7C3×#5005C212yesmaximal, complemented
8C3×#3019—31nomaximal
9#83394C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic, complemented
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—22no—
13C3×#1004—22no—
14C3×#1004—24no—
15C3×#1004C2214yes—
16C2×C3×#237—22no—
17C2×C3×D3×D4—22no—
18C2×C3×#235C2212yes—
19C32×#127C2212yescomplemented
20C32×#124C2212yescomplemented
21C32×#121—22no—
22C32×#120—22no—
23C32×#117C2211yescharacteristic, complemented
24C3×#951—22no—
25C3×#950—24no—
26C3×#949—22no—
27C3×#942C2214yescomplemented
28C3×#932C2214yescomplemented
29C2×C3×#208C2212yescomplemented
30C3×#833C2214yescomplemented
31C3×#805C2218yescomplemented
32C2×C3×H(5,𝔽2)—31no—
33C2×#1004C2×C311yescharacteristic, complemented
34C3×#575—32no—
35C3×#535—21no—
36C3×#535D311yescharacteristic, complemented
37C3×#535C2×C311yescharacteristic, complemented
38#5822C2×C312yescomplemented
39C3×#455—34no—
40C3×#453—34no—
41C3×#421—32no—
42C2×C3×#100—31no—
43C2×#833C2×C311yescharacteristic, complemented
44#5077C2×C314yescomplemented
45#5061C2×C314yescomplemented
46#5005C2×C312yescomplemented
47C24×C32D412yes—
48C23×C3×D3—22no—
49C32×#41—22no—
50C32×#41—22no—
51C2×C32×Q8C2311yescharacteristic, complemented
52C2×C32×D4—21no—
53C2×C32×D4—24no—
54C2×C32×D4—22no—
55C2×C32×D4—22no—
56C2×C32×D4D412yes—
57C2×C32×D4C2312yes—
58C2×C32×D4C2311yescharacteristic, complemented
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C2×C3×#67—24no—
62C2×C3×#67—28no—
63C2×C3×#67—22no—
64C2×C3×#67—28no—
65C22×C3×Dic3—22no—
66C3×#237—28no—
67C3×#237—28no—
68C3×D3×D4—28no—
69C3×D3×D4—28no—
70C3×#235—22no—
71C3×#235—22no—
72C3×#235D414yescomplemented
73C3×#235C2314yes—
74C2×C3×D12D412yescomplemented
75C2×C3×C4×D3—22no—
76C2×C3×Dic6D412yescomplemented
77C32×C4⋊C4—21no—
78C32×C22⋊C4—21no—
79C32×C22⋊C4—24no—
80C32×C42C2312yescomplemented
81C3×#216—24no—
82C3×#215—24no—
83C3×#214—24no—
84C3×#213—24no—
85C3×#208—22no—
86C3×#208C2314yescomplemented
87C2×C3×C3⋊C8—22no—
88#3019—31noSylow
89C3×H(5,𝔽2)—34no—
90C3×H(5,𝔽2)—64no—
91C3×H(5,𝔽2)—62no—
92C2×C3×#41—21no—
93C2×C3×#41—32no—
94C2×C3×#41—62no—
95C2×C3×#41C2×D311yescharacteristic, complemented
96C2×C3×#41C22×C311yescharacteristic, complemented
97C22×C3×D4—21no—
98C22×C3×D4—62no—
99C22×C3×D4—62no—
100C22×C3×D4C2×D311yescharacteristic
101C22×C3×D4C22×C311yescharacteristic
102C22×#67—22no—
103#1004—22no—
104#1004—24no—
105#1004C22×C314yes—
106C2×#237—22no—
107C2×D3×D4—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×#127—22no—
116C3×#127C2×D312yescomplemented
117C3×#127C22×C312yescomplemented
118C3×#124—22no—
119C3×#124C2×D312yescomplemented
120C3×#124C22×C312yescomplemented
121C3×#121—24no—
122C3×#121—22no—
123C3×#121—22no—
124C3×#120—24no—
125C3×#120—22no—
126C3×#120—22no—
127C3×#117—21no—
128C3×#117C2×D311yescharacteristic, complemented
129C3×#117C22×C311yescharacteristic, complemented
130#951—22no—
131#950—24no—
132#949—22no—
133#942C22×C314yescomplemented
134#932C22×C314yescomplemented
135C2×#208C22×C312yescomplemented
136C3×#104—38no—
137C3×#100—34no—
138#833C22×C314yescomplemented
139#805C22×C318yescomplemented
140C23×C32—21no—
141C23×C32—22no—
142C23×C32—22no—
143C23×C32—82no—
144C23×C32C2×D414yes—
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—28no—
148C22×C3×D3—84no—
149C32×Q8—22no—
150C32×D4—24no—
151C32×D4—24no—
152C32×D4—22no—
153C32×D4—41no—
154C32×D4—41no—
155C32×D4—84no—
156C2×C32×C4—22no—
157C2×C32×C4—21no—
158C2×C32×C4—42no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2411yescharacteristic
163C3×#67—216no—
164C3×#67—24no—
165C3×#67—24no—
166C2×C3×Dic3—28no—
167C2×C3×Dic3—22no—
168C3×D12—22no—
169C3×D12C2×D414yes—
170C3×C4×D3—24no—
171C3×C4×D3—24no—
172C3×Dic6—22no—
173C3×Dic6C2×D414yes—
174C3×C3⋊C8—24no—
175C2×H(5,𝔽2)—31no—
176#575—32no—
177#535C3×D311yescharacteristic, complemented
178#455—34no—
179#453—34no—
180#421—32no—
181C2×#100—31no—
182C24×C3—22no—
183C24×C3—62no—
184C24×C3#6712yes—
185C24×C3C3×D412yes—
186C23×D3—22no—
187C3×#41—22no—
188C3×#41—22no—
189C3×#41—22no—
190C3×#41—22no—
191C3×#41—34no—
192C3×#41—34no—
193C3×#41—42no—
194C3×#41—42no—
195C3×#41—68no—
196C3×#41—68no—
197C3×#41—62no—
198C3×#41—62no—
199C2×C3×Q8—21no—
200C2×C3×Q8—32no—
201C2×C3×Q8C22×D311yescharacteristic, complemented
202C2×C3×Q8C23×C311yescharacteristic, complemented
203C2×C3×D4—22no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—28no—
207C2×C3×D4—24no—
208C2×C3×D4—24no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—22no—
214C2×C3×D4—22no—
215C2×C3×D4—21no—
216C2×C3×D4—32no—
217C2×C3×D4—42no—
218C2×C3×D4—42no—
219C2×C3×D4—68no—
220C2×C3×D4—68no—
221C2×C3×D4—64no—
222C2×C3×D4—68no—
223C2×C3×D4—62no—
224C2×C3×D4—68no—
225C2×C3×D4#6712yes—
226C2×C3×D4C3×D412yes—
227C2×C3×D4C22×D312yes—
228C2×C3×D4C22×D311yescharacteristic, complemented
229C2×C3×D4C23×C312yes—
230C2×C3×D4C23×C311yescharacteristic, complemented
231C22×C3×C4—22no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—62no—
236C22×C3×C4—62no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C23×C311yescharacteristic
239C2×#67—24no—
240C2×#67—28no—
241C2×#67—22no—
242C2×#67—28no—
243C22×Dic3—22no—
244#237—28no—
245#237—28no—
246D3×D4—28no—
247D3×D4—28no—
248#235—22no—
249#235—22no—
250#235C3×D414yescomplemented
251#235C23×C314yes—
252C2×D12C3×D412yescomplemented
253C2×C4×D3—22no—
254C2×Dic6C3×D412yescomplemented
255C3×Q16—64no—
256C3×SD16—64no—
257C3×SD16—64no—
258C3×D8—64no—
259C3×M16—34no—
260C3×M16—62no—
261C2×C3×C8—62no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—28no—
267C3×C22⋊C4—21no—
268C3×C22⋊C4—24no—
269C3×C22⋊C4—21no—
270C3×C22⋊C4—24no—
271C3×C42—22no—
272C3×C42C22×D312yescomplemented
273C3×C42C23×C312yescomplemented
274#216—24no—
275#215—24no—
276#214—24no—
277#213—24no—
278#208—22no—
279#208C23×C314yescomplemented
280C2×C3⋊C8—22no—
281C22×C32—24no—
282C22×C32—41no—
283C22×C32—44no—
284C22×C32—42no—
285C22×C32—41no—
286C22×C32—44no—
287C22×C32—82no—
288C22×C32#12011yescharacteristic
289C22×C32#12011yescharacteristic
290C22×C32C22×D411yescharacteristic
291C2×C3×D3—24no—
292C2×C3×D3—44no—
293C2×C3×D3—88no—
294C32×C4—42no—
295C32×C4—41no—
296C32×C4#12012yes—
297C32×C4C22×D412yes—
298C3×Dic3—24no—
299H(5,𝔽2)—34no—
300H(5,𝔽2)—64no—
301H(5,𝔽2)—62no—
302C2×#41—32no—
303C2×#41—62no—
304C2×#41C2×C3×D311yescharacteristic, complemented
305C22×D4—62no—
306C22×D4—62no—
307C22×D4C2×C3×D311yescharacteristic
308#137—34no—
309#137—62no—
310AGL(1,ℤ/8)—34no—
311AGL(1,ℤ/8)—62no—
312#135—64no—
313C2×M16—32no—
314#127C2×C3×D312yescomplemented
315#124C2×C3×D312yescomplemented
316#121—22no—
317#120—22no—
318#117C2×C3×D311yescharacteristic, complemented
319#104—38no—
320#100—34no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—24no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—68no—
333C23×C3—62no—
334C23×C3—82no—
335C23×C3—82no—
336C23×C3—84no—
337C23×C3—244no—
338C23×C3C2×#6714yes—
339C23×C3C2×#6711yescharacteristic
340C23×C3C2×C3×D414yes—
341C23×C3C2×C3×D411yescharacteristic
342C22×D3—22no—
343C22×D3—28no—
344C22×D3—84no—
345C3×Q8—22no—
346C3×Q8—22no—
347C3×Q8—34no—
348C3×Q8—42no—
349C3×Q8—62no—
350C3×D4—24no—
351C3×D4—24no—
352C3×D4—24no—
353C3×D4—22no—
354C3×D4—24no—
355C3×D4—22no—
356C3×D4—34no—
357C3×D4—44no—
358C3×D4—44no—
359C3×D4—42no—
360C3×D4—42no—
361C3×D4—42no—
362C3×D4—41no—
363C3×D4—41no—
364C3×D4—41no—
365C3×D4—41no—
366C3×D4—616no—
367C3×D4—64no—
368C3×D4—64no—
369C3×D4—62no—
370C3×D4—84no—
371C3×D4—84no—
372C3×D4—88no—
373C2×C3×C4—24no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—44no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—68no—
387C2×C3×C4—62no—
388C2×C3×C4—64no—
389C2×C3×C4—64no—
390C2×C3×C4D3×D412yes—
391C2×C3×C4D3×D412yes—
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C2×C3×D412yes—
394C2×C3×C4C2×C3×D412yes—
395C2×C3×C4C2×C3×D411yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397C2×C3×C4C24×C311yescharacteristic
398#67—216no—
399#67—24no—
400#67—24no—
401C2×Dic3—28no—
402C2×Dic3—22no—
403D12—22no—
404D12C2×C3×D414yes—
405C4×D3—24no—
406C4×D3—24no—
407Dic6—22no—
408Dic6C2×C3×D414yes—
409C3×C8—64no—
410C3⋊C8—24no—
411C2×C32—21no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32—44no—
415C2×C32—81no—
416C2×C32C2×#12011yescharacteristic
417C3×D3—44no—
418C24—62no—
419C24C3×#6712yes—
420#41—22no—
421#41—22no—
422#41—34no—
423#41—34no—
424#41—68no—
425#41—68no—
426#41—62no—
427#41—62no—
428C2×Q8—32no—
429C2×Q8C22×C3×D311yescharacteristic, complemented
430C2×D4—21no—
431C2×D4—24no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—32no—
435C2×D4—68no—
436C2×D4—68no—
437C2×D4—64no—
438C2×D4—68no—
439C2×D4—62no—
440C2×D4—68no—
441C2×D4C3×#6712yes—
442C2×D4C22×C3×D312yes—
443C2×D4C22×C3×D311yescharacteristic, complemented
444C22×C4—21no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4C22×C3×D311yescharacteristic
448Q16—64no—
449SD16—64no—
450SD16—64no—
451D8—64no—
452M16—34no—
453M16—62no—
454C2×C8—62no—
455C4⋊C4—21no—
456C22⋊C4—21no—
457C22⋊C4—24no—
458C42C22×C3×D312yescomplemented
459C22×C3—24no—
460C22×C3—24no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—44no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—44no—
468C22×C3—44no—
469C22×C3—44no—
470C22×C3—42no—
471C22×C3—44no—
472C22×C3—42no—
473C22×C3—44no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—48no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—64no—
480C22×C3—84no—
481C22×C3—82no—
482C22×C3—82no—
483C22×C3—84no—
484C22×C3—124no—
485C22×C3—248no—
486C22×C3#93711yescharacteristic
487C22×C3#93711yescharacteristic
488C22×C3C3×#12011yescharacteristic
489C22×C3C3×#12011yescharacteristic
490C22×C3C22×#6711yescharacteristic
491C22×C3C22×C3×D411yescharacteristic
492C2×D3—24no—
493C2×D3—44no—
494C2×D3—88no—
495C3×C4—22no—
496C3×C4—22no—
497C3×C4—42no—
498C3×C4—44no—
499C3×C4—42no—
500C3×C4—42no—
501C3×C4—41no—
502C3×C4—41no—
503C3×C4—64no—
504C3×C4#93712yes—
505C3×C4C3×#12012yes—
506C3×C4C2×D3×D412yes—
507C3×C4C22×C3×D412yes—
508Dic3—24no—
509C32#301911yescharacteristic, complemented, Sylow
510C23—22no—
511C23—22no—
512C23—21no—
513C23—68no—
514C23—62no—
515C23—82no—
516C23—244no—
517C23C2×C3×#6714yes—
518C23C2×C3×#6711yescharacteristic
519Q8—22no—
520Q8—34no—
521Q8—62no—
522D4—24no—
523D4—24no—
524D4—22no—
525D4—34no—
526D4—41no—
527D4—41no—
528D4—616no—
529D4—64no—
530D4—64no—
531D4—62no—
532D4—84no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—42no—
536C2×C4—68no—
537C2×C4—62no—
538C2×C4—64no—
539C2×C4—64no—
540C2×C4C3×D3×D412yes—
541C2×C4C3×D3×D412yes—
542C2×C4C2×C3×#6711yescharacteristic
543C2×C4C23×C3×D311yescharacteristic
544C8—64no—
545C2×C3—22no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—41no—
554C2×C3—41no—
555C2×C3—44no—
556C2×C3—44no—
557C2×C3—84no—
558C2×C3—82no—
559C2×C3—81no—
560C2×C3—81no—
561C2×C3—124no—
562C2×C3C2×#93711yescharacteristic
563C2×C3C2×C3×#12011yescharacteristic
564D3—44no—
565C22—24no—
566C22—41no—
567C22—44no—
568C22—44no—
569C22—42no—
570C22—41no—
571C22—64no—
572C22—82no—
573C22—124no—
574C22—248no—
575C22C3×#93711yescharacteristic
576C22C3×#93711yescharacteristic
577C22C22×C3×#6711yescharacteristic
578C4—42no—
579C4—41no—
580C4—64no—
581C4C3×#93712yes—
582C4C2×C3×D3×D412yes—
583C3—21no—
584C3#8339411yescharacteristic, direct product factor
585C3C3×#301911yescharacteristic, complemented
586C2—21no—
587C2—21no—
588C2—21no—
589C2—44no—
590C2—81no—
591C2—124no—
592C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC2×C3C2×#937
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#535C2
socleC2×C32C2×#120
hypercenterC3×#535D3
hypocenterC3C3×#3019
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#535

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C32×#535C2semidirect
3. C3×#5822C2semidirect
4. C2×C3×#833C2semidirect
5. C3×#5077C2semidirect
6. C3×#5061C2semidirect
7. C3×#5005C2semidirect
9. #83394C3direct (N × H)
10. C2×C32×#41C22semidirect
19. C32×#127C22semidirect
20. C32×#124C22semidirect
23. C32×#117C22semidirect
27. C3×#942C22semidirect
28. C3×#932C22semidirect
29. C2×C3×#208C22semidirect
30. C3×#833C22semidirect
31. C3×#805C22semidirect
33. C2×#1004C2×C3semidirect
36. C3×#535D3semidirect
37. C3×#535C2×C3semidirect
38. #5822C2×C3semidirect
43. C2×#833C2×C3semidirect
44. #5077C2×C3semidirect
45. #5061C2×C3semidirect
46. #5005C2×C3semidirect
51. C2×C32×Q8C23semidirect
58. C2×C32×D4C23semidirect
72. C3×#235D4semidirect
74. C2×C3×D12D4semidirect
76. C2×C3×Dic6D4semidirect
80. C32×C42C23semidirect
86. C3×#208C23semidirect
95. C2×C3×#41C2×D3semidirect
96. C2×C3×#41C22×C3semidirect
116. C3×#127C2×D3semidirect
117. C3×#127C22×C3semidirect
119. C3×#124C2×D3semidirect
120. C3×#124C22×C3semidirect
128. C3×#117C2×D3semidirect
129. C3×#117C22×C3semidirect
133. #942C22×C3semidirect
134. #932C22×C3semidirect
135. C2×#208C22×C3semidirect
138. #833C22×C3semidirect
139. #805C22×C3semidirect
177. #535C3×D3semidirect
201. C2×C3×Q8C22×D3semidirect
202. C2×C3×Q8C23×C3semidirect
228. C2×C3×D4C22×D3semidirect
230. C2×C3×D4C23×C3semidirect
250. #235C3×D4semidirect
252. C2×D12C3×D4semidirect
254. C2×Dic6C3×D4semidirect
272. C3×C42C22×D3semidirect
273. C3×C42C23×C3semidirect
279. #208C23×C3semidirect
304. C2×#41C2×C3×D3semidirect
314. #127C2×C3×D3semidirect
315. #124C2×C3×D3semidirect
318. #117C2×C3×D3semidirect
429. C2×Q8C22×C3×D3semidirect
443. C2×D4C22×C3×D3semidirect
458. C42C22×C3×D3semidirect
509. C32#3019semidirect
584. C3#83394direct (N × H)
585. C3C3×#3019semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C32×#5352
C3×#58222
C2×C3×#8332
C3×#50772
C3×#50612
C3×#50052
C3×#30193
#833943