Finite Group Databasebeta

← C3×#83983 #11864485

Subgroups — C3×#83983 #11864485

Order 1152.

1529 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C2×C32×#137C211yesmaximal, characteristic, complemented
3C3×#5816C211yesmaximal, characteristic, complemented
4C22×C3×#216C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6C3×#5186C214yesmaximal, complemented
7C3×#5173C214yesmaximal, complemented
8C3×#5129C211yesmaximal, characteristic, complemented
9C3×#5120C211yesmaximal, characteristic, complemented
10C3×#3011—31nomaximal
11#83983C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C32×Q8C2211yescharacteristic
14C3×#1010—24no—
15C3×#1010—24no—
16C2×C3×D3×Q8C2212yes—
17C2×C3×#237—22no—
18C2×C3×#237C2212yes—
19C2×C3×#235—21no—
20C2×C3×#235C2211yescharacteristic
21C22×C3×Dic6—21no—
22C22×C3×Dic6C2211yescharacteristic
23C32×#137—24no—
24C2×C32×Q16C2212yes—
25C2×C32×SD16C2212yes—
26C2×C32×M16C2211yescharacteristic
27C3×#947—21no—
28C3×#946C2214yes—
29C3×#944—21no—
30C2×C3×#216—24no—
31C2×C3×#216C2214yes—
32C3×#929—22no—
33C3×#926C2211yescharacteristic
34C22×C3×C3⋊C8C2211yescharacteristic
35C3×#835C2212yes—
36C3×#832C2212yes—
37C3×(C2×D3)⋊C8C2214yes—
38C3×#816C2214yes—
39C2×C3×2−1+4—31no—
40C2×#1010C2×C311yescharacteristic
41C2×C3×#137—21no—
42C2×C3×#137D311yescharacteristic, complemented
43C2×C3×#137C2×C311yescharacteristic, complemented
44C22×C3×Q16—31no—
45C3×#536—31no—
46#5816C2×C311yescharacteristic, complemented
47C22×#216C2×C311yescharacteristic, complemented
48C3×#452—34no—
49C3×#451—34no—
50C3×#419—31no—
51C3×#416—31no—
52C3×#408—31no—
53#5233C2×C311yescharacteristic, complemented
54#5186C2×C314yescomplemented
55#5173C2×C314yescomplemented
56#5129C2×C311yescharacteristic, complemented
57#5120C2×C311yescharacteristic, complemented
58C32×#41—22no—
59C32×#41D414yes—
60C2×C32×Q8—21no—
61C2×C32×Q8—22no—
62C2×C32×Q8—22no—
63C2×C32×Q8C2312yes—
64C2×C32×Q8C2311yescharacteristic
65C2×C32×D4—21no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C2×C3×#67—22no—
71C2×C3×#67D412yes—
72C22×C3×Dic3—21no—
73C22×C3×Dic3—22no—
74C3×D3×Q8—24no—
75C3×D3×Q8—24no—
76C3×#237—216no—
77C3×#237—24no—
78C3×#237—24no—
79C3×#235—28no—
80C3×#235—22no—
81C3×#235—22no—
82C2×C3×D12D411yescharacteristic
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3C2312yes—
85C2×C3×Dic6—28no—
86C2×C3×Dic6—21no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—22no—
89C2×C3×Dic6D411yescharacteristic
90C2×C3×Dic6D414yes—
91C2×C3×Dic6C2312yes—
92C32×Q16—24no—
93C32×SD16—24no—
94C32×M16—22no—
95C2×C32×C8C2312yes—
96C3×#217—21no—
97C3×#216—28no—
98C3×(C2×D3)⋊C4—24no—
99C3×C4⋊Dic3C2312yes—
100C3×Dic3⋊C4—24no—
101C3×C4×Dic3—21no—
102C2×C3×C3⋊C8—22no—
103C2×C3×C3⋊C8C2312yes—
104#3011—31noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—61no—
111C2×C3×#41—62no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C22×C311yescharacteristic
114C22×C3×Q8—21no—
115C22×C3×Q8—32no—
116C22×C3×Q8—31no—
117C22×C3×Q8—61no—
118C22×C3×Q8C2×D311yescharacteristic
119C22×C3×Q8C22×C311yescharacteristic
120#1010—24no—
121#1010—24no—
122C2×D3×Q8C22×C312yes—
123C2×#237—22no—
124C2×#237C22×C312yes—
125C2×#235—21no—
126C2×#235C22×C311yescharacteristic
127C22×Dic6—21no—
128C22×Dic6C22×C311yescharacteristic
129C3×#137—28no—
130C3×#137—24no—
131C3×#137—24no—
132C2×C3×Q16—22no—
133C2×C3×Q16—34no—
134C2×C3×Q16—64no—
135C2×C3×Q16C2×D312yes—
136C2×C3×Q16C22×C312yes—
137C2×C3×SD16—22no—
138C2×C3×SD16C2×D312yes—
139C2×C3×SD16C22×C312yes—
140C2×C3×M16—21no—
141C2×C3×M16C2×D311yescharacteristic
142C2×C3×M16C22×C311yescharacteristic
143C22×C3×C8—31no—
144C3×C4⋊Q8—61no—
145C3×#124—61no—
146C3×#123—62no—
147C3×C22⋊Q8—34no—
148C3×#117—31no—
149#947—21no—
150#946C22×C314yes—
151#944—21no—
152C2×#216—24no—
153C2×#216C22×C314yes—
154#929—22no—
155#926C22×C311yescharacteristic
156C22×C3⋊C8C22×C311yescharacteristic
157C3×#103—32no—
158C3×#103—34no—
159C3×#102—32no—
160C3×C22⋊C8—34no—
161#835C22×C312yes—
162#832C22×C312yes—
163(C2×D3)⋊C8C22×C314yes—
164#816C22×C314yes—
165C23×C32—21no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3C2×D412yes—
168C32×Q8—22no—
169C32×Q8—21no—
170C32×Q8—22no—
171C32×Q8—42no—
172C32×Q8C2×D412yes—
173C32×D4—24no—
174C32×D4—21no—
175C32×D4C2×D412yes—
176C2×C32×C4—21no—
177C2×C32×C4—24no—
178C2×C32×C4—22no—
179C2×C32×C4—42no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2411yescharacteristic
184C3×#67—28no—
185C3×#67—24no—
186C2×C3×Dic3—28no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D412yes—
191C3×D12—22no—
192C3×C4×D3—28no—
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×Dic6—28no—
196C3×Dic6—22no—
197C3×Dic6—24no—
198C3×Dic6—22no—
199C3×Dic6C2×D414yes—
200C32×C8—22no—
201C3×C3⋊C8—22no—
202C2×2−1+4—31no—
203C2×#137C3×D311yescharacteristic, complemented
204C22×Q16—31no—
205#536—31no—
206#452—34no—
207#451—34no—
208#419—31no—
209#416—31no—
210#408—31no—
211C3×#41—22no—
212C3×#41—22no—
213C3×#41—24no—
214C3×#41—42no—
215C3×#41—68no—
216C3×#41—64no—
217C3×#41—616no—
218C3×#41—64no—
219C3×#41—62no—
220C3×#41—62no—
221C3×#41#6714yes—
222C3×#41C3×D414yes—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—24no—
226C2×C3×Q8—22no—
227C2×C3×Q8—22no—
228C2×C3×Q8—22no—
229C2×C3×Q8—22no—
230C2×C3×Q8—22no—
231C2×C3×Q8—21no—
232C2×C3×Q8—31no—
233C2×C3×Q8—34no—
234C2×C3×Q8—32no—
235C2×C3×Q8—41no—
236C2×C3×Q8—42no—
237C2×C3×Q8—62no—
238C2×C3×Q8—68no—
239C2×C3×Q8—64no—
240C2×C3×Q8—64no—
241C2×C3×Q8—61no—
242C2×C3×Q8—62no—
243C2×C3×Q8C22×D312yes—
244C2×C3×Q8C22×D311yescharacteristic
245C2×C3×Q8C23×C312yes—
246C2×C3×Q8C23×C311yescharacteristic
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—32no—
251C2×C3×D4—31no—
252C2×C3×D4—41no—
253C2×C3×D4—62no—
254C2×C3×D4C22×D311yescharacteristic
255C2×C3×D4C23×C311yescharacteristic
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—32no—
262C22×C3×C4—41no—
263C22×C3×C4—41no—
264C22×C3×C4—62no—
265C22×C3×C4—62no—
266C22×C3×C4—61no—
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C23×C311yescharacteristic
269C2×#67—22no—
270C2×#67C3×D412yes—
271C22×Dic3—21no—
272C22×Dic3—22no—
273D3×Q8—24no—
274D3×Q8—24no—
275#237—216no—
276#237—24no—
277#237—24no—
278#235—28no—
279#235—22no—
280#235—22no—
281C2×D12C3×D411yescharacteristic
282C2×C4×D3—22no—
283C2×C4×D3C23×C312yes—
284C2×Dic6—28no—
285C2×Dic6—21no—
286C2×Dic6—22no—
287C2×Dic6—22no—
288C2×Dic6C3×D411yescharacteristic
289C2×Dic6C3×D414yes—
290C2×Dic6C23×C312yes—
291C3×Q16—28no—
292C3×Q16—24no—
293C3×Q16—24no—
294C3×Q16—68no—
295C3×SD16—28no—
296C3×SD16—24no—
297C3×SD16—24no—
298C3×M16—24no—
299C3×M16—22no—
300C3×M16—22no—
301C2×C3×C8—22no—
302C2×C3×C8—32no—
303C2×C3×C8—62no—
304C2×C3×C8C22×D312yes—
305C2×C3×C8C23×C312yes—
306C3×C4⋊C4—32no—
307C3×C4⋊C4—64no—
308C3×C22⋊C4—64no—
309C3×C22⋊C4—61no—
310C3×C42—61no—
311#217—21no—
312#216—28no—
313(C2×D3)⋊C4—24no—
314C4⋊Dic3C23×C312yes—
315Dic3⋊C4—24no—
316C4×Dic3—21no—
317C2×C3⋊C8—22no—
318C2×C3⋊C8C23×C312yes—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—42no—
322C22×C32#12012yes—
323C22×C32C22×D411yescharacteristic
324C2×C3×D3—22no—
325C2×C3×D3—24no—
326C32×C4—22no—
327C32×C4—42no—
328C32×C4#12012yes—
329C32×C4C22×D411yescharacteristic
330C32×C4C22×D411yescharacteristic
331C3×Dic3—22no—
332C3×Dic3—24no—
333C3×Dic3—42no—
3342−1+4—64no—
3352−1+4—64no—
336C2×#41—31no—
337C2×#41—32no—
338C2×#41—61no—
339C2×#41—62no—
340C2×#41C2×C3×D311yescharacteristic
341C22×Q8—32no—
342C22×Q8—31no—
343C22×Q8—61no—
344C22×Q8C2×C3×D311yescharacteristic
345#137—24no—
346C2×Q16—34no—
347C2×Q16—64no—
348C2×Q16C2×C3×D312yes—
349C2×SD16C2×C3×D312yes—
350C2×M16C2×C3×D311yescharacteristic
351C22×C8—31no—
352C4⋊Q8—61no—
353#124—61no—
354#123—62no—
355C22⋊Q8—34no—
356#117—31no—
357#103—32no—
358#103—34no—
359#102—32no—
360C22⋊C8—34no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—32no—
365C23×C3—41no—
366C23×C3D3×D411yescharacteristic
367C23×C3C2×C3×D411yescharacteristic
368C22×D3C2×C3×D412yes—
369C3×Q8—21no—
370C3×Q8—21no—
371C3×Q8—24no—
372C3×Q8—22no—
373C3×Q8—22no—
374C3×Q8—22no—
375C3×Q8—22no—
376C3×Q8—22no—
377C3×Q8—34no—
378C3×Q8—42no—
379C3×Q8—41no—
380C3×Q8—44no—
381C3×Q8—42no—
382C3×Q8—42no—
383C3×Q8—68no—
384C3×Q8—62no—
385C3×Q8—64no—
386C3×Q8—62no—
387C3×Q8C2×#6712yes—
388C3×Q8C2×C3×D412yes—
389C3×D4—24no—
390C3×D4—24no—
391C3×D4—21no—
392C3×D4—21no—
393C3×D4—22no—
394C3×D4—41no—
395C3×D4—44no—
396C3×D4—68no—
397C3×D4—64no—
398C3×D4—62no—
399C3×D4C2×#6712yes—
400C3×D4C2×C3×D412yes—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—32no—
412C2×C3×C4—44no—
413C2×C3×C4—41no—
414C2×C3×C4—42no—
415C2×C3×C4—44no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—68no—
419C2×C3×C4—68no—
420C2×C3×C4—64no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4D3×D412yes—
427C2×C3×C4C2×#6712yes—
428C2×C3×C4C2×C3×D411yescharacteristic
429C2×C3×C4C2×C3×D412yes—
430C2×C3×C4C2×C3×D412yes—
431C2×C3×C4C23×D311yescharacteristic
432C2×C3×C4C24×C311yescharacteristic
433#67—28no—
434#67—24no—
435C2×Dic3—28no—
436C2×Dic3—24no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3C2×C3×D412yes—
440D12—22no—
441C4×D3—28no—
442C4×D3—22no—
443C4×D3—22no—
444Dic6—28no—
445Dic6—22no—
446Dic6—24no—
447Dic6—22no—
448Dic6C2×C3×D414yes—
449C3×C8—24no—
450C3×C8—22no—
451C3×C8—22no—
452C3×C8—62no—
453C3⋊C8—22no—
454C2×C32—22no—
455C2×C32—42no—
456C2×C32C2×#12011yescharacteristic
457C2×C32#57812yes—
458C3×D3—42no—
459#41—22no—
460#41—68no—
461#41—64no—
462#41—616no—
463#41—64no—
464#41—62no—
465#41—62no—
466#41C3×#6714yes—
467C2×Q8—21no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—31no—
471C2×Q8—32no—
472C2×Q8—34no—
473C2×Q8—62no—
474C2×Q8—68no—
475C2×Q8—64no—
476C2×Q8—64no—
477C2×Q8—61no—
478C2×Q8—62no—
479C2×Q8C22×C3×D312yes—
480C2×Q8C22×C3×D311yescharacteristic
481C2×D4—21no—
482C2×D4—32no—
483C2×D4—31no—
484C2×D4—62no—
485C2×D4C22×C3×D311yescharacteristic
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—32no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—61no—
492C22×C4C22×C3×D311yescharacteristic
493Q16—24no—
494Q16—68no—
495SD16—24no—
496M16—22no—
497C2×C8—32no—
498C2×C8—62no—
499C2×C8C22×C3×D312yes—
500C4⋊C4—32no—
501C4⋊C4—64no—
502C22⋊C4—64no—
503C22⋊C4—61no—
504C42—61no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—21no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—64no—
516C22×C3—62no—
517C22×C3—82no—
518C22×C3#93712yes—
519C22×C3C3×#12012yes—
520C22×C3C2×D3×D411yescharacteristic
521C22×C3C22×C3×D411yescharacteristic
522C2×D3—24no—
523C2×D3—22no—
524C3×C4—22no—
525C3×C4—22no—
526C3×C4—22no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—42no—
530C3×C4—44no—
531C3×C4—42no—
532C3×C4—42no—
533C3×C4—62no—
534C3×C4—64no—
535C3×C4—122no—
536C3×C4#93712yes—
537C3×C4C3×#12012yes—
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C22×#6711yescharacteristic
540C3×C4C22×C3×D411yescharacteristic
541C3×C4C22×C3×D411yescharacteristic
542Dic3—22no—
543Dic3—24no—
544Dic3—42no—
545C32#301111yescharacteristic, complemented, Sylow
546C23—21no—
547C23—32no—
548C23C3×D3×D411yescharacteristic
549Q8—21no—
550Q8—22no—
551Q8—22no—
552Q8—34no—
553Q8—42no—
554Q8—68no—
555Q8—62no—
556Q8—64no—
557Q8—62no—
558Q8C2×C3×#6712yes—
559D4—24no—
560D4—21no—
561D4—68no—
562D4—64no—
563D4—62no—
564D4C2×C3×#6712yes—
565C2×C4—21no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—32no—
569C2×C4—42no—
570C2×C4—68no—
571C2×C4—68no—
572C2×C4—64no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4C3×D3×D411yescharacteristic
578C2×C4C3×D3×D412yes—
579C2×C4C2×C3×#6712yes—
580C2×C4C23×C3×D311yescharacteristic
581C8—22no—
582C8—62no—
583C2×C3—22no—
584C2×C3—22no—
585C2×C3—22no—
586C2×C3—21no—
587C2×C3—42no—
588C2×C3—42no—
589C2×C3—42no—
590C2×C3—82no—
591C2×C3—122no—
592C2×C3#577912yes—
593C2×C3C2×#93711yescharacteristic
594C2×C3C2×C3×#12011yescharacteristic
595C2×C3C3×#57812yes—
596D3—42no—
597C22—22no—
598C22—22no—
599C22—42no—
600C22—64no—
601C22—62no—
602C22C3×#93712yes—
603C22C2×C3×D3×D411yescharacteristic
604C4—22no—
605C4—42no—
606C4—62no—
607C4—64no—
608C4—122no—
609C4C3×#93712yes—
610C4C2×C3×D3×D411yescharacteristic
611C4C22×C3×#6711yescharacteristic
612C3—21no—
613C3#8398311yescharacteristic, direct product factor
614C3C3×#301111yescharacteristic, complemented
615C2—22no—
616C2—42no—
617C2—122no—
618C2C3×#577912yes—
619C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#137C2
socleC22×C32C22×D4
prime radicalC2×C3×#1010C2
hypercenterC2×C3×#137D3
hypocenterC3C3×#3011
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
2. C2×C32×#137C2semidirect
3. C3×#5816C2semidirect
4. C22×C3×#216C2semidirect
5. C3×#5233C2semidirect
6. C3×#5186C2semidirect
7. C3×#5173C2semidirect
8. C3×#5129C2semidirect
9. C3×#5120C2semidirect
11. #83983C3direct (N × H)
42. C2×C3×#137D3semidirect
43. C2×C3×#137C2×C3semidirect
46. #5816C2×C3semidirect
47. C22×#216C2×C3semidirect
53. #5233C2×C3semidirect
54. #5186C2×C3semidirect
55. #5173C2×C3semidirect
56. #5129C2×C3semidirect
57. #5120C2×C3semidirect
203. C2×#137C3×D3semidirect
545. C32#3011semidirect
613. C3#83983direct (N × H)
614. C3C3×#3011semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×C32×#1372
C3×#58162
C22×C3×#2162
C3×#52332
C3×#51862
C3×#51732
C3×#51292
C3×#51202
C3×#30113
#839833