Finite Group Databasebeta

← C3×#83884 #11864476

Subgroups — C3×#83884 #11864476

Order 1152.

1529 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic
2C22×C32×Q16C211yesmaximal, characteristic, complemented
3C3×#5816C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5C3×#5225C211yesmaximal, characteristic, complemented
6C3×#5187C214yesmaximal, complemented
7C3×#5186C214yesmaximal, complemented
8C3×#5113C211yesmaximal, characteristic, complemented
9C3×#5110C211yesmaximal, characteristic, complemented
10C3×#3011—31nomaximal
11#83884C311yesmaximal, characteristic, direct product factor
12C22×C32×Q8C2211yescharacteristic
13C22×C32×Q8C2211yescharacteristic
14C3×#1007—24no—
15C3×#1007—24no—
16C2×C3×#239—21no—
17C2×C3×#239C2212yes—
18C2×C3×D3×Q8—21no—
19C2×C3×D3×Q8C2212yes—
20C2×C3×#235—22no—
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic
23C2×C32×Q16—24no—
24C2×C32×Q16C2214yes—
25C22×C32×C8C2211yescharacteristic
26C3×#947—21no—
27C3×#946C2214yes—
28C3×#944—21no—
29C2×C3×#216C2212yes—
30C3×#942—24no—
31C2×C3×#215C2212yes—
32C3×#929—22no—
33C3×#926C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35C3×#835C2214yes—
36C3×#821C2212yes—
37C3×(C2×D3)⋊C8C2214yes—
38C3×#816C2212yes—
39C2×C3×2−1+4—31no—
40C2×#1007C2×C311yescharacteristic
41C2×C3×#137—31no—
42C22×C3×Q16—21no—
43C22×C3×Q16D311yescharacteristic, complemented
44C22×C3×Q16C2×C311yescharacteristic, complemented
45C3×#536—31no—
46#5816C2×C311yescharacteristic, complemented
47C2×#942C2×C311yescharacteristic, complemented
48C3×#452—34no—
49C3×#451—34no—
50C3×#419—31no—
51C3×#416—31no—
52C3×#408—31no—
53#5225C2×C311yescharacteristic, complemented
54#5187C2×C314yescomplemented
55#5186C2×C314yescomplemented
56#5113C2×C311yescharacteristic, complemented
57#5110C2×C311yescharacteristic, complemented
58C2×C32×Q8—21no—
59C2×C32×Q8—22no—
60C2×C32×Q8—21no—
61C2×C32×Q8—22no—
62C2×C32×Q8—22no—
63C2×C32×Q8D414yes—
64C2×C32×Q8C2312yes—
65C2×C32×Q8C2312yes—
66C22×C32×C4—21no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×C3×#67—21no—
70C2×C3×#67D412yes—
71C3×#239—28no—
72C3×#239—24no—
73C3×#239—24no—
74C3×D3×Q8—28no—
75C3×D3×Q8—24no—
76C3×D3×Q8—24no—
77C3×#235—216no—
78C3×#235—22no—
79C3×#235—22no—
80C3×#235—22no—
81C3×#235D414yes—
82C2×C3×D12—22no—
83C2×C3×D12D411yescharacteristic
84C2×C3×D12C2311yescharacteristic
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3—21no—
87C2×C3×C4×D3—22no—
88C2×C3×C4×D3C2312yes—
89C2×C3×Dic6—22no—
90C2×C3×Dic6D411yescharacteristic
91C2×C3×Dic6C2311yescharacteristic
92C32×Q16—28no—
93C2×C32×C8—22no—
94C2×C32×C8C2312yes—
95C3×#217—21no—
96C3×#216—24no—
97C3×#215—24no—
98C3×(C2×D3)⋊C4—24no—
99C3×C4⋊Dic3C2312yes—
100C3×Dic3⋊C4—24no—
101C3×C4×Dic3—21no—
102C3×#208—22no—
103C2×C3×C3⋊C8C2312yes—
104#3011—31noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—31no—
108C2×C3×#41—32no—
109C2×C3×#41—31no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C22×C3×Q8—21no—
113C22×C3×Q8—21no—
114C22×C3×Q8—32no—
115C22×C3×Q8—61no—
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×Q8C2×D311yescharacteristic
118C22×C3×Q8C22×C311yescharacteristic
119C22×C3×Q8C22×C311yescharacteristic
120#1007—24no—
121#1007—24no—
122C2×#239—21no—
123C2×#239C22×C312yes—
124C2×D3×Q8—21no—
125C2×D3×Q8C22×C312yes—
126C2×#235—22no—
127C2×#235C22×C311yescharacteristic
128C2×#235C22×C311yescharacteristic
129C3×#137—64no—
130C2×C3×Q16—28no—
131C2×C3×Q16—24no—
132C2×C3×Q16—24no—
133C2×C3×Q16—24no—
134C2×C3×Q16—32no—
135C2×C3×Q16C2×D314yes—
136C2×C3×Q16C22×C314yes—
137C2×C3×SD16—32no—
138C2×C3×M16—31no—
139C22×C3×C8—21no—
140C22×C3×C8C2×D311yescharacteristic
141C22×C3×C8C22×C311yescharacteristic
142C3×C4⋊Q8—61no—
143C3×#124—61no—
144C3×#123—62no—
145C3×C22⋊Q8—34no—
146C3×#117—31no—
147#947—21no—
148#946C22×C314yes—
149#944—21no—
150C2×#216C22×C312yes—
151#942—24no—
152C2×#215C22×C312yes—
153#929—22no—
154#926C22×C311yescharacteristic
155C2×#208C22×C311yescharacteristic
156C3×#103—34no—
157C3×#103—32no—
158C3×#102—32no—
159C3×C22⋊C8—34no—
160#835C22×C314yes—
161#821C22×C312yes—
162(C2×D3)⋊C8C22×C314yes—
163#816C22×C312yes—
164C23×C32C2×D411yescharacteristic
165C22×C3×D3—21no—
166C22×C3×D3C2×D412yes—
167C32×Q8—22no—
168C32×Q8—24no—
169C32×Q8—22no—
170C32×Q8—22no—
171C32×Q8—42no—
172C32×Q8C2×D414yes—
173C2×C32×C4—24no—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—42no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2411yescharacteristic
181C3×#67—24no—
182C3×#67—24no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C2×D412yes—
186C3×D12—28no—
187C3×D12—22no—
188C3×D12—21no—
189C3×D12C2×D412yes—
190C3×C4×D3—28no—
191C3×C4×D3—28no—
192C3×C4×D3—24no—
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×Dic6—28no—
196C3×Dic6—22no—
197C3×Dic6—21no—
198C3×Dic6C2×D412yes—
199C32×C8—22no—
200C3×C3⋊C8—22no—
201C2×2−1+4—31no—
202C2×#137—31no—
203C22×Q16C3×D311yescharacteristic, complemented
204#536—31no—
205#452—34no—
206#451—34no—
207#419—31no—
208#416—31no—
209#408—31no—
210C3×#41—34no—
211C3×#41—616no—
212C3×#41—64no—
213C3×#41—68no—
214C3×#41—64no—
215C3×#41—62no—
216C3×#41—62no—
217C3×#41—62no—
218C2×C3×Q8—21no—
219C2×C3×Q8—22no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—22no—
223C2×C3×Q8—21no—
224C2×C3×Q8—24no—
225C2×C3×Q8—22no—
226C2×C3×Q8—22no—
227C2×C3×Q8—22no—
228C2×C3×Q8—22no—
229C2×C3×Q8—24no—
230C2×C3×Q8—22no—
231C2×C3×Q8—22no—
232C2×C3×Q8—31no—
233C2×C3×Q8—31no—
234C2×C3×Q8—41no—
235C2×C3×Q8—42no—
236C2×C3×Q8—41no—
237C2×C3×Q8—42no—
238C2×C3×Q8—62no—
239C2×C3×Q8—64no—
240C2×C3×Q8—68no—
241C2×C3×Q8—64no—
242C2×C3×Q8#6714yes—
243C2×C3×Q8C3×D414yes—
244C2×C3×Q8C22×D312yes—
245C2×C3×Q8C22×D312yes—
246C2×C3×Q8C23×C312yes—
247C2×C3×Q8C23×C312yes—
248C2×C3×D4—32no—
249C2×C3×D4—31no—
250C2×C3×D4—31no—
251C2×C3×D4—62no—
252C2×C3×D4—61no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—32no—
259C22×C3×C4—41no—
260C22×C3×C4—41no—
261C22×C3×C4—62no—
262C22×C3×C4—62no—
263C22×C3×C4—61no—
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C23×C311yescharacteristic
266C2×#67—21no—
267C2×#67C3×D412yes—
268#239—28no—
269#239—24no—
270#239—24no—
271D3×Q8—28no—
272D3×Q8—24no—
273D3×Q8—24no—
274#235—216no—
275#235—22no—
276#235—22no—
277#235—22no—
278#235C3×D414yes—
279C2×D12—22no—
280C2×D12C3×D411yescharacteristic
281C2×D12C23×C311yescharacteristic
282C2×C4×D3—22no—
283C2×C4×D3—21no—
284C2×C4×D3—22no—
285C2×C4×D3C23×C312yes—
286C2×Dic6—22no—
287C2×Dic6C3×D411yescharacteristic
288C2×Dic6C23×C311yescharacteristic
289C3×Q16—216no—
290C3×Q16—28no—
291C3×Q16—28no—
292C3×Q16—64no—
293C3×SD16—64no—
294C3×M16—62no—
295C2×C3×C8—24no—
296C2×C3×C8—22no—
297C2×C3×C8—22no—
298C2×C3×C8—22no—
299C2×C3×C8—32no—
300C2×C3×C8C22×D312yes—
301C2×C3×C8C23×C312yes—
302C3×C4⋊C4—32no—
303C3×C4⋊C4—64no—
304C3×C22⋊C4—64no—
305C3×C22⋊C4—61no—
306C3×C42—61no—
307#217—21no—
308#216—24no—
309#215—24no—
310(C2×D3)⋊C4—24no—
311C4⋊Dic3C23×C312yes—
312Dic3⋊C4—24no—
313C4×Dic3—21no—
314#208—22no—
315C2×C3⋊C8C23×C312yes—
316C22×C32—22no—
317C22×C32#12012yes—
318C22×C32C22×D411yescharacteristic
319C2×C3×D3—22no—
320C2×C3×D3—22no—
321C2×C3×D3—24no—
322C2×C3×D3—42no—
323C32×C4—24no—
324C32×C4—42no—
325C32×C4#12012yes—
326C32×C4C22×D411yescharacteristic
327C32×C4C22×D411yescharacteristic
328C3×Dic3—22no—
329C3×Dic3—22no—
330C3×Dic3—42no—
3312−1+4—64no—
3322−1+4—64no—
333C2×#41—31no—
334C2×#41—32no—
335C2×#41—31no—
336C2×#41—62no—
337C2×#41—61no—
338C22×Q8—32no—
339C22×Q8—61no—
340C22×Q8C2×C3×D311yescharacteristic
341C22×Q8C2×C3×D311yescharacteristic
342#137—64no—
343C2×Q16—24no—
344C2×Q16—32no—
345C2×Q16C2×C3×D314yes—
346C2×SD16—32no—
347C2×M16—31no—
348C22×C8C2×C3×D311yescharacteristic
349C4⋊Q8—61no—
350#124—61no—
351#123—62no—
352C22⋊Q8—34no—
353#117—31no—
354#103—34no—
355#103—32no—
356#102—32no—
357C22⋊C8—34no—
358C23×C3—21no—
359C23×C3—32no—
360C23×C3—61no—
361C23×C3D3×D411yescharacteristic
362C23×C3C2×C3×D411yescharacteristic
363C22×D3—21no—
364C22×D3C2×C3×D412yes—
365C3×Q8—24no—
366C3×Q8—24no—
367C3×Q8—22no—
368C3×Q8—22no—
369C3×Q8—24no—
370C3×Q8—22no—
371C3×Q8—22no—
372C3×Q8—22no—
373C3×Q8—22no—
374C3×Q8—24no—
375C3×Q8—32no—
376C3×Q8—44no—
377C3×Q8—42no—
378C3×Q8—42no—
379C3×Q8—44no—
380C3×Q8—42no—
381C3×Q8—42no—
382C3×Q8—68no—
383C3×Q8—62no—
384C3×Q8—61no—
385C3×Q8C2×#6714yes—
386C3×Q8C2×C3×D414yes—
387C3×D4—32no—
388C3×D4—68no—
389C3×D4—64no—
390C3×D4—64no—
391C3×D4—62no—
392C3×D4—61no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—32no—
404C2×C3×C4—44no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—44no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—68no—
411C2×C3×C4—68no—
412C2×C3×C4—61no—
413C2×C3×C4—64no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4D3×D412yes—
419C2×C3×C4C2×#6712yes—
420C2×C3×C4C2×C3×D411yescharacteristic
421C2×C3×C4C2×C3×D412yes—
422C2×C3×C4C2×C3×D412yes—
423C2×C3×C4C23×D311yescharacteristic
424C2×C3×C4C24×C311yescharacteristic
425#67—24no—
426#67—24no—
427C2×Dic3—21no—
428C2×Dic3—22no—
429C2×Dic3C2×C3×D412yes—
430D12—28no—
431D12—22no—
432D12—21no—
433D12C2×C3×D412yes—
434C4×D3—28no—
435C4×D3—28no—
436C4×D3—24no—
437C4×D3—22no—
438C4×D3—22no—
439Dic6—28no—
440Dic6—22no—
441Dic6—21no—
442Dic6C2×C3×D412yes—
443C3×C8—24no—
444C3×C8—22no—
445C3×C8—22no—
446C3×C8—62no—
447C3⋊C8—22no—
448C2×C32—22no—
449C2×C32C2×#12011yescharacteristic
450C2×C32#57812yes—
451C3×D3—42no—
452C3×D3—42no—
453#41—34no—
454#41—616no—
455#41—64no—
456#41—68no—
457#41—64no—
458#41—62no—
459#41—62no—
460#41—62no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—21no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—31no—
467C2×Q8—31no—
468C2×Q8—62no—
469C2×Q8—64no—
470C2×Q8—68no—
471C2×Q8—64no—
472C2×Q8C3×#6714yes—
473C2×Q8C22×C3×D312yes—
474C2×Q8C22×C3×D312yes—
475C2×D4—32no—
476C2×D4—31no—
477C2×D4—31no—
478C2×D4—62no—
479C2×D4—61no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—32no—
483C22×C4—62no—
484C22×C4—62no—
485C22×C4—61no—
486C22×C4C22×C3×D311yescharacteristic
487Q16—28no—
488Q16—64no—
489SD16—64no—
490M16—62no—
491C2×C8—22no—
492C2×C8—32no—
493C2×C8C22×C3×D312yes—
494C4⋊C4—32no—
495C4⋊C4—64no—
496C22⋊C4—64no—
497C22⋊C4—61no—
498C42—61no—
499C22×C3—24no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—64no—
505C22×C3—62no—
506C22×C3—62no—
507C22×C3—122no—
508C22×C3#93712yes—
509C22×C3C3×#12012yes—
510C22×C3C2×D3×D411yescharacteristic
511C22×C3C22×C3×D411yescharacteristic
512C2×D3—24no—
513C2×D3—22no—
514C2×D3—22no—
515C2×D3—42no—
516C3×C4—24no—
517C3×C4—24no—
518C3×C4—22no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—44no—
522C3×C4—44no—
523C3×C4—42no—
524C3×C4—42no—
525C3×C4—62no—
526C3×C4—62no—
527C3×C4—122no—
528C3×C4#93712yes—
529C3×C4C3×#12012yes—
530C3×C4C2×D3×D411yescharacteristic
531C3×C4C22×#6711yescharacteristic
532C3×C4C22×C3×D411yescharacteristic
533C3×C4C22×C3×D411yescharacteristic
534Dic3—22no—
535Dic3—22no—
536Dic3—42no—
537C32#301111yescharacteristic, complemented, Sylow
538C23—32no—
539C23—61no—
540C23C3×D3×D411yescharacteristic
541Q8—24no—
542Q8—22no—
543Q8—22no—
544Q8—22no—
545Q8—32no—
546Q8—42no—
547Q8—68no—
548Q8—62no—
549Q8—61no—
550Q8C2×C3×#6714yes—
551D4—32no—
552D4—68no—
553D4—64no—
554D4—64no—
555D4—62no—
556D4—61no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—32no—
561C2×C4—42no—
562C2×C4—68no—
563C2×C4—68no—
564C2×C4—61no—
565C2×C4—64no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4C3×D3×D411yescharacteristic
570C2×C4C3×D3×D412yes—
571C2×C4C2×C3×#6712yes—
572C2×C4C23×C3×D311yescharacteristic
573C8—22no—
574C8—62no—
575C2×C3—24no—
576C2×C3—22no—
577C2×C3—22no—
578C2×C3—22no—
579C2×C3—21no—
580C2×C3—122no—
581C2×C3—122no—
582C2×C3#576612yes—
583C2×C3C2×#93711yescharacteristic
584C2×C3C2×C3×#12011yescharacteristic
585C2×C3C3×#57812yes—
586D3—42no—
587D3—42no—
588C22—22no—
589C22—64no—
590C22—62no—
591C22—62no—
592C22—122no—
593C22C3×#93712yes—
594C22C2×C3×D3×D411yescharacteristic
595C4—24no—
596C4—42no—
597C4—62no—
598C4—62no—
599C4—122no—
600C4C3×#93712yes—
601C4C2×C3×D3×D411yescharacteristic
602C4C22×C3×#6711yescharacteristic
603C3—21no—
604C3#8388411yescharacteristic, direct product factor
605C3C3×#301111yescharacteristic, complemented
606C2—22no—
607C2—122no—
608C2—122no—
609C2C3×#576612yes—
610C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC22×C32×Q16C2
socleC22×C32C22×D4
prime radicalC2×C3×#1007C2
hypercenterC22×C3×Q16D3
hypocenterC3C3×#3011
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×Q16

Complements

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

NH ≅ G/Ntype
2. C22×C32×Q16C2semidirect
3. C3×#5816C2semidirect
4. C2×C3×#942C2semidirect
5. C3×#5225C2semidirect
6. C3×#5187C2semidirect
7. C3×#5186C2semidirect
8. C3×#5113C2semidirect
9. C3×#5110C2semidirect
11. #83884C3direct (N × H)
43. C22×C3×Q16D3semidirect
44. C22×C3×Q16C2×C3semidirect
46. #5816C2×C3semidirect
47. C2×#942C2×C3semidirect
53. #5225C2×C3semidirect
54. #5187C2×C3semidirect
55. #5186C2×C3semidirect
56. #5113C2×C3semidirect
57. #5110C2×C3semidirect
203. C22×Q16C3×D3semidirect
537. C32#3011semidirect
604. C3#83884direct (N × H)
605. C3C3×#3011semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C22×C32×Q162
C3×#58162
C2×C3×#9422
C3×#52252
C3×#51872
C3×#51862
C3×#51132
C3×#51102
C3×#30113
#838843