Finite Group Databasebeta

← C3×#80401 #11882304

Subgroups — C3×#80401 #11882304

Order 1152.

860 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
1C3×#5716C211yesmaximal, characteristic, complemented
2C3×#5580C211yesmaximal, characteristic, complemented
3C32×#460C211yesmaximal, characteristic, complemented
4C3×#5171C212yesmaximal, complemented
5C3×#5165C212yesmaximal, complemented
6C3×#5072C211yesmaximal, characteristic, complemented
7C3×#5021C211yesmaximal, characteristic, complemented
8C3×#4842C211yesmaximal, characteristic, complemented
9C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
10C3×#4775C212yesmaximal, complemented
11C3×#4763C212yesmaximal, complemented
12C3×#3247—31nomaximal
13#80401C311yesmaximal, characteristic, direct product factor
14C2×C3×#237—21no—
15C2×C32×SD16C2212yes—
16C32×#127C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C3×#947C2211yescharacteristic
19C3×#946C2211yescharacteristic
20C3×#938—21no—
21C3×#938C2212yes—
22C3×#936—21no—
23C3×D4×Dic3—21no—
24C3×D4×Dic3C2212yes—
25C2×C3×#213C2212yes—
26C2×C3×D3×C8C2212yes—
27C3×#898—21no—
28C3×#895C2211yescharacteristic
29C3×#894—21no—
30C3×#890C2211yescharacteristic
31C3×C4×D12—21no—
32C3×C4×D12C2211yescharacteristic
33C3×#872—21no—
34C3×C42×D3C2211yescharacteristic
35C3×#869C2211yescharacteristic
36C32×C4⋊C8C2211yescharacteristic
37C32×#102C2212yes—
38C3×#835C2212yes—
39C3×#832C2212yes—
40C3×#821C2212yes—
41C3×#817C2212yes—
42C3×Dic3⋊C8C2212yes—
43C3×#807C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#532—31no—
46C3×#529—31no—
47#5716C2×C311yescharacteristic, complemented
48#5580C2×C311yescharacteristic, complemented
49C3×#478—32no—
50C3×#477—31no—
51C3×#476—31no—
52C3×#466—32no—
53C3×#465—32no—
54C3×#463—32no—
55C3×#460—21no—
56C3×#460D311yescharacteristic, complemented
57C3×#460C2×C311yescharacteristic, complemented
58C3×#459—31no—
59C2×C3×C4⋊C8—31no—
60#5171C2×C312yescomplemented
61#5165C2×C312yescomplemented
62#5072C2×C311yescharacteristic, complemented
63#5021C2×C311yescharacteristic, complemented
64#4842C2×C311yescharacteristic, complemented
65D3×C4⋊C8C2×C311yescharacteristic, complemented
66#4775C2×C312yescomplemented
67#4763C2×C312yescomplemented
68C2×C32×Q8C2311yescharacteristic
69C2×C32×D4—21no—
70C2×C32×D4—21no—
71C2×C32×D4C2312yes—
72C2×C3×#67—22no—
73C22×C3×Dic3—22no—
74C3×#237—44no—
75C2×C3×D12—21no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×Dic6—21no—
82C32×SD16—42no—
83C2×C32×C8C2312yes—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C42—21no—
87C32×C42C2311yescharacteristic
88C3×#217—22no—
89C3×#217—22no—
90C3×#213—42no—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2312yes—
100C3×Dic3⋊C4—21no—
101C3×Dic3⋊C4—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106C3×D3×C8—42no—
107#3247—31noSylow
108C2×C3×#41—61no—
109C2×#237—21no—
110C2×C3×SD16—22no—
111C2×C3×SD16C2×D312yes—
112C2×C3×SD16C22×C312yes—
113C2×C3×D8—32no—
114C22×C3×C8—32no—
115C3×C4⋊Q8—31no—
116C3×#127—21no—
117C3×#127C2×D311yescharacteristic
118C3×#127C22×C311yescharacteristic
119C3×#126—61no—
120C3×#125—31no—
121C3×#124—31no—
122C3×#124—61no—
123C3×#123—61no—
124C3×C22⋊Q8—31no—
125C3×#121—32no—
126C3×#121—31no—
127C3×#121—61no—
128C3×C4×Q8—21no—
129C3×C4×Q8C2×D311yescharacteristic
130C3×C4×Q8C22×C311yescharacteristic
131C3×C4×D4—32no—
132C3×C4×D4—31no—
133C3×C4×D4—61no—
134C3×C4×D4—61no—
135C3×#117—61no—
136C2×C3×C42—31no—
137#947C22×C311yescharacteristic
138#946C22×C311yescharacteristic
139#938—21no—
140#938C22×C312yes—
141#936—21no—
142D4×Dic3—21no—
143D4×Dic3C22×C312yes—
144C2×#213C22×C312yes—
145C2×D3×C8C22×C312yes—
146#898—21no—
147#895C22×C311yescharacteristic
148#894—21no—
149#890C22×C311yescharacteristic
150C4×D12—21no—
151C4×D12C22×C311yescharacteristic
152#872—21no—
153C42×D3C22×C311yescharacteristic
154#869C22×C311yescharacteristic
155C3×#107—32no—
156C3×#106—32no—
157C3×C4⋊C8—21no—
158C3×C4⋊C8—32no—
159C3×C4⋊C8—31no—
160C3×C4⋊C8C2×D311yescharacteristic
161C3×C4⋊C8C22×C311yescharacteristic
162C3×#103—32no—
163C3×#102—22no—
164C3×#102—32no—
165C3×#102—32no—
166C3×#102C2×D312yes—
167C3×#102C22×C312yes—
168#835C22×C312yes—
169#832C22×C312yes—
170#821C22×C312yes—
171#817C22×C312yes—
172Dic3⋊C8C22×C312yes—
173#807C22×C312yes—
174C4⋊(C3⋊C8)C22×C311yescharacteristic
175C23×C32—22no—
176C22×C3×D3—21no—
177C22×C3×D3C2×D411yescharacteristic
178C32×Q8—21no—
179C32×Q8—21no—
180C32×D4—22no—
181C32×D4—22no—
182C32×D4—42no—
183C32×D4—42no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C3×#67—44no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—44no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×D12—21no—
197C3×D12—21no—
198C3×D12—42no—
199C3×C4×D3—22no—
200C3×C4×D3—22no—
201C3×C4×D3—21no—
202C3×C4×D3—21no—
203C3×C4×D3—42no—
204C3×Dic6—42no—
205C32×C8—22no—
206C3×C3⋊C8—22no—
207#532—31no—
208#529—31no—
209#478—32no—
210#477—31no—
211#476—31no—
212#466—32no—
213#465—32no—
214#463—32no—
215#460C3×D311yescharacteristic, complemented
216#459—31no—
217C2×C4⋊C8—31no—
218C3×#41—124no—
219C2×C3×Q8—21no—
220C2×C3×Q8—61no—
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×Q8C23×C311yescharacteristic
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—22no—
228C2×C3×D4—31no—
229C2×C3×D4—41no—
230C2×C3×D4—41no—
231C2×C3×D4—61no—
232C2×C3×D4—62no—
233C2×C3×D4C22×D312yes—
234C2×C3×D4C23×C312yes—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—62no—
239C22×C3×C4—61no—
240C2×#67—22no—
241C22×Dic3—22no—
242#237—44no—
243C2×D12—21no—
244C2×D12C23×C311yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3C3×D411yescharacteristic
247C2×C4×D3C3×D411yescharacteristic
248C2×C4×D3C23×C311yescharacteristic
249C2×Dic6—21no—
250C3×SD16—42no—
251C3×SD16—42no—
252C3×SD16—44no—
253C3×D8—122no—
254C2×C3×C8—22no—
255C2×C3×C8—32no—
256C2×C3×C8—122no—
257C2×C3×C8C22×D312yes—
258C2×C3×C8C23×C312yes—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—32no—
264C3×C4⋊C4—41no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4C22×D311yescharacteristic
270C3×C4⋊C4C23×C311yescharacteristic
271C3×C22⋊C4—61no—
272C3×C22⋊C4—61no—
273C3×C22⋊C4—61no—
274C3×C22⋊C4—61no—
275C3×C22⋊C4—62no—
276C3×C22⋊C4—62no—
277C3×C22⋊C4—61no—
278C3×C42—21no—
279C3×C42—21no—
280C3×C42—21no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—41no—
285C3×C42C22×D311yescharacteristic
286C3×C42C23×C311yescharacteristic
287#217—22no—
288#217—22no—
289#213—42no—
290(C2×D3)⋊C4—21no—
291(C2×D3)⋊C4—21no—
292(C2×D3)⋊C4—21no—
293(C2×D3)⋊C4—21no—
294(C2×D3)⋊C4—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3C23×C312yes—
298C4⋊Dic3C23×C311yescharacteristic
299Dic3⋊C4—21no—
300Dic3⋊C4—21no—
301C4×Dic3C3×D411yescharacteristic
302C4×Dic3C3×D411yescharacteristic
303C4×Dic3C23×C311yescharacteristic
304C2×C3⋊C8C23×C312yes—
305D3×C8—42no—
306C22×C32—42no—
307C22×C32—42no—
308C22×C32—42no—
309C22×C32C22×D411yescharacteristic
310C2×C3×D3—21no—
311C2×C3×D3—21no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3AGL(1,ℤ/8)12yes—
316C32×C4—21no—
317C32×C4—41no—
318C32×C4—41no—
319C32×C4#13512yes—
320C32×C4H(5,𝔽2)11yescharacteristic
321C32×C42−1+411yescharacteristic
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—21no—
325C3×Dic3—41no—
326C3×Dic3—42no—
327C2×#41—61no—
328C2×SD16C2×C3×D312yes—
329C2×D8—32no—
330C22×C8—32no—
331C4⋊Q8—31no—
332#127C2×C3×D311yescharacteristic
333#126—61no—
334#125—31no—
335#124—31no—
336#124—61no—
337#123—61no—
338C22⋊Q8—31no—
339#121—32no—
340#121—31no—
341#121—61no—
342C4×Q8C2×C3×D311yescharacteristic
343C4×D4—32no—
344C4×D4—31no—
345C4×D4—61no—
346C4×D4—61no—
347#117—61no—
348C2×C42—31no—
349#107—32no—
350#106—32no—
351C4⋊C8—32no—
352C4⋊C8—31no—
353C4⋊C8C2×C3×D311yescharacteristic
354#103—32no—
355#102—32no—
356#102—32no—
357#102C2×C3×D312yes—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—31no—
361C23×C3—42no—
362C23×C3—61no—
363C22×D3—21no—
364C22×D3C2×C3×D411yescharacteristic
365C3×Q8—22no—
366C3×Q8—21no—
367C3×Q8—21no—
368C3×Q8—21no—
369C3×Q8—21no—
370C3×Q8—41no—
371C3×Q8—122no—
372C3×D4—22no—
373C3×D4—22no—
374C3×D4—22no—
375C3×D4—22no—
376C3×D4—42no—
377C3×D4—42no—
378C3×D4—42no—
379C3×D4—42no—
380C3×D4—42no—
381C3×D4—42no—
382C3×D4—61no—
383C3×D4—61no—
384C3×D4—82no—
385C3×D4—82no—
386C3×D4—122no—
387C3×D4—124no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—31no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—61no—
403C2×C3×C4—61no—
404C2×C3×C4—61no—
405C2×C3×C4—62no—
406C2×C3×C4—124no—
407C2×C3×C4—122no—
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4C2×C3×D411yescharacteristic
411C2×C3×C4C2×C3×D411yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C24×C311yescharacteristic
414#67—44no—
415C2×Dic3—21no—
416C2×Dic3—22no—
417C2×Dic3—44no—
418C2×Dic3C2×C3×D411yescharacteristic
419C2×Dic3C2×C3×D411yescharacteristic
420C2×Dic3C2×C3×D411yescharacteristic
421D12—21no—
422D12—21no—
423D12—42no—
424C4×D3—22no—
425C4×D3—22no—
426C4×D3—21no—
427C4×D3—21no—
428C4×D3—42no—
429Dic6—42no—
430C3×C8—22no—
431C3×C8—22no—
432C3×C8—42no—
433C3×C8—62no—
434C3⋊C8—22no—
435C2×C32—82no—
436C2×C32#53711yescharacteristic
437C2×C32C2×#13511yescharacteristic
438C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
439C3×D3—22no—
440C3×D3—81no—
441#41—124no—
442C2×Q8—61no—
443C2×Q8C22×C3×D311yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—31no—
447C2×D4—61no—
448C2×D4—62no—
449C2×D4C22×C3×D312yes—
450C22×C4—31no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—62no—
454C22×C4—61no—
455SD16—42no—
456D8—122no—
457C2×C8—32no—
458C2×C8—122no—
459C2×C8C22×C3×D312yes—
460C4⋊C4—21no—
461C4⋊C4—31no—
462C4⋊C4—32no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4C22×C3×D311yescharacteristic
468C22⋊C4—61no—
469C22⋊C4—61no—
470C22⋊C4—61no—
471C22⋊C4—61no—
472C22⋊C4—62no—
473C22⋊C4—62no—
474C22⋊C4—61no—
475C42—21no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42C22×C3×D311yescharacteristic
480C22×C3—21no—
481C22×C3—32no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—42no—
486C22×C3—42no—
487C22×C3—42no—
488C22×C3—61no—
489C22×C3—61no—
490C22×C3—82no—
491C22×C3—82no—
492C22×C3—82no—
493C22×C3—121no—
494C22×C3—121no—
495C22×C3—121no—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C22×C3×D411yescharacteristic
498C2×D3—21no—
499C2×D3—21no—
500C2×D3—41no—
501C2×D3—41no—
502C2×D3—41no—
503C2×D3C3×AGL(1,ℤ/8)12yes—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—22no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—41no—
510C3×C4—42no—
511C3×C4—41no—
512C3×C4—41no—
513C3×C4—41no—
514C3×C4—41no—
515C3×C4—61no—
516C3×C4—61no—
517C3×C4—61no—
518C3×C4—81no—
519C3×C4—121no—
520C3×C4—122no—
521C3×C4#91612yes—
522C3×C4C3×#13512yes—
523C3×C4#100411yescharacteristic
524C3×C4#101011yescharacteristic
525C3×C4C3×H(5,𝔽2)11yescharacteristic
526C3×C4C3×2−1+411yescharacteristic
527Dic3—21no—
528Dic3—21no—
529Dic3—21no—
530Dic3—41no—
531Dic3—42no—
532C32#324711yescharacteristic, complemented, Sylow
533C23—22no—
534C23—31no—
535C23—61no—
536Q8—21no—
537Q8—21no—
538Q8—122no—
539D4—22no—
540D4—22no—
541D4—42no—
542D4—42no—
543D4—61no—
544D4—61no—
545D4—122no—
546D4—124no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—31no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—62no—
558C2×C4—124no—
559C2×C4—122no—
560C2×C4C3×D3×D411yescharacteristic
561C2×C4C3×D3×D411yescharacteristic
562C2×C4C23×C3×D311yescharacteristic
563C8—22no—
564C8—62no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—62no—
569C2×C3—82no—
570C2×C3—82no—
571C2×C3—162no—
572C2×C3—241no—
573C2×C3#560811yescharacteristic
574C2×C3C2×#91611yescharacteristic
575C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
576C2×C3C3×#53711yescharacteristic
577C2×C3C2×C3×#13511yescharacteristic
578C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
579D3—22no—
580D3—81no—
581C22—32no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—61no—
586C22—61no—
587C22—121no—
588C22—121no—
589C22—121no—
590C22C2×C3×D3×D411yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—61no—
595C4—61no—
596C4—61no—
597C4—121no—
598C4—122no—
599C4C3×#91612yes—
600C4C3×#100411yescharacteristic
601C4C3×#101011yescharacteristic
602C3—21no—
603C3#8040111yescharacteristic, direct product factor
604C3C3×#324711yescharacteristic, complemented
605C2—62no—
606C2—82no—
607C2—241no—
608C2C3×#560811yescharacteristic
609C2C2×C3×#91611yescharacteristic
610C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#460C2
socleC22×C32C22×D4
hypercenterC3×#460D3
hypocenterC3C3×#3247
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
1. C3×#5716C2semidirect
2. C3×#5580C2semidirect
3. C32×#460C2semidirect
4. C3×#5171C2semidirect
5. C3×#5165C2semidirect
6. C3×#5072C2semidirect
7. C3×#5021C2semidirect
8. C3×#4842C2semidirect
9. C3×D3×C4⋊C8C2semidirect
10. C3×#4775C2semidirect
11. C3×#4763C2semidirect
13. #80401C3direct (N × H)
47. #5716C2×C3semidirect
48. #5580C2×C3semidirect
56. C3×#460D3semidirect
57. C3×#460C2×C3semidirect
60. #5171C2×C3semidirect
61. #5165C2×C3semidirect
62. #5072C2×C3semidirect
63. #5021C2×C3semidirect
64. #4842C2×C3semidirect
65. D3×C4⋊C8C2×C3semidirect
66. #4775C2×C3semidirect
67. #4763C2×C3semidirect
215. #460C3×D3semidirect
532. C32#3247semidirect
603. C3#80401direct (N × H)
604. C3C3×#3247semidirect

Maximal subgroups

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

subgroupindex
C3×#57162
C3×#55802
C32×#4602
C3×#51712
C3×#51652
C3×#50722
C3×#50212
C3×#48422
C3×D3×C4⋊C82
C3×#47752
C3×#47632
C3×#32473
#804013